S(zp, zp) : post-structural readings of Gödel's proof 9788876991578, 8876991573

Table of contents :
Acknowledgement
Methodological Introduction
1. The components of this project
2. This project in contemporary academic context
3. The purpose of this project
4. The chapters
Analytic Introduction
1. Meaning
2. Leading questions
Introduction to Gödel's Argument
1. Logicism, intuitionism, formalism, realism and Kurt Gödel
2. Gödel's argument in brief
1 Textual Formations
1.1 Who speaks?
1.1.1 We and I
1.1.2 What we do
1.1.3 When, where and how we do it
1.1.4 Who do we do it with? (a slight detour)
1.1.5 Who does it to us?
1.2 The object: notion
1.2.1 Abbreviate notations
1.2.2 From primitive signs to numbers
1.2.3 From numbers back to signs through proofs
1.2.4 What is the meaning of it all?
1.2.5 Conclusion
1.3 A strategic point of diffraction
2 From the Formation through to the Hymen
2.1 Where is the meaning of it all?
2.2 Verisimilarity
2.3 Elements of verisimilarity
2.4 Iteration
2.5 Dangerous shifts of meaning
2.6 Omne symbolum de symbolo
2.7 ,
2.8 Variables
2.9 Across the sign of equality
2.10 Gödel's undecidable formula doesn't exist
3 The Surface of Mathematics
3.1 Numbers and the body
3.2 The dimensions of language
3.3 A concise psychoanalytic genealogy of language
3.4 The paradoxical object and the full language of pre-crisis mathematics
3.5 First Finalé: Gödel as Lacanian therapist
3.6 Second Finalé: Does Gödel's text make sense?
3.7 Third Finalé: Revolution in mathematical language?
Conclusion
Appendix/Overture: Gödel's Myth, Reverse Bricolage
1. Mathematics as the structure of myth
2. The myth
2.1. The creators
2.2. Primary articulation: elements of the world
2.3. Secondary articulation: creatures and names
2.4. A transformation within the secondary articulation: from creatures to names
2.5. Tertiary articulation: birth
2.6. Refining the tertiary articulation: birth oracles
2.7. A crisis in the code
2.8. Rehabilitating the code
3. This is not a myth
3.1. This is not a myth
3.2. This is not even a plot
3.3. And it spirals away from Gödel's proof
3.4. And away from structure
Bibliography

Citation preview

Roy Wagner

S(zp, zp): Post-Structural Readings of Gödel’s Proof

Polimetrica International Scientific Publisher

2009 Polimetrica ® S.a.s. Corso Milano, 26 20052 Monza – Milano – Italy Phone ++39.039.2301829 Web site: www.polimetrica.com ISBN 978-88-7699-157-8 Printed Edition ISBN 978-88-7699-158-5 Electronic Edition Cover design by Arch. Diego Recalcati The electronic edition of this book is not sold and is made available in free access. This book is published according to the terms of “Polimetrica License B”. “Polimetrica

Contents Acknowledgement

1

Methodological Introduction 1. The components of this project . . . . . . . . . 2. This project in contemporary academic context 3. The purpose of this project . . . . . . . . . . . . 4. The chapters . . . . . . . . . . . . . . . . . . . .

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Analytic Introduction 1. Meaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Leading questions . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction to G¨ odel’s Argument 1. Logicism, intuitionism, formalism, realism and Kurt G¨odel . . 2. G¨ odel’s argument in brief . . . . . . . . . . . . . . . . . . . . .

29 29 31

1 Textual Formations 1.1 Who speaks? . . . . . . . . . . . . . . . . . . . 1.1.1 We and I . . . . . . . . . . . . . . . . . 1.1.2 What we do . . . . . . . . . . . . . . . . 1.1.3 When, where and how we do it . . . . . 1.1.4 Who do we do it with? (a slight detour) 1.1.5 Who does it to us? . . . . . . . . . . . . 1.2 The object: notion . . . . . . . . . . . . . . . . 1.2.1 Abbreviate notations . . . . . . . . . . . 1.2.2 From primitive signs to numbers . . . .

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1.2.3 From numbers back to signs through proofs . . . . . Bibliography 1.2.4......................................................................................... What is the meaning of it all? . . . . . . . . . . .60. . 1.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . 4. The Ethics of Migration. 1.3 A strategic point of diffraction Reflections on Recent Migration Policies . . . . . . . . . . . . . . . . and “Non-policies” in Italy and Europe ........................................... 61 2Laura From the Formation through to the Hymen Zanfrini WherePolicies is the and meaning of itDemand all? . .for. Immigrant . . . . . . Labour . . . ....65. 4.12.1 Restrictive Structural 2.2 Verisimilarity . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Initiatives for Governing Family and Humanitarian 2.3 Elements of verisimilarity . .Workers’ . . . . . Migration . . . . . ............. . . . . .73. Migration: Labour Migration but not 2.4 Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 From Guest Workers to Unwelcome Guests .................................. 82 2.5 Dangerous shifts of meaning . . . . . . . . . . . . . . . . . 4.4 Selective Policies and the Brain Drain............................................ 87 2.6 Omne symbolum de symbolo . . . . . . . . . . . . . . . . . 4.52.7 Equal, Opportunity . . . . . . and . . .Denied . . . .Opportunities . . . . . . . ................................ . . . . . . . . . . .90.

75 81 87 89 95

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Bibliography ......................................................................................... 2.8 Variables . . . . . . . . . . . . . . . . . . . . . . . . . .97. . 137

2.9 Across the sign of equality . . . . . . . . . . . . . . . . . . . 141 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 2.10 G¨odel’s undecidable formula doesn’t exist . . . . . . . . . . 144 Urs Watter State Surface Interest and 35.1The of Responsibility Mathematics 151 towards their Citizens Living Abroad ........................................... 102 3.1 Numbers and the body . . . . . . . . . . . . . . . . . . . . . 152 5.23.2 Applied .............................................................................. TheEthics dimensions of language . . . . . . . . . . . . . . . 104 . . . 159 5.33.3 Migration Policypsychoanalytic and Ethics ......................................................... A concise genealogy of language . . . . 106 . . . 163

The paradoxical object ...................................................... and the full language 5.43.4 Migration Policy in Colombia 108 of pre-crisis mathematics . . . . . . . . . . . . . . . . . 109 . . . 168 5.5 “Colombia nos une”...................................................................... 3.5 First final´e: G¨ odel as Lacanian therapist . . . . . . . . . . . 171 5.6 Alianza País .................................................................................. 112 3.6 Second final´e: Does G¨ odel’s text make sense? . . . . . . . . 181 5.7 Challenges .................................................................................... 114 3.7 Third final´e: Revolution in mathematical language? . . . . . 188 Bibliography ....................................................................................... 116 Conclusion 195 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday Appendix/Overture: G¨ odel’s Myth, Reverse Bricolage

199

1. Mathematics as the structure of myth . . . . . . . . . . . . . . 199 2. The myth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 2.1. The creators . . . . . . . . . . . . . . . . . . . . . . . . 203 2.2. Primary articulation: elements of the world . . . . . . . 204 2.3. Secondary articulation: creatures and names . . . . . . 205 Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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2.4. A transformation within the secondary articulation: Bibliography from ......................................................................................... creatures to names . . . . . . . . . . . . . . . .60. . 2.5. Tertiary articulation: birth . . . . . . . . . . . . . . . . 4. The Ethics of Migration. 2.6. Refining the tertiary articulation: birth oracles . . . . . Reflections on Recent Migration Policies 2.7. A crisisininItaly the and codeEurope . . . ............................................ . . . . . . . . . . . . . .61. . and “Non-policies” 2.8. Rehabilitating the code . . . . . . . . . . . . . . . . . . Laura Zanfrini 3. This is not a myth . . . . . Demand . . . . .for. Immigrant . . . . . . Labour . . . ....65. . 4.1 Restrictive Policies and .Structural 3.1. This is not a myth . . . . . . . . . . . . . . . . . . . . . 4.2 Initiatives for Governing Family and Humanitarian 3.2. This is not even a plot . . . . . . . . . . . . . . . . . . Migration: Labour Migration but not Workers’ Migration ............. 73 3.3. And it spirals away from G¨odel’s proof . . . . . . . . . 4.3 From Guest Workers to Unwelcome Guests .................................. 82 3.4. And away from structure . . . . . . . . . . . . . . . . . 4.4 Selective Policies and the Brain Drain............................................ 87 Bibliography 4.5 Equal Opportunity and Denied Opportunities ................................ 90

209 211 212 215 218 219 220 222 224 228 231

Bibliography ......................................................................................... 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Acknowledgement

Bibliography ......................................................................................... 60

4. The Ethics of Migration. At one time on I was labelled a mathematical Reflections Recent Migration Policies prodigy. But due to insufficient luck, talent or motivation as successful as my teachers had and “Non-policies” in ItalyI wasn’t and Europe ........................................... 61 hoped. Laura Zanfrini Whatever was missing, it was definitely not the nowise short of excellent education I received Vitali Milman Prof. Efim Gluskin, 4.1 Restrictive Policiesfrom and Prof. Structural Demand forand Immigrant Labour .. 65 who are directly responsible for those mathematical achievements I did attain, 4.2 Initiatives for Governing Family and Humanitarian and Migration: for the kind of mathematical that some colleagues Labour Migration but insight not Workers’ Migration .............still 73 credit me with. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Despite my growing impatience with mathematics, the transition to 4.4 Selective Policies and the Brain Drain............................................ 87 the humanities was slow and undecided. At first I had no tolerance for any 4.5 the Equal Opportunity Denied Opportunities ................................ but most reductiveand materialist and formalist forms of thinking.90I would like to acknowledge professors Amal Jamal, Daniel Dor and Lyat Friedman Bibliography ......................................................................................... 97 for making other ways of thinking accessible to me in the earlier stages of 5.my Colombia: Including Emigrants in Their Societies of Origin .......Yehonatan 101 explorations. The part of my personal and intellectual friend Urs Watter Alshekh in this transition was no less crucial. 5.1 State Interest and Responsibility The idea for the dissertation on which this book is based arose from towards their Citizens Living Abroad ........................................... 102 two incidents. The first was a talk given by Dr. Dalit Baum in a context 5.2 Applied .............................................................................. 104 an althat I don’t Ethics completely recall (and neither does she). She presented 5.3 Migration andtoEthics 106Rather ternative idea Policy for how teach......................................................... mathematics to humanity students. than present aPolicy host of pretty mathematical riddles and drawings108 (starring 5.4 Migration in Colombia ...................................................... Mandelbrot sets and heart shaped curves) or giving a technical introduc5.5 “Colombia nos une”...................................................................... 109 tory freshman course (which would be quite pointless if given in isolation), 5.6 Alianza País .................................................................................. 112 she suggested that humanity students be guided in reading actual mathe5.7 Challenges .................................................................................... 114 these matical texts, applying their proficiency in textual analysis to explore texts’ horizons. The second incident was a classroom discussion in116 Prof. Adi Bibliography ....................................................................................... Ophir’s seminar on Derrida. While discussing Derrida’s theory of signs, a Working for thethis Well-being of Migrants ........................... 119 signs. student Together asked whether theory would also apply to mathematical Barry Halliday It was clear to me that it would, and in a more obvious way than it does for other uses of signs.

The first drafts of chapter 2, which is the core of this essay, were produced for presentation in Prof. Adi Ophir’s methodological seminar and the late Prof. Ruth Manor’s logic seminar. The first was a supportive framework, which gave me free range to explore ideas that I might not have

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ACKNOWLEDGEMENT Table of Contents

been able to present anywhere else. The second was a small and analytiBibliography cally minded ......................................................................................... group of critical young researchers, who forced me to 60 deal with G¨ odel’s text hands-on without cutting any corners. I was warned that Prof. 4. The Ethics of Migration. Manor would not quite tolerate my post-modern nonsense. As it turned Reflections on Recent Migration Policies out, was not only but actually protective and encouraging. and she “Non-policies” insupportive, Italy and Europe ........................................... 61 I Laura wish Zanfrini I had the chance to learn more from her, and share with her my research in its Policies more developed form.Demand for Immigrant Labour .. 65 4.1 Restrictive and Structural By the time I decided to write down the philosophy Ph.D. dissertation 4.2 Initiatives for Governing Family and Humanitarian on which this book is based, my choice supervisors was clear. I don’t Migration: Labour Migration but not of Workers’ Migration ............. 73 know where I would be, if either of these two incredibly busy people would have 4.3 From Guest Workers to Unwelcome Guests .................................. 82 turned me down. Prof. Anat Biletzki was the analytic critical mind I needed 4.4keep Selective Policies Brain Drain............................................ 87 to me ‘in line’; and but the what distinguishes her among such philosophers Opportunity and Denied Opportunities ................................ 90 come is4.5 a Equal rare ability to indulge positions that she completely rejects, and up with constructive reactions. Prof. Adi Ophir’s part was primarily Bibliography ......................................................................................... 97 to be patient enough to teach me everything I needed to know in order to safely 5.enter Colombia: Including Emigrants in Their Societies of Origin .......through 101 the pardes of post-structural thinking, and to guide me its Urs Watter thicket. He was even willing to take the leap of faith, which would land him 5.1the State Interest in deep end ofand theResponsibility formal logic pool for the benefit of seeing me through towards their Citizens Living Abroad ........................................... 102 this project. Without their guidance this book would have been impossible 5.2me Applied Ethics .............................................................................. 104 would for to write; without their critical reading and remarks this book have turned out far worse. Since the expertise of neither of my supervisors 5.3 Migration Policy and Ethics ......................................................... 106 completely exhausts the entire range of this essay, its many faults are due 5.4 Migration Policy in Colombia ...................................................... 108 entirely to me. 5.5 “Colombia nos une”...................................................................... 109 Various readers were generous enough to go over parts of this text. Alianza I5.6 would likePaís to .................................................................................. acknowledge Professors Claude Rosental, Eric 112 Brian and 5.7 Challenges .................................................................................... 114 Sabetai Unguru for their helpful comments. Prof. Unguru’s remarks were especially useful, as they came from an opposition stance, which Bibliography ....................................................................................... 116 at the same time was kind enough not to prejudge this entire work as complete Working Together for the Well-being of Migrants ........................... 119 hogwash. Barry Halliday

I would like to end this list of acknowledgements where it should have perhaps begun. My mother taught me to think. For her, and subsequently for me, thinking is something that should always be done from the point of view of someone else. My father tried to teach me how to be a mentsh. If I hadn’t been so busy thinking, perhaps I would have turned out better at this task. I love them both for all they’ve given me. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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Bibliography ......................................................................................... This book is based on the author’s Ph.D. dissertation composed at60 Tel Aviv University’s Cohn Institute for the History and Philosophy of Science and 4. The Ethics of Migration. Ideas. A shortened version of the second chapter appeared in 2008 as a Reflections on Recent Migration Policies paper in Perspectivesinon Science, 16(2),........................................... 196–230. and “Non-policies” Italy and Europe 61 Laura Zanfrini

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

Methodological Introduction

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90

1. The components of this project Bibliography ......................................................................................... 97 is not an analyticEmigrants project. I will not state a question, analyse it down to 5.This Colombia: Including in Their Societies of Origin ....... 101 its constitutive conceptual elements, and attempt to derive a solution. This Urs Watter is5.1 a synthetic project. I will cut-and-paste patches of texts, and attempt to State Interest and Responsibility sew towards them together so as force Abroad them into communication. Communication their Citizensto Living ........................................... 102 in this last sentence is not about the exchange of information. It has to do 5.2 Applied Ethics .............................................................................. 104 with different or remote places communicating with each other by 5.3 Migration Policy and Ethics ......................................................... 106 means of a passage or opening. I will attempt to conjure communication 5.4a Migration in Colombia ...................................................... 108 as tremor [´ ePolicy branlement], a shock, a displacement of force (Derrida 1 1988a, 1). 5.5 “Colombia nos une”...................................................................... 109 5.61 As Alianza País .................................................................................. a synthetic project that depends on French critical tradition, this 112 work replies on heavy use of.................................................................................... quotations. Quoted text here is not simply mentioned as 5.7a Challenges 114object to be commented on, it is also used as quoted. This double gesture deserves a mark more Bibliography 116 prominent than....................................................................................... the timid ‘...’. I therefore render quotations in boldface. Everything in boldface, except for headings, is quoted text, and all text that’s intended to be read Working for the Well-being of Migrants ........................... 119 as quotedTogether is in boldface. Italics inside quotations are always in the source text. I allowed to adapt spelling to UK standard, and made occasional minor punctuation Barrymyself Halliday changes to render the reading smoother. In a few places my quotations are presented in a sequence that does not correspond to their original order, and in one place (one only!) I allowed myself to indulge in the Talmudic liberty of quoting a text without a preceding not. In all such manipulated quotations the changes I allowed myself maintain the intention of the original message, as far as I can tell. Some of the other quotes, however, which are not manipulated formally, do subvert the ‘author’s intended meaning’ to the extent that I understand this term. This is not simply the cost, but to an extent the

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METHODOLOGICAL INTRODUCTION Table of Contents

The textual components that I will attempt to bring into communicaBibliography ......................................................................................... 60 tion are post-structural semiotic theory and a couple of logico-mathematical texts. By ‘logico-mathematical’ I refer to G¨odel’s proof of his first incom4. The Ethics of Migration. pleteness theorem. I read the proof in two versions: van Heijenoort’s 1967 Reflections on Recent Migration Policies translation of the original from 1931, and the 1965 published and “Non-policies” in Italypaper and Europe ........................................... 61 notes ofLaura the Zanfrini 1934 Princeton lectures. Both versions were approved and revised by G¨ o del himself. References to these texts for willImmigrant be denoted by (1931) 4.1 Restrictive Policies and Structural Demand Labour .. 65 and (1934) respectively, and page numbers will refer to the first volume of G¨odel 4.2 Initiatives for Governing Family and Humanitarian (1986–2003). I focus almost exclusively on the proofs of the first incomMigration: Labour Migration but not Workers’ Migration ............. 73 pleteness theorem in these texts, because they provide me with more than 4.3 From Guest Workers to Unwelcome Guests .................................. 82 enough to work with. I do, however, occasionally refer to parts of the texts 4.4 Selective Policies and theincompleteness Brain Drain............................................ 87 concerned with the second theorem and with the construction of an Opportunity arithmetic undecidable proposition. ................................ 90 4.5 Equal and Denied Opportunities I do not......................................................................................... assume a familiarity with G¨ odel’s argument, and Bibliography 97a deep mathematical understanding of the entire argument is not necessary in 5.order Colombia: Including Emigrants in Their with Societies Origin ....... 101 logic to follow this essay. Acquaintance the of elements of formal Urs Watter (propositional and predicate calculus) is, however, assumed. At some points 5.1 State Interest and Responsibility (such as the section The object: notion in chapter 1) the discussion may towards their Citizens ........................................... get technical; I made anLiving effort Abroad to contain such occurrences, and102 keep the 5.2 Applied Ethics .............................................................................. 104 text as accessible as possible to non-logicians without giving up a hands-on concrete analysis. 5.3 Migration Policy and Ethics ......................................................... 106 I use thePolicy term ‘post-structural semiotics’ to refer to French108 semiotics 5.4 Migration in Colombia ...................................................... and discourse analysis developed between 1967 and 1974 by five prominent 5.5 “Colombia nos une”...................................................................... 109 so-called ‘68 thinkers’ (Foucault, Barthes, Derrida, Kristeva and Deleuze). 5.6 Alianza .................................................................................. 112 and From some País of these thinkers I will borrow only guiding questions 5.7 Challenges .................................................................................... 114 methodologies, from others I will quote entire theoretic complexes. I will not provide here a presentation of the theoretical edifice Bibliography ....................................................................................... 116 that I integrate into my text. Such presentation will be provided ad-hoc, as we go Working Together Well-being of Migrants ........................... 119 along. To attemptfora the concise introduction to some of the relevant thinkers Barry Halliday would be either disrespectful to their distributed and non-stationary theoretic endeavours, or simply beyond the capacity of contemporary research, benefit of forcing communication. Where I omit parts of a quotation (which happens quite often) I include a non boldface ellipsis or other unbolded text. When I quote words or small fragments from previous quotations I may or may not use boldface, and usually omit the reference.

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which does not yet have the required perspective for such summaries. The Bibliography ......................................................................................... 60 textual patching of theory into my text, I believe, is the best presentation I can provide. I warn the reader, however, that this essay does assume 4. The Ethics of Migration. openness to post-structural ways of thinking and writing. Reflections on Recent Migration Policies The project that I aimand forEurope appears, at the very least, to go61against and “Non-policies” in Italy ........................................... the grain. Post-structural theory describes that which is unstable in lanLaura Zanfrini guage, that which is originally paradoxical, which resists formalisation, 4.1 Restrictive Policies and Structural Demandthat for Immigrant Labour .. 65 that which is different-in-itself, that which is iterable beyond intention and 4.2 Initiatives for Governing Family and Humanitarian context. Logico-mathematical the other hand, ............. are supposed to Migration: Labour Migration texts, but noton Workers’ Migration 73 be that stable rock to which science is anchored. ‘Two is two is two’ in 4.3 From Guest Workers to Unwelcome Guests .................................. 82 an apparently much more undeniable and reassuring manner than even ‘a 4.4 Selective Policies and Brain Drain............................................ 87 may murder is a murder is a the murder’. Where it comes to murder, there be circumstances; where 2 is concerned, some thinkers 4.5attenuating Equal Opportunity and Denied Opportunities ................................ 90 would 2 claim, there need not be any circumstances at all. Bibliography ......................................................................................... 97 But a description of mathematics as the antonym of post-structural 5.thinking Colombia: Emigrants Their Societies of Origin 101 is Including not precise. Some ofinthe thinkers guiding this ....... essay have alUrs Watter luded to G¨ odel’s incompleteness theorem at one time or another. In fact, 5.1 State Interest and Responsibility mathematics, together with poetry, held a distinguished position in the towards their Citizens Living Abroad ........................................... 102 constitution of post-structural semiotics. The attention mathematics received was due to.............................................................................. its non-phonetic script and its unique position 5.2 Applied Ethics 104 with respect to signification. The effective progress of mathematical 5.3 Migration Policy and Ethics ......................................................... 106 notation thus goes along with the deconstruction of metaphysics, 5.4 Migration Policy in Colombia ...................................................... 108 with the profound renewal of mathematics itself, and the con5.5 “Colombia nosfor une”...................................................................... 109model cept of science which mathematics has always been the 5.6 Alianza País35). .................................................................................. (Derrida 1981, Kristeva and Derrida mention G¨odel while112 analysing Mallarm´ e and Philippe Sollers, and Deleuze quotes Russell and Whitehead 5.7 Challenges .................................................................................... 114 while discussing Lewis Carroll’s ‘nonsense’. But as post-structural analyBibliography ....................................................................................... 116 sis has drifted further into literature, art, social studies, law and politics, it kept drifting from mathematics, and communication between the Working Togetheraway for the Well-being of Migrants ........................... 119 Barry Halliday inspiration and the post-structural practice has been dwinmathematical dling away.3 2 In the words of younger Husserl, I see that, wherever is talk of the proposition or truth that π is a transcendental number, there is nothing I have less in mind than an individual experience, or a feature of an individual experience of any person (Husserl 1970a, 300–301). 3 For the relations between mathematics and post-structural thinking see Duffy (2004)

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Post-structural thought used to be intimately related to modern poBibliography ......................................................................................... etry for a reason. As Kristeva puts it, paragrammatism (which I60 (mis)appropriate here as a generic term for post-structurally theorised semiotic 4. The Ethics of Migration. effects) being easier to describe at the level of poetic discourse, Reflections on Recent Migration Policies should be seized by semiotics first of all there, before exposing it and “Non-policies” in Italy and Europe ........................................... 61 in relation Laura Zanfrinito all thought productivity (Kristeva 1969, 176). Today, over 40 years later, it isand time to attempt a forcing of post-structural thinking 4.1 Restrictive Policies Structural Demand for Immigrant Labour .. 65 and that which has become its polar antonym, mathematics, into commu4.2 Initiatives for Governing Family and Humanitarian nication. In this revived effort I no longer seek to reposition mathematics Migration: Labour Migration but not Workers’ Migration ............. 73 as a source of theoretic inspiration. I wish to place it in the position of the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 analysand, a legitimate partner for post-structural semiotics and discourse 4.4 Selective Policies andofthe Brain Drain............................................ analysis in the process transference and counter-transference. 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97

2. This project in contemporary

5. Colombia: Including Emigrants in Their Societies of Origin ....... 101

academic context

Urs Watter

5.1 State Interest and in Responsibility The approach taken this book is related to the what Philip Kitcher called towards their Citizens ........................................... 102 away the maverick trend in theLiving studyAbroad of mathematics. This tradition turns 5.2 Applied Ethics .............................................................................. from a foundational quest for the fortification of mathematics, and104 proposes a5.3 social and textual analysis of mathematics as a human activity. However, Migration Policy and Ethics ......................................................... 106 even within the maverick stream of thought, post-structural and semiotic 5.4 Migration Policy in Colombia ...................................................... 108 approaches are rather rare (although not unprecedented, as witnessed by 5.5 “Colombia nos une”...................................................................... 109 some papers in Ernest (1994)). 5.6 Alianza .................................................................................. 112 trend AmongPaís more tenured approaches, the closest ally of the maverick

is5.7Wittgenstein’s philosophy of mathematics. For the later Wittgenstein Challenges .................................................................................... 114 mathematics is comprised of systems of rules, which are connected Bibliography ....................................................................................... 116to each other by other rules. These rules are not arbitrary in that they are pragWorking Together for the Well-being of Migrants ........................... matically and psychologically constrained; however, Wittgenstein119 refuses to Barry Halliday acknowledge the derivability of such rules from any unified system, regardless of whether this system is formal, empirical, transcendental or platonic (this reading of Wittgenstein is substantiated by the quotations on page 136). Of course, this Wittgenstein is not unrelated to the Wittgenstein of (around Deleuze), Charraud (1977) (concerning Lacan) and Tasi´ c (2001), Ernest (1994) and Plotnitsky (2002) for general discussions.

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the analytic tradition, who seeks to cure philosophical problems by setBibliography ......................................................................................... ting apart different uses of words in different language games. In60fact, in the context of G¨ odel’s theorem itself, Wittgenstein sought to set apart 4. The Ethics of Migration. and distinguish the different language games played with the word ‘true’ Reflections on Recent Migration Policies (Wittgenstein 1978, in 118–122, esp. §8). But this is not the approach and “Non-policies” Italy and Europe ........................................... 61 I take inLaura this Zanfrini essay. Here I insist on the way that the language game depends on unstable and permeable between differentLabour language 4.1 Restrictive Policies andboundaries Structural Demand forthe Immigrant .. 65 games that it encompasses. Rather than a source of problems, I show that such 4.2 Initiatives for Governing Family and Humanitarian unstable permeabilities are positive, constitutive forces for mathematical Migration: Labour Migration but not Workers’ Migration ............. 73 semiosis. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Another approach that’s related to the maverick tradition is Husserl’s 4.4 Selective Policies and the Brainand Drain............................................ 87(1989). phenomenology of mathematics its interpretation by Derrida 4.5 Equal and attempts Denied Opportunities But while Opportunity this approach to account................................ for the transition 90 from intuitive perception to a rigorous axiomatic geometry, here we’re concerned Bibliography ......................................................................................... 97 with semiotic processes that occur within rigorous mathematical produc5.tion, Colombia: Including Emigrants in Their Societies of Origin ....... 101 and yet are not subject to axiomatised formalities. Urs Watter

Several contemporary authors should be mentioned to put this book 5.1 State Interest and Responsibility in the present academic context. The first is Brian Rotman, who pioneered towards their Citizens Living Abroad ........................................... 102 a novel semiotic approach to mathematics (Rotman 1993). His division of 5.2 mathematical Applied Ethics .............................................................................. 104person, the sign-manipulating agency into a contextualised Migration andand Ethics ......................................................... 106with in a5.3 context free Policy subject, a mechanical agent is critically engaged the first chapter of this book. I show that mathematical meaning 5.4 Migration Policy in Colombia ...................................................... 108requires forms of temporality and agency that cross, undermine and suspend the 5.5 “Colombia nos une”...................................................................... 109 barriers between the above three aspects of the mathematical enunciative 5.6 Alianza País .................................................................................. 112 position. 5.7 Challenges .................................................................................... 114 The second author who should be mentioned here is Eric Livingston, Bibliography ....................................................................................... 116 whose early work, The Ethnomethodological Foundations of Mathematics (Livingston 1985) provides a detailed and careful analysis of the practice Working Together for the Well-being of Migrants ........................... 119 of reading and proving G¨ odel’s theorem. Livingston rejects the option of Barry Halliday relegating mathematical rigour and validity to a deferred transformation of the ‘everyday language’ proof into a formal reconstruction. The validity of the proof, according to Livingston, is anchored to the construction of mathematical practices and the organisation of these practices into a structure of practices of proving, identifiably, just that theorem. For Livingston, therefore, mathematical validity is an issue in the proRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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duction of social order (Livingston 1985, 17). Yehuda Rav’s work on Bibliography the semantic ......................................................................................... aspects of mathematical work (Rav 2007) provides60a more ‘freestyle’ version of related positions. My focus in this essay, however, is 4. The Ethics of Migration. not the production of structures of validity, but rather the deconstructed Reflections on Recent Migration Policies proliferation and shifting meaning. I demonstrate that mathematical and “Non-policies” in Italyofand Europe ........................................... 61 practices of iteration and substitution prevent syntactic order from tying Laura Zanfrini symbols to fixed meanings and uses, and that the construction 4.1 Restrictive Policies and Structural Demand for Immigrant Labour ..of 65mathematical meaning, rather than being restricted to specialised mathematical 4.2 Initiatives for Governing Family and Humanitarian and logical contexts, depends on more generic linguistic semiotic processes. Migration: Labour Migration but not Workers’ Migration ............. 73 As the main focus of this project is the plurality of mathematical 4.3 From Guest Workers to Unwelcome Guests .................................. 82 texts, one must acknowledge here the work of Claude Rosental concern4.4 the Selective Brain Drain............................................ 87textual ing pluralPolicies aspectsand of the classroom logic (Rosental 2008), and the 4.5 EqualofOpportunity and Denied Opportunities ................................ 90 analysis multiple functions and useful ambiguities of mathematical signs in Lefebvre (2002) and Grosholz (2007). My own analyses of Bibliography ......................................................................................... 97various other mathematical case studies using various theoretical perspectives, but 5.always Colombia: Including on Emigrants in Their Societies of Origin concentrating the plurality of mathematical texts,....... can101 be found Urs Watter in Wagner (2009a,b, forthcoming). 5.1 State and Responsibility LikeInterest readings proposed by the maverick tradition, my reading of G¨odel’s towards their Citizens Living Abroad ........................................... 102 proof is conducted ‘in context’, but unlike most maverick readings, not al5.2 Applied .............................................................................. ways in the Ethics historical context in which the texts were written. 104 Following 5.3 Migrationapproaches Policy and Ethics 106 of this hermeneutic such as......................................................... that of Gadamer (1975), the context project is the interaction between an old text and a contemporary 5.4 Migration Policy in Colombia ...................................................... 108reader. The texts mean something to me as I am reading, they confront me with 5.5 “Colombia nos une”...................................................................... 109 5.64 The Alianza País 112objection referee of .................................................................................. a paper based on part of this book made the following concerning my level of analysis: In case my complaint about remaining 5.7 Challenges .................................................................................... 114 at the rhetorical level is not clear, let me point out that the standard epsilonBibliography 116 delta way of ....................................................................................... writing about limits, which has to do with the succession of quantifiers for all epsilon there exists a delta ... . This is sometimes written Working Together forIfthe Well-being of Migrants as a mock dialogue. you choose epsilon, then I........................... can choose delta119 ... . That does turn the argument into such a dialogue. If one were to analyse Barrynot Halliday such a dialogue, one would have to reconstruct it in terms of quantifiers to see the structure of the argument. Like Livingston’s, my stance in this paper is diametrically opposite. I am concerned here with mathematical practice, not with formal reconstruction. mathematics can be practiced without formal reconstructions, but has never historically existed without surface dialogues. I do not mean to dismiss formal reconstructions. I do object to the dictum that one would have to reconstruct it in terms of quantifiers to analyse the successful functioning of mathematics.

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new horizons, and these effects of meaning are the stuff that I must account Bibliography ......................................................................................... 60 for. To get there I do, at some points, accept methodological restrictions of contextual reading. These methodological restrictions allow to bring up ef4. The Ethics of Migration. fects which, according to ideologies supportive of such methodologies, arise Reflections on Recent Migration Policies from the text without beingand imposed upon it. But since my project and “Non-policies” in Italy Europe ........................................... 61 is not limited to historic interpretation, and does not wish to reconstruct G¨odel’s Laura Zanfrini position, I hardly everand compare theDemand translated text with Labour the German 4.1 Restrictive Policies Structural for Immigrant .. 65 one, and consider both G¨ odel’s first paper and the subsequent lecture notes as 4.2 Initiatives for Governing Family and Humanitarian perfectly valid and equally relevant sources to work with. My project is Migration: Labour Migration but not Workers’ Migration ............. 73 about communicating texts, not intentions. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87

3. The purpose of this project 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography 97 aware Subject to its......................................................................................... own claims on language, post-structural theory is well of its own instability, its self-subversion, and its dependence on — as well as 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 interaction with — its objects of inquiry. Post-structural semiotics is thereUrs Watter fore not an established set of tools to be applied to objectified texts. I will 5.1 State Interest and Responsibility not pretend that my application of post-structural semiotic theory to the towards their Citizens Living Abroad ........................................... 102 logico-mathematical is an experiment or case study in any scientific sense; 5.2 Applied Ethics .............................................................................. 104 rather it is a self-reflective performance of a scholarly rite. In this essay I 5.3 Migration and Ethics ......................................................... 106 text. I will perform aPolicy post-structural reading with a logico-mathematical will force the post-structural and...................................................... logico-mathematical into communication. 5.4 Migration Policy in Colombia 108 The product of this project is not confined to a better understand5.5 “Colombia nos une”...................................................................... 109 ing of G¨ odel’s text or of post-structural semiotics. My primary question to 5.6 Alianza País .................................................................................. 112 texts I quote is hardly ever ‘what do you say?’. Rather, my questions to 5.7 Challenges .................................................................................... 114can I do quoted texts are usually of the form ‘how do you work?’ and ‘what Bibliography with you?’. A....................................................................................... response to these questions cannot pretend to bear116 the often neutral overtone of a term such as ‘understanding’. Answering the quesWorking Together for the Well-being of Migrants ........................... 119 tion ‘how do you work?’ requires an intervention, namely the application Barry Halliday of reading-tools, which necessarily transform the quoted text by breeding it with the hermeneutic and analytic stances of the reader and her or his tools. Such transformative intervention is precisely how texts are made to respond to the question ‘what can I do with you?’, and become partners to conversation.

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As the goal of this project is to produce the communication articuBibliography 60 to the lated above, ......................................................................................... my textual quilting will prove a successful endeavour extent that it is cut and integrated into other texts, to the extent that it is 4. The Ethics of Migration. quoted, reiterated and repeated, to the extent that, once worn out by the Reflections on Recent Migration Policies fittings and bodies which might serve........................................... to cover, it continues to61provide and “Non-policies” in Italyitand Europe manufacturers Laura Zanfrini of text with raw material for their production. A more optimistic writer might even to hope that while flowing as current 4.1 Restrictive Policies anddare Structural Demand for Immigrant Labour .. 65through circuits of textual proliferation, this text might be able to induce a field of 4.2 Initiatives for Governing Family and Humanitarian force acting on human practices that exceed the editing of texts, such as Migration: Labour Migration but not Workers’ Migration ............. 73 education and academic prioritising. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 I hope that my textual patch-work will prove useful for some readers 4.4 Selective Policies and the Brain Drain............................................ 87 of the text, be they mathematicians, philosophers or others. I hope that my 4.5 Equal Opportunity and Denied Opportunities 90 textual suturing will open the quoted texts to................................ further, not necessarily anticipated uses. These hopes, however, have a rather problematic interaction Bibliography ......................................................................................... 97 with notions of truth. Parts of this essay are designed to form a legitimate 5.analytic Colombia: Including Emigrants in Their what Societies of Origin ....... reading, as far as I understand distinguishes such101 readings Urs Watter — after all, even if one objects to their contemporary privileged status, one 5.1 admire State Interest Responsibility can their and productivity. But I play several language and truth games towards their Citizens Living Abroad ........................................... 102 with changing degrees of irony and commitment. I am indeed committed 5.2for Applied 104 — a fewEthics pages.............................................................................. or throughout this essay — to some determinations of truth. But telling the is ......................................................... not a primary business of this project 5.3 Migration Policy andtruth Ethics 106 (for example, the psychoanalytic edifice of chapter 3 is not supposed 5.4 Migration Policy in Colombia ...................................................... 108to be a true description of fact; it is used as a tool for thinking language and bodies 5.5 “Colombia nos une”...................................................................... 109 together). 5.6 Alianza País .................................................................................. 112 One important use I have in mind for this project is ethical: a re5.7 Challenges .................................................................................... 114 ethics evaluation of the authority invested in mathematical texts. The term 116 is reisBibliography meant here....................................................................................... as concern with taking responsibility for a text. Who sponsible for a text? Is it the author? the editor, publisher and distributor? Working Together for the Well-being of Migrants ........................... 119 the voices which express their statements in the text (statements which Barry Halliday may run contrary to those of the author, editor, publisher and distributor)? Is it the reader who interprets the text and, perhaps, replicates its statements? Is it the social or formal order of language that enables the writing of the text? Or is it simply truth and reality, to the extent that the text states the real truth? Given this complex web of responsibilities for a text, to what extent can we invest a text with authority — an authoritative Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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text? I believe that the picture I draw in this book has substantial impliBibliography ......................................................................................... 60 I hope cations, if concern with these questions afflicts mathematical texts. that the textual quilt I sew together will have an impact on the derivation 4. The Ethics of Migration. of authority from mathematics’ supposedly privileged access to truth and Reflections on Recent Migration Policies meaning, and on theinauthoritative privileges bestowed upon mathematics and “Non-policies” Italy and Europe ........................................... 61 inLaura contemporary Zanfrini academic discourse due to that supposition. But this issue of is Policies not the and same as thatDemand of validity. I have no Labour qualms..about the 4.1authority Restrictive Structural for Immigrant 65 logico-mathematical validity of G¨odel’s proof. 4.2 Initiatives for Governing Family and Humanitarian To summarise: Migration: Labour Migration but not Workers’ Migration ............. 73 4.3•From to Unwelcome Guests ThisGuest is notWorkers a historical essay. It does not.................................. frame G¨odel’s proof82 in terms of chains or flows practices or ideas. 4.4 Selective Policies andofthe Brain Drain............................................ 87 4.5•Equal and Denied Opportunities 90 ThisOpportunity is not a mathematical essay. It does................................ not explain the proof, nor Bibliography 97 does it ......................................................................................... cast doubts on its mathematical validity. 5. Colombia: Including Emigrants in Their of Origin 101 • This essay analyses G¨ odel’s proof Societies as an example of....... mathematical Urs Watter practices. ‘Mathematical practices’ stand here for reading (under-

standing) (producing) mathematical texts. 5.1 State Interestand and writing Responsibility towards their Citizens Living Abroad ........................................... 102 • I believe that there is no deeper essence to mathematics beyond its 5.2 Applied Ethics .............................................................................. 104 practices of reading and writing (in an extended sense, which includes 5.3 Migration Policy and Ethics ......................................................... contemplation, application and transcription). This essay,106 however, 5.4 Migration in rule Colombia ...................................................... 108 does notPolicy seek to out alternative beliefs. 5.5 “Colombia nos une”...................................................................... 109 • Articulating the features that distinguish mathematical practices from 5.6 Alianza .................................................................................. other País textual practices is an interesting task. This essay,112 however, touches upon this task only marginally. 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 • This essay shows that reading and writing G¨odel’s texts depend on theTogether paradoxical and unstable semiotic processes that post-structural Working for the Well-being of Migrants ........................... 119 theoreticians diagnosed in ‘softer’ textual practices. Barry Halliday

• As mathematical practices enjoy the paradoxical and unstable semiotic processes operative in ‘softer’ textual practices, it is difficult to make an a priori claim for mathematics’ privileged authority or distinguished access to truth. Claims that mathematical practices have a privileged authority or a distinguished access to truth had better be Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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established a-posteriori, in terms of the implications of mathematics, Bibliography ......................................................................................... 60 its results and applications. 4. The Ethics of Migration. Reflections on Recent Migration Policies 4. The chapters and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini The first chapter is devoted to a discursive analysis of G¨odel’s texts 4.1 Restrictive Policies and Structural Demand forin Immigrant Labour .. 65 guided by methodological devices articulated Foucault’s Archaeology of

Knowledge (Foucault 1972) Family and inand Barthes’ S/Z (Barthes 1974). My first 4.2 Initiatives for Governing Humanitarian Migration: Labour Migrationanalysis but not Workers’ Migration ............. 73 text attempt included a bit-by-bit of the introduction to the 1931 using the Guest methodology that Barthes Guests presented in S/Z. The process 4.3 From Workers to Unwelcome .................................. 82 was very productive, but presenting the results according to Barthes’ formal4.4 Selective Policies and the Brain Drain............................................ 87 ism appeared to be tedious and rhetorically difficult to sustain. I therefore 4.5 Equal Opportunity and Denied Opportunities ................................ 90 imported the results of this analysis into a slightly more ‘archaeological’ Bibliography ......................................................................................... 97 analysis of the text. Carrying such an archaeological analysis of G¨odel’s texts, however, is 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 not without its problems. Foucault explicitly determines his archaeology to Urs Watter refer to much larger bodies of texts. Indeed, he explains, I do not wish 5.1 State Interest and Responsibility to take as an object of analysis the conceptual architecture of an towards their Citizens Living Abroad ........................................... 102 isolated text, an individual oeuvre, or a science at a particular mo5.2 Applied Ethics .............................................................................. 104 ment in time. One stands back in relation to this manifest set of 5.3 Migration Policy Ethics ......................................................... 106 concepts; and oneand tries to determine according to what schemata (of simultaneous groupings, linear or reciprocal modifica5.4 series, Migration Policy in Colombia ...................................................... 108 tion) the statements may be linked to one another in a type of 5.5 “Colombia nos une”...................................................................... 109 discourse (Foucault 1972, 60). Nevertheless, the imposing of archaeologi5.6 Alianza País .................................................................................. 112 cal leading questions on G¨ odel’s texts, in conjunction with the conclusions 5.7 Challenges .................................................................................... 114point of carried over from the Barthesian analysis, provided a stimulating departure for....................................................................................... my discussion. Bibliography 116 In this chapter I quote a lot from G¨odel, and less from Barthes and Working Together for the Well-being of Migrants ........................... 119 Foucault. The main reason for this practice is that Foucault’s and Barthes’ Barry Halliday theories are still presented as theories in the traditional sense, namely as tools that efface themselves as they are being used to produce an objective analysis. Both Foucault’s Archaeology of Knowledge and Barthes’ S/Z stand at a liminal point between structuralism and post-structuralism, and therefore allow gradual transition into post-structural reading. The analyses are structural in that they articulate units and review their combinatorial Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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interrelations; they exceed structuralism in that the articulation of units is Bibliography ......................................................................................... opened to extra-textual intervention, in that they do not presume 60 to locate syntactical arrays that are independent of the reader, and in that the anal4. The Ethics of Migration. ysis is not governed by a belief in universal combinatorial determinations Reflections on Recent Migration Policies of possible results.5 in Italy and Europe ........................................... 61 and “Non-policies” One should not expect in this chapter an exhaustive appropriation of Laura Zanfrini Barthes’ and Foucault’s ways Labour large parts 4.1 Restrictive Policies andtheoretic Structuraledifices. DemandInformany Immigrant .. 65 of this chapter can be subsumed under more traditional hermeneutic frameworks, 4.2 Initiatives for Governing Family and Humanitarian suchMigration: as Gadamer’s decree that the text, whether law or gospel, Labour Migration but not Workers’ Migration ............. 73 if it is to be understood properly, i.e. according to the claim it makes, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 must be understood at every moment, in every particular situ4.4 Selective Policies anddifferent the Brain Drain............................................ ation, in a new and way. Understanding here is87always application (Gadamer 275). 4.5 Equal Opportunity and1975, Denied Opportunities ................................ 90 The second and third chapters include a synthesis of the Bibliography ......................................................................................... 97 mathematical texts with Derrida’s and Deleuze’s semiotic constructs respec5.tively. Colombia: Including Emigrants of Origin 101 both Substantial references to in theTheir workSocieties of Kristeva cross....... through Urs Watter chapters. From Derrida I quote mainly Dissemination (Derrida 1993), Of 5.1 State Interest(Derrida and Responsibility Grammatology 1976), the paper Signature, Event, Context from towards their Citizens Living Abroad ........................................... 102I quote Limited Inc. (Derrida 1988a), and a few other texts. From Deleuze 5.2 Applied The Logic ofEthics Sense.............................................................................. (Deleuze 1990) and Difference and Repetition104 (Deleuze 1994), and from Kristeva the ......................................................... non-translated Semeiotike (Kristeva 5.3 Migration Policy and Ethics 106 1969) and the Revolution in Poetic Language (Kristeva 1984) (the translations 5.4 Migration Policy in Colombia ...................................................... 108 from the former are my own). 5.5 “Colombia nos une”...................................................................... 109 As I wrote above, the introduction of the relevant theoretical elements 5.6 Alianza País .................................................................................. 112 ‘how will be threaded into the discussion of G¨odel’s proof. The question does the mathematical text make sense?’ is used as catalyst to114 instigate 5.7 Challenges .................................................................................... G¨ odel’s texts....................................................................................... and post-structural semiotics into interaction. Bibliography 116 In these two chapters I refer directly and explicitly to G¨ odel’s texts, Working Together the Well-being ........................... but do not quote for from them as oftenofasMigrants in the previous chapter. I119 preferred Barry Halliday this slightly looser form of interaction in order to allow my text enough motility and independence so as to be more readily applicable to other mathematical texts as well. I believe that semiotic analysis can only be performed concretely on each given text, but I attempted to open up my 5 These

characterisations of structuralism are more a caricature than a faithful description, but I do not wish to attempt a precise historic articulation here.

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concrete analysis so that it can be reappropriated concretely to other texts Bibliography ......................................................................................... 60 quite as well. Derrida, Deleuze and Kristeva, on the other hand, are quoted intensively. This is done not only in order to introduce the relevant theo4. The Ethics of Migration. retical constructs, but also in order to force these theoretical constructs to Reflections on Recent Migration Policies expand their horizoninso as to on G¨ odel’s texts, with which and “Non-policies” Italy andcomment Europe ........................................... 61 they were actually concerned. Lauranot Zanfrini The question of and similarity andDemand difference between Deleuze and Der4.1 Restrictive Policies Structural for Immigrant Labour .. 65 rida is starting to get some attention (e.g. Patton & Protevi 2003). I believe 4.2 Initiatives for Governing Family and Humanitarian thatMigration: it is muchLabour more interesting to not confront these two thinkers via73the meMigration but Workers’ Migration ............. diation of third elements than by seeking to list elements of congruence 4.3 From Guest Workers to Unwelcome Guests .................................. 82 and divergence between their positions as such (the latter approach is al4.4 Selective Policies theachievements). Brain Drain............................................ 87 fourth most disrespectful of and their I hope that the third and 4.5 Equalof Opportunity Denied Opportunities ................................ 90repeat, chapters this essayand serve to deepen our insight into how they differenciate and iter ate each other. Bibliography ......................................................................................... 97 The appendix concluding this book is a rather awkward attempt to 5.confront Colombia: in Their Origin 101 This G¨ oIncluding del’s proofEmigrants with narrative textsSocieties and the of notion of ....... structure. Urs Watter is a useful preliminary exercise, if we are to impose on a mathematical text 5.1 State Interestsemiotics and Responsibility post-structural — an approach that emerged from structuralism towards their Citizens Living Abroad ........................................... 102 and from literary criticism. 5.2 Applied Ethics .............................................................................. 104(reason, Mathematics is often presented as the structure of something 5.3 Migration Policy and But Ethics 106to take language, the universe). to......................................................... bring it closer to literature, I needed this way of thinking step further. I (ab)use L´evi-Strauss’ conceptual 5.4 Migration Policy inone Colombia ...................................................... 108 framework to attempt an assignment of G¨odel’s text into the position of 5.5 “Colombia nos une”...................................................................... 109 structure with respect to a made-up mythical text. Readers, who object to 5.6 Alianza País .................................................................................. 112 reading a text as something that it obviously is not, are referred to Borges’ 5.7 Challenges 114 Pierre Menard,.................................................................................... Author of the Quixote (Borges 1962, 45–55). I cannot improve upon his apologia for the method of anachronistic attribution. Bibliography ....................................................................................... 116

The failure of my fake reading of G¨odel’s proof as the structural analWorking Together for the Well-being of Migrants ........................... 119 ysis of a lost myth, which I set as my task to retrace, is grotesque but inBarry Halliday structive. It brings out the limitations of a ‘common structure’ hypothesis (common to myth and science, or to human ‘untamed thinking’ in general). It reaffirms the specificities of literary and mathematical texts, and explicates their relative discrepancies. The texts distributed across these discrepancies and specificities have, nevertheless, this much in common: they all deserve the benefit of a reading that respects their specificities and Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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discrepancies, and that does not assume that they must be subordinated Bibliography ......................................................................................... 60 to any particular given text or phenomena. There is also another excuse for this awkward first chapter. I felt that 4. The Ethics of Migration. it would be counter-productive to provide yet another layman account of Reflections on Recent Migration Policies G¨ odel’s argument; there areand quite a few........................................... such accounts, some of which are and “Non-policies” in Italy Europe 61 very good, (e.g. Nagel & Newman 1958), and I am unlikely to do any better. Laura Zanfrini The mythologising of and the Structural proof might make a little more accessible to 4.1 Restrictive Policies Demand foritImmigrant Labour .. 65 people with little logical background, without actually presuming to explain 4.2 Initiatives for Governing Family and Humanitarian the proof. Migration: Labour Migration but not Workers’ Migration ............. 73 This exercise has some merit, but is also somewhat detached from 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the rest of this project. It served me well, but I am not sure that it will 4.4 Selective Policies and the Drain............................................ perform the same service forBrain all readers. I therefore advise readers87familiar with G¨ odel’s argument readers with analytic tendencies to 90 skip this 4.5 Equal Opportunity andand Denied Opportunities ................................ chapter, or perhaps read it as an appendix. Other readers may97want to Bibliography ......................................................................................... read it first. 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

Analytic Introduction

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90

1. Meaning

Bibliography ......................................................................................... 97

This is not an analytic project. But I see no reason to prevent it from 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 being read as such. I see no reason not to read this project as attempting, Urs Watter through a careful analysis of a distinguished case study, a new attempt at 5.1 State Interest and Responsibility articulating the question ‘how does mathematical meaning work?’ towards their Citizens Living Abroad ........................................... 102 I will not confront this question by articulating minimal elements or 5.2 Applied Ethics .............................................................................. 104 determinations of meaning, and then describing how these minimal ele5.3 Migration and Ethics 106 ments combinePolicy to generate the......................................................... global meaning of an entire mathematical text. To the question does ...................................................... meaning operate?’ I reply, inspired 5.4 Migration Policy in‘how Colombia 108 by the thinkers whom I quote: Meaning is an operator which produces difference 5.5 “Colombia nos une”...................................................................... 109 across repetition. 5.6 Alianza País .................................................................................. 112 What kind of operator? A linguistic operator for those who took 5.7 linguistic Challengesturn, .................................................................................... 114 the an experiential operator for the phenomenologically in1 clined, a self-defeating transcendental operator for metaphysicians, Bibliography ....................................................................................... 116 and an embodied performative operator for theoreticians whose positions involve Working Together for the Well-being offeminist, Migrantscolonialist...). ........................... 119 the prefix ‘post’ (structural, modern, Barry Halliday I do not presume to exhaust with the above formula the entire scope of the operation of meaning. In addition to producing difference across repetition (manifest in such statements as ‘this same term is employed with different meanings’) it obviously produces repetition across difference (‘these 1 Self

defeating because it undermines the structure that metaphysicians usually require transcendental objects to hold on to.

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two different expressions mean the same thing’). Furthermore, bringing Bibliography ......................................................................................... 60 up meaning obviously has various other effects, such as the transcription of a given statement in terms of intention, extension, truth conditions, 4. The Ethics of Migration. truth value, assertibility conditions, grammatic or otherwise formal strucReflections on Recent Migration Policies ture, stimulus-response arrays, phenomenological reduction, ideal and “Non-policies” in Italy and Europe ........................................... 61 source and quotability, Laura Zanfrini to name but a few. But I do maintain that instilling difference across Policies repetition as fundamental operation of meaning as 4.1 Restrictive andisStructural Demand to for the Immigrant Labour .. 65 any of these other terms; ‘as fundamental’ and not ‘more fundamental’, 4.2 Initiatives for Governing Family and Humanitarian because imagining a linear chain of foundations which goes all the way Migration: Labour Migration but not Workers’ Migration ............. 73 down to a primary cause is precisely the image I do not have in mind (or, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 rather, have in mind under a stroke of erasure, repeated differently), when Selective Policies the Brain Drain............................................ 87 I4.4 define meaning as and an operator that instils difference across repetition. The fundamentality myDenied definition is demonstrated by articulating the 4.5 Equal Opportunityofand Opportunities ................................ 90 classification of phrases according to intention, extension, etc. as97 marking Bibliography ......................................................................................... different phrases as somehow repeating each other, or various repetitions 5.of Colombia: Emigrants Their Societies Originbe ....... 101 just to a phrase Including as carrying different in meanings. Still, itofwould more Ursthat Watter say my italicised definition above is not a definition of meaning, but the anResponsibility aspect of meaning, which is as definitive as any of its 5.1 articulation State Interestof and towards their Citizens Living Abroad ........................................... 102 other aspects. 5.2 Applied 104 coins Let’s beEthics more.............................................................................. explicit. In How to Do Things with Words Austin a5.3 disturbing He said......................................................... to me ‘shoot her!’ meaning by Migrationexample. Policy and Ethics 106‘shoot’ shoot and referring by ‘her’ to her (Austin 1962, 101). This example 5.4 Migration Policy in Colombia ...................................................... 108 is disturbing, because it convincingly demonstrates, but fails to explain, 5.5what “Colombia nossterile une”...................................................................... 109without in way the repetition of shoot and her (with and 5.6 Alianzamarks, País .................................................................................. quotation in a medium or italic font) serves to explain112 or clarify anything. It is .................................................................................... important to note that Austin’s intervention instils 5.7 Challenges 114 difference across repetition. shoot and ‘shoot’, her and her deploy different Bibliography ....................................................................................... 116 functions, different grammars, uses, intentions, extensions, references, affects and idealities if theyofhad been exactly the same,119 it would Working Together forbecause, the Well-being Migrants ........................... Barryserved Halliday have no purpose to repeat them.2 The fact of repetition entails that the elements shoot and her must decompose into smaller constitutive elements or discharge a sort of excess: the element ‘itself’ and the element’s ‘ghost’, use and mention, the text animated with meaning as opposed to 2 Is

this even possible? Can something repeat something else, which is exactly the same, without collapsing into unity?

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the quoted text. Note, however, that none of Austin’s locutions, illocutions Bibliography ......................................................................................... 60 been and perlocutions in his written discussion of ‘shoot her!’ have ever ‘actually’ used (I hope), in the sense that they have never given rise to a 4. The Ethics of Migration. single actual shot.3 Reflections on Recent Migration Policies This procedureinofItaly effectuating repetition to produce difference and “Non-policies” and Europe ........................................... 61 is not Laura Zanfriniof 20th century analytic philosophy. This procedure is, among the invention other things, aPolicies fundamental technique of the Talmud, the interpre4.1 Restrictive and Structural Demand forJewish Immigrant Labour .. 65 tation of the codices deriving laws from the old testament. In the Talmud 4.2 Initiatives for Governing Family and Humanitarian this Migration: procedureLabour is referred to bybut the pshita, which73literally Migration notAramaic Workers’term Migration ............. means simple or obvious. When the interpreter encounters a repetition of 4.3 From Guest Workers to Unwelcome Guests .................................. 82 an already stated fact or of what is already commonly known, he makes the 4.4 Selectivethat Policies the Brain Drain............................................ assumption the and apparent repetition is justified by a new and87original 4.5 Equal Opportunity and Denied Opportunities 90 by the statement which is folded within it. This novel ................................ meaning is excavated interpreter through instilling difference across the repetition. Interpretation Bibliography ......................................................................................... 97 abhors repetition. 5. Colombia: Including Emigrants in Their Societies of manoeuvre. Origin ....... 101 But there’s nothing particularly Jewish in this The most Urs Watter

exemplary analytic philosopher ever (who is not recognised as such only 5.1 StateofInterest and Responsibility because the trifling fact that he was confined not by 20th century westtowards their Citizens Living Abroad ........................................... 102 ern rationalism, but by 11th century Catholic dogma), Anselm of Canter5.2 Applied bury, writes:Ethics The .............................................................................. rational mind, then, when it conceives of104 itself in thought, has with itself its image born of itself that is, its thought 5.3 Migration Policy and Ethics ......................................................... 106 in likeness, as in if Colombia formed from its impression, although 5.4its Migration Policy ...................................................... 108it cannot, except in thought alone, separate itself from its image, which 5.5 “Colombia nos une”...................................................................... 109 image is its word. We see here that thought alone can instil a difference 5.6 Alianza .................................................................................. between thePaís thought image that repeats the thinking mind. And 112 in relation not just any.................................................................................... rational mind, but to that rational mind, a more114 excellent 5.7 to Challenges than which is....................................................................................... inconceivable, he writes: But although this is 116 true, yet Bibliography it is most remarkably clear that neither he, whose is the Word, Working the Well-being of Migrants ........................... 119 it is, can be Together his own for Word, nor can the Word be he, whose Word Barry Halliday although in so far as regards either what they are substantially, or what relation they bear to the created world, they ever preserve an indivisible unity. But in respect of the fact that he does 3 Likewise,

it seems to me that ‘Could you pass me the salt?’ appears much more often in classroom discussions of linguistic pragmatics than around dinner tables. It has been suggested, however, that perhaps I do not dine in very good company.

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not derive existence from that Word, but that Word from him, Bibliography 60 they admit ......................................................................................... an ineffable plurality, ineffable, certainly, for although necessity requires that they be two, it can in no wise be explained 4. The Ethics of Migration. why they are two (Anselm 1903, chapters 33, 38). Even when no differReflections on Recent Migration Policies ence can be claimedinconcerning substance and relation to the world, the and “Non-policies” Italy and Europe ........................................... 61 difference between expressing and expressed is instilled across the repeated Laura Zanfrini substance and Policies identical to Demand the created world. The Father 4.1 Restrictive andrelation Structural for Immigrant Labour .. 65and the Word, the Father and the Son, are forced apart, even though it can in no 4.2 Initiatives for Governing Family and Humanitarian wise be explained why they are two. Shoot and ‘shoot’, her and ‘her’. Migration: Labour Migration but not Workers’ Migration ............. 73 But difference across repetition doesn’t end there, with signifier and 4.3 From Guest Workers to Unwelcome Guests .................................. 82 signified, or with mention and use. A simple exercise of countertext (replac4.4 portions Selective of Policies andother the Brain 87 ing text by text Drain............................................ in order to investigate their differences) will demonstrate the and proliferation of difference across repetition. 4.5 Equal Opportunity Denied Opportunities ................................ 90Rather than meaning by ‘shoot’ shoot, let’s contemplate ‘meaning by97“meanBibliography ......................................................................................... ing” meaning’; rather than referring by ‘her’ to her — ‘referring by “by” 5.to Colombia: Emigrants in Their Societies Origin .......are 101actually by’. The Including first ‘meaning’ and ‘by’ of our object of statements Urs Watter 4 used. The second and third iterates of ‘meaning’ and ‘by’, on the other 5.1 State and Responsibility hand, actInterest respectively as the signifier and the signified of the mentioned towards their Citizens Living Abroad ‘meaning’ and of the mentioned ‘by’. ........................................... 102 5.2 Applied Ethics 104 If one is not .............................................................................. quite convinced that there are here three separate linguistic roles, then, an exercise of countertext can avail. Replace one 5.3 Migration Policyagain, and Ethics ......................................................... 106 of the occurrences of ‘meaning’ by ‘eating’ in the statement under analy5.4 Migration Policy in Colombia ...................................................... 108 sis. The results are: ‘eating by “meaning” meaning’, which sounds senseless 5.5 “Colombia nos une”...................................................................... 109 (in a ‘serious’ context); ‘meaning by “eating” meaning’, which would make 5.6 Alianza País .................................................................................. 112 finally sense, if we were describing a secret code or a slip of the tongue; and ‘meaning by “meaning” eating’, which would make sense under114 the same 5.7 Challenges .................................................................................... hypothesised circumstances, but demonstrates the asymmetry between the Bibliography ....................................................................................... 116 two aspects of the mentioned ‘meaning’. Working Together for the Well-being Migrants ........................... 119 The game obviously does not of end here. Consider now ‘meaning by Barry Halliday “meaning by ‘meaning’ meaning” meaning by “meaning” meaning’... This line of thinking leads to at least two alternatives (which do not presume to exhaust the scope of possibilities in dealing with this chain of ‘meaning’s): either assign a distinct role to each ‘meaning’, or, refusing to acknowledge 4 More

precisely, the first ‘meaning’ and ‘by’ of our object statements are presented as actually used, since no order is actually given, and no shot is taking place.

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a dissection of linguistic meaning into such contrived and esoteric elements, Bibliography ......................................................................................... 60 across discard the entire sequence as meaningless; either produce difference repetition, or refuse to assign meaning to each of the repeated elements. Ei4. The Ethics of Migration. ther way, we see that assigning meaning to text is bound here with treating Reflections on Recent Migration Policies repetitions differently. and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini There are, of course, other ways of confronting this long chain of

‘meaning’s: refuse to assign meaning to the for elements, butLabour acknowledge the 4.1 Restrictive Policies and Structural Demand Immigrant .. 65 meaning of the whole sentence. ‘What does it mean? It means that you 4.2 Initiatives for Governing Family and Humanitarian shouldn’t iterate too much!’ Herebut the constitutive questions............. would be Migration: Labour Migration not Workers’ Migration 73 ‘What does the entire sequence repeat?’ (to which we could answer: ‘the grammatic 4.3 From Guest Workers to Unwelcome Guests .................................. 82 operation of substitution of a phrase into a formula’) and ‘How is it different 4.4 Selective Policies and the (to Brain Drain............................................ from that which it repeats?’ which we could answer: ‘in that we87exclude Equal and Denied Opportunities ................................ it4.5from theOpportunity realm of making sense’). With this approach too, we90are still producing difference across repetition. Bibliography ......................................................................................... 97 In the discussion above are implicit two conceptions of meaning. The 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 first conception of meaning can be described as ‘structural’, and we shall Urs Watter quote its succinct definition from Barthes. According to the earlier Barthes 5.1semiotic State Interest andnecessarily Responsibilityrefer us to a relation between two all terms towards their Citizens Living Abroad ........................................... 102 relata (Barthes 1968, 35). To manage such relations between relata in a 5.2 Applied .............................................................................. 104 Segmanner thatEthics avoids collapse, one applies segregation and censorship. 5.3 Migration Policy andapart Ethicsby......................................................... 106 regation sets elements restricting their positions and interactions (e.g. objects and predicates, where an instance of the latter may apply to 5.4 Migration Policy in Colombia ...................................................... 108 an instance of the former, but not to itself, at least in first order logic). 5.5 “Colombia nos une”...................................................................... 109 Censorship strikes off texts that threaten the stability of the system (e.g. 5.6 Alianza País .................................................................................. Russell’s choice to strike off ‘the set of all sets that do not belong112 to them5.7 Challenges .................................................................................... 114 selves’ from his system). Bibliography ....................................................................................... 116 The second conception of meaning, which we will call ‘post-structural’, and the succinct formulation of which will be borrowed from Derrida, says Working Together for the Well-being of Migrants ........................... 119 that iterability... structures the mark. Iter, here comes from itara, Barry Halliday other in Sanskrit, and everything that follows can be read as the working out of the logic that ties repetition to alterity (Derrida 1988a, 7). Here meaning entails productivity (of difference from repetition), mystery (repetition is known to produce difference, even when it is not yet known which difference, even when repetition produces nothing but the mystery of a difference-to-be-specified, as in the pshita or the divine and its Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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word) and dissemination (distinct elements of meaning collapse or multiply Bibliography ......................................................................................... 60 as we try to pin them down). With this last conception in mind, searching for meaning is akin to a 4. The Ethics of Migration. clumsy search for marbles in the dark. As one searches for marbles in the Reflections on Recent Migration Policies dark, one bumps into the marbles, thereby causing them to roll,61bounce and “Non-policies” in Italy and Europe ........................................... off eachZanfrini other, and change their locations. Similarly, as one searches for Laura meanings of texts, oneand quotes them Demand and usesfor their words,Labour thereby changing 4.1 Restrictive Policies Structural Immigrant .. 65 their network of relative positions and significations. But unlike the clearly 4.2 Initiatives for Governing Family and Humanitarian individuated marbles, where meanings are concerned, there is no single Migration: Labour Migration but not Workers’ Migration ............. 73 articulation into meaning units (words? phrases? assertions?), and no clear 4.3 From Guest Workers to Unwelcome Guests .................................. 82 counterpart of the concept of ‘location’. 4.4 Selective Policies Brain From this pointand of the view oneDrain............................................ can caricature the projects of87 Derrida, Kristeva Deleuze and respectively as: (1) establishing that Barthes’ 4.5 Equaland Opportunity Denied Opportunities ................................ 90 definition of sign......................................................................................... keeps breaking down (‘deconstructing’) into the logic Bibliography 97 that ties repetition to alterity, (2) studying the operation of signs as material 5.iterates, Colombia: Emigrantsainrevised Their view Societies of Origin ....... 101 andIncluding (3) reconstructing of signification and meaning Urs Watter from the sign structurally determined as an ‘iterable’. These projects will 5.1confronted State Interest andG¨ Responsibility be with odel’s mathematical texts. My task in this project is towards their Citizens Living Abroad ........................................... 102as proto highlight within the mathematical text the aspect of meaning duction of difference across repetition, and to explore the effects 5.2 Applied Ethics .............................................................................. 104 of this operation. 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108

2. 5.5 Leading “Colombia nos questions une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 This work is led by the intuition that mathematical language, like other 5.7 Challenges .................................................................................... 114 at its forms of language, despite its peculiarities and particulars, enjoys, Bibliography 116 constiheart, the full....................................................................................... complexity of language as a process, with its genesis, tutive paradoxical forces, unbounded chains of referencing, and contingent Working Together for the Well-being of Migrants ........................... 119 strategic elaborations. Like language in general, logico-mathematical lanBarry Halliday guage is the admirable product of a mighty genius of construction, who succeeds in piling an infinitely complicated dome of concepts upon an unstable foundation, and, as it were, on running water. Of course, in order to be supported by such a foundation, his construction must be like one constructed of spiders’ webs: delicate enough to be carried along by the waves, strong enough Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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not to be blown apart by every wind (Nietzsche 1979, 85). Bibliography ......................................................................................... 60 It is important to note that my project does not aim to attack the logico-mathematical validity of G¨odel’s argument. G¨odel’s argument has 4. The Ethics of Migration. been subjecton toRecent extreme scrutiny,Policies and has resisted many attempts to interReflections Migration ject within it and undermine its scope (for early reception see61Dawson andgaps “Non-policies” in Italy and Europe ........................................... Laura75–77). ZanfriniMy aim is not to undermine G¨ 1997, odel’s text, but rather to study what makes itPolicies function It is also importantLabour to note that the 4.1 Restrictive andsuccessfully. Structural Demand for Immigrant .. 65 scope of this essay does not include G¨odel’s position in a history of math4.2 Initiatives for Governing Family and Humanitarian ematical ideas,Labour or a symptomatic of G¨odel’s text ............. that will73unveil a Migration: Migration butreading not Workers’ Migration deeper psychological or philosophical encoded message. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 My questions concern processes of semiosis: what is it in the language 4.4 Selective Policies and the Brain Drain............................................ 87 of the text, which allows it to function for a mathematical reader, be that 4.5 Equal Opportunity and ................................ 90 of this reader a contemporary ofDenied G¨ odel Opportunities or a contemporary of the reader text? To what extent does the functioning of the text have anything Bibliography ......................................................................................... 97 to do with post-structural key notions such as (non)-sense, difference and repe5.tition, Colombia: Including Emigrants in Their Societies transcription of Origin ....... formations 101 amnesia, hymen, castration, verisimilarity, Urs Watter and modalities of enunciation, to name but a few? Is mathematical language 5.1 State and Responsibility subject toInterest the paradoxical motions, genetic processes, and strategic manoeutowards their Citizens Living Abroad ........................................... 102 vres, which set ‘natural’ language in motion according to post-structural 5 5.2 Applied Ethics .............................................................................. 104 theorisation? 5.3 Migration Ethics ......................................................... 106matheLet’s givePolicy someand examples, in order to be more explicit. Can

matical language contain such problematic statements as Magritte’s 5.4 Migration Policy in Colombia ...................................................... 108 Ceci n’est pas une pipe, where Ceci may or may not refer to the drawn pipe, 5.5 “Colombia nos une”...................................................................... 109 the drawing of the pipe, the word pipe, the signified of the word pipe, as 5.6 Alianza País .................................................................................. 112 well as to itself as a manifest subject, pulling itself by its own hair outside 5.7 swamp Challenges .................................................................................... the of designation? Can mathematical language contain114 the kinds of shifts of meaning that we’re used to expect from poetry? Can 116 we find in Bibliography ....................................................................................... 5 If theTogether Working for the Well-being of Migrants 119language answer to these questions be positive, we should........................... expect mathematical

toBarry allowHalliday for another effect of ‘natural’ language: jokes. There are indeed many jokes about mathematicians, but that is not what we are after. I know at least one joke which is in mathematics. It is in mathematics both in the sense that it is written in strictly mathematical language, and in the sense that I know of at least two researchers who independently claimed to have written professional papers on this joke and its generalisations (Prof. Y. Rodity and the late Prof. S. Breuer from Tel-Aviv University). It is a joke in the sense that when told in an appropriate setting it makes people laugh out loud. Here is the joke: 166664 = 4. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the mathematical text outbursts of embodied desire, double articulation, Bibliography ......................................................................................... or a history of castration? Suppose all this is indeed the case, as 60 I will attempt to demonstrate; does it, or does it not establish within mathematics 4. The Ethics of Migration. a mathematical unconscious and a mathematical will to power, which will Reflections on Recent Migration Policies make the reservationin‘within mathematics’ redundant? and “Non-policies” Italy and Europe ........................................... 61 For the purpose of making my questions concrete I include a teaser Laura Zanfrini of analysisPolicies of a specific instance of repetition central to G¨ 4.1the Restrictive and Structural Demand for Immigrant Labour ..odel’s 65 text (the full analysis will take place in chapter 2; here I cannot provide a 4.2 Initiatives for Governing Family and Humanitarian decent exposition of context andbut details, but a summary odel’s Migration: Labour Migration not Workers’ Migrationaccount .............of73G¨ argument is provided in the penultimate section of this introduction). But 4.3 From Guest Workers to Unwelcome Guests .................................. 82 bear in mind that this is only a teaser, not an attempt to make an argument. 4.4 Selective Brain Drain............................................ 87 in a The firstPolicies step inand G¨ othe del’s argument is to enumerate all formulas 4.5 Equal Opportunity andEach Denied Opportunities ................................ 90 which certain formal language. formula is assigned a unique number, itBibliography shares with......................................................................................... no other, and which serves as a sort of name for the97 formula. Then, given numbers a and b, G¨odel denotes by S(za , zb ) the number that 5.corresponds Colombia: Including Emigrants in Their Societies of following Origin ....... 101 to the formula obtained through to the recipe: Urs Watter

Take the formula whose number is a 5.1•State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 • Substitute the number b for some specified free variable inside that 5.2 Applied Ethics .............................................................................. 104 formula 5.3 Migration Policy and Ethics ......................................................... 106 If5.4weMigration ignore aPolicy reading restricted...................................................... to a purely formal layer of the in Colombia 108text (a privilege which, of course, I will not claim without justification outside this 5.5 “Colombia nos une”...................................................................... 109 introduction), we see that the first number, a, refers to a formula, whereas 5.6 Alianza País .................................................................................. 112 the second, b, refers to a number. 5.7 Challenges .................................................................................... Now, if we take, as G¨ odel does, a repetition of the form114 S(zp , zp ), then the same p has different referents (formula and number). This Bibliography ....................................................................................... 116 alone is not alarming at all, and does not require post-structural contemplation. Working Together Well-being Migrants ........................... 119sentinel The word ‘watch’,for forthe example, can of play two different noun roles: Barry Halliday and clock. When we say ‘the watch strolled by the watch’, the same word has different referents. We can even play around with referent assignment: ‘the watch’s watch’ could mean either the sentinel’s clock, or the clock’s sentinel. All we have here is a simple case of polysemy. But, as I will show in chapter 2, this is not quite the case with G¨ odel’s S(zp , zp ). Indeed, in this repetition both p’s arise by substituting a single Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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number for the same free variable in a certain tailor-made formula. A sinBibliography ......................................................................................... 60 gle p adopts two different roles by means of a most pedantically regulated repetition. We shall ask about this instance of repetition whether it repeats 4. The Ethics of Migration. a given concept, or whether it is a motion of decontextualisation that proReflections on Recent Migration Policies duces, within repetition, difference and a........................................... residual meaning. The question is, and “Non-policies” in Italy and Europe 61 inLaura otherZanfrini words, does the emerging difference already exist a-priori, like the difference between theand twoStructural distinct Demand roles of ‘watch’ in ‘The watch’s 4.1 Restrictive Policies for Immigrant Labour .. 65watch’, or does this form of repetition produce an a-posteriori residual difference? 4.2 Initiatives for Governing Family and Humanitarian Does this repetition conform to a stable system of distinctions, or does it Migration: Labour Migration but not Workers’ Migration ............. 73 have the transformative, self-refuting role reminiscent of Mark Anthony’s 4.3 From Guest Workers to Unwelcome Guests .................................. 82 repetition for Brutus is an honourable man? 4.4 Selective Policies and theextends Brain Drain............................................ The question further to the very place into which p 87 is substituted. Is itOpportunity a well-confined vacuum, or is it rather like the ambivalent 4.5 Equal and Denied Opportunities ................................ 90 place of a misplaced......................................................................................... library book, a book which, according to Lacan, manque ` a Bibliography 97 sa place (Lacan 1966, 25) — missing in/from its place, a place occupied 5.(the Colombia: Emigrants Their Societies Origin .......book 101 is not book isIncluding where it’s at, in itsinplace), and yet of empty (the Urs Watter where it’s supposed to be, not in its place)? Does p, like the library book, or oyster, participate in producing and carrying its place? Could we 5.1an State Interest and Responsibility towards theirtoCitizens Living Abroad ........................................... 102 perhaps relate this awkward place Foucault’s analysis of Velasquez’ Las Meninas in Ethics The Order of Things? Here, the action of representation 5.2 Applied .............................................................................. 104 consists in bringing forms of invisibility into the 5.3 Migration Policy andthese Ethics two ......................................................... 106 place of the other, in an unstable superimposition — and in rendering 5.4 Migration Policy in Colombia ...................................................... 108 them both at the same moment at the other extremity of the pic5.5 “Colombia nospole une”...................................................................... 109 ture — at that which is the very height of its representation: that of a reflected depth in the far recess of the painting’s 5.6 Alianza País .................................................................................. 112depth. The mirror provides a metathesis of visibility, which affects 5.7 Challenges .................................................................................... 114 both (qui entame a` la fois) the space represented in the picture and its Bibliography ....................................................................................... 116 nature of representation; it allows us to see, in the centre of the canvas,Together that which in Well-being the painting is of necessity doubly119 invisible Working for the of Migrants ........................... Barry Halliday (Foucault 1973, 8).

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

Introduction to G¨ odel’s Argument

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90

1. Logicism, intuitionism, formalism, realism Bibliography ......................................................................................... 97 and Kurt G¨ odel 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

The philosophical juncture at which G¨odel operates and his own position 5.1 State Interest and Responsibility are not the concern of this book, but a basic acquaintance would neverthetowards their Citizens Living Abroad ........................................... 102 less be useful for the discussion. The three main paradigms for providing a 5.2 Applied Ethics .............................................................................. 104 foundation for mathematics at the time when G¨ odel wrote his proof were 5.3 Migration Policy and and Ethics ......................................................... 106 posiLogicism, Intuitionism, Formalism. The sketches of these three tions are quoted from odel’s own review of Carnap’s, Heyting’s and von 5.4 Migration Policy in G¨ Colombia ...................................................... 108 Neumann’s respective presentations (G¨odel 1986–2003, Vol. I, 243–249). 5.5 “Colombia nos une”...................................................................... 109 G¨ odel explains that the thesis of logicism is twofold, namely, (1) that 5.6 Alianza País .................................................................................. 112 all mathematical notions are reducible to logical ones through 5.7 Challenges .................................................................................... 114 are explicit definitions and (2) that all mathematical theorems deductively derivable from the principles of logic. Logicism Bibliography ....................................................................................... 116is, then, a full reduction of mathematics to the principles of logic. Working Together for the Well-being of Migrants ........................... 119 For the intuitionist, on the other hand, mathematics is a natural Barry Halliday function of the intellect, a product of the human spirit, and he therefore grants no objective existence, independent of thought, to mathematical entities. This conception — that mathematical objects exist only insofar as they can actually be comprehended by human thought — leads to a rejection of pure existence proofs, as well as of the principle of the excluded middle in all cases in 29

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which a decision among the alternatives cannot actually be made. Bibliography ......................................................................................... 60 The intuitionist, then, requires a constructive mental image, graspable by the finite human mind, for every concept and every method of inference to 4. The Ethics of Migration. be allowed in mathematics. Reflections on Recent Migration Policies The formalist position, in relation the two preceding positions, and “Non-policies” in Italy and Europeto ........................................... 61 tries Laura Zanfrini to have the cake and eat it too. The formalist’s goal in providing a foundation mathematics is ... to vindicate classical mathemat4.1 Restrictivefor Policies and Structural Demand for Immigrant Labour .. 65 ics while taking into account the doubts raised by intuitionists. 4.2 Initiatives for Governing Family and Humanitarian To do so, he directs his attention the fact that infinitary and nonMigration: Labour Migration but notto Workers’ Migration ............. 73 constructive modes of inference attain a thoroughly finitary mean4.3 From Guest Workers to Unwelcome Guests .................................. 82 ing if they are viewed, not as methods of conceptual thinking, 4.4 Selective Policies and the Brain Drain............................................ 87 but as a procedure for deriving formulas according to certain 4.5 Equal Opportunity Opportunities 90 out conventions, since and theDenied formulas and the................................ operations carried with them ......................................................................................... do, after all, have a finitary character. The validity of Bibliography 97 these finitely graspable and verifiable formula games is not to be measured 5.against Colombia: Including Theirmay Societies of Origin some intendedEmigrants meaning, in which involve infinite....... and101 non conUrs Watter structive manoeuvres; rather it is measured by their consistency with the 5.1 State Interest and Responsibility realm of finite mathematics. Any infinite or non-constructive speak will be towards their Citizens Living Abroad ........................................... 102 acceptable, as long as its deductions can be finitely verified according to 5.2 Applied Ethics .............................................................................. syntactic rules, and as long as it does not force contradictions 104 into finite and constructible mathematics. 5.3 Migration Policy and Ethics ......................................................... 106 G¨ odel does notinquite fit into either of these frameworks. 108 He adopts 5.4 Migration Policy Colombia ...................................................... Hilbert’s formalism, and already in his 1929 thesis (G¨ odel 1986–2003, Vol. 5.5 “Colombia nos une”...................................................................... 109 I, 60–101) establishes himself as a virtuoso of this newly established ap5.6 Alianza País .................................................................................. 112 proach to mathematics. He nevertheless refuses to accept Hilbert’s horizon 5.7reducing Challenges .................................................................................... 114 as the of mathematics to formal procedures, and rejects formalism basis for all mathematical knowledge. Indeed, G¨ odel’s incompleteness Bibliography ....................................................................................... 116 theorems undermine both the second component of the logicist agenda, and Working for the Well-being Migrants 119ground. the hopeTogether for a consistency proof thatofwould put ........................... formalism on firm Barry Halliday

All that does not mean that G¨odel is an intuitionist. He is willing to handicap himself by the intuitionists’ reductive arsenal of proof techniques in order for his results to be universally accepted, but refuses to acknowledge intuitionism as a sole guarantee for mathematical rigour. Despite G¨ odel’s ability to conform to the standards of formalism and intuitionism, Solomon Feferman defines him in his introduction to G¨odel’s colRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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lected works as a ‘Realist’ or ‘Platonist’. These terms stand for G¨odel’s Bibliography ......................................................................................... 60 precounter-intuitionist belief that mathematical concepts have a genuine determined existence, which bestows a unique a-priori truth value upon 4. The Ethics of Migration. all mathematical statements. Feferman states that in G¨odel’s view, not Reflections on Recent Migration Policies only formulas and logic can and serveEurope as a basis for mathematics, but 61 that also and “Non-policies” in Italy ........................................... mathematical Laura Zanfrini intuition (not to be confused with intuitionism) can be a4.1 source of genuine mathematical knowledge. This intuition Restrictive Policies and Structural Demand for Immigrant Labour .. 65 can be cultivated through deep study of a subject, and one can thus 4.2 Initiatives for Governing Family and Humanitarian be led to accept new basic statements as axioms odel 1986–2003, Migration: Labour Migration but not Workers’ Migration(G¨ ............. 73 Vol. I, 30–31). These claims are strongly supported by G¨odel’s paper What 4.3 From Guest Workers to Unwelcome Guests .................................. 82 is Cantor’s Continuum Hypothesis (G¨ odel 1986–2003, Vol. II, 254–270). To 4.4 Selective Policies and the Brain Drain............................................ appreciate G¨ odel’s position one should consider that while he had87 formally proved that a certainand mathematical statement is consistent with 4.5 Equal Opportunity Denied Opportunities ................................ 90axioms that he considered to be evident, he nevertheless conjectured that97 the very Bibliography ......................................................................................... same statement was actually false.1 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

2. odel’s argument 5.1 G¨ State Interest and Responsibility in brief towards their Citizens Living Abroad ........................................... 102 I5.2 will conclude this introduction with a brief partial overview 104 of G¨odel’s Applied Ethics .............................................................................. argument, which I hope will set this essay in its mathematical context. 5.3 Migration Policy and Ethics ......................................................... 106 G¨ odel’s argument concerns a standard formal system (based on Rus5.4 Migration Policy in Colombia ...................................................... 108 sell and Whitehead’s Principia Mathematica) with a fixed set of symbols for 5.5 “Colombia nos(such une”...................................................................... 109 etc.), logical operators as conjunction, negation, universal quantifier, functions, and variables. It is crucial that the formal system can 5.6 Alianzaconstants País .................................................................................. 112 represent the universal quantifier (∀, read ‘for all’), a negation connective 5.7 Challenges .................................................................................... 114 (¬, read ‘not’), and the natural numbers. Explicit and finitely verifiable Bibliography ....................................................................................... 116 syntactic criteria determine whether a given sequence of symbols is a le2 gitimateTogether formal expression, or in G¨oof del’s terminology, a formula.119 Finally, Working for the Well-being Migrants ........................... an explicit set of syntactic rules decides whether a sequence of formulas Barry Halliday constitutes a proof. 1I

refer here to the consistency of the Continuum Hypothesis with the ZF axioms proved in G¨ odel (1986–2003, Vol. II, 33–101) and objected to in G¨ odel (1986–2003, Vol. II, 254–270). 2 Formula here should be thought of as a proposition or statement, rather than as a formula for computing or constructing something. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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G¨ odel’s argument proves that, unless the formal system is inconsis3 Bibliography ......................................................................................... tent, there exists a formula in the language, such that neither this60 formula, nor its negation are provable. Such formulas are called undecidable. A for4. The Ethics of Migration. mal system that has undecidable formulas is called incomplete. Succinctly, Reflections on Recent Migration Policies G¨ odel’s first incompleteness theorem that if the formal system is and “Non-policies” in Italy and Europestates ........................................... 61 consistent, then it is incomplete. The scope of the argument was shown by Laura Zanfrini G¨ odel to coverPolicies not just specificDemand formal for system, but Labour to include 4.1 Restrictive andone Structural Immigrant .. 65 a wide variety of formal systems, which include all the ‘mainstream’ systems that 4.2 Initiatives for Governing Family and Humanitarian can Migration: represent natural numbers. but not Workers’ Migration ............. 73 Labour Migration The first component in the argument is a method for translating any 4.3 From Guest Workers to Unwelcome Guests .................................. 82 finite sequence of the formal language’s symbols into a number. This trans4.4 Selective and Brain Drain............................................ 87section lation methodPolicies will not bethe reviewed here (we review it in the second 4.5the Equal Opportunity Opportunities ................................ 90 of appendix), but and it isDenied important to note its following properties: Bibliography ......................................................................................... 97 1. No two symbol sequences correspond to the same number. 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 2. Watter Given a symbol sequence, its number can be computed by a finite Urs mechanisable procedure. 5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 3. Given a number, the symbol sequence that corresponds to it can be 5.2 Applied Ethics 104 computed by.............................................................................. a finite mechanisable procedure.4 5.3 Migration Policy and Ethics ......................................................... 106 Note that this enumeration covers all symbol sequences, and includes, 5.4 Migration Policy in Colombia ...................................................... 108 among others, those that make up legitimate formulas and legitimate proofs 5.5 “Colombia nossystem’s une”...................................................................... 109 according to the syntactic rules. 5.6 Alianza Paíscomponent .................................................................................. 112 formal The next of the argument is to prove that various

relations between formulas can be translated into arithmetic relations be5.7 Challenges .................................................................................... 114 tween the numbers corresponding to these formulas. ‘Arithmetic116 relations’ Bibliography ....................................................................................... refer here to relations based on arithmetic operations that can be expressed Working Together for the Well-being Migrants ........................... 119 the reby the limited vocabulary of G¨odel’sofformal language. For instance, Barry ‘The Halliday lation symbol sequence numbered x proves the formula numbered y’ can be translated into an arithmetic relation between the numbers x and 3 Inconsistency

means that there exists a formula, such that both it and its negation are provable. However, there is a delicate reservation here that I postpone until the conclusion of the argument. 4 Not all numbers need correspond to some sign-sequence, but that will not affect the argument. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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y, and this arithmetic relation can, in turn, be expressed in the formal lanBibliography ......................................................................................... 60 G¨ guage. We will denote here this formal relation by P (x, y). In fact, odel demonstrates that symbol sequence number x proves formula number y if 4. The Ethics of Migration. and only if the relation P (x, y) can be proved in the formal system; moreReflections on Recent Migration Policies over, symbol sequence number x fails to prove formula number61 y if and and “Non-policies” in Italy and Europe ........................................... only if Zanfrini the relation ¬P (x, y) — the negation of P (x, y) — can be proved in Laura the system. 4.1 formal Restrictive Policies and Structural Demand for Immigrant Labour .. 65 Via a clever construction G¨odel produces a number g, such that the 4.2 Initiatives for Governing Family and Humanitarian following formal sequence: Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests ∀x(¬P (x, g))5 .................................. 82 Selective g. Policies and the 87 that is4.4numbered Therefore g Brain is the Drain............................................ number of the formula that states 4.5number Equal Opportunity and Denied Opportunities ................................ 90 simply no x corresponds to a proof of the formula numbered g; put, the formula numbered g states that the formula numbered g 97 (itself) is Bibliography ......................................................................................... unprovable. The negation of the formula numbered g would say, then, that 5.the Colombia: in Their Societies of Origin ....... 101 formulaIncluding numberedEmigrants g is provable. Urs Watter

The argument is now easy to recapture. First we shall show that, 5.1 State Responsibilityformula number g cannot be proved. unless weInterest have anand inconsistency, towards their Citizens Living Abroad ........................................... 102 • Suppose that the formula numbered g had a proof. 5.2 Applied Ethics .............................................................................. 104 The proof of the numbered g would then be a sign-sequence. 5.3•Migration Policy andformula Ethics ......................................................... 106 Let its number be y. 5.4 Migration Policy in Colombia ...................................................... 108 We get that the sign-sequence numbered y is a proof of the 5.5•“Colombia nos une”...................................................................... 109formula numbered g. 5.6 Alianza País .................................................................................. 112 According.................................................................................... to the explanation above, this implies that we 114 can prove 5.7•Challenges P (y, g). Bibliography ....................................................................................... 116 • On the other hand, if we could prove the formula numbered g, namely Working Together for the Well-being of Migrants ........................... 119 (x, g), we could also substitute y for x and conclude ¬P (y, g). Barry∀x¬P Halliday • But the last two conclusions are inconsistent. Now we turn to showing that the negation of formula number g cannot be proved. 5 This

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• Suppose we could prove the negation of the formula numbered g. Bibliography ......................................................................................... 60 • This would mean that the formula numbered g would be provable. 4. The Ethics of Migration. • But we have just shown above that this would yield an inconsistency. Reflections on Recent Migration Policies and “Non-policies” in Italyrelied and Europe ........................................... 61 mean Note that this argument on a semantic move (‘this would Laura Zanfrini

that...’), based on our interpretation of the formula numbered g. This is 4.1 so Restrictive Policies and Structural Immigrant Labour 65 the called semantic argument. If Demand we workfor more rigorously we ..obtain the syntactic argument: 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 • Suppose we could prove the negation of the formula numbered g, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 namely the formula ¬∀x(¬P (x, g)). 4.4 Selective Policies and the Brain Drain............................................ 87 • We already know from the argument above that the formula num4.5 Equal Opportunity and Denied Opportunities ................................ 90 bered g cannot be proved. Bibliography ......................................................................................... 97 • Therefore, for every number x, the sign-sequence numbered x is not 5. Colombia: Including Emigrants in Their a proof of the formula numbered g. Societies of Origin ....... 101 Urs Watter

• It follows that for every x we can prove ¬P (x, g). 5.1 State Interest and Responsibility Citizens Living Abroad ........................................... 102 •towards This istheir inconsistent with the initial hypothesis. 5.2 Applied Ethics .............................................................................. 104 But the last statement is not completely precise. We would get an ex5.3 Migration Policy and Ethics ......................................................... plicit inconsistency if we proved in the penultimate step the 106 statement ∀x¬P (x, g). But what actually...................................................... got is ‘for every x we can prove 108 ¬P (x, g)’. 5.4 Migration Policy inwe Colombia There is no formal inference which allows to deduce the former109 from the 5.5 “Colombia nos une”...................................................................... latter. To obtain the latter formally, we would require a ‘template’ into 5.6 Alianza País .................................................................................. 112 which we could substitute x and get a proof of P (x, g); all we actually have .................................................................................... 114 is5.7 forChallenges each separate x a separate proof of P (x, g). Bibliography ....................................................................................... The situation that we have obtained (for every x a proof 116 of P (x, g) and at the same time a proof of ¬∀x¬P (x, g)) is termed by G¨odel ωWorking Together for the Well-being of Migrants ........................... 119 inconsistency, and his claim concerns this kind of inconsistency. G¨ odel Barry Halliday proves that unless the formal system is ω-inconsistent, it must contain an undecidable formula. This result was later improved by Rosser (1936) to replace ω-inconsistency by plain inconsistency (provability of a formula and its negation). G¨ odel concludes his argument with a move that cannot be validated in the formal system where the proof was set. What G¨odel showed is that Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the formula numbered g is unprovable. But, at the same time, the formula Bibliography 60 numbered g, ......................................................................................... as introduced above, claims that the formula numbered g is unprovable. Therefore, the formula numbered g makes a true claim. A 4. The Ethics of Migration. lot of attention has been given to this manoeuvre and to its validity. In Reflections on Recent Migration Policies particular, to retain in the consistency of this manoeuvre, the truth 61 appealed and “Non-policies” Italy and Europe ........................................... toLaura in this argument cannot be something provable in the formal system. Zanfrini This led Carnap and Tarski, followed by G¨ ofor delImmigrant himself (in section 4.1 Restrictive Policies and Structural Demand Labour .. 657 of the 1934 text), to construct hierarchical systems of languages, where the truth 4.2 Initiatives for Governing Family and Humanitarian predicate of each language belongs a higherMigration language. We will Migration: Labour Migration but nottoWorkers’ ............. 73 touch upon these issues in this book, but will not focus on them. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 There is one more delicate point. The argument as presented above 4.4 Selective Policies and version the BrainofDrain............................................ 87 corresponds to the 1934 the text. In the earlier 1931 version the place of meta-mathematical claims (dealing with symbol sequences, 4.5 Equal Opportunity and Denied Opportunities ................................ 90 proofs, etc.) is taken ......................................................................................... by arithmetic claims (dealing directly with the numbers Bibliography 97 corresponding to sequences, proofs, etc.). For example, instead of claiming 5.‘Formula Colombia: Including in Their Origin ....... 101 about number g is Emigrants provable’, the text Societies makes anofarithmetic claim Urs Watter the number g. This coding makes the proof a little more tedious, but in 5.1 Statecorrespondence Interest and Responsibility stricter with a view of mathematics as dealing with numtowards their Citizens Livingnotions Abroadas ........................................... 102 this bers, rather than with such proofs. On the other hand, coding through numbers distances the claim from an explicit determina5.2 Applied Ethics .............................................................................. 104 tion of undecidability. tension will be reviewed in the second 5.3 Migration Policy andThis Ethics ......................................................... 106section of the first chapter of this book. 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini Chapter 1 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65

4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73

Textual Formations

4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90

Bibliography 97 In this ......................................................................................... chapter we will analyse the subject position and transcription devices operated by G¨ odel’s text. The product will not 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 be a structured formation. We will hear a plurality of voices and Urs Watter observe the marks of reiterated reformulation. 5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 The questions leading the analysis in this chapter are derived from Barthes’ 5.2 Applied Ethics .............................................................................. 104 S/Z and from Foucault’s The Archaeology of Knowledge. The results of the 5.3 Migration Policy and Ethics ......................................................... analysis, however, are much more in line with Barthes than with106 Foucault, 5.4 Migration Policy Colombia ...................................................... 108 and are not very far in from some hermeneutic approaches.

If we stripnos down Foucault’s archaeology and Barthes’ semiotic 5.5 “Colombia une”...................................................................... 109analysis of their philosophical and political amplitude, and reduce them to bare tech5.6 Alianza País .................................................................................. 112 niques, it is easy to derive a compact schematic summary. In S/Z Barthes 5.7 Challenges .................................................................................... 114 traces five dimensions of analysis referred to as codes. A text (Balzac’s Bibliography 116is analSarrasine) is ....................................................................................... cut into many short chunks called lexias. Each lexia ysed according to the five codes. The immediate result may appear quite Working Together for the Well-being of Migrants ........................... 119 trivial, but a second glance reveals what the codes themselves miss: their Barry Halliday interaction. This transformation of the text opens a pathway to an original hermeneutic approach and to interesting reflections on the processes of semiosis that operate through texts. Barthes’ five codes are: • Proairetic code: actions and behaviours reported in the text; 37

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• Hermeneutic code: questions and enigmas posed by the text, their Bibliography ......................................................................................... 60 development and resolutions; 4. The• Ethics of Migration. Semantic code: connoted signifieds evoked to construct characters, Reflections on Recent Migration Policies atmospheres and otherand narrative and “Non-policies” in Italy Europeelements; ........................................... 61 Laura Zanfrini

• Symbolic code: structural relations (opposition, equivalence, etc.) be4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 tween elements in the text; 4.2 Initiatives for Governing Family and Humanitarian Migrationofbut not Workers’ Migration 73culture •Migration: Cultural Labour code: citations knowledge referred to an............. ambient 4.3 From Workers within to Unwelcome Guests(academic .................................. or toGuest institutions that culture disciplines,82popular

wisdom,Policies etc.) and the Brain Drain............................................ 87 4.4 Selective 4.5 Equal Opportunity and Denied Opportunities ................................ 90 That the articulation of these five codes is arbitrary and underdetermined ......................................................................................... 97syntheisBibliography explicitly acknowledged by Barthes. For example, the sequential sis of individual behaviours into macro actions (such as Barthes’ grouping 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 together of the elements ‘planning an attack’, ‘setting an ambush’ and Urs Watter ‘stabbing’ into the sequence of ‘murder’) is characterised as a result of an 5.1 State Interest and Responsibility artifice of reading (Barthes 1974, 19), which depends on the choices of towards their Citizens Living Abroad ........................................... 102 the reader. Rejecting the impulse of structuralist tradition, Barthes chooses 5.2 Applied Ethics .............................................................................. 104 to leave the codes as little determined as possible. The Hermeneutic and 5.3 Migration Policy Ethicsin......................................................... 106 to exProairetic codes are and grouped sequences, but no attempt is made tract or prescribe the such sequences; enigmas and 108 action se5.4 Migration Policy in grammar Colombia of ...................................................... quences can be broken down and patched together in many different 5.5 “Colombia nos une”...................................................................... 109 ways. The semantic, cultural and symbolic units are usually left as such; no at5.6 Alianza País .................................................................................. 112 tempt is made to constrain their various appearances within the text under Challenges 114 list of a5.7 certain logic. .................................................................................... The result may, at first sight, appear to be a grocery arbitrarily articulated elements of text. Bibliography ....................................................................................... 116

The choice of codes, however, is carefully designed in order to reflect Working Together for the Well-being of Migrants ........................... 119 both the internal consistency and the openness of the text. The cultural Barry Halliday and semantic codes bind the text tightly to its ‘outside’. The proairetic, symbolic and hermeneutic codes supposedly emerge from inside the text, but are admittedly manipulated by the reader. The five dimensions of analysis are five axes of interaction between a reader-in-the-world and the letter of the text. These codes reflect Derrida’s postulate that the text has no outside, in the sense that there is no clear and distinct articulation of Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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what is definitely irrelevant when reading a given text. Any element of the Bibliography ......................................................................................... 60 (supposed) outside may turn out to contribute to the process of semiosis. The main point of Barthes’ analytic technique is to demonstrate how 4. The Ethics of Migration. the five semi-arbitrary dimensions of analysis combine together to create Reflections on Recent Migration Policies effects of meaning and communication the reader. Barthes 61 thus disand “Non-policies” in Italy and Europe with ........................................... Laura Zanfrini places the focus of analysis from articulating the grammar of each code to observing theirPolicies relative Analysis is no longer the breaking 4.1 Restrictive andorchestration. Structural Demand for Immigrant Labour .. 65 down of a text into small elements and presuming to discover the for4.2 Initiatives for Governing Family and Humanitarian mal Migration: constraintsLabour set upon these but elements, but rather consists in observing Migration not Workers’ Migration ............. 73 how different elements combine with each other into an effect of meaning. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Meaning is no longer identified as a-priori structural constraints, but as a 4.4 Selective Policies and thebetween Brain Drain............................................ non-prescribed intercourse arbitrarily articulated units. 87 1 4.5 Equal Opportunity and Denied 90 Foucault’s technique, as laidOpportunities out in The ................................ Archaeology of Knowledge, consists in analysing discursive complexes along several formations. Bibliography ......................................................................................... 97 The first formation is that of objects. Objects are characterised by the institu5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 tions that form them, the places where they are to be observed, and the Urs Watter means by which they are measured and described. But it is not the map5.1 State Interest and Responsibility ping of objects according to these dimensions that is the focus of interest, as towards their Citizens Living Abroad ........................................... 102 objects of a given discourse need not have common loci or means of obser5.2 Applied Ethics .............................................................................. 104 vation. It is the constrained relation between various object-characteristics, 5.3 Migration Policy Ethics which is supposed toand reflect the......................................................... unity of a given discourse, and to106 constrain its object formation. 5.4 Migration Policy in Colombia ...................................................... 108 The othernos formations that characterise a given discourse include 5.5 “Colombia une”...................................................................... 109 modalities of enunciation (characterised by the questions ‘who speaks?’, ‘from 5.6 Alianza País .................................................................................. 112 within which institute?’ and ‘through what means of expression?’), the con5.7 Challenges .................................................................................... 114 ceptual formation (the arrangement of enunciations, co-relevance of enunciations, and ....................................................................................... the acceptable means of transcription), and the strategic Bibliography 116 formation (the branching of the discourse into several theoretic stances, the Working Together for the Well-being Migrants ........................... 119the disinteractions between these stances, ofand the interaction between Barry Halliday course and surrounding practices). The archaeologist’s task is to find the correlations between the various characteristics of objects, enunciative po1 I focus here on the set of tools introduced in the Archaeology’s second chapter, which are far from exhausting the book. The book in fact eventually turns against this simplified structural outlook. For my purposes at this point, however, this limited articulation of questions is extremely useful.

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sitions, concepts and strategies that individuate and articulate discourses. Bibliography ......................................................................................... 60 Foucault’s technique, like Barthes’, breaks the boundary between a textual ‘inside’ and a practical ‘outside’. But, at least at first sight, it ap4. The Ethics of Migration. pears that this way of analysis is highly structural, as it searches for the Reflections on Recent Migration Policies limitations and regularities inherent in the various characteristics61 of a disand “Non-policies” in Italy and Europe ........................................... course Laura (without Zanfrini assuming, though, that there should be universal structural features common to alland discourses). The factforthat tips over the supposedly 4.1 Restrictive Policies Structural Demand Immigrant Labour .. 65 structural attitude is the archaeological choice not to seek a recollection 4.2 Initiatives for Governing Family and Humanitarian of the original or aMigration memory truthMigration when delving Migration: Labour butof notthe Workers’ .............into 73 a discourse, but rather to actually make differences: to constitute them 4.3 From Guest Workers to Unwelcome Guests .................................. 82 as objects, to analyse them, and to define their concept (Foucault 4.4 Selective Policies and does the Brain 87 tool. 1972, 205). Archaeology not Drain............................................ presume to be a purely descriptive Archaeology is explicitly presented in this quotation as a form 90 of inter4.5 Equal Opportunity and Denied Opportunities ................................ vention. The ......................................................................................... articulation of objects, enunciative positions, concepts Bibliography 97 and strategies along their various characteristics is a re-articulation, an action 5.on Colombia: Including in Their Societies of Origin ....... 101 discourse, anythingEmigrants but an excavation. Urs Watter Making use of this technical arsenal, but not committing myself to

5.1 State Interest Responsibility exhausting it or and being faithful to it, I analyse G¨odel’s proof along the ditowards their Citizens Abroad ........................................... 102 mensions of enunciative Living position and along the network of transcriptions related to the use of terms such as mean, express and signify in the text. 5.2 Applied Ethics .............................................................................. 104 I5.3 conclude with a brief analysis of the strategic choices taken 106 in G¨ odel’s Migration Policy and Ethics ......................................................... text. 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109

1.1 Who speaks? 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Alice: Now, Kitty, let’s consider who it was that dreamed it all. Bibliography ....................................................................................... 116 This is a serious question, my dear, and you should not go on licking Together your paw that — asofifMigrants Dinah hadn’t washed119 you this Working forlike the Well-being ........................... morning! You see, Kitty, it must have been either me or the Barry Halliday Red King. He was part of my dream, of course — but then I was part of his dream, too! Was it the Red King, Kitty?

L. Carroll, Through the Looking-Glass and what Alice Found There, ch. XII.

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A more remote part of the platform. ... Bibliography ......................................................................................... 60 Ghost: ... but lend thy serious hearing to what I shall unfold Speak, I am bound to hear 4.Hamlet: The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy Europe ........................................... W.and Shakespeare, Hamlet, Act I, Scene V.61 Laura Zanfrini

4.1 Restrictive Policies and Structural Demand for .. 65 over a Who speaks these texts? Which dreamed it? Immigrant Who has Labour authority text? In the quotations above, invariably the king. But not the king as 4.2 Initiatives for Governing Family and Humanitarian Migration not Workers’ 73 and such.Migration: It is the Labour dead king, or thebutchess-piece for Migration the king,............. who speaks dreams. with that displaced king. 4.3 FromResponsibility Guest Workerslies to Unwelcome Guests .................................. 82 But I must protest. The dead king speak? The chess-piece for the 4.4 Selective Policies and the Brain Drain............................................ 87 king? We’re not going to get away with it so easily. When assigning speech 4.5 Equal Opportunity and Denied Opportunities ................................ 90 to the king, to his symbol, to the dead, we refuse to assume responsibility; Bibliography ......................................................................................... authority over speech must be better placed than that. Hence a 97 demand: ‘Hamlet, Alice, assume responsibility! it is you who speak! You dreamt it!’ 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 But Urs then WatterI must protest again. Alice speak? Victorian girls do not speak. Children should be seen and not heard. Hamlet speak? Hamlet is mad, and 5.1 State Interest and Responsibility the mad are never given the platform to speak. towards their Citizens Living Abroad ........................................... 102 Therefore Shakespeare speaks. Carroll speaks. But casting a name as 5.2 Applied Ethics .............................................................................. 104 the source of speech does not quite resolve the assignment of authority 5.3 Migration Policy andwho? EthicsThe ......................................................... over text. Shakespeare Earl of Oxford? The Stratford106 Bard? Or perhaps it is that other person named Shakespeare, the one who 5.4 Migration Policy in Colombia ...................................................... 108actually wrote the stuff,nos not to be confused with that person named Shakespeare 5.5 “Colombia une”...................................................................... 109 wearing the earring in the portrait? And Carroll, is it Lewis Carroll, writer? 5.6 Alianza País .................................................................................. 112 Charles Lutwidge Dodgson, mathematician? It might even have been the 5.7 Challenges Alice .................................................................................... photographer, Liddell’s special friend. Who speaks? Which114 dreamed it? Bibliography ....................................................................................... 116 It is none other, then, than the signifier who speaks, a signifier which Working Together for the Well-being of Migrants ........................... 119 is what represents the subject to another signifier (Lacan 2006, Barry Halliday 694), because Man is a sign and thus my language is the sum total of myself (Peirce 1931–1958, Vol. 5, §314). But no; we’re not going to get away with it so easily. No authority remains with a subject, if it is the king, the character, the name or the signifier who speak. Unless we acknowledge that We speak, no ethics can stop us from using foul language.

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Who speaks G¨ odel’s proof? Is it G¨ odel? Is it the sign? Is it MathematBibliography ......................................................................................... ics (I, truth, speak (Lacan 2006, 340))? Frege claimed that the 60 thought for example, which we expressed in the Pythagorean theorem is 4. The Ethics of Migration. timelessly true, true independently of whether anyone takes it to Reflections on Recent Migration Policies be It needs no bearer 29). Young Husserl concurred. andtrue. “Non-policies” in Italy and(Frege Europe1967, ........................................... 61 ILaura see that, wherever is talk of the proposition or truth that π is a Zanfrini transcendental number, there is nothing I have less in mind 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 than an individual experience, or a feature of an individual experience 4.2 Initiatives for Governing Family and Humanitarian of any person (Husserl 1970a,but 329–330). But if that were so, who Migration: Labour Migration not Workers’ Migration ............. 73 would be there to command but lend your serious hearing? and who would 4.3 From Guest Workers to Unwelcome Guests .................................. 82 there be to assume responsibility, that is, to respond: speak, I am bound 4.4hear? Selective to LetPolicies us read.and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 1.1.1 We and I 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 In G¨ odel’s texts it is a we who speaks. In order to study the enunciative Urs Watter position as articulated in G¨ odel’s text, we shall analyse the grammar of 5.1 State Interest and Responsibility this we. But before we do, I feel bound to acknowledge that we needn’t towards their Citizens Living Abroad ........................................... 102 read too much into this we. We is simply part of the code. Its use is as 5.2 Applied Ethics .............................................................................. 104needn’t imposed upon G¨ odel as is using I when I speak to a friend. So we 5.3 Migration and Ethics ......................................................... read too muchPolicy into we, no more, say, than Benveniste reads into106 I.

I, Benveniste is an...................................................... interface between an individual and lan5.4 Migration Policyexplains, in Colombia 108 guage. Language is so organised that it permits each speaker to 5.5 “Colombia nos une”...................................................................... 109 appropriate to himself an entire language by designating him5.6 Alianza País .................................................................................. 112 self as I . It is this precise interface, according to Benveniste, which turns 5.7 individual Challenges into .................................................................................... 114 not be the a subject, and without which subjectivity could formed. I achieves that as it refers to the act of individual discourse Bibliography ....................................................................................... 116 in which it is pronounced (Benveniste 1971, 226). In fact, I is “the Working Together the Well-being of Migrants 119 individual who for utters the present instance ........................... of discourse containing Barry Halliday the linguistic instance I.” (Benveniste 1971, 218). This unified functional view of appropriative I would be very convincing, if it weren’t for the multitude of different I’s appearing in Benveniste’s text. Despite the statement of the first quotation above, the I s in the previous paragraph do not function to appropriate language to individuals, but are signifiers referring to this appropriative interface (as witnessed by Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the italics and the constructions I refers and I is, rather than ‘I refer’ Bibliography and ‘I am’). ......................................................................................... 60 But this is not all. The non actual, non appropriative I breaks down 4. The Ethics of Migration. into smaller constituents. The last quotation above, under pains of circuReflections on Recent Migration Policies larity, must generate grammatical positions (referent and “Non-policies” in two Italydifferent and Europe ........................................... 61 and Laura Zanfrini referee, according to Benveniste). It begins with I ... the individual, and ends with Policies the linguistic instance I . for Surely, even ifLabour Man..is65a sign, 4.1 Restrictive and Structural Demand Immigrant or Benveniste puts it, “subjectivity” ... is only the emergence in 4.2asInitiatives for Governing Family and Humanitarian the Migration: being of Labour a fundamental property of language Migration but not Workers’ Migration(Benveniste ............. 73 1971, 224), it is not the individual who is a linguistic instance (at least not ac4.3 From Guest Workers to Unwelcome Guests .................................. 82 cording to any point of view that insists on articulating the individual and 4.4 Selective Policies and the Brain Drain............................................ 87 the subject as distinct). 4.5 Equal Opportunity andappropriative Denied Opportunities 90 himWe so far have an I, which................................ a speaker designates Bibliography ......................................................................................... 97 self as in order to appropriate to himself an entire language, the reported, non-actualised I , who is the speaking individual who uses this 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 interface, and the linguistic instance I . If only things were so simple! Urs Watter consider that the indicators I and you cannot exist as potentiali5.1 State Interest and Responsibility ties, they exist only insofar as they are actualised in the instance towards their Citizens Living Abroad ........................................... 102 of discourse (Benveniste 1971, 224). Here I is not that which a speaker 5.2 Appliedhimself Ethics .............................................................................. designates as, but that which a speaker designates himself104 with (the 5.3 Migration anddesignate Ethics ......................................................... speaker Emile Policy does not himself as an indicator when he 106 designates himself as I ). Policy Nor is in it Colombia the uttered linguistic instance, because an108 indicator 5.4 Migration ...................................................... is far more functional than a mere linguistic instance. But this I , that is, the 5.5 “Colombia nos une”...................................................................... 109 indicator, is obviously not the I who is “the individual who utters ... ”, 5.6 Alianza País .................................................................................. 112 because indicators are not individual people. We therefore have a fourth, 5.7 Challenges .................................................................................... 114 in the indicator I . But then we’re still not done. The I , which appears indicators and you cannot exist as potentialities can’t be BibliographyI....................................................................................... 116an indicator either, because indicators have, in that very sentence, been denied Working Together the Well-being of Migrants 119 the possibility of for existing unactualised in the........................... instance of discourse, Barry Halliday whereas the indicative function of the last I is still strictly a potentiality, the very potentiality, which would indicate, when and if it were eventually actualised in discourse. It is, so to speak, the signifier of the indicator.

It seems that whenever we try to articulate I, another structural dimension is forced upon it. Whatever instance of I we are given, science appears to objectify its function, and then signify that object. But there Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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is yet another, deeper rooted reason for the plurality of I’s, which goes Bibliography ......................................................................................... 60 beyond the machine of infinite regress. For if I referred to a particular constant individual, a permanent contradiction would be admitted 4. The Ethics of Migration. into language, and anarchy into its use. This is especially apparent Reflections on Recent Migration Policies when considering I’sinquotability, that is........................................... the fact that If I perceive and “Non-policies” Italy and Europe 61 two successive instances of discourse containing I, uttered in the same Laura Zanfrini voice, nothing guarantees to meDemand that one them isLabour not a..reported 4.1 Restrictive Policies and Structural for of Immigrant 65 discourse, a quotation in which I could be imputed to another. 4.2 Initiatives for Governing Family and Humanitarian On the other hand and at the same time It is by identifying himself as Migration: Labour Migration but not Workers’ Migration ............. 73 a unique person pronouncing I that each speaker sets himself up 4.3 From Guest Workers to Unwelcome Guests .................................. 82 in turn as the “subject.” (Benveniste 1971, 218, 220, 226). 4.4 Selective and the Brain Drain............................................ 87 I am ledPolicies to conjecture an extension to Benveniste’s claim, which the 4.5 Equal paragraphs Opportunity will and Denied 90 following attemptOpportunities to validate: ................................ it is not only intersubjectivity, but substantial components of the very experience of making mathematBibliography ......................................................................................... 97 ical sense too, which arise, at least in part, from confounding all these I’s 5.and Colombia: Emigrants Their Societies Origin ....... 101I shall all theseIncluding functional positions.inIn other words, of I shall be that Urs Watter be (Exodus 3, 14). 5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102

1.1.2 What do 5.2 Applied Ethics we .............................................................................. 104 5.3 Migration and Ethics ......................................................... 106 How does thePolicy enunciative position in G¨odel’s text, we, fare compared to Benveniste’s G¨ oin del’s 1931 text contains only three I’s, and108 the 1934 5.4 MigrationI’s? Policy Colombia ...................................................... text only one. nos These I’s are used in an acknowledgment, a reference to 5.5 “Colombia une”...................................................................... 109 previous work, a reference to a lecture, and to comment on the relation 5.6 Alianza País .................................................................................. 112 between G¨ odel’s work and Hilbert’s programme. But the person narrating, 5.7 Challenges .................................................................................... articulating, and conducting the proof is we. And since analysing114 the gramBibliography ....................................................................................... matic structure of the personal pronoun in the previous section 116 has led us to a futile proliferation of structural positions, let us concentrate on what Working Together for the Well-being of Migrants ........................... 119 we do. Taking an inventory of G¨odel’s texts we find that we abbreviate, acBarry Halliday complish, add, adjoin, allow, apply, assign, associate, assume, attach, carry out, come, compare, consider, construct, deduce, define, denote, depend, describe, derive, eliminate, employ, establish, exclude, express, find, find convenient, generalise, give, have, include, insert, intend, let, list, make, make use, map, mean, note, observe, obtain, order, proceed, prove, put, replace, require, restrict, say, see, shift, show, sketch, substitute, take into Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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account, turn to considerations, understand, use, wish, and write. Bibliography To make......................................................................................... sense of what we do, let us follow Foucault, who60 suggests that a mathematical text articulates various subject positions. Take the 4. The Ethics of Migration. example mathematical Reflectionsofona Recent Migrationtreatise. Policies In the sentence in the preface which oneinexplains this treatise was written and in “Non-policies” Italy and why Europe ........................................... 61 ... the Laura Zanfrini position of the enunciative subject can be occupied only by the author ... only one and possible subject the other hand, 4.1 Restrictive Policies Structural Demand...forOn Immigrant Labour .. 65 if in the main body of the treatise, one meets a proposition like ‘Two 4.2 Initiatives for Governing Family and Humanitarian quantities equal to Migration a third quantity are equal to each other’, Migration: Labour but not Workers’ Migration ............. 73 the subject of the statement is the absolutely neutral position, indif4.3 From Guest Workers to Unwelcome Guests .................................. 82 ferent to time, space, and circumstances, identical in any linguis4.4 system, Selective Policies Brain 87 any tic and in and anythe code ofDrain............................................ writing or symbolisation, that 4.5 Equal Opportunity and Denied ................................ 90Moreindividual may occupy when Opportunities affirming such a proposition. over, sentences like ‘We have already shown that...’ necessarily Bibliography ......................................................................................... 97 involve statements of precise contextual conditions that were not 5.implied Colombia: Emigrants in Their Societies of Origin ....... 101 fixed byIncluding the preceding formulation: the position is then Urs Watter within a domain constituted by a finite group of statements ... 5.1 State Interest Responsibility The subject of and such a statement ... will not be described as an intowards their Citizens Living Abroad ........................................... 102 lives dividual who has really carried out certain operations, who 5.2an Applied Ethics .............................................................................. in unbroken, never forgotten time (Foucault 1972, 94). 104 We may Policy try toand make systematic sense of these positions by 5.3 Migration Ethics ......................................................... 106relating them to the list of verbs above. Different verb types may articulate different 5.4 Migration Policy in Colombia ...................................................... 108 functional positions taken by we. Fortunately, such typological analysis 5.5 “Colombia nos une”...................................................................... 109 has already been conducted in the general context of mathematical texts 5.6Brian Alianza País .................................................................................. 112 by Rotman in Rotman (1993) and in the first chapter of Rotman (2000). His account, which claims to derive from Peirce, is as follows. 5.7 Challenges .................................................................................... 114 Three characters take part in a mathematical text. Bibliography ....................................................................................... 116 1. The first is for called the Person,ofwho speaks in the meta-Code. He Working Together the Well-being Migrants ........................... 119 speaks about mathematics, but not in mathematics. He considers the Barry Halliday idea or story behind the proof. He has access to natural language, the personal pronoun I, and indexicals such as here and now. His function is to be persuaded by the proof and to understand it. 2. The second character is the Subject. The Subject is the entity that defines, derives, considers and proves. His pronouncements are, acRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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cording to Rotman, voiced in a collective imperative: let us conBibliography ......................................................................................... 60 sider, define, demonstrate... (Rotman 1993, 71). The Subject is abstracted of any temporal, spatial and cultural considerations. The 4. The Ethics of Migration. subject’s psychology, in other words, is transcultural and Reflections on Recent Migration Policies disembodiedin(Rotman 15)............................................ The Subject makes mathematical and “Non-policies” Italy and2000, Europe 61 which are, in fact, predictions on the outcomes of sign Laurastatements, Zanfrini manipulations. x + y =Demand y + x isfor the prediction that.. if65he sub4.1 Restrictive PoliciesThus, and Structural Immigrant Labour stitute any number-signs for x and for y, and manipulate these signs 4.2 Initiatives for Governing Family and Humanitarian accordingLabour to theMigration orders coded inWorkers’ the ‘+’ sign, the results Migration: but not Migration .............of73the two sides of the equality will be the same. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 The last character is the The Agent is a reduced 87 image of 4.43.Selective Policies and the BrainAgent. Drain............................................ the Subject, whoand performs the sign manipulations, about which the 4.5 Equal Opportunity Denied Opportunities ................................ 90 Subject makes predictions. He is the one adding, counting, substitutBibliography ......................................................................................... 97 ing in a sort of thought-experiment or a dream that the subject is experiencing. The Agent, in unlike Subject, has ....... no ability to 5. Colombia: Including Emigrants Theirthe Societies of Origin 101 imagine and can only respond to signs in their truncated, Urs Watter skeletonised as signifiers devoid of intentioned mean5.1 State Interest and form Responsibility ing. In other words, the Agent is considered as an102 automatowards their Citizens Living Abroad ........................................... ton, a wholly mechanical and formal proxy for the Subject 5.2 Applied Ethics .............................................................................. 104 (Rotman 1993, 76). The Agent’s actions are expressed in an exclusive 5.3 Migration Policy and Ethics ......................................................... 106 imperative mood (add!, count!, integrate!).2 5.4 Migration Policy in Colombia ...................................................... 108 The Person constructs a narrative, the leading principle of an ar5.5 “Colombia nos une”...................................................................... 109 gument, in the meta-Code; this argument or proof takes the form 5.6 Alianza País .................................................................................. 112 of a thought experiment in the Code; in following the proof, the 5.7 Challenges .................................................................................... 114 the Subject imagines his Agent to perform actions and observes results; and....................................................................................... in the light of the narrative, the Person is persuaded Bibliography 116 that the assertion being proved — which is a prediction about Working Togethersign for the Well-being of to Migrants ........................... the Subject’s activities — is be believed (Rotman 119 2000, 35). Barry Halliday The hierarchy of semiotic agencies here, from imagined Agent to imagining Subject to indexically conscious Person structuring a thought experiment is isomorphic to that on which any dream rests: the Agent maps onto the figure dreamed about, the Subject 2 An

exclusive imperative is an imperative that does not include the person giving the order. ‘Eat!’ is an exclusive imperative. ‘Let’s eat!’ is an inclusive one. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the dreamer dreaming the dream, and the Person the dreamer Bibliography ......................................................................................... 60 ... the awake, consciously interpreting and recognising the dream dream-code ... is restricted in various ways, not least by the lack 4. The Ethics of Migration. of the ability to recognise the dream as dream, which makes it Reflections on Recent Migration Policies impossible for theindreamer articulate the dreamer’s kinship to and “Non-policies” Italy and to Europe ........................................... 61 the imago he or she dreams into being. Likewise, the restrictive Laura Zanfrini nature of thePolicies Codeand in Structural which the Subject operates, in particular 4.1 Restrictive Demand for Immigrant Labour .. 65 its lack of indexicality, prevents the mathematical Subject from 4.2 Initiatives for Governing Family and Humanitarian articulating status of itsbutcreated fiction (Rotman 1993,7378–79). Migration: the Labour Migration not Workers’ Migration ............. To explain his division (which is Guests akin to.................................. — but does not derive 4.3 From Guest Workers to Unwelcome 82 from and is not identical with — Foucault’s), Rotman appeals to the imagery of 4.4 Selective Policies and the Brain Drain............................................ 87 the dream. But his account fails to acknowledge a very unsettling, albeit 4.5 too Equal Opportunityoccurrence: and Denied lucid Opportunities ................................ 90the exnot uncommon, dreaming. Lucid dreaming is perience, where a dreamer is aware that she is dreaming, and where Bibliography ......................................................................................... 97control over the dream is negotiated between various subjective parts. We must not 5.neglect Colombia: Including Emigrants in Their Societies Origin ....... the possibility that the dream-code may beoflucid, and so,101 occasionUrs Watter ally, we should consider waking from the lucid dream. Such experience, I 5.1 State and Responsibility recall, canInterest be extremely unpleasant. Prominent physicist Richard Feynman, towards their Citizens Living Abroad ........................................... 102 however, provides a somewhat more optimistic account for this unpleasant 5.2 Applied During Ethics .............................................................................. experience. the time of making observations in my104 dreams, the process of waking up was a rather fearful one. As you’re 5.3 Migration Policy and Ethics ......................................................... 106 beginning to wake up there’s a moment when you feel rigid and tied 5.4 Migration Policy in Colombia ...................................................... 108 down, or underneath many layers of cotton batting. It’s hard to 5.5 “Colombia nos une”...................................................................... 109 explain, but there’s a moment when you get the feeling you can’t 5.6 Alianza País .................................................................................. 112to tell get out; you’re not sure you can wake up. So I would have 5.7 Challenges .................................................................................... 114 myself — after I was awake — that that’s ridiculous. There’s no disease I know of where a person falls asleep naturally and can’t Bibliography ....................................................................................... 116 wake up. You can always wake up. And after talking to myself Working Together forthat, the Well-being Migrants 119in fact many times like I becameofless and ........................... less afraid, and Barry Halliday I found the process of waking up rather thrilling — something like a roller coaster: After a while you’re not so scared, and you begin to enjoy it a little bit (Feynman 1985, 50). Let us, then, muster the courage to elucidate Rotman’s dream, and talk ourselves awake. Rotman’s divisions are based on both semantic and morphological markers. Morphologically, the Person is the one using the pronoun I as well Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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as indexicals and cultural markers. The Subject is characterised by collecBibliography ......................................................................................... 60 tive imperatives, and the Agent by exclusive imperatives. Unfortunately, such markers are absent from G¨odel’s text. Rotman claims that Even a 4. The Ethics of Migration. cursory examination of an arbitrary chosen item of mathematical Reflections on Recent Migration Policies communication reveal fundamental features of61 matheand “Non-policies”will in Italy and two Europe ........................................... matical discourse: its organisation as an exhortatory, commandLaura Zanfrini giving formalism its complete of any indexical 4.1 Restrictive Policiesand and Structural Demandlack for Immigrant Labour .. 65 terms (Rotman 1993, 71). I do not dispute that if one tries hard enough, one 4.2 Initiatives for Governing Family and Humanitarian could find such mathematical concise accounts of geometric Migration: Labour Migration texts but not(some Workers’ Migration ............. 73 constructions might be a good place to look). But our arbitrary texts, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 G¨ odel’s 1931 and 1934 texts (and, as far as I can tell, most mathematical 4.4 Selective andtothe Brain Drain............................................ 87 texts), do notPolicies conform these characterisations. 4.5 Equal and Denied Opportunities ................................ First,Opportunity there are very few imperatives in these texts. Perhaps90the imperative mood was considered ill-suited for civilised written communication Bibliography ......................................................................................... 97 in the Vienna and Princeton circles. Perhaps it never occurred to writers in 5.these Colombia: Emigrants in Their Societies of the Origin ....... 101 mood. circlesIncluding to dominate a mathematical text with imperative Urs Watter Instead of imperatives, we have the frequent use of the indicative mood 5.1both Stateactive Interest andpassive Responsibility in and voices, often attributed to the character we. In towards their Citizens Living Abroad ........................................... 102 addition, the texts contain 9 heres and 33 nows, some of which would be 5.2 Applied Ethics .............................................................................. difficult to marginalise to the meta-Code, as they are used to 104 order and demarcate thePolicy formal process. These indexicals form106 part of a 5.3 Migration anddeductive Ethics ......................................................... network of locative and temporal adverbial structures that operates 5.4 Migration Policy in Colombia ...................................................... 108 in the text. 5.5 “Colombia nos une”...................................................................... 109 This does not mean that Rotman’s analysis has broken down. The lack 5.6 Alianza País .................................................................................. 112 of morphological markers does not mean we cannot establish a structural 5.7 Challenges .................................................................................... 114 and division of the enunciative position. We may regroup verbs into subsets, Bibliography ....................................................................................... 116 verbs, identify the Subject with occurrences of we bundled up with some the Agent with occurrences of we bundled up with others, and the Person Working Together for the Well-being of Migrants ........................... 119 as related to yet another set of verbs and adverbials. But here we should Barry Halliday take into account one of Barthes’ observations concerning the threading of sequences of verbs. Actions, he explains, can fall into various sequences which should be indicated merely by listing them, since the sequence of actions is never more than the result of an artifice of reading: whoever reads the text amasses certain data under some generic titles for actions ... and this title embodies the seRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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quence; the sequence exists when and because it can be given a Bibliography ......................................................................................... 60a title name, it unfolds as this process of naming takes place, as is sought or confirmed; its basis is therefore more empirical than 4. The Ethics of Migration. rational, and it is useless to attempt to force it into a statutory orReflections on Recent Migration Policies der; its only logic in is Italy thatand of the “already-done” or “already-read” and “Non-policies” Europe ........................................... 61 (Barthes 1974, 19). A formal grouping of verbs risks being an arbitrary Laura Zanfrini empirical compulsion than aDemand well grounded structural conclusion. 4.1 Restrictive Policies rather and Structural for Immigrant Labour .. 65 Bearing this cautionary statement in mind, let’s try to allocate some 4.2 Initiatives for Governing Family and Humanitarian verbs appearing in the texts tobut the Subject and............. Agent,73and see Migration: Labour Migration notPerson, Workers’ Migration whether we can distinguish which verb belongs to which character, or 4.3 From Guest Workers to Unwelcome Guests .................................. 82 whether this distinction is an interpretive framework imposed on the math4.4 Selective and the Brain 87 excuse ematical text.Policies Let’s consider threeDrain............................................ examples. I hope that you will my to introduce details required for a technical understanding 4.5 failure Equal Opportunity andthe Denied Opportunities ................................ 90 of the quotations below. But, as will become evident, the distribution of Bibliography ......................................................................................... 97 actions between characters does not depend on such understanding. 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs WatterI: we can, for example, find a formula F (v) of PM 3 Example with oneInterest free variable v (of the type of a number sequence) such 5.1 State and Responsibility thattowards F (v), their interpreted according the meaning of the terms of Citizens Living Abroadto ........................................... 102 PM, says: v is a provable formula. Footnote: It would be very 5.2 Applied Ethics .............................................................................. 104 easy (although somewhat cumbersome) to actually write down 5.3 Migration Policy and Ethics ......................................................... 106 this formula (1931, 147). 5.4 Migration Policy in Colombia ...................................................... 108 This text appears in the introduction, in a paragraph that opens 5.5 “Colombia nos une”...................................................................... 109 with the statement: Before going into details, we shall first sketch the 5.6 Alianza País .................................................................................. 112 main idea of the proof, and must therefore be attributed to the Person. 5.7 Challenges .................................................................................... 114 is the But it is obviously not the Person who finds formulas. The Person Bibliography ....................................................................................... one who might try to write down the formula, since he is the116 only one who has enough embodiment to experience how cumbersome it is. But Working Together for the Well-being of Migrants ........................... 119 finding the formula, which in the context of this example is a tedious formal Barry Halliday procedure, is a task which the Subject should narrate and the Agent should perform. Now, which is the character who does the interpreting? Is it the Person who has an overview of all the different layers and significations of the argument, or is it the Subject, for whom interpreting would stand for 3 PM

is shorthand for Principia Mathematica, Russell and Whitehead’s logicomathematical formal system. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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establishing a correspondence between the provability of a meta-statement Bibliography ......................................................................................... 60 verify and the provability of a formula, a correspondence that the Agent can by symbolically manipulating the number sequence substituted for v? And 4. The Ethics of Migration. once the Person, Subject and Agent have thus collaborated, how come it Reflections on Recent Migration Policies isand the“Non-policies” formula, rather than and any Europe one of ........................................... them, which, like Balaam’s in Italy 61 ass, is 4 suddenly conferred with the power to say? Laura Zanfrini 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 Example II: we can define relations to be classes of ordered 4.2 Initiatives for Governing Humanitarian pairs, and ordered pairs Family to be and classes of classes; for example, the Migration: Labour Migration but not Workers’ Migration ............. 73 ordered pair a, b can be defined to be ((a), (a, b)) (1931, 153). 4.3 From Guest Workers to Unwelcome Guests .................................. 82 The notions relation, ordered pair and class are all already determined 4.4 Selective Policies and the Brain Drain............................................ 87 from the point of view of the mathematical Person. The authority to rep4.5 Equal Denied Opportunities ................................ 90 and resent oneOpportunity by another and is therefore contingent on the Person’s consent, itBibliography is therefore......................................................................................... he who can define. But the one to actually make97the definition, and perhaps prove the formal adequacy of the definition, is the 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Subject. Finally, it is the Agent, who, whenever hearing the Subject speak Urs Watter of the ordered pair a, b must replace such sign sequence by ((a), (a, b)), 5.1 State Interest and Responsibility and only then carry out his further manipulative tasks. In the Person’s towards their Citizens Living Abroad ........................................... 102 voice, the above statement reads: I agree to define. In the Subject’s voice Applied Ethics(and, .............................................................................. 104 it5.2 reads: I define perhaps, verify that the definition is adequate). In 5.3 Agent’s Migrationvoice Policy and Ethics ......................................................... 106 the it reads: I make the symbolic manipulations required by the 5.4 definition. Migration Policy in Colombia ...................................................... 108 5.5 “Colombia 109 and Example III: nos Weune”...................................................................... have noted that xBy is a recursive relation; 5.6 can Alianza País .................................................................................. we also prove that σ(x, y) is recursive, where σ(x, y) 112 is the number of the formula which results when we replace all 5.7 Challenges .................................................................................... 114free occurrences of w by zy in the formula whose number is x (1934, Bibliography ....................................................................................... 116 359–360). Working Together for the Well-being of Migrants ........................... 119 This Barrystatement Halliday seems to have some verbs relating to the Subject (note and prove), and some to the Agent (replace). However, it also contains temporal and locative elements. The noting is articulated as having occurred in the past. This is a psychological and relative past. If for instance, I skip 4 Some

logicians object that formulas don’t say, and shouldn’t be described as saying. This normative stance is irrelevant here. I am analysing how a specific mathematical text works. According to this text, Formulas do say. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the text’s discussion of recursive relations, and move directly to the main Bibliography 60 writargument (as......................................................................................... in fact I first did), then my reading Subject and G¨odel’s ing Subject get out of synch, and manifest a temporal relativity, whereas 4. The Ethics of Migration. the mathematical Subject is supposed to be free of such relativity. G¨ odel’s Reflections on Recent Migration Policies Subject’s present-perfect have is my Subject’s future-simple will. This deand “Non-policies” in Italy and Europe ........................................... 61 synchronisation Laura Zanfrini is in fact explicitly supported by the text, which states that the discussion of recursive functions is aforparenthetic consideration 4.1 Restrictive Policies and Structural Demand Immigrant Labour .. 65 that for the present has nothing to do with the formal system P 4.2 Initiatives for Governing Family and Humanitarian (1931, 157). The discrepancy between odel’s Person and............. mine has Migration: Labour Migration but not G¨ Workers’ Migration 73 seeped through to create a discrepancy between G¨ odel’s Subject and mine. The 4.3 From Guest Workers to Unwelcome Guests .................................. 82 embodied Person is allowed to carry the Subject along with it. 4.4 Selective Policies and the Brain Drain............................................ 87 On the other hand, the locative preposition in is, as far as the text 4.5 Equal Opportunity and Denied Opportunities ................................ 90 to any is concerned, an absolute disembodied location, which is invariant Subject and Agent (I do not claim that it is an absolute invariant,97 but only Bibliography ......................................................................................... that the text articulates it as such). That this locative be a disembodied 5.invariant Colombia: Emigrants Theirclaim Societies Origin ....... 101 is Including demonstrated by theintext’s that of such manipulations can Urs Watter be mechanised. However, even Rotman allows a restrictedly embodied man5.1 State Interest and Responsibility ifestation of locality into the mathematical code, as provided by the zero towards their Citizens Living Abroad ........................................... 102 point of reference. The point to be made here about “0” is that in 5.2 Applied 104 origin practice itsEthics two .............................................................................. senses — Coded number and metaCoded — inextricable from each other: in the course of manipulating 5.3are Migration Policy and Ethics ......................................................... 106 the number sign, the meta-sense is always present shadowing it, 5.4 Migration Policy in Colombia ...................................................... 108 being part of another layer of meaning which adjoins and pene5.5 “Colombia nos une”...................................................................... 109 trates the formal layer available in the code (Rotman 1993, 75). 5.6 Alianza País .................................................................................. 112 The three examples above are analysed according to Rotman’s artic5.7 Challenges .................................................................................... 114 There ulation, however problematic and obscure the analysis turned out. is, however, nothing in the text to impose such analysis. G¨odel’s116 verbs and Bibliography ....................................................................................... pronoun we do not seem to distinguish between the Person, Subject and Working Together the Well-being of Migrants ........................... 119a single Agent, but ratherfor to bundle them seamlessly together. We saw that Barry Halliday verb can order into action all three characters, and that their realms of authority are not clearly distinct. On top of this obscurity, a writer who were to take as a point of departure Foucault’s division quoted above, would likely end up with a somewhat different character distribution. I find no explicit textual evidence that such triple articulation permeates the text. And yet, we cannot ignore the fact that we can indeed Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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rewrite the text so as to conform to Rotman’s articulation. The fact of this Bibliography 60 It is capacity must......................................................................................... not be dismissed, because it is still a fact of the text. still a fact of the text that such a reading can be sustained, and as such 4. The Ethics of Migration. this fact may very well be relevant to the question of how the text works. Reflections on Recent Migration Policies This fact can contribute ourEurope understanding of how the text 61 interacts and “Non-policies” in Italytoand ........................................... with possible Laura Zanfrinireaders, even though it is no more a fact of the text than the effect of an outside intervention. The fact that a structure, which is not in 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 the text, can be imposed upon the text, that such imposition does effect 4.2 Initiatives for Governing Family and Humanitarian someMigration: changes, Labour but does not entirely the Migration text apart, and that Migration but notbreak Workers’ ............. 73 such imposition can appear, at least at first sight, quite convincing — these facts 4.3 From Guest Workers to Unwelcome Guests .................................. 82 testify to a critical feature of mathematical texts: openness.5 This is the 4.4 Selective Policies and Brain Drain............................................ 87 from same sort of openness, or the rather tolerance, which allows the extraction (or on) mathematical of platonist, logicist, formalist 4.5imposing Equal Opportunity and Deniedtexts Opportunities ................................ 90and intuitionist positions — even though these positions needn’t be discoverable Bibliography ......................................................................................... 97 from analysing mathematical texts according to terms they explicitly state. 5. Colombia: Including Their Origin ....... 101 What we imposeEmigrants on the textinfrom theSocieties outside of is not without precedent Urs Watter

inside. The roles suggested by Foucault and Rotman, as well as platonist, 5.1 Stateformalist Interest and logicist, andResponsibility intuitionist metaphysics/epistemologies are not comtowards their Citizens Living Abroad ........................................... 102 pletely foreign to the text. They are not arbitrary chance constructs that 5.2 Applied have nothingEthics to do.............................................................................. with the mathematical text. They can all be 104 supported to an extent by evidence excavated from within the text. Indeed, If this had 5.3 Migration Policy and Ethics ......................................................... 106 not the case, noinone would have been able to successfully impose 5.4 been Migration Policy Colombia ...................................................... 108 these constructs on mathematical texts, or at least not in ways that appear con5.5 “Colombia nos une”...................................................................... 109 vincing to the extent that they do. The mathematical text communicates 5.6 Alianza .................................................................................. with variousPaís structures, which are not completely foreign to it, 112 but which are properly endorsed by it either. This is precisely how a mathemat5.7 not Challenges .................................................................................... 114 ical text can ....................................................................................... signify: by communicating with its outside, by incorporating Bibliography 116 inside a residue of its outside, by denying its outside the clear and distinct Working Together for of theoutside. Well-being of Migrants ........................... 119 metaphysical status Barry Halliday

This diagnosis of openness lies well within the range spanned from Barthes’ and Foucault’s notions of authorship in Barthes (1977) and Fou5 An entirely different question is for what purpose we should want to impose upon a text Rotman’s (or any other) articulation. Rotman uses his imposed structure to argue for a radically finitist view, which I respect, and, with some modifications, endorse. Rotman’s rearticulation has its merits. But it is not ‘discovered’ within the text.

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cault (1984), through Eco’s conception of The Open Work (Eco 1989), to Bibliography ......................................................................................... 60 The Derrida’s maxim that there is no outside-text (Derrida 1976, 158). novelty is in demonstrating that mathematical texts are not outside this 4. The Ethics of Migration. range. Without such openness, without the text’s incorporation of exterReflections on Recent Migration Policies nally imposed enunciative the........................................... text would simply not communiand “Non-policies” in Italypositions, and Europe 61 cate with ‘foreign’ readers and hence soon fail to signify. But imposing upon Laura Zanfrini we three (Person, Subject, Agent) whoforare one is still awkward 4.1 the Restrictive Policies and Structural Demand Immigrant Labour .. 65 and contrived, and it is the interpretive gap between the text and the recon4.2 Initiatives for Governing Family and Humanitarian struction that Labour I seek to bring upbut and Facing we with the73 question Migration: Migration notexplore. Workers’ Migration ............. What is thy name? one should not confine to the asylum the possibility 4.3 From Guest Workers to Unwelcome Guests .................................. 82 of saying, My name is Legion: for we are many (Mark 5, 9). 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90

1.1.3

When, where and how we do it

Bibliography ......................................................................................... 97

Here is what we learnt from our critical engagement with Rotman’s three 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 characters (or more generally, from Barthes’ comments on grouping verbs Urs Watter together): that the text tolerates, at a price, divisions that are imposed on 5.1 State Interest and Responsibility it, and allows trace evidence of such divisions to be excavated from within towards their Citizens Living Abroad ........................................... 102 it. This openness to an outside (which undermines a clear inside/outside 5.2 Applied Ethics .............................................................................. 104 division, because it blurs the line between imposing something from the out5.3 Migration Policy and Ethics is ......................................................... 106 side and discovering it inside) a crucial constituent of the text’s semiotic capacity, but leaves without a...................................................... concrete analysis of the text’s enunciative 5.4 Migration Policy us in Colombia 108 position. We shall therefore try to determine this position via the adverbials 5.5 “Colombia nos une”...................................................................... 109 and modalities interacting with this position. 5.6 Alianza País .................................................................................. 112 Temporality makes its mark on the text in various forms. Tempo5.7 Challenges rality appears .................................................................................... in formal manipulations, which may take place 114 one after Bibliography ....................................................................................... 116 another, as in: we must therefore (1) eliminate the abbreviations and (2) add the omitted parentheses (1931, 156). Temporality also Working Together for the Well-being of Migrants ........................... 119 appears along the course of the argument, as in: We have noted that Barry Halliday xBy is a recursive relation (1934, 359), and in As will be shown later, however, the converse does not hold (1931, 173). Finally, temporality intervenes in reviewing and interpreting the text: such a proposition involves no faulty circularity, for initially it [only] asserts that a certain well-defined formula ... is unprovable. Only subsequently (and so to speak by chance) does it turn out that this formula is Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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precisely the one by which the proposition itself was expressed Bibliography (1931, 152). ......................................................................................... 60 But to appreciate the nature of this temporality, an important clue is 4. The Ethics of Migration. provided by on theRecent transmutation ‘outside world’ temporality into ‘matheReflections MigrationofPolicies matical’ temporality.inThis in the........................................... following passage: Suppose and “Non-policies” Italyhappens and Europe 61 that Laura Zanfrini on 4 May 1934, A makes the single statement, “Every statement which A makes on and 4 May 1934Demand is false.” This statement 4.1 Restrictive Policies Structural for Immigrant Labour .. 65clearly cannot be true. Also it cannot be false, since the only way for it to 4.2 Initiatives for Governing Family and Humanitarian be false is forLabour A to Migration have made a true statement in ............. the time Migration: but not Workers’ Migration 73 specified and in that time he made only the single statement (1934, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 362). 4.4 Selective Policies and the Brain Drain............................................ 87 This form of the liar paradox is then translated into mathematical 4.5 Equal Opportunity and constructed Denied Opportunities ................................ form. Recall that G¨ odel an explicit enumeration of 90 formulas in his formal ......................................................................................... system. Then a formula is constructed claiming that97formula Bibliography number so-and-so has a certain property F (interpreted as being false). The 5.construction Colombia: Including Emigrants in number Their Societies Originis....... is so designed that the of that of formula the 101 very numUrs Watter ber so-and-so mentioned inside the formula. The formula therefore says of 5.1 State Responsibility itself thatInterest it hasand property F (namely, is false). But where in the transitowards their Citizens Living Abroad ........................................... 102 tion from 4 May 1934 to the self-referential statement did temporality 5.2 Applied Ethics .............................................................................. 104 disappear? 5.3 Migration Policy and Ethics ......................................................... 1064 May Temporality has been converted into enumeration. The date 1934 served only to in designate claim. This designation device is trans5.4 Migration Policy ColombiaA’s ...................................................... 108 formed into G¨ odel’s enumeration. The form of temporality acknowledged 5.5 “Colombia nos une”...................................................................... 109 here by the text is so reductive, it is not even properly serial. The numbers 5.6 Alianza País .................................................................................. 112 conferred upon formulas have nothing to do with the order in which they 5.7 Challenges 114 appear. Time is.................................................................................... but a pool of events and designations, which excludes cooccurrence, which does not display any equivalent of duration Bibliographybut ....................................................................................... 116 (some possible exceptions will be treated below). Working Together for the Well-being of Migrants ........................... 119 But the most interesting aspect is not the articulation of time into Barry Halliday a set of mere mutual exclusions, but the ambiguous relation between the enunciative position and this temporality. On the one hand, the enunciative position is within time, as the above quotations explicitly mark. However, the same position has the capacity to review the entire temporal pool. What will be shown and what we have noted is readily available for the current moment of the discussion. Whatever happened initially and subRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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sequently in the quotation standing four paragraphs above is bundled toBibliography ......................................................................................... 60 gether in a contemporary moment where the proposition is self-referential, but involves no faulty circularity. Even hypothetical moments of an un4. The Ethics of Migration. specified time can all be bundled up and reviewed together: for any relevant Reflections on Recent Migration Policies system of axioms κ, in there are ........................................... propositions ... that are and “Non-policies” Italy always and Europe 61 undecidable ... as soon as some specific proposition is not κ-PROVABLE Laura Zanfrini (1931, 195). Policies and Structural Demand for Immigrant Labour .. 65 4.1 Restrictive The enunciative position, which within time, and at the same time 4.2 Initiatives for Governing Family andisHumanitarian can Migration: observe time and even form it by the operation of enumerating Labour Migration but not Workers’ Migration ............. 73its minimal elements — this complex position contributes to the complex process 4.3 From Guest Workers to Unwelcome Guests .................................. 82 of semiosis. First, temporality as a set of mutual exclusions registers the 4.4 Selective Policies and the Brain Drain............................................ 87 distinct elements (formal propositions) studied by the mathematical text. 4.5 Equal Opportunityasand Denied Opportunities Second, temporality a sequence of past and ................................ future occurrences 90 helps order and narrate the text for the reader. Finally, by taking a stance that can Bibliography ......................................................................................... 97 inspect all these different times, G¨odel counters the grave accusation that 5.his Colombia: Including Emigrants in Their Societies of Origin ....... 101 argument is groundless, and shows that his proposition involves no Urs Watter faulty circularity. In so far as temporality is reduced to the articulation 5.1mutual State Interest and elements, Responsibility of exclusive there is a sort of circularity (self reference) towards their Citizens Living Abroad ........................................... 102 — the referent formula and referee formula are one and the same. But in so 5.2as Applied Ethics .............................................................................. far temporality has a before and an after, in so far as initially104 it [only] asserts ... and Only subsequently (and so to speak by chance) 5.3 Migration Policy and Ethics ......................................................... 106 does it5.4turn out ...Policy — ininthat sense ...................................................... we obtain a non-circular turn of108 events. Migration Colombia The extraction of meaning from the text depends here on instilling 5.5 “Colombia nos une”...................................................................... 109 a difference across the self-referring instance. The fact that the order of 5.6 Alianza País .................................................................................. 112 arguing and reading is not absolute, but revisable by any reader, does not 5.7 Challenges .................................................................................... 114 weaken the argument that depends on its distinct temporal sequencing. The fact that....................................................................................... one has to adopt an omni-temporal point of view in Bibliography 116order to complete the story does not weaken it either. But the enunciative position Working for the Well-being of Migrants of ........................... 119 must beTogether able to endorse all these conceptions temporality in order to Barry Halliday put G¨ odel’s argument together. The argument’s validity depends on a multiplicity within the enunciative position. If the enunciative position were severed into several positions, each endorsing only one conception of time, the argument would simply not stick together. Some researchers insist on discarding the narrative, and reading the proof ‘purely formally’, without retaining notions of reference and expresRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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sion operative in the proof. This reading is of course tenable, but leaves Bibliography the reader in ......................................................................................... a senseless position. In this reading all that G¨odel’s60 theorem provides us with is a couple of highly complex arithmetic propositions con4. The Ethics of Migration. cerning some very big numbers. Unless these numbers are allowed to refer to Reflections on Recent Migration Policies formulas, there is noinincompleteness theorem. But we may go even61further: and “Non-policies” Italy and Europe ........................................... ifLaura we refuse to let signs refer, all we have is a bunch of symbols that obey Zanfrini some combinatorial restrictions — not even for an Immigrant arithmetical statement. 4.1 Restrictive Policies and Structural Demand Labour .. 65 But we shall leave this strand of the discussion to the third chapter. 4.2 Initiatives for Governing Family and Humanitarian Going from the notion of time to Workers’ that of space, we find that73 space in Migration: Labour Migration but not Migration ............. the text is usually reduced to relative locations in sequences. This relative, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 disembodied notion of space is further abstracted by formulations such as: 4.4 Selective Policies and the Brain Drain............................................ 87 a formula will be a finite sequence of natural numbers which is 4.5 Equal Opportunity and Denied Opportunities ................................ function 90 accompanied by the footnote: That is, a number-theoretic defined on an initial segment of the natural numbers. (Numbers, Bibliography ......................................................................................... 97 of course, cannot be arranged in a spatial order) (1931, 147). The 5.spatial Colombia: Including Emigrants Their Societies Origin ....... 101 concept of sequence is in here reduced to aof function providing an Urs Watter ordinal ‘location name’ for every element in the de-spatialised sequence. 5.1 State Interestspatial and Responsibility The underlying configuration is dismissed and marked as impossible towards their Citizens Living Abroad ........................................... 102 due to the non spatial abstraction of numbers. 5.2 Applied .............................................................................. 104 posiSpatialEthics notions in the text are rarely related to the enunciative 5.3 Migration Policy Ethics ......................................................... 106princition. Two of the few and exception are: This makes no difficulty in ple. However, in order not to...................................................... run into formulas of entirely108 unman5.4 Migration Policy in Colombia ageable lengths ... the construction of the undecidable proposition 5.5 “Colombia nos une”...................................................................... 109 would have to be slightly modified (1931, 149) and The proof that 5.6 Alianza País .................................................................................. 112 so-and-so holds is too long to give here (1934, 359). Here the physi5.7limitations Challenges .................................................................................... 114 cal of space, and likely also time (or perhaps spatialised-time), suddenly intervene. Bibliography ....................................................................................... 116

The discrepancy between this last notion of space-time and the ones Working Together for the Well-being of Migrants ........................... 119 observed immediately before are better accounted for by an analysis of Barry Halliday modality in the text. The text appears to distinguish difficulty in principle from actual difficulties. Consider, for instance, that we always understand by “formula of the formal system PM ” a formula written without abbreviations (that is, without the use of definitions). It is well known that [in PM ] definitions serve only to abbreviate notations and therefore are dispensable in principle (1931, 147). It Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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is obvious that abbreviative definitions cannot be dispensed with, if matheBibliography ......................................................................................... 60 matics is something to be practiced by physically and culturally constrained humans of a kind we tend to meet. The above statement, therefore, serves, 4. The Ethics of Migration. rather than to make a claim, to articulate the field where the argument is Reflections on Recent Migration Policies to apply. The argument is and to apply in ........................................... the realm of in principle, and “Non-policies” in Italy Europe 61 which we shall later relate to other conceptual layers of the proof. One should Laura Zanfrini bear in mind that in practice mathematicians hardly ever write.. 65 proofs in 4.1 Restrictive Policies and Structural Demand for Immigrant Labour as precisely articulated formal systems as PM at all. 4.2 Initiatives for Governing Family and Humanitarian Similar considerations apply alreadyMigration quoted statement, Migration: Labour Migration but to notthe Workers’ ............. 73 which appears on the same page: It would be very easy (although somewhat 4.3 From Guest Workers to Unwelcome Guests .................................. 82 cumbersome) to actually write down this formula. Easy, perhaps — 4.4 Selective Policies and the BrainitDrain............................................ 87 but not humanly feasible. Today may be feasible to program a computer 4.5output Equal Opportunity and Denied Opportunities 90 to such a formula, but extremely cruel,................................ and quite likely unfeasible, to expect a human to examine the output. Either way, this option Bibliography ......................................................................................... 97 was not available to G¨ odel. Again, we have a statement that operates in the 5.language Colombia: Including in Their Societies of Origin ....... 101 game of theEmigrants in principle grammar, where things can be done Urs Watter that cannot actually be done. 5.1 State and Responsibility We Interest may appear to have found a textual support for the Agent vs. towards their Citizens ........................................... 102 Agent, Subject-Person division. ItLiving is the Abroad disembodied, unlimitedly industrious 5.2 Applied Ethics .............................................................................. 104 even who can do whatever can be done in principle. The Person, perhaps the excluded from......................................................... this capacity. But whereas we do106 have two 5.3 Subject, Migrationare Policy and Ethics distinct modalities in the text, there is no indication that the enunciative 5.4 Migration Policy in Colombia ...................................................... 108 position is in fact divided according to these modalities.6 Consider for in5.5 “Colombia nos une”...................................................................... 109 stance the statement (also on the same page) it can be shown that the 5.6 Alianza País .................................................................................. 112 can notions “formula”, “proof array”, and “provable formula” be in.................................................................................... the system PM ; that is, we can, for example, 5.7 defined Challenges 114 find aBibliography formula F....................................................................................... (v) of PM ... such that F (v) ... says: v is a 116 provable formula. The first can will in fact be achieved in the text. But the next Working Togetherthe for kind the Well-being of achieved Migrants in ........................... 119the last can is precisely that is only principle, and Barry Halliday can falls somewhere in the middle, depending on what aspect of finding is at stake. The enunciator must endorse both modalities if it is to attain 6 Claiming that any grammatical division (or even that any modal division) necessarily entails a division of the enunciative position leads to grotesque results. The imperative and indicative moods are distinct, but they do not necessarily require distinct enunciative positions to function properly. Indeed, Austin’s How to Do Things with Words ends up questioning the distinctions between indicatives and performatives.

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both human accessibility (actual capacity) and the mathematical ideal (in Bibliography ......................................................................................... 60 principle capacity). The text does not show any sign that the enunciator relates differently to these seamlessly interwoven layers of capacity — and 4. The Ethics of Migration. yet these layers are distinguished by the text itself, when it briefly insists Reflections on Recent Migration Policies on the in principleinreservation. and “Non-policies” Italy and Europe ........................................... 61 Laura Zanfrini What I have been trying to show is that the texts make sense and lend

themselves to the extraction of meanings by,foronImmigrant the one hand, 4.1 Restrictive Policies and Structural Demand Laboursupporting, .. 65 to a certain extent, divisions of the speaker, while, on the other hand, 4.2 Initiatives for Governing Family and Humanitarian refusing to be Labour pinned Migration down to such divisions. The enunciative position has Migration: but not Workers’ Migration ............. 73 been shown to be distributed across various roles — but without actually 4.3 From Guest Workers to Unwelcome Guests .................................. 82 grounding any stable textual articulation of such roles; it has been shown 4.4endorse Selectivevarious Policiesincompatible and the Brainmodalities Drain............................................ 87 and to of temporality, spatiality 4.5 Equal— Opportunity Denied ................................ capacity and thenand bind themOpportunities together into intelligibility by 90 avoiding clear distinctions followed by explicit syntheses. The text relies on Bibliography ......................................................................................... 97 many diverse positions to explain itself, to make the reader understand; but the 5.text Colombia: Emigrants Theirposition, Societies or of Origin .......positions 101 cannotIncluding commit itself to anyinsingle set these as Urs Watter entirely apart, as by doing that it would simply fall apart. 5.1 State and Responsibility The Interest text manages to produce its meaning by distributing differences towards their Citizens Living Abroad ........................................... 102 across the repeated enunciative stance. The semiotic machine embodied by 5.2 Applied Ethics 104 ties a the morpheme we.............................................................................. is, like Benveniste’s I, a blurring interface that plurality of readers, writers and their forms of being to texts in 106 ways that 5.3 Migration Policy and Ethics ......................................................... make sense. Regardless of popular belief, mathematical texts, such as these, 5.4 Migration Policy in Colombia ...................................................... 108 do not make sense by pure formal clarity. They make sense by having it 5.5 “Colombia nos une”...................................................................... 109 both ways (and more). 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114

1.1.4

Who do we do it with? (a slight detour)

Bibliography ....................................................................................... 116

Whoever we are, they can’t stand alone. I use I only when I am speakWorking Together for the Well-being of Migrants ........................... 119 ing to someone who will be a you in my address. It is this condiBarry Halliday tion of dialogue that is constitutive of person, for it implies that reciprocally I becomes you in the address of the one who in his turn designates himself as I ... This polarity of persons is the fundamental condition in language, of which the process of communication, in which we share, is only a pragmatic consequence (Benveniste 1971, 224–225). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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A polar position to the texts’ enunciative position is established in the Bibliography 60 very first lines......................................................................................... of the introduction to the 1931 text. The development of mathematics toward greater precision, G¨odel explains, has led, as 4. The Ethics of Migration. is well known, to the formalisation of large tracts of it, so that Reflections on Recent Migration Policies one can prove any using nothing but a few mechanical and “Non-policies” in theorem Italy and Europe ........................................... 61 rules. The most comprehensive formal systems that have been set Laura Zanfrini up theand system Principia mathematica (PM) 4.1 hitherto Restrictive are Policies Structural Demand for Immigrant Labour .. 65on the one hand and the Zermelo-Fraenkel axiom system of set theory 4.2 Initiatives for Governing Family and Humanitarian on Migration: the otherLabour ... These twobut systems are Migration so comprehensive Migration not Workers’ ............. 73 that in them all methods of proof are formalised, that is reduced to a 4.3 From Guest Workers to Unwelcome Guests .................................. 82 few axioms and rules of inference. One might therefore conjecture 4.4 Selective Policies and Brainof Drain............................................ that these axioms andtherules inference are sufficient to87decide any mathematical can at all be formally expressed 4.5 Equal Opportunity question and Deniedthat Opportunities ................................ 90 in these systems. It will be shown below that this is not the Bibliography ......................................................................................... 97 case, that on the contrary there are in the two systems mentioned 5.relatively Colombia: Including Emigrantsinin the Their Societies Origin ....... 101cannot simple problems theory of of integers that Urs Watter be decided on the basis of the axioms (1931, 145). 5.1 State and to Responsibility The Interest footnotes the second sentence acknowledge Whitehead and towards their Citizens Living Abroad ........................................... 102 Russell, Fraenkel, von Neumann and Hilbert and Bernays as authors of for5.2 Applied mal systems.Ethics These.............................................................................. various authors are invoked as if they belong 104 to a single unified front, binding together fundamentally logicist agenda 106 of Russell, 5.3 Migration Policy and Ethics the ......................................................... Hilbert’s finitism, Zermelo’s realist point of view and von-Neumann’s 5.4 Migration Policy in Colombia ...................................................... 108 pragmatist formalism, subjugating all to an ideological field negatively marked 5.5 “Colombia nos une”...................................................................... 109 by the adjective mechanical. This adjective, along with the verb reduce, 5.6 Alianza País .................................................................................. 112 suggests a non-voluntary, non-subjective and impoverished mathematical 5.7 Challenges .................................................................................... 114 had practice. Indeed, at the time of writing the paper machines had already the kind of connotation to be canonically presented in Chaplin’s Bibliography ....................................................................................... 116Modern Times (1936). At the same time, the use of the term mechanical in the Working for the Well-being of Migrants ........................... context Together of formalism is far from obvious. A mechanical approach119 will only Barry Halliday be established a few years later by Church and Turing. In the above quotation a position of ‘they’ has been set-up and characterised. ‘They’ are ascribed a mighty achievement. Due to ‘their’ work, one can prove any theorem using nothing but a few mechanical rules. An unsuspecting reader may be lured to believe that a certain saturation has been achieved within large tracts of mathematics, whereby Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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given a theorem, a proof can (mechanically!) be produced. And indeed, Bibliography 60 that those readers......................................................................................... who swallow the bait7 might therefore conjecture these axioms and rules of inference are sufficient to decide any 4. The Ethics of Migration. mathematical question that can at all be formally expressed in Reflections on Recent Migration Policies these systems (1931, 145).and Europe ........................................... 61 and “Non-policies” in Italy Laura Zanfrini Note that the constative assertion is reduced by the hypothetical

modal might. Policies The text, not for yetImmigrant clarify to Labour the possibly 4.1 Restrictive andhowever, Structuraldoes Demand .. 65 misled reader that the formalist project allows to transcribe and verify by few 4.2 Initiatives for Governing Family and Humanitarian mechanical only those proofs are already discovered. Migration:rules Labour Migration but notthat Workers’ Migration .............Unproven 73 and unrefuted theorems remain unproven and unrefuted regardless of the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 formalist project. The modal shift from constative to hypothetical serves to 4.4 Selective Policies and the Brain Drain............................................ 87 muddle the reader, who is now watching the conjecture he was manipulated 4.5 Equal Opportunity Opportunities 90 into forming subjectedand to Denied the doubt inscribed ................................ in a might. And indeed, It will be shown below that this is not the case, that on the contrary Bibliography ......................................................................................... 97 there are in the two systems mentioned relatively simple prob5.lems Colombia: Emigrants Theircannot Societies Origin ....... in theIncluding theory of integersinthat beofdecided on 101 the basis Urs Watter of the axioms (1931, 145). But is it an oversight that an explicit defini5.1 State Interest and Responsibility tion of undecidability (there exists a statement such that neither it nor its towards their Citizens Living Abroad ........................................... 102 negation can be proved) is postponed to the bottom of the next page? The 5.2 Applied Ethics 104talking specialist may have.............................................................................. known exactly which undecidability G¨odel was about. Other mathematicians probably still kept in suspense. 5.3 Migration Policy and Ethics were ......................................................... 106 The rhetorical we...................................................... have just reviewed is standard.108 A picture 5.4 Migration Policy structure in Colombia is painted, then questioned, and finally announced invalid. Let’s analyse 5.5 “Colombia nos une”...................................................................... 109 it in Barthes’ terminology. The first chunk of quoted text (lexia) paints Alianza País .................................................................................. 112 a5.6 picture through Cultural Coding: a reference to institutional knowledge 5.7 Challenges .................................................................................... 114 (the work of the formalist ‘school’), and of Semantic Coding: the negative signified connotation of mechanical reduction. The second lexia appeals to Bibliography ....................................................................................... 116 Hermeneutic Coding: the modal shift operated by the might sets up a Working Together for thevery Well-being of Migrants ........................... lure to undermine the picture painted. Finally, we resort to119 Symbolic Barry Halliday Coding: a pivotal antagonistic this is not the case, and Proairetic Coding: the action of showing by an implicit agent, in order to invalidate the former 7 The translation appears to be more misleading than the original, which speaks of Beweisen (proofs) rather than theorems. But even the original claim is stronger than what was considered as commonly accepted at the time, and indeed, G¨ odel himself casts a doubt on this claim at the end of the paper (1931, 195).

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picture. This minor triumph of Barthesian analysis is almost too neat to Bibliography ......................................................................................... accept. The emerging message of deliverance is reflected not so60 much in the bits of information provided by each of the codes, but in the very 4. The Ethics of Migration. passage from one to the other: from institutional knowledge and connoted Reflections on Recent Migration Policies negativity, through in a mystery, a symbolic rapture by an agentless and “Non-policies” Italy andto Europe ........................................... 61 act. This is Zanfrini the structure of deliverance. Laura The enunciative in the text takes advantage of this manoeu4.1 Restrictive Policies position and Structural Demand for Immigrant Labour .. 65 vre. For the It will be shown to emerge both as a legitimate offspring and 4.2 Initiatives for Governing Family and Humanitarian a parricidal revolutionary with respect to a certain lineage,............. a paternal Migration: Labour Migration but not Workers’ Migration 73 position has to be, in the space of a few lines, both established and denounced. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 This position is established by forcing together Russell, Hilbert, Fraenkel 4.4 Selective Policies andathe Brain Drain............................................ 87 and von Neumann into straw-coalition, ignoring the fact that formalism 8 4.5 Equal Opportunity Denied Opportunities 90 was extremely young, and highly unstable, and far................................ from resting on a consensus among the contributors named above. This paternal position immediately Bibliography ......................................................................................... 97 falls victim to a parricide performed by branding this straw-formalism with 5.the Colombia: Emigrants and in Their Societies Origin ....... 101 suspect Including mark of mechanism, assigning to itof the ambiguous and misUrs Watter leading formulation axioms and rules of inference are sufficient to 5.1 Stateany Interest and Responsibility decide mathematical question, which formalists would not have towards their Citizens Living Abroad ........................................... 102 dared to claim as achieved. 5.2 Applied Ethics .............................................................................. The positioning accomplished here relies on the ability of a104 standard rhetorical manoeuvre to impose itself on a discursive field that is still 5.3 Migration Policy and Ethics ......................................................... 106 underdetermined and emerging. This move provides the rhetorical support (which 5.4 Migration Policy in Colombia ...................................................... 108 is, of course, not the only support) for putting it, later in the text, that The 5.5 “Colombia nos une”...................................................................... 109 solution suggested by Whitehead and Russell, that a proposition 5.6 Alianza .................................................................................. 112 cannot sayPaís something about itself, is too drastic (1934, 362). Indeed, the tension between belonging to, and breaking away 5.7 Challenges .................................................................................... 114 from ‘them’, which....................................................................................... gives rise to the text’s impersonal it and collective116 we enunBibliography ciative positions, is particularly manifest in the manoeuvres around the Working Together forsays the Well-being of Migrants proposition that about itself that it is........................... not provable 119 [in PM ], Barry Halliday which, as a footnote we have already quoted explains, involves no faulty circularity, for initially it [only] asserts that a certain well-defined formula ... is unprovable. Only subsequently (and so to speak by chance) does it turn out that this formula is precisely the one by 8 Merely

13 years had passed from Hilbert’s 1918 formulation; see Kleene’s introduction to G¨ odel’s 1931 paper in G¨ odel (1986–2003, 126). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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which the proposition itself was expressed (1931, 151). The enunBibliography ......................................................................................... 60 ciative position endorses here at once the aversion from and attraction to self-reference. No one would deny that the self-referential proposition was 4. The Ethics of Migration. constructed with the explicit intention of emulating self-reference inside a Reflections on Recent Migration Policies formal system. And in yetItaly the and mereEurope possibility of telling a revisionist61history, and “Non-policies” ........................................... obviously false as a history, relating the accidental genesis of this selfLaura Zanfrini reference, is sufficient contemporary logic both toLabour embrace odel’s 4.1 Restrictive Policies to andallow Structural Demand for Immigrant .. 65G¨ form of self reference,9 and to be revolutionised by it. The text remains 4.2 Initiatives for Governing Family and Humanitarian formalist. But Labour into this mechanic realm of formalism an Migration: Migration but not Workers’ Migrationquietly .............sneaks 73 element of so to speak ... chance. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 But all this rhetorical mechanics and revisionist historical articulation 4.4 Selective Policies and the Brain Drain............................................ 87 of meta-mathematical positions relates to the preamble to the introduction, 4.5 Equal Opportunity and Denied Opportunities ................................ 90 back and, for fear of being accused of lurking in the margins, we must move into the core ......................................................................................... of the mathematical text. Bibliography 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101

1.1.5 Who does it to us? Urs Watter

A5.1formalist ‘they’ position was set-up in order to simultaneously counter State Interest and Responsibility Living Abroad 102position and towards producetheir theCitizens text’s enunciative we........................................... position. But this ‘they’ is5.2far from exhausting the stance polar to the enunciative we.104 In order Applied Ethics .............................................................................. to complete the articulation of this polarity, let us track down the few 5.3 Migration Policy and Ethics ......................................................... 106 occasions where we is demoted from the subject position to the object 5.4 Migration Policy in Colombia ...................................................... 108 position us. 5.5 “Colombia nos une”...................................................................... 109 there First, we must acknowledge how rare this move is. In both texts are ninePaís occurrences of us, of which three appear in the inclusive im5.6 only Alianza .................................................................................. 112 perative let us. Nevertheless, these occurrences are revealing of the pres5.7 Challenges .................................................................................... 114 ence of the enunciative position in the much more frequent impersonal and Bibliography ....................................................................................... 116 passive constructions.10 9 ThereTogether Working for the Well-being of Migrants ........................... 119 is selfare, of course, logicians who altogether deny that G¨ odel’s proposition

Barry Halliday referential. But I don’t believe anyone would deny that self-reference was a leading principle in the construction of the proposition. 10 I should have, perhaps, analysed the impersonal and passive constructions in the text. Indeed, Foucault writes that the subjective formation is situated at the level of ‘it is said’ (Foucault 1972, 122). However, since the relation between some of these constructions and the enunciative position is debatable (for instance, in statements of the form ‘it follows that...’), I preferred to focus on the textual occasions where the voice emanating from the enunciative position is explicitly marked as such (lest I be accused

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We are told that if a formal decision ... of the SENTENTIAL Bibliography FORMULA......................................................................................... 17Genr ... is presented to us, we can actually60give ... a PROOF of Neg(17Genr) (1931, 177). Ignoring the meaning of 17Genr, 4. The Ethics of Migration. we observe that polar to we a position is established, which may present Reflections on Recent Migration Policies us mathematical offerings. Confronting this position, we becomes a andwith “Non-policies” in Italy and Europe ........................................... 61 reactive (giving once presented), rather than an initiating instance. Laura Zanfrini But this polar position is not confined to aImmigrant giving role. We.. can 4.1 Restrictive Policies and Structural Demand for Labour 65 have before us a proposition that says about itself that it is not prov4.2 Initiatives for Governing Family and Humanitarian ableMigration: (1931, 149–151) — the polar position canMigration speak. In............. fact, more Labour Migration but not Workers’ 73 than just speaking, it can modify the capacities of the enunciative position. A 4.3 From Guest Workers to Unwelcome Guests .................................. 82 certain proof, for example, allows us to actually derive a contradic4.4 Selective and theofBrain 87getting tion ... oncePolicies a PROOF w ...Drain............................................ is given (1931, 195) (without 4.5 Equal Denied of Opportunities ................................ into what Opportunity it is, such aand PROOF w is supposed not to exist). 90 We is therefore a subject position in both senses of the word: Bibliography ......................................................................................... 97subject of and subject to. However, the proposition that says, which we have 5.before Colombia: Emigrants Societies of Even Origin ....... 101 us, Including is explicitly producedinbyTheir we in the text. the hypothetical Urs Watter

object PROOF of w above, if provided at all, must necessarily be provided 5.1someone State Interest by who and canResponsibility present proofs, and therefore share we’s enunciative towards their Citizens LivingaAbroad ........................................... 102 as is position. We, it seems, plays game of catch with itself, or rather, 5.2 Applied 104 now obvious,Ethics with .............................................................................. themselves. We havePolicy manyand voices, positions from which we speak. 5.3 Migration Ethicsmany ......................................................... 106 We speak to and of ourselves and our creations, who in turn, as the above 5.4 Migration Policy in Colombia ...................................................... 108 quotations demonstrate, do not hesitate to speak back and challenge. In 5.5 “Colombia nos une”...................................................................... 109 some sense (a sense I wish to impose) we are none but G¨odel and I, the 5.6 Alianza País .................................................................................. 112private, reader, in the most intimate moment of reading — intimate but not because I know.................................................................................... many others have done it with him too, and because, 5.7 Challenges 114 to a certain extent, here I am doing it with him in public. Perhaps these so many Bibliography ....................................................................................... 116 discursive partners are the cause of this text being infested with so much Working Together the Well-being Migrants 119 meaning. Having for intercourse with soofmany codes........................... (encoded and decoded by Barry Halliday so many partners), it is bound to say many things. We, which is supposed to establish a single common denominator, ends up, it seems to me, forcing the text open to many different entangled codes and complicit partners. So many different entangling codes indeed, that it is no longer clear that one could speak of any individual code at all. of hearing voices). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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I would like to conclude this discussion with the words by which Bibliography ......................................................................................... 60 short Barthes described the ambiguous enunciative position in Balzac’s story Sarrasine. Who is speaking? he asks. Is it a scientific voice ... 4. The Ethics of Migration. Is it a phenomenalist voice naming what he sees? ... Here it is imReflections on Recent Migration Policies possible to attribute an and origin, a point of view, to the statement. and “Non-policies” in Italy Europe ........................................... 61 Now, this impossibility is one of the ways in which the plural Laura Zanfrini nature of a text canand beStructural appreciated ...for it Immigrant may happen that 4.1 Restrictive Policies Demand Labour .. 65 in the classic text, always haunted by the appropriation of speech, the 4.2 Initiatives for Governing Family and Humanitarian voice gets lost, as though itbut had out through a hole Migration: Labour Migration notleaked Workers’ Migration ............. 73 in the discourse. The best way to conceive the classical plural is then to 4.3 From Guest Workers to Unwelcome Guests .................................. 82 listen to the text as an iridescent exchange carried on by multiple 4.4 Selective Policies and the Brain Drain............................................ voices, on different wavelengths and subject from time to87 time to a4.5 sudden dissolve, and leaving a Opportunities gap which enables the utterance to Equal Opportunity Denied ................................ 90 shift from one point of view to another, without warning: Bibliography ......................................................................................... 97 the writing is set up across this tonal instability (which in the mod5.ern Colombia: Includingatonality), Emigrants inwhich Their makes SocietiesitofaOrigin ....... 101 text becomes glistening texture Urs Watter of ephemeral origins (Barthes 1974, 41–42). 5.1 State Interest and Responsibility I couldtheir use Citizens Foucault’s words to conclude this section. In 102 the protowards Living Abroad ........................................... posed analysis, instead of referring back to the synthesis or the 5.2 Applied Ethics .............................................................................. 104 unifying function of a subject, the various enunciative modalities 5.3 Migration and Ethics 106 sites, manifest his Policy dispersion. To......................................................... the various statuses, the various the various positions that he...................................................... can occupy or be given when 5.4 Migration Policy in Colombia 108 making a discourse. the discontinuity of the planes from 109 which he 5.5 “Colombia nos To une”...................................................................... speaks. And if these planes are linked by a system of relations, this 5.6 Alianza País .................................................................................. 112 system is not established by the synthetic activity of a conscious5.7 Challenges 114 but ness identical.................................................................................... with itself, dumb and anterior to all speech, Bibliography ....................................................................................... 116 by the specificity of a discursive practice. I shall abandon any attempt, therefore, to see discourse as a phenomenon of expression Working Together for the Well-being of Migrants ........................... 119 — the verbal translation of a previously established synthesis; Barry Halliday instead, I shall look for a field of regularity for various positions of subjectivity. Thus conceived, discourse is not the majestic unfolding manifestation of a thinking, knowing, speaking subject, but, on the contrary, a totality, in which the dispersion of the subject and his discontinuity with himself may be determined (Foucault 1972, 54–55). I would like to endorse this quote, but I am not Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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sure that the terms regularity, totality, and may be determined are Bibliographyhere ......................................................................................... 60 pronounced with the cautious and critical tone in which I would like 11 to have heard them. I am worried that this quote underplays the capacity 4. The Ethics of Migration. of a textual we to disperse and integrate, regularise and breach, totalise Reflections on Recent Migration Policies and determine andand render undecidable. If we do not underplay and re-open, “Non-policies” in Italy Europe ........................................... 61 these Lauracapacities, Zanfrini we can perhaps acknowledge not only the rigorous aspect of but also its disruptive creative force. And so ..I 65 shall not 4.1mathematics, Restrictive Policies and Structural Demand for Immigrant Labour be satisfied before I come again (now divulging in a voice drenched with 4.2 Initiatives for Governing Family and Humanitarian the fluid complexity so many but enunciative distributions Migration: LabourofMigration not Workers’ Migration compacted ............. 73 into a brief contractive exhale: we — no longer opposing a trinity, but embracing 4.3 From Guest Workers to Unwelcome Guests .................................. 82 its charge, embracing it too) to exclaim My name is Lesion: for we are 4.4 Selective Policies and the Brain Drain............................................ 87 many. 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97

1.2

The object: notion

5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Foucault’s Urs Wattermethodology considers objects and concepts as distinct elements that require separate analyses. However, forcing discursive objects and con5.1 State Interest and Responsibility cepts apart in mathematical texts is usually less straightforward than towards their Citizens Living Abroad ........................................... 102 maintaining their distinction in other contexts of knowledge (such as psychia5.2 Applied Ethics .............................................................................. 104 try, linguistics or economy). In mathematics what we speak about, and 5.3 Migration Policyitand Ethics ......................................................... 106through what we say about tend to intermingle. We may study numbers 5.4 Migration Colombia ...................................................... 108 as a the concept ofPolicy order,in but then go on to study the concept of order mathematical and subject it to quantitative classifications, 5.5 “Colombia object nos une”...................................................................... 109turning 12 numbers from objects to regulative concepts. 5.6 Alianza País .................................................................................. 112 In the texts under our consideration the problem is even more acute. 5.7 Challenges .................................................................................... 114 G¨ odel’s texts manifest an explicit and persistent motif of objectifying conBibliography ....................................................................................... 116 that cepts (or, in his terminology, notions). Therefore, rather than assume objects and concepts can be distinguished and im/exposing modalities of Working Together for the Well-being of Migrants ........................... 119 such on/in the texts, I would rather bundle objects and conBarryarticulation Halliday cepts together. As Foucault suggests, I will analyse statements (which observe objects and operate concepts) from the point of view of transcription, that is as elements that men produce, manipulate, use, transform, 11 They

most likely are so pronounced in other parts of The Archaeology. object/concept tension has been widely discussed in the literature. Two of the most prominent relevant references are Frege (1983) and Benacerraf (1983a). 12 This

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exchange, combine, decompose and recompose, and possibly deBibliography ......................................................................................... 60 of the stroy (Foucault 1972, 105). More precisely, I will analyse the roles verbs mean, express, interpret, represent, correspond, denote, sig4. The Ethics of Migration. nify, say and understand in recasting relations between objects/notions Reflections on Recent Migration Policies and in the texts.and Europe ........................................... 61 andstatements “Non-policies” in Italy Laura Zanfrini

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1.2.1

Abbreviate notations

4.2 Initiatives for Governing Family and Humanitarian TheMigration: most trivial use Migration of the verbs is in introducing definitions Labour but above not Workers’ Migration ............. 73 that abbreviate notations, and are therefore, according to the text, dispens4.3 From Guest Workers to Unwelcome Guests .................................. 82 able in principle (1931, 147). Typical examples include statements such 4.4 Selective Policies and the Brain Drain............................................ 87 as Bew x means: x is a provable formula and we denote the nth 4.5 Equal Opportunity and Denied Opportunities 90 verbs class sign in the sequence of all class signs by ................................ R(n) (1931, 149). The say and understand are also used to the same effect, as does 97 the verb Bibliography ......................................................................................... represent, which may occupy such a role, as indicated by the parallelism 5.German Colombia:letters Including in abbreviation Their Societies for of Origin 101 willEmigrants be used in finite....... sequences of Urs Watter natural numbers i.e., X for x1 , . . . , xn ; Y for y1 , . . . , ym . Greek letters 5.1 and Responsibility φ, ψ,State χ . . .Interest will represent functions (1934, 347). towards their Citizens Living Abroad ........................................... 102 The trivialising view of such abbreviate notations is most markedly 5.2 Applied .............................................................................. 104 and expressed byEthics the parallelism If φ denotes an unknown function, and Ethics ......................................................... ψ5.3 . . , ψk arePolicy known functions ... (1934, 368). To denote 106 and to be 1 , .Migration 13 are collapsed here to one and the same status. This trivialising 5.4 Migration Policy in Colombia ...................................................... 108view of abbreviate notations as completely lucid was criticised as circular in Quine’s 5.5 “Colombia nos une”...................................................................... 109 classic Two Dogmas of Empiricism (Quine 1961, chapter 2). Quine does 5.6 Alianza exclude fromPaís his.................................................................................. claim abbreviations in strictly formal languages; 112 in G¨ odel’s 5.7 Challenges .................................................................................... 114 text, however, we can see the dangers of treating abbreviate notations too na¨ ıvely, even ....................................................................................... when one is very close to the strictly formal context. Bibliography 116

One of the abbreviations that G¨odel introduces is the following: We Working Together for the Well-being of Migrants abbreviate certain formal expressions as ........................... follows: z0 for119 0, z1 for Barry Halliday N (0), z2 for N (N (0)), etc. (1934, 358) N (x) here is the formal representation of the successor of x, i.e. of x + 1. Instead of writing a numeral the way it should be written in the formal system, say N (N (0)) for the number 2, one writes the shorthand z2 . There seems to be no danger here. z2 does 13 Unless

one reads here an ontological statement, that the unknown can only be denoted, whereas what is known actually is. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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not belong to the formal system, but whenever we see it, we know which Bibliography ......................................................................................... 60 text of the formal system must replace it. But things become more delicate when we encounter zp , where p is 4. The Ethics of Migration. the extremely andMigration uncomputed number of a certain complicated forReflections on big Recent Policies mula. The supposedly na¨ıveand abbreviation enables G¨ odel not only61to write and “Non-policies” in Italy Europe ........................................... Laura Zanfrini a text that would otherwise be too long to write in a publishable article to mention obstacleforfor a referee), but.. also 4.1 (not Restrictive Policiesan andimpossible Structural Demand Immigrant Labour 65 does away with thefor need to conduct a complicated computation. What goes on 4.2 Initiatives Governing Family and Humanitarian hereMigration: is not simply saving time and effort, but also rendering possible Labour Migration but not Workers’ Migration ............. 73 what would otherwise be practically impossible, a qualitative leap that enables 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the writer and reader to avoid completely, and not only to abbreviate, a 4.4 Selective Policies and the Brain Drain............................................ 87 certain computation. 4.5 Equal Opportunity andleap Denied Opportunities 90 to the But the qualitative from the numeral................................ in the formal system Bibliography ......................................................................................... supposed abbreviation does not end here. Consider the statement 97 N (zn ) = zn+1 on the same page, where n is a variable. This ‘abbreviated’ statement 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 is impossible to expand into a text in the formal system. Indeed, while zn Urs Watter contains the variable n, the formal system has no means of expressing a 5.1 State Interest and Responsibility sequence of embedded N ’s of a variable length. This ‘abbreviated’ statetowards their Citizens Living Abroad ........................................... 102 ment therefore contracts infinitely many statements of the formal system. Applied 104 It5.2does not Ethics simply.............................................................................. abbreviate an expression, but essentially enriches the 5.3 Migration Policyofand ......................................................... 106zn as a expressive abilities theEthics writer. Of course, one could reconstruct place holder for a variable in the formal system (say, w), rather than for 5.4 Migration Policy in Colombia ...................................................... 108 a numeral that depends on a variable (even though this is not how G¨ odel 5.5 “Colombia nos une”...................................................................... 109 presents it). In that case one would expand N (zn ) = zn+1 into the formal 5.6 Alianza País .................................................................................. 112 statement N (w) = N (w), as there is no ‘more primitive’ way to express 5.7 right Challenges the hand .................................................................................... side. The original statement N (zn ) = zn+1 , which114 is not an explicit tautology, turns into an explicit tautology. The abbreviate Bibliography ....................................................................................... 116 notation turns out to be more manipulative and less na¨ıve than would seem at Working Together Well-being of Migrants ........................... first sight. To say for thatthe abbreviate notations are dispensable in 119 principle Barry Halliday is to use a very extreme form of that in principle grammar, which we reviewed in the previous section.

This observation suggests how the use of a supposedly simple abbreviation almost imperceptibly crosses the line between languages, and how it forms a first step in confounding variables and constants (a concern to be further pursued in the eighth section of the next chapter). Indeed, where Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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we think of zn as containing a variable n, this n is a variable of arithBibliography 60 zn is metic rather ......................................................................................... than a variable of G¨odel’s formal system, and therefore not an abbreviation of a text in the formal system, but the application to 4. The Ethics of Migration. a variable of a function from the realm of non-negative integers into the Reflections on Recent Migration Policies formal system. If, alternatively, we insist on maintaining that this and “Non-policies” in Italy and Europe ........................................... 61 n is a constant, then we must confront such phrases as each natural number Laura Zanfrini n4.1 (1934, 358), Policies which make the border between constant Labour and variable Restrictive and Structural Demand for Immigrant .. 65 very fluid indeed. 4.2 Initiatives for Governing Family and Humanitarian I am not Labour claiming that there is aWorkers’ formal error in the proof,73because Migration: Migration but not Migration ............. one can easily circumvent the problem via a proper logical reformulation. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Since the problem can be easily circumvented, from a logical point of view 4.4 observation Selective Policies and thebut Brain Drain............................................ 87 my is nothing nit-picking of marginal interest. I neverthe4.5 Equal and Denied Opportunities ................................ less insist Opportunity upon this issue here, because from the point of view of 90 a critical reading this issue is suggestive of the distance between the actual text and Bibliography ......................................................................................... 97 a supposedly underlying correct logical reformulation. What I reject is a 5.reading Colombia: Their Societies of Origin ....... 101supposthatIncluding ignores Emigrants the surfaceintext and restricts itself to the Urs Watter edly underlying formal text, which might be practically unwritable or at 5.1 State Interest Responsibility least, were it to and stand alone, inaccessible for mere mortals of our limited towards their Citizens Abroad ........................................... capacities. It is the gap Living between actual text and the shadow of102 the sup5.2 Applied Ethics .............................................................................. 104 posedly precise formal text (especially as this gap interacts with the observations concerning transcription devices to be106 surveyed 5.3 Migration Policythe andmore Ethicscomplex ......................................................... below), that bestows upon the bigger picture the productive blurriness I 5.4 Migration Policy in Colombia ...................................................... 108 wish to bring to the foreground as enabling the text’s intelligibility. Note 5.5 “Colombia nos une”...................................................................... 109 that this productive blurriness is effectuated in part by using the same verbs 5.6 Alianza País .................................................................................. (mean, represent, denote, say and understand) to express 112 the above (relatively) simple form of transcription and the other more complicated 5.7 Challenges .................................................................................... 114 transcription forms to be surveyed below. Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119

1.2.2 From primitive signs to numbers Barry Halliday A major innovation and an essential pivot point of G¨ odel’s manoeuvre consists in relating metamathematical notions to arithmetic ones. Such a move requires, of course, a preliminary articulation of both fields. Notions which relate to the system considered purely formally, the text posits, may be called metamathematical (1934, 355). MetamathematiRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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cal notions include for example, “variable”, “formula”, “sentential 15 ......................................................................................... 60 Bibliography formula”, “axiom” ,”provable formula”, and so on (1931, 157). The licence to transform the metamathematical into arithmetic comes 4. The Ethics of Migration. from the factonthat for Migration metamathematical considerations it does not Reflections Recent Policies matter what objects areand chosen as........................................... primitive signs, and we and “Non-policies” in Italy Europe 61 shall Laura Zanfrini assign natural numbers to this use. Consequently, a formula will be finite sequence natural numbers (1931, 147). 4.1 a Restrictive Policies andof Structural Demand for Immigrant LabourThere .. 65 is no metamathematical objection, the text proclaims, to replace the primitive 4.2 Initiatives for Governing Family and Humanitarian symbols ∀, x and → by the numbers 2 and 3.Migration Metamathematics Migration: Labour Migration but not1,Workers’ ............. 73 is thus articulated as the discursive domain that considers systems purely formally, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 but is ignorant of the choice of primitive signs; it considers the outward ap4.4 Selective Policies and the Brain pearance of formal expressions, butDrain............................................ not the specific content of this87 outward 4.5 Equal Opportunity and Denied Opportunities ................................ 90 appearance. This vague situation, however, turns out to be not sufficiently Bibliography ......................................................................................... 97 felicitous for the text, and is therefore amended by two footnotes on the same 5.page. Colombia: Emigrants in Theirnumbers Societies of 101 First, Including rather than assign natural toOrigin the role....... of primitive Urs Watter

signs, we map the primitive signs one-to-one onto some natural 5.1 State Interest and Responsibility numbers. And since Numbers, of course, cannot be arranged in a towards their Citizens Living Abroad ........................................... 102 spatial order (they are, after all, abstract notions), a formula turns out 5.2be Applied 104 to not a Ethics finite .............................................................................. sequence of natural numbers, but a more abstract construct: a function that assigns numbers-as-place-names to numbers-as5.3 Migration Policy and Ethics ......................................................... 106 mapped-onto-primitive-signs-taking-these-places. 5.4 Migration Policy in Colombia ...................................................... 108 These amendments reflect the stance that numbers are not just any 5.5 “Colombia nos une”...................................................................... 109 objects chosen as primitive signs. Rather, they impose their abstraction 5.6 Alianza País to .................................................................................. 112system. (not being able take a concrete physical place) upon the formal Challenges .................................................................................... I5.7 bother with this nit-picking, because this is our first evidence114 as to the manner in which the texts cross over from the signifier as a concrete Bibliography ....................................................................................... 116 object (a primitive sign that can be written on paper) to the signifier as a Working Together for the of Migrants ........................... structural abstraction orWell-being platonic object (a number). The proof119 will carry Barry Halliday 16 with it this double setting. 14 A formula here is a sequence of signs that obeys the syntactical requirements of the given formal system. One should think here of a ‘proposition’, ‘statement’ or ‘expression’ rather than of a formula for computing or constructing something. 15 A formula without free variables. 16 At least double! We’ve already seen how such settings tend to proliferate when discussing Benveniste’s I and Austin’s shoot above.

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However, we shall have to be more specific in order to reflect the full Bibliography 60 is esextent of the ......................................................................................... relation between metamathematics and arithmetic that tablished in the texts. The texts describe an explicit dictionary, which trans4. The Ethics of Migration. lates each sign of a formal system into an integer (not unlike children who Reflections on Recent Migration Policies make up codes by replacing eachEurope letter of........................................... the alphabet by some other and “Non-policies” in Italy and 61 sign). As a result, a formula in the formal system, which is a sequence of signs, can Laura Zanfrini be a sequence of integers. Then some arithmetic 4.1translated Restrictive into Policies and Structural Demand for Immigrant Labour ..procedure 65 is applied to transform each such integer sequence into a single integer, in 4.2 Initiatives for Governing Family and Humanitarian a way that guarantees that no two formal expressions are ............. transformed Migration: Labour Migration but not Workers’ Migration 73 into the same integer. This representation, correspondence, understand4.3 From Guest Workers to Unwelcome Guests .................................. 82 ing or expression of meaning17 is a mechanico-computational process 4.4translation. Selective Policies the Brain Drain............................................ 87 XXX of Claimsand about formal objects (‘the sequence of signs is4.5anEqual axiom’, ‘the sequence of signs XXX is................................ a proof of the sequence of Opportunity and Denied Opportunities 90 signs Y Y Y ’) ......................................................................................... become, via this transliteration, claims about numbers Bibliography 97 (‘the number x represents a sequence of signs which is an axiom’, ‘the number 5.xColombia: Emigrants TheirisSocieties ....... 101of signs representsIncluding a sequence of signs in which a proof of of Origin the sequence Urs Watter represented by the number y’). 5.1 State and Responsibility The Interest arithmetic relations between (or classes of ) natural numtowards their Citizens Living ........................................... 102 bers that in this manner areAbroad associated with the metamathemat5.2 Applied Ethics .............................................................................. 104 ical notions defined so far, for example, “variable”, “formula”, “sentential “axiom”, “provable formula”, and 5.3 Migration formula”, Policy and Ethics ......................................................... 106so on, will be denoted by the same words in small capitals (1931, 157); 5.4 Migration Policy in Colombia ...................................................... 108 that is, rather than say ‘the number x represents a sequence of signs which 5.5 “Colombia nos une”...................................................................... 109 is an axiom’, we say ‘the number x is an axiom’; rather than say that ‘the 5.6 Alianza País .................................................................................. number x represents a sequence of signs which is a proof of the112 sequence of represented by the number y’ we say that ‘x is a proof 5.7signs Challenges .................................................................................... 114 of y’. This typographic device articulates two distinct domains: the lower case Bibliography ....................................................................................... 116 metamathematics, and the small-capitals arithmetic. Working Together for the Well-being of Migrants ........................... However, rather than transliterating between two stable and119 indepenBarrydomains Halliday — metamathematics and arithmetic — this textual device dent 17 I make a point of noting the verbs used in this context to indicate that the text does not attempt to segregate the various mechanisms of transcription documented in the various subsections of this section by distinguishing specific verbs for each form of transcription. This is part of the rhetorical technique of simultaneously distinguishing and conflating discursive modes in order to produce meaning, that is to assert repetition across differences.

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appears, at certain times, to uproot and haul the entire edifice of metaBibliography ......................................................................................... 60 a full mathematics into arithmetic; not just a transliteration, but rather transubstantiation. The introduction specifies that metamathematical 4. The Ethics of Migration. notions (propositions) thus become notions (propositions) about Reflections on Recent Migration Policies natural numbers in orItaly sequences of them (1931, 147). This statement, and “Non-policies” and Europe ........................................... 61 perhaps not entirely clear, is further detailed in a footnote, which explains Laura Zanfrini that the procedure described an isomorphic 4.1 Restrictive Policies and Structuralabove Demandyields for Immigrant Labour .. 65 image of the system PM 18 in the domain of arithmetic, and all meta4.2 Initiatives for Governing Family and Humanitarian mathematical arguments as wellMigration be carried out73in this Migration: Labour Migrationcan but just not Workers’ ............. isomorphic image. This is what we do below when we sketch the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 proof; that is, by “formula”, “proposition”, “variable”, and so on, 4.4 must Selective Policies and the Brainthe Drain............................................ we always understand corresponding objects of 87 the isomorphic image. Here weDenied no longer have metamathematics transliterated 4.5 Equal Opportunity and Opportunities ................................ 90 into arithmetic, but, rather, metamathematics discarded or abandoned in Bibliography ......................................................................................... 97 favour of its image as a sub-domain of arithmetic. 5. Colombia: Including Emigrants Societies of Origin are .......ambiguous, 101 Many references in the textsintoTheir the metamathematical

Urs conform Watter with either interpretation (transliteration and transubstantiand 5.1 StateItInterest and Responsibility ation). does seem, however, that the 1931 text tends towards keeping towards their Citizens Living Abroad ........................................... 102 in the metamathematics and arithmetic distinct, and prefers to operate 5.2 Applieddomain, Ethics .............................................................................. 104the disarithmetic whereas the 1934 text leans towards blurring tinction between metamathematics and its arithmetic image, and operates 5.3 Migration Policy and Ethics ......................................................... 106 sometimes in one domain, sometimes in the other, and sometimes treats 5.4 Migration Policy in Colombia ...................................................... 108 both domains at once. 5.5 “Colombia nos une”...................................................................... 109 This confounding of domains seems to relate closely to a fact of the 5.6 Alianza .................................................................................. 112 a few texts, which,País although stated explicitly and obviously, took me quite readings to properly absorb. The texts do not quite attempt 114 to mathe5.7 Challenges .................................................................................... matically prove that some formal systems contain an undecidable Bibliography ....................................................................................... 116formula (namely, a proposition such that neither it nor its negation are provable). Working Together the mathematically Well-being of Migrants ........................... 119x and y, What the texts dofor prove is that there are numbers, Barry have Halliday which the property of being formulas, such that one of which has the arithmetic property of being the negation of the other, and such that both x and y have the arithmetic property of being not provable. There is no attempt to control mathematically the transliteration/transubstantiation of formal systems into arithmetic, and to show that the arithmetic statements 18 PM

is Principia Mathematica, the main formal system G¨ odel uses in his argument.

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indeed imply the existence of undecidable formulas in formal systems. Bibliography ......................................................................................... Before we explain this seemingly broken link, let us make 60 this gap more manifest. I claimed above that the assertion ‘the number x represents 4. The Ethics of Migration. aReflections sequence of which is an Policies axiom’ is an arithmetic assertion. This onsigns Recent Migration would be true only ifinwe could claim using strictly arithmetic and “Non-policies” Italy and express Europe this ........................................... 61 Laura Zanfrini tools (logical connectives and operators, the equality predicate, and the addition and multiplication The text does explicitly present 4.1 Restrictive Policies and functions). Structural Demand for Immigrant Labour .. 65 such transliteration. slow and gradual process allows to translate all the meta4.2 Initiatives forAGoverning Family and Humanitarian mathematical notions, which are relevant to theMigration argument, into arithmetic Migration: Labour Migration but not Workers’ ............. 73 notions. However, when, for instance, the text defines the operation x ∗ y 4.3 From Guest Workers to Unwelcome Guests .................................. 82 (which, given the number x of a sequence of signs XXX, and the number 4.4 Selective Policies and the Brain Drain............................................ 87 y of the sequence of signs Y Y Y , returns the number corresponding to the 4.5 Equal Opportunity Denied Opportunities 90 concatenation of the and sequences: XXXY Y Y ),................................ an arithmetic definition is given, which is then followed by the comment x ∗ y corresponds to the Bibliography ......................................................................................... 97 operation of “concatenating” two finite number sequences (1931, 5.165). Colombia: in Their Societies Origin ....... 101formula What Including is missing Emigrants is an attempt to validate thatofthe arithmetic Urs Watter indeed corresponds to the metamathematical operation. Such attempt is 5.1 only State missing Interest and Responsibility not in this and in other specific occurrences. Nowhere do the towards their Citizens Living Abroad ........................................... 102 texts attempt to mathematically validate the claimed correspondence. 5.2 Applied Ethics .............................................................................. It is crucial to explain here that I make no claim that 104 the corre5.3 Migration Policy and Ethicsmetamathematics ......................................................... spondence assumed between and arithmetic 106 should be marked as invalid. do, nevertheless, insist on pointing out that the text 5.4 Migration PolicyI in Colombia ...................................................... 108 does not manifest a need to validate the correspondence. The text contracts 5.5 “Colombia nos une”...................................................................... 109 two a-priori distinct domains: the material domain of text (formal relations 5.6 Alianza País .................................................................................. 112 between signs) and the ideal domain of numbers (arithmetic relations be5.7 Challenges .................................................................................... 114 tween numbers). But the link that is supposed to validate the contraction isBibliography not given. ....................................................................................... 116

It is easy to excuse this ‘broken’ link. In G¨ odel’s view the actual formal Working Together for the Well-being of Migrants ........................... 119 system and its metamathematical study are not mathematical objects. The Barry Halliday term meta reflects, in this case, an outside. Obviously, there can be no mathematical validation of a link between something mathematical and something non-mathematical. The link is to be established by G¨odel and the readers, who are to acknowledge a valid but non-mathematical link. It is only after we have managed to carry over metamathematics into arithmetic that we can start to analyse things mathematically. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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This formative attitude allows for the manifest ambiguous relation Bibliography ......................................................................................... 60 between metamathematics and arithmetic in the text. The transfiguration of the former into the latter is meant both to articulate and set metamath4. The Ethics of Migration. ematics and arithmetic apart, and at the same time to suppress the former Reflections on Recent Migration Policies and it into the latter. andincorporate “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

The braid of the two understandings, says Barthes, creates 4.1 equivocation. Restrictive Policies and Structural Demand for Immigrantresults Labour ..from 65 two an And in fact the equivocation voices, received on an equal basis: there is an interference of two 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ 73 lines of destination. Put another way, theMigration double ............. understanding (double the to basis for a play words, cannot be 4.3 Fromentendre), Guest Workers Unwelcome Guestson .................................. 82 analysed in simple terms of Brain signification (two signifieds for 87 one sig4.4 Selective Policies and the Drain............................................ nifier); for that there must be the distinction of two recipients; 4.5 Equal Opportunity and Denied Opportunities ................................ 90 and if ... both recipients are not given in the story, if the play on Bibliography ......................................................................................... 97 words seems to be addressed to one person only (for example, the reader), this person must be imagined as being divided into 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 two subjects, two cultures, two languages, two zones of listenUrs Watter ing (whence the traditional affinity between puns and “folly” or 5.1 State Interest and Responsibility madness: dressed motley, a divided costume, 102 was once towardsthe theirFool, Citizens Livingin Abroad ........................................... the purveyor of the double understanding ). In relation to an ide5.2 Applied Ethics .............................................................................. 104 ally pure message (as in mathematics), the division of reception 5.3 MigrationaPolicy and Ethics ......................................................... 106 constitutes “noise,” it makes communication obscure, fallacious, hazardous: Yet this noise, this uncertainty are108 emitted 5.4 Migrationuncertain. Policy in Colombia ...................................................... by discourse with a view toward a communication: 109 they are 5.5 the “Colombia nos une”...................................................................... given to the reader so that he may feed on them: what the reader 5.6 Alianza País .................................................................................. 112 reads is a countercommunication; and if we grant that the double 5.7 Challenges .................................................................................... 114 words understanding far exceeds the limited case of the play on Bibliography ....................................................................................... 116 or the equivocation and permeates in various forms and densities, all classic writing (by very reason of its polysemic vocation), we Working Together for the Well-being of Migrants ........................... 119 see that literatures are in fact arts of “noise”; what the reader Barry Halliday consumes is this defect in communication, this deficient message; what the whole structuration erects for him and offers him as the most precious nourishment is a countercommunication; the reader is an accomplice, not of this or that character, but of the discourse itself insofar as it plays on the division of reception, the impurity of communication (Barthes 1974, 145). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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I hope to have demonstrated, and to continue to demonstrate, how Bibliography ......................................................................................... 60 even in mathematics there is no, pace Barthes, ideally pure message (as in mathematics). I hope to show how noise and double under4. The Ethics of Migration. standing operate at the heart of a mathematical text to produce counReflections on Recent Migration Policies tercommunication. follyEurope and the plurality of speakers/readers is and “Non-policies” in How Italy and ........................................... 61 operative in the process of semiosis without imposing a simplistic duality Laura Zanfrini on text. This would mean that mathematics fails,Labour or that it would 4.1the Restrictive Policies andnot Structural Demand for Immigrant .. 65 be any less useful. It would, however, mean that the hypothesis that math4.2 Initiatives for Governing Family and Humanitarian ematics succeeds to the extent that it Workers’ does because of its ............. supposed Migration: Labour Migration but not Migration 73purity — this hypothesis will find itself undermined. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Here we have extracted two models that act simultaneously: in the 4.4 Selective Policies and the Brain Drain............................................ 87 one the grammar of metamathematics (I mean here, of course, that part 4.5metamathematics Equal Opportunitythat and Denied Opportunities 90 of is imported into the................................ arithmetical language), explicitly articulated as a-priori non-mathematical, is made parallel to a subBibliography ......................................................................................... 97 grammar of arithmetical grammar; in the other model metamathematics 5.isColombia: Including Emigrants in Their Societiesinside of Origin ....... 101I claim already an arithmetic sub-grammar operating arithmetic. Urs Watter here that the process of semiosis in the text involves a simultaneous attempt 5.1keep Statethese Interest Responsibility to twoand models apart, and rely upon both. towards their Citizens Living Abroad ........................................... 102 Indeed, the first model suggests two separate manoeuvres: the first of 5.2 Applied which wouldEthics be a .............................................................................. non-mathematical endorsement of a relation 104 between a 5.3 Migration Policy anddomain, Ethics ......................................................... 106 material and an ideal and the second would be a mathematical analysis, which no longer has anything to do with the non-mathematical 5.4 Migration Policy in Colombia ...................................................... 108 domain (the metamathematics of formal systems). If we were to endorse 5.5 “Colombia nos une”...................................................................... 109 this first model alone, then G¨odel’s argument would be a combination of 5.6 Alianza País .................................................................................. 112 a non-mathematical argument (correspondence between metamathematics 5.7 Challenges and arithmetic).................................................................................... and a mathematical argument (the proof of the 114 arithmetic analogue of undecidability). We could then make no mathematical Bibliography ....................................................................................... 116 claim concerning the undecidability of formal systems as such. Working Together for the Well-being of Migrants ........................... 119 If, on the other hand, we were to endorse the second model alone, then Barry Halliday we could no longer rigorously segregate mathematics from metamathematics. This is a problem, as the formal articulation of language and metalanguage rules over the entire argument as it is laid out in G¨odel’s text. Without this articulation, for example, the distinction of the semantic and syntactic argument collapses, as this distinction is all about whether a certain universal quantifier is to be attributed to the language or to the metaRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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language (see the section G¨ odel’s argument in brief in the introduction). Bibliography ......................................................................................... 60 mathMore importantly, if we reduce meta-language to its image inside ematical language, it is much more difficult to argue against the faulty 4. The Ethics of Migration. circularity of the proof in the way that G¨odel does, as it would then Reflections on Recent Migration Policies involve an immediate, rather an indirect form of self-reference and “Non-policies” in Italy andthan Europe ........................................... 61 (see page below). Laura85Zanfrini Each model threatens to upsetDemand an important aspectLabour of the.. text. 4.1 Restrictive Policies and Structural for Immigrant 65 The first threatens mathematical jurisdiction over its meta, whereas the second 4.2 Initiatives for Governing Family and Humanitarian threatens the independence of mathematics from its meta. The confoundMigration: Labour Migration but not Workers’ Migration ............. 73 ing of the two models into one seamless ambiguity is a crucial component 4.3 From Guest Workers to Unwelcome Guests .................................. 82 for enabling G¨ odel’s end-product: a mathematical analysis of a metamath4.4 Selective Policies and the Drain............................................ 87 ematical object.19 True, thisBrain ambiguous combo still upsets the boundary 4.5 Equalmathematics Opportunity and Opportunities ................................ 90 between andDenied its outside; but at least it allows mathematics to say something......................................................................................... about formal systems. The argument works, not despite Bibliography 97 this upsetting of boundaries, but due the incorporation of these upset bound5.aries. Colombia: Including in Their Societies of Origin ....... 101 Ambiguity hereEmigrants is not destructive, but rather conductive and proUrs Watter 20 ductive of meaning. And I would like to show that the textual formation 5.1 State Interest andtexts Responsibility operated in G¨ odel’s is in fact even more complex and productive than towards their Citizens Living Abroad ........................................... 102 is suggested by this initial ambiguity. 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics back ......................................................... 106 1.2.3 From numbers to signs through proofs 5.4 Migration Policy in Colombia ...................................................... 108 The manoeuvre we have just surveyed, complex as it is, is only half the 5.5 “Colombia nos une”...................................................................... 109 story. Now that we are in the abstract realm of arithmetic, we have to 5.6 Alianzaeverything País .................................................................................. 112 re-encode into a formal system, in order to guarantee that our proof can be carried out in full rigour according to the prevailing114 standards 5.7 Challenges .................................................................................... Bibliography ....................................................................................... 116between 19 This situation has some bearing on the debate concerning the distinction synthetic and analytic statements (e.g. Putnam 1975, chapter 2), and may therefore shed

Working for the Well-being of between Migrants some lightTogether on the history of the relationship G¨ o........................... del and the Vienna119 circle.

20 In this Barry Halliday context the following observation by historian of mathematics Jacob Klein

suggests itself (his concepts of the first and second class are roughly equivalent to what we might call ‘concepts’ and ‘meta-concepts’ or ‘concepts about concepts’ respectively; for Klein numbers are concepts of the first class and variables are concepts of the second): in algebra we use concepts of the second class as though they were concepts of the first class ... what we call a symbol is nothing else but a concept of the second class interpreted as a concept of the first class (Klein 1985, 62–63). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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of 1930s formalists and intuitionists. We are already laden with a double unBibliography(arithmetic ......................................................................................... 60 derstanding and metamathematical) of the terms “formula”, “proposition”, “variable”, when the plot thickens, and we are told that 4. The Ethics of Migration. these doubly determined notions can (at least in part) be expressed Reflections on Recent Migration Policies by symbols ofinthe PM ........................................... itself. In particular, it61can be andthe “Non-policies” Italysystem and Europe shown that the notions “formula”, “proof array”, and “provable Laura Zanfrini formula” canPolicies be defined in theDemand systemforPM (1931, Labour 147). .. 65 4.1 Restrictive and Structural Immigrant G¨ odel does not take for granted that his metamathematical/arithmetic 4.2 Initiatives for Governing Family and Humanitarian notions can indeed beMigration expressedbut bynot theWorkers’ limited resources the formal Migration: Labour Migrationof ............. 73 system PM. Unlike the previous transliteration/transubstantiation, this trans4.3 From Guest Workers to Unwelcome Guests .................................. 82 formation from the language of arithmetic into the formal system PM is 4.4 Selective Policies and 87 of the not left unvalidated. In the fact,Brain the Drain............................................ most technical and tedious part 4.5 Equal Opportunity andshowing Denied Opportunities ................................ 90for the argument is devoted to that such translation is possible relevant metamathematical/arithmetic claims. The extent to which Bibliography ......................................................................................... 97 this translation is not taken for granted is reflected in the comment (apparently 5.made Colombia: Including Societies of Originthat ....... 101 to reconcile theEmigrants supportersinofTheir Hilbert’s programme) it is conUrs Watter ceivable that there exist finitary proofs that cannot be expressed 5.1the Stateformalism Interest and of Responsibility in P 21 (1931, 195). But despite (or perhaps because towards Citizens Abroad 102 escape of) the care their invested intoLiving managing this........................................... translation, it too does not 5.2 Applied Ethics .............................................................................. 104 multiplicity. The firstPolicy criterion regulates the transformation of an 106 arithmetic 5.3 Migration and that Ethics ......................................................... statement intoPolicy a statement in the language PM, the one most carefully ar5.4 Migration in Colombia ...................................................... 108 ticulated, relies on provability. Let n, m, k . . . be integers, and zn , zm , zk . . . 5.5 “Colombia nos une”...................................................................... 109 stand for the signs that represent them in the formal language PM. Given 5.6arithmetic Alianza País .................................................................................. an function Φ and a function G in the language PM,112 we shall say that the .................................................................................... formal functional expression G(u1 , u2 , . . .) represents 5.7 Challenges 114 Φ(x ... if G(zm , zn , . . .) = zk is provable formally whenever l , x2 , . . .) ....................................................................................... Bibliography 116 Φ(m, n, . . .) = k holds (1934, 358). Two mathematical procedures are to Working Together the Well-being(sometimes of Migrantsalso ........................... 119 be related, if this for representation referred to as expresBarry Halliday sion (1934, 359,361)) is to be valid: the arithmetic computation of Φ and the formal proof of statements about G. The text in fact promises a procedure, which, for some arithmetic functions Φ (the so called recursive functions, which we needn’t define here), constructs representations G in 21 For

our purposes the reader may ignore the differences between the various formal systems that G¨ odel refers to, in particular P and PM. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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PM, and transforms the computations of Φ into formal proofs concerning Bibliography ......................................................................................... 60 G. This formulation is careful not to have anything to do with mean4. The Ethics of Migration. ing, whatever may mean at this point. This point is explicitly Reflections on meaning Recent Migration Policies stated in the text. To the theorem, which guarantees the and “Non-policies” in introduce Italy and Europe ........................................... 61repreLaura Zanfrini sentability of recursive arithmetic functions by formal expressions, the text explains that the fact and that can be Demand formulated vaguelyLabour by saying 4.1 Restrictive Policies Structural for Immigrant .. 65 that every recursive relation is definable in the system P (if the usual 4.2 Initiatives for Governing Family and Humanitarian meaning is given the formulas of this system) is expressed in Migration: LabourtoMigration but not Workers’ Migration ............. 73 precise language, without reference to any interpretation of the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 formulas of P, by the following theorem (1931, 171). The formal ex4.4 Selective Policies and the Brain Drain............................................ 87 pression G will be equivalent to the arithmetic function Φ not because of 4.5 Equal Denied what theyOpportunity mean, but and because theOpportunities computation................................ of the latter can 90 be transformed into a......................................................................................... proof concerning the former. And therefore, one may Bibliography 97 alter somewhat the text of the representing G (even at the cost of slight shifts 5.of Colombia: Including in Their Societieslink of Origin ....... 101 This meaning), as long Emigrants as the computation–proof is maintained. Urs Watter slight abuse of notation is made explicit by the statement claiming that If 5.1 State Interest and Responsibility the value of Φ(x 1, x 2 , . . .) is independent of some variable xp , then towards their Citizens Living Abroad ........................................... G(u1 , u2 , . . .) need not contain the corresponding variable102 up (1934, 5.2 Applied Ethics .............................................................................. 104 358). It is somewhat strange, that when the text is supposed to prove 5.3 Migration Policy and Ethicsthen, ......................................................... 106 this representability of arithmetic functions by formal expressions, it ap5.4 Migration Policy in Colombia ...................................................... 108 peals to the fact that some formula intuitively has the desired sig5.5 “Colombia nos une”...................................................................... 109 nificance (1934, 359), and therefore means whatever it should mean for 5.6 argument Alianza País the to.................................................................................. work. Rather than prove what is promised, the112 1934 text regrets that the.................................................................................... proof is too long to give here. The 1931 text too 5.7 Challenges 114 regrets that it will give only an outline of the proof of this theorem Bibliography ....................................................................................... 116 because the proof does not present any difficulty in principle22 and Working Together for the171), Well-being 119 is rather long (1931, and inofa Migrants footnote ........................... on the next page explains Barry Halliday that when this proof is carried out in detail a certain element in it of course, is not defined indirectly with the help of its meaning but in terms of its purely formal structure. I must hasten to say that my mathematical training leads me to cast 22 For

a discussion of the in principle, consult the third subsection of the previous section of this chapter. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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no doubt on the conjecture that a complete formal proof can, in principle, Bibliography 60 such be given. But......................................................................................... I am not willing to discard as insignificant the fact that a proof is not in fact given, and that the syntactic operations of compu4. The Ethics of Migration. tation and formal proof are put in abeyance inside the cadre of semantic Reflections on Recent Migration Policies explanation. This isinexactly theEurope kind of........................................... gap between actual and61hypothand “Non-policies” Italy and esised which allows to confer one sort of understanding on another Laura text, Zanfrini phenomenon, across differences, conducing intelligibility. 4.1 Restrictive forcing Policiesrepetition and Structural Demand for Immigrant Labour .. 65 That an exact formal proof can, in principle, be written I do not doubt. 4.2 Initiatives for Governing Family and Humanitarian But Migration: that suchLabour a proofMigration can stand withoutMigration the accompaniment but alone not Workers’ ............. 73 of a semantic explanation I find hard to believe. However, since the problem of 4.3 From Guest Workers to Unwelcome Guests .................................. 82 a ‘purely formal’ text will be considered in the final chapter of this book, I 4.4 Selective leave it aside Policies for now.and the Brain Drain............................................ 87 4.5 Equal Opportunity Denied Opportunities 90 which Before we turn toand analyse the articulation................................ of semantic meaning, the text fails ......................................................................................... or neglects to adequately set apart from the above 97 formalist Bibliography notion of representation or expression, we should point out how the am5.biguity Colombia: Including Emigrants in subsection Their Societies of Origin considered in the previous interacts with....... the 101 ambiguity Urs Watter considered here. 5.1 State Interest and Responsibility Representation is supposed to convert an arithmetic expression and towards their Citizens Living Abroad ........................................... 102 computation into a formal expression and proof. This conversion is meant 5.2link Applied Ethics .............................................................................. to the arithmetic and formal points of view by going from 104 arithmetic 5.3aMigration Policy and Ethics ......................................................... 106 to the to new formal coding, rather than going back from arithmetic original metamathematical claim. However, we have noted above108 that one 5.4 Migration Policy in Colombia ...................................................... should not be able to prove mathematically a statement about a meta5.5 “Colombia nos une”...................................................................... 109 mathematical notion such as expression or proof, since this may result 5.6 Alianza País .................................................................................. 112 in ‘crossing the line’ between mathematics and its meta. And when we dis5.7 Challenges .................................................................................... cuss the provability of a formal coding of an arithmetic relation 114 expressing aBibliography metamathematical claim, the same problem reappears. ....................................................................................... 116 The 1931 text takes this objection more seriously than the 1934 text. Working Together for the Well-being of Migrants ........................... 119 The 1934 text simply states that given a valid arithmetic relation, the Barry Halliday provability of the relation’s representation by a formal expression follows (1934, 358–359). Theorem V of the 1931 text (page 171), however, states that given a valid arithmetic relation, the arithmetic property provable holds for the number encoding the formal expression. In the 1931 text, we make metamathematical claims, translate them into arithmetic ones, code these arithmetic claims formally, and then encode the provability of these Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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formal claims arithmetically again. Theorem V then states that the earlier Bibliography ......................................................................................... arithmetic relations imply the latter ones. The refusal to deal with60a metamathematical notion unless it is turned arithmetical, for a moment, takes 4. The Ethics of Migration. the upper hand. But by 1934 the need for a second arithmetic re-encoding Reflections on Recent Migration Policies of objects in and claims about is ignored, except,61perhaps and “Non-policies” in Italy and formal Europesystems ........................................... (this not quite clear), in the footnote on page 360, added in the 1964 LauraisZanfrini publication, which saysand that the formal expression that was constructed is 4.1 Restrictive Policies Structural Demand for Immigrant Labour .. 65 not the undecidable sentence, but only denotes it. 4.2 Initiatives for Governing Family and Humanitarian This 30 years clarification onlyMigration to deepen the ambiguity Migration: Labourlate Migration but notserves Workers’ ............. 73 built into both texts. If the text is to be finite, the process of translation 4.3 From Guest Workers to Unwelcome Guests .................................. 82 must somewhere come to an end. One has to work, eventually, either in 4.4 Selective Policies and the Brain Drain............................................ 87 arithmetic or in a formal system. The 1931 text ends up working in arith4.5 Equal and Deniedmay Opportunities ................................ 90 who metic. ButOpportunity such an abstraction be frowned upon by formalists, require mathematics to be done in a formal system. The 1934 text Bibliography ......................................................................................... 97 ends up working at the level of formal texts, but thirty years later reopens the 5.question. Colombia: Including Emigrantsregulating in Their Societies of Origin ....... 101 The double-entendre the metamathematics-arithmetic Urs Watter interface interacts here with the carefully articulated formal representation 5.1arithmetic State Interest Responsibility of in and formal systems to produce a potentially infinite chain of towards their Citizens Living Abroad ........................................... 102 translations. 5.2 Applied Ethics .............................................................................. 104 — is The decision to stop at a certain level — formal or arithmetic 5.3 Migration Ethics ......................................................... 106 arbitrary. OnePolicy moreand translation is always implicit. One more translation may always bePolicy lurking inside the text only to be made explicit108 30 years 5.4 Migration in Colombia ...................................................... later. To point out the gravity of the situation, one should understand that 5.5 “Colombia nos une”...................................................................... 109 an arithmetic-to-formal-to-arithmetic translation does not end up with the 5.6 Alianza País .................................................................................. 112 original arithmetic statement. The original arithmetic statement or num5.7 is Challenges .................................................................................... 114 ber very different from the number produced by the double translation. G¨ odel’s translation processes are not inverses of each other. Further Bibliography ....................................................................................... 116 translations will continue to render resulting objects more and more complex. Working Together for the Well-being of Migrants ........................... 119 The issue is that nothing compels us to stop at the arithmetic level. Barry Halliday Should we, perhaps, take the arithmetic statement, express it in a formal language, and prove it in this language? But why stop there? Why not use G¨ odel’s numbering to encode the latter proof and theorem as numbers, and validate the arithmetic statement that a proof relation holds between these two numbers? And why not state and prove this arithmetic claim formally? And why not encode everything arithmetically again? Obviously, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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Explanations must come to an end (Wittgenstein 1953, §1). But this Bibliography ......................................................................................... 60 fact doesn’t prescribe any specific endpoint. Trying to simultaneously maintain formal and platonic points of view 4. The Ethics of Migration. puts the argument into a perpetual spin. One more translation is always Reflections on Recent Migration Policies implicitly there. On in theItaly other hand, trying to keep to a single point and “Non-policies” and Europe ........................................... 61of view Laura Zanfrini (either arithmetic-platonist or metamathematical-formalist) would leave us with no explicit validation either for the link theLabour ideal ..arithmetic 4.1 Restrictive Policies and Structural Demand forbetween Immigrant 65 and concrete formal application (in the platonist case), or between the 4.2 Initiatives for Governing Family and Humanitarian formal text andLabour what Migration it is supposed to Workers’ signify orMigration represent............. (in the 73 formalist Migration: but not 23 case). 4.3 From Guest Workers to Unwelcome Guests .................................. 82 G¨ odel chooses both at once. For G¨odel the link between ideal arith4.4 Selective Policies and the Brain Drain............................................ 87 metic and concrete formal text is valid because the ideal arithmetic domain 4.5 Equal Opportunity and Denied Opportunities ................................ 90 imand concrete formal domain are formally isomorphic (an isomorphic age of the system PM in the domain of arithmetic). The97link beBibliography ......................................................................................... tween the purely formal text and its interpretation (a proof of undecidabil5.ity) Colombia: Emigrants TheirtoSocieties of Origin ....... 101 is validIncluding because G¨ odel can in resort a platonically-inspired common Urs Watter ideal source for the purpose of linking them together (as he states, the 5.1 State Interest meaning whichand weResponsibility attach to the symbols is a leading principle in towards their Citizens Living Abroad ........................................... 102 the setting up of the system). 5.2 Applied .............................................................................. Surely, Ethics the platonic-formalist combo is not the only possible104 solution. Wittgenstein, for instance, argues in his Lectures on the Foundations of 5.3 Migration Policy and Ethics ......................................................... 106 Mathematics for a conventional and practical link between the various ways 5.4 Migration Policy in Colombia ...................................................... 108 of computing, proving and interpreting, rather than an ‘ideal’ or ‘structural’ 5.5 “Colombia nos une”...................................................................... 109 one.24 I am also well aware that devoted formalists and devoted platonists 5.6 defend Alianzatheir País .................................................................................. 112 can stances at least every bit as successfully as I can undermine 5.7 Challenges 114 them, so I do .................................................................................... not argue for the necessity of G¨ odel’s platonist-formalist combo. In fact I do not make any metaphysical argument at all.116 I merely Bibliography ....................................................................................... track down how a double-entendre is operative in the generation of meaning Working Together forthe thetext’s Well-being in G¨ odel’s text, on terms.of Migrants ........................... 119 Barry Halliday

I am presumptuous enough to conjecture that effects of meaning depend on an at least double entendre: the superimposition of more than one point of view and the constitution as the same of the different. I do not aim to prove this conjecture, because I cannot imagine a system that is 23 One 24 See

of the most celebrated discussion of such dilemmas is Benacerraf (1983b). footnote on page 104.

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rigorous enough to justify the term ‘prove’, and general enough to contain Bibliography ......................................................................................... the entire scope of the conjecture. In fact, I cannot even imagine 60 a system that can formulate the above conjecture as a rigorous conjecture. But as a 4. The Ethics of Migration. regulative idea, I find that this claim has a lot to do with how mathematics Reflections on Recent Migration Policies works. and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 1.2.4 What is the meaning of it all? 4.2 Initiatives for Governing Family and Humanitarian BackMigration: to the text. We Migration found an but operative ambiguity in the relation Labour not Workers’ Migration ............. 73 of the metamathematical discussion of a formal system and its arithmetic 4.3 From Guest Workers to Unwelcome Guests .................................. 82 image (independent strata translatable into each other, or a non-mathematical 4.4 Selective Policies and the Brain Drain............................................ 87 domain suppressible in favour of an arithmetic one). Maintaining this am4.5 Equal Denied Opportunities ................................ 90 biguity is Opportunity crucial for and a mathematical treatment of a metamathematical Bibliography ......................................................................................... 97 into claim. We also found that in justifying the translation from arithmetic a formal system, semantic arguments (based on the meaning of symbols) 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 took the place of formal considerations, even though formal considerations Urs Watter should and could in principle be applied. We also pointed out an indeci5.1 State andterminate Responsibility sion as toInterest where to the process of translation between arithmetic towards their Citizens Living Abroad ........................................... 102 and formal languages that is operative in the argument. We then went on 5.2assert Applied .............................................................................. 104 to theEthics generative power of this indecision, and the way it crossbreeds 5.3 Migration and Ethics formalism andPolicy platonism into a......................................................... meaningful mathematical analysis106 of formal systems. 5.4 Migration Policy in Colombia ...................................................... 108

Next we would like to show how the first ambiguity (allowing to main5.5 “Colombia nos une”...................................................................... 109 tain and infringe upon the boundary between mathematics and metamath5.6 Alianza País .................................................................................. 112 ematics) cross-breeds with the role of semantics in an argument that should, 5.7principle, Challengesbe .................................................................................... in syntactic. To do that we shall try to understand114 the grammar of the term meaning in this complex formation. Bibliography ....................................................................................... 116 One vein in the text constructs meaning as formal and arbitrary. Working Together for the Well-being of Migrants ........................... 119 It is easy to state with complete precision which sequences of Barry Halliday primitive signs are meaningful formulas and which are not (1931, 147). If it is indeed easy, it is because meaningfulness is defined here as an arbitrary feature of formal systems. A formal mathematical system is a system of symbols together with rules for employing them. The individual symbols are called undefined terms. Formulas are finite sequences of the undefined terms. There shall be defined a class Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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of formulas called meaningful formulas (1934, 346). Just so opens Bibliography the 1934 text.......................................................................................... But surely, some restriction must be made on this 60 arbitrary set of meaningful formulas. Indeed, on the same page we require that 4. The Ethics of Migration. ... the definitions of meaningful formulas ... be constructive; that Reflections on Recent Migration Policies isand ... “Non-policies” there shall be a finite procedure for determining whether in Italy and Europe ........................................... 61 aLaura given formula A is a meaningful formula. Here constructive is a Zanfrini formal requirement. here, is simply the effectLabour of (or ..a 65 title for) 4.1 Restrictive PoliciesMeaning, and Structural Demand for Immigrant this formal requirement. 4.2 Initiatives for Governing Family and Humanitarian But meaning is not always but thisnot formal effect.Migration While a............. formal73system Migration: Labour Migration Workers’ consists only of symbols and mechanical rules relating to them, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 explains the text, the meaning which we attach to the symbols is a 4.4 Selective Policiesinand thesetting Brain Drain............................................ 87 Meanleading principle the up of the system (1934, 349). 4.5 is Equal Opportunity andbut Denied Opportunities ................................ 90That is ing not in the system, it has actually been around all along. how undefined terms can actually stay undefined and at the same Bibliography ......................................................................................... 97 time have meaning. And that is why the statement that the undefined terms, 5.in Colombia: Emigrants .......(x)) 101means additionIncluding to variables, shallinbeTheir ... ¬,Societies ∨, &, →, of ≡,Origin Π (Πx(F Urs Watter “F (x) is true for all natural numbers x”, and may be regarded as 5.1 State Interest and Responsibility the logical product of F(x) over all x) (1934, 350) — that is why this towards their Citizens Living Abroad ........................................... 102 apparstatement can appear safely without provoking protests against the 5.2 oxymoron Applied Ethics .............................................................................. 104 ent between undefined and the following definition preceded by the term means. 5.3 Migration Policy and Ethics ......................................................... 106 But the relation formal system and its meaning 108 is best ex5.4 Migration Policy inbetween Colombiaa ...................................................... pressed by the claim that at a certain point in the argument, the meaning 5.5 “Colombia nos une”...................................................................... 109 of the symbols is immaterial, and it is desirable that it be for5.6 Alianza País355). .................................................................................. gotten (1934, Meaning, it appears, is a sort of clip-on. It112 was there 5.7 Challenges .................................................................................... 114 from the setting up, but it can be detached and re-attached at will (or desire). Bibliography ....................................................................................... 116 I shall spare the reader the quotations, which demonstrate that meanWorking for the Well-being Migrants ........................... ing canTogether be attached to formulas in of the formal system as well as119 to arithBarry Halliday metic expressions, that it can be preserved despite some formal modifications (such as binding a variable that does not have a free appearance in a given formula), and that one can express it, interpret according to it, and even replace it by the terms saying, significance, correspondence, expression and representation. But this clip-on meaning, which clips-on to various terms and systems, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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and which is replaceable by many of the other terms that operated in our Bibliography ......................................................................................... 60 than discussion above, is perhaps somewhat more constrained and imposing it first appears to be. In the 1964 postscript to the 1934 version, the text 4. The Ethics of Migration. suggests that the term finite procedure, which appeared at the beginning Reflections on Recent Migration Policies of the“Non-policies” 1934 text, should mean mechanical procedure. It goes on61 to claim and in Italy and Europe ........................................... that this meaning, however, is required by the concept of formal Laura Zanfrini system, whose essence it is thatDemand reasoning is completely 4.1 Restrictive Policies and Structural for Immigrant Labour ..replaced 65 by mechanical operations on formulas (1934, 370). Meaning here is 4.2 Initiatives for Governing Family and Humanitarian constrained byLabour some Migration prevailingbut concept and essence. This preeminent Migration: not Workers’ Migration ............. 73 meaning can also constrain formal notions like provability. Indeed, We 4.3 From Guest Workers to Unwelcome Guests .................................. 82 have seen that in a formal system we can construct statements 4.4 Selective Policiessystem, and the Brain Drain............................................ 87 some about the formal of which some can be proved and 25 cannot, what they say about the system (1934, 4.5 Equalaccording Opportunityto and Denied Opportunities ................................ 90 362). One could raise technical objections to using the above quotations as Bibliography ......................................................................................... 97 evidence for the claims that meaning is constrained by something prior to it 5.(essence), Colombia: and Including Emigrants in Their Societies of Originare .......constrained 101 that formal properties (such as provability) Urs Watter rather than strictly by finite procedures of verification. But by meaning, 5.1 State Interest andthe Responsibility one cannot escape fact that meaning is sometimes added arbitrarily, towards their Citizens Living ........................................... 102 and but at other occasions has Abroad always-already-been-there.

One may hypothesise that we’re dealing with two different 5.2 Applied Ethics .............................................................................. 104notions, which only accidentally, so to speak, share the same term; that in 5.3 Migration Policy and Ethics ......................................................... 106fact the former should be entitled artificial or formal meaning, and the latter proper 5.4 Migration Policy in Colombia ...................................................... 108 meaning. But a simple example can refute this hypothesis. Consider the 5.5 “Colombia nos une”...................................................................... arithmetic operation x∗y, which takes the number x representing109 a formula 5.6 Alianza 112 XXX and País the .................................................................................. number y representing a formula Y Y Y , and returns the number that represents the concatenation of the formulas: XXXY 5.7 Challenges .................................................................................... 114Y Y . As we have already observed, there is no attempt to justify that this arithmetic Bibliography ....................................................................................... 116 operation, defined by the equation Working Together the Well-being ........................... 119 x ∗ y ≡for εz{z ≤ [P r(l(x)of+Migrants l(y))]x+y & Barry Halliday

(n)[n ≤ l(x) → nGlz = nGlx]& (n)[O < n ≤ l(y) → (n + l(x))Glz = nGly]},

does indeed correspond to concatenation. The justification is folded within the proper meaning of the formal terms. But this generation of meaning 25 It

is easy to demonstrate that in this section of G¨ odel’s text the verbs say and mean are used as synonyms. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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(meaningitis?) presupposes the representation of a formula XXX by a Bibliography ......................................................................................... 60 and number x, which is an artificial ad-hoc constructed representation, which is only formal ly constrained. The correspondence depends on the 4. The Ethics of Migration. seamless cooperation between the artificial and proper meanings. The above Reflections on Recent Migration Policies formula means whatever it and is intended mean only if these two61 forms of and “Non-policies” in Italy Europe to ........................................... meaning build upon each other to produce an integral meaning. Even if we Laura Zanfrini insist that artificial and meanings terms, the meaning 4.1 Restrictive Policies andproper Structural Demandare fordifferent Immigrant Labour .. 65 of x ∗ y is a hybrid of the two forms of meaning. The full meaning of the 4.2 Initiatives for Governing Family and Humanitarian textMigration: is created Labour only if we allow the hypothesised formations of73 meaning Migration but two not Workers’ Migration ............. to advance past their differences. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 But even before these two hypothesised formations of meaning meld 4.4 Selective Policies and the Brain Drain............................................ 87 into an integral formation, each of these meanings already contains the 4.5 Equal Opportunity and Denied Opportunities ................................ 90 other. When the text constructs the arbitrary transcription of formulas into numbers,......................................................................................... it already builds on the proper meanings of the words Bibliography 97 and signs that are used to introduce the artificial meaning. And in order for the 5.undefined Colombia: Including Their Societies of their Origin ....... 101 terms of Emigrants the formalinsystem to express proper meaning, Urs Watter the one which was a leading principle in their articulation, an arbitrarily 5.1 Statecorrespondence Interest and Responsibility directed had to be imposed on specific signs (the N (·) of the towards Citizens Living ........................................... 1934 was antheir arbitrary choice forAbroad the successor function (·) + 1, in102 the sense 5.2 Applied Ethics .............................................................................. 104 that it could have been replaced by many other conventional signs, such as f of thePolicy 1931 and text), and ......................................................... an arbitrary form of number representation 5.3the Migration Ethics 106 26 (unary rather than, say, decimal) had to be enforced. As the two hypoth5.4 Migration Policy in Colombia ...................................................... 108 esised meaning formations depend on each other, and combine to produce 5.5 “Colombia nos une”...................................................................... 109 an integral meaning, I no longer see any use in hypothesising two separate 5.6 Alianza País .................................................................................. 112 for a meaning formations. I therefore endorse G¨ odel’s unified terminology complex notion.................................................................................... of meaning. 5.7 Challenges 114 The discussion above refers to the tension between traditional Bibliography ....................................................................................... 116 and ad-hoc relations between symbols and meanings. But even the relation beWorking Togetherasfor the Well-being Migrants ........................... tween meaning expressed contentofand meaning as the formal 119 constraint Barry Halliday of constructivity (the existence of a finite mechanical procedure for checking whether syntactic rules are obeyed) cannot be properly set apart. A formal system is built with an aim to express content, that is with meaning 26 A

unary representation of numbers is a representation based on an alphabet consisting of only one repeatable sign. If this sign is, say, 1, then the number 5 would be represented as 11111. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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as a leading principle. But it is also constructed under the demand of Bibliographysyntax, ......................................................................................... 60 constructive which is also a leading principle. These two principles obviously constrain each other. The tension between ‘natural’ and ‘formal’ 4. The Ethics of Migration. languages is located precisely in the interaction between the two requireReflections on Recent Migration Policies ments. Expressible meaning is Europe reduced........................................... and distorted precisely in and “Non-policies” in Italy and 61 favour ofLaura a constructive syntax. Meaning in a formal system is already a hybrid Zanfrini product of twoPolicies leadingand principles. 4.1 Restrictive Structural Demand for Immigrant Labour .. 65 On top of ambiguities internal to the transcription mechanisms 4.2 Initiatives forthe Governing Family and Humanitarian surveyed in this section (abbreviate notations, of metamathMigration: Labour Migration but not Workers’representation Migration ............. 73 ematics by arithmetic, representation of arithmetic in a formal system, and 4.3 From Guest Workers to Unwelcome Guests .................................. 82 meaning), we must note that these transcription mechanisms are not mor4.4 Selective Policies and the Brain Drain............................................ 87 phologically articulated by different terms. The terms representation, 4.5 Equal Opportunity andetc. Denied ................................ expression, meaning, eachOpportunities carry a reference to more than 90 one form of transcription. In some uses of these terms it is not perfectly clear Bibliography ......................................................................................... 97 which transcription mechanism they refer to. This suggests further interdepen5.dence Colombia: Including Emigrants in Their Societies of Origin .......intercourse 101 between the different modalities of transcription, complex Urs Watter and hybrid descendants. 5.1 State Interest and Responsibility The texts do not signify despite these ambiguities. My purpose is to towards their Citizens Living Abroad ........................................... 102 point out that it is because of these ambiguities that the texts signify suc5.2 Applied Ethics .............................................................................. 104 cessfully. Semiosis is not only an effect of the segregative articulation of 5.3 Migration and Ethicsbut ......................................................... 106and inthese forms ofPolicy transcription, also of their internal multiplicity stability, and of theirincross breeding to a point where it is no longer 5.4 Migration Policy Colombia ...................................................... 108possible to tell, on certain occasions, which belongs where and which gave rise to 5.5 “Colombia nos une”...................................................................... 109 which; where it is no longer possible to limit in advance their potential for 5.6 Alianza País .................................................................................. 112 further cross-production. 5.7 Challenges .................................................................................... G¨ odel’s text is not unaware of the collapsing borders, and114 makes an Bibliography ....................................................................................... attempt to rescue these borders from the onslaught of nomadic 116 modalities of transcription. We therefore have before us a proposition that says Working Together for the Well-being of Migrants ........................... 119 about itself that it is not provable [in PM ] (1931, 149–151), states Barry Halliday the text. In order to say something like that, the process of saying to which G¨ odel’s undecidable formula is subject must take into account the entire edifice of interweaving meaning formations and modalities of transcription, and to recall that meaning which, at some other point, it is desirable that it be forgotten (1934, 355). In order to rearticulate this apparently muddled interaction, a footnote states: Contrary to appearances, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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such a proposition involves no faulty circularity, for initially it Bibliography ......................................................................................... 60 the [only] asserts that a certain well-defined formula (namely, one obtained from the qth formula in the lexicographic order by 4. The Ethics of Migration. a certain substitution) is unprovable. Only subsequently (and so Reflections on Recent Migration Policies to speak by chance) doesand it turn out that this formula is precisely and “Non-policies” in Italy Europe ........................................... 61 the one by which the proposition itself was expressed (1931, 151). Laura Zanfrini According to this statement, first one transcription operated, and then, by 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 chance, when we applied another form of transcription — lo and behold 4.2 Initiatives for Governing Family and Humanitarian our Migration: surprise —Labour the proposition turns to referMigration to itself.............. Everything Migration but notout Workers’ 73 here is properly articulated into distinct serial steps. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 This reconstruction is too little too late. The first interpretation alone 4.4 Selective Policies and the Brain Drain............................................ 87 (a certain well-defined formula ... is unprovable) already requires to combine alland transcription devices described in this section. 4.5 Equalpractically Opportunity Denied Opportunities ................................ 90 And to claim that ......................................................................................... the subsequent identification of that formula as self-referential Bibliography 97 is, so to speak, a chance event, is a very unconvincing disappearing5.reappearing Colombia: Including Their Societies of Origin 101of tranact. The Emigrants beautifullyinchimeric combinations of ....... forms Urs Watter scription are all components in the genesis of the self reference, which — State be Interest and Responsibility it5.1 would impossible to deny — was in fact a leading principle in the towards their Citizens Living Abroad ........................................... 102 setting up of the formula. True, one could, perhaps, re-edit the argument such that the 5.2 Applied Ethics .............................................................................. 104effect of self emerge as a surprise to the reader; this potential 5.3 reference Migration will Policy and Ethics ......................................................... 106editing must not be ignored. But neither can the fact be ignored that this is not the 5.4 Migration Policy in Colombia ...................................................... 108 case; that the texts opted not to surprise the reader; that no text of G¨ odel’s 5.5 “Colombia nos une”...................................................................... 109 proof that I know of ever attempted such narrative; and that chance has 5.6doAlianza Paísleading .................................................................................. to with the principle of the argument only in a so 112 to speak kind of way. The text is meaningful because the event reconstructed as 5.7 Challenges .................................................................................... 114 chance was predestined from the onset. Even if the texts pretend to set Bibliography ....................................................................................... 116 their transcriptions apart, in a time outside the time of the texts, in the time of Together the writerfor and the readers, the different transcriptions Working theofWell-being of Migrants ........................... 119depend Barry on eachHalliday other and cross into each other. What we sought to demonstrate above is how these different transcriptions remain entangled even inside the very text which supposedly sets them as independent and distinct.

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Conclusion

Bibliography ......................................................................................... 60 You can never go back home; a formal system may be nothing but signs rules, but when statements about the formal system are 4.and The syntactic Ethics of Migration. Reflections on Recent Migration Policies about numbers and are then retransformed into arithmetic statements and “Non-policies” in Italy and Europe 61 is the transcribed into the formal system we........................................... started with, it no longer Laura Zanfrini formal system we started with. Because now this formal system is doubly4.1 Restrictivewith Policies and Structural for Immigrant Labour 65 impregnated expression, withDemand representation and with ..meaning.

Every sequence of primitive signs articulated according to the gram4.2 Initiatives for Governing Family and is Humanitarian Labour Migration but not Workers’ Migration ............. 73 to its marMigration: of formalism, according to the grammar of arithmetic, according meaning a leading andGuests according to their interdependence 4.3 From as Guest Workersprinciple, to Unwelcome .................................. 82 and cross-breeding. no longer simply are, they also say, 87 and they 4.4 Selective PoliciesFormulas and the Brain Drain............................................ say in cross-bred codes and tongues, in an unbounded, uncontainable field 4.5 Equal Opportunity and Denied Opportunities ................................ 90 of voices and potentialities — the cross products of the grammars articuBibliography ......................................................................................... 97 lated above with each other and with their readers. And now reading the texts according to this inarticulate mush of codes and transcription mech5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 anisms is no longer a mere contingency; now it is constitutive of the proof. Urs Watter Without blurring the carefully laid boundaries the proof won’t be intelli5.1 State Interest and Responsibility gible. The entire argument is anAbroad elaborate double — or rather multiple — towards their Citizens Living ........................................... 102 entendre. It is still valid, but its validity relies on its multiplicity. 5.2 Applied Ethics .............................................................................. 104 An important question remains only partly confronted: is the semio5.3 Migration andbecause Ethics ......................................................... 106 sis of the text Policy possible we have, to begin with, a set of articulated codes, which later interdependent and cross-productive,108 or do we 5.4 Migration Policybecome in Colombia ...................................................... a-posteriori reconstruct an articulation of codes derived from an 5.5 “Colombia nos une”...................................................................... 109alwaysalready cross-bred border-crossing, pulling the rug from under the hypoth5.6 Alianza País .................................................................................. 112 esis that we actually have an underlying system of separate codes to begin 5.7 Challenges 114 with? This will.................................................................................... be a main concern for the two following chapters. Bibliography ....................................................................................... The following chapters will also confront the claim that the116 argument does not depend on a double-entendre or self reference at all; that once we Working Together for the Well-being of Migrants ........................... 119 formalise the entire argument, and display it in a purely formal language, Barry Halliday all issues of (double) meaning disappear. I don’t doubt that a formal transcription is possible in principle. I will argue that it alone cannot signify in the way that the actual texts do, and that unless the formal text is burdened with some manipulative intervention, unless it takes upon itself the burden of a multiple meaning, it will not be able to signify at all. To conclude this section, I feel it is best to point to a constituent of Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the fragile mechanism that allows to separate-and-breed, or articulate-andBibliography confound, the......................................................................................... various formations of transcription employed by 60 the text. This mechanism is exposed by the wonderfully telling indication, which 4. The Ethics of Migration. suggests that the meaning of the symbols is immaterial, and it is Reflections on Recent Migration Policies desirable that it be forgotten (1934,........................................... 355). and “Non-policies” in Italy and Europe 61 Laura Zanfrini One may indeed desire to forget, especially things immaterial.27 But

the act Policies of forgetting is impossible, while one is deliberately 4.1 actual Restrictive and Structural Demand for Immigrant Labour .. 65desiring to forget. One cannot forget something while willing to forget it (forget 4.2 Initiatives for Governing Family and Humanitarian the phrase ‘pink elephant’ !). Forgetting and desiring to forget are 73 mutually Migration: Labour Migration but not Workers’ Migration ............. exclusive. How does one desire to forget? Does one state ‘I wish to forget’ ? 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Does one count sheep to force the would-be-forgotten out of one’s mind? 4.4isSelective BrainisDrain............................................ Or it that Policies ‘desiringand to the forget’ akin to ‘pretending to forget’;87 one acts 4.5 Equal Opportunity and Denied Opportunities ................................ 90 as if one has already forgotten, while in fact one actually remembers. This pretended forgetfulness is precisely the sort of interaction between Bibliography ......................................................................................... 97various forms of transcription, which allows them to breed and interact while main5.taining Colombia: Including Emigrants in Their Originbe ....... 101 a claim — a claim without whichSocieties the textsofwould hard-pressed Urs Watter

to function successfully — to stay apart. 5.1 State The Interest freedomand to Responsibility forget is one of the essential factors in the openness of towards their Citizens Living Abroad ........................................... 102 the text to the reader’s semiotic intervention. For a certain kind of reading, Applied Ethics .............................................................................. a5.2 kind of reading that I attempt to demonstrate is possible (I104 dare not say compulsory) even a mathematical text, forgetting is not 5.3 Migration Policy andfor Ethics ......................................................... 106only an opportunity, but is actually a constitutive act. — With regard 5.4 Migration Policy in Colombia ...................................................... 108to the plural text, forgetting a meaning cannot therefore be seen as a 5.5 “Colombia nos une”...................................................................... 109 fault. Forgetting in relation to what? What is the sum of the text? 5.6 Alianza can País .................................................................................. 112 Meanings indeed be forgotten, but only if we have chosen to 5.7 Challenges .................................................................................... 114 bring to bear upon the text a singular scrutiny. Yet reading does not consist ....................................................................................... in stopping the chain of systems, in establishing a Bibliography 116 truth, a legality of the text, and consequently leading its reader Working Togetheritfor the Well-being of Migrants 119 into “errors”; consists in coupling these ........................... systems, not according Barry Halliday to their finite quantity, but according to their plurality (which is a being not a listing): I pass, I intersect, I articulate, I release, I do not count. Forgetting meaning is not a matter for excuses, 27 In

German, G¨ odel’s mother tongue, more so even than in English, immaterial (immateriell) suggests the opposite of material, rather than the opposite of relevant. Meaning, the text can be read to quietly suggest, is not material. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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an unfortunate defect in performance; it is an affirmative value, ......................................................................................... 60 aBibliography way of asserting the irresponsibility of the text, the pluralism of systems (if I closed their list, I would inevitably reconstitute 4. The Ethics of Migration. a singular, theological meaning): it is precisely because I forget Reflections on Recent Migration Policies that I read (Barthes 1974,and 10–11, translation modified). and “Non-policies” in Italy Europe ........................................... 61 Laura Zanfrini

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65

1.3 A strategic point of diffraction 4.2 Initiatives for Governing Family and Humanitarian

Migration: Labour Migration but not Workers’ Migration ............. 73 One of the reasons that G¨ odel’s text attracts so much attention is that it 4.3 From Guest Workers to Unwelcome Guests .................................. 82 is a crucial point of diffraction in the history of logic and mathematics. Selectivefrom Policies the Brain Drain............................................ 87 proIt4.4emerged the and context of Hilbert’s formalist-finitist-axiomatic gramme, to an important broke away from this programme. 4.5 Equal but Opportunity and Deniedextent Opportunities ................................ 90 However, to describe the text as a junction along this narrative requires a Bibliography ......................................................................................... 97 broader context than just the text of the proof. I would like therefore to 5.describe Colombia: Societies of strategic Origin ....... 101 on a G¨ oIncluding del’s text Emigrants as a pointinofTheir diffraction and choices Urs Watter smaller scale relevant to this twice-written text. The purpose of this brief discussion is to bring to light the many conflicting reader positions G¨odel 5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102the plunegotiated with, a plurality which is an important constituent of rality of the Ethics text itself. 5.2 Applied .............................................................................. 104

The first Policy and most stated issue is that of self reference. 5.3 Migration and obviously Ethics ......................................................... 106 The solution suggested by Whitehead and Russell, that a proposition 5.4 Migration Policy in Colombia ...................................................... 108 cannot say something about itself, is too drastic. We saw that we 5.5 “Colombia une”...................................................................... 109 themcan constructnos propositions which make statements about 5.6 Alianza País .................................................................................. selves (1934, 362). The narrative described above, that of so 112 to speak by discovery, whereby a certain given formula stated 114 that some 5.7 chance Challenges .................................................................................... well-defined formula was unprovable, and then, subsequently, it turned out Bibliography ....................................................................................... 116 that both formulas were one and the same — this narrative is the edifice meant to supportfor thethereintroduction self reference into logic.119 There is Working Together Well-being of of Migrants ........................... Barry Halliday support for allowing such formulas into logic. On the same also syntactic page we are reminded that in fact, these are arithmetic propositions which involve only recursively defined28 functions, and therefore are undoubtedly meaningful statements. 28 The

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This syntactic status of G¨odel’s self-referential propositions guaranBibliography ......................................................................................... tees that Hilbert and the intuitionists accept the proposition,60whereas the revisionist narrative confronts the possible objections of more logicist 4. The Ethics of Migration. thinkers such as Russell, concerned with impredicativity.29 G¨ odel manages Reflections on Recent Migration Policies to force self-reference into logic by having it comply with the standards of and “Non-policies” in Italy and Europe ........................................... 61 those may consider self-reference objectionable. Laurawho Zanfrini But therePolicies remains still a position, an ascetic formalist position, 4.1 Restrictive and Structural Demand for Immigrant Labour .. 65 which will accept the formula, but decline the suggestion that it is self referen4.2 Initiatives for Governing Family and Humanitarian tial.Migration: It will agree thatMigration the formula (as Workers’ well as its negation) is unprovable, Labour but not Migration ............. 73 but refuse to accept that it says that any formula, and in particular itself, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 is unprovable. The text makes an effort to accommodate this position as 4.4 Selective andalready the Brain Drain............................................ 87 is not well. Various Policies footnotes quoted above suggest that the text 4.5 proof, Equal Opportunity and Denied Opportunities ................................ 90 the but an indication of how to carry it out, and that whatever is constructed is not the unprovable and irrefutable proposition, but only inBibliography ......................................................................................... 97 dicates this proposition (e.g. Note that “[R(q); q]” ... is merely a meta5.mathematical Colombia: Including Emigrants Their Societies ofproposition. Origin ....... 101 description of in the undecidable But, as Urs Watter soon as the formula S has been obtained, we can, of course, also 5.1 State Interest Responsibility determine the and number q and, therewith, actually write down the towards their Citizens Living Abroad ........................................... 102 undecidable proposition itself (1931, 149)). 5.2 Applied 104 At thisEthics point .............................................................................. the readers are required to choose whether they consider the text to bePolicy a proof, or only an explanation of how to construct the 5.3 Migration and Ethics ......................................................... 106 proof; whether this text stands by itself, or hovers over some unwritten 5.4 Migration Policy in Colombia ...................................................... 108 — but writable — formal text; whether one takes the mechanical stance 5.5 “Colombia nos une”...................................................................... 109 attributed by G¨ odel to all his predecessor formalists,30 or whether one 5.6 Alianza País .................................................................................. 112 allows the text to signify, sometimes even so to speak by chance. It 5.7 Challenges .................................................................................... 114 seems that the text supports both positions at once. On the one hand it deploys formal Theorem–Proof arrays, and on the other hand Bibliography ....................................................................................... 116it keeps recalling the writable, but unwritten, accompanying text. This choice (or Working Together the Well-being 119 that rather refusal to for choose) is relatedoftoMigrants another ........................... point of diffraction, Barry Halliday which tries to regulate the relations between syntax and semantics. The sketch of the argument offered in the 1931 introduction works only provided we concede to the hypotheses articulated in the following quota29 Impredicativity is a certain form of circularity, which was a major theme of concern in the context of Russell’s critique on Frege’s logic. 30 See the fourth subsection of the previous section of this chapter.

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tion. The method of proof just explained can clearly be applied to Bibliography 60 any formal ......................................................................................... system that, first, when interpreted as representing a system of notions and propositions, has at its disposal suffi4. The Ethics of Migration. cient means of expression to define the notions occurring in the Reflections on Recent Migration Policies argument above (in particular, the notion “provable formula”) and “Non-policies” in Italy and Europe ........................................... 61 and inZanfrini which, second, every provable formula is true in the interLaura pretation considered. secondDemand hypothesis refers to Labour truth,..which the 4.1 Restrictive Policies andThe Structural for Immigrant 65 formalist tradition attempts to exclude from mathematical argumentation 4.2 Initiatives for Governing Family and Humanitarian in favour of the notion of formal purpose of carrying Migration: Labour Migration butprovability. not Workers’The Migration ............. 73 out the above proof with full precision in what follows is, among 4.3 From Guest Workers to Unwelcome Guests .................................. 82 other things, to replace the second of the assumptions just men4.4 Selective the Brain Drain............................................ 87 The tioned by aPolicies purelyand formal and much weaker one (1931, 151). text promises to rise toand theDenied challenge of setting................................ truth aside. But the 4.5 Equal Opportunity Opportunities 90 immediately following statement suddenly reintroduces semantics into97the picBibliography ......................................................................................... ture. From the remark that [R(q); q] says about itself that it is not 5.provable, Colombia: it Including in Their Societies of Origin 101 followsEmigrants at once that [R(q); q] is true, for ....... [R(q); q] is inUrs Watter deed unprovable (being undecidable). Thus, the proposition that State Interest and Responsibility is5.1undecidable in the system PM still was decided by metamathtowards their Citizens Living 102 and ematical considerations. TheAbroad text is ........................................... willing to adopt strict formalist intuitionist wherever it can, but not at the expense of doing 5.2 Appliedstandards Ethics .............................................................................. 104 away with points ofPolicy view that accept......................................................... truth as a legitimate notion. G¨o106 del is well 5.3 Migration and Ethics aware that this part of the argument will not be universally accepted; but 5.4 Migration Policy in Colombia ...................................................... 108 he chooses not to suppress it. 5.5 “Colombia nos une”...................................................................... The text does indeed stand at a point of diffraction, but it109 refuses to 5.6 Alianza PaísG¨ .................................................................................. 112 texts, make a choice. odel’s own preferences were stated openly in various and are reconstructible from various others, but it is quite striking to watch 5.7 Challenges .................................................................................... 114 how the text refuses to yield both to G¨odel’s and to his opponent-readers’ Bibliography ....................................................................................... 116 points of view. Working for the Well-being Migrants ........................... 119 there ForTogether those readers who endorse aofsemantic and signifying outlook, Barry Halliday awaits another ingenious point of diffraction. Since self reference is allowed, the standard solution to the liar paradox is foreclosed. With self reference allowed one cannot argue that when I say that I am lying, the enunciating I and enunciated I are not the same I in order to avoid a paradox.31 Instead of rearticulating the subject, another rearticulation is suggested. Let us 31 Such

as Lacan, among others, does in Lacan (1978, 139).

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quote the immaculately phrased argument. Bibliography ......................................................................................... 60 Suppose that on 4 May 1934, A makes the single statement, “Every statement which A makes on 4 May 1934 is false.” This 4. The Ethics of Migration. statement clearly cannot be true. Also it cannot be false, since the Reflections on Recent Migration Policies only way for it to in beItaly false is Europe for A to have made a true statement and “Non-policies” and ........................................... 61 in theZanfrini time specified and in that time he made only the single Laura statement. odel’s solution reliesDemand on his claim that A Labour must ..specify a 4.1 RestrictiveG¨ Policies and Structural for Immigrant 65 language B and say that every statement that he made in the 4.2 Initiatives for Governing Family and Humanitarian given time was a false statement B. ButMigration “false statement Migration: Labour Migration but notin Workers’ ............. 73 in B” cannot be expressed in B (for reasons that G¨ odel had already presented 4.3 From Guest Workers to Unwelcome Guests .................................. 82 by this point, but which we shall not include here), and so his statement 4.4 Selective Policies the Brain Drain............................................ 87 The was in some otherand language, and the paradox disappears. paradox be considered asOpportunities a proof that “false statement 4.5 Equal can Opportunity and Denied ................................ 90 in B” cannot be expressed in B (1934, 362–363). Bibliography ......................................................................................... 97 Rather than split the subject into enunciating and enunciated, the 5.language Colombia: Emigrants in of Their Societiesand of Origin ....... 101 is Including split into the language enunciation the object language. Urs Watter These two languages cannot coincide according to the text, because oth5.1 State Interest and erwise a paradox willResponsibility ensue. G¨ odel’s solution to the paradox is stipulating towards their Citizens Living ........................................... 102 notion that one cannot express in anyAbroad properly specified language B the ‘false (or, for that.............................................................................. matter, true) in B’. This solution is a combination of 5.2 Applied Ethics 104 segregation and censorship. First, one segregates the different languages we 5.3 Migration Policy and Ethics ......................................................... 106 speak. Then one censors any reference in a given language to its own notion 5.4 Migration Policy in Colombia ...................................................... 108 of truth. 5.5 “Colombia nos une”...................................................................... 109will be This rearticulation of languages and repositioning of truth 5.6 Alianza Paísfinal .................................................................................. analysed in the chapter of this book from the point of view of112 Deleuze’s conception of language. Here I would like to conclude by pointing out that 5.7 Challenges .................................................................................... 114 this solution is not at all forced upon the text; that there is here a strategic Bibliography ....................................................................................... 116 choice, which might be interesting to study from an archaeological point of view.Together The list for below intended of only to validate the existence Working the isWell-being Migrants ........................... 119of other Barry Halliday possibilities that merit consideration. It does not presume to be exhaustive. 1. A solution adopted by the most radical formalists and intuitionists, consists of giving up the notion of truth altogether. We simply no longer assume that there is such a well defined complete notion, and settle for notions of provability. A somewhat different approach is to restrict the use of the term ‘truth’. This direction is related to Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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Wittgenstein’s analysis of G¨ odel’s semantic argument (Wittgenstein Bibliography ......................................................................................... 60 1978, 118–122). 4. The of Migration. 2. Ethics Wittgenstein suggests (in the context of Russell’s antinomy in Frege’s Reflections on Recent Migration Policies set theoretic calculus) to simply not carry out the paradoxical arguand “Non-policies” in Italy and Europe ........................................... 61 He concedes that it is possible to carry it out, but objects Laurament. Zanfrini that it is useless, and is therefore simply better ignored, as if it was 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 never discovered. If you based something on Frege’s system, I 4.2 Initiatives for Governing Familynecessarily and Humanitarian don’t see that it would be detrimental if there Migration: Labour Migration but not Workers’ Migration ............. 73 were a contradiction in it, as long as this contradiction is 4.3 From Guestsor.................................. 82 caljustGuest not Workers used astoaUnwelcome thoroughfare a circus. Then this 4.4 Selective Policiesits andparticular the Brain Drain............................................ 87 might culus fulfils purpose. — This calculus be used (a) to base something on (as Frege does), or 4.5 Equal Opportunity and Denied Opportunities ................................ 90 (b) to calculate with (as nobody ever does). So we might say: EvBibliography ......................................................................................... 97 erything in the calculus works all right as long as we do not pass through the contradiction (Wittgenstein 1975, 5. Colombia: Including Emigrants in Their Societies of Origin .......227). 101 ConUrs Watter temporary research mathematicians sometime express similar views concerning the Responsibility interface between set theory and category theory: At 5.1 State Interest and towards their Citizens Abroad 102 the moment theLiving situation is........................................... not unlike the one prevailing th in theEthics 18 .............................................................................. century in the infinitesimal calculus ... 104 we know 5.2 Applied about the dangerous spots, where not to swim, and try to 5.3 Migration Policy and Ethics ......................................................... 106 stay away while continuing our exploration.32 5.4 Migration Policy in Colombia ...................................................... 108

We can also adopt a radical finitist view, and deny the existence of 5.53.“Colombia nos une”...................................................................... 109 an infinite sequence of natural numbers (see Rotman (1993) for such 5.6 Alianza País .................................................................................. 112 an option and for references to similar approaches). Another radical 5.7 Challenges .................................................................................... 114 finitist approach may be adopted, which denies the unlimited recurBibliography sive use....................................................................................... of rules of inference. If the length of a proof is 116 limited in advance, some contradictions may be prevented. To a certain extent Working Together for the Well-being of Migrants ........................... 119 possibility is taken up by the study of the complexity of proofs, Barrythis Halliday which was suggested in a letter sent by G¨odel to von Neumann (G¨odel 1986–2003, Vol. V, 373–377). 32 This

statement appeared in a printed abstract of Pierre Cartier’s talk ‘Living in a contradictory world: categories vs. sets’, which took place in the ‘Trends in the mathematical representation of space’ conference in Boston University, December 1, 2007. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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4. We may, as was (to some extent) suggested by G¨odel and attempted Bibliography ......................................................................................... by several authors (G¨ odel 1986–2003, Vol. I, 139), no longer60subject formal systems to finite mechanical procedures of verification. 4. The Ethics of Migration. Reflections on avenue Recent to Migration 5. Another explore Policies consists of giving up the unrestricted use and “Non-policies” in Italy and Europe ........................................... 61 of negation or the universal quantifier. If we deny the possibility of Laura Zanfrini attaching them to just any formula, G¨odel’s construction might be 4.1 Restrictive Policies Demandfor forsuch Immigrant Labour .. 65 avoided (I could and not Structural find a reference a strategy, but it would 4.2 Initiatives for Governing and Humanitarian not surprise me to findFamily that such a strategy exists in the literature). Migration: Labour Migration but not Workers’ Migration ............. 73 6. Finally, we may allow the paradox to remain within our formal sys4.3 From Guest Workers to Unwelcome Guests .................................. 82 tem, but attempt to contain it by adapting the rules of inference 4.4 Selective and the Brain Drain............................................ 87 any in such Policies a way that a contradiction does not immediately imply 4.5 Equal Opportunity and Denied ................................ 90 formula in the system. G¨ oOpportunities del himself encounters such a system in his review of a paper by Church (G¨ o del 1986–2003, Vol. I, 256–259). Bibliography ......................................................................................... 97 Today this direction is studied under the title of relevance or para5. Colombia: Including consistent logics.Emigrants in Their Societies of Origin ....... 101 Urs Watter

Each of these solutions carries its own implications. Some solutions were 5.1 State Interest and Responsibility towardsbriefly their Citizens Living Abroad 102 others suggested in the literature and ........................................... never seriously investigated, led the establishment of ‘deviant’ systems of logic that are still 5.2 to Applied Ethics .............................................................................. 104actively researched. I will not attempt to analyse the epistemic and strategic im5.3 Migration Policy and Ethics ......................................................... 106 plications of any of these solutions, as this is an entirely different project 5.4odel’s Migration Policy in ...................................................... (G¨ motivation forColombia suggesting his solution is easy to derive108 from his 5.5 “Colombia une”...................................................................... 109commuplatonic stance,nos but from the point of view of the larger research nity the question is, I believe, largely open). The above list was112 included 5.6 Alianza País .................................................................................. only to point out that G¨ odel’s solution, largely accepted today, is but a 5.7 Challenges .................................................................................... 114 strategic choice, and not an inevitability. Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini Chapter 2 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65

4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73

From the Formation through to the Hymen

4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97

5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter In this chapter we will follow formalists in reducing everything to the repetition of syntactic rules. But rather than rid our5.1 State Interest and Responsibility towards Citizens we Living selves their of meaning willAbroad see it ........................................... proliferate into reflections102 on and across can only eventually be determined as in104 be5.2 Applied Ethicswhat .............................................................................. tween. 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108

2.1 Where is the meaning of it all? 109 5.5 “Colombia nos une”...................................................................... 5.6 Alianza País .................................................................................. 112 Let us almost-repeat the analysis of the subsection of the former chapter, 5.7 Challenges .................................................................................... 114employ whose title is almost-identical to the title above; but let us now ....................................................................................... aBibliography somewhat wider lens. A clip-on concept of meaning is most 116 strikingly introduced by G¨ odel’s declaration that while a formal system consists Working Together for the Well-being of Migrants ........................... 119 only of symbols and mechanical rules relating to them, the meanBarry Halliday ing which we attach to the symbols is a leading principle in the setting up of the system (1934, 349).

Three statements can be derived from this declaration. First, meaning precedes the formal system. Indeed, it was there already in its setting up. Second, the formal system does not contain meaning. Indeed, a formal system consists only of symbols and mechanical rules. 95

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Third, meaning is something we attach to the symbols. This clipBibliography ......................................................................................... 60 predoff/clip-on portrayal of meaning echoes one of Derrida’s essential icates in a minimal determination of the classical concept of writ4. The Ethics of Migration. ing ... a written sign carries with it a force that breaks with its Reflections on Recent Migration Policies context, that is, with the collectivity of presences organising and “Non-policies” in Italy and Europe ........................................... 61 the moment of its inscription (Derrida 1988a, 9). Laura Zanfrini While meaning thereDemand since before the creation of ..the 4.1 Restrictive Policieshas andbeen Structural for Immigrant Labour 65 formal system, the formal system itself as a collection of symbols and rules has the 4.2 Initiatives for Governing Family and Humanitarian forceMigration: to break Labour loose from the presence of that meaning, underlies it. Migration but not Workers’ Migrationwhich ............. 73 But wherein lies this force? Does it lie within the sign, within its form and 4.3 From Guest Workers to Unwelcome Guests .................................. 82 structural deployment, or is this force in fact to be attributed to the active 4.4 Selective Policies and the Brain Drain............................................ 87 intervention of a writer/reader/user? Is force part of the metaphysics of 4.5 sign, Equal or Opportunity DeniedPeirce Opportunities ................................ the is it part and of what or Wittgenstein would call90its use? There is at least one piece of evidence that supports the second conjecture. Bibliography ......................................................................................... 97 Now we turn to some considerations which for the present 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 have nothing to do with a formal system (1934, 346) is the first Urs Watter sentence of the second section of the 1934 text. These nothing-to-do con5.1 State Interest and definition Responsibility siderations are the of the technical notion of recursive functions towards their Citizens Living Abroad ........................................... 102 (which we mentioned already several times, but do not intend to define in 5.2 Applied .............................................................................. 104 formal this essay). Ethics Despite having nothing to do, for the present, with 5.3 Migration and Ethics ......................................................... 106 nothsystems, thesePolicy considerations use formal notations. Despite having ing do, forPolicy the present, with formal systems, these considerations 5.4 to Migration in Colombia ...................................................... 108 are carefully designed in order to be imported into a formal system. And 5.5 “Colombia nos une”...................................................................... 109 despite having nothing to do, for the present, with formal systems, these 5.6 Alianza País .................................................................................. 112 5 of considerations are indeed imported into a formal system in section 5.7 1934 Challenges the text.1 .................................................................................... But still, for the present, these considerations114 are independent. The conclusion is that it is not the formal similarity or the Bibliography ....................................................................................... 116possible future application that clips meaning onto these considerations. It is the Working Together for the Well-being of Migrants ........................... 119 have declaration that these are considerations which for the present Barry Halliday nothing to do with a formal system, which toggles their relation to formal systems off, and the subsequent argument, which toggles the relation 1 The 1931 text similarly states on page 157 that We now insert a parenthetic consideration that for the present has nothing to do with the formal system P. In this text it is theorem V that transports these considerations into the formal system.

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between recursive functions and formal systems back on. The supplemental Bibliography ......................................................................................... 60 meaning is thus bestowed upon the text by an adjacent text. But it is also important to mind the temporal adverbial for the 4. The Ethics of Migration. present. This adverbial does not only mark that the text reserves the Reflections on Recent Migration Policies right to switch on and off a and certain meaning or a certain something and “Non-policies” in Italy Europe ........................................... 61 to do Laura Zanfrini with formal systems. It also recalls, at the very moment when something to is foreclosed, that something tofor doImmigrant can, at some none-present 4.1do Restrictive Policies andthis Structural Demand Labour .. 65 moment, be reaffirmed. This statement articulates what is now barred as 4.2 Initiatives for Governing Family and Humanitarian something that may in fact be pertinent, provided we escape, as we may, Migration: Labour Migration but not Workers’ Migration ............. 73 the chronology of the text, and skip a few pages. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 When introducing the transformation of symbols and formulas into 4.4 Selective Policies and the Brain Drain............................................ 87 numbers, G¨ odel states that the meaning of symbols is immaterial, 4.5 Equal and Denied ................................ 90 forand it is Opportunity desirable that it be Opportunities forgotten (1934, 355). This desired Bibliography ......................................................................................... 97 than getfulness is obviously impossible. What worse way to induce oblivion by explicitly willing it? This, like the nothing to do declaration, does not 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 simply clip off a certain meaning, it clips it on-and-off. This link is presently Urs Watter off, while right now, before our very eyes, absently on. The different con5.1 State Interest and Responsibility texts, the different meanings, do not exclude each other completely. They towards their Citizens Living Abroad ........................................... 102 coexist in a temporality where the present does not exclude the future and 5.2 past Applied .............................................................................. the — Ethics a temporality, which should perhaps be encumbered104 with the 5.3 Migration Policy and Ethics ......................................................... 106 phenomenological terms of anticipation and retention. If G¨ odel Policy can clip meaning on and off so arbitrarily it is108 because, 5.4 Migration in Colombia ...................................................... for Mathematical objects have an independent existence 5.5him, “Colombia nos une”...................................................................... 109 and reality analogous to that of physical objects. Mathematical state5.6 Alianza País .................................................................................. 112 ments refer to such a reality, and the question of their truth is 5.7 Challengesby .................................................................................... determined objective facts which are independent of114 our own Bibliography ....................................................................................... 116 thoughts and constructions. We may have no direct perception of underlying mathematical objects, just as with underlying physiWorking Together for the Well-being of Migrants ........................... 119 cal objects, but — again by analogy — the existence of such is Barry Halliday necessary to deduce immediate sense perceptions ... While mathematical objects and their properties may not be immediately accessible to us, mathematical intuition can be a source of genuine mathematical knowledge (G¨odel 1986–2003, Vol. I, 30–31). This reconstruction of G¨ odel’s view by Solomon Feferman is akin to Frege’s statement that A third realm must be recognised. What belongs to Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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this corresponds to ideas, in that it cannot be perceived by the Bibliography 60 senses, but ......................................................................................... with things, in that it needs no bearer to the contents of whose consciousness to belong. Thus the thought, for exam4. The Ethics of Migration. ple, which we expressed in the Pythagorean theorem is timelessly Reflections on Recent Migration Policies true, true independently of Europe whether anyone takes it to be and “Non-policies” in Italy and ........................................... 61 true. ItLaura needs no bearer. It is not true for the first time when it is Zanfrini discovered, is like a planetDemand which,for already before anyone 4.1 Restrictivebut Policies and Structural Immigrant Labour .. 65 has seen it, has been in interaction with other planets (Frege 1967, 29). 4.2 Initiatives for Governing Family and Humanitarian If meaning were Migration indeed anbut ideal object of Migration that sort,............. then clipping it Migration: Labour not Workers’ 73 onto and clipping it off of the text would be a perfectly legitimate manoeu4.3 From Guest Workers to Unwelcome Guests .................................. 82 vre. The text is a ladder in our ascent towards ideal objective meaning. 4.4 Selective Policies andcan the Brain Drain............................................ 87 Many different ladders be used to that effect. The same ladder can lead us toOpportunity many destinations. a ladder ................................ can, of course, also 4.5 Equal and DeniedAnd Opportunities 90 be left unclimbed. Bibliography ......................................................................................... 97 But if this image is to be accepted, and the ladder is but a vehicle 5.to, Colombia: in Their of Origin ....... 101 and not Including the carrierEmigrants of, meaning, thenSocieties the crossing of the gap between Urs Watter text and meaning must be accounted for. I shall not attempt to account for 5.1 State Interest Responsibility this crossing (theand way G¨ odel treats this problem is surveyed in the second towards their Citizens Living Abroad ........................................... 102the gap section of the previous chapter); nor will I attempt to prove that is5.2unbridgeable, and that in fact it needn’t be bridged, because,104 one may Applied Ethics .............................................................................. claim, there isPolicy no such meaning is nothing but 106 our use of 5.3 Migration and gap, Ethicsbecause ......................................................... the text (the first of those tasks is the concern of the glorious platonist 5.4 Migration Policy in Colombia ...................................................... 108 tradition, whereas the second task has been the focus of the pragmatist5.5 “Colombia nos une”...................................................................... 109 will I analytic traditions stemming from Peirce and Wittgenstein). Nor 5.6 Alianza .................................................................................. 112 attempt to País suggest that meaning lies latent within the text, constricting its but leaving some freedom to decompose and recompose114 the pieces 5.7form, Challenges .................................................................................... (this would be a structuralist approach). Here I will attempt to investigate Bibliography ....................................................................................... 116 the possibility that what is clipped on-and-off is not meanings to texts, but texts toTogether other texts. I will try to investigate to........................... what extent such Working for2the Well-being of Migrants 119clip-art Barry Halliday can produce the effect of meaning.

2I

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2.2

Verisimilarity

Bibliography ......................................................................................... 60 We have not given up on the possibility that the attachment and detach4.ment The Ethics of Migration. of meaning has to do with the structure of the sign itself, rather than Reflections on Recent Migration Policies with those operating sign. before........................................... we resuscitate this possibility, we and “Non-policies” inthe Italy andBut Europe 61 must off the pretence that meaning is indeed so easy to clip on-andLaurahold Zanfrini off. If it were so easily clipped on-and-off, one could simply clip on to an 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 arbitrary text such as ∃x(x = 0) the meaning ‘both this statement and its 4.2 Initiatives for Governing Family and Humanitarian negation are unprovable’, and circumvent G¨odel’s tedious construction. Or, Migration: Labour Migration but not Workers’ Migration ............. 73 in a less caricatural design, if it were so easy to clip meaning on-and-off, 4.3might From Guest Workers to Unwelcome Guests we simply enumerate the formulas of .................................. the formal system 82 Principia 4.4 Selective Policies and the Brain Drain............................................ 87 that Mathematica (PM) arbitrarily, assigning the number 10 to the formula reads ‘formula numberand 10 Denied in PM Opportunities is unprovable’, thereby enabling90 the logic 4.5 Equal Opportunity ................................ of the proof and generating an undecidable proposition.3 Bibliography ......................................................................................... 97 But there are two pertinent objections to such slight of hand. First, 5.‘unprovable’ Colombia: Including Emigrants in Their Societies of Origin ....... is not part of the vocabulary of PM, and in order for101 the stateUrs Watter ment ‘formula number 10 in PM is unprovable’ to be assigned a number at 5.1 this Statestatement Interest and Responsibility all, (and the notion of unprovability) must be expressed by towards their Citizens Living Abroad ........................................... 102we may the resources of that language (or whatever other formal system choose to work with). 5.2 Applied Ethics .............................................................................. 104

Second, and more the way we express the statement 5.3 Migration Policy andimportantly, Ethics ......................................................... 106 ‘formula number x is unprovable’ in the language PM already depends on the 5.4 Migration Policy in Colombia ...................................................... 108 assignment of numbers to formulas. Indeed, PM is concerned with num5.5 “Colombia nos une”...................................................................... 109 bers, and it is only after we have coded formulas by numbers that PM 5.6 Alianza .................................................................................. 112 can refer to País formulas at all, and in particular articulate their provability. 5.7 Challenges .................................................................................... 114

3 Here is a sketch of the semantic argument that would apply in such a situation Bibliography ....................................................................................... (where provability refers to provability in the restricted formal sense of PM 116 ): If formula numbered 10 were provable, then the formula ‘formula number 10 in PM is unprovWorking Together for the of Migrants 119 — a able’ would be provable, andWell-being therefore formula number........................... 10 would be unprovable Barry Halliday contradiction. If, on the other hand, the negation of formula number 10 were provable, then ‘formula number 10 in PM is provable’ would be provable, which, according to the previous deduction results in a contradiction. Therefore neither formula number 10 nor its negation are provable; formula number 10 is undecidable. In particular, the claim that ‘formula number 10 in PM is unprovable’, since it has just been demonstrated to be unprovable, turns out to constitute a true claim (the truth of formula number 10 does not contradict its undecidability, because our demonstration that the formula is true does not constitute a proof in the restricted formal sense of PM ).

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Consequently, the formula expressing ‘formula number 10 in PM is unprovBibliography 60 able’ can only......................................................................................... be written after the assignment of numbers to formulas is effected, and after the term ‘unprovable’ is articulated in PM. As a result, 4. The Ethics of Migration. once we have articulated a formula in PM meaning ‘formula number 10 in Reflections on Recent Migration Policies PM unprovable’, this formula already........................................... has a number. If after the and is “Non-policies” in Italy and Europe 61fact we change the system of formula enumeration so as to assign to that formula Laura Zanfrini the 10,Policies the expression of ‘unprovability’ in PM Labour (which.. depended 4.1 number Restrictive and Structural Demand for Immigrant 65 on the original enumeration) might no longer express ‘unprovability’ with 4.2 Initiatives for Governing Family and Humanitarian respect to the Labour new enumeration, our formula might............. no longer Migration: Migration butand not Workers’ Migration 73 mean ‘formula number 10 in PM is unprovable’. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 G¨ odel’s task, then, was to be able to present the following process. 4.4 Selective Policies and the Drain............................................ 87system First, construct a system of Brain formula enumeration; then, given that 4.5enumeration, Equal Opportunity and Denied ................................ of to translate into Opportunities the formal system the statement90 ‘formula number x in ......................................................................................... PM is unprovable’; finally, to find a number g, such Bibliography 97 that the formula that means ‘formula number g in PM is unprovable’ indeed 5.turns Colombia: Emigrants in Their Societies Originline: .......the 101 assignout toIncluding be assigned the number g. Here’s the of bottom Urs Watter ment of non-ordinary meaning to formulas turns out to be quite harshly 5.1 State Interest and Responsibility constrained, for something that is supposed to be arbitrary. towards their Citizens Living Abroad ........................................... In order to produce G¨ odel’s effect of meaning, it is not 102 enough to 5.2 Applied Ethics .............................................................................. declaratively impose a certain meaning on a certain formula. The104 meaning4 imposing-declarations must obey constraints of verisimilarity. The verisim5.3 Migration Policy and Ethics ......................................................... 106 ilar, explains Kristeva, is an assembly (the symbolic gesture par ex5.4 Migration Policy in Colombia ...................................................... 108 cellence, cf. Greek sumballein = putting together) of two different 5.5 “Colombia nos une”...................................................................... 109 discourses, of which one ... projects upon the other, which serves 5.6its Alianza País .................................................................................. as mirror, and identifies with it beyond difference112 (Kristeva 1969, 212). In order for G¨ odel’s enumeration to be acceptable, the114 elements 5.7 Challenges .................................................................................... of the meaning attachment mechanism must be considered as identical on Bibliography ....................................................................................... 116 some level. The elements that G¨odel identifies beyond difference are Working for the Well-being of Migrants ........................... numbersTogether on the one hand and symbols of a formal system on 119 the other. Barryidentification Halliday This is that which allows for the isomorphic image of the 4 The notion of vraisemblance is developed by Kristeva in her early semiotic work to explain how a fictitious literary text produces a sense of truth and reality — how we come to accept the literary text as a valid source of reflection on the world, even though it is entirely made up. This notion has little to do with classical notions of vraisemblance, which refer to non-rigorous persuasion as preliminary for mathematical proof (Brian 1994, 60, 216)

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5

system PM in the domain of arithmetic (1931, 147). Bibliography ......................................................................................... 60 However, such identification requires readers to operate discursive mechanisms that set aside any differences between symbols of a formal 4. The Ethics of Migration. text and numbers, despite the fact that almost every participant in the Reflections on Recent Migration Policies various manifestations of academic mathematical discourse in the and “Non-policies” in Italy and Europe ........................................... 61 early Laura Zanfrini 1930s would assert that there were some significant differences. It is the fact that such identification beyondDemand difference was acceptable 4.1 Restrictive Policies and Structural for Immigrant Labour ..by 65enough leading participants in the mathematical discourse of the time, regardless of 4.2 Initiatives for Governing Family and Humanitarian 6 the acknowledged difference, which allowed for the effect of verisimilarity. Migration: Labour Migration but not Workers’ Migration ............. 73 In order to effect verisimilarity, Kristeva explains, the semantics of the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 verisimilar postulates a resemblance with the law of a given soci4.4 Selective Policies and the Brain Drain............................................ 87 ety at a given point of time and frames it within a historic present 4.5the Equal Opportunity and verisimilar Denied Opportunities ................................ 90 the ... semantics of the requires a resemblance with fundamental semantic units that is established enough to cross Bibliography ......................................................................................... 97the relevant discourse’s threshold of replication. Only then does it present itself 5.as Colombia: Including in Their Societies of Origin ....... 101 being “outside time”, Emigrants “identification”, “effectiveness”, while Urs Watter more profoundly and uniquely conforming (conformist) to a (dis5.1 State Interest Responsibility cursive) order and already there (Kristeva 1969, 212–213). Verisimilarity towards their Citizens Living Abroad ........................................... 102 is precisely the effect of outside-time-effective-identification based on Applied Ethics .............................................................................. 104 a5.2 contingency of discourse. 5.3 Migration Policy and Ethics ......................................................... 106 5 Kristeva

writes Having reserved to science the domain of veridicity, that absolute knowledge whose every enunciation is drenched (irrigu´ ee), secretes a5.5 domain of ambiguity, a yes-and-no in which truth is a present memory “Colombia nos une”...................................................................... 109 (a secondary presence, but still there), phantom-like and originary: it’s the 5.6 Alianza País .................................................................................. 112 extra-veridical domain of sense as verisimilar (Kristeva 1969, 211–212). In the course of my quotations mathematical discourse is placed in the position of the verisimilar 5.7 Challenges .................................................................................... 114 (literary, extra-veridical), rather than the scientific (true). This manipulation entails (or Bibliography ....................................................................................... 116 or the depends on) either a renunciation of certain privileges of the scientific discourse, marking of mathematical discourse as a fiction beyond science. For the current context, Working theeither. Well-being of Migrants ........................... 119 however, Together I need not for justify 6 TheHalliday Barry point here is not merely historical. The contemporary reader too must make a similar identification beyond difference. We could indeed imagine a future reader for whom this specific difference would be completely crossed out. My belief, however, which can only be demonstrated by a text-by-text analysis, is that any reader would have to identify beyond difference some discursive strata, or else end up with no meaning at all. My motivation in stating this belief is ethical. This belief has to do with assigning authority to texts and taking responsibility for their interpretation. This ethical dimension will be discussed more explicitly at the end of this chapter.

5.4 Migration Policy in Colombia ...................................................... 108

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In order for G¨ odel’s transcription mechanism, which turns formulas Bibliography ......................................................................................... 60it must into numbers, to be acceptable (to appear ‘real’, to be verisimilar), bind different semantic units to each other. But it is not only a ques4. The Ethics of Migration. tion of semantics. In order to achieve verisimilarity, it must also verisimuReflections on Recent Migration Policies late syntax. The in syntactic would be the principle of and a“Non-policies” Italy andverisimilar Europe ........................................... 61 derivability Laura Zanfrini(of different parts of a concrete discourse) from the global formalPolicies system. A discourse is for syntactically verisimilar if 4.1 Restrictive and Structural Demand Immigrant Labour .. 65 one can derive each of its sequences from the structured totality 4.2 Initiatives for Governing Family and Humanitarian thatMigration: this discourse is ... The procedure of assembling Labour Migration but semantic not Workers’ Migration ............. 73 together two incompatible entities (the semantic verisimulation) 4.3 From Guest Workers to Unwelcome Guests .................................. 82 having provided the “effect of resemblance”, it is now a ques4.4 Selective Policies and the Brain Drain............................................ 87effect. tion of verisimulating the very process that leads to this The syntax of the and verisimilar takes charge of this task (Kristeva 4.5 Equal Opportunity Denied Opportunities ................................ 90 1969, 213–214). The reader recognises beyond the logical grid, Bibliography ......................................................................................... 97 which is that of an informative statement, an “object” whose “truth” 5.isColombia: in Their Societies of Origin ....... 101 norm tolerableIncluding thanks Emigrants to its conformity with the grammatical Urs Watter (Kristeva 1969, 230). 5.1 State and Responsibility It is Interest remarkably easy to manipulate Kristeva’s concept of verisimilartowards their Citizens Living Abroad ........................................... 102 ity, arising from a comparison of fiction literature and scientific texts, into 5.2 verisimilarity Applied Ethicsthat .............................................................................. 104 to clip the G¨ odel’s text must deploy in order to be able its Semantic units are coupled together: numbers are 5.3meanings Migrationon-and-off. Policy and Ethics ......................................................... 106 coupled to primitive signs, numbers are coupled to formulas, numbers are 5.4 Migration Policy in Colombia ...................................................... 108 coupled to their representations inside a formal system (sequences of primi5.5 “Colombia nos une”...................................................................... 109 tive signs), arithmetic functions are coupled to formal functional expressions, 5.6 Alianza País .................................................................................. 112 But it and metamathematical notions are coupled to arithmetic functions. Challenges .................................................................................... 114 conis5.7 crucial to note that what reigns over these couplings is a rigorous structive syntactic edifice. Only by submitting to these heavy constraints Bibliography ....................................................................................... 116 could the texts under our study announce and/or put in abeyance meanings Working Together for the Well-being of Migrants ........................... 119 of formulas and arithmetic expressions. Barry Halliday

The role of verisimilarity in G¨ odel’s text is clearly indicated in the representation of metamathematical operations by arithmetic ones. Recall that, when introducing the operation x ∗ y, after it is defined formally/arithmetically, it is claimed that x ∗ y is the number of the formula obtained by concatenating formula number x and formula number y; but recall also that no effort whatsoever was made to justify this claim (we Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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discussed this issue in subsection 1.2.2 above). Indeed, one cannot propose Bibliography 60 is not an arithmetic......................................................................................... validation here, because concatenation of formulas an arithmetic operation. This representation of concatenation by an arith4. The Ethics of Migration. metic operation is held as evident, and it is so held, because it is based on Reflections on Recent Migration Policies constructions analogous in their syntax............................................ The syntactic analogy then and “Non-policies” in Italy and Europe 61 allows for a semantic Laura Zanfrini coupling. And this syntactically founded edifice of semantic taken to sound without scrutiny. One.. 65 could, of 4.1coupling Restrictiveis Policies andbeStructural Demand further for Immigrant Labour course, generate a formal system that would deal with both sign-sequences 4.2 Initiatives for Governing Family and Humanitarian and Migration: numerals in orderMigration to create but a formal framework for discussing concateLabour not Workers’ Migration ............. 73 nations and the arithmetic operation ∗ at once, but G¨odel shows no need 4.3 From Guest Workers to Unwelcome Guests .................................. 82 to do so. One could test the analogy between concatenation and the opera4.4 Selective Policies thex’s Brain tion ∗ empirically for and some andDrain............................................ y’s, but, again, G¨odel expresses87no need to so (possibly because he distinguishes arithmetic from any empirical 4.5do Equal Opportunity and Denied Opportunities ................................ 90 counterpart). Bibliography ......................................................................................... 97 The analogy between concatenation and the operation ∗ stands as it 5.is. Colombia: Including Emigrants in Their Societies of Origin ....... 101 to be This syntactically founded edifice of semantic coupling is taken Urs Watter sound without further scrutiny. But this is not a gap in the proof. This is 5.1 State Interest Responsibility what enables theand truth. This “like” — substitutive preposition that towards their Citizens allows to take one forLiving the Abroad other ........................................... is the operator that holds102 together 5.2 Applied .............................................................................. 104 saythe complexEthics and ambiguous relations of representation, expression, ing, signifyingPolicy and meaning analysed in the previous chapter, whereby the 5.3 Migration and Ethics ......................................................... 106 signifier designates at least two signifieds, the form indicates at 5.4 Migration Policy in Colombia ...................................................... 108 least two contents, content supposes at least two interpretations, 5.5 “Colombia nos une”...................................................................... 109 unand thus to infinity, all verisimilar because placed together 5.6 Alianza País .................................................................................. 112 the der the same signifier (or under the same form, or under same content, and thus to infinity). But our aim is to go 5.7 Challenges .................................................................................... 114on and demonstrate that they tip into vertigo: the nebulosity of sense in Bibliography ....................................................................................... 116 which the verisimilar speech (the sign) is eventually submerged (Kristeva 1969, 221–222). Indeed, we saw how ........................... the transcription between Working Together for the Well-being of Migrants 119 Barry Halliday formal, arithmetic and metamathematical texts advances indefinitely, that is, until the point where the text arbitrarily marks it as come to an end.7 7 One may object that these issues are unique to G¨ odel’s project as a metamathematical project. This observation is not entirely unfounded. However, the discrepancies between informal and formal versions of texts, semantic content that is lost in translation, meta-arguments based on similarity of technical arguments, and semantic coupling of different practices — all these phenomena reflect the issues raised above, and are part

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What binds together the whirling metamathematical, arithmetic and 8 Bibliography ......................................................................................... formal texts is nothing but a common syntax and common terms,60 a commonality most strikingly exemplified by the typographical rendering of the 4. The Ethics of Migration. metamathematical-turned-arithmetical by small capitals in the 1931 text Reflections on Recent Migration Policies (a formula in PM may be and unprovable, in which case the corresponding and “Non-policies” in Italy Europe ........................................... 61 number is labelled unprovable); but it is even more strikingly exempliLaura Zanfrini fied by the typographical identity Demand in the for 1934 text (both formulas 4.1 Restrictive Policies and Structural Immigrant Labour .. 65 and corresponding numbers are said to be unprovable). But this commonality 4.2 Initiatives for Governing Family and Humanitarian has Migration: its limits. G¨ odel’s Migration informal semantic argument (see the section73G¨ odel’s Labour but not Workers’ Migration ............. argument in brief in the introduction of this book) shows that consistency 4.3 From Guest Workers to Unwelcome Guests .................................. 82 implies incompleteness. However, the formal translation only shows that Selective Policies(ω-consistency) and the Brain Drain............................................ 87 a4.4 stronger property implies incompleteness.9 Something is 4.5 Equal Opportunity and Denied Opportunities ................................ 90

and parcel of contemporary ‘standard’ mathematics. The ways in which they contribute Bibliography to mathematical......................................................................................... semiosis must, however, be analysed on a text by text basis 97 in order to properly reflect contextual contingencies. 8 One may claim that these discursive strata are held together by some essential 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 analogy. I will not comment on this claim, because this would take me too far off my line Urs Watter of thought, and because the texts we study do not suggest such a claim. But in order not 5.1leave State Interest and completely Responsibility to this possibility unchallenged, I will note that Wittgenstein has led towards theiragainst Citizens Living as Abroad ........................................... 102 a fierce onslaught ‘analogy’ presumed origin for mathematical validity, and views mathematical practice as a set of rules binding different practices by declaring 5.2 Applied Ethics .............................................................................. 104 them analogous — a declaration that is psychologically and practically constrained, but 5.3 constrained Migration Policy and Ethicsor......................................................... 106 not by mathematics by an abstract notion of ‘analogy’. Consider for instance Wittgenstein’s comments on using the vertices of a pentagram to count to 10. 5.4 Migration Policy in Colombia ...................................................... 108 You might call it two ways of counting glued together. We could have had one way of countingnos byune”...................................................................... putting people on the crossing points of the pentagram 5.5 “Colombia 109 and another way of counting by assigning numerals up to ten persons. What 5.6 Alianza País .................................................................................. 112 looks like counting, in the case of a pentagram, is a way of correlating these two ways of counting. [A rule is made] (Wittgenstein 1975, 118). Consider 5.7 Challenges .................................................................................... 114 also the following impressive dialogue, which starts with the words of Wittgenstein: Suppose Bibliography ....................................................................................... 116 you had correlated cardinal numbers, and someone said, “now correlate all the cardinals to all the squares.” Would you know what to do? Has it already Working Together Well-being of Migrants ........................... 119 been decided whatfor wethe must call a one-one correlation of the cardinal numbers Barry Halliday to another class? Or is it a matter of saying, “This technique we might call correlating the cardinals to the even numbers”? Turing: The order points in a certain direction, but leaves you a certain margin. Wittgenstein: Yes, but is it a mathematical margin or a psychological and practical margin? That is, would one say, “Oh no, no one would call this one-one correlation”? Turing: The latter Wittgenstein: Yes.—It is not a mathematical margin (Wittgenstein 1975, 168). 9 According to the semantic argument, the provability of a statement implies its truth

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lost in translation. But even this loss-in-translation is not enough to invalBibliography 60 idate informal......................................................................................... assertions based on syntactic and semantic verisimilarity. A structural approach would assume that semiotic systems have struc4. The Ethics of Migration. tures, whichon the researcher should discover and compare. Post-structural Reflections Recent Migration Policies critique challenges this assumption. The extraction of structure61from a and “Non-policies” in Italy and Europe ........................................... Laura Zanfrini system is no longer considered a discovery, but an act of discursively constrained gluingPolicies together one system to another system,Labour the latter 4.1 Restrictive andofStructural Demand for Immigrant .. 65system dubbed the former’s structure. Post-structural critiques will further indi4.2 Initiatives for Governing Family and Humanitarian cateMigration: that the structuring of semiotic can never be............. definitively Labour Migration but notsystems Workers’ Migration 73 settled, and that the means of comparing structures are contingent as well. It’s 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the contingency of establishing an isomorphic image of the system PM 4.4the Selective Policies and the Brainthat Drain............................................ in domain of arithmetic the notion of verisimilarity 87 serves to 4.5 Equal and Denied Opportunities 90 bring up. IOpportunity am not denying here the possibility................................ of mechanically translating formulas into......................................................................................... numerals. I am insisting here on the contingency of97 allowing Bibliography such mechanical translation as a framework for doing mathematics. The 5.contingency Colombia: Including Emigrants in Their Societies Origin .......that 101 allows I am pointing out here is akin to the of contingency Urs Watter us to identify magnitudes and numbers — an identification, which classical 5.1 State Interest and Responsibility Greek geometers were loath to endorse. towards their Citizens Living Abroad ........................................... I do not appeal to the notion of verisimilarity to trivialise 102 or make a 5.2 AppliedofEthics .............................................................................. 104neither caricature the mathematical endeavour. There’s nothing trivial, philosophically nor pragmatically, in the subjugation of the mathematical 5.3 Migration Policy and Ethics ......................................................... 106 text to verisimulating constraints. A form of verisimilarity that is accepted 5.4 Migration Policy in Colombia ...................................................... 108 by prevailing discursive standards is precisely what’s lacking in the con5.5 “Colombia nos une”...................................................................... 109 struction that arbitrarily assigns the number 10 to the statement ‘formula 5.6 Alianza País .................................................................................. number 10 in PM is unprovable’. And the concretely different 112 discursive criteria for verisimilarity in formal mathematics and (some versions of) 5.7 Challenges .................................................................................... 114 philosophical logic are precisely what allows the statement ‘this 116 statement Bibliography ....................................................................................... is false’ to serve as an object of study in the latter, but not in the forWorking Together for the Well-being of Migrants 119 in the mer discursive field. Both fields, however, have........................... earned their place Barry Halliday production of human knowledge. — in this particular argument the truth that some statement is unprovable. The syntactic argument replaces the passage through truth by a passage through the adequacy of the coding of metamathematical relations by formal expressions of arithmetic relations (1931, theorem V). In fact, both arguments obey distinct syntactic constraints, and both require attaching meaning to text, at least if they are meant to demonstrate the incompleteness of a formal system, rather than just a senseless formal statement. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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And still, within certain historical limits, formal mathematics, philoBibliography 60 along sophical logic,......................................................................................... and literary fiction all allow themselves to be carried by the radical gesture of verisimilarity, which is a putting together 4. The Ethics of Migration. of opposite units of meaning sufficient for leading (the imposReflections on Recent Migration Policies sible) to truth; linking together provability and non-provability, and “Non-policies” in Italy and Europe ........................................... 61linking 10 together non-provability and truth, such that the two opposites (the Laura Zanfrini same and thePolicies different ... ) synthesise a same, 4.1 Restrictive and Structural Demandthemselves for ImmigrantinLabour .. 65 which is still verisimilar (Kristeva 1969, 219). 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 FromElements Guest Workers to Guests .................................. 82 2.3 ofUnwelcome verisimilarity 4.4 Selective Policies and the Brain Drain............................................ 87 Having introduced the language of verisimilarity into the texts under dis4.5 EqualweOpportunity and Denied Opportunities ................................ 90 there. cussion, must articulate the detail of how verisimilarity functions ......................................................................................... 97 IBibliography will not attempt an exhaustive survey of all elements that contribute to an effect of verisimilarity in those texts, but only indicate some elements, 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 which put mathematical verisimilarity in a wider context, and which will Urs Watter later implicate the texts we study in the processes of semiosis that I am 5.1 State Interest and Responsibility fishing for. towards their Citizens Living Abroad ........................................... 102 In reading texts by Raymond Roussel, Kristeva uncovers the struc5.2 Applied Ethics .............................................................................. 104 ture of the canonical subject-predicate sentence as a principal 5.3 Migration Policy and Ethics ......................................................... syntactic rule of the verisimilar. It is well evident that this106 structure and its recursive reiteration is indeed a principal syntactic rule in the pro5.4 Migration Policy in Colombia ...................................................... 108 duction of common formal systems, including, of course, those to 5.5 “Colombia nos une”...................................................................... 109 which G¨odel refers. But I am more interested in what Kristeva finds in the inte5.6 Alianza País .................................................................................. 112 rior of this law, where various secondary syntactic figures of the 5.7 Challengesare .................................................................................... 114 verisimilar recognisable, in which are included: repetition, doubling, enumeration (Kristeva 1969, 230), and which give 116 rise to the Bibliography ....................................................................................... effects of linearity (origin-destination), and motivation (syllogism) Working for the Well-being of Migrants ........................... 119 triggeredTogether by the syntactic verisimulating machine (Kristeva 1969, 214). Barry Halliday G¨ odel’s main tool is the enumeration of formulas in a formal system. Reading the work of Roussel, Kristeva writes that it is enough that “absurd” facts be arranged in a sequence of enumerations so that absurdity is taken over by each element of the sequence, in order 10 Indeed,

G¨ odel’s semantic argument, as presented in the footnote on page 99, includes deducing unprovability from provability and truth from unprovability. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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for that absurdity to become verisimilar due to its derivability Bibliography ......................................................................................... 60 from a given syntactic grid. As her analysis continues, it appears to become more and more directly applicable to G¨odel’s stratagem. In the 4. The Ethics of Migration. same way, the enumeration of signs which deceive and of false Reflections on Recent Migration Policies statements, as are in included in Europe G¨odel’s ........................................... enumeration, is not unverisimiand “Non-policies” Italy and 61 lar; their sequence, as a syntactic ensemble of units derivable from Laura Zanfrini each other, constitutes a verisimilar (Kristeva 4.1 Restrictive Policies and Structural Demanddiscourse for Immigrant Labour ..1969, 65 233– 234). 4.2 Initiatives for Governing Family and Humanitarian Consider Labour the following taxonomy of animals. (a) those that73belong Migration: Migration but not Workers’ Migration ............. to the emperor; (b) embalmed ones; (c) those that are trained; 4.3 From Guest Workers to Unwelcome Guests .................................. 82 (d) suckling pigs; (e) mermaids; (f ) fabulous ones; (g) stray dogs; (h) 4.4 Selective Policies and the Brain Drain............................................ 87 those that are included in this classification; (i) those that tremble 4.5ifEqual Opportunities ................................ 90with a as theyOpportunity were mad;and (j)Denied innumerable ones; (k) those drawn very fine camel’s-hair brush; (l) etcetera; (m) those that have Bibliography ......................................................................................... 97 just broken the flower vase; (n) those that at a distance resemble flies 5.(Borges Colombia: Including in Their Societies of Origin ....... 101 and 1999, 231). IfEmigrants G¨ odel’s enumeration appears less unmotivated Urs Watter objectionable than the above taxonomy of animals, which Foucault quotes 5.1 State Interest Responsibility from Borges, whoand quotes it from Franz Kuhn, who is said to have quoted it towards their Citizens Living Abroad ........................................... 102 from the unknown (or false) Chinese encyclopaedia entitled ‘The 5.2 AppliedEmpirium Ethics .............................................................................. Celestial of Benevolent Knowledge’ (Foucault 104 1973, xv), it5.3 is Migration because G¨ odel’s and enumeration follows a process, which sufficiently Policy Ethics ......................................................... 106 many participants in the relevant discourses recognise and replicate as a syntactic 5.4 Migration Policy in Colombia ...................................................... 108 computational apparatus. Other than that, it is no more ‘motivated’ or 5.5 “Colombia nos une”...................................................................... 109 ‘justified’ than John Wilkins’ analytical language or the Aarne-Thompson 5.6 Alianza País .................................................................................. 112 system for classifying folktales, and yet it serves as an acceptable basis for 5.7 Challenges .................................................................................... 114 analysis. Bibliography 116 proxWe are....................................................................................... all familiar with the disconcerting effect of the imity of extremes, or, quite simply, with the sudden vicinity of Working Together for the Well-being of Migrants ........................... 119 things that have no relation to each other; the mere act of enuBarry Halliday meration that heaps them all together has a power of enchantment all its own: ‘I am no longer hungry,’ Eusthenes said. ‘Until the morrow, safe from my saliva all the following shall be: Aspics, Acalephs, Acanthocephalates, Amoebocytes, Ammonites, Axolotls, Amblystomas, Aphislions, Anacondas, Ascarids, Amphisbaenas, Angleworms, Amphipods, Anaerobes, Annelids, AnRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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thozoans. ...’ But all these worms and snakes, all these creatures Bibliography ......................................................................................... 60 which redolent of decay and slime are slithering, like the syllables designate them, in Eusthenes’ saliva: that is where they all have 4. The Ethics of Migration. their common locus ... startling though their propinquity may Reflections on Recent Migration Policies be, is nevertheless warranted by........................................... that and, by that in, 61 by that andit “Non-policies” in Italy and Europe on whose solidity provides proof of the possibility of juxtaposiLaura Zanfrini tion. It was certainly that for arachnids, 4.1 Restrictive Policies andimprobable Structural Demand Immigrantammonites, Labour .. 65 and annelids should one day mingle on Eusthenes’ tongue, but, af4.2 Initiatives for Governing Family and Humanitarian ter Migration: all, that Labour welcoming andbut voracious mouth certainly Migration not Workers’ Migration .............provided 73 them with a feasible lodging, a roof under which to coexist (Fou4.3 From Guest Workers to Unwelcome Guests .................................. 82 cault 1973, xvi). 4.4 Selective Policies and the Brain Drain............................................ 87 Not so much unlike Eusthenes’ list (borrowed by Foucault from Ra4.5 Equal Opportunity and Denied Opportunities ................................ 90 belais’ Gargantua and Pantagruel ), G¨ odel’s enumeration allows to accept Bibliography ......................................................................................... in bulk an entire sequence comprising provable and unprovable, 97 true and false formulas. The sequence even allows sneaking in sequences of primitive 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 signs that are not even syntactically correct formulas in the formal language Urs Watter under consideration. It creates a sense of homogeneity, which collects the 5.1 State Interest and Responsibility sensible andtheir the Citizens senselessLiving into aAbroad common reservoir. Invulnerable towards ........................................... 102 to all determined opposition between reason and unreason (divisions of 5.2 Applied Ethics .............................................................................. 104 formulas into meaningful and meaningless, provable and unprovable, true 5.3 Migration Policy Ethics ......................................................... 106 of the and false) it is the and point starting from which the narrative determined ofColombia this opposition, this opened or broken-off di5.4 Migration forms Policy in ...................................................... 108 alogue (between texts and meanings), can appear as 109 such and 5.5 “Colombia nosformal une”...................................................................... be stated. The generation of this totality is the very gesture, which pre5.6 Alianza País .................................................................................. 112 scribes a position outside this totality (is this the position of meaning?). 5.7isChallenges .................................................................................... 114 It the point at which the project of thinking this totality by Bibliography 116by exescaping it ....................................................................................... is embedded. By escaping it: that is to say, ceeding the totality, by exceeding the formal system and attaining its Working Together for the Well-being of Migrants ........................... 119 meta-discourse and the discourse of its truth. Even if nonmeaning has Barry Halliday invaded the totality of the world, up to and including the very contents of my thought ... even if I do not in fact grasp the totality, if I neither understand nor embrace it, I still formulate the project of doing so by presuming to enumerate everything, and this project is meaningful in such a way that it can be defined only in relation to a precomprehension of the infinite and undetermined Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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totality. I count, therefore I mean (Derrida 1978, 56, translation modified). Bibliography 60 We must......................................................................................... not forget, however, that enumeration is a form of repetition. fact, repetition is a necessary condition for the entire syntactic edifice. 4.In The Ethics of Migration. ItReflections underlies on notRecent only counting enumerating but also computing and Migrationand Policies andfollowing “Non-policies” in Italy and Repetition Europe ........................................... 61 conthe of syntactic rules. appears in the texts under Laura Zanfrini sideration not only through the interlingual transcription (the languages of text, bePolicies they formal, arithmetical, ‘natural’ 4.1the Restrictive and Structural Demandmetamathematical, for Immigrant Labouror .. 65 are forced to repeat an articulation of the statement ‘this statement is un4.2 Initiatives for Governing Family and Humanitarian provable’, eachLabour constrained by its and ............. syntax),73but also Migration: Migration butown not semantic Workers’ units Migration through the very possibility of following syntactic rules. Syntactic rules are 4.3 From Guest Workers to Unwelcome Guests .................................. 82 anchored to a line of repetition. One cannot establish syntactic coherence 4.4 Selective Policies and the Brain Drain............................................ 87 without an apparatus, which verifies that the statement to be examined 4.5 Equal and Denied Opportunities ................................ 90 withrepeats theOpportunity syntactic rule. One cannot establish any form of analogy out recourse ......................................................................................... to the claim that one analogue repeats aspects of the Bibliography 97 other. To escape the fundamental and necessary condition of repetition, one must 5.imagine Colombia: Includingthat Emigrants Theirstandards, Societies ofand Origin ....... 101 a discourse denies in rituals, anything but selfUrs Watter validating epiphanic experience. It is tempting to conjecture that no such 5.1 State Interest and Responsibility human discursive community can exist. It is certain that no such discursive towards their Citizens Living Abroad ........................................... 102 community could read this text (although, perhaps, if we allow ourselves 5.2wander Appliedinto Ethics .............................................................................. 104 could to such incredibly far-fetched speculation, such a society perhaps consume it).and Repetition is the foundation of syntactic verisimula5.3 Migration Policy Ethics ......................................................... 106 tion, or at least it would be, if we could establish what repetition 5.4 Migration Policy in Colombia ...................................................... 108 fundamentally is. 5.5 “Colombia nos une”...................................................................... 109 Kristeva considers repetition in modern literature as stemming from 5.6 Alianza País .................................................................................. 112 the same obsession of repetition in the European literature of 5.7 Challenges .................................................................................... 114 (the the late Middle Ages and the beginning of the Renaissance Bibliography the ....................................................................................... chronicles, first novels in prose, the lives of saints, 116 etc.). She continues with the following genealogy, citing Bakhtine. Advanced reWorking Together for the Well-being of Migrants ........................... 119 search has demonstrated the vocal, phonetic and market-place Barry Halliday origin of such enunciations: they arrive directly from the fair, the market, from the sonorous life of the commercial town or the army embarking on a journey. Hollered in full voice by merchants and heralds, the repetitive formulas (tournures) are the very kernels of a discursive practice generated within and for informing, and which is structured like a message, like a connection between Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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a speaker and a recipient. They subsequently penetrate written Bibliography ......................................................................................... texts (La Sale, Rabelais, etc.). In producing themselves60at the very moment where the European structure escapes the domina4. The Ethics of Migration. tion of the symbol (Middle Ages) to submit itself to the authority Reflections on Recent Migration Policies of the sign (modernity), phenomenon indicates once again and “Non-policies” in Italy this and Europe ........................................... 61 the extent to which the structure of the verisimilar tale relies on the Laura Zanfrini structure of Policies phonetic 1969, 232-233). 4.1 Restrictive andcommunication Structural Demand (Kristeva for Immigrant Labour .. 65 Kristeva for concludes herFamily narrative with an analysis of her own object 4.2 Initiatives Governing and Humanitarian of study: Raymond Roussel’s threefold Impressions d’Afrique. Migration: Labour Migration but not Workers’ Migration .............But 73 to an extent that we must still investigate, this narrative seems applicable to the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 texts under our own analysis as well. A verisimulation of information and 4.4 Selective Policies and the Brain Drain............................................ 87 truth is generated by the same pseudo-informative repetition. The more 4.5 Equalarticulated, Opportunity and Deniedminute, Opportunities ................................ 90 carefully tediously and syntactically computable the repetition — the more likely it is to appear verisimilar. The more languages Bibliography ......................................................................................... 97 it binds together, the more discursive strata it relates — the more likely it 5.isColombia: in Their Societies of Origin 101 to appearIncluding as a validEmigrants piece of information, consumed by an ....... eager crowd in Urs Watter the market of scientifico-philosophical ideas. Within certain material limits, 5.1 Staterepetition Interest andthere Responsibility without is no verisimilarity. towards their Citizens Living Abroad ........................................... 102 If the function of the “sense” of discourse is a function of re5.2 Applied Ethics .............................................................................. 104 semblance beyond difference ... one could say that the verisimilar 5.3isMigration andof Ethics 106 (Kris... a secondPolicy degree the ......................................................... symbolic relation of resemblance teva 1969, 211). If we refuse to...................................................... read this second degree as 108 secondary 5.4 Migration Policy in Colombia with respect to the primal truth of science, then discursive verisimilar5.5 “Colombia nos une”...................................................................... 109 ity would be secondary with respect to a radical repetition, the primitive 5.6 Alianza País .................................................................................. 112 manoeuvre that imposes the relations of repetition and similarity on dis5.7 Challenges tinctly different.................................................................................... material entities (e.g. the word ‘it’ that has just 114 appeared, and the word....................................................................................... to appear next: ‘it’; the application of an inference116 rule, and Bibliography its next application; the formulation of an inference rule, and its applicaWorking Together for the of Migrants ........................... 119perhaps tion). This repetition is aWell-being euphemism for controlled difference, or Barry Halliday for would-be-controlled difference, a difference that we wish-to-control with our will-to-power (the Nietzchean concept which Deleuze reads in his Logic of Sense as a will-to-elevate-to-the-nth -power, a will-to-repeat). If the verisimilar is a second degree of resemblance, but not with respect to a true resemblance of the first degree, then the verisimilar is secondary to a primary repetition, which primality, as we shall endeavRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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our to see, is analogous to the primality of Freudian primary repression, Bibliography ......................................................................................... 60 there. namely a primality that is never actually present but always-already This is why the verisimilar is an effect, a result, a product that 4. The Ethics of Migration. forgets the artifice of its production. This is also why the textual Reflections on Recent Migration Policies productivity that underlies theEurope verisimilar is the inherent measure of and “Non-policies” in Italy and ........................................... 61 the mathematical (of the text), but it is not the mathematical (the Laura Zanfrini text), in the Policies same way that allDemand work for is the inherent measure of 4.1 Restrictive and Structural Immigrant Labour .. 65 value without being the value itself (Kristeva 1969, 213, 238–239). 4.2 Initiatives for Governing Family and Humanitarian OurMigration: goal is to Labour observeMigration this inherent text, the processes but notmeasure Workers’ of Migration ............. 73 that produce semiosis, that produce verisimilarity, that generate the function of 4.3 From Guest Workers to Unwelcome Guests .................................. 82 sense or meaning as resemblance beyond difference, a process whose 4.4 SelectiveKristeva Policies and the Brain 87 articulation attributes toDrain............................................ Jacques Derrida. 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 2.4 Iteration 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 For there is no word, nor in general a sign, which is not conUrs Watter stituted by the possibility of repeating itself. A sign which does 5.1 State Interest and Responsibility not towards repeattheir itself, which is not already divided by repetition Citizens Living Abroad ........................................... 102 in its “first time”, is not a sign (Derrida 1978, 246). For for the sign, rep5.2 Applied Ethics .............................................................................. 104 etition is seminal (or rather disseminal, borrowing Derrida’s term which 5.3shall Migration Policy and Ethics ......................................................... 106it does we explore below). If something is not repeated and quoted, not function as a sign, but remains a plain object. For meaning, 5.4 Migration Policy in Colombia ...................................................... 108 unlike communication as une”...................................................................... theorised in information theory, is not the effect 5.5 “Colombia nos 109 of an Alice transmitting a sequence of bits to a Bob, a Bob whose sole role is to 5.6 Alianza País .................................................................................. 112 consume and make vanish the message, a Bob whose sole role is to restore 5.7 quiet Challenges .................................................................................... 114 the and peace. Bibliography 116 Meaning....................................................................................... requires verisimilarity, and verisimilarity requires repetition.

There is no meaning unless (to borrow again the imagery of information Working Together for the Well-being of Migrants ........................... 119 theory) there is an Eve to eavesdrop on the message — to eavesdrop means Barry Halliday here to transcribe the text: to intercept it, to use it (meaning, after all, is use), to repeat it, to verisimulate with it. And since it is Eve who verisimulates meaning, Alice and Bob are discardable (but we do not discard the possibility that, on occasion, Eve happens to coincide with either Alice or Bob). In order for my “written communication” to retain its function as writing, i.e., its readability, it must remain readable Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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despite the absolute disappearance of any receiver, determined Bibliography in general. ......................................................................................... My communication must be repeatable — 60 iterable — in the absolute absence of the receiver or of any empirically 4. The Ethics of Migration. determinable collectivity of receivers. This iterability (iter, once Reflections on Recent Migration Policies again, comes from other in ........................................... Sanskrit, and everything and “Non-policies” in itara, Italy and Europe 61 that follows can be read as the working out of the logic that ties repeLaura Zanfrini tition to alterity), the markfor of Immigrant writing itself, 4.1 Restrictive Policiesstructures and Structural Demand Labourno .. 65matter what particular type of writing is involved ... A writing that was 4.2 Initiatives for Governing Family and Humanitarian not Migration: structurally readable — beyond the death Labour Migration—butiterable not Workers’ Migration ............. 73 of the addressee would not be writing (Derrida 1988a, 7). 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Alice and Bob may be dead (dead like Frege, dead like Russell, like 4.4 Selective Policies and the Brain Drain............................................ 87 Hilbert, or, perhaps, dead like I will someday be; but also, dead like the 4.5 Equal Opportunity and Denied Opportunities ................................ 90 writer of the bulk of this essay already is when I insert this annotation). Imagine a writing whose code would be so idiomatic as to Bibliography ......................................................................................... 97 be established and known, as secret cipher, by only two “subjects.” 5.Could Colombia: in Their the Societies of Origin 101 we Including maintainEmigrants that, following death of the....... receiver, or Urs Watter even both partners, the mark left by one of them is still writing? 5.1 State Interest and Responsibility Yes, to the extent that, organised by a code, even an unknown towards their Citizens Living Abroad ........................................... 102 and nonlinguistic one, it is constituted in its identity as a mark by 5.2iterability, Applied Ethics 104 hence its in .............................................................................. the absence of such and such a person, and ultimately every determinable “subject.” 106 This im5.3 MigrationofPolicy andempirically Ethics ......................................................... plies that there is no such thing as a code — organon of iterability 5.4 Migration Policy in Colombia ...................................................... 108 — which could be structurally secret. The possibility of repeating 5.5 “Colombia nos une”...................................................................... 109 and thus of identifying the marks is implicit in every code, making 5.6itAlianza País .................................................................................. 112 of a network [une grille] that is communicable, transmittable, 5.7 Challenges .................................................................................... 114 user decipherable, iterable for a third, and hence for any possible in general (Derrida 1988a, 7–8). Bibliography ....................................................................................... 116 The letters of the dead Frege, Russell and Hilbert (the last two still Working Together for the Well-being of Migrants ........................... 119 alive at the time) were intercepted, reiterated, verisimulated, resignified by Barry Halliday G¨ odel. And by Derrida, and by us, you and I, reading this text. But, as we have already seen, criteria of verisimilarity vary from discourse to discourse. And the sign, intercepted, does not have the capacity to carry its context and rules of formation along with it. The text is therefore structurally open to other verisimulating, unanticipated meaning-generating transcriptions. Derrida’s concept of the decipherable is a re-encoding of the terms Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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transmission and iteration. For Derrida, to decipher the text, which reBibliography mains beyond......................................................................................... its generator and addressee, we need only repeat60it, and, perhaps, verisimulate with it. 4. The Ethics of Migration. This is not only Derrida’s metaphysical stance. This is also what G¨odel Reflections on Recent Migration Policies does. He verisimulates with and signsEurope to the point of deciphering in them and “Non-policies” in Italy ........................................... 61 a vast Laura Zanfrini of fundamental concepts such as provability and truth. This rearticulation is4.1how he usesPolicies the text. Land, theDemand communists used to say, ..belongs to Restrictive and Structural for Immigrant Labour 65 whoever provides it with water. Text, as G¨ odel uses it, belongs to whoever 4.2 Initiatives for Governing Family and Humanitarian repeats it verisimilarly. Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82

2.5 Dangerous of meaning 4.4 Selective Policies and theshifts Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Actually, the process whereby material mathematics is put into Bibliography ......................................................................................... 97 selfformal-logical form, where expanded formal logic is made sufficient as pure analysis or theory of manifolds, is perfectly le5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 gitimate, Urs Watter indeed necessary; the same is true of the technisation which from time to time completely loses itself in merely tech5.1 State Interest and Responsibility nical thinking. But all this Abroad can and must be a method 102 which is towards their Citizens Living ........................................... understood and practiced in a fully conscious way. It can be this, 5.2 Applied Ethics .............................................................................. 104 however, only if care is taken to avoid dangerous shifts of mean5.3 Migration Policy and Ethics ......................................................... ing by keeping always immediately in mind the original 106 bestowal of upon inthe method, through which it has the 5.4meaning Migration Policy Colombia ...................................................... 108 sense of about the world. Even more, it109 must be 5.5achieving “Colombia knowledge nos une”...................................................................... freed of the character of an unquestioned tradition which, from 5.6 Alianza País .................................................................................. 112 the first invention of the new idea and method, allowed elements 5.7obscurity Challenges to .................................................................................... of flow into its meaning (Husserl 1970b, 47). 114 Bibliography Derrida ....................................................................................... reasserts the link between Husserl’s reproach above116 to Plato’s stance. The advancement of science can be pursued, says Derrida’s Working Together for the Well-being of Migrants ........................... 119 Husserl, even when the sense of its origin has been lost. But then Barry Halliday the very logicality of the scientific gesture, imprisoned in mediacy, breaks down into a sort of oneiric and inhuman absurdity. Did not Plato describe this situation? ... “Geometry and the studies [sciences] that accompany it” are exiled far from their fundamental intuitions. They are incapable of “vision” (idein) and riveted to the hypotheses held as their principles. Confusing symbol with Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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truth, they seem to us to dream (or¯ omen o ¯s oneirottousi) (ReBibliography ......................................................................................... 60 public VII, 533c) (Derrida 1989, 107). But this position is not restricted to old masters. I believe that this po4. The Ethics of Migration. sition underlies HarveyMigration Friedman’sPolicies motivation for seeking to replace G¨ odel’s Reflections on Recent theorem by a questin for simple meaningful finite mathematical and “Non-policies” Italyaand Europe ........................................... 61 Laura Zanfrini theorem that can only be proved by going beyond the usual axioms for mathematics 1998, 805). Could it Labour be that.. 65 syntactic 4.1 Restrictive Policies and (Friedman Structural Demand for Immigrant verisimilarity is not enough for a statement to have genuine meaning? Could 4.2 Initiatives for Governing Family and Humanitarian we avoid dangerous shifts of but meaning? Migration: Labour Migration not Workers’ Migration ............. 73 Leaving this question aside until the end.................................. of this chapter, we note 4.3 From Guest Workers to Unwelcome Guests 82 that dangerous shifts of meaning as articulated above are highly tangible in 4.4 Selective Policies and the Brain Drain............................................ 87 G¨ odel’s text, especially, we observe again, in the gap between the so called 4.5 Equal Opportunity and Denied Opportunities ................................ 90 ‘semantic’ and ‘syntactic’ arguments. The semantic argument presented in the 1931 introduction (see the section G¨ odel’s argument in brief Bibliography ......................................................................................... 97 in the introduction above) proves that one must choose between undecidability 5.and Colombia: Including in Their Societies of Origin ....... 101G¨ consistency. If weEmigrants assume that the formal system is decidable, odel’s Urs Watter argument shows that it cannot be consistent. However, the syntactic ar5.1 State which Interestisand Responsibility gument, supposed to transcribe the semantic argument inside the towards their Citizens Living Abroad ........................................... 102 formal system, brings us to a slightly different conclusion: if we assume 5.2 Applied Ethics .............................................................................. that the formal system is decidable, then we conclude that it 104 is only ωinconsistent, property which......................................................... is weaker, and perhaps less objectionable, 5.3 MigrationaPolicy and Ethics 106 than inconsistency. 5.4 Migration Policy in Colombia ...................................................... 108 The point is that the two linguistic strata end up diverging beyond 5.5 “Colombia nos une”...................................................................... 109 the common meaning that is supposed to be their leading principle and 5.6 Alianza País .................................................................................. 112 make them reflect each other. This divergence has led to a state of affairs 5.7 Challenges .................................................................................... 114 others where some mathematicians accept the semantic argument, while do not. This ....................................................................................... does not create a crisis in mathematics, because 116 almost all Bibliography mathematicians consider the discrepancy to depend on the syntactic and Working for inside the Well-being ofworks, Migrants 119 framesemanticTogether framework which one and........................... are clear on which Barry Halliday work allows which argument. Which framework, if any, is actually true, and in what sense of the term true — these are considered extra mathematical questions. A tradition of mathematicians, which has become dominant (at least as far as most philosophers are concerned) has been developing a particular discursive strategy since the mid 19th century, which became fully operaRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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th

tional at the beginning of the 20 century under the influence of the Hilbert Bibliography 60 and and Bourbaki......................................................................................... schools. While mathematical production is constrained manipulated by many mechanisms, a mathematical argument’s validity de4. The Ethics of Migration. pends heavily on criteria of verifiable syntactic verisimilarity. Reflections on Recent Migration Policies I do not mean to the role........................................... of syntactic verisimilarity61criteria. and “Non-policies” inexaggerate Italy and Europe Laura Zanfrini No mathematician has ever translated any but the simplest and shortest proofs into a formal The enterprise of for automatic, 4.1 Restrictive Policiestext. and Structural Demand Immigrantcomputerised Labour .. 65 proof checking (e.g. for Cantone et al.Family 2004) and hardly ever finds mathematical applica4.2 Initiatives Governing Humanitarian tion,Migration: not only Labour due to Migration technical but difficulties, but also due to lack of73interest not Workers’ Migration ............. by the mathematical community. There are even ways to discredit a math4.3 From Guest Workers to Unwelcome Guests .................................. 82 ematical argument without indicating a syntactic error (for instance, show4.4 Selective Policies and the Brain Drain............................................ 87 ing it to be inconsistent with other accepted results). But a mathematical 4.5 Equal Opportunity and Denied Opportunities 90 setdebate concerning a suggested argument is not................................ considered completely tled until a consensus is established concerning a formal error (which Bibliography ......................................................................................... 97 need not be identified at the most ‘elementary’ formal level, as such level of for5.malisation Colombia:isIncluding Emigrants in TheirorSocieties Originof....... practically never reached), until theofcritics the101 argument Urs Watter withdraw their claims for such error. Note, however, that in pointing out 5.1 State Interest andremains Responsibility formal errors, there some room for debating the manner of formally towards their Citizens Living Abroad ........................................... 102 transcribing an argument that best captures the argument’s intention. 5.2 Applied 104matheIn theirEthics quest.............................................................................. for consensus, substantial tracts of mainstream 5.3 Migration Policy and Ethics ......................................................... 106 And matical discourse bestowed upon syntax the power of final arbitration. in so mathematical discourse has given up protecting itself 5.4doing Migration Policy in Colombia ...................................................... 108against those supposedly dangerous shifts of meaning, which Husserl was wor5.5 “Colombia nos une”...................................................................... 109 ried about. The rules of mathematical syntax have changed, and may keep 5.6 Alianza País .................................................................................. 112 on changing. But at this historic moment, due to the strategy of relegating 5.7 Challenges .................................................................................... 114 substantial authority to syntax, mathematics is one of the contemporary human discourses most exposed to the only partly controllable shifting (itBibliography ....................................................................................... 116 eration, diff´erance) of meaning. Many mathematicians embrace this fact, Working Together forit. theToday’s Well-being of Migrants 119 rather than oppose mathematics will........................... not have any substantial Barry Halliday qualms with an equivalent of Bombelli’s ‘sophistic’ techniques (the introduction of computation with roots of negative numbers) or of the violation of Euclid’s fifth axiom, as long as they are syntactically verisimilar.

To the verifier of mathematical validity, Meaning, as G¨odel writes, is immaterial. It’s not that mathematicians don’t debate questions of meaning (we have quoted Friedman above who does). It is that mathematicians Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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are not required to agree on issues of meaning in order to maintain collaboBibliography ......................................................................................... rative mathematical production. Mathematicians should agree on 60 priorities (otherwise, they cease to communicate, resulting in the deep fragmentation 4. The Ethics of Migration. of mathematics today, which makes it very hard for specialists in different Reflections on Recent Migration Policies fields to understandineach Mathematicians should agree on and “Non-policies” Italyother). and Europe ........................................... 61 syntax (where syntax should be understood as rules of repetition and recursion Laura Zanfrini that, under current and historic generate 4.1 Restrictive Policiesmaterial and Structural Demandconditions, for Immigrant Labour ..consensus; 65 Wittgenstein devoted hundreds of paragraphs to convince philosophers that 4.2 Initiatives for Governing Family and Humanitarian nothing more Labour ‘essential’ can underlie the following of (syntactic) Migration: Migration but not Workers’ Migration ............. 73 rules). Where it can be decided that a sign has escaped mathematical syntax, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 there an outside of mathematics can be warded. Where the relations be4.4 Selective Policies and theand Brain Drain............................................ 87 there tween a mathematical sign mathematical syntax are undecidable, 11 the of mathematics are undecidable as well. 4.5 limits Equal Opportunity and Denied Opportunities ................................ 90 Due to this concrete and historic contingency of mathematics, Bibliography ......................................................................................... 97 poststructural conceptions of semiosis are in a way easier to establish in math5.ematical Colombia: Including Emigrants Their Societies of Origin ....... sign, 101 more discourse than in other in discourses. The mathematical Urs Watter

obviously than any other sign, is thoroughly exposed to supposedly dan5.1 Stateshifts Interestof andmeaning. Responsibility gerous I will show how such shifts operate inside towards their Citizens Living Abroadthe ........................................... 102 G¨ odel’s proof in the section following next. 5.2 Applied Ethics .............................................................................. 104 into But what is this supposed danger, which I insist on welcoming mathematics? Husserl’s danger is obviously not that of a formal 5.3 Migration Policy and Ethics ......................................................... 106contradiction. I do not claim shifts...................................................... of meaning will necessarily entail a formal 5.4 Migration Policy in that Colombia 108 collapse of logical systems. The danger is that meanings associated with 5.5 “Colombia nos une”...................................................................... 109 the motion of mathematical signs will run amok, and lose their original 5.6 AlianzaSuch País .................................................................................. 112 new grounding. danger is indeed prevalent in mathematical discourse: meaning formations may not only diverge from original ones, but114 may even 5.7 Challenges .................................................................................... prove to be semantically contradictory. Bibliography ....................................................................................... 116 A classic example is that of the square root of −1. One can prove Working Together for the Well-being Migrants ........................... 119 that such an object does not exist.ofBut the proof does not prevent the Barry Halliday introduction of this very object into mathematics. To avoid a formal contradiction, the non-existence of a square root of −1 is rearticulated as the non-existence of a real square root of −1. Ridding mathematical structures as in the joke 661646 = 4, which despite the correct result is a formal mistake, but at the same time could be considered as a correct formal manipulation under certain restrictive conditions to be explicitly specified. 11 Such

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of formal contradiction is not a difficult task for a proficient logician. But Bibliography ......................................................................................... during this manoeuvre to escape formal contradiction, the term 60 ‘number’ too is irreducibly displaced away from its origin. 4. The Ethics of Migration. Such processes prevail throughout Reflections on Recent Migration Policiesmathematics. The transformations of the“Non-policies” term ‘line’, forinexample, it went........................................... through non-Euclidean 61 and algeand Italy andas Europe Laura Zanfrini braised geometry, form a geometric analogue of the transformations that afflicted the concept number through theforintroduction of negative 4.1 Restrictive Policiesof and Structural Demand Immigrant Labour .. 65 and complex numbers. This process still goes on today. The recently defined 4.2 Initiatives for Governing Family and Humanitarian 12 notion of noncommutative geometry a contemporary example. Migration: Labour Migration but notis Workers’ Migration ............. 73 But,Guest again,Workers why is all this so dangerous? After all, we know 82 well that 4.3 From to Unwelcome Guests .................................. one can, a-posteriori, look back and articulate a common ‘essence’ shared 4.4 Selective Policies and the Brain Drain............................................ 87 by the entire genealogy of notions such as ‘number’, ‘line’ or ‘geometry’ 4.5 Equal Opportunity Denied Opportunities ................................ 90 (or, at least, by thoseand components of the genealogy deemed relevant for the extractor......................................................................................... of ‘essence’). The danger is that such ‘essences’ fail Bibliography 97 to be original in a phenomenological sense, yielding the equivalent of applying 5.propositional Colombia: Including Emigrants Their Societies of Origin 101 logical analysis to ainsentence that’s senseless as....... to its content, Urs Watter such as the sum of the angles of a triangle is equal to the colour 5.1 State Interest and220), Responsibility red (Husserl 1969, which, according to Husserl, renders the law of towards their Citizens Living Abroad ........................................... 102 excluded middle defunct. Rearticulated meanings of mathematical terms 5.2 Applied Ethicsthe .............................................................................. 104 may result from motion of signs and from the narrative ingenuity of the constructors of and post-hoc dangerously imposing established 5.3 Migration Policy Ethics meaning, ......................................................... 106 rules on objects that exceed their scope of application. 5.4 Migration Policy in Colombia ...................................................... 108 Nevertheless, even if the phenomenological grounding of meanings re5.5 “Colombia nos une”...................................................................... 109 main obscure for author and readers alike, no referee will complain that a 5.6 Alianza País .................................................................................. 112 submitted proof is formally sound, but unacceptable because the original 5.7 Challenges .................................................................................... 114 that bestowal of meaning has been given up (the referee may complain the result is ....................................................................................... irrelevant or uninteresting, or protest against a certain Bibliography 116 terminology). Contemporary mathematical discourse simply does not require Working Together for Well-beingtoofan Migrants ........................... the establishment of the an adherence original bestowal of 119 meaning. Barry Halliday

And still, to properly assess Husserl’s danger we must ask what is this phenomenological origin? Is it some early 20th century axiomatisa12 The study of geometric objects through associated algebraic structures has been abstracted to the point where the resulting generalised algebras may no longer have any underlying geometric objects. These algebraic objects, however, are still studied using geometric terms and motivations.

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tion? Does it perhaps lurk inside Euclid’s Elements? Or is the origin the Bibliography 60 origin first historic ......................................................................................... instance of number ever to appear? For Husserl the relates to historicity, but is not assignable a concrete moment in linear 4. The Ethics of Migration. time. Husserl’s origin is the very phenomenological inauguration of mathReflections on Recent Migration Policies ematical reasoning. in Derrida reads into Husserl’s Origin of Geometry and “Non-policies” Italy and Europe ........................................... 61 that, according to Husserl himself, this inauguration is none other than an openLaura Zanfrini ness to unanticipated articulations of meaning. More precisely, starting 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 from this inaugural infinitisation (Greek mathematics as an infinitely 4.2 Initiatives for Governing Family and Humanitarian openMigration: potentiality for Migration the production theorems within............. a fixed73axiomaLabour but not of Workers’ Migration tisation) mathematics cognises new infinitisations (axiomatisations) 4.3 From Guest Workers to Unwelcome Guests .................................. 82 which are so many interior revolutions (Derrida 1989, 127). Only if 4.4 origin Selective and the Brain Drain............................................ the is Policies understood as openness to revolution, says Derrida’s87 Husserl, can we remain committed to it. Opportunities But such commitment is not dominated 4.5 Equal Opportunity and Denied ................................ 90 by any present meaning, cannot be fettered to any platonic determination, Bibliography ......................................................................................... 97 and challenges any attempt to confine rules to specific realms of objects (by 5.performing Colombia: Including Emigrants in Their of Societies of Origin ....... 101logic to the mathematical equivalent applying propositional Urs Watter statements that are senseless as to their content, we may be committing State Interest Responsibility a5.1 fallacy, but weand may also inaugurate new strata of sense, whose use is towards their Citizens Living ‘reactionary’ Abroad ........................................... 102 not subordinate to attempted phenomenological analyses of origins). If this openness is the origin we must adhere to, then this 5.2 Applied Ethics .............................................................................. 104 origin is5.3precisely the inaugural submission to dangerous shifts of 106 meaning. Migration Policy and Ethics ......................................................... And therefore, from the point of view of post-structural thinking, this is 5.4 Migration Policy in Colombia ...................................................... 108 not so much a danger, as a constitutive condition for semiosis as such. 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112

2.6 Omne symbolum de symbolo 5.7 Challenges .................................................................................... 114

Bibliography 116 The picture ....................................................................................... painted above may be considered nonsensical, unscientific, counter-productive. Before I go on to establish it at the micro-level of Working Together for the Well-being of Migrants ........................... 119 G¨ odel’s proof, I wish to indicate that this position is actually quite pragBarry Halliday matic, at least in the sense of invoking some thinkers subsumed under that term. The picture above may appear awkward, since we are used to expect that mim´ esis of truth by a text has to follow the process of truth ... its order, its law; since it is in the name of truth, its only reference — reference itself — that mim´ esis is judged, proscribed Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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or prescribed according to a regular alternation. In G¨odel’s texts, Bibliography ......................................................................................... 60 and however, which are subject to the authority of verisimulating syntax of repetition (which bring about dangerous shifts of meaning) reference 4. The Ethics of Migration. is discretely but absolutely displaced in the workings of a certain Reflections on Recent Migration Policies syntax, wheneverinany writing both........................................... marks and goes back 61 over its and “Non-policies” Italy and Europe mark an undecidable stroke. Marking here is writing along with Laura with Zanfrini syntax; going Policies back over mark Demand is syntax’s undermining of ..the 4.1 Restrictive and the Structural for Immigrant Labour 65 act of reference governed by truth. Marking lays down discursive strata; at the 4.2 Initiatives for Governing Family and Humanitarian sameMigration: time, having forsaken the but providence of referential in 73 favour of Labour Migration not Workers’ Migrationtruth ............. the rules of syntax, marking conflates the discursive strata into a complex 4.3 From Guest Workers to Unwelcome Guests .................................. 82 mesh of inter-representations. The undecidability here is of course not sim4.4 that Selective Policies and the Brain Drain............................................ 87 mesh ply of G¨ odel’s formula, but that of the complex and unstable of This double mark escapes the pertinence or 4.5inter-representation. Equal Opportunity and Denied Opportunities ................................ 90 authority of......................................................................................... truth: it does not overturn it but rather inscribes it Bibliography 97 within its play as one of its functions and parts (Derrida 1993, 193). 5. Colombia: Emigrants in Their Societies ofintervention, Origin ....... 101 When Including read as part of Derrida’s metaphysical such subUrs Watter jection of truth to formations of repetition tends to be viewed as highly 5.1 State Interest and Responsibility disconcerting. However, in the presence of G¨odel’s rearticulation of truth towards their Citizens Living Abroad as at once presiding over each and every........................................... language, and at the same102 time nec13 5.2 Applied Ethics 104 essarily subject to.............................................................................. the confines of the syntax of some (meta) language,

Derrida’s formulation much of its mystery.14 In fact, one106 can sum5.3 Migration Policy andloses Ethics ......................................................... marise this reading by combining the voices of Peirce and Derrida, as in 5.4 Migration Policy in Colombia ...................................................... 108 the following passage from Of Grammatology (Derrida 1976, 48–50). 5.5 “Colombia nos une”...................................................................... 109 Symbols grow. They come into being by development from 5.6 Alianza País .................................................................................. other signs, particularly from icons, or from mixed signs112 partaking of the nature of icons and symbols. We think only 114 in signs. 5.7 Challenges .................................................................................... These mental signs are of mixed nature; the symbol parts116 of them Bibliography ....................................................................................... are called concepts. So it is only out of symbols that a new symWorking for the Well-being Migrants ........................... 119 Vol. bol canTogether grow. Omne symbolumofde symbolo (Peirce 1931–1958, Barry Halliday 2, §302). 13 See

section 7 of the 1934 text, where G¨ odel follows Carnap and Tarski. This is where G¨ odel claims that the truth of a given language cannot be expressed in that language, as surveyed in the last section of the first chapter. 14 In the next section I will attempt to restore some of this challenging mystery by applying it not to the rearticulation of the concept of truth, but rather to the operation of substitution and to the hymen which allows it. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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Peirce complies with two apparently incomparable exigenBibliography ......................................................................................... 60 cies. The mistake here would be to sacrifice one for the other. It must be recognised that the symbolic (in Peirce’s sense the Saus4. The Ethics of Migration. surian “arbitrariness of the sign”) is rooted in the non symbolic, Reflections on Recent Migration Policies in an“Non-policies” anterior andinrelated of........................................... signification: “Symbols and Italy andorder Europe 61 grow. They Laura come Zanfriniinto being by development from other signs, particularly from icons, or and from mixedDemand signs.”forBut these Labour roots ..must 4.1 Restrictive Policies Structural Immigrant 65 not compromise the structural originality of the field of symbols, the 4.2 Initiatives for Governing Family and Humanitarian anatomy of a domain, a production, andMigration a play:............. “So it73is only Migration: Labour Migration but not Workers’ out of symbols that a new symbol can grow. Omne symbolum de 4.3 From Guest Workers to Unwelcome Guests .................................. 82 symbolo.” 4.4 Selective Policies and the Brain Drain............................................ 87 But in both cases, the genetic root-system refers from sign 4.5 Equal Opportunity Denied Opportunities 90 to sign. No ground and of nonsignification —................................ understood as insignificance or an......................................................................................... intuition of a present truth — stretches out97to give Bibliography it foundation under the play and the coming into being of signs. 5.Logic, Colombia: Including TheiraSocieties of Origin .......in101 according toEmigrants Peirce, isinonly semiotic: “Logic, its genUrs Watter eral sense, is, as I believe I have shown, only another name for 5.1 State Interest and Responsibility semiotics (semeiotike), the quasi-necessary, or formal, doctrine towards their Citizens Living Abroad ........................................... 102 of signs.” And logic in the classical sense, logic “properly speak5.2 Applied Ethics .............................................................................. ing,” nonformal logic commanded by the value of truth, 104 occupies in semiotics a determined and not a fundamental 5.3that Migration Policy only and Ethics ......................................................... 106 level ... It is a matter of elaborating ... a formal doctrine of conditions 5.4 Migration Policy in Colombia ...................................................... 108 which a discourse must satisfy, in order to have a sense, in order 5.5 “Colombia nos une”...................................................................... 109 to “mean,” even if it is false or contradictory. The general mor5.6 Alianza 112 phology of País that.................................................................................. meaning (Bedeutung, vouloir-dire) is independent 5.7all Challenges 114 of logic of.................................................................................... truth ... Bibliography 116 critePeirce ....................................................................................... considers the indefiniteness of reference as the rion that allows us to recognise that we are indeed dealing with Working Together for the Well-being of Migrants ........................... 119 a system of signs. What broaches the movement of signification Barry Halliday is what makes its interruption impossible. The thing itself is a sign ... According to the “phaneoroscopy” or “Phenomenology” of Peirce, manifestation itself does not reveal a presence, it makes a sign. One may read in the Principle of Phenomenology that “the idea of manifestation is the idea of a sign.” There is thus no phenomenality reducing the sign or the representer so that Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the thing signified may be allowed to glow finally in the lumiBibliography 60 nosity of its......................................................................................... presence. The so-called “thing itself ” is always already a representamen shielded from the simplicity of intuitive 4. The Ethics of Migration. evidence. The representamen functions only by giving rise to an Reflections on Recent Migration Policies interpretant that in itself a sign and so on to infinity. and “Non-policies” Italybecomes and Europe ........................................... 61 The self-identity Laura Zanfrini of the signified conceals itself unceasingly and is always on the Policies move. and The property of the representamen is to be 4.1 Restrictive Structural Demand for Immigrant Labour .. 65 itself and another, to be produced as a structure of reference, 4.2 Initiatives for Governing Family and Humanitarian to be separated from itself.but The propertyMigration of the ............. representamen Migration: Labour Migration not Workers’ 73 is not to be proper [propre], that is to say absolutely proximate 4.3 From Guest Workers to Unwelcome Guests .................................. 82 to itself (propre, proprius). The represented is always already a 4.4 Selective Policies and the Brain Drain............................................ 87 representamen. Definition of the sign: 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Anything which determines something else (its interpretant) to refer to an object to which itself refers (its object) in the Bibliography ......................................................................................... 97 same way, this interpretant becoming in turn a sign, and so on ad 5.infinitum. Colombia: Including Their Societies of Origin ....... comes 101 ... If theEmigrants series ofin successive interpretants to Urs Watter an end, the sign is thereby rendered imperfect, at least (Peirce 5.1 State Interest Responsibility 1931–1958, vol. 2,and §303). towards their Citizens Living Abroad ........................................... 102 Under the sovereignty of repetition and verisimulating syntax there .............................................................................. 104 and is5.2 noApplied divisionEthics between ‘motivated’ sign (iconic, reflecting its reference) 5.3 Migration Policy Ethics ......................................................... 106 all we ‘unmotivated sign’. and When recursive syntax is relegated authority, have is a becoming-unmotivated of what may be, on a different 5.4 Migration Policy in Colombia ...................................................... 108 level, motivated. The syntax uproots the sign from whatever supposed ground 5.5 “Colombia nos une”...................................................................... 109 allegedly generated it, and turns it into trace. In fact, there is no 5.6 Alianza País .................................................................................. 112 unmotivated trace: the trace is indefinitely its own becoming5.7 Challenges .................................................................................... 114emerge unmotivated (Derrida 1976, 47). Yes, the sign did supposedly historically certain concrete practices, but it is not this supposed oriBibliographyfrom ....................................................................................... 116 gin that rules over its use. It is rather syntax, revision, and unanticipated Working for the Well-being of Migrants ........................... 119 and practicesTogether that appropriate the sign and manipulate it. This indefinite Barry Halliday disseminal motion of appropriation and rearticulation is that which Derrida calls trace (a theoretical model of this supposed ground and alleged generation, a debate which at once allows the sign to be materially generated and but always-already subject to its own becoming unmotivated, is deferred to the next chapter). The long quotation above was meant to supply theoretic support to Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the mesh of meanings in G¨ odel’s text and to its rearticulation of the concept Bibliography ......................................................................................... 60 of truth (surveyed in sections 2 and 3 of the first chapter) as processes of submission to verisimulating syntax. In order to re-stitch this theoretical 4. The Ethics of Migration. debate to the mathematical context, let’s recapture another paragraph that Reflections on Recent Migration Policies Derrida quotes frominPeirce (Peirce 1940,........................................... 99), one which I covered61up with and “Non-policies” Italy and Europe an ellipsis in the preceding quotation. Laura Zanfrini The science of and semiotics, Peirce, borrowing from medieval 4.1 Restrictive Policies Structuralwrites Demand for Immigrant Labour .. 65 thinkers, has three branches. The first is called by Duns Scotus 4.2 Initiatives for Governing 15 Family and Humanitarian grammatica term itMigration pure grammar. Migration: speculativa. Labour MigrationWe but may not Workers’ ............. 73 It has for its task to ascertain what must be true of the representamen 4.3 From Guest Workers to Unwelcome Guests .................................. 82 used by every scientific intelligence in order that they may em4.4 Selective Policies and thesecond Brain Drain............................................ 87 body any meaning. The is logic proper. It is the science of 4.5 Equal Opportunity and Denied ................................ 90 scienwhat is quasi-necessarily trueOpportunities of the representamina of any tific intelligence in order that they may hold good of any97object, Bibliography ......................................................................................... that is, may be true. Or say, logic proper is the formal science of 5.the Colombia: Including Emigrants in Their Societies of Origin 101in imconditions of the truth of representations. The ....... third, Urs Watter itation of Kant’s fashion of preserving old associations of words 5.1finding State Interest and Responsibility in nomenclature for new conceptions, I call pure rhetoric. towards their Citizens Living Abroad 102intelliIts task is to ascertain the laws by ........................................... which in every scientific 5.2 Applied Ethicsgives .............................................................................. gence one sign birth to another, and especially one104 thought brings forth another. 5.3 Migration Policy and Ethics ......................................................... 106 This trichotomy the semiotic project recognises a stratum108 on which 5.4 Migration Policy inofColombia ...................................................... G¨ odel’s text can articulate a grammar that precedes truth — this is the 5.5 “Colombia nos une”...................................................................... 109 grammatica speculativa, which deals with the constitutive conditions for 5.6 Alianza País .................................................................................. embodying meaning, and which precedes logic as dealing with112 representamina holding.................................................................................... good or being true. To an extent, this is G¨odel’s attempt 5.7 Challenges 114 when he articulates and enumerates all formulas in a formal system Bibliography ....................................................................................... 116 in total disregard of their potential meaninglessness and falseness. But perhaps Working for the Well-being of Migrants ........................... 119 even G¨ odel’s Together task is even more radical, because in this list he does away Barry Halliday with meaning (or at least one layer of meaning). This is a moment of the desirable that it be forgotten, where truth and meaning are cast away so as to allow a survey of the syntactic field of opportunities, and to allow this survey to carry the text adrift. Upon such foundation rest formal 15 Derrida

corrects the reference and attributes the grammatica speculativa to Thomas

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systems (that is, perhaps, why formal systems often tolerate inference maBibliography noeuvres such......................................................................................... as reductio ad absurdum, which allows folly and 60 deceit to establish a confined madhouse in which to carry out their frolicking and 4. The Ethics of Migration. deliver to the outside an antagonistic revelation of truth). Reflections on Recent Migration Policies Husserl’s dangerous shifts of meaning, the constant motion of and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini becoming-unmotivated without an original ground to protect us against the motility ofPolicies signs, and do Structural not arise Demand only from the repetition in 4.1 Restrictive for Immigrant Labourinscribed .. 65 verisimulating syntax. These dangers arise also form a redirect link to the 4.2 Initiatives for Governing Family and Humanitarian hubris of enumerating everything (all Workers’ formulasMigration of a formal language), of Migration: Labour Migration but not ............. 73 desiring to forget meanings, of presuming to control formulas of folly and 4.3 From Guest Workers to Unwelcome Guests .................................. 82 deceit. For even if the totality of what I think is imbued with false4.4 Selective Policies andasthe Drain............................................ hood and madness, in Brain reductio ad absurdum, even if the 87 totality 4.5the Equal Opportunity and exist, Deniedas Opportunities 90 and of world does not in the open................................ hierarchy of languages their truth predicates, even if nonmeaning has invaded the 97 totality Bibliography ......................................................................................... of the world, up to and including the very contents of my thought, 5.because Colombia: Including Societies Originto....... 101 I still meaning has Emigrants lapsed intoin anTheir oblivion of theofdesire forget, Urs Watter think, I am while I think, or if we are somewhat less metaphysically 5.1 State Interestatand presumptuous, theResponsibility very least, I still mean. I repeat, therefore I mean. towards their Citizens Living Abroad 102 — for But this crisis in which reason........................................... is madder than madness 5.2 Applied .............................................................................. 104 and reason in itsEthics manifestation as syntactic verisimilarity is nonmeaning oblivion — and which is more rational than reason, 5.3 Migration Policyinand Ethicsmadness ......................................................... 106 for it is closer to the wellspring of sense, that phenomenological 5.4 Migration Policy in Colombia ...................................................... 108 origin reformulated as an openness to shifts of meaning that veers between 5.5 “Colombia nos une”...................................................................... 109 crisis forgetting and recollecting, between clipping meaning on and off, this 5.6 Alianza País .................................................................................. has already begun and is interminable ... And nowhere 112 else and never before has the manifestation of crisis been able to enrich 5.7 Challenges .................................................................................... 114 and reassemble all its potentialities, all the energy of its meaning, as Bibliography ....................................................................................... 116 much, perhaps, as in G¨ odel’s 1931 and 1934 texts (Derrida 1978, 56, 62). Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

2.7

,

That the sign carries within itself the potential to escape and revolutionise its context, that the sign cannot be guarded against dangerous shifts of meaning, are claims that Derrida has insisted on rediscovering Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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across a myriad of semiotic and metaphysical approaches, arguably samBibliography ......................................................................................... 60 pling the better part of western intellectual history. Without presuming to exhaust Derrida’s analyses, I will proceed to comment, using his tools, on 4. The Ethics of Migration. the mathematical-semiotic implications of relegating authority to syntactic Reflections on Recent Migration Policies verisimilarity and ofinthe (dis)seminal privilege of repetition. My task and “Non-policies” Italy and Europe ........................................... 61 is to demonstrate Laura Zanfrinithese implications not on a historic scale, but within the confines of the synchrony of aStructural ‘single’ mathematical text — G¨ odel’s..proof. For 4.1 Restrictive Policies and Demand for Immigrant Labour 65 those who follow Derrida, finding it all in a mathematical text is clearly to 4.2 Initiatives for Governing Family and Humanitarian be expected —Labour but such expectations for aMigration dangerous assumption of Migration: Migration but not make Workers’ ............. 73 closure, until they challenge the reader in their own singular ways. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Up to this point we have synthesised a pragmatist-oriented reading of 4.4 Selective Policies and the Brain Drain............................................ 87 Derrida with our analysis of semiosis in G¨ odel’s 1931 and 1934 texts. This 4.5 Equal Opportunity and Denied Opportunities ................................ synthesis, this quilt, is meant to re-cover mathematical discourse 90 in its attempt to reign over meaning and truth while subjecting itself to the Bibliography ......................................................................................... 97 rules of verisimulating syntax. Reiteration is manifest in this project as a com5.plex Colombia: Including Emigrantsdeciphering. in Their Societies of Origin 101 both large scale reappropriative This last phrase....... describes Urs Watter G¨ odel’s manoeuvre of rearticulating meaning and truth with respect to an 5.1 State Interest and Responsibility entire (meaning/less, un/true) field of textual combinations (formulas), as towards their Citizens Living Abroad ........................................... 102 well as this essay’s feeding of the 1931 and 1934 texts into the work of 5.2 Applied .............................................................................. Derrida andEthics Kristeva. Such reappropriative manoeuvres needn’t104 maintain meaning (main-tenir, grab by the hand, arrest). In such macroscopic 5.3 Migration Policy and Ethics ......................................................... 106 assemblages meaning is indeed repeated, but only provided we keep in 108 mind that 5.4 Migration Policy in Colombia ...................................................... repetition is resemblance beyond difference, and that resemblance is 5.5 “Colombia nos une”...................................................................... 109 not strictly a precondition for repetition, but, in fact, conditions repetition 5.6much Alianza País .................................................................................. 112 as as it arises as its effect. 5.7 Challenges .................................................................................... 114 This bird’s-eye view is not enough. In order to imbue the mathematical text with the....................................................................................... rule (both sovereign and decreed) of iteration, the Bibliography 116 effects elaborated above must intervene when the most ‘simple’ forms of repetition Working Together for thethe Well-being of Migrants ........................... 119 occur. To demonstrate hold of the sign’s motility on the mathematical Barry Halliday text we must explicate how, from the very first moment I recognise a sign as a sign, I already re-cognise a sign (1) as a sign (2) — how, in the mathematical text, I recognise that a sign is open to repetition, which will resemble it beyond factual differences. Consider, for instance, the elementary repetition quoted from the 1934 text: S(zp , zp ). We’ll quickly review the meaning of this text. To keep Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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things containable, I will not repeat the explication of the many comBibliography ......................................................................................... 60 plex discursive interrelations and ambiguities involved in accounting for S(zp , zp ). However, it is desirable (I so desire) that this thick of meaning 4. The Ethics of Migration. not be forgotten.16 Reflections on Recent Migration Policies First, we distinguish number and numeral. A numeral and “Non-policies” in Italybetween and Europe ........................................... 61 is the representation Laura Zanfrini of a number in the formal language. The number 3, for instance, will be Policies represented by the Demand numeralfor N (N (N (0)))Labour — which 4.1 Restrictive and Structural Immigrant .. 65means ‘the successor of the successor of the successor of zero’. Any other number x 4.2 Initiatives for Governing Family and Humanitarian will Migration: be similarly represented sequence of Migration x such N ’s (x iterations of Labour Migration by butanot Workers’ ............. 73 the successor function). Since such strings cannot be (practically or essen4.3 From Guest Workers to Unwelcome Guests .................................. 82 tially) written for very large constants and for variables, these strings are 4.4 Selective Policies and the Brain denoted by the compact text zx . Drain............................................ The numeral N (N (N (0))), for 87 instance, is4.5 thus denoted by z3and . zxDenied denotes a text in the formal system, but Equal Opportunity Opportunities ................................ 90 is not itself a text in......................................................................................... the formal system. Bibliography 97 The term S(za , zb ) is a function, expressed in the formal language, 5.which Colombia: Emigrants in Their Societies Origin takesIncluding as input two numerals (denoted by zaofand zb ), ....... and 101 outputs a Urs Watter third numeral. This third numeral is obtainable in the following way: 5.1 State Interest and Responsibility 1.towards Take the the number a. theirformula Citizensrepresented Living Abroadby ........................................... 102 5.22.Applied Ethicsthe .............................................................................. 104 of the Substitute numeral denoted by zb for all free occurrences 5.3 Migration andformula Ethics ......................................................... 106 variable Policy w in this (if the formula contains such occurrences). 5.4 Migration Policy in Colombia ...................................................... 108 3. Compute the number representing the resulting formula. 5.5 “Colombia nos une”...................................................................... 109 4. Output the numeral that represents this number. 5.6 Alianza País .................................................................................. 112

If, example,.................................................................................... z11 had denoted the numeral representing the formula 5.7for Challenges 114 w = 0,Bibliography then S(z11....................................................................................... , z3 ) would have been the numeral representing the 116formula N (N (N (0))) = 0. Working the Well-being of Migrants ........................... 119 But It Together is not yetfor necessary to explain what the number p means. Barry Halliday note that if one considers the term S(zp , zp ), then the first zp represents 16 ... he disguises every proper name as a description and every description as a proper name, showing by way of this ruse, that such a possibility, always an open one, was constitutive of writing, to the extent that literature (and mathematics) works it over on all sides. You never know whether he names or describes, nor whether the thing he describes-names is the thing or the name, the common or proper name.(Derrida 1984, 118).

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a formula, whereas the second zp denotes a numeral to be substituted into Bibliography that formula.......................................................................................... zp is repeated, but its meaning is changed. One 60 could, of course, in theory if not in practice, write down the formal expression for S, 4. The Ethics of Migration. and carry out the argument with no reference to the meaning of zp . In fact, Reflections on Recent Migration Policies in order to carry outinthe formal proof one needn’t even recognise61 that the and “Non-policies” Italy and Europe ........................................... text denoted Laura Zanfriniby zp is a numeral. In fact one needn’t even realise that one has proved undecidability at the end ofDemand the argument — oneLabour can, in.. principle, 4.1 Restrictive Policies and Structural for Immigrant 65 formally prove the statement without even realising that one has proved 4.2 Initiatives for Governing Family and Humanitarian an arithmetical statement. But but I will the analysis of............. (whatever Migration: Labour Migration notdefer Workers’ Migration 73 is left of) semiosis in such a reading to the next chapter. For the time being we’ll 4.3 From Guest Workers to Unwelcome Guests .................................. 82 follow the texts under our analysis in embracing the discourse of meaning, 4.4 Selective Policies the Brain Drain............................................ and acknowledge the and change in meaning of the repeated term. 87 4.5 Equal ................................ This Opportunity situation is,and of Denied course, Opportunities not unique to the mathematical90text. In poetic language units are non-repeatable or, to put it otherwise, Bibliography ......................................................................................... 97 the repeated unit is not the same, so that one can guarantee 5.that Colombia: Including Emigrants in Their Societies Origin .......repetition 101 once repeated it is already another. Theofapparent Urs Watter XX is not equivalent to X. There appears a phenomenon, unob5.1 State Interest Responsibility servable on theand (manifest) phonetic level of the poetic text, but towards their Citizens Living Abroad ........................................... 102 which is a specifically poetic effect of sense, and which consists 5.2reading Applied Ethics .............................................................................. 104 somein within the (repeated) sequence both itself and thing else (Kristeva 1969, 259). Kristeva goes on to quote examples by 5.3 Migration Policy and Ethics ......................................................... 106 Baudelaire, Mallarm´ e (L’Azur! L’Azur!, L’Azur!, L’Azur!) and Poe 5.4 Migration Policy in Colombia ...................................................... 108 (Nevermore). 5.5 “Colombia nos une”...................................................................... 109 But in fact one does not even need to consider the poetic as special 5.6 Alianza País .................................................................................. 112 in this way, or pretend that the difference does not exist on the phonetic 5.7 Challenges .................................................................................... 114several level. For example, we may hear in the course of a lecture Bibliography ....................................................................................... repetitions of the word Messieurs! (‘Gentlemen!’). We 116 feel that in each case it is the same expression: and yet there are variations Working Together for the Well-being of Migrants ........................... 119 of delivery and intonation which give rise in the several instances Barry Halliday to very noticeable phonic differences — differences as marked as those which in other cases serve to differentiate one word from another (e.g. pomme from paume, goutte from goˆ ute, fuir from fouir, etc.). Furthermore, this feeling of identity persists in spite of the fact that from a semantic point of view too there is not absolute reduplication from one Messieurs! to the next (Saussure Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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1966, 106–107). To that adds Oswald Ducrot that it is evident that the Bibliography ......................................................................................... 60 simple repetition of the word conferred on its second appearance a nuance of irritation or of pleading absent from the first (Wahl 4. The Ethics of Migration. 1968, 45). Reflections on Recent Migration Policies But so far, we have only observed simple polysemy of the sign and “Non-policies” in Italy and Europe a........................................... 61 zp : it Laura Zanfrini could signify a number or a formula, depending on its syntactic place. This is4.1 not a very exciting not as as the difference Restrictive Policies observation, and Structuraland Demand forradical Immigrant Labour .. 65 that arises from the fact ofFamily repetition. After all, if polysemy can be dis4.2 Initiatives forvery Governing and Humanitarian ambiguated by syntactic position, and the second zp represents numeral Migration: Labour Migration but not Workers’ Migration .............a73 rather than a formula because it is differently syntactically placed, then 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the second zp is not a proper repetition of the first at all (in the same way 4.4 Selective Policies and the Brain Drain............................................ 87 that the noun stand is not a proper repetition of the verb stand ). Meaning, 4.5 Equal Opportunities ................................ here, one Opportunity may object,and is Denied not dangerously shifted by repetition; 90 meaning may turn out to be well-defined and stable, if we consider the interaction Bibliography ......................................................................................... 97 between the position and the sign. Meaning could, perhaps, be held fast to 5.its Colombia: place. Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

But the delicate point here, as in the examples of Kristeva and de 5.1 State Interest and Responsibility Saussure above, is not the discernible differences of intonation, phonic subtowards their Citizens Living Abroad ........................................... 102 stance or syntactic and semantic role. What confers the nuance of irritation 5.2pleading Applied on Ethics 104 The or the.............................................................................. second Messieurs! is the very fact of repetition. 5.3 Migration Policydifferences and Ethics ......................................................... 106to conmeasurable phonic themselves do not lead de Saussure sider the repeated term as an independent entity. The repeated term 5.4 Migration Policy in Colombia ...................................................... 108 exists by definition only in so far as it is preceded by that which it repeats. If it is 5.5 “Colombia nos une”...................................................................... 109 not so preceded, it is simply not a repeated term, regardless of its phonetic 5.6 Alianza País .................................................................................. 112 regularities or singularities. This is the sense in which the repeated term 5.7 Challenges .................................................................................... 114 term must be different from any non-repeated equivalent: the non-repeated stands alone; ....................................................................................... the repeated one does not. Unlike the non-repeated116 term, the Bibliography repeated term cannot be isolated and made to stand alone; if it were, it Working Together forathe Well-being would no longer be repeated term.of Migrants ........................... 119 Barry Halliday

Indeed, the effect of repetition in our mathematical case, S(zp , zp ), is much more radical than a simple polysemy determined by syntactic position. In order to demonstrate this claim we must unveil the number p, and quickly review a portion of G¨ odel’s argument. p is the number denoting the following formula: Πv[¬B(v, S(w, w))], where Π is the universal quantifier, ¬ is the negation sign, S is the functional expression defined above, and Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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B is a predicate in the formal system that represents provability (B(za , zb ) Bibliography ......................................................................................... 60 repreholds if and only if the number a represents the proof of the formula sented by the number b). v and w are numeral variables. This formula reads 4. The Ethics of Migration. that for any numeral that we may substitute for v, this numeral does not Reflections on Recent Migration Policies represent a proof of in the formula represented by S(w, w) — once 61 w is suband “Non-policies” Italy and Europe ........................................... stituted by a numeral. Since numerals cover all possible proofs, the formula Laura Zanfrini represented byPolicies the number p reads: the formula represented 4.1 Restrictive and Structural Demand for Immigrant Labourby .. 65S(w, w) (after substitution of a numeral for w) is unprovable. Note that whether 4.2 Initiatives for Governing Family and Humanitarian thatMigration: statementLabour will turn out to hold or Workers’ not, to beMigration true or false, may Migration but not ............. 73depend on what we will substitute for w. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Let us now use the 1934 text’s notation to recapture the argument 4.4 Selective Policies and 87 from the introduction to the the Brain 1931 Drain............................................ text. Let’s also use the 1931 typographic 4.5 Equal Opportunity and Denied ................................ 90 convention, which substitutes forOpportunities ‘the numeral denoted by zx represents a(n) (un)provable formula’ the shorthand ‘zx is (un)provable’. 97 Bibliography ......................................................................................... According to the definition of S, the expression S(zp , zq ) represents 5.the Colombia: in Their Societies of Origin ....... 101 formulaIncluding number pEmigrants (the formula Πv[¬B(v, S(w, w))]) with zq substiUrs Watter tuted for the free variable w. S(zp , zq ) therefore represents the formula 5.1 State Interest Πv[¬B(v, S(zq , zqand ))],Responsibility which claims that S(zq , zq ) is unprovable. In other towards their Citizens Living Abroad ........................................... 102 words, if S(zp , zq ) is provable, then the S(zq , zq ) is unprovable. This .............................................................................. 104p , zp ) is is5.2soApplied for anyEthics q. Now let’s substitute p for q. We get that if S(z provable, then S(zand ) is unprovable, and end up in a contradiction. 5.3 Migration Policy ......................................................... 106 p , zpEthics We shall Policy not continue here ...................................................... with G¨odel to derive a contradiction 5.4 Migration in Colombia 108 from the possibility that the negation of S(zp , zp ) is provable, and to conclude 5.5 “Colombia nos une”...................................................................... 109 that S(zp , zp ) is undecidable. Instead, we shall study more carefully the 5.6 Alianza País .................................................................................. 112 motion of the sign in these last transitions. 5.7 Challenges .................................................................................... 114 First, Suppose we narrate the substitution above in the following way. Bibliography 116a result, we substitute....................................................................................... zp for zq in the first expression, S(zp , zq ), and then, as following the directive of syntactic rules of substitution, substitute zp for zq Working Together for the Well-being of Migrants ........................... 119 in the second expression, S(zq , zq ), as well. Awkwardly enough, zp , which Barry Halliday first took upon itself the place and meaning of a numeral, subsequently was severed into two positions inside the function S. In this narrative, this zp substituted into the left hand position in S(zq , zq ), does it retain the meaning of numeral, because it is obtained by substituting something that ‘first took upon itself the place and meaning of a number’, or does it now mean formula, because it stands in the syntactic position of a numeral Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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representing a formula? This question is undecidable, in the sense that Bibliography ......................................................................................... 60answer there is no point in trying to choose between the two answers. The is that we have here dangerous shifts of meaning. If this narrative of 4. The Ethics of Migration. the substitution is valid, then syntactic systems that permit substitution Reflections on Recent Migration Policies are extremely likely to be imbued with dangerous anddemonstrated “Non-policies”toinbe Italy and Europe ........................................... 61 shifts of meaning. Laura Zanfrini Things doPolicies not improve if we re-narrate the substitution procedure as 4.1 Restrictive and Structural Demand for Immigrant Labour .. 65 the substitution of zp for all three zq positions at once. A single zp , which is 4.2 Initiatives for Governing Family and Humanitarian placeless (and Labour if meaning is attached syntactic position,............. also necessarily Migration: Migration but nottoWorkers’ Migration 73 meaningless), turns out to be endowed with two distinct meanings, in two 4.3 From Guest Workers to Unwelcome Guests .................................. 82 cases a numeral, and in the third a formula. If, indeed, nothing has meaning 4.4 Selective Policies and the Drain............................................ until it is placed (attached toBrain a position in the text) then before the87 meaning is4.5 shifted being substituted into various meaning articulating positions, Equal by Opportunity and Denied Opportunities ................................ 90 itBibliography is not there at all. It is dangerously shifted, but with respect ......................................................................................... 97 to no present precedent. It’s presence is always already shifted. This narrative 5.demonstrates Colombia: Including in indefatigability: Their Societies ofOmne Origin symbolum ....... 101 Peirce’sEmigrants principle of de Urs Watter symbolo. 5.1 State Interest Responsibility Either way, and zp does not simply mean a formula or a numeral. It carries towards their Citizens Living Abroadthe ........................................... within it the potential for penetrating function S, so as to be 102 integrated 5.2 Applied .............................................................................. 104 as forinto a chain Ethics of events and formations, which relates signs to signs mulas and numerals. zp Ethics means......................................................... through its own becoming unmotivated in 5.3 Migration Policy and 106 materially and discursively constrained forms of verisimulation. zp means 5.4 Migration Policy in Colombia ...................................................... 108 through its force of splitting into (among other things) a formula and a 5.5 “Colombia numeral, itself nos andune”...................................................................... another, where it is not quite clear which is 109 itself, and 5.6 Alianza .................................................................................. 112 which is thePaís other. But the semiotic effect we have here is not exhausted by114 mere un5.7 Challenges .................................................................................... decidability between numerals and formulas. zp is disseminated into an Bibliography ....................................................................................... 116 unbounded proliferation. Indeed, as S(zp , zp ) does not include any free occurrences of w, itfor canthe beWell-being easily verified that Working Together of Migrants ........................... 119 Barry Halliday

S(zp , zp ) = S(S(zp , zp ), zp ) = S(zp , S(zp , zp )) = S(S(zp , zp ), S(zp , zp )), and that each of these zp ’s can again be replaced by S(zp , zp ). The sign divides into itself and an excess, driving itself further and further inside, multiplying itself unboundedly. Similarly, if by N we designate the function, which converts a formula Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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into the numeral that represents it, we obtain the following metamathematBibliography ical equation:......................................................................................... 60 S(z , z ) = zN (Πv[¬B(v,S(zp ,zp ))]) . 4. The Ethics of Migration.p p Reflections on Recent Migration Policies Here again the right hand side can be substituted into the S(zp , zp ) in the and “Non-policies” in Italy and Europe ........................................... 61 right side: Laurahand Zanfrini 4.1 Restrictive Policies Demand for Immigrant Labour .. 65 S(z , zand ) =Structural z , p

p

N (Πv[¬B(v,zN (Πv[¬B(v,S(zp ,zp ))]) )])

4.2 Initiatives for Governing Family and Humanitarian Migration: Labourlonger Migration not Workers’ Migration 73 itself making the formula and but longer, driving the sign p............. away from indefinitely along reiterated substitutions, obscuring its provenance 4.3 From Guest Workers to Unwelcome Guests .................................. 82 and its meaning as leading principle, deferring away. 4.4 Selective Policies and the Brain Drain............................................ 87 The sign zp splits, and its articulation as meaning formula or nu4.5 Equal Opportunity and Denied Opportunities ................................ 90 meral loses its validity, grasp and explanatory force. Its articulation into Bibliography ......................................................................................... 97 numeral/formula roles would not help us follow the above manipulations.

The meaning that the sign occupies in these formal manipulations (if it oc5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 cupies any meaning at all) is an intermediate syntactic-operational meanUrs Watter ing, no longer concerned with reference. In repetition zp disseminates its 5.1 State Interest and Responsibility own articulation, retroactively generating an effect that’s captured by fortowards their Citizens Living Abroad ........................................... 102 malist readings. But it leaves what Derrida calls trace. It pivots around 5.2 Applied Ethics .............................................................................. 104 the comma, which acts like two mirrors facing each other, multiplying the 5.3 Migration Policy and Ethics 106 space inscribed between them ......................................................... (around it) indefinitely.17 The syntactic to anchor meaning to position sought108 to protect 5.4 Migration Policyattempt in Colombia ...................................................... meaning against dangerous shifts. The assumption was that nothing 5.5 “Colombia nos une”...................................................................... 109 was more stable than place itself; obviously, you can never move a place away 5.6 Alianza País .................................................................................. 112 from itself. But the error in this line of thinking is in imagining place as 5.7 Challenges .................................................................................... 114place is pinned down to some sort of stable ambient ether. In fact, the Bibliography ....................................................................................... 116the lack always relative to a perspective, to an articulation of boundary or thereof, and to other places. The place moves with respect to the beholder. Working Together for the Well-being of Migrants ........................... 119 Cutting a piece of text (for the purpose, say, of substituting it somewhere) Barry Halliday rearticulates the places carried along by the cut chunk of text with respect to the new boundaries created by the quotation marks, parentheses, or commas that inscribe it. In a textual practice, which allows quotation and 17 It

may appear that while I argue for an indefinite proliferation of the text S(zp , zp ), I accept that it has a proper starting point, the initial text S(zp , zp ). I defer to the final section of this chapter my denial of this stance. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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iteration — that is in any textual practice — place is just as mobile as the Bibliography ......................................................................................... 60 sign that occupies it.18 The semiotic processes that take place in mathematical texts are ob4. The Ethics of Migration. viously not on identical those that take place in other texts. In contemReflections Recentto Migration Policies porary mathematicsinthe primary authoritative warden is syntax.61 In other and “Non-policies” Italy and Europe ........................................... Laura Zanfrini discourses meaning may be warded by other formative agents. To appreciate the between, one hand, the for semiotic effects of mathemati4.1 relation Restrictive Policies on andthe Structural Demand Immigrant Labour .. 65 cal repetition and self substitution, and, on the other hand, some semiotic 4.2 Initiatives for Governing Family and Humanitarian effects in otherLabour areas Migration of language claiming that............. one is 73 reducible Migration: but (without not Workers’ Migration to the others!), I would like to study an example that may, at first glance, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 appear completely unrelated.19 4.4 Selective Policies and the Brain Drain............................................ 87 This non-mathematical case of apparent repetition and self-predication 4.5 Equal Opportunity Denied Opportunities ................................ is Jay Livingston’s andand Ray Evans’ popular song Que sera sera. 90 The chorus reads: Que sera sera, whatever will be will be, the future’s Bibliography ......................................................................................... 97 not ours to see, que sera sera. The poetic structure and context (which I 5.omit) Colombia: Including Emigrants in aTheir Societies of Origin ....... Que 101 sera indicate that we have here double translation. First, Urs Watter is translated as whatever will be and the repeated sera as will be. 5.1 State Then queInterest sera and andResponsibility whatever will be are transcribed as the future. towards their Citizens Living Abroad ........................................... 102 18 inherent instability of place does not depend on 20th century relativistic physics 5.2This Applied Ethics .............................................................................. 104 or on Leibniz’ metaphysical adventures. Eriugena, a 9th century philosopher, claims that 5.3 definition Migration Policy and and Ethics 106 but in the [of bodies of ......................................................... things devoid of reason] are nowhere the rational soul. In it therefore will also be the places of all things that are 5.4 Migration Policy in Colombia ...................................................... 108 comprehended in place. But if the rational soul is incorporeal, which no wise man doubts, it nos is plain that whatever is understood in it must be incorpo5.5 “Colombia une”...................................................................... 109 real; [and] place is understood in the soul, as has already been determined: 5.6 Alianza País .................................................................................. 112 therefore it is incorporeal (Eriugena 1978, 135). Eriugena displaces place from the world into the rational soul in order to protect it from the motion it would have 5.7 Challenges .................................................................................... 114to suffer were it in the world. On this side of the linguistic turn, however, such na¨ıve form of Bibliography ....................................................................................... 116bound to ideality is foreclosed. On this side of the linguistic turn, ideal place would be the sign that occupies it, and drift along with it. 19 Before Working Together Well-being of Migrants ........................... 119confined we do thisfor wethe should raise the question of generality. Is my analysis toBarry theseHalliday specific texts by G¨ odel, or is it generally applicable to mathematics? I personally am uncomfortable with analyses that are not concrete. I do believe that much of my analysis is generalisable, but concede that any specific claim above might depend on the singularity of the texts I analyse. The philosophical challenge is to relate this singularity to the singularities of other mathematical texts, and experience the plurality of mathematics in the process. No guarantee can be given a priori for the success of such a venture. This is partly why I believe that generalising my claims is no less an ethical than a rational choice.

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So far everything is rather dictionary-like. But the further transcription of Bibliography 60 the next sera......................................................................................... and will be as not ours to see is beyond any dictionary. When everything is recomposed back to the original que sera sera, some 4. The Ethics of Migration. dangerous shifts of meaning are deeply wedged into the repetition. Reflections on Recent Migration Policies But this shift of not ........................................... depend merely on poetic 61 licence. I and “Non-policies” inmeaning Italy anddoes Europe Laura Zanfrini believe that even in a casual conversation with speakers, who don’t have a strong grasp ofPolicies the idiomatic aspects of Spanish or English, the ..apparently 4.1 Restrictive and Structural Demand for Immigrant Labour 65 gratuitous repetition in whatever will be will be will typically be un4.2 Initiatives for Governing Family and Humanitarian derstood as first referring to what about to come, and then as expressing Migration: Labour Migration butisnot Workers’ Migration ............. 73 an inability to see into the future. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 So, what does sera have to do with restricted vision? Let’s try to 4.4 Selective Policies and the Brain Drain............................................ 87 disperse some of the mystery around the semiotic process folded into this 4.5 Equal andatDenied Opportunities ................................ little verse.Opportunity We can look this statement through Grice’s concept90 of implicature or through Sperber and Wilson’s concept of relevance. When Bibliography ......................................................................................... 97 I say that whatever will be will be I violate the maxim of quantity: I do not 5.give Colombia: Including Emigrants in Their of Origin ....... 101 any additional information. I also failSocieties to provide a relevant answer to Urs Watter the question that appears in the song: what will I be? This violation is 5.1 StateifInterest rectified I infer and thatResponsibility the information inscribed in the apparently irrelevant towards their Citizens Living Abroad ........................................... 102 and uninformative que sera sera is simply this: that I don’t know what 5.2 Applied .............................................................................. you will be. Ethics This is how the meaning of will be, the future, is104 linked to ignorance andPolicy to theand lack of prescience. 5.3 Migration Ethics ......................................................... 106 And yet,Policy the additional meaning of sera as lack of prescience, 5.4 Migration in Colombia ...................................................... 108 while inferable from a well articulated theory, is not a simple product of the sign 5.5 “Colombia nos une”...................................................................... 109 sera and its syntactic role. It is a product of a semiotic quest for reference, 5.6 Alianza País .................................................................................. 112 of the failure of this quest, and of the substitution of this failure for the 5.7 Challenges .................................................................................... 114 object of the quest (in a sort of Wonderland il/logic, if one finds nothing, then nothing ....................................................................................... is what one was looking for). For subsequent use116 note that Bibliography this post-factum theoretical explanation of the transcription of whatever Working forthe the future’s Well-being of ours Migrants ........................... 119 will be Together will be as not to see is actually not required Barry Halliday knowledge for someone to use that phrase in that sense. The theoretical explanation hovers over the fact of use. Since Que sera sera may appear to be an irrelevant example here, I will insert a missing link between the mathematical text and the poetic one. This missing link is the well-known paradox of the liar, or of the statement that states of itself: This statement is false. In the poetic text it Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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was asserted of whatever will be that it will be. In the paradox a stateBibliography ment imposes......................................................................................... itself on itself.20 The relation between the paradox60and our mathematical example leaps to the eye, as is professed by G¨odel himself 4. The Ethics of Migration. (1931, 149). In all three examples — the liar, the song and G¨ odel’s proof Reflections on Recent Migration Policies — when something says of itself nothing more than itself, an effect and “Non-policies” in Italy and Europe ........................................... 61 arises ofLaura lack Zanfrini of knowledge. Russell and Whitehead’s exclusion of self-reference from mathematics is one more example of for this effect. Kripke’s of 4.1 Restrictive Policies and Structural Demand Immigrant Labour .. theory 65 truth, which relates self-reference to a truth value that may be interpreted 4.2 Initiatives for Governing Family and Humanitarian as undecidability, is yet another.but not Workers’ Migration ............. 73 Migration: Labour Migration Returning to the mathematical text, G¨odel shows that from the prov4.3 From Guest Workers to Unwelcome Guests .................................. 82 ability of S(zp , zq ) one can derive that S(zq , zq ) is unprovable. From this 4.4 Selective and from the Brain 87 , z ) is one can go onPolicies to derive the Drain............................................ provability of S(zp , zp ) that S(z p p 4.5 Equal Opportunity and Denied is Opportunities 90 over unprovable. But this derivation every bit as................................ a-posteriori, hovering the fact, as is......................................................................................... the above Gricean or Relevance Theoretic analysis 97 of semioBibliography sis in que sera sera. This derivation is, of course, necessary if we are to 5.operate Colombia: Includingsystem, Emigrants Their Societies Origin ....... 101 But a deductive as doinG¨ odel, Grice andofSperber & Wilson. Urs Watter it is not quite necessary for our use of the text. The self substitution of 5.1 numeral State Interest and Responsibility the p, representing a formula, into that very same formula, as selftowards their Citizens Living ........................................... substitution, as self-predication,Abroad is already as linked to ignorance102 as the self 5.2 Applied Ethics .............................................................................. 104 predication of will be or of this statement is false. The link between self-substitution, self-predication and other forms of gratuitous 106 repetition 5.3 Migration Policy and Ethics ......................................................... on the one hand, and lack of knowledge on the other, does not require a 5.4 Migration Policy in Colombia ...................................................... 108 mathematical proof. It precedes, conditions and inspires G¨odel’s construc5.5 “Colombia nos une”...................................................................... 109 tion of his undecidable formula. Undecidability here is not only an effect of 5.6 Alianza Paísbut .................................................................................. G¨ odel’s proof, also part of a more general semiotic effect of 112 gratuitous repetition. It is.................................................................................... the superposition of both effects that makes G¨ odel’s 5.7 Challenges 114 proof function as an intelligible mathematical text. Bibliography ....................................................................................... 116 But this picture of repetition as manifesting lack of knowledge is only Working for the Well-being 119 that half the Together story. Controlled repetitionofis Migrants in fact so........................... intensely productive Barry Halliday 20 This

characterisation might appear too strong. One may assert that all we do is impose a predicate (false) on a given entity (the statement), in the same way that we may impose a predicate (false) on the statement ‘the earth is flat’. However, the statement does not exist except as manifestation of falsehood. It cannot be stated independently of its being false. There is nothing to the statement except that it is false. In this sense, what it predicates on itself is itself. One may say that it manifests the predicate, rather than attributes it. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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it can produce effects of intention. Even at the babbling stage the Bibliography ......................................................................................... phoneme group /pa/ can be heard, explains L´evi-Strauss. 60 But the difference between /pa/ and /papa/ does not reside simply in the 4. The Ethics of Migration. reduplication: /pa/ is a noise, /papa/ is a word. The reduplication Reflections on Recent Migration Policies indicates intention the of the speaker; it endows 61 the secand “Non-policies” in on Italy andpart Europe ........................................... ond syllable Laura Zanfrini with a function different from that which would have been performed by and theStructural first separately, in the form of.. a65poten4.1 Restrictive Policies Demand fororImmigrant Labour tially limitless series of identical sounds /papapapapa/ produced 4.2 Initiatives for Governing Family and Humanitarian by mere babbling. Therefore second /pa/ is not a repetition Migration: Labour Migration butthe not Workers’ Migration ............. 73 of the first, nor has it the same signification. It is a sign that, like 4.3 From Guest Workers to Unwelcome Guests .................................. 82 itself, the first /pa/ too was a sign, and that as a pair they fall 4.4 Selective Policiesof andsignifiers, the Brain Drain............................................ 87 into the category not of things signified. (L´evi-Strauss 21 1969, 339–340). 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Such an......................................................................................... effect, the manifestation of a privileged site of meaning, apBibliography 97 pears in the other examples that we reviewed above as well. Doris Day’s 5.Que Colombia: in Their Societies of Origin ....... sera Including sera was Emigrants originally performed for Hitchcock’s The 101 Man who Urs Watter Knew Too Much, and, indeed, the statement that the future’s not ours 5.1 State Responsibility too see, Interest on top and of its effect of ignorance, potentially indicates privileged towards their Citizens Living ........................................... 102 knowledge. If the future’s notAbroad ours to see, then the grammatic possibil5.2 Applied Ethics .............................................................................. 104 ity of the future being someone else’s to see emerges even before we are required to articulate this other privileged site/sight as God, leader, 5.3 Migration Policy and Ethics ......................................................... 106 fate, chance... 5.4 Migration Policy in Colombia ...................................................... 108 A similar effect arises in some ‘solutions’ of the liar’s paradox (e.g. La5.5 “Colombia nos une”...................................................................... 109 can 1978, 189), which attempt to sever the subject of enunciation from the 5.6 Alianza subject País .................................................................................. enunciated (the statement that asserts falsity from the 112 statement of falsity.................................................................................... is asserted). Here again a privileged site emerges,114 that of a 5.7which Challenges subject dominating the statement-object. Bibliography ....................................................................................... 116 This effect becomes manifest in G¨odel’s text, when G¨odel decides, Working Together the for the Well-being of Migrants ........................... 119the fact openly violating formal syntactic framework, to derive from Barry Halliday that S(zp , zp ) is unprovable, and from the fact that it states that it is unprovable, that it is true (1931, 151). G¨ odel transgresses the confines of ignorance, and claims deliverance to truth beyond the confines of syntax. An extra-syntactic domain of privileged access to truth is formed. But this 21 Several

parents have protested that this statement is false. I include it anyway, because I believe it is more than simply an empirical observation. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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violation of syntactic authority and emergence of a higher truth, this very Bibliography ......................................................................................... 60 emergence too, we must recall, is also subject to some syntactic system — the logic of ‘natural’ or ‘metamathematical’ language. And just as in the 4. The Ethics of Migration. Gricean and Relevance Theoretic analyses of Que sera sera, as well as in Reflections on Recent Migration Policies the ‘solution’ in of Italy the liar a theoretical syntactic or 61 semantic andabove “Non-policies” andparadox, Europe ........................................... regulatory framework may be re-constructed to contain the transgressive Laura Zanfrini 22 rapture to truth beyond 4.1 Restrictive Policies andsyntax. Structural Demand for Immigrant Labour .. 65 That these two effects, ignorance and transgressive rapture, are inti4.2 Initiatives for Governing Family and Humanitarian mately relatedLabour is demonstrated in Derrida’s reading of Kierkegaard’s Migration: Migration but not Workers’ Migration ............. 73 Tout autre est tout autre (literally, Every other is every other). This statement 4.3 From Guest Workers to Unwelcome Guests .................................. 82 relates total ignorance of the other to a paradoxical source of responsibility: Policies the Brain Drain............................................ if4.4 mySelective decisions do notand depend on knowledge or on the authority of 87 an other, 4.5 Equal Opportunity and Denied Opportunities ................................ 90 then these decisions are mine; I am responsible for my ignorant decisions. I bring this text......................................................................................... here to emphasise the ethical moment of the semiotic Bibliography 97 effects under investigation. Is not this dictum — tout autre est tout autre 5.— Colombia: Including in Their Societies of Originanything ....... 101 that in the first placeEmigrants a tautology? It doesn’t signify Urs Watter one doesn’t already know unless one brings to bear upon it an in5.1 State Interest and would Responsibility terpretation that distinguish between the two homonyms towards their Citizens Living Abroad ........................................... 102 tout and tout, an indefinite pronominal adjective (some, someone, 5.2 Applied 104 some otherEthics one).............................................................................. and an adverb of quantity (totally, absolutely, radically, infinitely other), resulting in the interpretation: ‘every 5.3 Migration Policy and Ethics ......................................................... 106 other one is completely other’. But ... then one must also distinguish be5.4 Migration Policy in Colombia ...................................................... 108 tween the two autres. If the first tout is an indefinite pronominal 5.5 “Colombia nos une”...................................................................... 109 adjective, then the first autre becomes a noun and the second, 5.6all Alianza País .................................................................................. 112 has a in probability, an adjective or attribute. One no longer case of tautology, but instead a radical heterology; indeed 5.7 Challenges .................................................................................... 114 this introduces the principle of the most irreducible heterology. Or Bibliography ....................................................................................... 116 else, as a further alternative, one might consider that in both Working Together foror theheterology, Well-being ofwith Migrants ........................... 119 cases (tautology or without the homonym) Barry Halliday the two autres are repeated in the monotony of a tautology that wins out after all, the monotony of a principle of identity that, thanks to the copula and sense of being, would here take over alterity itself, nothing less than that, in order to say: the other is 22 Such

reconstruction was indeed carried through by Tarski and by Carnap, and cited in section 7 of G¨ odel’s 1934 text. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the other, that is always so, the alterity of the other is the alterity Bibliography ......................................................................................... of the other. And the secret of this formula would close60 upon a hetero-tautological speculation that always risks meaning noth4. The Ethics of Migration. ing. But we know from experience that the speculative always Reflections on Recent Migration Policies requires a hetero-tautological position. That is its definition acand “Non-policies” in Italy and Europe ........................................... 61 cording to Hegel’s speculative idealism ... The hetero-tautological Laura Zanfrini position introduces theStructural law of speculation, and ofLabour speculation on 4.1 Restrictive Policies and Demand for Immigrant .. 65 every secret (Derrida 1995, 82–83).23 4.2 Initiatives for Governing Family and Humanitarian The effectLabour of repetition S(z zp ) is every bit as............. dramatic p , Workers’ Migration: Migrationinbut not Migration 73 as the transition from ‘statement number so-and-so is unprovable’ to ‘I am an 4.3 From Guest Workers to Unwelcome Guests .................................. 82 unprovable statement’, whence self-reference, which effects both ignorance 4.4 Selective Policies and the Brain Drain............................................ 87 and privileged meaning, and then appeals to transgression and rapture, 4.5 Equalwhere Opportunity 90 emerges there and wasDenied never Opportunities as much as ................................ a self, only an enumerated list of formulas. The miracle of self consciousness (Wo Es war, 97 soll Ich Bibliography ......................................................................................... werden) is evoked here, and no amount of astute formalism commanding 5.to Colombia: Including Their of Originits ....... 101 turn a blind eye canEmigrants take awayin from G¨oSocieties del’s proposition self-reference Urs Watter

as manifested when G¨ odel’s argument is presented and explained. This self5.1 State Interest and Responsibility reference is indeed avowed by G¨odel himself in (1931, 149) and (1934, 362), towards their Citizens Living Abroad ........................................... 102 only to be immediately disavowed (1931, 151, ff. 15). 5.2 Applied .............................................................................. 104 S(z , z Ethics ) manifests privileged meaning just as /papa/ manifests an p

p

5.3 Migration Policy and/pa/ Ethicsand ......................................................... 106 derive intention lacking from as Que sera sera and the liar privileged sitesPolicy knowledge by transgressing ignorance. S(zp , zp ) 108 turns old, 5.4 Migration in Colombia ...................................................... habitual patterns and noises (such as S(zp , w), ‘this not-yet-specified state5.5 “Colombia nos une”...................................................................... 109 5.6 Alianzainstance País .................................................................................. 112 23 Another of relating vacuous repetition to privileged meaning is Maimonides’ interpretation of the repetition in the statement I am that I am as a manifest 5.7 Challenges .................................................................................... 114 proof of the necessary existence of God: The first noun which is to be described is ehyeh; Bibliography ....................................................................................... 116 the second, by which the first is described, is likewise ehyeh, the identical word, as if to show that the object which is to be described and the atWorking Together for Well-being ofthis Migrants ........................... 119This is, tribute by which it is the described are in case necessarily identical. Barry Halliday therefore, the expression of the idea that God exists, but not in the ordinary sense of the term; or, in other words, He is “the existing Being which is the existing Being”, that is to say, the Being whose existence is absolute. The proof which he was to give consisted in demonstrating that there is a Being of absolute existence, that has never been and never will be without existence (Maimonides 1904, I.63). Note that my conflation of logic and theology is not entirely out of context. G¨ odel himself worked on formalising Anselm’s ontological argument (G¨ odel 1986–2003, Vol. III, 403–404). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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ment is unprovable’) into a statement that explodes with novelty, not beBibliography 60 cause S(zp , zp......................................................................................... ) or ‘I am an unprovable statement’ is any more expressive than ‘this not-yet-specified statement is unprovable’, but because it links to 4. The Ethics of Migration. a chain reaction of a sign with itself in different positions, which traverses Reflections on Recent Migration Policies language from poetry through everyday use, to the infant’s and “Non-policies” inand Italyethics, and Europe ........................................... 61 first words, encompassing some of the most challenging logical paradoxes, forcLaura Zanfrini ing logicand toStructural accept what untilfora Immigrant few years Labour earlier..had 4.1 mathematical Restrictive Policies Demand 65 never even been formulated inside it as a question: that there is an undecidable 4.2 Initiatives for Governing Family and Humanitarian statement (and, according to G¨ odel, that thisMigration undecidable statement is Migration: Labour Migration but not Workers’ ............. 73 true). 4.3 From Guest Workers to Unwelcome Guests .................................. 82 A portrayal of mathematical meaning and truth as bound to everyday 4.4 Selective Policies and as theenumeration’s Brain Drain............................................ 87 as well semiotic processes (such power of enchantment 4.5its Equal Opportunity Denied Opportunities ................................ as constitution of and knowledge, and repetition’s manifestation90of both ignorance and......................................................................................... privileged meaning); a portrayal of mathematical 97 discourse Bibliography as necessarily imbued with dangerous shifts of meaning; a portrayal 5.where Colombia: Including meaning Emigrants in Their of Origin ....... 101 mathematical and truth Societies are, on the one hand, subject to Urs Watter syntax, but, on the other, can exceed any given syntactic determination; a 5.1 State Interest and Responsibility portrayal where even this excess of mathematical truth and meaning with towards their Citizens Abroadto ........................................... respect to the syntax thatLiving is supposed contain them, even this 102 excess can 5.2a-posteriori Applied Ethics .............................................................................. 104— such be contained by syntactic and semiotic constructions a5.3 portrayal to me much more decent and valid than the Migrationappears Policy and Ethics ......................................................... 106 images of clarity and distinctness that usually appear in the literature. This is all 5.4 Migration Policy in Colombia ...................................................... 108 the more so if such a portrayal draws attention to the ethical impact of the 5.5 “Colombia nos une”...................................................................... motility of the sign (as I shall further attempt below), and depicts109 all of the 5.6 Alianza País .................................................................................. 112 above as inevitable and productive surges of constrained and disseminated responsibility, than as hindrances to be circumvented by some 5.7 Challengesrather .................................................................................... 114 longed for, self-fulfilling, authoritative Characteristica Universalis. Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119

2.8 Variables Barry Halliday

In G¨ odel’s text the variable is the unstable ground upon which the above operations are inscribed. It is there to be replaced. If I treated the text S(zp , w) above as a numeral, it was by abuse of terminology. In order for it to become a numeral w must be substituted. It is a screen: at once the visible projection surface for images, and that which prevents one Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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from seeing the other side. It is a place holder. It says: substitute here. Bibliography ......................................................................................... Holds in reserve and exposes to view (Derrida 1993, 314). 60 And the place it covers over is surrounded by other signs, which push and pull the 4. The Ethics of Migration. variable screen so as to reform the image projected upon it. Indeed, as we Reflections on Recent Migration Policies saw at times in the variable becomes a numeral, at other times andabove, “Non-policies” Italy and Europe ........................................... 61 a formula; sustains both, as well as the projected ‘mitosis’ and dissemination LauraitZanfrini of terms Policies by further substitution. 4.1these Restrictive and self Structural Demand for Immigrant Labour .. 65 The variable does notFamily discriminate. Anything that fits its frame (a 4.2 Initiatives for Governing and Humanitarian Migration: Labour Migration but not Workers’ Migration .............that 73 yield syntactic prescription) is welcome. It does not reject substitutions falsities. as it ingests, absorbs and interiorises everything, 4.3 FromInsofar Guest Workers to Unwelcome Guests .................................. 82 proper or not, the variable, like aDrain............................................ sponge, is certainly “ignoble”. 4.4 Selective Policies and the Brain 87 Like its name, it takes in water everywhere. But it is far from neutral; it 4.5 Equal Opportunity and Denied Opportunities ................................ 90 can also, when applied to a surface, expunge, wipe and efface Bibliography ......................................................................................... 97 (Derrida 1984, 72). 5. Colombia: Including in Their of Origin ....... 101 thus This variable asEmigrants surface and screen,Societies or as tain of this mirror Urs Watter reflects — imperfectly — what comes to it — imperfectly — It is 5.1 State Interest and Responsibility the ghost of what it reflects, the shadow deformed and reformed towards their Citizens Abroad ........................................... 102 fixity according to the figureLiving of what is called present: the upright of stands before me; “the inscriptions... appear 104 inverted, 5.2what Applied Ethics .............................................................................. righted, fixed . Theand variable is destined to become a constant106 (or to be 5.3 Migration Policy Ethics ......................................................... bound, but I will not dwell on this interesting and complex operation here). 5.4 Migration Policy in Colombia ...................................................... 108 The operation of substitution is what lifts the veil screen (Derrida 5.5 “Colombia nos une”...................................................................... 109 where 1993, 314) to produce not al¯etheia, but the hall of funny mirrors 5.6 Alianza País .................................................................................. 112 al¯ etheia is inscribed. As if mirrors would not be in the world, simply, included in the totality of all onta, and their images, 114 but that 5.7 Challenges .................................................................................... things “present”, on the contrary, would be in them (Derrida 1993, Bibliography ....................................................................................... 116 324). The entire blank page is a variable that may be substituted by a text. The place (in thefor world or in the rational soul)........................... is a variable that Working Together the Well-being of Migrants 119may be Barry Halliday substituted by a blank page.

The variable mimes. It mimes the operation of the constant that is to replace it. But the miming is so perfect, that the variable and the constant sometimes cannot be distinguished. Where G¨odel writes by [α; n] we denote the formula that results from the class sign α when the free variable is replaced by the sign denoting the natural number Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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24

n (1931, 149), n is a variable — it can stand for any number. On the Bibliography 60 other hand, n......................................................................................... is said to be a natural number replacing a free variable, not a variable, and a numeral sign in the formal language can denote the 4. The Ethics of Migration. natural number n only if n is a specific constant. It seems that if G¨odel Reflections on Recent Migration Policies were to be a little more careful, he should have written the free 61 variable and “Non-policies” in Italy and Europe ........................................... isLaura replaced by the sign denoting the natural number substituted for Zanfrini n, the Policies actual natural number in abeyance. 4.1leaving Restrictive and Structural Demand for Immigrant Labour .. 65 But in fact it simply doesn’t matter. There is no formal syntactic rule 4.2 Initiatives for Governing Family and Humanitarian to distinguish free variable from constant (noMigration equivalent of the 73 syntactic Migration: aLabour Migration butanot Workers’ ............. rule that distinguishes free and bound variables), apart from an explicit 4.3 From Guest Workers to Unwelcome Guests .................................. 82 meta-declaration, which is often not provided explicitly. The free variable 4.4 Selective Policies andbe thedistinguished Brain Drain............................................ 87 and the constant cannot from ‘inside the text’.25 Constants 4.5 Equal Opportunity Opportunities 90 and free variables can and onlyDenied be told apart. And,................................ indeed, nothing changes in the formal appearance of things when n is substituted on the same97page by Bibliography ......................................................................................... a certain specific natural number q, except for the designating letter. 5.And Colombia: Including Emigrants Societies Origin 101specific since this introductory partinofTheir the text doesofnot yet ....... fix the Urs Watter details of a formal system, q still is, to an extent, a variable depending on 5.1 precise State Interest Responsibility the formaland system to be used.26 That is how the mime operates, towards Citizens Living ........................................... whose act their is confined to a Abroad perceptual allusion without 102 breaking 5.2 Applied Ethics .............................................................................. 104 the ice or the mirror: he thus sets up a medium, a pure medium, of (Derrida Mallarm´ e in Derrida 1993, 294). 106 5.3fiction Migration Policy quoting and Ethics ......................................................... The variable on which the constant projects has, 108 as we saw 5.4 Migration Policyscreen in Colombia ...................................................... in the previous section, the capacity to substitute something that contains 5.5 “Colombia nos une”...................................................................... 109 itself into itself (the substitution of S(zp , zp ) for zp in S(zp , zp )). It can 5.6 Alianzareplicate País .................................................................................. 112mimes self-divide, itself, refer to itself. This mime of substitution reference. He.................................................................................... is not an imitator; he mimes imitation ... 5.7 Challenges 114In this perpetual ... one can never know what the allusion Bibliographyallusion ....................................................................................... 116alludes to, unless it is to itself in the process of alluding, weaving its Working for the Well-being of Migrants ........................... 119 hymen Together and manufacturing its text. Wherein allusion becomes a Barry Halliday game conforming only to its own formal rules (Derrida 1993, 219). 24 For us here class sign is formula, the free variable is w, and the sign denoting the natural number n is the numeral denoted by zn . 25 Actually, even a variable, which appears free within a specific chunk of text, can be bound in the context of a larger chunk of text. 26 Is an incontestable constant, such as 0, really a constant? Not to the extent that it can stand for the minimal element of any model of the natural numbers.

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All this happens on the hymen surface of the variable, around the Bibliography ......................................................................................... comma, between parentheses. Does it matter that the comma, 60 the focal point of self replication is in fact absent from the formal system? Does it 4. The Ethics of Migration. matter that a proper formal text in the system that G¨odel employs contains Reflections on Recent Migration Policies no commas, that commas areand confined to........................................... the shorthand that covers61over the and “Non-policies” in Italy Europe formal text? Does it matter that Quine (1995, chapter XXIII) has devised Laura Zanfrini a4.1 formal system of predicate calculus withfor noImmigrant commas Labour or variables? Restrictive Policies and Structural Demand .. 65 But just as ladders can be thrown away, so the screen, the mirror, its tain, the 4.2 Initiatives for Governing Family and Humanitarian hymen are all dispensable. The but irreplaceable of the73 variable, Migration: Labour Migration not Workers’ character Migration ............. which everything seemed to grant to it, was laid out like a trap ... 4.3 From Guest Workers to Unwelcome Guests .................................. 82 it produces its effect first and foremost through its syntax, which 4.4 Selective and the Brain Drain............................................ 87 disposes thePolicies “entre” (between) in such a way that the suspense is4.5due only to the and placement ... It is the................................ “between”, whether it Equal Opportunity Denied Opportunities 90 names fusion or separation, that thus carries all the force Bibliography ......................................................................................... 97 of the operation (Derrida 1993, 220). 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 It is not the variable, it is the gap. What underlies all these effects is Urs Watter the gap that allows to rupture the text, sever a syntagma, and graft it some5.1 State Interest and Responsibility where else, regardless of Living what itAbroad once represented, what it represents towards their Citizens ........................................... 102 now, what it will go on to represent (formulas, numerals, self-reference, undecid5.2 Applied Ethics .............................................................................. 104 ability...). This force of rupture is tied to the spacing [espacement] 5.3 Migration Policythe andwritten Ethics ......................................................... 106it from that constitutes sign: spacing which separates other elements of in the internal contextual chain (the always 5.4 Migration Policy Colombia ...................................................... 108 open possibility of nos its disengagement and graft), but also from 109 all forms 5.5 “Colombia une”...................................................................... of present reference (whether past or future in the modified form 5.6 Alianza País .................................................................................. 112 of the present that is past or to come), objective or subjective. 5.7 Challenges 114rather This spacing .................................................................................... is not the simple negativity of a lacuna but Bibliography ....................................................................................... 116longer the emergence of the mark (Derrida 1988a, 9–10). One no even has the authority to say that “between” is a purely syntacWorking Together for the Well-being of Migrants ........................... 119 tic function. Through the re-marking of its semantic void, it in Barry Halliday fact begins to signify ... Its semantic void signifies, but it signifies spacing and articulation; it has as its meaning the possibility of syntax (indeed, it is the operation with semantically meaningless terms that highlights most the rules of pure syntax, those that require cutting along the spaces between the signs in order to substitute and apply syntactic rules). And by ordering the application of verisimulating syntax this gap Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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orders the play of meaning. Neither purely syntactic nor purely Bibliographybut ......................................................................................... semantic, rather the point where syntactic verisimulation, 60 which is a necessary condition for effecting meaning, is found to depend on the se4. The Ethics of Migration. mantics of understanding and applying rules, it marks the articulated Reflections on Recent Migration Policies opening of that opposition 1993, 222). and “Non-policies” in Italy and(Derrida Europe ........................................... 61 Laura ItZanfrini is the sustained, discrete violence of an incision that is not

apparent in the thickness of theDemand text, afor calculated insemination of 4.1 Restrictive Policies and Structural Immigrant Labour .. 65 the proliferating allogene through which the two texts, the grafted 4.2 Initiatives for Governing Family and Humanitarian and Migration: the grafted-onto, are transformed, deform each other, Labour Migration but not Workers’ Migration .............contami73 nate each other’s content, tend at times to reject each other, or 4.3 From Guest Workers to Unwelcome Guests .................................. 82 pass elliptically one into the other and become regenerated in 4.4 Selective Policies and the the Brain Drain............................................ the repetition, along edges of an overcast seam {un 87 surjet}. 4.5 Equal Opportunity and Deniedto Opportunities ................................ 90 of its Each grafted text continues radiate back toward the site removal, transforming that, too, as it affects the new territory Bibliography ......................................................................................... 97 (Derrida 1993, 355). The fact that grafting and substitution are syntac5.tically Colombia: Including Emigrants Their Societies of Originthe .......meaning 101 defined does not prevent in them from rearticulating of Urs Watter both the graft and the host. And the proof of that is in our reading of 5.1pState S(z , zp ). Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104

2.9 Across theEthics sign of equality 5.3 Migration Policy and ......................................................... 106 5.4many Migration in my Colombia ...................................................... In ways Policy some of work here would have been easier, had108 I focused 5.5equality “Colombia nos une”...................................................................... on rather than the variable. The motion across equality,109 as in 5.6 Alianza País .................................................................................. 112 S(zp , zp ) = S(S(zp , zp ), S(zp , zp )), 5.7 Challenges .................................................................................... 114 ....................................................................................... 116 a difisBibliography modelled after and mimes the copula. Equality operates by erasing ference, by allowing both terms that surround the equality to communicate Working Together for the Well-being of Migrants ........................... 119 and become each other. Equality is not there in advance, because, a-priori, Barry Halliday the texts around the equality are recognised as different; these texts would, for instance, be assigned different numbers in a G¨ odel-like enumeration of formulas. But since equality is not there (not established) until it is traversed (until the texts surrounding it are shown to be the same), one may conclude that it is never traversed at all (Derrida 1993, 353). It is not there, established, until it is traversed, and therefore at the moment of its Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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appearance as established it must already be traversed. Whenever it holds, ......................................................................................... 60 itBibliography is already traversed. It is always already traversed. At some point, Wittgenstein was fretful over the instability of equal4. The Ethics of Migration. 27 ity. Identity of theMigration object I Policies express by identity of the sign and Reflections on Recent not means of in a sign of identity. Difference of the objects by and by “Non-policies” Italy and Europe ........................................... 61 Laura Zanfrini difference of the signs (Wittgenstein 1922, §5.53). The identity sign is therefore notPolicies an essential constituent notation 4.1 Restrictive and Structural Demand of forlogical Immigrant Labour ..(Wittgen65 stein 1922, §5.533). And we see that the apparent propositions like: 4.2 Initiatives for Governing Family and Humanitarian “a = a”, “a Labour = b.b = c. ⊃ a but = c”, “(x).x =Migration x”. “(∃x).x = 73 a”, etc. Migration: Migration not Workers’ ............. cannot be written in a correct logical notation at all (Wittgenstein 4.3 From Guest Workers to Unwelcome Guests .................................. 82 1922, §5.534). But contemporary mathematics did not seem to be moved.28 4.4 Selective Policies the Brain Drain............................................ Perhaps it was not soand moved, because contemporary mathematics 87 accepted 4.5 Equal unconsciously, Opportunity andand Denied Opportunities 90 logic (latently, against the most ................................ severe forms of astute represented young Wittgenstein) that This being-traversed Bibliographyby ......................................................................................... 97 is not something that happens by accident to the mirror of equality; it 5.isColombia: Including in Their Societies Origin inscribed within Emigrants its structure. This is as of much as....... to 101 say that, Urs Watter forever producing itself, it never comes to be. Like the horizon 5.1 State 1993, Interest353). and Responsibility (Derrida towards their Citizens Living Abroad ........................................... 102 The difference between a traditional conception of mathematical semio5.2 Applied Ethics .............................................................................. 104 sis and the one I am attempting to establish here can, perhaps, be made to rest upon the copula (Derrida 1993, 353). The form of equality 5.3 Migration Policy and Ethics ......................................................... 106essentialises the text, it, immobilises it. Its motion is 5.4 Migration Policy substantialises in Colombia ...................................................... 108 thus reduced to a series of stances and its writing to a thematic 5.5 “Colombia nos une”...................................................................... 109 exercise. But to go beyond this traditional stance It is not enough to 5.6 Alianza País .................................................................................. install plurivocity in order to recover the interminable112 motion of Writing does not simply weave several threads 5.7writing. Challenges .................................................................................... 114 into a Bibliography ....................................................................................... 27 I am abducting Wittgenstein’s text here twice. First by neglecting its116 relation to the work of Frege and Russell, and second by ignoring the possible differences between

Working Together for theaspects Well-being of Migrants 119them out identity and equality. Both are relevant for this ........................... analysis, but I leave

inBarry orderHalliday not to digress too far. 28 Had we listened to Wittgenstein, who set rules to prevent dangerous shifts of meaning (e.g.: write ... not “f (a, b). a = b”, but “f (a, a)” (Wittgenstein 1922, §5.531)), rules that deny different variables the right to host identical values, could we then have avoided the monstrous transformation of S(zp , zq ) into S(zp , zp )? Perhaps. But I doubt that we could practice mathematics with these rules; and if we could, then monsters would most likely emerge from the friction between the sign and the gaps that would articulate it.

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single term in such a way that one might end up unravelling all Bibliography ......................................................................................... the “contents” just by pulling a few strings (Derrida 1993,60 350). The point of dissipation can be recognised in the following question 4. The Ethics of Migration. (but doesn’t have to be, for it is nowhere among the onta): does the copula Reflections on Recent Migration Policies interrelate pre-existing entities eventually discovered to have already reand “Non-policies” in Italy and Europe ........................................... 61 sembled each other, or does it install resemblance beyond difference? Laura Zanfrini There are at least twoand ways to answer this question: 4.1 Restrictive Policies Structural Demand for Immigrant Labour .. 65 4.21.Initiatives for Governing Family and Humanitarian The copula interrelates pre-existing entities eventually discovered to Migration: Labour Migration but not Workers’ ............. 73 have already resembled each other (this isMigration polysemy: an articulated 4.3 From Guest Workers to Unwelcome Guests .................................. closed range of meanings that can belong to a certain sign).82 4.42.Selective and the Brain 87 I canI cannotPolicies answer, because theDrain............................................ question keeps undeciding itself. 4.5 Equal Opportunity and Denied Opportunities 90 and not answer, because whenever I pretend................................ to install resemblances differences, they escape (this is dissemination: the range 97 of meanBibliography ......................................................................................... ings is not confined, it rearticulates the very attempts to exhaust and 5. Colombia: Including articulate it). Emigrants in Their Societies of Origin ....... 101 Urs Watter

The difference between discursive polysemy and textual dissem5.1 State Interest and Responsibility ination, between the two answers above, is precisely difference towards their Citizens Living Abroad ........................................... 102 itself, “an implacable difference”. This difference is of course indispens5.2 Applied Ethics .............................................................................. 104 able to the production of meaning (and that is why between pol5.3 Migration Policy and Ethics ......................................................... 106 ysemy and dissemination the difference is very slight). But to the 5.4 Migration in Colombia ...................................................... 108 says extent that Policy meaning presents itself, gathers itself together, itself, and is nos ableune”...................................................................... to stand there, it erases difference and casts it 5.5 “Colombia 109 aside (Derrida 351). 5.6 Alianza País1993, .................................................................................. 112 Wittgenstein would be right to comment that the above question is 5.7 Challenges .................................................................................... 114 meaningless, because it exceeds the rules of the logical language game. But Bibliography ....................................................................................... 116 trifling for those of us, who refuse to give up a question just for the mere fact of its meaninglessness, this is a place where meaning can be made Working Together for the Well-being of Migrants ........................... 119 toBarry spring up: in refusing the authority of pre-existing entities. This is an Halliday ethical moment.

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2.10

G¨ odel’s undecidable formula doesn’t exist

Bibliography ......................................................................................... 60 4. The Ethics of Migration. And modernonmathematics embraces such refusal almost to the point of Reflections Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 was dissipation. Even if we could decide whether the undecidable formula Laura Zanfrini a formal text, a number, the numeral representing it, or any former or 29 4.1 Restrictive Policies and Structural Demand for Immigrant Labour One .. 65 might further encoding, there is still no undecidable proposition. have been led to believe that there was, had G¨ o del not devoted no less 4.2 Initiatives for Governing Family and Humanitarian Labour Migration notthe Workers’ ............. thanMigration: five different footnotes to but stress claim Migration that, despite the 73 fact that the proposition is only denoted, abbreviated 4.3 undecidable From Guest Workers to Unwelcome Guestsrepresented, .................................. 82 in the text — despite all this the undecidable proposition can be written down. 4.4 Selective Policies and the Brain Drain............................................ 87 But it can’t. It’s too long. It contains too many signs to be written down. 4.5 Equal Opportunity Denied Opportunities ................................ 90 them, And so does S(zp , zp ).and And so does zp alone. All we can do is denote Bibliography ......................................................................................... 97 represent them, and abbreviate them.

I will not resort here to the party-trick of comparing the number of 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 signs in the formula to the number of particles in the universe, because Urs Watter I don’t believe that particles in the universe are numbered, and because 5.1 State Interest and Responsibility even if the former number were smaller, it would still be too large for the towards their Citizens Living Abroad ........................................... 102 undecidable proposition to be written and read by humans. And no, it 5.2 Applied Ethics .............................................................................. 104 does not matter either, whether the formula can or cannot be produced 5.3aMigration Ethics ......................................................... 106 by physicallyPolicy viableand machine (one which does not violate thermodynamic laws), and which would be reliable enough to write the undecidable 5.4 Migration Policy in Colombia ...................................................... 108formula 30 correctly with high probability. It doesn’t even matter whether odel’s 5.5 “Colombia nos une”...................................................................... 109G¨ argument can be modified to provide a much shorter undecidable formula 5.6 Alianza País .................................................................................. 112 (indeed, it can). The only thing of importance here is that contemporary 5.7 Challengesendorses .................................................................................... mathematics G¨ odel’s construction as it stands in the114 1931 and 1934 texts regardless of whether it can or cannot be actually written Bibliography ....................................................................................... 116 down in the formal system PM. That is what mathematical discourse does today: Working for the Well-being of Migrants ........................... 119 it writesTogether over. Barry Halliday

But the issue at hand isn’t just a technical strategic choice of mathematical discourse. No extreme form of finitism could resolve the difficulty above. For even if we were able to produce the undecidable formula, we 29 See

subsection 2.3 of the first chapter of this book. kind of line of thinking can be found, for instance, in chapter 3 of Rotman

30 This

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would still have to somehow verify, or consume, the construction. And it Bibliography ......................................................................................... 60 would doesn’t matter either whether our ability to verify the construction or would not depend on mechanical means. None of this matters because 4. The Ethics of Migration. the construction is always too complex to be digested all at once, in one Reflections on Recent Migration Policies moment of present epiphany. TheEurope reader........................................... (verifier, consumer) of the61formula and “Non-policies” in Italy and will always be broken between a self and the tools (pen and paper) used in Laura Zanfrini verifying or reading the And even for if we were to Labour learn the 4.1 Restrictive Policies andformula. Structural Demand Immigrant .. 65formula by heart, so as no tools may stand between the formula and our selves, we 4.2 Initiatives for Governing Family and Humanitarian would still be split between a past we began to chant............. the formula, Migration: Labour Migration butwhere not Workers’ Migration 73 and the future where we will end this chant. We change so much between the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 beginning and the end.31 Recall the moment when G¨ odel announces that 4.4 Selective Policies and the Brain Drain............................................ 87 that the meaning of the symbols is immaterial, and it is desirable it4.5 beEqual forgotten. We have alreadyOpportunities noted that willing to forget is not Opportunity and Denied ................................ 90a likely strategy. At this point, the objective is not to fulfil desire, but to 97 let desire Bibliography ......................................................................................... operate as a mechanism of generating the complex temporality that allows 5.joining Colombia: in Their Such Societies of Originundermines ....... 101 and Including disjoining Emigrants text and meaning. temporality the Urs Watter presence of meaning in a text. It places meaning between desire and ful5.1 State Interest and Responsibility filment, perpetration and remembrance: here anticipating, there towards their Citizens Living ........................................... 102 recalling, in the future, in Abroad the past, under the false auspices of a5.2 present. That .............................................................................. is how the mime operates, whose act is 104 confined Applied Ethics to allusion without breaking the ice or the mirror; he 5.3perpetual Migration Policy and Ethics ......................................................... 106 thus sets up a medium, a pure medium, of fiction (Derrida quoting 5.4 Migration Policy in Colombia ...................................................... 108 Mallarm´e in Derrida 1993, 294). And this splitting of the reader between a 5.5 “Colombia noswould une”...................................................................... 109 digit future and a past hold, even if the formula consisted of a single 5.6 Alianza 112 integer. For País even.................................................................................. a single digit integer is always linked to its non-present past and future:.................................................................................... the time when we learnt to recognise the sign, the meaning 5.7 Challenges 114 it once had, the meaning it could have, the time when we will use it next. Bibliography ....................................................................................... 116 Among the two paragraphs above, the first is within the reach of conWorking Together for the Well-being Migrants ........................... temporary mathematical discourse of (empirically or scientifically119 grounded Barry Halliday finitist critiques, such as Rotman’s cited above), whereas the second is framed within post-structural philosophy, which, on a sociological level, is quite foreign to it. With these two paragraphs I am about to conclude this 31 For

a serious presentation of this provocation I refer the reader to the discussion of the effect of time on Husserl’s concept of presence in Derrida’s Speech and Phenomena (Derrida 1979). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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chapter (I only have 13 marked quotation left, which I’d like to include. I Bibliography ......................................................................................... may give some of them up, because I am tired, and so, I believe, are60you). In reading what follows, it is desirable (I so desire) that you perform a dou4. The Ethics of Migration. ble reading. Once forgetting the second (post-structural) paragraph, and Reflections on Recent Migration Policies once remembering it;inonce that........................................... the undecidable formula61 does not and “Non-policies” Italyrecalling and Europe exist Laurabecause Zanfriniit is simply too large, and once recalling that it does not exist because it keeps disseminating between its possible histories and..future ref4.1 Restrictive Policies and Structural Demand for Immigrant Labour 65 erences. The first approach would reflect material constraints that curtail 4.2 Initiatives for Governing Family and Humanitarian unbounded recursions and the authority of non-presentable formal73 texts, as Migration: Labour Migration but not Workers’ Migration ............. well as such issues of underdetermination as the L¨owenhim-Skolem ‘para4.3 From Guest Workers to Unwelcome Guests .................................. 82 dox’ and the openness of increasing and bifurcating logical hierarchies. The 4.4 Selective Policies andrelate the Brain Drain............................................ 87 with second approach would mathematics to post-structural concerns the dissemination of Opportunities marks, decisions and closure. The 4.5 unbounded Equal Opportunity and Denied ................................ 90 choice of reading that you may (or may not) make is ethical. After all,97 he who Bibliography ......................................................................................... understands me finally recognises that semiotics is senseless. And 5.despite Colombia: Emigrants Their Societiespropositions of Origin ....... 101 the Including fact that There caninbe no ethical (WittgenUrs Watter stein 1922, §§6.54, 6.42), the proposition that I make in this essay, I make 5.1entirely State Interest andItResponsibility as ethical. is ethical in its concern with the privileged authority towards their Citizens Living Abroad 102at least of mathematics as discourse, some of it ........................................... well earned, but some based in on the myth of its unified, well-grounded semiotic stability. 5.2part Applied Ethics .............................................................................. 104 5.3 Migration and Ethics ......................................................... The 1931Policy and 1934 texts don’t represent anything that106 has ever been or can Policy ever in become present: nothing that comes before or 5.4 Migration Colombia ...................................................... 108 after the mimodrama. The mimodrama is that of a formal text, 5.5 “Colombia nos une”...................................................................... 109 which has never been committed, has never been properly written down as 5.6 Alianza País .................................................................................. 112 such, and yet nevertheless turns into a suicide of Hilbert’s programme 5.7establish Challenges .................................................................................... 114 formal to consistency through finitary means. The fully elaborated Bibliography text was never....................................................................................... written, yet still it has authority over that realm of116 unwritten formal texts, an authority that overturns Hilbert’s aspirations, without an Working Together for the Well-being of Migrants ........................... 119 epistemically violent revolution of the discourse, without striking or sufBarry Halliday fering a blow, etc. (Derrida 1993, 210). The structure of the comma, variable, equality and gap of substitution (the hymen, the entre) that enables mathematical writing lives in texts, ‘on paper’, indicating something that can’t be brought forth. It only takes place when it doesn’t take place, when nothing really happens, when there is an all-consuming consummation without violence, or a violence without blows, or Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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a blow without marks, a mark without a mark (a margin), etc., Bibliography ......................................................................................... 60 nothwhen the veil, without being, torn, and when the prosecution has ing except a written proof, a written confession (social scientists know well 4. The Ethics of Migration. that if you torture the numbers, they will confess). Reflections on Recent Migration Policies We have already particles of the text (such as 61 variables and “Non-policies” in seen Italythat and some Europe ........................................... Laura Zanfrini and equality signs) act like mirrors — but mirrors that do indeed come to stand as a source, an echoDemand that would somehow precede 4.1 Restrictive Policieslike and Structural for Immigrant Labour .. 65 the origin which it seems to answer — the “real”, the “originary”, 4.2 Initiatives for Governing Family and Humanitarian the Migration: “true”, the “present”, only on the rebound Labour Migrationbeing but notconstituted Workers’ Migration ............. 73 from the duplication in which alone they can arise (Derrida 1993, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 323).32 This double mark escapes the pertinence or authority of 4.4 Selective and overturn the Brain Drain............................................ 87 the truth: itPolicies does not it but rather inscribes it within its 4.5 Equal Opportunity and Denied Opportunities ................................ 90 play as one of its functions or parts, just as Carnap, Tarski and G¨odel inscribe truth......................................................................................... in their open hierarchy of meta-languages, each 97 language Bibliography in the hierarchy articulating the truth of its object language — but more 5.importantly, Colombia: Including Emigrantstext in Their Societies of Origin .......a101 as each shorthand derives its authority from longhand Urs Watter transcription that needn’t exist, or needn’t be present-able. This displace5.1 State Interest and Responsibility ment does not take place, has not taken place once, as an event. It towards their Citizens Living Abroad does not occupy a simple place. It........................................... does not take place in102 writing. 5.2 Applied Ethics .............................................................................. 104 This dis-location (is what) writes/is written. It is not in the text. It is5.3 inMigration writing about in ......................................................... reading it, in its use, its reiteration (Derrida Policythe andtext, Ethics 106 1993, 193). 5.4 Migration Policy in Colombia ...................................................... 108 When, in G¨odel’s 1934 text, it was desirable that the meaning at5.5 “Colombia nos une”...................................................................... 109 tached to symbols be forgotten, we found that it didn’t actually matter 5.6 Alianza País .................................................................................. whether we forgot or not, whether we could forget or not, whether112 we could 5.7 Challenges .................................................................................... 114 fulfil this desire to forget. It was the desire that the meaning of symbols be forgotten that was enough to manipulate the interaction between Bibliography ....................................................................................... 116 meanings and texts. Therefore, there is no longer any difference between Working Together forfulfilment the Well-being of Migrants 119 any desire ... and the of presence .............................. there is no longer Barry Halliday difference between desire and its satisfaction. And this is closely related to the dysfunctionality of the difference between an actual presentation and a mere indication of G¨odel’s undecidable formula, which by now 32 Kristeva

quotes Lenin: It is exact that men begin with that (the natural principle), but truth is not in the beginning, but in the end, more precisely in the continuation (Kristeva 1969, 213). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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should have become undecidable in a more than formal sense. Bibliography ......................................................................................... 60 It is not only the difference (between desire and fulfilment) that is abolished, but also the difference between difference and 4. The Ethics of Migration. nondifference. Nonpresence, the gaping void of desire, and presReflections on Recent Migration Policies ence, the fulfilment of enjoyment, amount to the same.61 By the and “Non-policies” in Italy and Europe ........................................... Laura Zanfrini same token {du mˆ eme coup} in G¨odel’s proof there is no longer any textual difference theDemand image for and the thing, 4.1 Restrictive Policiesbetween and Structural Immigrant Labourthe .. 65empty signifier andfor the full signifier, imitator and the imitated, etc. 4.2 Initiatives Governing Family the and Humanitarian We saw how z loses footing when we ask what it means as it goes73through Migration: pLabour Migration but not Workers’ Migration ............. processes of substitution, and how it stands for something that could never 4.3 From Guest Workers to Unwelcome Guests .................................. 82 be made present. But it does not follow, by virtue of this hymen of 4.4 Selective Policies and the Brain Drain............................................ 87 confusion, that there is now only one term ... it does not follow 4.5 Equal Opportunity Denied Opportunities that what remains and is ... the imitated, or................................ the thing itself,90simply present in person. It does not follow that all we have is the plain97 mark zp , Bibliography ......................................................................................... simply present (Derrida 1993, 209). Without its meaning and function of 5.representation Colombia: Including Emigrants in Their of Origin ....... 101 forzp alone cannot enable anSocieties intelligible proof concerning Urs Watter mal systems. Mathematical discourse simply does not require the difference 5.1 State desire Interestand andfulfilment, Responsibility between between present and absent, to function in towards their Citizens Living Abroad ........................................... 102 a way that would completely dominate practice. But dysfunctional differ5.2 Applied Ethics .............................................................................. 104 ability ence is indispensable to the production of meaning, to our to effects desire and consummation, of presence and 5.3produce Migration Policyofand Ethics ......................................................... 106absence of intelligible proof. All these notions are disseminated by 5.4meaning Migrationand Policy in Colombia ...................................................... 108 dysfunctional differences through inscription under the auspices of mathe5.5 “Colombia nos une”...................................................................... 109 matical discourse. 5.6 Alianza País .................................................................................. 112 Structure (the differential) is a necessary condition for the 5.7 Challenges 114 The semantic, but.................................................................................... the semantic is not itself, in itself, structural. seminal, on ....................................................................................... the contrary, disseminates itself without ever Bibliography 116having been itself, and without coming back to itself. The process of subWorking the Well-being of Migrants ........................... 119 stitutionTogether of zp , itsfor very engagement in division, its involvement in Barry Halliday its own multiplication, its substitution into itself, self-reference, unlimited nestings of S(zp , zp ) inside itself, its denoting of a text that cannot be forced into presence, the effect of undecidability, this is what constitutes the mathematical mark as such in its living proliferation. It exists in number (Derrida 1993, 351). What is this number? Number is what counts oranges, number is Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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what measures voltages. But oranges get squashed into uncountable mush, Bibliography 60 indiand voltages ......................................................................................... are subject to ‘measurement errors’. Number is merely cated by the empirical. The diametrically opposite alternative to this con4. The Ethics of Migration. ception is to take Peano’s approach: numbers are unbounded collections Reflections on Recent Migration Policies of signs that obey certain rules — syntactic rules that61nothing and “Non-policies” in Italy syntactic and Europe ........................................... present can ever properly fulfil; this solution is that which contemporary Laura Zanfrini mathematical refers to under the title Labour of its foundations. 4.1 Restrictive scholarship Policies and usually Structural Demand for Immigrant .. 65 Nevertheless, this merely indicated column of numbers, the exhaustive, me4.2 Initiatives for Governing Family and Humanitarian chanical enumeration of all formulas a formal Migration system, is............. the centre-piece Migration: Labour Migration but notinWorkers’ 73 of G¨ odel’s text. It ties together the various strata of the argument (arith4.3 From Guest Workers to Unwelcome Guests .................................. 82 metic, formal systems, metamathematics). But this column has no being, 4.4 Selective Policies andwhether the Brain Drain............................................ 87 to no nor any being-there, here or elsewhere. It belongs one ... youOpportunity will neverand absolutely control its extension. You 90 will not 4.5 Equal Denied Opportunities ................................ take it from......................................................................................... somewhere else and put it here. You will not cite Bibliography 97 it to appear. Yet despite this column’s not being (a being), not falling 5.under Colombia: Societies of Origin ....... 101 lives the Including power ofEmigrants the is, allinofTheir western metaphysics, which Urs Watter in the certainty of that is, has revolved around the column. Not 5.1 State Interest Responsibility without seeingand it but on the contrary in the belief that it sees it. towards their Citizens Living Abroad 102as of a And can be sure, in truth, of the ........................................... contours of its collapse, centre or aEthics proper place (Derrida 1993, 352, translation modified). 5.2 Applied .............................................................................. 104 All this does not deny numbers and mathematical marks their 5.3 Migration Policy and Ethics ......................................................... 106 usefulness: they do allow us to count and measure. This should, however, make an 5.4 Migration Policy in Colombia ...................................................... 108 impact on their authority. If we accept that mathematical semiosis shares 5.5 “Colombia nos une”...................................................................... 109 so much of its unstable generative processes with other forms of language, it 5.6 Alianza .................................................................................. makes little País sense to assume that it has an a-priori privilege. The112 authority 5.7 Challenges .................................................................................... 114 of mathematics should therefore be judged according to its applications and results (use value, exchange value), rather than its pretensions to superior Bibliography ....................................................................................... 116 form. Working Together for the Well-being of Migrants ........................... 119 It’s as a web of unfounded indications that mathematics becomes unBarry Halliday boundedly usable, exchangeable without being given up, inexhaustible. Acknowledging the disappearance of numbers as a present source, the death of that representative voice, the voice that makes numbers present, that voice which is already dead, does not amount to some absolute silence that would at last make way for some mythical purity of writing, some finally isolated graphy. Rather, it gives rise to an Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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authorless voice ... that no ideal signified or thought can entirely Bibliography cover in its ......................................................................................... sensible stamp without leaving something out60 (Derrida 1993, 332). Because a written sign ... is a mark that remains (Derrida 4. The Ethics of Migration. 1988a, 9, translation modified). And therefore The movement of signiReflections on Recent Migration Policies fication adds something, which results in the fact that 61 there is and “Non-policies” in Italy and Europe ........................................... always more, but this addition is a floating one because it comes Laura Zanfrini to vicarious function,Demand to supplement a lack on.. the 4.1perform RestrictiveaPolicies and Structural for Immigrant Labour 65 part of the signified (Derrida 1978, 289). 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini Chapter 3 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65

4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73

The Surface of Mathematics

4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97

5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter We finally come to consider the interface between bodies and texts. Psychoanalytic theory and modern logic lead us to the 5.1 State Interest and Responsibility surfacetheir of language, and toAbroad the lining that separates and relates towards Citizens Living ........................................... 102 words and the actions they order. There we make sense. 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policywhen and Ethics ......................................................... The idea is that I give you an order, there are the 106 words — then something the sense of the words — then your 5.4 Migration Policyelse, in Colombia ...................................................... 108action ... they nos go on to say that the series of cardinal numbers is 5.5And “Colombia une”...................................................................... 109 known to us by a ground-intuition — that is, we know at each 5.6 Alianza País .................................................................................. 112 step what the operation of adding 1 will give. We might as well 5.7 Challenges .................................................................................... 114 say that we need, not an intuition at each step, but a decision. — Bibliography ....................................................................................... 116simply Actually there is neither. You don’t make a decision: you do a certain thing. It is a question of a certain practice (WittgenWorking Together for the Well-being of Migrants ........................... 119 stein 1975, 185, 237). No intermediation, says Wittgenstein. No sense, no Barry Halliday intuition, no decision between words and actions. Wittgenstein and his disciples are right to define meaning by means of use, concurs Deleuze (1990, 146). Nothing comes between words and actions. But Deleuze goes on to articulate that use is in the relation between representation and something extra-representative, a nonrepresented and merely expressed entity. Use relates the sys-

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tem of representation to a surface of expressed sense. And representation, Bibliography ......................................................................................... 60 letter when it does not reach this point, remains only a dead confronting that which it represents, and stupid in its represen4. The Ethics of Migration. tativeness. Reflections on Recent Migration Policies Formal mathematical can........................................... be dwindled to become such and “Non-policies” in Italy language and Europe 61 dead Laura It Zanfrini letter. can degenerate into conglomerates of words and actions, without enveloping thePolicies event at borders, without bringing Labour about.. 65 this lin4.1 Restrictive andits Structural Demand for Immigrant ing or hem (Deleuze 1990, 146), this phantasmatic surface, this effect of 4.2 Initiatives for Governing Family and Humanitarian meaning. It is the taskMigration of this chapter place mathematical language, Migration: Labour but notto Workers’ Migration ............. 73 at a particular moment in its history, within the theoretical edifice of Deleuze’s 4.3 From Guest Workers to Unwelcome Guests .................................. 82 linguistic surfaces — surfaces that do not come between words and actions, 4.4 Selective Policies and the Brain Drain............................................ 87 but develop sense somewhere in their vicinity. 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 3.1 Numbers and the body 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Let’s open with an analysis, inspired by Deleuze’s reappropriation of tranUrs Watter scendental philosophy, of what makes numbers possible. Since we have to 5.1 State Interest and Responsibility start from somewhere, the skin will be our somewhat arbitrarily chosen towards their Citizens Living Abroad ........................................... 102 surface of incision. Not because the skin or the body that it envelops are 5.2 Applied Ethics .............................................................................. 104 taken to be unproblematic genuine givens, but because the body’s inside 5.3 Migration Policy and Ethics ......................................................... and outside are privileged by the capacity of our scalpel — words106 — to cut along the skin.Policy It is in easy to articulate an inside and an outside 108 of a body 5.4 Migration Colombia ...................................................... with words (if we to use sharper tools, we might have cut through the 5.5 “Colombia noswere une”...................................................................... 109 body, and caused some pain). 5.6 Alianza País .................................................................................. 112 Since there is nothing between words and actions, we shall begin our 5.7 Challenges .................................................................................... search for meaning within the body, which speaks and acts. And114 the body ....................................................................................... 116 (into), isBibliography explicitly there as we read G¨ odel’s texts. Things stand, hold, run are carried (through), constructed; we say, write, see, and there is even Working Together for the Well-being of Migrants ........................... 119 a left-hand (side). These idiomatic uses establish an echo of a link between Barry Halliday the actions of the body and the meaning of a mathematical text. But even without these idiomatic links, G¨odel’s text is ordered around the series of cardinal numbers and syntactic steps, which build upon the embodied operation of adding 1. Numbers order G¨ odel’s text. Every string of signs in the formal language is numbered by this text. Formulas become numbers. More generally, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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numbers are a privileged constituent in contemporary accounts of the founBibliography ......................................................................................... dation of mathematics. And the series of cardinal numbers is the60 result of the operation of adding 1. So numbers depend on the operation of the 4. The Ethics of Migration. body (or, at the very least, of the embodied mind). Numbers are extracted Reflections on Recent Migration Policies from the body’s steps. But and one Europe should be wary of hypothesising 61 the body and “Non-policies” in Italy ........................................... asLaura the origin Zanfriniof numbers. The body is, we insist, the effect of our somewhat arbitrary verbal incision the skin. We for may have cutLabour along ..a65 different 4.1 Restrictive Policies andalong Structural Demand Immigrant surface, using different cutting instruments. And the body, while numbers 4.2 Initiatives for Governing Family and Humanitarian pulsate inside it (the heart beats), while it keepsMigration adding 1............. (taking73another Migration: Labour Migration but not Workers’ step), yet the body alone cannot synthesise numbers. Numbers require a 4.3 From Guest Workers to Unwelcome Guests .................................. 82 transcendental account. 4.4 Selective Policies andthe theheart Brain beats. Drain............................................ 87 Steps follow, and But that alone is not enough, as 4.5 Equal Opportunity and Denied ................................ each step is different, and as each Opportunities heartbeat is distinct. In order to90 contract steps and heartbeats into a form of repetition, a synthesis must Bibliography ......................................................................................... 97 occur. The first synthesis would be the passive synthesis — the contraction of 5.instances Colombia: EmigrantsPassive in Their Societiesrefers of Origin toIncluding form a repetition. synthesis to ....... the 101 fusion of Urs Watter successive tick-tocks in a contemplative soul ... it constitutes our 5.1 State Responsibility habit ofInterest living,and our expectation that ‘it’ will continue ... When towards their Citizens Living Abroad ........................................... 102 of an we say that a habit is a contraction we are speaking not 5.2 Applied Ethicsaction .............................................................................. instantaneous which combines with another to 104 form an element of repetition, but rather of the fusion of that repetition 5.3 Migration Policy and Ethics ......................................................... 106 in the contemplating mind (Deleuze 1994, 74). 5.4 Migration Policy in Colombia ...................................................... 108 We must not be so hasty as to ask here who is this contemplative 5.5 “Colombia nos une”...................................................................... 109 soul or mind. Such question would presume that they have the form of Alianza1País 112 a5.6 someone. But.................................................................................. we may ask what it is to contemplate. To contemplate .................................................................................... is5.7toChallenges question. Is it not the peculiarity of questions to 114 ‘draw’ a response? ... ‘What difference is there...?’ This is the question Bibliography ....................................................................................... 116 the contemplating soul puts to repetition, and to which it draws a reWorking for the Well-being Migrants ........................... sponse Together from repetition (Deleuze of 1994, 78). What difference119 is there Barry Halliday between the first and the second step? Between the second and third heartbeat? In order to count the repetitions, both similarity and difference must be acknowledged by a contemplative soul. Without asserting the differ1 Here

we can allow for contemplative souls as components of consciousness that are incommensurable with a so called thinking subject. Many contemplative souls may simultaneously partake in a given thinking subject and its others. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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ence within repetition, we would not have 1, 2, 3, . . ., but merely 1, 1, 1, . . ., Bibliography ......................................................................................... 60 or perhaps even just 1 — a constant death. This is what we have in a formal language, if we accept the most 4. The Ethics of Migration. repressive and finitist accounts. Reflectionsformalist on Recent Migration Policies We repeat signs, we repeat mechanic procedures for whether a certain sequence of 61 primitive and “Non-policies” in determining Italy and Europe ........................................... Laura Zanfrini signs is a meaningful formula, an axiom, a proof. This is all there is. A mathematical systemDemand is a system of symbols 4.1formal Restrictive Policies and Structural for Immigrant Labour ..together 65 with rules for employing them (1934, 346). But even in this account 4.2 Initiatives for Governing Family and Humanitarian the formal system is not just the symbols, it is the symbols along with the Migration: Labour Migration but not Workers’ Migration ............. 73 rules, later to be specified as mechanical. And even if these rules order 4.3 From Guest Workers to Unwelcome Guests .................................. 82 nothing but machines, they still incite a cohort of contemplative souls, 4.4 Selective Policies and the Brain Drain............................................ 87 which accompany the text, and draw from it an effect of repetition. 4.5 Equal and Denied Opportunities 90 is not But Opportunity even this conjunction of body and................................ contemplative soul Bibliography ......................................................................................... enough to produce numbers. Formal languages do not acknowledge97 numbers until they are written down. Deleuze’s generalised formulation of this fact 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 states that material repetition comes undone even as it occurs, and Urs Watter can be represented only by the active synthesis which projects 5.1 State Interest and Responsibility its elements into a space of conservation and calculation (Deleuze towards their Citizens Living Abroad ........................................... 102 1994, 84). Without this space of conservation we cannot hold on to 5.2 Applied Ethics .............................................................................. 104 repetition. 5.3 Migration Policycontext and Ethics ......................................................... 106 In the specific of mathematics, Derrida reads the necessity to

add an active, Policy inscriptive, retentive synthesis to the passive one in108 Husserl’s 5.4 Migration in Colombia ...................................................... Origin of Geometry. By itself the speaking subject, in the 5.5 “Colombia nos une”...................................................................... 109 strict sense of the term, is incapable of absolutely grounding the ideal 5.6 Alianza País .................................................................................. 112 Objectivity of sense. Oral communication (i.e. present, immedi5.7 Challenges .................................................................................... 114 ate and synchronic communication) among the protogeometers is Bibliography ....................................................................................... 116to be” not sufficient to give ideal objectivities their “continuing and “persisting factual existence,” thanks to which they perdure Working Together for the Well-being of Migrants ........................... 119 “even during periods in which the inventor and his fellows are Barry Halliday no longer awake to such an exchange or even, more universally, no longer alive.” To be absolutely ideal, the object must still be freed of every tie with an actual present subjectivity in general. Therefore, it must perdure “even when no one has actualised it in evidence” (164 [modified]). Speech [language oral ] has freed the object of individual subjectivity but leaves it bound to its beginRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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ning and to the synchrony of an exchange within the institutive Bibliography ......................................................................................... 60 community. The possibility of writing will assure the absolute traditionalisation of the object, its absolute ideal Objectivity — 4. The Ethics of Migration. i.e., the purity of its relation to a universal transcendental subReflections on Recent Migration Policies jectivity. Writing in will doand this by emancipating sense from61its acand “Non-policies” Italy Europe ........................................... tually present evidence for a real subject and from its present Laura Zanfrini circulation determined community. “TheLabour decisive 4.1 Restrictivewithin Policiesaand Structural Demand for Immigrant .. 65 function of written expression, of expression which documents, is that 4.2 Initiatives for Governing Family and Humanitarian it makes communication possible withoutMigration immediate or 73 mediate Migration: Labour Migration but not Workers’ ............. address; it is, so to speak, communication become virtual” (164 4.3 From Guest Workers to Unwelcome Guests .................................. 82 [modified]) (Derrida 1989, 87; internal quotes refer to the same volume, 4.4 Selective Policies and thetranslation Brain Drain............................................ 87 which includes an English of Husserl’s text) 4.5 Equal Opportunity 90 blank Numbers have toand be Denied activelyOpportunities synthesised,................................ transcribed onto the page or onto ......................................................................................... an otherwise restrictive and imposing space of representation Bibliography 97 in order to function as numbers, rather than disappear across the threshold 5.of Colombia: Including Emigrants in Theirinto Societies of (attrition, Origin .......mechanical 101 the contemplative soul’s breakdown fatigue Urs Watter fault, computation error). Indeed, G¨odel’s argument cannot be performed 5.1 Statenumerical Interest and Responsibility without symbols or expressions representing numbers towards their Citizens Living Abroad ........................................... 102 (1934, 350). 5.2 Applied Ethics .............................................................................. But even that is not enough. Numbers are numbers not 104 simply by 5.3 Migration Policy and Ethics ......................................................... 106In order virtue of passive contraction and active synthesis of representation. to on, to keep on repeating, they require a much farther reaching 5.4goMigration Policy in Colombia ...................................................... 108form of repetition. They require an Eternal return. Eternal return affects only 5.5 “Colombia nos une”...................................................................... 109 the new, what is produced under the condition of default (passive 5.6 Alianza País .................................................................................. 112 synthesis) and by the intermediary of metamorphosis (active synthe5.7 Challenges sis). However,.................................................................................... eternal return causes neither the condition114 nor the agent to return: on the contrary, it repudiates these and Bibliography ....................................................................................... 116expels them with all its centrifugal force. It constitutes the autonomy Working Together for Well-being of Migrants ........................... 119 of the product, thethe independence of the work. It is repetition by Barry Halliday excess which leaves intact nothing of the default or the becoming equal. It is itself the new, complete novelty (Deleuze 1994, 90).

Let us try to explain. When exposed to the centrifuge of reiteration, which is called here eternal return, numbers are repeated by different agents on different surfaces of representation in different contexts. In this process, numbers lose the agent who counts them, the body where they pulsate, and Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the page on which they are inscribed. But the result is far from ideal. NumBibliography ......................................................................................... 60 which bers do not become the platonic object independent of experience, 2 Frege and Husserl affirmed. This is so because as we strip the repeated 4. The Ethics of Migration. (or quoted, reiterated) texts bare of any specific agent and context, we are Reflections on Recent Migration Policies not with a steady but rather with ever 61 changing andleft “Non-policies” incommon Italy anddenominator, Europe ........................................... forms reforms of writing. These ever evolving forms open the text to Laura and Zanfrini unanticipated reformulation, ratherDemand than establish an ideal common 4.1 Restrictive Policies and Structural for Immigrant Labour .. 65 form. What is repeated in the eternal return is this opening to new forms of writ4.2 Initiatives for Governing Family and Humanitarian ing, Migration: and to an Labour interaction with new agents, newMigration experiences, new 73 uses and Migration but not Workers’ ............. new contexts. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Numbers, the experience of numbers, the repetitive operation of adding 4.4 Selective andinto the Brain Drain............................................ 1, become thePolicies opening novelty of that which is repeatedly87 different 4.5 Equal and Denied 90 is diffrom itself.Opportunity What eternal return Opportunities sets before us................................ (always in advance) ference itself,......................................................................................... the active difference that propels the sequence of 97 numbers, Bibliography and causes them to proceed rather than stay put. This iteration, or eternal 5.return, Colombia: Including Their Societies of Origin ....... contingent 101 produces as anEmigrants effect theinillusion of a division between

Urs Watter circumstances and ideal content, as well as what we have asserted above 5.1constitutive State Interestconditions: and Responsibility as the supposedly neutral space of conservation towards their Citizens Living Abroad ........................................... 102of their and calculation upon which numbers are represented, the illusion 5.2 Applied Ethics .............................................................................. 104syntheindependent existence there, and, finally, the experience of passive sis, contraction into instances of primitive repetition, the 106 effect of a 5.3 their Migration Policy and Ethics ......................................................... clear-cut repetition of tick by tock. 5.4 Migration Policy in Colombia ...................................................... 108 This eternal return is described, again, in a context closer to our own, 5.5 “Colombia nos une”...................................................................... 109 namely in Derrida’s reading of Husserl’s Origin of Geometry. We compare 5.6 Alianza País .................................................................................. 112 First, here Greek mathematics with subsequent mathematical revolutions. in mathematics, On the basis of a finite apriori system, an 5.7Greek Challenges .................................................................................... 114 infinite number of mathematical operations and transformations Bibliography ....................................................................................... 116 is already possible in that system, even if they are not infinitely Working Together thedespite Well-being Migrants ........................... 119we are creative. Abovefor all, theofclosedness of the system, Barry Halliday within mathematical infinity because we have definitely idealised and gone beyond the factual and sensible finitudes. This is the finite infinity. The infinite infinity of the modern revolution can be announced in the finite infinity of Antiquity’s creation. While investigating the sense of what they created — mathematical 2 See

their quotes in the opening of the first section of chapter 1.

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aprioriness — the Greeks simply would not have investigated Bibliography ......................................................................................... 60 the sense of all the powers of infinity which were enclosed in that aprioriness ... That will be done only progressively and later 4. The Ethics of Migration. on, by interconnecting revolutionary developments conforming to Reflections on Recent Migration Policies the historicity of mathematics and to a creativity andprofound “Non-policies” in Italy and Europe ........................................... 61 which always proceeds by disclosure (Derrida 1989, 130). Laura Zanfrini The structure of and thisStructural process Demand of origination opens up a new 4.1 Restrictive Policies for Immigrant Labour .. 65form of telos. For if such infinitisation is aHumanitarian new birth of geometry in its 4.2 Initiatives for Governing Family and authentic primordial intention (which weMigration notice ............. still remained Migration: Labour Migration but not Workers’ 73 hidden to a certain extent by the closure of the previous sys4.3 From Guest Workers to Unwelcome Guests .................................. 82 tem), we may wonder if it is still legitimate to speak of an ori4.4 Selective Policies and the Brain Drain............................................ 87 gin of geometry. Does not geometry have an infinite number of 4.5 Equal Opportunity and Denied Opportunities ................................ 90 birth births (or birth certificates) in which, each time, another isBibliography announced, while still being concealed? Must we not say ......................................................................................... 97 that geometry is on the way towards its origin, instead of proceeding 5.from Colombia: Including Emigrants it? (Derrida 1989, 131). in Their Societies of Origin ....... 101 Urs Watter

This process of origination has a crucial role in G¨odel’s text. Its man5.1 State Interest and Responsibility ifestation is the never quite completely determined anticipation of the next towards their Citizens Living Abroad ........................................... 102 step in the argument, which is constrained by rigorous forms of repetition, 5.2 Applied Ethicsitself .............................................................................. but folds within the unexpected — that which the reader104 does not, 5.3 Migration Policycould, and Ethics ......................................................... 106 of well and perhaps never discover by himself. From the repetition known mechanic manipulations the novelty of a conclusion, 5.4 Migration Policy in Colombiaarises ...................................................... 108an overwhelming discovery and surprise. This is the opening that allows numbers 5.5 “Colombia nos une”...................................................................... 109 to become formulas (sometimes provable, sometimes unprovable), and 5.6 Alianza País .................................................................................. 112 that allows the sequences of numbers and formulas to interrelate, while 5.7 Challenges .................................................................................... 114 maintaining the potential of these sequences to keep on communicating with other levels of representation (arithmetic, formal, metamathematical) Bibliography ....................................................................................... 116 in ways that we do not yet anticipate. Without this opening of numbers Working the Well-being of Migrants ........................... 119 to their Together rigorouslyfor restricted, yet unprecedented use, without this opening, Barry Halliday which (according to Derrida’s Husserl) would constitute the origin of mathematical objects, G¨ odel’s argument simply could not come to be written. Following Deleuze, we provided a transcendental account of three levels of repetition. First the articulation of concrete repetition by a ‘contemplative soul’ (which can be as simple as a mechanical procedure). Second, the articulation of repetition on a space of representation (whether a piece Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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of paper or objective ideality). Finally, the repeated opening of the entire Bibliography 60 acts framework to......................................................................................... novel implementations of difference and repetition, novel of communication between rigorously established distributions of difference 4. The Ethics of Migration. and repetition. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe This transcendental account opens........................................... up a mystery. What is it61that alLaura Zanfrini lows differences to communicate into eternal return? Is it really difference which relatesPolicies different to different intensive 4.1 Restrictive and Structural Demandinforthese Immigrant Labour ..systems? 65 Does the difference between differences relates difference to it4.2 Initiatives for Governing Family and Humanitarian self Migration: without Labour any other intermediary? ... what is this agent, Migration but not Workers’ Migration ............. 73 this force which ensures communication? Thunderbolts explode 4.3 From Guest Workers to Unwelcome Guests .................................. 82 between different intensities, but they are preceded by an invisible, 4.4 Selective Policies and the Brain Drain............................................ 87 imperceptible dark precursor, which determines their path in ad4.5 Equal Opportunityevery and Denied Opportunities 90 which vance ... Likewise, system contains ................................ its dark precursor ensures the......................................................................................... communication of its peripheral series. In its Bibliography 97 role as communicator between sequences of different elements, the dark precur5.sor Colombia: Including in Their Societies of Origin 101 would have to beEmigrants the in-itself of difference or the....... ‘differently Urs Watter different’ — in other words, difference in the second degree, the 5.1 State Interest and Responsibility self-different which relates different to different by itself. Because towards their Citizens Living Abroad ........................................... 102 the path it traces is invisible and becomes visible only in reverse, 5.2the Applied Ethics .............................................................................. to extent that it is travelled over and covered by 104 the phenomena it induces within system, it has no place other 5.3 Migration Policy and Ethics the ......................................................... 106 than that from which it is ‘missing’, no identity other than that 5.4 Migration Policy in Colombia ...................................................... 108 which it lacks: it is precisely the object = x, the one which is ‘lacking 5.5 “Colombia nos une”...................................................................... 109 in its place’ as it lacks its own identity (Deleuze 1994, 119–120). 5.6 Alianza País .................................................................................. 112 Retracing the dark precursor, first in the generation of a ‘natural’ 5.7 Challenges .................................................................................... language surface, and then in the generation of the mathematical114 language Bibliography ....................................................................................... surface that G¨ odel’s texts unfold, is what we shall do next. But116 before we do that, it is important to understand the repercussions of this retracing. Working Together for the Well-being of Migrants ........................... 119 Since if we recover the dark precursor, we must ask whether identity and Barry Halliday resemblance are the preconditions of the functioning of this dark precursor, or are they, on the contrary, its effects? If the latter, might it necessarily project upon itself the illusion of a fictive identity, and upon the series which it relates the illusion of a retrospective resemblance? Identity and resemblance would then be no more than inevitable illusions — in other words, concepts of Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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reflection which would account for our inveterate habit of thinkBibliography ......................................................................................... 60 ... it ing difference on the basis of the categories of representation is in the nature of the surface of representation to cancel difference, 4. The Ethics of Migration. but only on the surface (Deleuze 1994, 119, 240). Reflections on Recent Migration Policies The question raised thisEurope last quotation is whether eternal and “Non-policies” in Italyinand ........................................... 61 return Zanfrini isLaura an effect, or, despite the fact that (according to Derrida’s description above) it only Policies manifests as theDemand future of previous limited 4.1 Restrictive anditself Structural forour Immigrant Labour .. 65systems of thought and calculation, eternal return as described above is actually 4.2 Initiatives for Governing Family and Humanitarian seminal, disseminal, constitutive opening —Migration but an opening which is Migration: Labour aMigration but not Workers’ ............. 73 impossible to determine and fully represent, because it is always ahead of 4.3 From Guest Workers to Unwelcome Guests .................................. 82 itself. We’ll return to this question after we articulate a theory of language 4.4 Selective Policies that can sustain it. and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 3.2 The dimensions of language 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 InUrs order to characterise mathematical language and consider its specificity Watter compared to other forms of language, we will use Deleuze’s account of 5.1 State Interest and Responsibility language in his Logic of Sense. First, we will review his analysis of the static towards their Citizens Living Abroad ........................................... 102 dimensions of language. Then, since mathematical language is dynamic, we 5.2 Applied Ethics .............................................................................. 104 will briefly review his genetic account of language, and try to describe the 5.3 Migration Policyand and G¨ Ethics 106 formalist reduction odel’s......................................................... reaction in terms of this dynamic account. Our point of reference for this account of language will be mathemat5.4 Migration Policy in Colombia ...................................................... 108 th ical language asnos it une”...................................................................... stood before the late 19 century foundations109 crisis, at 5.5 “Colombia the verge of the discovery of paradoxes in Cantor’s set theory. Of course, 5.6 Alianza País .................................................................................. 112 many mathematical languages were employed before this crisis, and each 5.7 Challenges 114 had its specific.................................................................................... peculiarities. The analysis that follows cannot properly deBibliography ....................................................................................... 116 scribe all these languages at once. Still, for the purposes of this introductory

account I prefer to introduce a myth of a hypothetically reconstructed preWorking Together for the Well-being of Migrants ........................... 119 crisis mathematical language that ranges from Greek mathematics to the Barry Halliday 19th century, rather than commit myself to some specific historic moment. Many authors agree in recognizing three distinct relations within the proposition. We shall consider these relations below, following Deleuze (1990, 12–15). The first is called denotation or indication: it is the relation of the proposition to an external state of affairs (datum) ... Logically, the denotation has as its elements and its Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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criterion the true and the false. “True” signifies that a denotation ......................................................................................... isBibliography effectively filled by the state of affairs ... or that the60 correct image has been selected ... “False” signifies that the denotation is 4. The Ethics of Migration. not filled, whether as a result of a defect in the selected images Reflections on Recent Migration Policies or a result of the radical impossibility of producing an andas“Non-policies” in Italy and Europe ........................................... 61 image which can be associated with the words. Laura Zanfrini Pre-crisisPolicies mathematics had a strong commitment to denotation. 4.1 Restrictive and Structural Demand for Immigrant Labour .. 65 Mathematical descriptions often referred to states of affairs. They were not tied4.2 Initiatives for Governing Family and Humanitarian down to them,Labour perhaps they did depend on them, but, 73 as a rule Migration: Migration butnot noteven Workers’ Migration ............. (with many exceptions, just like in ‘natural’ language), mathematical ob4.3 From Guest Workers to Unwelcome Guests .................................. 82 jects were usually reified in some way. The diagram, economic or geometric 4.4 Selective Policies and the Brain Drain............................................ 87 interpretation and physical observation went hand in hand with mathemat4.5 Equal Opportunity and Denied Opportunities ical analysis. This is why the introduction of ................................ complex numbers 90 was considered much......................................................................................... more objectionable before the introduction of the97 complex Bibliography plane model than once it had been established. This is why non-Euclidean 5.geometry Colombia:required Including Emigrants in Their Societies of Originas....... 101the disc models (the half-plane with semicircles lines, Urs Watter with circular arcs as lines, the pseudo-sphere), rather than just an axioma5.1 State in Interest Responsibility tisation, orderand to be properly endorsed. This is probably the motivation towards their Citizens Living Abroad ........................................... 102 behind Weierstrass’, Dedekind’s and Cauchy’s attempts to ontologically re5.2 Applied Ethics .............................................................................. form infinitesimals and real numbers. In pre-crisis mathematics 104 one could definitely ask whether given mathematical description was true106 for a cer5.3 Migration Policy anda Ethics ......................................................... tain state of affairs. 5.4 Migration Policy in Colombia ...................................................... 108 A secondnosrelation of the proposition is often called 5.5 “Colombia une”...................................................................... 109“manifestation”. It concerns the relation of the proposition to the per5.6 Alianza País .................................................................................. 112 son who speaks and expresses himself. Manifestation is therefore 5.7 Challenges 114 presented as .................................................................................... a statement of desires and beliefs which correspond Bibliography ....................................................................................... 116 not to the proposition. Desires and beliefs are causal inferences, associations. Desire is the internal causality of an image with reWorking Together for the Well-being of Migrants ........................... 119 spect to the existence of the object or the corresponding state Barry Halliday of affairs. Correlatively, belief is the anticipation of the object or state of affairs insofar as its existence must be produced by an external causality ... there are in the proposition “manifesters” like the special particles I, you, tomorrow, always, elsewhere, everywhere, etc. ... from denotation to manifestation, a displacement of logical values occurs which is represented by the Cogito: no Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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longer the true and the false, but veracity and illusion. Bibliography ......................................................................................... 60 The dimension of manifestation may appear problematic. Mathematical language has hardly ever said ‘I’. But this is a very narrow-sighted 4. The Ethics of Migration. objection. while rarely saying ‘I’, has often said ‘we’. PreReflectionsMathematics, on Recent Migration Policies crisis mathematical language often manifested a universal consciousness — and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini be it veracious or illusionary — which then underlay various attempts to form a Characteristica Universalis, systemsfor which were meant to65serve as 4.1 Restrictive Policies and Structural Demand Immigrant Labour .. symbolic manifestations of the spirit thought or nature (Leibniz and the 4.2 Initiatives for Governing Family andofHumanitarian Pythagoreans are two obvious examples). Mathematical axioms 73 are manMigration: Labour Migration but not Workers’ Migration ............. ifestations, if not of beliefs, then of convictions. The order of implication 4.3 From Guest Workers to Unwelcome Guests .................................. 82 was often reconstructed as manifesting an order of causality (what this 4.4 Selective Policies and the Brain Drain............................................ 87 act of reconstruction itself manifested is a different concern). It was ‘be4.5 Equal Opportunity and Denied Opportunities ................................ 90happen cause’ of the mathematical analysis that certain phenomena had to (it was ‘because’ of the inverse square law that planets revolved97in ellipBibliography ......................................................................................... tic trajectories). I admit, however, that the question of desire in pre-crisis 5.mathematical Colombia: Including Emigrants in Their and Societies Origin a....... 101textual languages is more delicate, wouldofrequire closer Urs Watter analysis. 5.1 State Interest and Responsibility We ought to reserve the term “signification” for a third ditowards their Citizens Living Abroad ........................................... 102 mension of the proposition. Here it is a question of the relation 5.2the Applied Ethics of word to .............................................................................. universal or general concepts, and of 104 syntactic 5.3 Migration Policy Ethics ......................................................... 106 connections to theand implications of the concepts ... Signification is defined by this order of conceptual implication where the 5.4 Migration Policy in Colombia ...................................................... 108proposition under consideration intervenes only as an element of a 5.5 “Colombia nos une”...................................................................... 109 “demonstration”, in the most general sense of the word, that is, 5.6 Alianza País .................................................................................. 112 either as premise or conclusion. Thus, “implies” and “therefore” 5.7 Challenges .................................................................................... 114signifiare essentially linguistic signifiers ... The logical value of cation or demonstration thus understood is no longer the Bibliography ....................................................................................... 116truth, as is shown by the hypothetical mode of implications, but rather Working Together for the Well-being of Migrants ........................... 119 which the conditions of truth, the aggregate of conditions under Barry Halliday the proposition “would be” true ... the condition of truth is not opposed to the false, but to the absurd: that which is without signification or that which may be neither true nor false. As for the dimension of signification — conceptual abstraction and the logical order of implication — this has been the most venerated dimension of mathematical language since Euclidean times, if not before. In Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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many ways mathematical language inspired (and distorted) the subsequent Bibliography ......................................................................................... significational analysis of natural language. One can find in many60 thinkers an explicit wish to impose upon natural language the sound significational 4. The Ethics of Migration. structure operative in mathematical language. The questions of ‘conditions Reflections on Recent Migration Policies of truth’ saturated mathematics long before this phrase was even61 coined. and “Non-policies” in Italy and Europe ........................................... These are the traditional dimensions of a functioning language as arLaura Zanfrini ticulated by Deleuze. points to things, manifests a speaker, 4.1 Restrictive Policies Language and Structural Demand for Immigrant Labour .. 65 and establishes an inferential order. While trying to track down which of these 4.2 Initiatives for Governing Family and Humanitarian dimensions establishes the others, discovers that ............. each already Migration: Labour Migration butDeleuze not Workers’ Migration 73 presupposes the others (I will not repeat his argument here). The question 4.3 From Guest Workers to Unwelcome Guests .................................. 82 arises whether there is something, aliquid, which merges neither with 4.4 Selective Policies thethe Brain Drain............................................ 87 the the proposition or and with terms of the proposition, nor with object orOpportunity with the state of affairs which ................................ the proposition denotes, 4.5 Equal and Denied Opportunities 90 neither with the “lived”, or representation, or mental 97 activity Bibliography ......................................................................................... of the person who expresses herself in the proposition, nor with 5.concepts Colombia:or Including Emigrants in Their Societies even signified essences? If thereofis,Origin then ....... this 101 additional Urs Watter dimension, sense, or that which is expressed by the proposition, 5.1 State and Responsibility would beInterest irreducible to individual states of affairs, particular imtowards their Citizens Abroad ........................................... ages, personal beliefs, Living and universal and general concepts102 (Deleuze 1990, 19). Ethics .............................................................................. 104 5.2 Applied Deleuze points out Ethics a long......................................................... history of attempts to assert or 106 deny such 5.3 Migration Policy and an additional fourth dimension of language. How such a dimension would 5.4 Migration Policy in Colombia ...................................................... 108 be generated will be reviewed below. Deleuze opts to first track down this 5.5 “Colombia nosthrough une”...................................................................... fourth dimension an analysis of the relations between the109 three tra5.6 Alianza País .................................................................................. 112 ditional dimensions of language (denotation, manifestation, signification), and through recording their ‘paradoxes’. We will, however, defer 5.7 Challenges .................................................................................... 114 an explication of the internal characterisation and explicit manifestation of this Bibliography ....................................................................................... 116 fourth dimension of sense until the first final´e of this chapter for technical and rhetorical reasons. Working Together for the Well-being of Migrants ........................... 119 BarrySince Halliday the task of demonstrating the role of such a dimension in an analysis of a fully-fledged language is independent of the task of explaining how it would come to be, our first approach to this fourth dimension will be genetic. We will review the narrative of how such a dimension comes to be in ‘natural language’, and attempt to locate the relevant parallel elements in our (mythical) language of pre-crisis mathematics.

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3.3

A concise psychoanalytic genealogy of language

Bibliography ......................................................................................... 60 4. The Ethics of Migration. In the first section we Migration associated Policies counting and the production of numbers Reflections on Recent and “Non-policies” in Italy and Europe 61 with embodied repetition. We saw that........................................... the gesture that constituted Laura Zanfrini the sign was a gesture of despatialisation: it reduces the volume 4.1three Restrictive Policiesembodied and Structural DemandtoforaImmigrant Labour .. 65 the of dimensional experience surface of inscription, practice to a chain of sounds (Kristeva 1969, 78). Active synthesis 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 The derived from the depths of the body a superficiality of text and script. operative question is howtothe volume ofGuests the body ends up despatialised 4.3 From Guest Workers Unwelcome .................................. 82 onto a surface. Or inversely, without forgetting that the text presents a 4.4 Selective Policies and the Brain Drain............................................ 87 system of signs, we seek to open up in the interior of this system 4.5 Equal Opportunity Deniedthe Opportunities ................................ 90 and another scene: thatandwhich screen of structure covers, Bibliography ......................................................................................... 97 which is signification as operation whose structure is but displaced

fallout (Kristeva 1969, 279). 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 I will now briefly sample Deleuze’s account (with some help from Urs Watter Kristeva; both accounts emanate from Melanie Klein and Jacques Lacan, 5.1 State Interest and Responsibility but are not quite subject to them) of the derivation of language (the surface) towards their Citizens Living Abroad ........................................... 102 from body (the volume). This digression, which will set mathematics aside 5.2 Applied Ethics .............................................................................. 104 for a while, is to be justified by the reintegration that will follow next. In 5.3 Migration Policy containable, and Ethics ......................................................... 106 will be order to keep things the details that I shall provide here scanty and incomplete. This is acceptable here, because I only wish 5.4 Migration Policy in Colombia ...................................................... 108 to set up the possibility of a narrative whereby what we shall call a paradoxical 5.5 “Colombia nos une”...................................................................... 109 element produces a surface of sense. 5.6 Alianza País .................................................................................. 112 Our first surface will be the skin (recall, however, that our initial inci5.7 Challenges .................................................................................... 114 is not sion along the surface of the skin, rather than along any other surface, Bibliography ....................................................................................... 116 an absolute starting point, but is contingent on our surgical instruments, namely words). The skin, however, is not quite our starting point. Before Working Together for the Well-being of Migrants ........................... 119 we have the surface of the skin, before there is an inside and an outside of Barry Halliday the body, there is no difference between eating and speaking. Chrysippus taught: “if you say something, it passes through your lips; so, if you say “chariot”, a chariot passes through your lips” (Deleuze 1990, 8). Food passes through your lips, sounds pass through your lips; in either case your body vibrates. The limits of the body and the limits of the world coincide; both are the limits of sensation. As there is no surface, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the inside and the outside, the container and the contained, no Bibliography 60 corlonger have......................................................................................... a precise limit. Therefore everything is body and poreal. Everything is a mixture of bodies, and inside the body, 4. The Ethics of Migration. interlocking and penetration (Deleuze 1990, 87). Everything falls into Reflections on Recent Migration Policies the wherein words are no longer anything and anonymous “Non-policies”pulsation in Italy and Europe ........................................... 61 but affections Laura Zanfrini of the body — everything falls back into the primary order which (Deleuze 125). 4.1 Restrictive Policiesgrumbles and Structural Demand1990, for Immigrant Labour .. 65 Discrete quantities of energy move through the body of the 4.2 Initiatives for Governing Family and Humanitarian subject who Labour is notMigration yet constituted as such and,............. in the73course Migration: but not Workers’ Migration of his development, they are arranged according to the various 4.3 From Guest Workers to Unwelcome Guests .................................. 82 constraints imposed on this body ... in this way the drives, which 4.4 Selective Policies and as thewell Brainas Drain............................................ 87 what are “energy” charges “physical” marks, articulate 4.5 call Equalthe Opportunity Denied Opportunities ................................ 90drives we chora:3 and a nonexpressive totality formed by the and their stases in a motility that is as full of movement97as it is Bibliography ......................................................................................... regulated (Kristeva 1984, 25). 5. Colombia: Including Emigrants clappings, in Their Societies of Origin ....... 101 crackThe depth is clamorous: crackings, gnashings, Urs Watter

lings, explosions, the shattered sounds of internal objects. But that State and Responsibility is5.1 not all.Interest Something, from among all the sounds of the depth, extowards their Citizens Living Abroad ........................................... 102 3 We

borrow the term chora from Plato’s Timaeus to denote an essentially mobile and extremely provisional articulation constituted by movements and their ephemeral stases. differentiate this uncertain and indeterminate ar5.3 Migration Policy andWe Ethics ......................................................... 106 ticulation from a disposition that already depends on representation, lends 5.4 Migration Policy in Colombia ...................................................... 108 itself to phenomenological, spatial intuitions, and gives rise to a geometry (Kristeva 1984, 25–26). It does not have the characteristics of an existent, by 5.5 “Colombia nos une”...................................................................... 109 which we mean an existent that would be receivable in the ontologic, that Alianza País .................................................................................. is5.6 those of an intelligible or sensible existent. There is kh¯ ora but112 the kh¯ ora does not exist. The effacement of the article should for the moment 5.7 Challenges .................................................................................... 114suspend the determination ... and the reference to something which is not a thing but Bibliography which insists,....................................................................................... in its so enigmatic uniqueness, lets itself be called116 or causes itself to be named without answering, without giving itself to be seen, conWorking Together for(Derrida the Well-being of Although Migrants ........................... 119 ceived, determined 1988b, 237). our theoretical description Halliday ofBarry the chora is itself part of the discourse of representation that offers it as evidence, the chora, as rupture and articulation (rhythm), precedes evidence, verisimilarity, spatiality, and temporality. Our discourse — all discourse — moves with and against the chora in the sense that it simultaneously depends upon and refuses it. Although the chora can be designated and regulated, it can never be definitely posited: as a result, one can situate the chora and, if necessary, lend it a topology, but one can never give it axiomatic form (Kristeva 1984, 26).

5.2 Applied Ethics .............................................................................. 104

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tracts a Voice (Deleuze 1990, 193). The voice is distinguished from the Bibliography ......................................................................................... 60 clamour of partial objects by its being found only as lost, of appearing for the first time as already there. It speaks and comes from on 4. The Ethics of Migration. high (Deleuze 1990, 193). The unique position of the Voice with respect Reflections on Recent Migration Policies to the“Non-policies” clamour is theinprimitive of the topography that61opposes and Italy and emergence Europe ........................................... good bad, height to depth, and which, between the two, embarks on LauratoZanfrini 4 developing what will later become the surface the skin.Labour 4.1 Restrictive Policies and Structural Demand for of Immigrant .. 65 Here is how this could take place. When the body produces noises, 4.2 Initiatives for Governing Family and Humanitarian it also feels a rumble in the digestive echo of ............. the noises Migration: Labour Migration but notsystem, Workers’the Migration 73 in the diaphragm. Food and noise are one; they both rumble in the stomach. But 4.3 From Guest Workers to Unwelcome Guests .................................. 82 sometimes the noise is only heard, while the stomach stays still. The effect Selective Policies the Brainarticulates Drain............................................ 87 is4.4double. First, this and experience the eardrum and separates it from the diaphragm. it articulates this................................ noise in the form of90a Voice, 4.5 Equal OpportunitySecond, and Denied Opportunities namely as always having been there, as an independent outside.5 97 Bibliography ......................................................................................... The Voice with its outside-inside or high-low topography already es5.tablishes Colombia: Emigrants in Their Societies of ....... 101object), theIncluding dimensions of language: it designates (anOrigin already-lost Urs Watter signifies (an order of preexistence and outside), and manifests (itself as 5.1 State Interest Responsibility withdrawn). Butand since all these dimensions relate to the lost, unknown, towards their Citizens AbroadAnd ........................................... 102 sense, withdrawn, this is not yetLiving a language. so we are left outside far from itEthics ... in.............................................................................. a pre-sense (pr´ e-sens) of heights (Deleuze 5.2 Applied 104 1990, 194). 5.3 Migration Policy and Ethics ......................................................... 106 What we have below the Voice is not yet the unified surface of the 5.4 Migration Policy in Colombia ...................................................... 108 skin; the skin does not yet exist. In fact, each zone is the dynamic 5.5 “Colombia une”...................................................................... 109 formation of nos a surface space around a singularity constituted by 5.6 Alianza .................................................................................. the orificePaís (ear, mouth, anus, penis, vagina...). Each zone is112 able to be in all directions up to the vicinity of another 5.7 prolonged Challenges .................................................................................... 114 zone depending on another singularity. Our sexual body is initially a Bibliography ....................................................................................... 116 Harlequin’s cloak (Deleuze 1990, 197). In order to put the various zones 4 A more Working Together the Well-being of Migrants orthodoxfor Lacanian account would place the........................... mirror before the 119 voice. Cap-

Barry of Halliday tation the child’s unified body image in the mirror and the drive investment in this image ... permit the constitution of objects detached from the semiotic chora. An imaged ego is formed, whose positing leads to the positing of the object, which is likewise, separate and signifiable ... The sign can be conceived as the voice that is projected from the agitated body (from the semiotic chora) onto the facing imago or onto the object, which simultaneously detach from the surrounding continuity (Kristeva 1984, 46–47). 5 We suppress the role of Deleuze’s unifying body without organs in this narrative.

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together, we require an equivalent of the dark precursor from the first Bibliography section above.......................................................................................... 60 In order to put things together (unify the fragmented body and relate 4. The Ethics of Migration. the high andon the low), Migration according Policies to Deleuze, the boy projects the image of Reflections Recent the (the form in ofItaly an independent preeminent outside) upon61his own andVoice “Non-policies” and Europe ........................................... Laura The Zanfrini penis. phallus is thus constituted. Now that it is endowed with the self ofStructural the Voice, the penis-become-phallus 4.1 contained Restrictive structure Policies and Demand for Immigrant Labour will .. 65 form a complete surface around it. It will be able to resist the violent chora and 4.2 Initiatives for Governing Family and Humanitarian partial objectsLabour that upset the emerging inside/outside division. of Migration: Migration but not Workers’ Migration .............Instead 73 being detached and elevated, the power of the Voice will be forced here, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 on the skin, within hand-reach. The heights will be brought down to the 4.4 Selective Policies and thedepths Brain Drain............................................ 87 and surface, and the clamorous will be integrated under this surface 4.5 Equal and Denied Opportunities ................................ 90 shut in anOpportunity inside. But this......................................................................................... plan must fail. In trying to grab hold of the Voice97and pin Bibliography it onto the body, its very essence as withdrawn independent outside is 5.betrayed. Colombia:This Including Emigrants in Their Societies ofonly Origin 101 essence could not be found but as....... if recovered Urs Watter — recovered in absence and in forgetfulness — but never given in State Interest and of Responsibility a5.1 simple presence the “thing” which would eliminate forgetting towards their Citizens Living Abroad ........................................... 102 (Deleuze 1990, 205–206). Brought down onto the body, the Voice loses its 6 5.2 Applied Ethics .............................................................................. 104 constitutive structure. 5.3 Migration Policy andthe Ethics ......................................................... 106 is the In this narrative, phallus has two aspects. The first aspect intention of organising the surface of the body, and summoning the with5.4 Migration Policy in Colombia ...................................................... 108 drawn pre-eminence. The second aspect is the consequence of collapsing 5.5 “Colombia nos une”...................................................................... 109 the structure of the Voice. These incompatible effects cannot take place on 5.6 same Alianza País .................................................................................. the surface. This is precisely where the surface splits. The 112 phallus of 5.7 Challenges .................................................................................... 114 good intentions organises the surface of the skin into a complete unity. The phallus of the....................................................................................... tragic consequences, that of castration, doubles the116 surface of Bibliography the skin with a second withdrawn screen, the cerebral or metaphysical Working for the the Well-being ........................... 119 anew surfaceTogether on which phantasmofisMigrants going to develop, begin Barry Halliday with a beginning which now accompanies it at each step, run to its own finality, represent pure events (Deleuze 1990, 218). A surface of consequences, of independent and preeminent pure events is formed, a surface of sense. 6I

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The first move (projecting the Voice onto the penis) contracted the Bibliography ......................................................................................... high-low topography onto a single surface. But the result was 60 symbolic castration — a splitting of this surface into skin and phantasmatic surface. 4. The Ethics of Migration. The second surface, the surface of phantasm or sense, is derived from the Reflections on Recent Migration Policies phallus as paradoxical the attempt to make present that and “Non-policies” in element, Italy and as Europe ........................................... 61 which isLaura unpresentable. It issues from the crack/scar of this failed stitching of the Zanfrini Voice onto the Policies penis, from the markDemand of castration as connecting 4.1 Restrictive and Structural for Immigrant Labour the .. 65surface of the skin to that of phantasm. But this second surface grows out from 4.2 Initiatives for Governing Family and Humanitarian this Migration: crack to become separatebut surface. Labour aMigration not Workers’ Migration ............. 73 FromGuest the Workers integrated surface of the body, which betrayed the 4.3 From to Unwelcome Guests .................................. 82 withdrawal of the Voice, was derived a second surface, which respects this with4.4 Selective Policies and the Brain Drain............................................ 87 drawal. This splitting into embodied intentions and phantasmatic conse4.5 Equal Denied Opportunities ................................ quences is Opportunity precisely theand structure of language. The resonance of the90surfaces allows for the......................................................................................... dimensions of language to emerge. The resonance between the Bibliography 97 embodied surface and the surface of the phantasm generates the first lan5.guage. Colombia: in Their Societies ofphonemes, Origin .......are 101chained The Including patches ofEmigrants body surface, as elementary Urs Watter together under the rule of the organising phallus to form morphemes and 5.1 State Interest andsurface Responsibility semantemes. This resonates with the topography of the Voice’s towards their Citizens Living Abroad ........................................... 102 pre-sense — the dimensions of denotation, manifestation and signification 5.2 Applied Ethics .............................................................................. 104 and already articulated by the Voice. This resonance between phantasm the is a Policy first language. 5.3 body Migration and Ethics ......................................................... 106 It is a question of a dual surface effect ... which precedes all 5.4 Migration Policy in Colombia ...................................................... 108 relations between states of affairs and propositions. The109 fact that 5.5 “Colombia nos une”...................................................................... the second, phantasmatic surface emanates from the crack of castration, the 5.6 Alianza País .................................................................................. 112 projection of the Voice onto penis, is why when the phantasmatic surface Challenges .................................................................................... is5.7developed with different effects which at last found114 denotaBibliography ....................................................................................... 116 units tions, manifestations and significations as ordered linguistic (which, we recall, emerged from the heights of the Voice), elements like Working Together for the Well-being of Migrants ........................... 119 phonemes, morphemes, and semantemes (which, we recall emerged Barry Halliday from the sexual surface of the skin) seem to turn up on this new plane, but seem to lose their sexual, or embodied, resonance. This resonance is repressed or neutralised, while the underlying embodiment is swept aside by the new topography. Sexuality and embodiment exist only as an allusion, as vapour or dust, showing a path along which language has passed, but which it continues to erase like Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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so many extremely disturbing childhood memories (Deleuze 1990, Bibliography ......................................................................................... 60 242). Language and sense are effects of a paradoxical element, the attempt 4. The Ethics of Migration. to impose withdrawn Voice Policies on the present penis, of a non-sensical Reflectionsthe on Recent Migration binding together of in good and........................................... tragic results, an image61of unity and “Non-policies” Italyintentions and Europe Laura dissolves Zanfrini itself into two. which To wrap Policies up thisand digression, mustfor relate the two myths 4.1 Restrictive Structural we Demand Immigrant Labour .. 65 — the psychoanalytic myth of the generation of language and the myth of the 4.2 Initiatives for Governing Family and Humanitarian language of pre-crisis mathematics. will now Migration point out............. the paradoxical Migration: Labour Migration but notI Workers’ 73 element, that which takes the role of the phallus in tying together pre4.3 From Guest Workers to Unwelcome Guests .................................. 82 crisis mathematics into a doubly-articulated language, a language with 4.4 Selective Policies and the Brain Drain............................................ 87 phonemes, morphemes and semantemes, with denotation, manifestation 4.5 Equal Opportunity Denied Opportunities 90 and signification — a and surface of sense hovering................................ over bodies and things. Bibliography ......................................................................................... 97 5.3.4 Colombia: Including Emigrants in Their Societies of Origin 101 The paradoxical object and the ....... full Urs Watter

language of pre-crisis mathematics

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 Note, however, that we’re not going to tell a story of how a mathematical 5.2 Applied .............................................................................. 104 given language wasEthics generated. pre-crisis mathematical language is already 5.3established Migration Policy and Ethics ......................................................... as language, and we’re not going to provide it with 106 a creation myth. What we intend to do is find in this language the de-sexualised 5.4 Migration Policy in Colombia ...................................................... 108 traces of the creation myth above: a place holder for a phallus, a paradoxical 5.5 “Colombia nos une”...................................................................... 109 element that is structured as the Voice projected onto the penis. 5.6 Alianza País .................................................................................. 112 It is in fact remarkably easy to find a paradoxical element, a trace of 5.7 phallus, Challenges .................................................................................... 114surfaces the around which pre-crisis mathematics splits into two that are tied....................................................................................... together into a linguistic complex. In fact, there 116 are many Bibliography such elements; but here we will consider as a canonical example the very Working Together for the Well-being of Migrants ........................... 119 element that instigated the Cantorian crisis: infinity. Barry Halliday

To explicate in what way the infinite is paradoxical, we must first provide criteria to recognise the paradoxical object, which so far we only know as the phallus, that superposition of the withdrawn Voice on the bodily penis. These criteria are borrowed by Deleuze from Lacan, and underlie the paradoxical element’s capacity to relate and split words and things, facts and their senses. The paradoxical object is missing always its own Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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equilibrium, at once excess and deficiency, never equal, missing Bibliography ......................................................................................... 60 place, its own resemblance, its own identity, its own origin, its own and always displaced in relation to itself. It is floating signifier 4. The Ethics of Migration. and floated signified, place without occupant and occupant withReflections on Recent Migration Policies out place, the empty (which can also create an61excess and “Non-policies” in Italysquare and Europe ........................................... through its void) and a supernumerary object (which can also Laura Zanfrini create a lackPolicies by being this excess number). ThisLabour is the.. 65 very ob4.1 Restrictive and Structural Demand for Immigrant ject which brings about the resonance of the two series, words and 4.2 Initiatives for Governing Family and Humanitarian things, which it relates (Deleuzebut 1990, 228). Migration: Labour Migration not Workers’ Migration ............. 73 It almost seems that this description was tailor made for the concept 4.3 From Guest Workers to Unwelcome Guests .................................. 82 of infinity, as it stood in Zeno’s paradoxes, early calculus, and in Cantor’s 4.4 Selective PoliciesItand theonce Brainexcess Drain............................................ theory of cardinals. is at and deficiency. Excess,87because Opportunityitand Denied Opportunities ................................ it4.5 is Equal un-containable, keeps advancing, whether as an unlimited90 series of steps, of subdivisions, or of the uncontainable hierarchy of ordinals Bibliography ......................................................................................... 97 and cardinals. Deficiency, because whenever it seems to be encountered, there 5.isColombia: Including Emigrants in Their of Origin ....... 101another still something missing, a further step, aSocieties subsequent subdivision, Urs Watter 1 to add, a greater cardinal ahead. 5.1 State Interest and Responsibility Infinity is never equal to itself, missing its own resemblance, betowards their Citizens Living Abroad ........................................... 102 cause, on the one hand, it is equivalent to a proper part of itself, without, 5.2the Applied Ethics .............................................................................. 104 oneon other, being equal to this part. The integers can be mapped to-one onto the proper of even integers; the infinitesimal106 dx bears 5.3 Migration Policy and subset Ethics ......................................................... 1 2 an ambiguous relation of dis/similarity to dx and d x. It is missing its 2 5.4 Migration Policy in Colombia ...................................................... 108 own origin, because the sequence of integers (negative and positive to5.5 “Colombia nos une”...................................................................... 109 gether) does not have an origin. Even the sequence of steps in the race 5.6 Alianza País .................................................................................. 112 between Achilles and the turtle, which does have an origin (two origins), 5.7 Challenges 114 would fails to reach a.................................................................................... final destination (tracking the argument backwards undermine the origin as well). Bibliography ....................................................................................... 116 The infinite cannot be placed. The infinitesimal fails to have a poWorking Togetherthe forpoint the Well-being of Migrants ........................... 119 tie an sition between and extension; nothing can capture and Barry Halliday infinite sequence to a concrete place, it always escapes the place and disappears towards the eventual or metaphysical. The infinite is always displaced in relation to itself. This is true for Hilbert’s Hotel7 as it is true 7A

hotel with infinitely many rooms is in full capacity. One evening, infinitely many new guests arrive. The hotel manager resolves the crisis in the following manner: first she sends each guest from their room, room number x, to room number 2x; then the newly Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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for its early echo, Zeno’s stadium paradox. Bibliography ......................................................................................... 60 The infinite is a floating signifier, because it denotes no present image or state of affairs. It is a floated signified, because no chain of words, 4. The Ethics of Migration. however elaborate, canMigration fully capture the infinite. It is a place without Reflections on Recent Policies occupant or empty square, because........................................... no concrete image or object can and “Non-policies” in Italy and Europe 61 Laura ‘fill theZanfrini shoes’ of the infinite or check the ‘I am infinite’ box. This void articulates thePolicies infiniteand as an excessDemand beyondfor any concreteLabour image..or 4.1 Restrictive Structural Immigrant 65object. No place, name or number can be assigned to the infinite, as some order 4.2 Initiatives for Governing Family and Humanitarian of infinity always exceeds them.but The is anMigration effect of............. lack, something Migration: Labour Migration notresult Workers’ 73 missing in our reservoir of places, numbers, and names. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 This paradoxical element, in the form of a hypothesised pre-existing, 4.4 Selective Policies and the Brain Drain............................................ 87 complete but withdrawn object, is projected upon the ‘body’ of applicable 4.5 Equal Opportunity Denied Opportunities ................................ 90it, unimathematics with theand good intentions of organising it, completing fying it, resolving its open questions. Due to this projection of the Bibliography ......................................................................................... 97 image of infinity, the discrete-becoming-continuous is replaced by the continuous, 5.the Colombia: Including Emigrants in Their Societies of Originare .......replaced 101 small-becoming-smaller and the large-becoming-larger by Urs Watter the infinitely small and infinitely large respectively. We obtain the full in5.1 State finite lineInterest as welland as Responsibility the dimensionless point. It allows different zones of towards their Citizens Living Abroad ........................................... 102 mathematical language (algebra, geometry, analysis) to be unified under 5.2 Applied Ethics .............................................................................. Cartesian analytic geometry, which later develops into algebraic 104 geometry, th the field that came to dominate 19 century mathematics. And the 5.3 Migration Policy and Ethics ......................................................... 106 movement of foundations seeks to found all mathematical objects on the infinite 5.4 Migration Policy in Colombia ...................................................... 108 sequence of positive integers as its final common ground. 5.5 “Colombia nos une”...................................................................... 109 But the infinite paradoxical object, like the phallus in the psychoana5.6 Alianza País .................................................................................. 112demonlytic myth, ends up castrating the body of applicable mathematics, 5.7 Challenges strating a lack .................................................................................... within it, and destroying the intended prospects 114 of making mathematical reasoning concretely present. It opens up a ‘metaphysical’ Bibliography ....................................................................................... 116 mathematical surface, a surface where the operation of linguistic effects in Working Together for the Well-being Migrants ........................... 119 follow discussing the mathematical infinity of carry out their own deployment, Barry Halliday their own logic, with only a faint echo of ‘underlying’ or ‘applied’ situations. This metaphysical surface echoes the surface of ‘real world’ mathematics, but is at the same time not completely dominated by its constraints. Zeno’s paradoxes, the Pythagorean crisis, Berkeley’s critique of calculus and the arrived guests are assigned to the odd-numbered rooms, which have now all become vacant. Everyone goes to bed content. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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paradoxes in Cantor’s theory are all perfect candidates for an explicit manBibliography ......................................................................................... 60 ifestation of this process. However, since the fourth dimension of language (sense, the expressed, 4. The Ethics of Migration. that which is not reducible to denotation, manifestation and signification) Reflections on Recent Migration Policies will articulated asininsisting in the proposition, and since we andbe “Non-policies” Italy andonly Europe ........................................... 61 do not Lauraa Zanfrini have concrete set of propositions for our mythically reconstructed precrisis mathematical language, the task of concretely explicating 4.1 Restrictive Policies and Structural Demand for Immigrant Labour ..the 65 effects of sense in pre-crisis mathematics beyond the indication of some paradoxical 4.2 Initiatives for Governing Family and Humanitarian elements is unmanageable. Our but indication of theMigration crucial role of the Migration: Labour Migration not Workers’ ............. 73infinite paradoxical element in the constitution of pre-crisis mathematical language 4.3 From Guest Workers to Unwelcome Guests .................................. 82 will therefore be demonstrated by our diagnosis of the ‘depressive’ state of 4.4 Selective Policies and that the Brain Drain............................................ mathematical language resulted from the finitist-formalist87 attempt 4.5remove Equal Opportunity and Denied Opportunities 90 to this paradoxical element. We will ................................ go on to describe explicitly G¨ odel’s ‘therapy’ for this mathematical depression, and then, finally, Bibliography ......................................................................................... 97 turn to describe the operations of the fourth dimension of sense as they insist in 5.contemporary Colombia: Including Emigrants in Their Societies of Origin ....... 101 mathematical language. Urs Watter

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3.5towards First final´ eLiving : G¨ o del ........................................... as Lacanian therapist their Citizens Abroad 102 5.2 Applied Ethics .............................................................................. 104 My task here is to eventually point out the role of a fourth dimension 5.3sense Migration and Ethics ......................................................... 106the atof in G¨ oPolicy del’s mathematical language. But I will first follow tempts to extract and the paradoxical element from mathematical 5.4 Migration Policy in discard Colombia ...................................................... 108 language, go onnos toune”...................................................................... point out the tragic consequences of this well-intended 5.5 “Colombia 109 attempt, and finally reconstruct G¨odel’s intervention as a therapeutic move 5.6 Alianza País .................................................................................. 112 that would restore to mathematical language its fullness (or, rather, open5.7 Challenges .................................................................................... 114 ness). Bibliography ....................................................................................... Benacerraf and Putnam point out to an ideal, shared by116 thinkers with views as mutually antagonistic as those of Hilbert and Brouwer, Working Together for the Well-being of Migrants ........................... 119 of eliminating the infinite from mathematics altogether (Benacerraf Barry Halliday & Putnam 1983, 6). The finitist-formalist attempt reduced the mathematical infinite to a finite system of symbols together with rules for employing them (1934, 346). When thus reduced, the following image of mathematical practice emerges, as painted by von Neumann in 1931: even if the statements of classical mathematics should turn out to be false as to content, nevertheless, classical mathematics inRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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volves an internally closed procedure which operates according to Bibliography ......................................................................................... 60 bafixed rules known to all mathematicians and which consists sically in constructing successively certain combinations of prim4. The Ethics of Migration. itive symbols which are considered “correct” or “proved”. This Reflections on Recent Migration Policies construction-procedure, moreover, is “finitary” and directly and “Non-policies” in Italy and Europe ........................................... 61 constructive (von Neumann 1983, 61–62). Laura Zanfrini The resulting mathematical language shrugs its shoulder at the prospects 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 of false statements (even if the statements of classical mathematics 4.2 Initiatives for Governing Family and Humanitarian should turn Labour out toMigration be falsebut asnot toWorkers’ contentMigration ...), as long as the Migration: ............. 73 mathematical procedure is sound. Statements are no longer true or false, but 4.3 From Guest Workers to Unwelcome Guests .................................. 82 only provable or unprovable. The rule of denotation is thus crossed out 4.4 Selective Policies andmathematical the Brain Drain............................................ from the horizon of the language. Manifestation too87loses its footing. formal language hasOpportunities no symbol for ‘we’. One may point out 4.5 EqualThe Opportunity and Denied ................................ 90 to the axioms......................................................................................... as forms of manifestation; however, the possibility of Bibliography 97 repositioning axioms as assumptions, turning each statement into a conditional 5.statement Colombia:assuming Includingthe Emigrants Their Societies of into Origin ....... weak 101 form axioms, in transforms axioms a very Urs Watter of manifestation, if at all. 5.1 State and Responsibility The Interest only dimension left is signification. Formal languages are subtowards their Citizens Living Abroad ........................................... 102analyse ject to machines (or rules), which determine implication, which 5.2 Applied conditions, Ethics .............................................................................. provability and which separate meaningful symbol104 combinations from meaningless rules must be finitely and mechanically 5.3 Migration Policy and ones. Ethics All ......................................................... 106 verifiable. The resulting language is one dimensional. The chains of sym5.4 Migration Policy in Colombia ...................................................... 108 bols in the language are subject to a dimension of signification, but this 5.5 “Colombia nosfloating une”...................................................................... dimension is not above — it is tied to the ground, just109 as in the 5.6 Alianza País .................................................................................. 112 attempt to anchor the Voice to the surface of the body.8 This kind .................................................................................... of language is a sort of concrete analogue of the dimension5.7 Challenges 114 less language on the surface of the skin: symbols (phonemes), syntactically Bibliography ....................................................................................... 116 organised into chains (morphemes), and related to each other by rules of inference, which allow syntax to feign flat, reduced, semantics. 119 But above Working Together for the Well-being ofaMigrants ........................... Barry Halliday and below this surface there is nothing, and this surface does not even manifest itself. This stupid surface relates only to the syntactic machines 8 In this context one may describe intuitionism as an attempt to reduce mathematical language to a single dimension of manifestation: The intuitionist mathematician proposes to do mathematics as a natural function of his intellect, as a free vital activity of thought (Heyting 1983, 52). Logicism would lie a little closer to a two dimensional language displaying signification and, to a very limited extent, denotation.

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operating on it. It does not express. Bibliography ......................................................................................... 60 Any contemporary mathematical argument can (in principle) be transcribed into this language. This includes, of course, G¨odel’s text. Such 4. The Ethics of Migration. readings seek view Migration mathematical texts from the point of view of the Reflections onto Recent Policies machines operating in onItaly the and stupid surface. But unless the symbols and “Non-policies” Europe ........................................... 61 are alLaura to Zanfrini lowed designate (so that numbers designate formulas, rather than just be related them), unless are allowed to manifest (a 4.1syntactically Restrictive Policies andtoStructural Demandthey for Immigrant Labour .. 65 formal system that has authority over other formal systems, and can per4.2 Initiatives for Governing Family and Humanitarian formMigration: self-reference), theybut arenot allowed to signify (not only their Labourunless Migration Workers’ Migration ............. 73 own step-by-step validity, but open ended concepts of completeness and truth), 4.3 From Guest Workers to Unwelcome Guests .................................. 82 G¨ odel’s proof, which would remain a proof, would not be a proof of in4.4 Selective Policies Braina Drain............................................ completeness. It will and onlytheplace certain chain of symbols at the87bottom 4.5a Equal and Denied Opportunities ................................ 90 of proof.Opportunity Even the interpretation of this chain of symbols as making an arithmetic claim — the unprovability of a couple of integers — which Bibliography ......................................................................................... 97 conditions their intended metamathematical interpretation as claiming the 5.unprovability Colombia: Including Emigrants Their Societies of Origin ....... of a formula, wouldinremain inaccessible without a 101 dimension Urs Watter of denotation. If the formally transcribed proof were effectuated and pre5.1 State sented asInterest such toand a Responsibility reader, the reader would be nothing but the passive towards their Citizens Livingrules Abroad 102 never synthesiser of formulas under of ........................................... inference. This reader would 5.2 Applied Ethics .............................................................................. 104 this decipher a message of incompleteness in the proof, simply because reader would Policy never and decipher message. Deciphering messages106 would be 5.3 Migration Ethics a......................................................... beyond this reader’s horizons. 5.4 Migration Policy in Colombia ...................................................... 108 Unless the formal text is immersed in the volume of underlying ob5.5 “Colombia nos une”...................................................................... 109 jects, overlaying concepts, and self-manifesting desire (the indispensable el5.6 Alianza País .................................................................................. 112correct, ement of motivation in a proof), the proof will remain mechanically 5.7 Challenges 114 but most likely.................................................................................... unreadable, and most certainly impossible to understand. Unless someone were to take the elements of the proof and reiterate Bibliography ....................................................................................... 116 them into the framework of a full (four dimensional) language, the proof would Working Together for the Well-being of Migrants ........................... 119 9 TheHalliday Barry following quotation brought to my attention by Menachem Fisch is quite ap-

pealing here. 19th century mathematician and logician Augustus De Morgan claims that a person who makes the transformations of algebra by the defined laws of operation only is comparable to one who puts a dissected map together by the backs of the pieces alone; whereas the person who looks at the front, and uses his knowledge of geography to help, more resembles the investigator and mathematician (De Morgan’s 1842 On the foundation of Algebra quoted in Fisch (1999, 148)). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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be nothing but a dead letter. Bibliography ......................................................................................... This is the point where G¨ odel intervenes. His restoration of60fullness and sense to mathematical language is threefold. First, G¨odel reminisces. 4. The Ethics of Migration. While a formal system consists only of symbols and mechanical Reflections on Recent Migration Policies rules relating to them, explains, meaning which we attach to and “Non-policies” in Italyheand Europethe ........................................... 61 Laura Zanfrini is a leading principle in the setting up of the system the symbols (1934, 349). G¨ odel reminds us thatDemand even if for weImmigrant find language in.. this 4.1 Restrictive Policies and Structural Labour 65 state of formalist depression, this language must have had a healthy history of 4.2 Initiatives for Governing Family and Humanitarian full Migration: livelihood.Labour G¨ odel’s first move is to reconstitute a past. In this Migration but not Workers’ Migration ............. 73 past, which G¨ odel is about to reconstruct, there shall be meaning, expression, 4.3 From Guest Workers to Unwelcome Guests .................................. 82 signif ication, denotation, and the entire multidimensional transcription 4.4 Selectivereviewed Policies and the first Brainchapter Drain............................................ 87 mechanism in the of this book. 4.5 Equal and Denied Opportunities 90 This Opportunity to-be-reconstituted past will also be................................ drenched with a manifesting we, and ......................................................................................... even include a desire (to forget). This is not the 97 past of a Bibliography recollection, a re-presenting of something that was present at a now-gone5.but-once-present Colombia: Including Emigrants TheirtoSocieties of Origin ....... 101 moment. G¨ odelinrefers no concrete moment; his formal Urs Watter system is one of unboundedly many variations circulating at the time. The 5.1 State Interest past to which G¨oand del Responsibility refers is re-produced ad-hoc, as in nostalgic reministowards their Citizens Living Abroad ........................................... 102 cence. Instead of representing a past-present as a present-present it seeks 5.2recreate AppliedaEthics .............................................................................. to new surface of active synthesis. But the origin, the104 attached meaning in the setting up of the system does not restore the 5.3 Migration Policy and Ethics ......................................................... 106specific history of a given language. Instead, it hypothesises a visionary past, and 5.4 Migration Policy in Colombia ...................................................... 108 reforms an entire history of formal languages from Boole to Hilbert, drawn 5.5 “Colombia nos une”...................................................................... 109 through radical attachments and detachments of texts and meanings to a 5.6 Alianza País .................................................................................. 112 horizon of eternal return.11 5.7 Challenges .................................................................................... The product of G¨ odel’s reminiscence, his recollection of a114 past that never took place and that opens the road for new futures, his multiple arBibliography ....................................................................................... 116 ticulation of meaning as leading principle, as mechanical verificationability Working Together for the Well-being of Migrants ........................... 119 10 Of course, Barry Hallidaysuch reiteration needn’t be compatible with G¨odel’s framework. The elements of the ‘dead’ formal proof are open to outside interventions and interpretations, which may read into the proof various mathematical and/or non-mathematical meanings (G¨ odel’s numerological coding of formulas is not the only numerology that the text can sustain). 11 See Deleuze’s notes on Proustian reminiscence in Deleuze (1994, 122), and, once again, Derrida’s reading of Husserl’s Origin of Geometry (Derrida 1989) as presented above.

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of formal rules, and as something forgettable that can be detached from Bibliography 60 which and attached......................................................................................... to texts — all this constitutes a paradoxical element, ties the language and its meta/outside while maintaining their distinction, 4. The Ethics of Migration. and, in turn, as we shall see, opens up an entire dimension of sense. Reflections on Recent Migration Policies and “Non-policies” in to Italy and Europe ........................................... But what comes substitute the lost paradoxical element in61G¨odel’s Laura Zanfrini

move is not meaning. His choice is much more bold, perhaps even shocking. 4.1dares Restrictive Policies and Structural Demand for Immigrant 65 He summon the high object par-excellence, a variantLabour of the..psychoanalytic Voice. He to play the role of the paradoxical element. 4.2 Initiatives forsummons Governingtruth Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 Truth, we recall, has lost its bearing on the formal system together 4.3 From Guest Workers to Unwelcome Guests .................................. 82 with the discarding of denotation. What was left behind was but a syn4.4 Selective Policies and the Brain Drain............................................ tactic determination of provability. G¨odel summons truth, but as87distinct from provability. According to his formulation................................ “false statement 4.5 Equal Opportunity and Denied Opportunities 90 in the language B” ......................................................................................... cannot be expressed in B, and the same goes for 97 the predBibliography icate ‘true’ (1934, 363). The truth predicate of any given language must be 5.expressed Colombia:inIncluding Emigrants inIn Their Societies of Origin ....... 101 yet another language. his construction, therefore, truth, like Ursphallus, Watter is excess (the truth predicate of a language always exceeds the 5.1 State Interestand anddeficiency Responsibility that language) (no articulation of truth can rule over the towards their Citizens Living Abroad ........................................... 102 lanfull hierarchy of languages). Truth predicates keep changing between guages, having no .............................................................................. stable place, self-resemblance or identity.104 They are 5.2 Applied Ethics displaced from language to language, so they have no origin. No106 predicate 5.3 Migration Policy and Ethics ......................................................... can exhaust truth, and truth cannot be fully formulated, leaving it on the 5.4 Migration Policy in Colombia ...................................................... 108 one hand a floating signifier and empty box, and on the other a name5.5 “Colombia une”...................................................................... 109lack of less object andnos floating signified; at once excess of demand and 5.6 Alianza(as País .................................................................................. 112 and fulfilment well as the opposite: excess of possible truth predicates, lack of a complete verification procedure). 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... With this paradoxical object the surface of language is not116 just doubled, it proliferates unlimitedly, generating an infinite hierarchy of bifurcatWorking Together for the Well-being of Migrants ........................... 119 ing language surfaces, restoring through this hierarchy the infinity that had Barry Halliday been previously excluded. Each surface is at once a full language doubled by another surface of the sense insisting in its propositions. In relegating truth to the position of paradoxical element, the fullness of mathematical language has been reinstated under the splitting law of castration, and the past one-dimensional depression is healed. This is, perhaps, why G¨odel’s proof did not create a mathematical crisis. It did not create a crisis, because Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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it was a therapy, rather than a pathology. Bibliography 60 accept But this......................................................................................... still is not enough. Some mathematicians and logicians G¨ odel’s proof, but reject his concept of truth. They nevertheless enjoy ac4. The Ethics of Migration. cess to a full,onfour dimensional, language. This is so because Reflections Recent Migrationmathematical Policies the element is reintroduced not only in the form of truth, but andparadoxical “Non-policies” in Italy and Europe ........................................... 61 Laura also in Zanfrini the form of self-reference, which G¨odel restores after it had been discarded by Russell To clarify this point, let’s ..read 4.1 Restrictive Policiesand and Whitehead. Structural Demand for Immigrant Labour 65 more about the structure of the paradoxical object. It is a two sided entity, 4.2 Initiatives for Governing Family and Humanitarian equally present in the signifying signified series. it is the Migration: Labour Migration but notand Workers’ Migration ............. 73 mirror. Thus, it is at once word and thing, name and object, sense 4.3 From Guest Workers to Unwelcome Guests .................................. 82 and denotatum, expression and designation, etc. It guarantees 4.4 Selectivethe Policies and the Brain 87 therefore, convergence ofDrain............................................ the two series which it traverses, 4.5 Equal Opportunity andcondition Denied Opportunities ................................ 90 but precisely on the that it makes them endlessly diverge. It has the property of being always displaced in relation to Bibliography ......................................................................................... 97 itself. If the terms of each series (signifier and signified) are relatively 5.displaced, Colombia: Including Emigrants Their Societies of Origin ....... 101 they in relation to one in another, it is primarily because Urs Watter have in themselves an absolute place; but this absolute place is al5.1 State Interest andby Responsibility ways determined the terms’ distance from this element which towards their Citizens Living ........................................... 102 We is always displaced, in the Abroad two series, in relation to itself. 5.2 Applied Ethicsthe .............................................................................. must say that paradoxical entity is never where we104 look for it, and conversely that we never find it where it is. As Lacan 5.3 Migration Policy and Ethics ......................................................... 106 says, 5.4 Migration Policy in Colombia ...................................................... 108 12 We should perhaps account for our use of the term ‘Lacanian’ in the title of this section. The obvious reason is, of course, our heavy reliance on Lacanian 5.5 “Colombia nos une”...................................................................... 109concepts, mediated through Kristeva and Deleuze. But there is a little more to it than just that. 5.6 early Alianza País .................................................................................. The texts of Lacan can be read as suggesting that allowing the signifier112 to exhaust the it can occupy under the laws of symbolic order is a road to mental 5.7positions Challenges .................................................................................... 114 health. For example, little Hans, left in the lurch at the age of five by the failings of his Bibliography ....................................................................................... 116 to him symbolic entourage, and faced with the suddenly actualised enigma of his sex and his existence, develops — under the direction of Freud and his Working Together for the Well-being Migrants father, who is Freud’s disciple — allof the possible........................... permutations of119 a limited Barry Halliday number of signifiers in the form of a myth, around the signifying crystal of his phobia. We see here that, even at the individual level, man can find a solution to the impossible by exhausting all possible forms of impossibilities that are encountered when the solution is put into the form of a signifying equation (Lacan 2006, 432). To an extent, this is precisely G¨ odel’s operation: exploring permutations and forms of impossibilities around the kernel of self-reference or truth, in order to escape a fixation that immobilises mathematical language, and prevents it from functioning along all its dimensions. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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it is placed out of place (elle manque ` a sa place) ... It belongs to Bibliography ......................................................................................... this element which is always absent from its proper place,60proper resemblance, and proper identity to be the object of a fundamen4. The Ethics of Migration. tal question which is displaced along with it: what is the Snark? Reflections on Recent Migration Policies what is the Phlizz? What This ........................................... (C ¸ a)? (Deleuze 1990, 40–41, 57; and “Non-policies” in Italy and is Europe 61 translation modified). Laura Zanfrini Let’s begin with This then. This has been the focusLabour of many 4.1 Restrictive Policies and Structural Demand for Immigrant .. 65a philosophical debate. In these debates its status ranges between the most distin4.2 Initiatives for Governing Family and Humanitarian guished model Labour of denotation andbut itsnot most defective specimen. Its ambiguous Migration: Migration Workers’ Migration ............. 73 role is not restricted to the occasion of the liar’s ‘This statement is false’. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 This is also the paradoxical element of Magritte’s This is not a pipe (see 4.4 Selective Policies the Brain Drain............................................ 87 (which Foucault 1983): Thisand which may or may not point to the diagram 4.5 Equal Opportunity and Denied Opportunities ................................ 90or may may or may not be a pipe or a drawing of a pipe), and which may not manifest ......................................................................................... itself (that is indeed a pipe, but This, this word, 97 This, is Bibliography certainly not). G¨ odel installs This at the core of his argument. S(w, w) is 5.This. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

Let us recall again the construction of G¨ odel’s undecidable formula. 5.1 State Interest andisResponsibility Πv[¬B(v, S(w, w))] shorthand for the formula (numbered p), which says their Citizens Living Abroad thattowards the formula, whose number is S(w,........................................... w), is not provable. Recall102 also that 5.2aApplied Ethics .............................................................................. 104number S(z , zb ) is defined so as to yield the number representing formula a, zb (thePolicy numeral corresponding to the number b) is substituted for 5.3after Migration and Ethics ......................................................... 106 13 the free variable w. 5.4 Migration Policy in Colombia ...................................................... 108 Here, the undetermined S(w, w) is as undetermined as This. It has 5.5 “Colombia nos une”...................................................................... 109 the potential to refer to many different formulas, to numbers, and, most im5.6 AlianzatoPaís .................................................................................. 112rule, we portantly, itself. If we substitute S(zp , zp ) according to the above obtain the number of the formula Πv[¬B(v, S(w, w))] with zp substituted 5.7 Challenges .................................................................................... 114 for w. In other words, we obtain Πv[¬B(v, S(zp , zp ))]. This formula Bibliography ....................................................................................... 116 says of itself: This statement is unprovable. Constructing this This with the limWorking Together for the Well-being of Migrants ........................... 119 mirror ited tools of a depressed formal system, installing this self-referring Barry this Halliday inside formal language, this is G¨odel’s most overwhelming achievement. To observe that S(zp , zp ) can take the place of the paradoxical element, note that it is both signifying (a number) and signified (by a numeral), it is at once mirror (reflecting itself as its own subject), name (of a formula), thing (a sign sequence), word (on the page), object (of study), 13 See

section 7 of Chapter 2 for more detail.

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sense (the undecidable formula, the collapse of Hilbert’s programme), deBibliography ......................................................................................... notatum, expression and designation. Being all at once, it60guarantees the convergence of series. Through this element the language is now 4. The Ethics of Migration. bound together with what it denotes. The language subsumes itself into Reflections on Recent Migration Policies its objects. S(zp , zp )inkeeps relating to itself as 61 if it were and “Non-policies” Italy displacing and Europe itself, ........................................... something else, which can again relate to itself as an other in turn.14 This Laura Zanfrini is4.1the absolute core and element around which, for which,Labour the argument is Restrictive Policies Structural Demand for Immigrant .. 65 drawn. Everything else in the argument is relatively placed with respect 4.2 Initiatives for Governing Family and Humanitarian to This, despite the claim that but its not self-referential structure was discovered Migration: Labour Migration Workers’ Migration ............. 73 so to speak by chance. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 And, as we have already established in the previous chapter, it is 4.4 Selective andfor the it Brain Drain............................................ 87 except never wherePolicies we look — it is never properly written down, 4.5the Equal Opportunity and Denied Opportunities ................................ in form of shorthand, denotation, representation; again and 90 again we are told that......................................................................................... in principle we can compute it. And yet, it is never Bibliography 97 considered a fault that the computation is never conducted; that it may be 5.materially Colombia:impossible Including Emigrants ....... 101for any to conductinit;Their that Societies it would of beOrigin unreasonable Urs Watter human to conduct it, or even for a human to verify its implementation by State Interest andpresentation Responsibility a5.1 machine; that its necessarily depends on deferring authority towards their Citizens Living Abroad ........................................... 102 of judgement to an indefinite, hypothetical, in principle.15 5.2 Applied .............................................................................. 104 At the Ethics same time, by providing us with an extreme test case, it allows to regular divergence between the series 106 of number 5.3maintain Migrationthe Policy and cases Ethicsof ......................................................... and formula, formula meaning. Relative to S(zp , zp ), the ‘regular’ 5.4 Migration Policy inand Colombia ...................................................... 108 case of S(za , zb ) is easy to handle. There we know — not without problems, but 5.5 “Colombia nos une”...................................................................... 109 much more clearly than for S(zp , zp ) — which numeral means number (zb ), 5.6 Alianza Paísmeans .................................................................................. 112 order. which numeral formula (za ), and which refers to which in what In it is through this relative clarity that the self-referential114 structure 5.7fact, Challenges .................................................................................... Bibliography 116 14 I refer here ....................................................................................... to the analysis in section 7 of Chapter 2, specifically to the discussion of the nested substitution of S(zp , zp ) into itself.

15 I leave Working Together for thetoWell-being of Migrants ........................... 119 in these it as an exercise repeat the analysis of G¨ odel’s articulation of truth

Barryand Halliday terms, to demonstrate how “... truth joys (jouit). Truth is not the conclusion of a system, truth is joying. There are people who go looking for truth, it doesn’t have to be looked for, it just comes; it can be found in bed, but how does one get it into bed? By talking of other things, as so often happens. By talking of other things, not philosophy, not truth, but something else. It is then frequently seen as a good in itself: in effect, it is often covered in veils, like a bride. Above all, one must refrain from using it until after it has joyed — please excuse all this...” (Derrida quoting Francis Ponge in Derrida (1984, 94)). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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of S(zp , zp ) can be narrated as successive rather than as circular, and said Bibliography ......................................................................................... 60 to be discovered so to speak by chance. Indeed, many readers follow G¨ odel in denying the circularity of self4. The Ethics of Migration. reference and in providing revisionary Reflections on Recent Migration Policiesaccounts. Contrary to appearances, such a proposition no faulty circularity, 61 for iniand “Non-policies” in Italy andinvolves Europe ........................................... Laura Zanfrini tially it [only] asserts that a certain well-defined formula (namely, the one obtained the qthDemand formula in the lexicographic or4.1 Restrictive Policiesfrom and Structural for Immigrant Labour .. 65 der by a certain substitution) is unprovable. 4.2 Initiatives for Governing Family and Humanitarian Only subsequently (and so to speak by chance) does it turn out that ............. this formula is Migration: Labour Migration but not Workers’ Migration 73 precisely the one by which the proposition itself was expressed 4.3 From Guest Workers to Unwelcome Guests .................................. 82 (1931, 151). Many readers indeed would deny the conjunction of functions 4.4 Selective Policies and the Brain Drain............................................ 87 I imposed on S(zp , zp ) above, and claim that it can fit correctly only into Opportunity anda Denied ................................ 90be proa4.5 fewEqual of them. But such revisionOpportunities and restrictive reading can only duced after the fact. This is the lightning of representation having Bibliography ......................................................................................... 97 erased the trail of the dark precursor, which had conjured it. Nothing happened 5.here Colombia: Including Emigrants Societies of .......can 101prevent by chance, and no narrativeinorTheir transcription of Origin the proof Urs Watter the reader from passing through the mirror of S(zp , zp ) and finding there 5.1 conflation State Interest Responsibility the ofand several layers and dimensions of language. I have never towards their Citizens Living Abroad ........................................... 102 met, and cannot imagine, the person who would understand G¨ odel’s argu5.2 Applied Ethics .............................................................................. 104symbols ment as a ‘lucky monster’ produced from the chance assembly of monkey-typed in a one language. 5.3 Migration Policy anddimensional Ethics ......................................................... 106 Which doesn’t that there is anything wrong in revising 5.4 Migration Policy mean in Colombia ...................................................... 108the narrative this way. And there is nothing wrong in manipulating someone to 5.5 “Colombia nos une”...................................................................... 109 understand the argument as a ‘lucky monster’ by way of a clever contrived 5.6 Alianza País .................................................................................. 112 experiment. The paradoxical object does not rule over the text. The text Challengessubject .................................................................................... 114 and is5.7inherently only to what comes from the outside: iteration revision. No one can protect the text from being quoted away from Bibliography ....................................................................................... 116 its circumstances, and no one need try. The law of the paradoxical object is to Working forto thedisappear. Well-being of Migrants ........................... 119 allow itsTogether selfless self This is its essence. If we occasionally beBarry Halliday tray it, it is only to induce the ensuing effects of castration: the emergence of a new phantasmatic surface. And yet, wherever something makes sense, the paradoxical object will have been found, provided we maintain a right for looking. Whether we ought to be content with these three dimensions (denotation, manifestation, signification) or whether we should add a fourth — which Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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would be sense is an economic or strategic question. It is not Bibliography ......................................................................................... 60 that we must construct an a posteriori model corresponding to previous dimensions, but rather the model itself must have the 4. The Ethics of Migration. aptitude to function a priori from within (Deleuze 1990, 17). But this Reflections on Recent Migration Policies strategic choice doesin not exclude a positivist, empiricist, or Wittgensteinian and “Non-policies” Italy and Europe ........................................... 61 critique that would dismiss this text and my reading as pure nonsense. Sense Laura Zanfrini and nonsense are not antagonistic; cross-constitute 4.1 Restrictive Policies and Structuralrather, Demandthey for Immigrant Labour each .. 65 other, as would be the case were such critique to claim that a sensible view should 4.2 Initiatives for Governing Family and Humanitarian crossMigration: out and cover my nonsensical discourse. Labourover Migration but not Workers’ Migration ............. 73 The claims of the discourse of (non)sense cannot be properly proved. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 They are posited as a priori, and posited in a way that guarantees that 4.4 Selective Policies and—theindeed, Brain Drain............................................ 87 there they cannot be refuted dark precursors are, by definition, to effaced. The discourse of (non)sense is there to answer an economic 4.5beEqual Opportunity and Denied Opportunities ................................ 90 or strategic......................................................................................... concern. This strategic concern that constitutes 97 this disBibliography course is, I believe, a concern with enabling intervention into established 5.discourses Colombia:— Including Emigrants in Their of Origin 101 a strategic instrument thatSocieties would respect, to ....... an extent, the Urs Watter discourses’ stated limitations, but permit them to link via postulated con5.1 State nebulae Interest and Responsibility stitutive to outside interventions, and, just as importantly, permit towards their Citizens Living Abroad ........................................... 102 them to discard such former interventions. The discourse of (non)sense is therefore a discourse designed for the reconfiguration of responsibility. 5.2 Applied Ethics .............................................................................. 104 This discourse of (non)sense necessary to the extent that every text has 5.3 Migration Policy andisEthics ......................................................... 106 undergone some sort of outside intervention ‘before’ it ‘began’ to denote, manifest 5.4 Migration Policy in Colombia ...................................................... 108 and signify; it is necessary to the extent that any discourse can ‘desire to 5.5 “Colombia nosintervention; une”...................................................................... 109 interforget’ any given it is necessary to the extent that such 5.6 Alianza .................................................................................. 112 ventions andPaís desires can be reconstructed as ‘primordial’ or ‘eschatological’ nonsense. But we never claim that (non)sense ever necessarily is. 5.7 Challenges .................................................................................... 114 Which brings us to the moment where we explicate the dimension Bibliography ....................................................................................... 116 of sense. Not through its mythically contrived generative narrative, nor throughTogether paradoxical objects that may or may not, will or will 119 not, have Working for the Well-being of Migrants ........................... Barryproduced Halliday in hindsight in order to be pointed out as that which was been effaced in order for the language to function and for its surface to arise. Now is the moment to observe sense functioning in the mathematical text.

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3.6

Second final´ e: Does G¨ odel’s text make sense?

Bibliography ......................................................................................... 60 4. The Ethics of Migration. Sense is the on event expressed by the proposition and insisting in it. As an Reflections Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 to the independent surface it has its own motility, which is not subjected Laura Zanfrini other logical dimensions of language. It is not about true and false deno4.1 Restrictive Policies Structural manifestations, Demand for Immigrant Labourand .. 65 absurd tations, veracious andand illusionary or possible significations. It operates by crossing out these determinations and holding 4.2 Initiatives for Governing Family and Humanitarian on to what is left, what is left insisting in the words. Migration: Labour Migration but not Workers’ Migration ............. 73

I amGuest now taking back the statement that.................................. I made at the opening 4.3 From Workers to Unwelcome Guests 82 of this chapter, which said that sense did not come between words and actions, 4.4 Selective Policies and the Brain Drain............................................ 87 propositions and the body, speaking and eating; it does. But when we say 4.5 Equal Opportunity is andright Denied Opportunities deny ................................ 90 ‘add 1’, Wittgenstein to emphatically that we first attain the Bibliography sense of the ......................................................................................... decree, and then perform the actions. Sense is not97a stage between words and actions. Sense is the surface that separates words from 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 action, and that allows them their respective in(ter)dependence, a form of Urs Watter restricted relative dependence that Wittgenstein need not deny. Sense is 5.1 State Interest and Responsibility not a station on the way from words to actions. It is, rather, the frontier, towards their Citizens Living Abroad ........................................... 102 the cutting edge, or the articulation of the difference between the 5.2 Applied two terms,Ethics since.............................................................................. it has at its disposal an impenetrability104 which is 5.3 own, Migration andwhich Ethics ......................................................... 106 its andPolicy within it is reflected (Deleuze 1990, 28). What is Policy this surface of events, which insists in words, but 108 is not yet 5.4 Migration in Colombia ...................................................... effected in action? In ‘natural’ language, according to Deleuze,109 it can be 5.5 “Colombia nos une”...................................................................... found in the infinitive form of the verb, that which is not yet temporalised, 5.6 Alianza País .................................................................................. 112 not yet effected in a subject or a pronoun. In formal languages it is even 5.7 Challenges .................................................................................... 114operatmore straightforward to find sense. It can be found in the predicate ing on a free variable. In the string P (x) insists the predicate P unsubjected Bibliography ....................................................................................... 116 to a quantifier and uneffectuated by substitution. As such it doesn’t desWorking Together for the Well-being of Migrants ........................... 119 ignate, and can’t be true or false; it does not manifest any consciousness, Barry Halliday desire, belief or causality, and cannot be veracious or illusory. This holds for G¨ odel’s text as well as for any formal language. But formal language, which is concerned with covering over the unstable operation of sense, quickly reacts. In G¨odel’s text we read that an expression A in which the distinct free variables t1 , . . . , tn occur shall mean the same as Πt1 (. . . (Πtn (A)) . . .) (1934, 352) (Π here is the Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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universal quantifier). In order to yield to the order of signification, a free Bibliography ......................................................................................... 60 this variable is assumed to be bound by a universal quantifier. Even where semantic rearticulation is not explicitly stated, it is standardly implicit 4. The Ethics of Migration. in rules of inference that derive ΠxA from A (this is why I cannot claim Reflections on Recent Migration Policies that (x) does not signify even as it ........................................... stands it is already involved and P “Non-policies” in Italy— and Europe 61 in an inferential relation). Laura Zanfrini In formalPolicies logic, according to Demand the rulefor quoted above, the ..variable is 4.1 Restrictive and Structural Immigrant Labour 65 never free. Unless otherwise determined, it represents the universal. But 4.2 Initiatives for Governing Family and Humanitarian sense insists inLabour formalMigration languages extent Migration that the ............. free variable, for Migration: butto notthe Workers’ 73 the brief period between the moment it is written and the moment it is 4.3 From Guest Workers to Unwelcome Guests .................................. 82 bound by a quantifier or subjected to an inference rule, during that small 4.4 Selective Policies BrainThis Drain............................................ portion of text, it isand stillthefree. empty point in time is the87time of 4.5 pure Equalevent, Opportunity Opportunities ................................ 90crossed the of the and pureDenied unsignifying predicate. This moment is over by the rules of formal logic. But formal logic could not exist97without Bibliography ......................................................................................... this moment. This moment insists in the language. To decide whether the 5.variable Colombia: Including Emigrants in Their on Societies of Originis....... 101 itself (or the predicate operating a free variable) a paradoxical Urs Watter

element, one is required to decide how to read it. Is it read during the ever 5.1 State Interest and Responsibility splitting, centrifugal time, in which it makes sense (the time which Deleuze towards their Citizens LivingbyAbroad ........................................... 102 of the calls Aion), or is it absorbed the sequential and centripetal time 5.2 Applied Ethics .............................................................................. 104 argument? In the Fifth chapter of The......................................................... Logic of Sense Deleuze presents four 5.3 Migration Policy and Ethics 106 ‘paradoxes’ where sense is reflected and developed for its own sake (Deleuze 5.4 Migration Policy in Colombia ...................................................... 108 1990, 28). We will follow these paradoxes to demonstrate how the predicate 5.5 “Colombia nos une”...................................................................... 109 operating on a free variable manifests the neutral motility of sense. 5.6 Alianza País .................................................................................. 112 The paradox of regress or of indefinite proliferation. Accord5.7 Challenges .................................................................................... 114 But ing to this paradox, I never state the sense of what I am saying. on the other hand, I can always take the sense of what116 I say as Bibliography ....................................................................................... the object of another proposition whose sense, in turn, I cannot Working for into the Well-being of Migrants ........................... state. ITogether thus enter the infinite regress of that which is119 presupBarry Halliday posed. This regress testifies both to the great impotence of the speaker and to the highest power of language: my impotence to state the sense of what I say, to say at the same time something and its meaning; but also the infinite power of language to speak about words (Deleuze 1990, 28–29). I can never write the sense of P (x), the event of its writing as not yet Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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actualised, not yet subjected to denotation, manifestation and signification Bibliography 60 But if — I can only......................................................................................... write P (x) and let its sense insist in what I write. the formal language is allowed the liberties of higher types, the writer has 4. The Ethics of Migration. the privilege of predicating over predicates, and over variables standing for Reflections on Recent Migration Policies predicates (if not, then the and meta language has this privilege). I can and “Non-policies” in Italy Europe ........................................... 61 write Q(P ); Zanfrini now the fact that there is a question whether I predicate over the Laura text P or over Policies what it and stands for is precisely indicative of Labour the lining 4.1 Restrictive Structural Demand for Immigrant .. 65of sense in this predication, distinguishing signs from what they express. Either way, 4.2 Initiatives for Governing Family and Humanitarian Q(PMigration: ) is not itsLabour own sense. It expresses a sense, which we may go on Migration but not Workers’ Migration ............. 73talking about (predicating over Q), regressing indefinitely. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 In a similar way, according to G¨odel (together with Tarski and Car4.4 Selective Policies and the Brain Drain............................................ 87 nap) each language has a truth predicate, which is written in another lan4.5 Equal Opportunity andwhich Deniedrules Opportunities ................................ guage, another language over the one whose truth we90 are considering. The language where the truth predicate is formulated Bibliography ......................................................................................... 97is ruled over, again, by a truth predicate formulated in yet another language. And 5.so Colombia: Including Emigrants Theirexpress Societies offormula Origin ....... on. We speak one language at in a time, one at a101 time, and Urs Watter can never express at the same time a statement and its sense or its truth 5.1 State Interest and Responsibility predicate. But we may go on forever speaking about the sense and truth towards their Citizens Living Abroad ........................................... 102 predicates of what we expressed. 5.2 Applied Ethics .............................................................................. 104There The paradox of sterile division, or of dry reiteration. Migration Policy Ethics ......................................................... is5.3indeed a way of and avoiding the above infinite regress. It is 106 to fix the proposition, to immobilise just long enough to extract from it 5.4 Migration Policy in Colombiait, ...................................................... 108 its sense — the thin film at the limit of the things and words ... 5.5 “Colombia nos une”...................................................................... 109 As an attribute of states of affairs, sense is extra being. It is not 5.6 Alianza País .................................................................................. 112 of being, it is an aliquid which is appropriate to non-being. As 5.7 Challenges 114 exist, that which is.................................................................................... expressed in the proposition, sense does not but inheres....................................................................................... or subsists in the proposition ... The two paradoxes, Bibliography 116 that of infinite regress and that of sterile division, form the two Working Together for the Well-being Migrants 119 terms of an alternative: one or of the other ........................... (Deleuze 1990, 31–32). Barry Halliday

Above we traced an analysis of P (x), as a predicate operating on a free variable, during the empty time where it is free from denotation and manifestation. This analysis was in fact inspired by the formulation of this second paradox. If we observe P (x) inside this form of time, what we grasp there is its sense — the boundary between the written letters and what we may do with them: designate, manifest, signify, and generally obey their Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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orders. But this moment of separation is also that which allows us to do Bibliography with the text ......................................................................................... something else, to actualise differently the event of its60writing, to inscribe it in an order not yet specified or anticipated. 4. The Ethics of Migration. But allonthis mayMigration be too obscure. odel’s text the invocation of Reflections Recent PoliciesIn G¨ sense as the sterile double theEurope text appears more visibly when 61 numbers, and “Non-policies” in Italyofand ........................................... Laura Zanfrini for instance, are assigned the role of symbols in a formal system, but as such that of course, cannot be Demand arranged in a spatial order 4.1 Restrictive Policies and Structural for Immigrant Labour .. 65 (1931, 147). Here we for encounter the Family sterile,and unwritable numbers, which hover above 4.2 Initiatives Governing Humanitarian the Migration: concrete symbols and concrete number representations. This73 moment Labour Migration but not Workers’ Migration ............. of abstraction is the transition between the concrete letters of a formal 4.3 From Guest Workers to Unwelcome Guests .................................. 82 text, and the denotations, manifestations and significations to which they 4.4 Selective Policies and the Brain Drain............................................ 87 will give rise once they will have gone through G¨odel’s double encoding (of 4.5 Equal Denied Opportunities ................................ 90 formal textOpportunity as numbersand and of properties of numbers as formal expressions). Bibliography We must......................................................................................... not confuse, however, these sterile numbers of the97 lining of sense with ideal, platonic numbers. The latter are subject to the reign of 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 truth, veracity and signification as elements in a distinct order relation Urs Watter and arithmetic structure. This is why G¨odel’s argument, in order to apply 5.1 State Interest and Responsibility to formal systems, must concern itself with sterile numbers. In order for towards their Citizens Living Abroad ........................................... 102 the argument to function, the numbers, which are no longer effectuated 5.2physical Applied scribblings Ethics .............................................................................. as on paper, must — and this is crucial if 104 we are to 5.3 Migration Policy and ......................................................... accept these numbers as Ethics arbitrary elements of a formal system — 106 not yet be immersed in the sequential algebra of the positive integers, which 5.4 Migration Policy in Colombia ...................................................... 108denotes phenomena in the world, manifests the form of the unbounded sequence, 5.5 “Colombia nos une”...................................................................... 109 signifies in the structure of arithmetic, and is generally much too charged 5.6 Alianza País .................................................................................. 112 to function as the arbitrary symbols of a formal system. 5.7 Challenges .................................................................................... But our sterile numbers are distinct from platonic numbers114 in yet anBibliography ....................................................................................... other important way. Platonic numbers fail to enjoy the motility116 conferred upon sterile numbers by the changing texts and contexts at the verge of Working Together for the Well-being of Migrants ........................... 119 which sterile numbers hover. This is the motility that allows sterile numBarry Halliday bers to stand for so many different things (formulas, numerals, statements) — things that platonic numbers cannot be confused with. This instability is precisely what separates the motion of eternal return from the stability of ideal origin. When we extract an ideal object from a text, we extract the same object every single time. When we extract the sense insisting in the proposition by discarding its material bearer (namely, every time we Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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quote a text) we do something different at each and every instance (we Bibliography ......................................................................................... 60 re-contextualise differently every time we quote). Every time we quote, we have the opportunity to fold the second, phantasmatic surface between the 4. The Ethics of Migration. surfaces of text and action in a different way. The distinct forms of materiReflections on Recent Migration Policies ality constrain the extractions sense and make of them events 61 affirming and “Non-policies” in Italy andofEurope ........................................... difference. Only then can we start imagining active and passive syntheses Laura Zanfrini of rulingand over such extractions. 4.1repetitions Restrictive as Policies Structural Demand for Immigrant Labour .. 65 The paradox of neutrality, of essence’s third estate ... 4.2 Initiatives for Governing Family and or Humanitarian Sense is strictly the same from the point view of............. quality, Migration: Labour Migration but not Workers’of Migration 73 quantity, relation, or modality. For all of these points of view affect 4.3 From Guest Workers to Unwelcome Guests .................................. 82 denotation and the diverse aspects of its actualisation or fulfil4.4 Selective Policies and the Brain Drain............................................ 87 ment in a state of affairs ... “God is” and “God is not” must have 4.5 Equal Denied Opportunities ................................ 90 the sameOpportunity sense, by and virtue of the autonomy of sense in relation to the existence of the denotatum ... Sense is indifferent to all oppoBibliography ......................................................................................... 97 sites. This is so because all of these opposites are but modes of 5.the Colombia: Including Emigrantsininits Their Societiesofofdenotation Origin ....... 101 proposition considered relations and sigUrs Watter nification, and not the traits of sense which is expressed (Deleuze 5.1 State Interest and Responsibility 1990, 32–35). towards their Citizens Living Abroad ........................................... 102 Again, we point to the analysis of the free P (x) above. Lacking a 5.2 Applied .............................................................................. 104sense of truth value, Ethics the free P (x) and the free ¬P (x) both express the 5.3 Migration Policytext, and Ethics either. In G¨ odel’s this is......................................................... precisely where the desire that106 meaningattachment bePolicy forgotten comes...................................................... in. The text is stripped of all modalities, 5.4 Migration in Colombia 108 qualities, quantities, and relations. Yet it still makes sense. It makes sense 5.5 “Colombia nos une”...................................................................... 109 as an event of writing, an event to be coded under the mechanism of formula 5.6 Alianza País .................................................................................. 112 enumeration. Indeed, a formula and its negation will be encoded by different 5.7 Challenges numbers, but it.................................................................................... is not because they are a formula and its negation114 that they are coded differently. The coding of formulas as numbers does not116 mind the Bibliography ....................................................................................... different significance of, say, ¬ and ∀; it can easily exchange the two and Working the Well-being Migrants ........................... 119 coding continueTogether to serve for effectively. It can of also indifferently exchange the Barry Halliday of P (x) and ¬P (x). But it is possible to make this point in other ways. The undecidable proposition, which escapes, together with its negation, the determination ‘provable’, manifests, for a brief moment, its sense independently of the semantic machine. Both the formula and its negation reflect in each other a single event; they both express the same moment of undecidability. A simRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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ilar manifestation of sense occurs with the inference rule described above, Bibliography 60 with a which allows ......................................................................................... to add a universal quantifier to a provable proposition free variable in precisely defined syntactic circumstances. Here, again, sense 4. The Ethics of Migration. insists in crossing over the boundary of the universal/particular dichotomy. Reflections on Recent Migration Policies These manifestations sense do not cross out the differences61 between and “Non-policies” in Italyofand Europe ........................................... Laura Zanfrini proposition and its negation, or between a statement with the undecidable or a universal on Demand the contrary, the differences 4.1without Restrictive Policies quantifier; and Structural for Immigrant Labour established .. 65 through the link of sense cross over their common sense. These differences 4.2 Initiatives for Governing Family and Humanitarian mayMigration: be articulated many ways. without this sense, without the LabourinMigration but notBut Workers’ Migration ............. 73 ability to redistribute universality and particularity, there would not have 4.3 From Guest Workers to Unwelcome Guests .................................. 82 been any link between particular and universal that would allow the former 4.4imply, Selective Policies andconditions, the Brain Drain............................................ to under certain the latter; without sense there 87 might be 4.5 Equal Opportunity and Denied Opportunities ................................ 90 mutual exclusion, but not a relation of mutual exclusion between a formula and its negation. Bibliography ......................................................................................... 97 The paradox of the absurd, or of the impossible objects ... the 5.propositions Colombia: Including in Their Societies of objects Origin ....... 101 whichEmigrants designate contradictory themselves Urs Watter have a sense. Their denotation, however, cannot at all be ful5.1 State Interest and Responsibility filled; nor do they have a signification, which would define a type towards their Citizens Living Abroad ........................................... 102 of possibility of fulfilment. They are without signification, that 5.2they Applied .............................................................................. 104objects is, areEthics absurd. Nevertheless, they have a sense. Such include square circles, matter without extension, perpetum 5.3 Migration Policy and Ethics ......................................................... 106mobile ... If we distinguish two sorts of beings, the being of the real 5.4 Migration Policy in Colombia ...................................................... 108 as the matter of denotation and the being of the possible as the form 5.5 “Colombia nos une”...................................................................... 109 of significations, we must yet add this extra-being which defines Alianza País .................................................................................. 112 a5.6 minimum common to the real, the possible and the impossible 5.7 Challenges 114 (Deleuze 1990, .................................................................................... 35). Nothing....................................................................................... prevents the formal appearance of P (x)&¬P (x).116 Nothing Bibliography even prevents the meaningless P P ((x from appearing. The latter is disWorking Together for the Well-being of Migrants ........................... carded by the formal system, but only after the system states 119 rules that Barry Halliday acknowledge it as something we must discard. But neither the contradictory nor the meaningless are excluded from G¨ odel’s enumeration. Beyond actuality and possibility, even those strings of symbols that are not meaningful formulas participate in the enumeration of formulas. G¨odel’s text allows the absurd to be processed by its machines. And to the list above of terms in G¨oodel’s mathematical language Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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without formally determinable universal designation, signification and posBibliography ......................................................................................... 60 sibility of fulfilment we must add, according to G¨ odel’s own rearticulation, one more term: Truth. Surely truth, truth which is beyond any specific 4. The Ethics of Migration. language, has some sense to it. Reflections on Recent Migration Policies It is under thein common and sterilising lining 61 of sense, and “Non-policies” Italy and regressing Europe ........................................... or, rather, through it, that the dimensions of denotation, manifestation Laura Zanfrini and signification function. The resonance that denotation 4.1 Restrictive Policies and Structural Demand for effectuates Immigrant Labour .. 65 (resonance between words and bodies), manifestation (resonance between words 4.2 Initiatives for Governing Family and Humanitarian and Migration: consciousness), (inferential resonance between Laboursignification Migration but not Workers’ Migration .............words 73 and words), this resonance depends on the possibility of resonance itself. It de4.3 From Guest Workers to Unwelcome Guests .................................. 82 pends on a paradoxical element that renders separate the two, which are 4.4 Selective Policies each and the Brain Drain............................................ 87 from supposed to resound other, first and foremost by separating itself itself. It depends on aand milieu, onOpportunities the between ................................ across which the series 4.5 Equal Opportunity Denied 90 resonate, a sterile film without which there will be no separation of97the two Bibliography ......................................................................................... which resound, but only a rumbling of partial objects or the stillness of 5.the Colombia: Including Emigrants in Their Societies Origin ....... 101 catatonic body without organs. A film, whose of only property is setting Urs Watter apart by conducting resonance. A resonance in itself. A hymen. 5.1 State andthat Responsibility I do Interest not claim this spacing must be filled or accounted for. This is towards their Citizens Living ........................................... 102 simply the doubling across whichAbroad intervention, interpretation, transcription can take place. But they don’t have to take place. Indeed, Explanations 5.2 Applied Ethics .............................................................................. 104 come to an Policy end somewhere (Wittgenstein 1953, §1). And106 Wittgen5.3 Migration and Ethics ......................................................... stein is right in juxtaposing the moment where explanations come to an 5.4 Migration Policy in Colombia ...................................................... 108 end to the moment where someone ‘acts’ and the moment where some5.5 “Colombia nos une”...................................................................... 109 thing is used (this is why, perhaps, he makes a point of invoking the end 5.6explanations Alianza País .................................................................................. 112 of already at the very first aphorism of the Philosophical Investigations). Eventually, we give up this doubling, where intervention, 5.7 Challenges .................................................................................... 114 interpretation, transcription can take; we cross over it, make the quantum Bibliography ....................................................................................... 116 leap, no holds barred, no questions asked. But explanations needn’t come to an end right now. This dis-joint,ofthe potential to go on explaining Working Together for the Well-being Migrants ........................... 119 furBarry Halliday ther some other time, somewhere else, allows us to cut-and-paste, re-edit the film, re-fold the hymen, interpret further, and end up elsewhere, where we do other things with our words. There is never a moment of final articulation, even where, just like here, explanations come to an end.

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3.7

Third final´ e: Revolution in mathematical language?

Bibliography ......................................................................................... 60 4. The Ethics of Migration. In her Engendrement la Formule, the closing paper of Semeiotike (which Reflections on Recentde Migration Policies and “Non-policies” in Italy and Europe appeared in the same year as Deleuze’s ........................................... Logic of Sense), Kristeva61lays out Laura Zanfrini some elements, which appear to correspond to Deleuze’s surface of sense. 4.1 Restrictive Policies Demand for Immigrant 65 The infinitive form of and the Structural verb receives special attention,Labour and is.. identified

as scene of for signification whereand that which is accomplished is not 4.2a Initiatives Governing Family Humanitarian but not Migration ............. 73 facing yet,Migration: because Labour it is inMigration the process ofWorkers’ being. We are therefore a4.3 modality of Workers signification that designates a generation escaping From Guest to Unwelcome Guests .................................. 82 time, escaping “situation” and “narration”, having no beginning 4.4 Selective Policies and the Brain Drain............................................ 87 nor end, neither subject nor recipient, but forming itself in a 4.5 Equal Opportunity and Denied Opportunities ................................ 90 growth which, in order to underpin achievement and beginning, Bibliography 97 subobtains the ......................................................................................... value of a rule, of an order, of a law, for which the ject and his temporal and personal modalities are suspended ... 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Oriented toward signification as a process of generation, it desigUrs Watter nates that that which “expresses” itself is a constant becoming, a 5.1 State Interest and Responsibility growth never limited in the time and in instances of speech, but towards their Citizens Living Abroad ........................................... 102 always there, obstinately present, a present being become law, 5.2 Applied Ethics .............................................................................. 104 which, at once, is absent both from being and from the present 5.3 Migration Policy and Ethics ......................................................... 106 (Kristeva 1969, 326–327). Kristeva Policy also brings up a notion of number (the paper we quote is 5.4 Migration in Colombia ...................................................... 108 instigated by anos reading of Sollers’ Nombres), which brings to mind odel’s 5.5 “Colombia une”...................................................................... 109G¨ operation of formula enumeration. This number is the first movement of 5.6 Alianza País .................................................................................. 112 organisation, that is of demarcation and ordination. A movement 5.7 Challenges .................................................................................... 114covers that differs from the simple “to signify” and, we would say, ....................................................................................... 116placed. aBibliography vaster space where “to signify” can be understood and Kristeva posits an infinite enumerator that disposes of an enumerWorking Together for the Well-being of Migrants ........................... 119 ated (graphic or phonic ensembles) before finding it a referent Barry Halliday or a signified and turning it into a sign. Mark, knot, ranking, pointing-towards/anaphore/: such are the functions of the enumerator. Sticks, scratches, knots, shells, nuts: such are the first numbers (in the 4th millennium before Christ the Maya already counted by knots and by bundles of ropes). Ranking sticks ... is already an arrangement of the infinite and the basis of the system Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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of enumeration (Kristeva 1969, 294–295). Bibliography ......................................................................................... But Kristeva is not interested in the project of capturing 60 the conductive lining between the body and words. The infinitive form and the 4. The Ethics of Migration. infinite enumerator serve as expressive Reflections on Recent Migration Policies indicators of the semiotic generative process, the genotext, which precedes the phenotext, namely61written and “Non-policies” in Italy and Europe ........................................... Laura Zanfrini and spoken words. her interest is not in the mediation of so-called sense between genotextPolicies and phenotext, but in the genotextual process, and the ways 4.1 Restrictive and Structural Demand for Immigrant Labour .. 65 by which it secretes the phenotext. The genotext, according to Kristeva, is 4.2 Initiatives for Governing Family and Humanitarian the Migration: unstructured process, akin but to that which weMigration formerly............. discussed Labour Migration not Workers’ 73 under the term ‘chora’, the nonexpressive totality formed by the drives 4.3 From Guest Workers to Unwelcome Guests .................................. 82 and their stases in a motility that is as full of movement as it is 4.4 Selective(Kristeva Policies and the26). Brain Drain............................................ 87 regulated 1984, 4.5 Equal Opportunity andgenotext Denied Opportunities ................................ Designating the in a text requires pointing90 out the transfers of ......................................................................................... drive energy that can be detected in phonematic Bibliography 97 devices (such as the accumulation or repetition of phonemes or 5.rhyme) Colombia: Including Emigrants Theiras Societies of Origin 101 and melodic devices in (such intonation and....... rhythm), in Urs Watter the way semantic and categorial fields are set out in syntacti5.1 State Responsibility cal and Interest logicaland features, or in the economy of mimesis (fantasy, towards their Citizens Living Abroad ........................................... 102 the deferment of denotation, narrative, etc.). The genotext is thus 5.2 Applied Ethics .............................................................................. the only transfer of drive energies that organises a space104 in which the subject is not and yetEthics a split unity that will become blurred, 5.3 Migration Policy ......................................................... 106 giving rise to the symbolic. Instead, the space it organises is one in 5.4 Migration Policy in Colombia ...................................................... 108 which the subject will be generated as such by a process of fa5.5 “Colombia nos une”...................................................................... 109 cilitations and marks within the constraints of the biological and 5.6 Alianza País .................................................................................. 112 social structures. 5.7 Challenges 114 the In other .................................................................................... words, even though it can be seen in language, genotext is ....................................................................................... not linguistic (in the sense understood by structural Bibliography 116 or generative linguistics). It is, rather, a process, which tends to Working Together for the that Well-being of Migrants(unstable, ........................... 119 articulate structures are ephemeral threatened by Barry Halliday drive charges, “quanta” rather than “marks”) and nonsignifying (devices that do not have a double articulation) (Kristeva 1984, 86). In G¨ odel’s text, therefore, in order to summon the genotext we need to discuss the way semantics is set out in syntactical and logical features, and the complex economy of mimesis. We have already accomplished the bulk of these tasks in the two preceding chapters. But in order to look Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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into the genotext we should read the verisimulating syntax, the reduction of Bibliography ......................................................................................... 60system semantic determination to syntactical verification, and the elaborate of denoting, saying, meaning, expressing, etc. as motions of discrete 4. The Ethics of Migration. quanta, which are not yet doubly articulated into signifier-signified, subjectReflections on Recent Migration Policies object positions. To in reach we must obey G¨ odel’s desire and “Non-policies” Italythe andgenotext Europe ........................................... 61 that meaning be forgotten. Laura Zanfrini In a way,Policies the finitist-formalist reduced the meaningless 4.1 Restrictive and Structural Demand forlanguage ImmigrantisLabour .. 65 linguistic surface, which undoes double articulation, and which arises if we 4.2 Initiatives for Governing Family and Humanitarian attempt to reverse theMigration effects ofbut what genotext has produced. As such, Migration: Labour not the Workers’ Migration ............. 73 this language can only enumerate and count, like rhythmical knots and 4.3 From Guest Workers to Unwelcome Guests .................................. 82 sticks. Such marks do indeed mark, but they fail to function as signs. The 4.4 Selective Policies and theinsists Brain on Drain............................................ 87 as an formalist-finitist approach freezing these marks on paper, 4.5 Equal Opportunity and Denied ................................ 90 labour end-product set and done, rather Opportunities than let it pulsate and conduct the 16 of genotext. What separates the dead language of formal logic from Bibliography ......................................................................................... 97 living mathematical languages is indicated by G¨ odel’s insistence on building a full, 5.meaningful Colombia: Including Emigrants Their Societies Origin ....... 101 language on top of theinmarks, which theofsemiotic combinatorial Urs Watter

process discharges onto the surface of the page. What keeps the formal 5.1 State Interest Responsibility language dead is and an attempt to undo the double symbolic articulation and towards their Citizens Living(after Abroad ........................................... 102 withdraw from what Kristeva Husserl) calls a thetic phase. 5.2 Applied Ethics .............................................................................. We shall distinguish the semiotic (drives and their 104 articulations) from Policy the realm of signification, which is always 106 that of a 5.3 Migration and Ethics ......................................................... proposition or a judgement, in other words, a realm of positions. 5.4 Migration Policy in Colombia ...................................................... 108 This positionality, which Husserlian phenomenology orchestrates 5.5 “Colombia nos une”...................................................................... 109 through the concepts of doxa, position, and thesis, is structured 5.6aAlianza .................................................................................. 112 as break País in the signifying process, establishing the identification 5.7the Challenges 114 of subject.................................................................................... and its object as preconditions of propositionality. We shall call this break, which produces the positing of 116 significaBibliography ....................................................................................... tion, a thetic phase. All enunciation, whether of a word or of a Working Together for the ........................... 119words, sentence, is thetic. ItWell-being requires of anMigrants identification; in other Barry Halliday the subject must separate from and through his image, from and through his objects. This image and objects must first be posited in a space that becomes symbolic because it connects the two 16 This

language merits the adjective ‘dead’, among other reasons, because, while many people are proficient in it, it is never a first language, not even a first mathematical language, for anyone. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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separated positions, recording them or redistributing them in an Bibliography ......................................................................................... 60 open combinatorial system (Kristeva 1984, 43). We have already recounted the narrative that extracts from the semi4. The Ethics of Migration. otic chora realm of signification, going through the mirror (or Voice) and Reflectionsa on Recent Migration Policies castration. But onceinestablished, the thetic position is never completely and “Non-policies” Italy and Europe ........................................... 61 Laura Zanfrini safe. The unstable motility of the semiotic chora can always transgress the thetic position.Policies This transgression appears as a breach [effraction] 4.1 Restrictive and Structural Demand for Immigrant Labour .. 65 subsequent to the thetic phase, which makes that phase negative 4.2 Initiatives for Governing Family and Humanitarian andMigration: tends toLabour fuse the layers of signifier/signified/referent Migration but not Workers’ Migration ............. 73 into a network of traces, following the facilitation of the drives. Such 4.3 From Guest Workers to Unwelcome Guests .................................. 82 a breach does not constitute a positing. It is not at all thetic ... 4.4 Selective Policies and the Brain Drain............................................ 87 On the contrary, the transgression breaks up the thetic, splits 4.5fills Equal andspaces, Denied Opportunities ................................ it, itOpportunity with empty and uses its device only to90 remove the “residues of first symbolisations” and make them “reason” Bibliography ......................................................................................... 97 [“raisonner ”] within the symbolic chain. This explosion of the 5.semiotic Colombia:inIncluding Emigrants in Their Societies of Origin ....... 101 a rethe symbolic is ... a transgression of position, Urs Watter versed reactivation of the contradiction that instituted this very 5.1 State Interest and Responsibility position. towards their Citizens Living Abroad ........................................... 102 The proof is that this negativity has a tendency to suppress 5.2 Applied 104 the thetic Ethics phase,.............................................................................. to de-syn-thesise it. In the extreme, negativity 5.3 Migration Policythe and Ethics aims to foreclose thetic......................................................... phase, which, after a period 106 of explosive semioticPolicy motility, may result in the loss of the symbolic 5.4 Migration in Colombia ...................................................... 108 function, as seen in schizophrenia (Kristeva 1984, 69). This is precisely the 5.5 “Colombia nos une”...................................................................... 109 pathology of the formal language. An explosion of combinatorial-semiotic 5.6 Alianza País .................................................................................. 112 motility, which threatened to destroy the symbolic function, together with 5.7 Challenges .................................................................................... 114 lanthe volume and inter-surface resonances of pre-crisis mathematical guage. Bibliography ....................................................................................... 116 But the alternatives are not clearly-cut along the axis of maintainWorking Together for the Well-being of Migrants ........................... 119 ing or destroying the thetic position. The very motion of transgression, the Barry Halliday very motion of rejection, may have productive and healthy consequences. In G¨ odel’s text, something happens with the combinatorial structure, which may be the written correlate of the fact that rejection, which is an energetic process at the level of drives, may pass through the vocal apparatus. The oral cavity and the glottis free discharges through a finite system of phonemes specific to each language, by increasing Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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their frequency, by accumulating or repeating them, and thus deBibliographythe ......................................................................................... 60 termining choice of morphemes ... In so doing, the rejection that invests the oral cavity awakens in and through it the “li4. The Ethics of Migration. bidinal”, “unifying”, “positive” drive which characterises, at the Reflections on Recent Migration Policies earliest stages, this sameand cavity ... ........................................... Through the new phonematic and “Non-policies” in Italy Europe 61 and rhythmic Laura Zanfrini network it produces, rejection becomes a source of “aesthetic” without the line of ..meaning, 4.1 Restrictivepleasure. Policies andThus, Structural Demandleaving for Immigrant Labour 65 it cuts up and reorganises that line by imprinting on it the path 4.2 Initiatives for Governing Family and Humanitarian of drives through body.but not Workers’ Migration ............. 73 Migration: Labourthe Migration Rejection therefore ... reconstitutes real objects, “creates” 4.3 From Guest Workers to Unwelcome Guests .................................. 82 new ones, reinvents the real, and re-symbolises it. Although in so 4.4 Selective Policies and the Brain Drain............................................ 87 doing rejection recalls the schizoid regressive process, it is more 4.5 Equal Opportunity and Denied Opportunities ................................ important to note that rejection positivises that process,90affirming it by introducing the process into the signifying sphere: Bibliography ......................................................................................... 97 the latter thus finds itself separate, divided, put in process ... This 5.symbolisation Colombia: Including Emigrants Their Societies Origin .......contradic101 of rejection is in the place of an of untenable Urs Watter tion which only a limited number of subjects can reach ... this 5.1 State Interest and Responsibility motorial discharge and corporeal spasm are invested in the sign towards their Citizens Living Abroad ........................................... 102 — in language — which is itself already divided, reintroducing 5.2 Applied Ethicswithin .............................................................................. 104 sepaand unfolding it the very mechanics by which the ration between words and ......................................................... things is produced. rejection 106 thus un5.3 Migration Policy and Ethics folds, dismantles, and readjusts both the vocal register ... and the 5.4 Migration Policy in Colombia ...................................................... 108 logical register (Kristeva 1984, 154–155). 5.5 “Colombia nos une”...................................................................... 109 Whether the manual or cerebral spasms of writing can indeed repro5.6 Alianza País .................................................................................. 112 duce this process of the vocal system, whereby a semiotic eruption does not 5.7 Challenges .................................................................................... 114 destroy, but rather readjusts the thetic position; whether such spasms can Bibliography ....................................................................................... produce a logical structure and not just “aesthetic” pleasure116 — these are questions ranging far beyond the reach of this essay. But if we follow Working Together for the Well-being of Migrants ........................... 119 this line of thought, and neglect its grip on reality, then the mimetic tranBarry Halliday scription of metamathematical concepts into arithmetic and formal ones, the persevering enumeration of formulas, and the spastic repetition inside S(zp , zp ) would be articulated as energetic eruptions of rejection that mobilise G¨ odel’s reformulation of the mathematico-logical field without at all destroying it. We may then view formalists as those who were lost in the rumbling of semiotic motility and succumbed to schizophrenia, whereas Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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G¨ odel would become the person who entered the semiotic Pardes and Bibliography emerged with......................................................................................... a brand new thetic articulation of self-reference and60truth.17 Kristeva’s thesis is entangled with a Marxist agenda, and her main 4. The Ethics of Migration. concern is the of the constructive Reflections onrelevance Recent Migration Policies rejection that she articulates to revolutionary practice. She marks several........................................... alternatives. The first is to and “Non-policies” in Italy and Europe 61shatter Laura Zanfrini conceptual unity into rhythms, logical distortions (Lautr´ eamont), paragrams, syntactic inventions (Mallarm´ e), all of which 4.1 Restrictiveand Policies and Structural Demand for Immigrant Labour .. 65 register, within the signifier, the passage beyond its boundary. In 4.2 Initiatives for Governing Family and Humanitarian these texts itLabour is no Migration longer abut question of mere anxiety, but73of sepMigration: not Workers’ Migration ............. aration, which is so dangerous for the subject’s unity that, as 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Artaud’s text testifies, signifying unity itself vanishes into glos4.4 Selective Policies and186). the Brain Drain............................................ 87 solalia (Kristeva 1984, 4.5 Equal Opportunity and Denied ................................ 90 text, The second alternative, thatOpportunities which is most applicable to G¨odel’s isBibliography the subjection of rejection to the narcissistic subject and to the subject of ......................................................................................... 97 knowledge. The narcissistic moment tends to attach the process of 5.rejection Colombia:to Including Emigrants Their Societies of Origin ....... 101 dethe unity of theinego, thus preventing rejection’s Urs Watter structive and innovative vigour from going beyond the enclosure 5.1subjectivity State Interest and of andResponsibility opening up towards a revolutionary ideology towards their Citizens Living Abroad ........................................... 102 capable of transforming the social machine ... knowledge, to es5.2 Applied Ethics .............................................................................. 104 tablish itself, will proceed through a supplementary reversal of meaning, by repressing meaning’s heterogeneity and by ordering 5.3 Migration Policy and Ethics ......................................................... 106 it5.4into concepts structures based on the divided unity Migration Policyor in Colombia ...................................................... 108 of its subject: the subject of science or theory (Kristeva 1984, 186–188). 5.5 “Colombia nos une”...................................................................... 109 After all, G¨ odel, while affecting some changes in the rules of the game, 5.6 Alianza País .................................................................................. 112society. never hoped to (and never did) revolutionise logic, not to mention 5.7 Challenges .................................................................................... 114

17 The fact that the relevant psychological biographies indicate the exact opposite is Bibliography ....................................................................................... 116 died of rather ironic. G¨ odel suffered mental problems, was hospitalised, and eventually paranoia (he refused to eat for fear of being poisoned). Georg Cantor is another person Working Together for theand Well-being of reflect Migrants 119 whose mathematical views mental state those........................... of G¨ odel. The most prominent Barry Halliday however, Hilbert and von Neumann, seem to have conducted healthy, finitist-formalists, or at least normal, mental lives. Of course, Hilbert and von Neumann were much more pragmatic with respect to mathematics than the astute position of formalism would suggest, and both G¨ odel and Cantor were obsessed with a sort of realism that would make it difficult to accept the unstable split of double articulation that, according to psychoanalytic theory, is important for a healthy existence. But since we are discussing the mythical language of pre-crisis mathematics, I impose mythical versions of the relevant characters as well.

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If anything, he aimed to strengthen the hold over mathematics of unifying Bibliography views (realism......................................................................................... and present intuition as sources of knowledge). 60 But Kristeva also believes in a third alternative. An alternative whereby 4. The Ethics of Migration. working with language could provide rejection with a free reign to Reflections on Recent Migration Policies the of itsinstruggles — not ........................................... to founder under those and violence “Non-policies” Italy and Europe 61blows, but instead Laura Zanfrini to carry them into the clash of socio-historical contradictions Constantly keeping thefor signifying course.. 65 open to 4.1 Restrictive...Policies and Structural Demand Immigrant Labour material rejection; preventing the total sublimation of rejection 4.2 Initiatives for Governing Family and Humanitarian andMigration: its repression by introducing it evenMigration in the ............. signifying Labour Migration but not Workers’ 73 texture [tissu] and its chromatic, musical, and paragrammatic dif4.3 From Guest Workers to Unwelcome Guests .................................. 82 ferences; and thus unfolding the gamut of pleasure in order to 4.4 Selective Policies andspeak: the Brain Drain............................................ make heterogeneity this constitutes a productive87 contradiction. long as this is kept................................ within the confines 4.5 EqualAs Opportunity and entire Deniedprocess Opportunities 90 of the subject, the capitalist machine can tolerate it. But combining heterogeBibliography ......................................................................................... 97 neous contradiction, whose mechanism the text possesses, with 5.revolutionary Colombia: Including Emigrants Their Societiessocial of Origin .......(relations 101 critique of thein established order Watter ofUrs production – relations of reproduction): this is precisely what 5.1 State Interest ideology and Responsibility the dominant and its various mechanisms of liberalism, towards their Citizens Living Abroad ........................................... oppression, and defence find intolerable. It is also what102 is most

difficult. InEthics other.............................................................................. words, the moment of the semantic and104 ideolog5.2 Applied ical binding Policy of drive should be a binding in and106 through 5.3 Migration andrejection Ethics ......................................................... an analytical-and-revolutionary discourse, removing the subject 5.4 Migration Policy in Colombia ...................................................... 108 from signifying experience in order to situate him within the rev5.5 “Colombia nos une”...................................................................... olutionary changes in social relations and close to their109 various 5.6 Alianza País(Kristeva .................................................................................. 112 protagonists 1984, 189–191). It seems, .................................................................................... today, incredibly na¨ıve to believe that linguistic114 bursts of 5.7 Challenges drives are the fragile element that is missing from revolutionary pracBibliography ....................................................................................... 116 tice. But actually, today, any discourse that includes the term revolution seems incredibly dim and questionable hope however still Working Together na¨ forıve. theA Well-being of Migrants ........................... 119 can be Barry Halliday traced: considering the privileged position of mathematics in contemporary intellectual order, could the resurfacing of paradoxical, (non)sensical and genotextual processes, which facilitate semiosis in mathematical texts, contribute towards loosening the grasp of logocentrism, along with its entire political agenda, on contemporary thought?

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

Conclusion

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73

4.3 From Guest Workers to Unwelcome Guests .................................. 82 Everything I’ve written so far is related to what may be viewed as a univer4.4 Selective Policies and the Brain Drain............................................ 87 salisable dogma: the sign is materially constituted by bodies, but iterable 4.5 Equal Opportunity and Denied Opportunities ................................ outside any given context. This universalisability of the dogma, 90 however, isBibliography never to be......................................................................................... taken for granted. What’s interesting about this 97 dogma is not the supposed fact that it is universally true. What might be interesting 5.about Colombia: Including Emigrantsininwhat Theirway Societies of Origin ....... 101 it is to show specifically it is true for various different Urs Watter texts. It is the singular and contingent manners of forcing different texts 5.1interact State Interest and this Responsibility to through dogma that might be interesting to explore. Netowards their Citizens Living Abroad ........................................... 102 glecting such particular research is neglecting the specific relations between 5.2 Applied Ethics .............................................................................. 104 signs and authorities as they are deployed in the various circumstances of our 5.3 lives. Migration Policy and Ethics ......................................................... 106

I could, of course, give up ...................................................... particular analyses, and try to 108 assess the 5.4 Migration Policy in Colombia generalisability of my claims from G¨odel’s text to other mathematical 5.5 “Colombia nos une”...................................................................... 109 texts. Doing that would go along the following lines. First, I would show how 5.6 Alianza País .................................................................................. 112 semantic verisimulation works across a myriad of mathematical texts. Ev5.7 Challenges .................................................................................... ery mathematical concept that is at least doubly determined 114 (and that Bibliography ....................................................................................... 116 might cover practically all mathematical objects) would do: geometric objects, which are determined both through geometric axiomatisations and Working Together for the Well-being of Migrants ........................... 119 analytic models; numbers, which can be represented geometrically, modelBarry Halliday theoretically, or algebraically; predicates, which may be viewed intentionally or extensionally; random variables, which are conceived as throws of dice and at the same time as plain old deterministic distribution functions. In Each of these cases two (or more) things are subsumed under a single sign — all that even before we bring up the relation between mathematical formalisms and whatever they are supposed to model. 195

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Then I would go on to syntactic verisimulation. The authority of logBibliography ical syntax is......................................................................................... felt everywhere in modern mathematics (without 60 necessarily dominating the mathematician’s ‘everyday’ practice). The emphasis on 4. The Ethics of Migration. rigid and rigorous rules is no doubt a characteristic of a vast plethora of Reflections on Recent Migration Policies mathematical languages. And shouldn’t be hard to show how,61when a and “Non-policies” in Italy anditEurope ........................................... sign is Zanfrini governed by the authority of a repetitive syntax rather than by Laura some attempt Policies to hold and on to an essential meaning, this sign is also 4.1 Restrictive Structural Demand for Immigrant Labour .. 65subject to dangerous shifts of meaning.1 4.2 Initiatives for Governing Family and Humanitarian Next, I could claim that the above dangerous shifts of meaning Migration: Labour Migration but not Workers’ Migration ............. 73 open the way to dissemination and diff´erance. This would require showing 4.3 From Guest Workers to Unwelcome Guests .................................. 82 how there is always a potential for reiterating syntactic rules in a way that 4.4 Selective the Brain semiotic Drain............................................ will carry thePolicies sign toand unexpected positions, and that will87drive it 4.5 Equal anditDenied ................................ 90 away fromOpportunity any reference might Opportunities be supposed to hold on to. The genealogy of a basic geometric notion such as ‘line’ or a basic algebraic notion Bibliography ......................................................................................... 97 such as ‘number’ would surely reveal a garden of forking paths, which could not 5.be Colombia: Including Emigrants in Their of Origin .......historically, 101 anticipated from the onset, and whichSocieties is reflected not only Urs Watter

but even in the confines of clearly demarcated ‘single’ texts. 5.1 State Interest and Responsibility At that point, my analysis of variables, constants and substitution, towards their Citizens Living Abroad ........................................... 102 and the corresponding analysis of equality from chapter 2, are already gen5.2 Applied .............................................................................. 104 exceed eral enough Ethics to cover large tracts of mathematical reasoning that G¨ odel’s text or formal will then be practically an exercise 5.3 Migration Policy andlogic. EthicsIt......................................................... 106 to extract from all of the above some operative paradoxical elements reflecting 5.4 Migration Policy in Colombia ...................................................... 108 the position of infinity, truth and self reference in chapter 3. 5.5 “Colombia nos une”...................................................................... 109 In graph theory such paradoxical element would be the node, which Alianza País .................................................................................. 112 combiis5.6 a not yet distributed singular point, at the same time an abstract 5.7 Challenges .................................................................................... 114 in a natorial placeless mark and the element determining relative position configuration. In probability we have the uniformly distributed point Bibliography ....................................................................................... 116 on a segment, which, formally speaking, is not quite a point, but is already rich Working for the Well-being theories. of Migrants ........................... 119the well enough Together to span entire probabilistic In geometry we have Barry Halliday known tensions between points as constituting lines and points as object on lines. In set theory we have the empty set, which can constitute the entire universe of sets by embedding itself in ever proliferating arrays of 1A

complementary tradition of deconstructive research has been dealing with dangerous shifts of meaning arising from attempts to hold on to essential meanings, and might be relevant for some less syntactically grounded mathematical discourses. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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curly brackets. And in arithmetic we have the constitutive iterand, which Bibliography ......................................................................................... must be left undefined, but is already nonsensical enough to yield60the non a-priori part of mathematics (according to Poincar´e), as well as Zeno’s and 4. The Ethics of Migration. the Skolem-L¨ owenheim paradoxes. Constituted around such points of referReflections on Recent Migration Policies ence, the emerging languages would easily be coaxed61to yield and “Non-policies”mathematical in Italy and Europe ........................................... concrete expressions of Deleuze’s four paradoxes of sense. Laura Zanfrini All I wrote above an outline of a programme. outline 4.1 Restrictive Policies andis Structural Demand for ImmigrantThis Labour .. 65 alone is obviously nothing but unsubstantiated speculation. But I don’t think 4.2 Initiatives for Governing Family and Humanitarian it would be too hardMigration to followbut such project Migration through. ............. Nevertheless, all Migration: Labour not aWorkers’ 73 this is precisely what I do not want to do. Imposing what I’ve extracted 4.3 From Guest Workers to Unwelcome Guests .................................. 82 from G¨ odel via French post-structuralists on the entire field of mathematics 4.4 Selective Policies and the BraintoDrain............................................ 87 worse; would precisely be succumbing the structuralist fallacy. Even doing thatOpportunity would riskand arresting And................................ what I would like90to do is 4.5 Equal Denied thought. Opportunities keep thought......................................................................................... moving. Therefore I will not try to generalise the structures Bibliography 97 and motions I’ve explicated in this essay. I will try, instead, to explore 5.further Colombia: Includingbetween Emigrants in Their Societies of Origin ....... 101Wagner interactions philosophies and mathematics (e.g. Urs Watter 2009a,b, forthcoming). 5.1 State Interest and Responsibility These explorations and those to follow are not about generalising my towards their Citizens Living 102 That observations concerning G¨ odel’sAbroad text to........................................... other mathematical corpuses. would be toEthics slow .............................................................................. thinking down. These explorations generalise104 a way of 5.2 Applied thinking that Policy insists and on finding in mathematical texts irreducibly unstable 5.3 Migration Ethics ......................................................... 106 cores. These experiments try to respect the peculiarities and contingencies 5.4 Migration Policy in Colombia ...................................................... 108 of the analysed texts by confronting them with analyses that turn out 5.5 “Colombia une”...................................................................... 109 of my productive andnos challenging on these texts’ terms, not on the terms 5.6 Alianza País .................................................................................. 112 former negotiations with G¨ odel’s proof. As long as.................................................................................... my experiments serve the purpose of attracting114 attention 5.7 Challenges to the problems of authority over meaning and of responsibility for its Bibliography ....................................................................................... 116 production in mathematical (and other) texts, I believe there’s a point to pursuing them.for When the horizons of critical........................... judgement are119 no longer Working Together the Well-being of Migrants Barry Halliday challenged by these experiments, then, perhaps, the time would come to summarise, universalise, and move on.

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

Appendix/Overture: G¨ odel’s Myth, Reverse Bricolage

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97

Here we shall pretend to reconstruct a myth, the structural 5. Colombia: Including Emigrants in Their Societies of Origin .......anal101 Urs Watter ysis of which is G¨ odel’s proof. The imminent failure is telling of some disparities relating narrative and mathematical texts. 5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104

1. Mathematics as the structure of myth

5.3 Migration Policy and Ethics ......................................................... 106

It5.4is Migration commonplace that mathematics is a language, and my Policytoinsay Colombia ...................................................... 108analysis in essay will assume as much. But some care is required 5.5this “Colombia nosindeed une”...................................................................... 109 when taking seriously the statement that mathematics is a language. That math5.6 Alianza País .................................................................................. 112 ematics is a language entails a question, which is unique and awkward, in 5.7 Challenges .................................................................................... 114 that it rarely requires being asked of other languages: whose language is mathematics? Thus wrote Galileo: Philosophy is written in this Bibliography ....................................................................................... 116 grand book — the universe — which stands continuously open to our Working Together for the Well-being of Migrants ........................... 119 gaze. But the book cannot be understood unless one first learns to Barry Halliday comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these one is wandering about in a dark labyrinth (Galileo 1960, 183–184). In this statement mathematics is not a 199

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language that represents the universe, but a language in which the universe 60 and isBibliography written. It ......................................................................................... has to be discerned from within the universe. It underlies structures the universe. It is the language of the universe. 4. The Ethics of Migration. This point of view, which will not be the point of view of the next Reflections on Recent Migration Policies chapters, is far from today. I thought it necessary, therefore, to and “Non-policies” in extinct Italy and Europe ........................................... 61 Lauraby Zanfrini begin reflecting on mathematics as an underlying structure, or as coding something else.Policies Mathematics mightDemand very well underlie and structure the 4.1 Restrictive and Structural for Immigrant Labour .. 65 universe, or, more modestly articulated, if not the actual universe, at least 4.2 Initiatives for Governing Family and Humanitarian its reflection philosophy andbut rational thought; but acknowledging, on Migration:in Labour Migration not Workers’ Migration ............. 73 this side of the linguistic turn, that our access to philosophy, thought or 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the universe depends on language, we are left with the hypothesis that 4.4 Selective Policies the Brain 87 and mathematics should and underlie the Drain............................................ expressions of philosophy, thought 4.5 universe: Equal Opportunity Denied Opportunities ................................ 90 the texts andand practices. To seriously validate or refute the hypothesis that mathematics Bibliography ......................................................................................... 97 is an underlying structure would require the confrontation of mathematics with 5.an Colombia: Including Emigrants in Theirwhich Societies of Origin ....... 101by it. I endless body of texts and practices, might be structured Urs Watter do not venture to even embark on such a project. In this chapter I will make 5.1 State Interest and Responsibility only a single modest experiment. I will take one piece of mathematics, and towards their Citizens Living Abroad ........................................... 102 inquire whether it can be regarded as the underlying structure of a very 5.2 Applied .............................................................................. 104 proof specific kindEthics of textualised thought: mythical narrative. Can G¨odel’s be the structure a mythical text? 5.3regarded MigrationasPolicy and Ethicsunderlying ......................................................... 106 This experiment cannot prove or disprove the viability of 5.4 Migration Policy in Colombia ...................................................... 108viewing mathematics as an underlying structure of anything in general. It will, 5.5 “Colombia nos une”...................................................................... 109 however, be rather telling in the context of the mathematics/language re5.6 Alianza País .................................................................................. 112 lation. It will begin to suggest how much we must distort our practices in 5.7 Challenges order to place .................................................................................... mathematics behind a non-mathematical text. It114 will also point out how specific mathematics is, viewed as it will be in the next Bibliography ....................................................................................... 116 chapters: not as a background language in the sense posed by Galileo, but as Working Together for theby Well-being of Migrants ........................... 119 that which is conveyed a language, laid out in a text, and operated by Barry Halliday readers. My choice to confront mathematics with myth, rather than with any other kind of text, is a contingent choice, which is justified by various pragmatic arguments. First, if mathematics is the language of as exhaustive a book as Galileo’s universe, then myth, with its overarching unity spread across distributed authors and story-tellers, is the best literary genre to take Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the place of this universal book. Second, this essay offers a post-structural Bibliography 60 reading of G¨ o......................................................................................... del’s proof, and the intricate relations between structuralism and post-structuralism justify starting with a structural analysis as pre4. The Ethics of Migration. liminary. As the most highly evolved mechanism for structurally analysing Reflections on Recent Migration Policies texts is elaborated in L´evi-Strauss’ four........................................... volumes of his Introduction and “Non-policies” in Italy and Europe 61 to a Science of Mythology, myth seems to be a good place to start. Laura Zanfrini We note Policies that there are at least twoforways in which L´e..vi-Strauss’ 4.1 Restrictive and Structural Demand Immigrant Labour 65 method is supportive of our experiment. First, L´evi-Strauss can be read as 4.2 Initiatives for Governing Family and Humanitarian allowing for treating meaning rather pragmatically, as interMigration: Labourstructure Migrationand but not Workers’ Migration ............. 73 pretive interventions rather than as facts to be simply extracted from data. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 For L´evi-Strauss The real question is not whether our endeavour 4.4understand Selective Policies and theaBrain 87 to involves gainDrain............................................ or a loss of meaning, but whether 4.5 Equal Opportunity and Denied 90 been the meaning we preserve is ofOpportunities more value................................ than that we have judicious enough to relinquish (L´evi-Strauss 1966, 253). He97also exBibliography ......................................................................................... plains that the unity of the myth is never more than tendential 5.and Colombia: Including in Their Societies ....... 101 projective and Emigrants cannot reflect a state or of a Origin particular moment Urs Watter of the myth. It is a phenomenon of the imagination resulting from 5.1 State Interestatand Responsibility and its function is to endow the the attempt interpretation; towards their Citizens Living and Abroad 102 into myth with synthetic form to ........................................... prevent its disintegration 1 Applied Ethics .............................................................................. 104 a5.2 confusion of opposites (L´evi-Strauss 1969, 5). The textual experiment are about to undertake relies upon 5.3 Migration Policy and Ethicswe ......................................................... 106 these positions. Meaning, it says, is an object of value, entangled in an economy 5.4 Migration Policy in Colombia ...................................................... 108 of preservation and relinquishment. Unity is imagined for the purpose 5.5 “Colombia nos une”...................................................................... 109 1 It

would be misleading not to counterbalance these two quotations by two other,

5.6 Alianza .................................................................................. which reflect País the stance of structuralism seeking to uncover structure as112 underlying the interface that must already be there, in disregard to its value, 5.7empirico-intelligible Challenges .................................................................................... 114 simply because it is there: since, my ambition being to discover the conditions Bibliography ....................................................................................... 116 in which systems of truths become mutually convertible and therefore simultaneously acceptable to several different subjects, the pattern of those Working Together forthe thecharacter Well-being ........................... 119 conditions takes on of of anMigrants autonomous object, independent of Barry Halliday any subject (L´ evi-Strauss 1969, 11). Paul Ricoeur called this aspect of L´ evi-Strauss’ work Kantism without a transcendental subject. To see how it integrates with the quotations above, consider that the methodological rules that the researcher will have to evolve in order to translate these foreign mythical systems in terms of his own system and vice versa, will reveal a pattern of basic and universal laws... The mythological code has neither been invented nor brought in from without. It is inherent in mythology itself, where we simply discover its presence (L´ evi-Strauss 1969, 11–12). Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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of synthesis. And as such, we choose to bracket the supposed discovery Bibliography and revealed......................................................................................... presence of basic and universal laws. From this60point of view the extraction of meaning and unity from myth is a rather open-ended 4. The Ethics of Migration. practice, which is to be judged instrumentally. Reflections on Recent Migration Policies Second, L´evi-Strauss’ are as close as one and “Non-policies” in Italy structuring and Europepractices ........................................... 61 gets to Laura Zanfriniin the structural realm. Indeed, L´ mathematics evi-Strauss warns us that the occasional use of logico-mathematical in 4.1 Restrictive Policies andapparently Structural Demand for Immigrant Laboursymbols .. 65 his book should not be taken too seriously. There is only a super4.2 Initiatives for Governing Family and Humanitarian ficial resemblance formulas the equations Migration: Labourbetween Migration my but not Workers’and Migration ............. 73 of the mathematician (L´evi-Strauss 1969, 30). But in this science-fiction chap4.3 From Guest Workers to Unwelcome Guests .................................. 82 ter we will pretend that the structural analysis of myth has in fact reached 4.4 postulated Selective Policies andwhere the Brain Drain............................................ 87 to a the future, it will be possible to subject myth 4.5 Equal logico-mathematical Opportunity and Denied Opportunities 90 genuine analysis (L´e................................ vi-Strauss 1969, 31). These circumstances give our experiment fair grounds for productivBibliography ......................................................................................... 97 ity. They allow us to ask: what is the value of preserving or relinquishing 5.G¨ Colombia: Including in Their Origin ....... odel’s proof, not as Emigrants a meaningful text, Societies but as theof meaning of 101 something Urs Watter else (a mythical narrative)? More precisely, we ask whether we should as5.1 State and Responsibility sign to G¨ oInterest del’s proof the synthesising function of structural unity inherent towards their Citizens Living Abroad ........................................... 102 in something else (a mythical narrative), or whether it is of more value to 5.2 Applied .............................................................................. 104extent, consider it asEthics meaning and structure laid out in text, as, to a certain we will. and Ethics ......................................................... 106 5.3eventually Migration Policy Our experiment consist...................................................... of pretending that there is a 108 lost myth, 5.4 Migration Policy inwill Colombia or perhaps a collection of lost myths, which G¨odel analysed structurally in 5.5 “Colombia nos une”...................................................................... 109 two similar ways (his 1931 and 1934 texts). We will pretend that all we have 5.6 from Alianza .................................................................................. 112 left thePaís myth is G¨ odel’s analysis. Our aim is to recover the underlying 5.7 Challenges 114 myth. To do so .................................................................................... requires the production of a narrative supposedly structured by the proof, ....................................................................................... which looks like a possible myth. Bibliography 116 The myth I pretend to recover is a creation myth. It recounts how Working Together for thetoWell-being Migrants ........................... certain creatures came be created,ofnamed, and born, and how119 the incesBarry Halliday tuous rules governing their birth ended up undoing the order of the created world. This attempt of excavating a myth from underneath G¨odel’s proof will fail an instructive and glorious (in the Humpty-Dumpty sense) failure. The next section will follow the ingredients and argument of the proof, and in parallel reconstruct the myth, which we pretend that the proof structures. As the proof grows more intricate, so will the myth grow more Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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involved. The third section will analyse the failure of this odd exercise, and Bibliography 60 texts. discuss what ......................................................................................... we can learn from this failure concerning mathematical 4. The Ethics of Migration. Reflections on Recent Migration Policies 2. The myth and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

2.1. The creators

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65

We expect a creation Family myth to articulate a creator position, but sup4.2 might Initiatives for Governing and Humanitarian Labour Migration Workers’ Migration ............. pressMigration: the narrator position. G¨obut del’snottext, however, confounds the73two positions. On the Workers one handtoitUnwelcome makes suchGuests statements as: We now 82 proceed 4.3 From Guest .................................. to carry out with full precision the analysis sketched above (1931, 4.4 Selective Policies and the Brain Drain............................................ 87 151), assuming the narrator position, talking about the myth. On the other 4.5 Equal Opportunity and Denied hand G¨ odel’s text includes such Opportunities comments as:................................ We now assign 90 natural Bibliography 97manipnumbers to ......................................................................................... the primitive signs (1931, 157), performing analytic ulations, which structurally reflect the creative mythical actions of creators 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 in the myth (actions that we shall later retrace to mythical ‘naming’). Urs Watter

In both cases We is at once singular and plural. In the first case, it 5.1 State Interest and Responsibility is the scientific We, which imposes on the reader the actions of the writer towards their Citizens Living Abroad ........................................... 102 by referring them to an abstract communal entity. In the second case it 5.2 Applied Ethics .............................................................................. 104 is a creating power, whose distinguished position is manifested by a plural 5.3 Migration Policy andthe Ethics ......................................................... mark (the royal ‘We’, Hebrew plural divine name ‘Elohim’, 106 as well as the God who is three who are one). 5.4 Christian Migration Policy in Colombia ...................................................... 108 Clearly, this is not accidental. It reflects G¨ odel’s 5.5 “Colombia nos confounding une”...................................................................... 109 articulation of the structural creator position in the myth as homologous to the 5.6 Alianza País .................................................................................. 112 contemporary structural position of the scientific We. The creating power 5.7the Challenges .................................................................................... 114 in myth below, like the scientific We, should therefore be conceived as ....................................................................................... aBibliography pervasive communal spirit, which is not subject to the whims 116 of any individual component, and yet exists only insofar as it succeeds in possessing Working Together for the Well-being of Migrants ........................... 119 many of these individuals. Like the scientific We, this form of possession, Barry Halliday however, is not an arbitrary external compulsion. It has the curious feature of simultaneously imposing an external edict on every individual in the community, and but conditioning the validity of this edict on the individuals’ communal reaffirmation. We conclude that the myth underlying G¨odel’s structural analysis was not recounted from the point of view of subjected creatures (as in the Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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priestly formula of ‘God created light, the earth, and eventually us huBibliography 60view of mans’, where......................................................................................... creation requires no scrutiny), but from the point of the creating powers themselves, who form a critical discursive community, 4. The Ethics of Migration. perhaps somewhat like the Greek Olympus. As we shall see, this structural Reflections on Recent Migration Policies position implies, likein in theand case of the........................................... Olympic gods, that the61 creating and “Non-policies” Italy Europe powers are not an absolute beginning, but rather a link in a complex hiLaura Zanfrini erarchy of creation, subject to an open-ended chain that stretches 4.1 Restrictive Policies and Structural Demand for genetic Immigrant Labour .. 65 beyond any individual creator. 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 2.2. Primary articulation: elements of the world 82 4.4 Selective Policies and the Brain Drain............................................ 87 The creating power (the above We) is to set the elements of which the 4.5 Equal Opportunity and Denied by Opportunities world, structurally transformed G¨ odel into................................ a Formal System,90 consists. These elements are structurally described as Primitive Signs in 97 a logical Bibliography ......................................................................................... formal system: an infinite pool of variables, which are further divided into 5.types, Colombia: Emigrants in Their Societies Origin ....... 101 and aIncluding finite collection of constants — logicalofconnectives, numerals, Urs Watter basic predicates and functions, together with punctuation marks such as 5.1 State Interest and Responsibility parentheses. towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 Figure 1: List of logical constants and variables in the formal system that we will 5.3 Migration Policy andfrom Ethics 106 a little use. I diverge somewhat G¨ o......................................................... del’s notation in order to make things more tractable.Policy in Colombia ...................................................... 108 5.4 Migration

5.5 “Colombia nos une”...................................................................... 109 Logical Constants: 5.6•Alianza País .................................................................................. 112 Connectives: ¬ (not), ∧ (and), ∨ (or), → (implies) 5.7•Challenges .................................................................................... 114 Quantifiers: ∀ (for all), ∃ (there exists) Bibliography ....................................................................................... 116 • Parentheses: (, ) • Numeral: 0

Working Together for the Well-being of Migrants ........................... 119 • Function: Barry Halliday +1 Logical Variables: • Propositional variables: p1 , p2 , p3 · · · (standing for propositions) • Numerical variables: x1 , x2 , x3 · · · (standing for numerals) • Function variables: f1 , f2 , f3 · · · (standing for functions)

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In structural terms, these are the elements of a primary articulation: meanBibliography ......................................................................................... 60 346), ingless components, explicitly referred to as undefined terms (1934, not unlike phonemes. One should refrain from taking this primary articula4. The Ethics of Migration. tion too seriously. As L´evi-Strauss admits, As happens in the case of an Reflections on Recent Migration Policies optical microscope, which incapable of revealing the ultimate and “Non-policies” in Italy andisEurope ........................................... 61 structure of matter to the observer, we can only choose between Laura Zanfrini various degrees of enlargement: each one reveals aLabour level of organi4.1 Restrictive Policies and Structural Demand for Immigrant .. 65 sation which has no more than a relative truth and, while it lasts, 4.2 Initiatives for Governing Family and Humanitarian excludes the Labour perception of other (L´eMigration vi-Strauss 1969, 73 3). Migration: Migration but not levels Workers’ ............. The list of elements, therefore, corresponds not to some absolute ba4.3 From Guest Workers to Unwelcome Guests .................................. 82 sic elements of the underlying myth, but to the structural necessity to 4.4 Selective and the This Brainexplains Drain............................................ 87 mark a pointPolicies of departure. why the two analyses offered by 4.5 Equal and1934 Denied Opportunities 90 G¨ odel (theOpportunity 1931 and the texts) diverge as ................................ to the exact identification of the elements ......................................................................................... of the formal system that structures the underlying 97 mythical Bibliography world.2 5. Colombia: Including in Their Societies Origin ....... Since this level ofEmigrants articulation is at least partlyofarbitrary, it 101 alone does Urs Watter not enable us to retrace the underlying elements of the mythical world. We 5.1 State andfor Responsibility shall haveInterest to settle assuming that the created mythical world could be towards their Citizens Living Abroad broken down, although perhaps not in ........................................... a unique and unequivocal102 way, into Ethics .............................................................................. a5.2 setApplied of distinct elements, which G¨odel managed to retrieve from104 the myth. 5.3 Migration Policy and Ethics ......................................................... 106

2.3. Secondary articulation: creatures and names 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia une”...................................................................... 109 of the The next step nos in G¨ odel’s structural analysis is to define the laws secondary articulation, that which collects elementary signs to form 5.6 Alianza País .................................................................................. 112 meaningful formulas. These are fairly standard, but, since we have two versions 5.7 Challenges .................................................................................... 114 of a primary articulation, we have some divergence concerning the exact Bibliography ....................................................................................... 116 rules of the second articulation as well. Since I could not retrace the exact mythicalTogether details underlying each element in each........................... version, there is no point Working for the Well-being of Migrants 119 inBarry presenting G¨ o del’s elaborate formal system in full. Halliday Mythically, the second articulation is a structural generalisation about the entities that the created world could host. These are not yet necessar2 One analysis allows for infinitely many types of variables, while the other for only three; one allows for 7 constants, while the other names 13; one decomposes the infinite list of variables into finite combinations of finitely many numerals, while the other is content to invoke an infinity of elementary variables.

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ily fully fledged living mythical creatures, and, obviously, not all entities Bibliography ......................................................................................... allowed by the mythical rules of combination (as reconstructed in60G¨ odel’s analysis) will have a role in the myth itself. 4. The Ethics of Migration. It is crucial to note that G¨odel’s structural analysis allows logical Reflections on Recent Migration Policies formulas containinginfree variables that ........................................... can eventually be substituted by and “Non-policies” Italy and Europe 61 non-variable expressions. Some mythical entities, therefore, have the strucLaura Zanfrini tural role of moulds can be substituted It is also important to 4.1 Restrictive Policiesthat and Structural Demand forinto. Immigrant Labour .. 65 note that some formulas can be combined to form larger formulas. Some 4.2 Initiatives for Governing Family and Humanitarian mythical entities, therefore, should beWorkers’ regardedMigration as limbs............. and organs Migration: Labour Migration but not 73 that can be put together. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies andofthe Brain Drain............................................ Figure 2: Combinations signs that follow some carefully specified87 syntactic rules (which we omit) are formulas. 4.5 Equal Opportunity andcalled Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97

The following are examples of formulas.

• (0 + 1)Including + 1 (the number 2) in Their Societies of Origin ....... 101 5. Colombia: Emigrants

Urs Watter • x + 1 (a number form with x as free variable)

5.1•State and Responsibility x = Interest 0 (a proposition containing x as free variable) towards their Citizens Living Abroad ........................................... 102 • ∀x(x = 0) (the (false) proposition ‘all numbers equal zero’ containing x as bound variable)

5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106

The following are examples of combinations of signs, which do not meet the 5.4 Migration Policy in Colombia ...................................................... 108 syntactic criteria for formulas

5.5 “Colombia nos une”...................................................................... 109 • ((x¬

5.6•Alianza País .................................................................................. 112 ∀x 5.7•Challenges (x = 0) →.................................................................................... 114 Bibliography ....................................................................................... 116

Within this complex zoology, there is a marked division of entities into two Working Together for the Well-being of Migrants ........................... 119 main kinds. The first kind is structurally interpreted as numbers and as Barry Halliday number-forms (the latter are expressions containing variables, which may be substituted for so as to form numbers; e.g. x + 1, which is not yet a number, but will become a number if we substitute, say, 4 for x). The second kind is structured as logico-arithmetic propositions, namely claims concerning variables or numbers. Both these kinds of entities are generated from the same basic elements of the primary articulation following carefully Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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specified rules. Entities of either kind may be composed with additional Bibliography ......................................................................................... 60 elements to create new entities of either kind. What is the mythical division that gave rise to the number/proposition 4. The Ethics of Migration. structural The reconstruction Reflectionsdichotomy? on Recent Migration Policies has at this stage very little to go on. the hugein plethora of Europe imaginable mythical objects one must andAmong “Non-policies” Italy and ........................................... 61 find Zanfrini ontology that respects the structure offered by G¨ aLaura fundamental odel’s text. At stage everything is Structural still highly underdetermined. is only.. the 4.1this Restrictive Policies and Demand for ImmigrantItLabour 65 structural analysis in its entirety, which can correspond to an underlying myth. 4.2 Initiatives for Governing Family and Humanitarian TheMigration: isolation of partial constituents the structural analysis Labour Migration but notofWorkers’ Migration .............will 73 necessarily leave too many degrees of freedom. The reader is therefore asked to 4.3 From Guest Workers to Unwelcome Guests .................................. 82 indulge my suggestions, and judge them only when the account is complete 4.4 Selective and the 87 (the proof of Policies the pudding is Brain in theDrain............................................ eating). 4.5 Equal Opportunityare and Denied Opportunities My suggestions that the first structural................................ entity, numbers and90 numberforms, corresponds to names, parts of names, and moulds that may97become Bibliography ......................................................................................... names. The second structural entity, propositions (with or without free vari5.ables), Colombia: Emigrants in Their of and Origin ....... 101 shallIncluding correspond to bodies, parts Societies of bodies, moulds that may Urs Watter become bodies of creatures inhabiting the mythical world. Before we go 5.1 State Interest and Responsibility into the relations between bodies and names, we shall have to be a little towards their Citizens Living Abroad ........................................... 102 more specific concerning the mechanisms through which the basic elements 5.2 Applied Ethicsto .............................................................................. 104 can be composed form bodies and names. 5.3 Migration Policyofand Ethics ......................................................... 106 and Three forms creation (composing elements to form bodies names) must Policy be explicitly described, as without them the myth 5.4 Migration in Colombia ...................................................... 108 cannot be elaborated. The first is structurally articulated as adding the connective 5.5 “Colombia nos une”...................................................................... 109 ¬ (‘not’) to a propositional formula. The underlying mythical relation is 5.6 Alianza País .................................................................................. 112 reconstructed as that of nemesis. For each body, the powers We can create Challenges .................................................................................... 114 They a5.7 nemesis. A body and its nemesis are in a relation of strict exclusion. are not supposed to be both born into the created world (more on Bibliography ....................................................................................... 116this below). The question of which should be born — a creature or its nemesis — Working Together the Well-being Migrants ........................... 119 is a main concernfor addressed by the of myth. Barry Halliday

The second and third forms of creation are closely related. One is structurally articulated as the substitution of a constant for a free variable (for instance, turning the formula x > 0 into 4 > 0). The other is structurally articulated as binding a free variable (for instance, turning the formula x > 0 into ∀x(x > 0)). Free variables, in G¨ odel’s system, are not supposed to remain free indefinitely. We can therefore infer that free Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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variables are the structural representation of incompleteness in bodies and Bibliography ......................................................................................... 60 names, cavities that must eventually be filled. These formal manoeuvres suggest that some entities created by We, 4. The Ethics of Migration. our myth shall recount, are incomplete. Reflections on Recent Migration Policies They are only moulds. They contain (free variables) thatEurope have to........................................... be replaced if the incomplete and cavities “Non-policies” in Italy and 61 body Laura Zanfrini — which, as we shall see, can be viewed as a sort of Golem — is to be animated. These cavities seem to include the mouths and vaginas mythical 4.1 Restrictive Policies and Structural Demand for Immigrant Labourof .. 65 creatures. The substitution of a number for a free variable is the struc4.2 Initiatives for Governing Family and Humanitarian turalMigration: representation feeding but a name into a Golem’s mouth cavity, LabourofMigration not Workers’ Migration ............. 73 thus producing an animated creature, following the example of Jewish myth. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 As for binding free variables — there the difficulty is more pronounced. 4.4 Selective Policies and the Brain Drain............................................ 87 In one sense, a bound variable is replaced by all possible values, and we can 4.5 Equal Opportunity and Denied ................................ 90 image think of feeding the Golem with Opportunities all possible names. An alternative isBibliography gagging (binding) the Golem’s mouth cavity, preventing it from ......................................................................................... 97 being fed a name. Indeed, a bound variable, on the one hand, is not substituted, 5.but Colombia: Emigrants Their Societies ofBut Origin 101 which on the Including other, can no longerin be substituted. for ....... reasons Urs Watter will become apparent later, I suggest a third (less than perfect) solution. 5.1 StateaInterest and Responsibility Binding variable will be taken as the structural formulation of replacing a towards their Citizens Living Abroad ........................................... 102 vagina-cavity by a phallus, a sort of symbolic castration.3 The procreative 5.2 Applied Ethics .............................................................................. 104 associations will prove useful for retracing the myth. Finally, ifPolicy a free structuring the mythical role of106 a vagina5.3 Migration andvariable Ethics ......................................................... cavity is substituted rather than bound, the myth would have to 5.4 Migration Policy in Colombia ...................................................... 108recount how a name was inserted into the vagina. This operation will be mythically 5.5 “Colombia nos une”...................................................................... 109 identified as impregnation. 5.6 Alianza País .................................................................................. 112 So far we have a creating power We, the basic elements (primitive 5.7 Challenges 114 allow signs) of which.................................................................................... a world (formal system) is created, the rules that composing the elements into parts and moulds of Golems and 116 into parts Bibliography ....................................................................................... and moulds of names, and finally some distinguished forms of creation: a Working for the Well-being ........................... nemesis Together for each creature (adding aof¬ Migrants prefix), feeding a name to119 a Golem Barry Halliday (substituting a number for a free variable), replacing the vagina of a Golem by a phallus (binding a free variable), and impregnating a Golem by placing a name into its vagina (substitution again). 3 This

might have some obscure relation to Philo of Alexandria’s interpretation of the Jewish creation myth as consisting of creating first a heavenly man, then an earthly man, and only subsequently gendered man and woman. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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It is important to understand that a fed, impregnated, or phallusBibliography ......................................................................................... endowed Golem is not the same creature as the original Golem.60Indeed, any manipulation of a formula turns it into a new formula, and therefore 4. The Ethics of Migration. any manipulation of a mythical individual turns it into a new individual Reflections on Recent Migration Policies entity, which will later be endowed with........................................... a new individual name. 61 and “Non-policies” in Italy and Europe Laura Zanfrini

4.1 Restrictive Policies and Structural Demand Immigrant Labour .. 65 2.4. A transformation within the for secondary articulation: 4.2 Initiatives for Governingto Family and Humanitarian from creatures names

Migration: Labour Migration but not Workers’ Migration ............. 73 In odel’sGuest structural each primitive sign is assigned a82numeri4.3G¨ From Workersanalysis, to Unwelcome Guests .................................. cal value; as a result logical formulas, which are sequences of primitive 4.4 Selective Policies and the Brain Drain............................................ 87 signs, correspond to sequences of numbers. These number sequences are 4.5 Equal Opportunity and Denied ................................ 90 a sincompounded via explicitly statedOpportunities arithmetic operations to produce Bibliography ......................................................................................... 97 gle number. The result is that each sequence of signs (and in particular,

each formula) is assigned a number. The apparently strange arithmetic op5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 eration governing the assignment (see the Figure below) is chosen so as Urs Watter to guarantee that no two sequences share the same number, and no two 5.1 State Interest and Responsibility numbers share the same sequence of signs. towards their Citizens Living Abroad ........................................... 102 This strange structural description seems to recapture a mythical sys5.2 Applied Ethics .............................................................................. 104 tem of expressive naming. The name of a creature is calculated from its 5.3 Migration Each Policyofand ......................................................... composition. theEthics world’s elements has a name, and the 106 name of a creature is produced combining these names in a carefully 108 prescribed 5.4 Migration Policy inby Colombia ...................................................... manner. The system of naming is so constructed, that no two creatures are 5.5 “Colombia nos une”...................................................................... 109 ever endowed with the same name. 5.6 Alianza País .................................................................................. 112 We must introduce a certain duality into our reconstructed myth in 5.7 Challenges .................................................................................... 114 which order to account for the logical division between arithmetic numbers, Bibliography 116 numappear when ....................................................................................... talking about the formal system (such as the arithmetic ber 4), and representations of numbers by numerals in the formal system Working Together for the Well-being of Migrants ........................... 119 (such as the string ((((0) + 1) + 1) + 1) + 1, which represents 4). Naming, Barry Halliday therefore, cannot occur in the world of the created (the formal system). A creature’s true name exists in the thought of the creating powers We (the realm of arithmetic). But We can represent (or write) names by objects that can be introduced into the world (number-formulas in the formal system), and these name-representing-objects (hieroglyphs?) can impregnate or be fed into Golems. The true name is not a created object among others, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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but it can be represented by a created object. This mythical element might Bibliography ......................................................................................... 60 have something to do with Walter Benjamin’s myth in On Language as Such and the Language of Man (Benjamin 1966), which builds on a long 4. The Ethics of Migration. tradition of reflection on divine vs. human languages. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

Figure 3: Transforming logical formulas into numbers. 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 Each primitive sign is assigned a number.

4.2 Initiatives for Governing Family and Humanitarian •Migration: ∀ is assigned the Migration number 1 but not Workers’ Migration ............. 73 Labour ( is assigned the number 2 4.3•From Guest Workers to Unwelcome Guests .................................. 82 ) is assigned the and number 3 4.4•Selective Policies the Brain Drain............................................ 87 x is assigned the number 4 Opportunities ................................ 90 4.5•Equal Opportunity and Denied • = is assigned the number 5 Bibliography ......................................................................................... 97 • 0 is assigned the number 6

5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 etc. Urs Watter

Each formula thenand corresponds to a sequence of numbers. The formula 5.1 State Interest Responsibility

towards their Citizens Living Abroad ........................................... 102 ∀x(x = 0)

5.2 Applied Ethics .............................................................................. 104 corresponds term-by-term to the sequence

5.3 Migration Policy and Ethics ......................................................... 106

1, ...................................................... 4, 2, 4, 5, 6, 3. 5.4 Migration Policy in Colombia 108

5.5 “Colombia une”...................................................................... 109 are the This sequence isnos converted into a product of prime powers. The bases prime numbers, and the exponents are the elements of the corresponding sequence: 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 21 × 34 × 52 × 74 × 115 × 136 × 173 Bibliography ....................................................................................... 116 = 37, 137, 912, 361, 784, 015, 131, 350 Working Together for is the Well-being ........................... The resulting number not an elementofofMigrants the formal system, because119 it is not a

Barry Halliday sequence of primitive symbols of the formal system. This number, however, can be represented in the system as a long chain of +1’s: (. . . ((0 + 1) + 1) . . . + 1) + 1

The procedure of naming (which, again, is somewhat different in G¨ odel’s two structural accounts) allows for a highly intricate cosmology. Manipulations of the composition of creatures correspond to manipulations of their Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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names. At the same time, whatever We do with these names can be reBibliography ......................................................................................... 60formed flected by representations of names in the created world. A link is between creatures, their true names, and the representations of these names 4. The Ethics of Migration. in the created world. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

2.5. Tertiary articulation: birth

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 So G¨ odel’sfor structural analysis no reference to semantics. We had 4.2far Initiatives Governing Familymade and Humanitarian syntactic rules governing the composition of primitive into Migration: Labour Migration but not Workers’ Migration signs ............. 73 logical formulas, but ignored the question of whether these formulas are true or 4.3 From Guest Workers to Unwelcome Guests .................................. 82 false. The next element in the structural analysis is the notion of proof, 4.4 Selective Policies and the Brain Drain............................................ 87 which is a syntactic precursor of a semantic division. 4.5 Equal Opportunity and Denied lays Opportunities ................................ G¨ odel’s structural analysis down explicit syntactic rules90 that de-

termine which sequences of logical formulas are to be accepted as Bibliography ......................................................................................... 97 proofs, and constitutes a division between provable and non-provable formulas. 5.Provable Colombia: Including in Their of Origin 101 line of formulas areEmigrants simply those that Societies can appear at the ....... bottom Urs Watter a proof. 5.1 State Interest and Responsibility What is the mythical element structured in this way? We view proofs towards their Citizens Living Abroad ........................................... 102 as the generation of formulas from other formulas, and hypothesise that this 5.2 Applied Ethics .............................................................................. 104 structure emerged from a mythical concept of begetting. Many formulas can 5.3formed, Migration Policymight and Ethics be which never......................................................... be proved. Equivalently, not all106 creatures we discussed will be...................................................... born into the world. The introduction of 5.4have Migration Policysoinfar Colombia 108 creatures into the world of the living is selective, and subject to an explicit 5.5 “Colombia nos une”...................................................................... 109 articulation. 5.6 Alianza País .................................................................................. 112 Again, the list of birth/proof rules is tedious. It begins with axioms, 5.7 Challenges .................................................................................... 114 by We which structurally determine the first creatures, unborn, introduced into the world....................................................................................... of the living. It then specifies rules of inference, which Bibliography 116 structure laws of birth, specifying which lineages can give birth to which creaWorking Together for the of Migrants 119tedious tures. This technical andWell-being tedious account may ........................... echo the long and Barry Halliday biblical genealogies of the books of Genesis and Chronicles. Note that in the reconstructed mythical world, as in many other mythical worlds, a creature does not necessarily require two parents. Some forms of birth involve a single parent, while others involve more. In our mythical world a birth is ascribed to an entire lineage (a proof), starting from the first creatures introduced into the world (axioms). The structural analysis Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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— and therefore, we must assume, the myth too — generalises the rules asBibliography ......................................................................................... 60 numsigning numbers (names) to formulas (creatures) into rules assigning bers (names) to sequences of formulas (lineages). Not only individuals, but 4. The Ethics of Migration. entire dynasties as well, are assigned expressive mythical names. Reflections on Recent Migration Policies For our purposes we need to single........................................... out one important formal and “Non-policies” in Italy and Europe 61 rule of Laura Zanfrini inference. This is the rule that allows to derive from the formula ∀xP (x) (for every x, property P holds of x)Demand the conclusion P (a) (property 4.1 Restrictive Policies and Structural for Immigrant Labour .. 65P holds of a), where P is any predicate, and a is any number-formula. This rule 4.2 Initiatives for Governing Family and Humanitarian allows to replace the Migration binding ofbut a not variable by aMigration substitution. In 73 mythical Migration: Labour Workers’ ............. terms, this rule allows a Golem, whose cavity is replaced by a phallus (the 4.3 From Guest Workers to Unwelcome Guests .................................. 82 variable in its formula is bound), to give birth to any Golem of the exact 4.4 Selective Policies and the BrainisDrain............................................ same composition, whose cavity impregnated by any name (the87variable 4.5the Equal Opportunity and Denied Opportunities ................................ 90 which in formula is substituted by some number-formula). In our myth, seems to draw here upon the myth of symbolic castration, the phallus is Bibliography ......................................................................................... 97 the master-father of all names. 5. Colombia: Emigrants in Their Societies of Origin .......the 101issue of G¨ odel’sIncluding structural analysis explicitly recommends to forget Urs Watter

proofs (the component of the myth related to begetting) while introducing 5.1 issue State Interest and Responsibility the of numbering formulas (the component of the myth relating to towards their Citizens Living Abroad ........................................... 102 naming). It could be that the two myths derive from two different sources. Ethics .............................................................................. 104 is the It5.2isApplied clear, however, that the myth, which we are about to unfold, product of combining mythical sources. It seems that odel’s 5.3 Migration Policy andthese Ethicstwo ......................................................... 106G¨ analysis demonstrates how two different mythical structures interact 5.4 Migration Policy in Colombia ...................................................... 108 with each other to yield a crisis, and how the mythical bricoleurs manage to 5.5 “Colombia nos une”...................................................................... 109 bring the crisis into a safe resolution, which reconciles it with the demands 5.6the Alianza País .................................................................................. 112 of Savage Mind. 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116

2.6. Refining the tertiary articulation: birth oracles Working Together for the Well-being of Migrants ........................... 119 We seem to have believed that the rules governing begetting guaranteed a Barry Halliday harmony in the world of the born. First, We believed that if a creature is born, its nemesis cannot be born. This is structurally presented as the law of contradiction: a formula and its negation should not both be provable. We also seem to have believed that if a person is not born, then its nemesis must eventually be born. This is structurally reflected by the law of excluded middle: for any formula, either it or its negation should be provable. But Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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We’s belief was clouded by the shadow of a doubt. Bibliography ......................................................................................... We indeed made precise rules to determine which lineages60 can give birth to which creatures. But if We were to determine whether a certain 4. The Ethics of Migration. creature could born,Migration We would have to check whether it could be born Reflections on be Recent Policies of each and every possible — an ........................................... infinite task, which even We and “Non-policies” in Italylineage and Europe 61 could Laura Zanfrini not perform. Concerned aboutand foreseeing vicissitudes of procreation, 4.1 Restrictive Policies Structuralthe Demand for Immigrant Labour .. 65We set out create oracles. A heavily constrained and intricate ritual resulted in 4.2 to Initiatives for Governing Family and Humanitarian 4 the creation ofLabour a Golem called Bew represented by 73 a certain Migration: Migration but not(structurally Workers’ Migration ............. intricate predicate marked ‘Bew’). Bew had two cavities, a vagina 4.3 From Guest Workers to Unwelcome Guests .................................. 82 and a mouth. To determine whether a certain creature could be born to a certain 4.4 Selective Policies and the Brain Drain............................................ 87 lineage of ancestors (whether a certain sequence of formulas proves a certain 4.5 Equal Opportunity Denied Opportunities ................................ 90 and conclusion), We wouldand impregnate Bew with the name of the lineage, feed Bew with......................................................................................... the name of the creature (this corresponds to substituting the Bibliography 97 variables in the ‘Bew’ predicate). If a thus impregnated-and-fed-Bew was 5.subsequently Colombia: Including Emigrants Their Societies of Origin ....... 101 born into the worldin(the ‘Bew’ predicate, after substitution, Urs Watter is provable), then the said creature could indeed be born to the said lineage 5.1 State Interest and Responsibility (the sequence of formulas indeed proves the conclusion). If the impregnatedtowards their Citizens Living Abroad ........................................... 102 and-fed-Bew’s nemesis was born (the negation of the ‘Bew’ predicate after 5.2 Applied Ethics .............................................................................. 104 of the substitution was provable), then the creature could not be born lineage (the sequence of Ethics formulas does not prove the conclusion).106 5.3 Migration Policy and ......................................................... One birth — that of impregnated-and-fed-Bew or of its nemesis — 5.4 Migration Policy in Colombia ...................................................... 108 was to foretell another birth — that of a certain creature to a certain 5.5 “Colombia nos une”...................................................................... 109 lineage. What made Bew a useful oracle was that, since Bew was created 5.6 Alianza País .................................................................................. 112 via a specially constrained ritual, We could always contemplate their way 5.7 Challenges 114nemesis into discovering.................................................................................... whether the impregnated-and-fed-Bew — or its — were to be....................................................................................... born (one can always verify whether ‘Bew’ predicates, Bibliography 116 after any substitution, are provable or refutable). This feature of the myth is Working Together for the Migrants ........................... 1195 which structurally captured byWell-being the logicaloffeature of recursive functions, Barry Halliday allows to transform some problems of provability, including the provability of Bew predicates, into mechanical arithmetic computation. Impregnatedand-fed-Bew serves as an oracle, because We do not really have to wait 4 Since the structural analysis provides no hints concerning the names of the relevant characters, I will make up names from the notation in G¨ odel’s text. 5 In today’s terms, primitive recursive.

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until it, or its nemesis, is born (until someone discovers a proof). We can Bibliography ......................................................................................... 60 foresee its birth in We’s minds (through some computational algorithm), and subsequently foretell the births of other creatures to given lineages. 4. The Ethics of Migration. This is the most intricate, the most tedious, the most technical part Reflections on Recent Migration Policies of G¨ o del’s structuralinanalysis. 4 pages, including 45 steps, the and “Non-policies” Italy andOver Europe ........................................... 61 mythical ritual of the creation of Bew is recast into the structural language of Laura Zanfrini recursive functions. description is so intricate, 4.1 Restrictive PoliciesThe and structural Structural Demand for Immigrant Labour ..that 65 every step is not only formally written, but also informally explained. It is in 4.2 Initiatives for Governing Family and Humanitarian fact Migration: so tedious,Labour that G¨ odel’s second structural (the 1934 text) Migration but not Workers’account Migration ............. 73 only summarises the process. Obviously, the structural analysis is based on a 4.3 From Guest Workers to Unwelcome Guests .................................. 82 mythical incantation, which included an extremely detailed ritual protocol, 4.4 Selective andhope the Brain Drain............................................ and which wePolicies have no of recapturing. This ritual served to87guarantee could tell inDenied advance (compute algorithmically) whether an 4.5 that EqualWe Opportunity and Opportunities ................................ 90 impregnated-and-fed-Bew was to be born, that is, whether the lineage Bibliography ......................................................................................... 97 (sequence of formulas), whose name (number) impregnated (was substituted 5.into Colombia: Including in TheirBew, Societies of give Origin .......to 101 one free variable Emigrants of the predicate) could birth (proves) Urs Watter the creature (formula) whose name (number) was fed into (was substituted 5.1 State Interest and(the Responsibility into) Bew’s mouth other free variable in the ‘Bew’ predicate). towards their Citizens Living Abroad ........................................... 102 Did the original myth really contain such an incredibly intricate account of theEthics Bew’s creation ritual? It is hard to believe that 104 any myth 5.2 Applied .............................................................................. should be so incredibly Perhaps the difficulty here was106 in recap5.3 Migration Policy and detailed. Ethics ......................................................... turing a simple line of thought by G¨odel’s structural language. One should 5.4 Migration Policy in Colombia ...................................................... 108 bear in mind that for the people who originally recounted the myth, the 5.5 “Colombia nos une”...................................................................... 109 If the ritual, albeit described in full detail, was only a metaphysical reality. 5.6 Alianza País .................................................................................. original recounters of the myth did insist on such minute detail,112 it would have served to .................................................................................... convince them that they (or We) could, in principle, re5.7 Challenges 114 produce the ritual, given enough time and resources. But the fact remains Bibliography ....................................................................................... 116 that, living among the real concerns of the real world, having little to do with mythical creatures, they would of never have had the motivation Working Together for the Well-being Migrants ........................... 119to even Barry try — Halliday the point of the myth obviously being, as structuralism instructs us, its message or structure, and not its imagined replication.

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2.7. A crisis in the code Bibliography ......................................................................................... 60 With the creation of Bew the conclusion of the myth is near. We were with Bew alone. We started remoulding and varying it. The 4.not Thecontent Ethics of Migration. Reflections on Recent Policies immediate motivation Migration for these manipulations is not quite coded inside the and “Non-policies” in Italy and Europe ........................................... structural analysis, although G¨odel does provide a motivational61analogy Laura Zanfrini by bringing up Richard’s and the liar paradoxes. Perhaps the mythical 4.1 Restrictive and Structural for Immigrant Labour .. 65 motivation hadPolicies to do with the everDemand fateful quest for absolute knowledge. 4.2 Initiatives for Governing Family Humanitarian Perhaps We wanted to know moreand about the future inhabitants of their Migration: Labour Migration but not Workers’ Migration .............search 73 world. Perhaps this is one of those myths where an excessive for knowledge wreaks havoc.toOn the other Guests hand, perhaps We’s motivation 4.3 From Guest Workers Unwelcome .................................. 82 was absent from the myth which, we presume, was more intent 4.4 Selective Policies anditself, the Brain Drain............................................ 87 on the consequences. Perhaps We just followed L´evi-Strauss’ terms and relations 4.5 Equal Opportunity and Denied Opportunities ................................ 90 inversion formula of his structurally constitutive kind of permutation Bibliography ......................................................................................... 97 group (L´evi-Strauss 1976, 228). At anyIncluding rate, We’s experiments resulted in the creation Qew,6 a 5. Colombia: Emigrants in Their Societies of Origin .......of 101 modified nemesis of Bew, which had the following queer oracle capacity: Urs Watter impregnated with the name of a lineage, and fed the name of a Golem, Qew 5.1 State Interest and Responsibility disclosed whether the lineage could give........................................... birth, not to the named Golem, but towards their Citizens Living Abroad 102 to the Golem-fed-its-own-name (this self-feeding structurally translates as 5.2 Applied Ethics .............................................................................. 104 a formula, whose free variable is substituted by the number that designates 5.3 Migration Policy If and Ethics ......................................................... 106 that very formula). that birth was possible, impregnated-and-fed-Qew’s 5.46 Migration Policy in Colombia ...................................................... 108 For those who wish to keep track of the relation between this section and G¨ odel’s 5.5 “Colombia nos une”...................................................................... 109 proof, here are the relevant definitions: When xPaís is a.................................................................................. number, zx is the corresponding numeral in the formal 112 system. 5.6•Alianza Bew(zx , zy.................................................................................... ) is a predicate computable in terms of recursive functions, 5.7•Challenges 114which is provable if and only if the string of sign sequences numbered x proves the formula

Bibliography ....................................................................................... 116 numbered y.

• S(z , z ) is the numeral representing the formula obtained by substituting zb into all free occurrences of the variable w in the formula numbered a.

a b Working Together for the Well-being of Migrants ........................... 119

Barry Halliday

• Q(v, w) = ¬Bew(v, S(w, w)). • zp is the numeral representing the formula ∀vQ(v, w). • It follows that S(zp , zp ) is the numeral corresponding to the formula ∀v¬Bew(v, S(zp , zp )). As a result the numeral S(zp , zp ) belongs to a formula, which claims of itself that it is unprovable. G¨ odel’s proof can now be concluded as in the introduction. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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nemesis would be born. If the birth could not take place, impregnatedBibliography ......................................................................................... and-fed-Qew would be born. The birth of Qew, impregnated with 60 a lineage and fed a Golem’s name, was tantamount to the following prophecy: this 4. The Ethics of Migration. lineage cannot give birth to that Golem-fed-its-own-name. Reflections on Recent Migration Policies The Golem Qew then with a phallus to replace its and “Non-policies” inwas Italy andendowed Europe ........................................... 61vagina. Laura Zanfrini According to the laws of begetting, if Qew-endowed-with-a-phallus-and-feda-Golem’s-name was born, it couldDemand then give birth to Qew-impregnated4.1 Restrictive Policies and Structural for Immigrant Labour .. 65 with-any-lineage-name-and-fed-the-Golem’s-name. Such swarm of births, 4.2 Initiatives for Governing Family and Humanitarian according to the paragraph above, would prophesise: no lineage Migration: Labour Migration but not Workers’ Migration .............could 73 give birth to this Golem-fed-its-own-name. In other words: This Golem-fed-its4.3 From Guest Workers to Unwelcome Guests .................................. 82 own-name cannot be born! Qew endowed with a phallus came to be known 4.4Zp. Selective Policies and the Brain Drain............................................ 87 as 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Figure 4: The oracle Qew. Bibliography ......................................................................................... 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 Figure 5: Zp — Qew endowed with a phallus. 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Finally Zp was fed its own name. The birth of Zp-fed-its-own-name, which 60 would isBibliography none other ......................................................................................... than Qew-endowed-with-a-phallus-and-fed-Zp’s-name, signify (according to the previous paragraph): Zp-fed-its-own-name can4. The Ethics of Migration. not be born. To put things succinctly, Zp-fed-its-own-name was a creature Reflections on Recent Migration Policies whose very birth would prophesise that ........................................... he himself could not be born. and “Non-policies” in Italy and Europe 61 This strange contorted and grotesque creature was named Szpzp. Laura Zanfrini 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65

Figure 6: Family Szpzp — ZpHumanitarian fed his own name. 4.2 Initiatives for Governing and Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 Surely, such a creature as Szpzp cannot be born into a harmonious world. 5.3 Migration Policy andnot Ethics ......................................................... 106 Szpzp And, since Szpzp will be born, its nemesis must be born. Now prophesied that Szpzp be born; therefore the birth of Szpzp’s 5.4 Migration Policy in won’t Colombia ...................................................... 108nemesis must prophesise Szpzp would be born, which would bring,109 as above, 5.5 “Colombia nosthat une”...................................................................... disharmony again!7 5.6 Alianza País .................................................................................. 112 7

is some .................................................................................... sort of weak form of the semantic argument presented in 114 the analytic 5.7This Challenges introduction. Trying to mythically capture the syntactic argument is even more awkward Bibliography 116 and unpleasant........................................................................................ Here is how it would go: The error, however, We hoped, was in their own reasoning, in their careless analysis Working Together of Migrants ........................... 119 of the situation, andfor notthe in Well-being the created world itself. Entangled in contemplating the Barry Halliday monstrosity in their mind, We went into a deep meditative sleep, trying to carefully foretell the destiny of Szpzp. In We’s meditation, We dreamt that Szpzp (that is, Zp-fed-its-own-name) was born into the world of the living, fathered by some obscure, unknown, lineage. This birth must have been reflected by the oracle Golem Qew: the nemesis of Qew-impregnatedwith-the-obscure-lineage-name-and-fed-the-name-Zp had been born. The days went on, and Szpzp went on to bear his own children. And as Szpzp was but the Golem Qew-endowed-with-a-phallus-and-fed-the-name-Zp, it begot Qew-impregnated-with-theRoy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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We were obviously upset. The world seemed to be bound to disharBibliography ......................................................................................... 60 hope mony regardless of which was to be born, Szpzp or its nemesis. The that for any possible creature, either it or its nemesis would be born — but 4. The Ethics of Migration. not both at once — was shattered. The entire created world was at risk of Reflections on Recent Migration Policies being destroyed by its own dismayed creators... and “Non-policies” in Italy and Europe ........................................... 61 Laura Zanfrini

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 2.8. Rehabilitating the code 4.2 Initiatives for Governing Family Humanitarian G¨ odel’s structural analysis goes on and to explain that the structure discovered Migration: Labour Migration but not Workers’ Migration ............. 73 is in fact a common feature of many myths, not only the two versions of 4.3 myth From Guest Workers Unwelcome Guests .................................. the analysed in theto1931 and 1934 texts. Any creation myth82(formal 4.4 Selective and the Brain Drain............................................ 87 system) basedPolicies on a world with explicitly verifiable rules of birth (inference rules), a system of names (the natural numbers), a notion of nemesis 4.5 Equal Opportunity and Denied Opportunities ................................ 90 (negation), a phallus (a universal quantifier), and hypothesised harmony (law of Bibliography ......................................................................................... 97 contradiction) must have this structure. G¨odel must have been using the varietyIncluding of existing formal systems represent a large collection of 5.large Colombia: Emigrants in Their to Societies of Origin ....... 101 Urs Watter variants of the myth he analysed. G¨ odel also and seems to have found an appendix to the myth, which, I 5.1 State Interest Responsibility towards Citizens 102 in the would guess,their came from aLiving later Abroad source,........................................... representing some evolution social structure underlying the production of the myth. To his 104 structural 5.2 Applied Ethics .............................................................................. analysis he appended remarks suggesting that the notion of proof should be 5.3 Migration Policy and Ethics ......................................................... 106 separated from the notion of truth: every formula proved must be true, but 5.4 Migration Policy in Colombia ...................................................... 108 not all true formulas can be proved. Provability, in the structural analysis, “Colombia nos une”...................................................................... 109 formal is5.5 relative to a formal system. Truth, on the other hand, exceeds any 5.6 Alianza País .................................................................................. 112 obscure-lineage-name-and-fed-the-name-Zp. Into this dream — or rather this nightmare — were born both an impregnated-and-fed-Qew and its very own nemesis. 5.7world, Challenges .................................................................................... 114 Harmony was broken. We woke up, and rejected the dream as false. Bibliography The following....................................................................................... night, We dreamt of a world where Szpzp could not be116 born, and instead Szpzp’s nemesis was born. This, again, was prophesied by the Golem Qew. Into Working Together for the of of Migrants ........................... 119 this second dream world wereWell-being born a swarm Qew’s: Every Golem Qew-impregnatedBarry Halliday with-any-lineage-name-and-fed-the-name-Zp had been born, testifying that Zp-fed-itsown-name (namely Szpzp) could not be born to any lineage whatsoever. But this swarm of creatures were precisely all the children of Qew-endowed-with-a-phallus-and-fed-thename-Zp — of Szpzp himself. Into this dream — or rather nightmare — world, were born the nemesis of Szpzp, as well as all of Szpzp’s children. This world too was deemed disharmonious. We woke up, and rejected that dream as false as well. Contemplating these dreams We faced a grim reality: Neither Szpzp, nor its nemesis could be allowed into the world of the living without breaking its harmony. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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system. Bibliography ......................................................................................... This step seems to reflect the following mythical manoeuvre.60Neither Szpzp nor its nemesis can be born into the world of the living without 4. The Ethics of Migration. upsetting its harmony. However, higher worlds (formal systems) may exist, Reflections on Recent Migration Policies which look upon theinworld of We. And........................................... these higher vantage points and “Non-policies” Italy and Europe 61 allow Zanfrini toLaura verify that Szpzp, while it should not be allowed into the world of We’s born creatures Policies (it is not provable in Demand the givenforformal system), does conform 4.1 Restrictive and Structural Immigrant Labour .. 65 with the harmony of the larger universe (it is true, and also provable in 4.2 Initiatives for Governing Family and Humanitarian higher formal systems). None ofbut these higher vantage points is perfect. In Migration: Labour Migration not Workers’ Migration ............. 73 each such ‘higher world’ We could contemplate disharmonious creatures. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 But these creatures, it is hoped, could be placed in the larger scheme of 4.4 Selective Policies andfrom the Brain Drain............................................ things when considered higher points of view. The structural87analysis 4.5 Equal Opportunity Opportunities ................................ 90 seems to indicate thatand allDenied these higher vantage points can be conjured in the thoughts ......................................................................................... and dreams of the creating power We. At the same97time, it Bibliography gives the distinct impression that We are not omnipotent, but subject to 5.some Colombia: Including Emigrants Their Societies of Origin ....... 101 unattainable higher cosmicinharmony. Urs Watter

A clear formulation of this peculiar structure is not provided in full, 5.1 State and Responsibility and seemsInterest to have been deliberately avoided in G¨odel’s analysis. This evatowards their Citizens Living 102may be sion may be rooted in G¨ odel’s Abroad concern........................................... that such further analysis 5.2 Applied .............................................................................. 104G¨ criticised as Ethics not relying on explicitly documented myths but on odel’s own views of Policy structure. Another hypothesis is that this complete 5.3 Migration and Ethics ......................................................... 106 hierarchy is beyond the expressive power of G¨ odel’s language of structural 5.4 Migration Policy in Colombia ...................................................... 108 analysis; alternatively (assuming that G¨odel’s language of structural anal5.5 “Colombia nos adequate), une”...................................................................... 109 this ysis was perfectly the complete myth, which would express 5.6encompassing Alianza País .................................................................................. 112— told. all hierarchy, never was — perhaps never could be This hypothesised complete myth (the myth of logical truth) reflects the 5.7 Challenges .................................................................................... 114 unattainable telos of evolving formal systems — or of mythical structures. Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119

3. This is not a myth Barry Halliday

Of course, I could insist that the exercise was successful. Not only did I manage to reconstruct a myth underlying G¨ odel’s proof, but this myth is well correlated with some prominent structural motifs. My improvised myth, an anthropological structuralist zealot could argue, is all about how breaking totemic and incestuous taboos (eating one’s own name, being Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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impregnated by one’s own ancestors) leads to a breach of social harmony. Bibliography ......................................................................................... 60 This would in fact be a major triumph for the science of mythology. It would imply that even a mathematical text is, up to a transformation, 4. The Ethics of Migration. some sort of analogue of the Tukuna myth analysed by L´evi-Strauss (1978, Reflections on Recent Migration Policies Part I), in that it recaptures theEurope structure of improper coupling, 61 or of the and “Non-policies” in Italy and ........................................... Oedipus myth, in that it asserts the relation between riddles (questions Laura Zanfrini without answers, undecidable statements) andImmigrant incest (L´ evi-Strauss 4.1 Restrictive Policies and Structural Demand for Labour .. 65 1976, 21–24). 4.2 Initiatives for Governing Family and Humanitarian A fundamentalist psychoanalytic structuralist could............. join in73as well. Migration: Labour Migration but not Workers’ Migration G¨ odel’s proof turns out to affirm the danger of forcing an equivalence (al4.3 From Guest Workers to Unwelcome Guests .................................. 82 lowing replacement) between the name-of-the-father or the phallus and 4.4 Selective Brainout Drain............................................ other proper Policies names, and and the brings the hazardous repercussions 87 of failing to asunder the subject of enunciation and................................ the enunciated subject (in 4.5set Equal Opportunity and Denied Opportunities 90 such circumstances as when a creature carries the message that he-himself Bibliography ......................................................................................... 97 cannot be born) (cf. Lacan 1978, 139). 5. Colombia: in Their Societies of Origin ....... 101 If this Including zealot andEmigrants that fundamentalist successfully survived the sevUrs Watter enties and persist on living to this day, far be it from me to upset their 5.1 State Interest Responsibility omniscience. Butand I believe most readers would prefer to reject the story I towards their Citizens Living Abroad ........................................... have pretended to uncover as underlying G¨ odel’s proof, and not102 only due 5.2the Applied .............................................................................. 104 to trivialEthics and boring fact that no myth ever actually did underlie the proof. I will devote the Ethics rest of......................................................... this chapter to analyse the various 5.3 Migration Policy and 106 ways in which my myth fails both as a myth and as a structural equivalent of 5.4 Migration Policy in Colombia ...................................................... 108 G¨ odel’s proof, and to study what, if anything, this failure can teach us 5.5 “Colombia une”...................................................................... 109 concerning the nos functioning of a mathematical text. 5.6 Alianza País .................................................................................. 112 5.7 Challenges 114 3.1. This is.................................................................................... not a myth 116 IBibliography do not deny....................................................................................... (in fact, I strongly embrace) the claim that every mathematical argument is accompanied by some sort of narrative. E. M. Forster’s8 Working Together for the Well-being of Migrants ........................... 119 8 It isHalliday Barry not terribly easy to justify my choice of Forster as authority. His analysis is

indeed a classic, but is rather far behind contemporary research in narratology. Nevertheless, his definitions and critique provide me with more than enough to go on, and in our context his argument is still convincing even today. Another reason is Forster’s special position (both as theoretician and as writer) observing a crucial junction between English and French literary modernism. This position echoes the special position of structuralism as a juncture between analytic reasoning and continental thought. But I must also concede that I choose to quote Forster as homage to his beautiful work. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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definitions of story and plot as forms of narrative are enlightening in this Bibliography ......................................................................................... respect. Let us define a plot, he suggests. We have defined a 60 story as a narrative of events arranged in their time-sequence. A plot is 4. The Ethics of Migration. also a narrative of events, the emphasis falling on causality. “The Reflections on Recent Migration Policies king died and then the and queen died,” is a story. “The king and “Non-policies” in Italy Europe ........................................... 61 died, and the queen died of grief ” is a plot. The time-sequence Laurathen Zanfrini is4.1preserved, but the of causality it. ..Or Restrictive Policies andsense Structural Demand forovershadows Immigrant Labour 65again: “The queen died, no one knew why, until it was discovered that 4.2 Initiatives for Governing Family and Humanitarian it was through griefMigration at the death the king.” This is a plot Migration: Labour but not of Workers’ Migration ............. 73 with a mystery in it, a form capable of high development. It suspends 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the time-sequence, it moves as far away from the story as its lim4.4 Selective the Brain Drain............................................ itations willPolicies allow.and Consider the death of the queen. If87 it is in a4.5 story say ‘andand then?’ it is in a plot we ask ‘why?’ Equalwe Opportunity DeniedIfOpportunities ................................ 90 That isBibliography the fundamental difference between these two aspects97of the ......................................................................................... novel. A plot cannot be told to a gasping audience of cave men or 5.to Colombia: Including Emigrants Their Societiesdescendant of Origin .......the 101 movie a tyrannical sultan or to in their modern Urs Watter public. They can only be kept awake by ‘and then – and then —’ 5.1 State Responsibility they canInterest only and supply curiosity. But a plot demands intelligence towards their Citizens Living Abroad ........................................... 102 and memory also (Forster 1927, 82–83). 5.2 Applied Ethics .............................................................................. We can’t deny that a mathematical argument is indeed a104 sequence of together by a......................................................... chain of why?s. Let us put aside 5.3assertions Migrationtied Policy and Ethics 106for now the question of whether ‘assertions’ can indeed stand for events. 5.4 Migration Policy in Colombia ...................................................... 108A host of theoreticians will endorse such affinity, while quite a few others will 5.5 “Colombia nos une”...................................................................... 109 protest. But if we replace event by ‘state of affairs’, and accept that even Alianza País is .................................................................................. 112 if5.6 mathematics not quite about ‘states of affairs’, our understanding of 5.7 Challenges .................................................................................... 114 it does nevertheless make an at least allegorical use of this term, surely we could bring Forster’s definition of plot and mathematical texts close Bibliography ....................................................................................... 116enough together to espouse them to each other on the grounds of the operative Working why?. Together for the Well-being of Migrants ........................... 119 Barry Halliday

But Forster’s definition is also useful for stating an objection to the claim that my narrative above can serve as a myth. The cave dwellers’ myth revolves around and then?. My narrative does indeed attempt to suppress the mathematical why?, and linearise it into a sequence of and then?s (the question why is such-and-such unprovable is replaced by a sequence of ‘and then this was created, and then that was created, and then it was Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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prophesied that this couldn’t be born, and then...’). But this sequence of Bibliography and thens is......................................................................................... precisely the kind of sequence that wouldn’t keep 60 any cave dweller community awake. It is too hard to follow; the interrelations are 4. The Ethics of Migration. too complex and have too little to do with daily lives; the shadows of the Reflections on Recent Migration Policies mathematical fetish in forItaly justification (why?) hang over the narrative and “Non-policies” and Europe ........................................... 61 to the point paralysing it. The trace of the why?, even if no ‘because’ explicitly LauraofZanfrini appears in myPolicies story, is quite suppressed. the structure of 4.1 Restrictive andnot Structural Demand for Respecting Immigrant Labour .. 65 mathematical justification is (unfortunately?) related to repressing, to an 4.2 Initiatives for Governing Family and Humanitarian extent, an enthraling and then?. A Workers’ mathematical proof, it seems, Migration: Labour Migration but not Migration ............. 73 may have the making of a plot (why?), but lacks the making of a story (and 4.3 From Guest Workers to Unwelcome Guests .................................. 82 then?). 4.4 Selective Policies Brain Drain............................................ But indeed, theand linethebetween and then? and why? is not87all that 4.5 Equal More Opportunity and Denied Opportunities 90 clear-cut. than anything, this distinction ................................ is an approximate excuse for the evident failure of my impromptu myth to enthral. The question97 could be Bibliography ......................................................................................... raised, therefore, what if a more talented story teller (or better yet, a myth5.telling Colombia: Including Emigrants in Their Societies of it? Origin ....... community) were to take my text and process Could it 101 then come Urs Watter to function as a myth? Suppose indeed that it did. Would the transformed 5.1 State Interest and Responsibility myth, suppressing the why? for and then?, still be structurally reducible towards their Citizens LivingisAbroad 102 of the 9 to G¨ odel’s math? The answer bound........................................... to depend on the motivation 5.2 Applied Ethicsthis .............................................................................. 104 skills. person by whom myth is to be reduced, and on their excavation Indeed, the most ‘scientifically’ oriented critique against the structuralist 5.3 Migration Policy and Ethics ......................................................... 106 study of myths is that it lacks a clear articulation of myth`emes (mythical 5.4 Migration Policy in Colombia ...................................................... 108 elementary units), which makes the analysis rather arbitrary (e.g. Sperber 5.5 “Colombia une”...................................................................... 109 1973). I believenos that only through such arbitrariness could the structure of 5.6 proof Alianza .................................................................................. the bePaís observed in such hypothesised myth. But since the112 suggested myth-reprocessing experiment is likely never to take place, I 114 leave this 5.7 Challenges .................................................................................... doubtful train of thought and proceed in another direction. Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119

3.2. This is not even a plot Barry Halliday

If we had excavated a plot behind G¨odel’s text, the question whether this plot did or did not conform to the requirements of the mythical genre could be confined to the margins; such a feat would be a remarkable enough achievement in itself. But while I did acknowledge that every mathemat9I

will shortly turn to discuss whether my own text, as it stands, is in fact so reducible.

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ical argument is accompanied by some sort of narrative, I do not believe Bibliography ......................................................................................... that a plot can exhaust a mathematical argument, or lie behind 60 it. Some sorts of plots are often produced by mathematicians so as to accompany 4. The Ethics of Migration. their understanding of mathematical texts. But to ask for a relation more Reflections on Recent Migration Policies fundamental than that is toand impose. As........................................... we shall detail now, my61 attempt and “Non-policies” in Italy Europe above Laura indicates Zanfrini some typical obstructions. My mythPolicies refers to levels of articulation, butLabour provides 4.1 Restrictive andseveral Structural Demand for Immigrant .. 65 almost no Thisfor can be excused under pretence of recovering a plot from 4.2detail. Initiatives Governing Family andthe Humanitarian under a structural analysis: ‘the structural account, which as a structural Migration: Labour Migration but not Workers’ Migration ............. 73 account must be common to many overlaying texts, simply did not give 4.3 From Guest Workers to Unwelcome Guests .................................. 82 me enough to go on’, I could claim. ‘The structural analysis indicated the 4.4 Selective Policies and the Brain Drain............................................ 87 structure of an articulation, but did not reveal its actual elements’. 4.5 Equal Opportunity andfalse. Denied Opportunities 90 But this is grossly The problem is................................ not underdetermination. If Bibliography the primary, ......................................................................................... secondary, tertiary articulations, along with their 97 transformations and refinements, if all these had been underdetermined, we could 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 have simply filled in the gaps, and added arbitrary determinations consisUrs Watter tent with those specified, until some mythical content corresponding to the 5.1 State Interest and Responsibility mathematical structure would have been derived. The trouble is that the towards their Citizens Living Abroad ........................................... 102 situation is exactly opposite. G¨odel’s articulations are so incredibly overde5.2 Appliedthat Ethics 104 that termined, one.............................................................................. would be hard-pressed to find narrative features 5.3 Migration Policy and Ethics ......................................................... 106 still could be successfully disguised as non-mathematical, and that would emulate the given structure. 5.4 Migration Policy in Colombia ...................................................... 108

If my myth a genuine plot, it could work its way around the 5.5 “Colombia noswere une”...................................................................... 109 problem. It would rely on an element mentioned in Forster’s text: mystery. 5.6 Alianza País .................................................................................. 112 I would recount how the elements of the world are known only to the 5.7 Challenges ancients or the .................................................................................... gods, or perhaps how the arcane book coding these114 elements Bibliography had been lost....................................................................................... or destroyed, leaving the recounters of the myth 116 with mere fragments of knowledge forlorn. But this is precisely a technique that would Working Together for the Well-being of Migrants ........................... 119 set the emerging plot apart from the mathematical text. The mathematical Barry Halliday text insists on providing elements of structure, which it itself admits are not important. In section 6 of the 1934 text G¨odel describes how only very few characteristics of a formal system are required to carry out his proof; and yet G¨ odel chooses to conduct the proof in an explicit formal system, and to painstakingly verify that it obeys all the stated characteristics. A touch of mystery, which a good plot couldn’t do without, is exactly what Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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the mathematical text attempts to eradicate. Bibliography ......................................................................................... Such eradication attempts are of course unsuccessful. Mystery60 is prevalent in mathematical texts in many ways: from the awe-struck expression 4. The Ethics of Migration. of the layman formulas; through the incredibly many Reflections onfacing Recentmathematical Migration Policies details which are omitted toand keepEurope proofs........................................... readably-long; on to keeping and “Non-policies” in Italy 61 some ofLaura the Zanfrini most important links of an argument to the ‘end’, where a proof will be cathartically culminating the statement 4.1 Restrictive Policiescompleted; and Structural Demand forwith Immigrant Labour .. 65of open problems, which the text leaves for the reader to confront. 4.2 Initiatives for Governing Family and Humanitarian But whileLabour in narrative texts can function an end73 in itself, Migration: Migration butmystery not Workers’ Migrationas............. for the mathematical text as it operates in contemporary academic math4.3 From Guest Workers to Unwelcome Guests .................................. 82 ematical circles an unsettleable mystery often functions as a hindrance 4.4 Selective Policies and the Brain Drain............................................ 87 or threat. This is the very threat that makes G¨ odel produce reasons to 4.5 Equal Opportunity and Denied Opportunities ................................ argue that, while the statement labelled S(zp , zp ) is unprovable90and irrefutable, it must be marked as true. Other logicians resolve the 97 same difBibliography ......................................................................................... ficulty by stating that the predicates ‘true’ and ‘false’ simply do not apply 5.to Colombia: Including Emigrants Their Societies of Origin ....... 101 the statement marked S(zp , zin p ). This again pushes mystery aside. On Urs Watter the other hand, ‘It has a definite truth value, which we could never know’ Interest and Responsibility is5.1a State mystery-endorsing position, which contemporary mathematical texts towards their Citizens Living Abroad ........................................... 102 appear to refuse. 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106

3.3. And it spirals away from G¨ odel’s proof

5.4 Migration Policy in Colombia ...................................................... 108 So I locatednos theune”...................................................................... gap between the mathematical text and mythical 5.5far “Colombia 109 texts or plots in the former’s fetish for justification (an operative why?), and 5.6 Alianza País .................................................................................. 112 in its aversion from explicitly endorsing mystery. The generality of these 5.7 Challenges .................................................................................... 114 may characterisations is correlated with their triviality. My demonstration have its merits, but these conclusions alone do not justify as lengthy Bibliography ....................................................................................... 116a story as I’ve concocted. My point is not these banal generalities. The devil, as is Working Together Well-being Migrants 119 well known, is in for the the details. Let us of survey some........................... of them. Barry Halliday

The first articulation in the myth presents a chart of elements. The first articulation in the proof provides a list of signs. But elementary substances and signs occupy different functional positions. They obey different grammars, at least on an ‘ordinary’ level. That G¨ odel’s proof is making a (more or less successful) effort at working across this gap, namely at objectifying signs without destroying their signification, is not to be taken Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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lightly. If my myth were to respect this endeavour, it should have been ......................................................................................... 60 aBibliography semiotic myth concerning the vicissitudes of writing (in the generalised sense of making signs). Such myths exist — the Egyptian myth of Theuth 4. The Ethics of Migration. and Thamus, which Plato invokes in the Phaedrus (and Derrida (1993) in Reflections on Recent Migration Policies Plato’s Pharmacy) in is Italy an example. But ........................................... to tell a story where Thamus inand “Non-policies” and Europe 61 structs Theuth in the dangers of making signs by telling him a G¨ odelian Laura Zanfrini story about story-telling is Demand some form of makingLabour signs).. would be 4.1 Restrictive Policies and (which Structural for Immigrant 65 no more than to provide a dramatic setting for G¨odel’s proof — a far cry 4.2 Initiatives for Governing Family and Humanitarian fromMigration: its pretended transubstantiation into a myth. Labour Migration but not Workers’ Migration ............. 73 The text’s second articulation arrays primitive signs to produce for4.3 From Guest Workers to Unwelcome Guests .................................. 82 mulas, or, in mythical terminology, collects elements to form creatures. 4.4 Selective Policiesofand the articulation Brain Drain............................................ 87 negaThree components this received special attention: 4.5 Equal Opportunity and Denied Opportunities ................................ 90 tion/nemesis, substitution/feeding-impregnation and binding/endowing-withphallus. I do consider the confounding of universal quantification and Bibliography ......................................................................................... 97 symbolic castration an interesting direction to pursue. But in order to allow this 5.structural Colombia:parallelism Including Emigrants Their Societies to emerge,in the story had to of beOrigin swept ....... away101 from the Urs Watter structure of the proof. Free variables, which can be substituted or bound, 5.1 State Interest andasResponsibility were reconstructed cavities, which could be fed, impregnated, or replaced towards their Citizens Abroadthree? ........................................... 102 with a phallus. How did Living two become The culprit is the articulation 5.2the Applied Ethics .............................................................................. of homogeneous position of free variable (any free variable has104 the same 11 status as, and is replaceable by, any other) into two distinct positions: 5.3 Migration Policy and Ethics ......................................................... 106 vagina and mouth. The personification (or Golemisation) of formulas de5.4 Migration Policy in Colombia ...................................................... 108 manded it. 5.5 “Colombia nos une”...................................................................... 109 Of course, this structural deformation could have been avoided. The 5.6 Alianza Paíshave .................................................................................. 112 But cavities could been homogeneously marked as ears or nostrils. 5.7do Challenges 114 to so would.................................................................................... be a very early confession of failure. Which cave-dwelling audience would sit through a story about creatures plugging their116 ears with Bibliography ....................................................................................... names or shoving lineages up their noses? Which reader of plot would not Working the Well-being of Migrants 119 mathcall the Together arbitrary for nostril combinatorics for what ........................... it is: a thinly veiled Barry Halliday 10 I

believe that this effort is a feature of a large portion of modern mathematics, rather than a unique feature of G¨ odel’s text — the very feature that allows mathematics to support both realist and formalist philosophies. This effort is also a feature of structuralism, culminating in an implosion from which post-structuralism erupted. The first point will be treated in the third chapter of this book. The second point will only be skimmed over in the next subsection. 11 All free variables relevant to the story are of the same logical type. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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ematical text. The semantically constrained combinations and the content Bibliographythat ......................................................................................... 60 restrictions a myth or narrative must endure limit the capacity to transform proof into myth. 4. The Ethics of Migration. Then appears theMigration transformation Reflections on Recent Policiesinternal to the second articulation: the between creatures and names. There I suppressed61the fact andhomology “Non-policies” in Italy and Europe ........................................... Laura that in Zanfrini G¨ odel’s proof every name (arithmetic number), which is represented formally (a numeral theStructural formal system), has, again, its own ..arithmetic 4.1 Restrictive Policiesinand Demand for Immigrant Labour 65 representation, which can, again, be formally transformed into a different 4.2 Initiatives for Governing Family and Humanitarian numeral representing it in the but formal system. My myth ............. may have Migration: Labour Migration not Workers’ Migration 73 a fair degree of incestuous and cannibalistic features, but it doesn’t even begin 4.3 From Guest Workers to Unwelcome Guests .................................. 82 to measure up to the criss-crossing and self-reflective features included in 4.4 Selective Policies and the Brain Drain............................................ 87 G¨ odel’s tour-de-force. 4.5 Equal Opportunity and Denied Opportunities ................................ 90 The third articulation, introducing proof/birth, includes another important incongruity. Mythical creatures tend to have a unique lineage Bibliography ......................................................................................... 97 (or, at most, a few alternative accounts of lineage). But a formula, if it can be 5.proved Colombia: Including Emigrants Theirdifferent Societiesproofs. of Origin ....... 101 raises at all, must have infinitelyinmany This, again, Urs Watter the object-sign tension, which my myth tries to suppress. When a formula State Interest and Responsibility is5.1 introduced with different proofs, is it still the same formula? When I subtowards their Citizens Living Abroad ........................................... 102 stitute a numeral indicating a formula into a free variable contained in that 5.2 Applied Ethics same formula, are .............................................................................. the ‘substituted’ and ‘host’ formula the same 104 formula? 5.3 Migration and Ethicsmy ......................................................... 106 The costPolicy of restricting mythical entities to occupy object-like, rather than semiotic was the transcription of semiotic 5.4 Migration Policy infunctional Colombia positions ...................................................... 108 problems onto a different locus. I had to insist that a fed or impregnated 5.5 “Colombia nos une”...................................................................... 109 Golem is altogether different (differently named and differently begotten) 5.6 Alianza País .................................................................................. 112 from an unfed or unimpregnated one, rather than consider them as the 5.7 Challenges 114 same creature, .................................................................................... which has undergone some non-essential modification. Bibliography 116 In fact, ....................................................................................... the entire structure of signification, internal to G¨ odel’s argument, is obliterated from within the myth at a high cost, and imposed Working Together for the Well-being of Migrants ........................... 119 upon it as a secondary, external function, through the question ‘what does Barry Halliday the myth signify?’. This disappearing-reappearing act is, to some extent, a general feature of structural analyses: structures tend to flaunt a certain idiosyncratic, self-regulating reflexivity (they are what they mean), which places them in a paradoxical position relative to that which they are supposed to structure, and makes it difficult for them to live up to their raison-d’ˆetre as structures-of. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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By the time the refined version of the third articulation was to be inBibliography ......................................................................................... 60 (but cluded, my capacity as story-teller was already completely exhausted I doubt that other story tellers could ‘stay in the ring’ more than a couple 4. The Ethics of Migration. of rounds longer). Within the articulated construction of formulas, a privReflections on Recent Migration Policies ileged class of formulas is demarcated: formulas that can be expressed in and “Non-policies” in Italy and Europe ........................................... 61 terms recursive functions, and whose provability can therefore be decided Lauraof Zanfrini by finite algorithmic computation. This privileged class was ..mythically 4.1aRestrictive Policies and Structural Demand for Immigrant Labour 65 reconstructed as oracles: magical creatures, whose birth can be divined, 4.2 Initiatives for Governing Family and Humanitarian and Migration: further indicates the begetting-possibility other creatures to other Labour Migration but not Workers’ of Migration ............. 73 lineages. I couldn’t find any mythical excuse for their special role, and if 4.3 From Guest Workers to Unwelcome Guests .................................. 82 one were to read carefully, I couldn’t even justify their necessity. After all 4.4 Selective Policies and the Brain Drain............................................ 87 deterWe, who have full knowledge of the third articulation, can already mine whether a givenand creature be born to a given lineage 90 (without 4.5 Equal Opportunity Denied can Opportunities ................................ assuming, of ......................................................................................... course, to know whether a given creature could be97born to Bibliography any lineage, as this would require checking whether it can be born to each 5.and Colombia: Including Emigrants Their Societies of Origin 101need an every possible lineage — anininfinite task). Why would....... We Urs Watter oracle? One could come up with an excuse (say, We wanted to allow lower 5.1 StatetoInterest entities accessand thisResponsibility knowledge, or to simplify the process of acquisition towards their Citizens Abroad ........................................... 102 more of this knowledge). But Living to do that would be, again, either to force implausible on the myth, or to let the myth follow its own 5.2 Applied features Ethics .............................................................................. 104thread, losing its footing in the text. 5.3 Migration Policy and mathematical Ethics ......................................................... 106 Eventually, the final´e comes. The creation of Qew and its variations, 5.4 Migration Policy in Colombia ...................................................... 108 and the discovery of disharmony that these creatures entail. At this point, “Colombia I5.5 believe, even nos theune”...................................................................... most cooperative reader would be let down.109 After all 5.6 contorted Alianza Paísefforts .................................................................................. 112 logical my one is left with nothing but a thinly veiled riddle. The details of mismatch are fundamental: temporality is 114 differently 5.7 Challenges .................................................................................... structured in the myth and in the proof, the plot involves no births except Bibliography ....................................................................................... 116 those of oracles (whose role was supposed to be restricted to the prediction of ‘normal’ births,for completely absentof from the myth), and I eventually Working Together the Well-being Migrants ........................... 119 chose Halliday toBarry confine the syntactic argument to the margin in order not to drag the reader through an even more monstrous cacophony.

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3.4. And away from structure Bibliography ......................................................................................... 60 The myth is forced to follow the limitations imposed by the restrictive of myth and plot away from G¨odel’s proof. Reflexively complex 4.devices The Ethics of Migration. Reflections on Recent Policies functional positions in Migration the proof are violently suppressed. The transformaand “Non-policies” in Italy and Europe ........................................... tion of proof to myth fails to restrict its impact to the elements, and61violates Laura Zanfrini structure as well. To quote Jean Starobinski (paraphrasing de Saussure’s 4.1 Restrictive Policies and Structural Demand Immigrant Labour 65narraaccount of mythical transformation): In theforstructural order..of tive, the basic substanceFamily of symbolism is not only used but also 4.2 Initiatives for Governing and Humanitarian Migration: Migration butcan not be Workers’ Migration ............. 73a modmodified. ForLabour structure itself modified and become ifier. If one simply varies the “external” links of the original 4.3 From Guest Workers to Unwelcome Guests .................................. 82 material, apparently become entirely changed 4.4 Selective Policies “intrinsic” and the Brain characters Drain............................................ 87 (Starobinski 1979, 6). And my experiment is but one more demonstration 4.5 Equal Opportunity and Denied Opportunities ................................ 90 of a how a transformation, which is supposed to be structure preserving, Bibliography ......................................................................................... 97 carries structure away.

But even after all these sacrifices, our story still doesn’t sound like 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 aUrs proper Wattermyth, or even a proper story for that matter. The restrictions of the mathematical proof, the logic of its persistent why?, even though 5.1 State Interest and Responsibility theytowards were not properly were ........................................... still violent enough to constrain the their Citizensrespected, Living Abroad 102 myth to the extent that it can no longer be identified as myth. Mathemat5.2 Applied Ethics .............................................................................. 104 ical traces arrange events with emphasis on causality; the ground 5.3 Migration Policy Ethics ......................................................... 106 in its plan is a plot, andand the characters are ordered to acquiesce requirements ... characters are involved in various snares,108 they are 5.4 Migration Policy in Colombia ...................................................... finally boundnos hand and foot ... and yet, for all the sacrifices 5.5 “Colombia une”...................................................................... 109 made to it, we never see action as a living thing ... the characters have 5.6 Alianza País .................................................................................. 112 been required to contribute too much to the plot ... their vitality 5.7 Challenges .................................................................................... has been impoverished, they have grown dry and thin.114 We have Bibliography ....................................................................................... 116 1927, emphasised causality more than the medium permits (Forster 89–90). Working Together for the Well-being of Migrants ........................... 119 Our product, a narrative stifled under an imposing logical structure, Barry Halliday Forster explains, is typical of the novels of his time. Sometimes a plot triumphs too completely. The characters have to suspend their natures at every turn, or else are so swept away by the course of Fate that our sense of their reality is weakened ... In the losing battle that the plot fights with the characters, it often takes a cowardly revenge. Nearly all novels are feeble at the end. This is Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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because the plot requires to bound up ... and usually the characBibliography 60 ters go dead......................................................................................... while the novelist is at work, and our final impression of them is through deadness ... most novels do fail here — there is 4. The Ethics of Migration. this disastrous standstill while logic takes over the command from Reflections on Recent Migration Policies flesh and blood ... in nothing is heard hammering and screwing ... and “Non-policies” Italy and Europebut ........................................... 61 The have been getting out of hand, laying foundations Lauracharacters Zanfrini and declining to build on them afterwards, and Labour now the 4.1 Restrictive Policies and Structural Demand for Immigrant .. 65novelist has to labour personally, in order that the job may be done 4.2 Initiatives for Governing Family and Humanitarian on time. He Labour pretends that the characters are acting for him. He Migration: Migration but not Workers’ Migration ............. 73 keeps mentioning their names and using inverted commas. But 4.3 From Guest Workers to Unwelcome Guests .................................. 82 the characters are gone or dead. The plot, then, is the novel in its 4.4 Selective Policies and the Brain Drain............................................ 87 logical intellectual aspect: it requires mystery, but the mysteries are solved later on:and the reader may be ................................ moving about in90worlds 4.5 Equal Opportunity Denied Opportunities unrealised, but the novelist has no misgivings (Forster 1927, Bibliography ......................................................................................... 9789–92). The logical aspect of plot, as Forster articulates and our experiment 5.verifies, Colombia: Including in Their Societies of Origin 101 losing is exactly thatEmigrants which a story cannot take upon itself....... without Urs Watter its vitality. No wonder, then, that my little exercise did not succeed in 5.1 Stateproof Interest andliving Responsibility turning into narrative. I believe this here is an indication of towards their Citizens Living Abroad ........................................... 102 inherent incapacities that structural analyses impose. But this indication 5.2 Applied Ethics 104 alone does not rule.............................................................................. out, of course, that one could generate non-narrative texts, which would structurally analysable into G¨odel’s proof, and 5.3 Migration Policybeand Ethics ......................................................... 106 would, perhaps, lead, in some obscure way, to claiming that mathematics is indeed 5.4 Migration Policy in Colombia ...................................................... 108 the structure of philosophy, thought or the universe. I will not deprive such 5.5 “Colombia nos une”...................................................................... 109 hopes from those who depend upon them. But since I am going to read 5.6 Alianza País .................................................................................. 112literary G¨ odel’s proof with tools designed mostly in the context of analysing 5.7 Challenges .................................................................................... texts, it is important, as a means of precaution, to expose and114 explicate the tensions between these two kinds of texts. Bibliography ....................................................................................... 116 That every mathematical argument is accompanied by narrative is Working Together for the Well-being of Migrants ........................... 119 difficult to doubt. But that such narrative underlies the argument, or is Barry Halliday structurally codified inside it, is far too strong a claim. Should one study which similarities can and cannot be produced between different texts, and which transformations can force one text to become another? Undoubtedly, this is worth studying, as long as one bears in mind that the similarities are imposed, not exposed, and that the transformations do not emerge, but are rather projected. And when extracting narrative from a mathematical text, Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

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one should remember that (as in the case of de Saussure’s quest for hidden Bibliography ......................................................................................... messages in Latin poetry) Every complex structure furnishes60an observer with a range of elements which will allow him to choose a 4. The Ethics of Migration. sub-ensemble apparently endowed with sense, and which nothing Reflections on Recent Migration Policies prohibits a priori ina Italy logical chronological antecedence (Starobinand “Non-policies” andor Europe ........................................... 61 ski 1979, 44). The derivation of structure is constrained by the structured Laura Zanfrini phenomena, doesn’t quite retain an ‘original’ structure. 4.1 Restrictivebut Policies and Structural Demand for Immigrant Labour Could .. 65 this functional oddity be related to the possibility that structure does not sim4.2 Initiatives for Governing Family and Humanitarian ply exist, but attains some less but straightforward ontological position? Migration: Labour Migration not Workers’ Migration ............. 73 That both mathematical and narrative texts are phenomena of lan4.3 From Guest Workers to Unwelcome Guests .................................. 82 guage is hard to deny. But to study the process of semiosis in one through a 4.4 Selective Policies the Brain corresponding processand in the other Drain............................................ would jump the gun. The basic 87 processes of may or may be universal, but ................................ their specificities deserve to 4.5semiosis Equal Opportunity andnot Denied Opportunities 90 be concretely......................................................................................... studied within each discourse where they make their Bibliography 97 mark. In this book I therefore analyse semiosis in G¨ odel’s mathematical text with 5.tools Colombia: Including Emigrants in Theirfor Societies of Origin ....... 101 that have originally been designed the study of literary texts, but Urs Watter in doing so I do not assume that mathematics is literature. In the novel, 5.1 Statewrites, Interestall andhuman Responsibility Forster happiness and misery does not take the towards their Citizens Living Abroad form of actions, it seeks means of ........................................... expression other than102 through the plot, itEthics must.............................................................................. not be rigidly canalised (Forster 1927, 90–91). 5.2 Applied 104 This essay merely aims toand show that......................................................... in the mathematical text, all meaning 5.3 Migration Policy Ethics 106 does not take the form of logic, it seeks means of expression other than through 5.4 Migration Policy in Colombia ...................................................... 108 inference rules, it must not be rigidly canalised. 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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Bibliography ......................................................................................... 60 4. The Ethics of Migration. Reflections on Recent Migration Policies and “Non-policies” in Italy and Europe ........................................... 61

Bibliography Laura Zanfrini

4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Labour Migration but not Workers’ Migration [1] Migration: Anselm (St.), “Monologium”. In Of the Opinions of ............. Leading73 PhilosophersGuest and Workers Writersto on the Ontological Argument. Chicago: 4.3 From Unwelcome Guests .................................. 82 The Open Court Publishing Company, 1903. Also available online at 4.4 Selective Policies and the Brain Drain............................................ 87 http://www.ccel.org/ccel/anselm/basic works.i.html. 4.5 Equal Opportunity and Denied Opportunities ................................ 90 [2] Austin, J.L., How to Do Things with Words. Cambridge: Harvard UniBibliography ......................................................................................... 97 versity Press, 1962.

[3] Barthes, R., Elements of Semiology. New York: Noonday Press, 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 1968. Urs Watter R., S/Z. New York: Hill and Wang, 1974. [4] Barthes,

5.1 Interest Responsibility [5] State Barthes, R.,and Image Music Text. S Heath, ed. London: Fontana, 1977. towards their Citizens Living Abroad ........................................... 102 [6] Benacerraf, P., “What numbers could not be”. In P. Benacerraf & H. 5.2 Applied Ethics 104 second Putnam, eds. .............................................................................. Philosophy of Mathematics — Selected Readings, 5.3 Migration Policy and Ethics ......................................................... 106 edition, 272–294. Cambridge: Cambridge University Press, 1983a. 5.4 Policy in Colombia ...................................................... [7] Migration Benacerraf, P., “Mathematical truth”. In P. Benacerraf & H.108 Putnam, eds. Philosophy of Mathematics — Selected Readings, second 5.5 “Colombia nos une”...................................................................... 109edition, 403–420. Cambridge: Cambridge University Press, 1983b. 5.6 Alianza País .................................................................................. 112 [8] Benacerraf, P. & H. Putnam, eds. Philosophy of Mathematics — 5.7 Challenges .................................................................................... 114 Selected Readings, second edition. Cambridge: Cambridge University Bibliography ....................................................................................... 116 Press, 1983.

[9] Benjamin, W., Writings, 1. M. ........................... Bullock & M.W.119 Jennings, Working Together forSelected the Well-being of Vol. Migrants eds. Cambridge: Belknap Press, 1996. Barry Halliday [10] Benveniste, E., Problems in General Linguistics. Coral Gable: University of Miami Press, 1971. [11] Borges, J.L., Ficciones. A. Kerrigan, ed. New York: Grove Press, 1962. [12] Borges, J.L., Selected Non-Fictions, Vol. 3. New York: Penguin Books, 1999. 231

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BIBLIOGRAPHY Table of Contents

[13] Brian, E., La Mesure de l’Etat. Paris: Albin Michel, 1994. Bibliography ......................................................................................... 60 [14] Cantone, D., E.G. Omodeo, J.T. Schwartz & P. Ursino, “Notes from logbook of a proof-checker’s project”. In N. Dershowitz, ed. Veri4. The the Ethics of Migration. fication:onTheory Practice. New York: Springer, 2004. Reflections Recentand Migration Policies and “Non-policies” in Italy and Europe ........................................... 61 [15] Charraud, N., Lacan et les Math´ematiques, Paris: Anthropos 1997. Laura Zanfrini

[16] Dawson Jr., J.W., Logical Dilemmas: the Life and Work of Kurt G¨ odel, 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 Wellesley: A.K. Peters, 1997. 4.2 Initiatives for Governing Family and Humanitarian [17] Migration: Deleuze, G., Difference andbutRepetition. New York: Columbia Labour Migration not Workers’ Migration ............. 73University Press, 1994. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 [18] Deleuze,Policies G., Logic New York: Columbia University 4.4 Selective and of theSense. Brain Drain............................................ 87 Press, 1990. 4.5 Equal Opportunity and Denied Opportunities ................................ 90 [19] Derrida, J., Edmund Husserl’s Origin of Geometry, an Introduction. Bibliography ......................................................................................... 97 Lincoln: University of Nebraska Press, 1989. 5.[20] Colombia: Including Emigrants in Their SocietiesJohn of Origin ....... 101 Derrida, J., Of Grammatology. Baltimore: Hopkins University Urs Watter

Press, 1976. 5.1 State Interest and Responsibility [21] towards Derrida, J., Citizens WritingLiving and Difference. Chicago: University of Chicago their Abroad ........................................... 102 Press, 1978. 5.2 Applied Ethics .............................................................................. 104 [22] Derrida, J., Speech and Phenomena. Evanston: Northwestern Univer5.3 Migration Policy and Ethics ......................................................... 106 sity Press, 1979. 5.4 Migration Policy in Colombia ...................................................... 108 [23] Derrida, J., Positions. Chicago: University of Chicago Press, 1981. 5.5 “Colombia nos une”...................................................................... 109 [24] Derrida, J., Dissemination. London: Athlone Press, 1993. 5.6 Alianza País .................................................................................. 112 [25] Derrida, J., Signeponge. New York: Columbia University Press, 1984. 5.7 Challenges .................................................................................... 114 [26] Derrida, ....................................................................................... J., Limited Inc.. Evanston: Northwestern University Bibliography 116 Press, 1988a. Working Together for the Well-being of Migrants ........................... 119 [27] Derrida, J., The Derrida Reader: Writing Performances. J. Wolfreys, Barry Halliday ed. Edinburgh: Edinburgh University Press, 1988b. [28] Derrida, J., The Gift of Death. Chicago: The University of Chicago Press, 1995. [29] Duffy, S., ed. Virtual Mathematics. Manchester: Clinamen Press, 2004. [30] Eco, U., The Open Work. Cambridge: Harvard University Press, 1989. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

BIBLIOGRAPHY 10

233 Table of Contents

[31] Eriugena, J.S., Periphyseon, Liber Primus. Dublin: Dublin Institute Bibliography ......................................................................................... 60 for Advanced Studies, 1978. ed. Mathematics, Education, and Philosophy: an Interna4.[32] The Ernest, Ethics ofP.,Migration. tional Perspective. London: Falmer Reflections on Recent Migration PoliciesPress, 1994. and “Non-policies” in Italy and Europe ........................................... 61 [33] Feynman, R.P., “Surely You’re Joking, Mr. Feynman!”. New York: Laura Zanfrini W.W. Norton, 1985. 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 [34] Fisch, M., “The making of Peacock’s treatise on algebra: a case of cre4.2 Initiatives for Governing Family and Humanitarian ative indecision”. Archive for History of Exact Science, 54 (1999):137– Migration: Labour Migration but not Workers’ Migration ............. 73 179. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 [35] Forster, E.M., Aspects of the Novel. London: E. Arnold, 1927. 4.4 Selective Policies and the Brain Drain............................................ 87 [36] Foucault, M., The Order of Things: an Archaeology of the Human 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Sciences. New York: Vintage Books, 1973. Bibliography ......................................................................................... 97 [37] Foucault, M., The Archaeology of Knowledge. New York: Pantheon Books, Including 1972. 5. Colombia: Emigrants in Their Societies of Origin ....... 101 Urs Watter

[38] Foucault, M., This is Not a Pipe. J. Harkness, ed. Berkeley: University 5.1 State Interest and Responsibility of California Press, 1983. towards their Citizens Living Abroad ........................................... 102 [39] Foucault, M., The Foucault Reader. P. Rabinow, ed. Hamondsworth: 5.2 Applied Ethics .............................................................................. 104 Penguin, 1984. 5.3 Migration Policy and Ethics ......................................................... 106 [40] Frege, G., “The thought: a logical enquiry”. In P.F. Strawson, ed. 5.4 Migration Policy in Colombia Philosophical Logic. Oxford:...................................................... Oxford university Press, 1967. 108 5.5 “Colombia nos une”...................................................................... 109 [41] Frege, G., “The concept of number”. In P. Benacerraf & H. Putnam, 5.6 Alianza País .................................................................................. 112edition, eds. Philosophy of Mathematics — Selected Readings, second 130–159. Cambridge: Cambridge University Press, 1983. 114 5.7 Challenges .................................................................................... Bibliography ....................................................................................... [42] Friedman, H.M., “Finite functions and the necessary use of116 large cardinals”. Annals of Mathematics, 148 (1998): 803–893. Working Together for the Well-being of Migrants ........................... 119 [43] Gadamer, Barry Halliday H.G., Truth and Method. New York: Seabury Press, 1975.

[44] Galilei, G., “Il saggiatore”. In S. Drake & C.D. O’Malley, eds. The Controversy on the Comets of 1618. Philadelphia: University of Pennsylvania Press, 1960. [45] G¨ odel, K., Collected Works. S. Fereferman et al., eds. Oxford: Oxford University Press, 1986–2003. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

234 10

BIBLIOGRAPHY Table of Contents

[46] Grosholz, E.R., Representation and Productive Ambiguity in MatheBibliography ......................................................................................... 60 matics and the Sciences. Oxford: Oxford University Press, 2007. “The intuitionist foundations of mathematics”. In P. Be4.[47] The Heyting, Ethics of A., Migration. nacerrafon&Recent H. Putnam, eds.Policies Philosophy of Mathematics — Selected Reflections Migration and Readings, “Non-policies” in Italy and 52–60. EuropeCambridge: ........................................... 61 second edition, Cambridge University Laura Zanfrini Press, 1983.

4.1 Restrictive Policies andand Structural Demand forLogic. Immigrant [48] Husserl, E., Formal Transcendental The Labour Hague:.. 65 Martinus 4.2 Initiatives for Governing Family and Humanitarian Nijhoff, 1969. Migration: Labour Migration but not Workers’ Migration ............. 73 [49] Husserl, E., Logical Investigations, Vol. 1. London: Routledge & Kegan 4.3 From Guest Workers to Unwelcome Guests .................................. 82 Paul, 1970a. 4.4 Selective Policies and the Brain Drain............................................ 87 [50] Husserl, E., The Crisis of European Sciences and Transcendental Phe4.5 Equal Opportunity and Denied Opportunities ................................ 90 nomenology. Evanston: Northwestern University Press, 1970b. Bibliography [51] Klein, J.,......................................................................................... “Modern rationalism”. In R.B. Williamson & E.97Zucker-

man, eds. Jacob Klein: Lectures and Essays. Annapolis: The St. John’s 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Press, Watter 1985. [52] Kristeva, J.,and Semeiotike. Paris: Editions du Seuil, 1969. 5.1 State Interest Responsibility towards their Citizens Living Abroad ........................................... 102 [53] Kristeva, J., Revolution in Poetic Language. New York: Columbia Uni5.2 Applied Ethics .............................................................................. 104 versity Press, 1984. 5.3 Migration andParis: EthicsEditions ......................................................... 106 [54] Lacan, J.,Policy Ecrits. du Seuil, 1966. 5.4 Migration in Colombia 108 York: [55] Lacan, J.,Policy Ecrits, The First...................................................... Complete Edition in English. New 5.5 “Colombia nos une”...................................................................... 109 W.W. Norton, 2006. 5.6 Alianza .................................................................................. 112 New [56] Lacan, País J., The Four Fundamental Concepts of Psychoanalysis. York: W.W. Norton, 1978. 5.7 Challenges .................................................................................... 114 Bibliography 116 [57] Lefebvre,....................................................................................... M., “Construction et d´econstruction des diagrammes de Dynkin”. Actes de la Recherche en Sciences Sociales, 141–142(2002): Working Together for the Well-being of Migrants ........................... 119 121–124. Barry Halliday

[58] L´evi-Strauss, C., The Savage Mind. Chicago: University of Chicago Press, 1966. [59] L´evi-Strauss, C., The Raw and the Cooked. New York: Harper & Row, 1969. [60] L´evi-Strauss, C., The Origin of Table Manners. London: J. Cape, 1978. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

BIBLIOGRAPHY 10

235 Table of Contents

[61] L´evi-Strauss, C., Structural Anthropology, Vol. II. New York: Basic Bibliography ......................................................................................... 60 Books, 1976. E., The Ethnomethodological Foundations of Mathematics. 4.[62] The Livingston, Ethics of Migration. London:onRoutledge, 1985. Policies Reflections Recent Migration and “Non-policies” in Italy andto Europe ........................................... 61 [63] Maimonides, M., Guide the Perplexed. London: Routledge & Laura Zanfrini

Kegan Paul, 1904. Also available online at http://www.sacred4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 texts.com/jud/gfp/index.htm. 4.2 Initiatives Family Humanitarian [64] Nagel, E.for & Governing J.R. Newman, G¨ oand del’s Proof. New York: New York UniMigration: Labour Migration but not Workers’ Migration ............. 73 versity Press, 1958. 4.3 From Guest Workers to Unwelcome Guests .................................. 82 [65] Nietzsche, F., “On truth and lies in a nonmoral sense”. In Daniel 4.4 Selective Policies and the Brain 87 NoteBreazeale, ed. Philosophy andDrain............................................ Truth: Selections from Nietzsche’s books Opportunity of the Earlyand 1870’s . New Jersey: Humanities Press International, 4.5 Equal Denied Opportunities ................................ 90 1979. ......................................................................................... 97 Bibliography

[66] Patton, P. & J. Protevi, eds. Between Deleuze and Derrida. New York: 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Continuum, 2003. Urs Watter

[67] Peirce, C.S., Collected Papers. C. Hartshorne & P. Weiss, eds. Cam5.1 State Interest and Responsibility bridge: their Harvard University Press, ........................................... 1931–1958. towards Citizens Living Abroad 102 [68] Peirce, Ethics C.S., The Philosophy of Peirce: Selected Writings. J. Buchler, 5.2 Applied .............................................................................. 104 ed. New York: Harcourt, Brace, 1940. 5.3 Migration Policy and Ethics ......................................................... 106 [69] Plotnitsky, A., The Knowable and the Unknowable. Ann Arbor: The 5.4 Migration Policy in Colombia ...................................................... 108 University of Michigan Press, 2002. 5.5 “Colombia nos une”...................................................................... 109 [70] Putnam, H., Mind, Language and Reality. Cambridge: Cambridge Uni5.6 Alianza País .................................................................................. 112 versity Press, 1975. 5.7 Challenges .................................................................................... 114 [71] Quine, W.V.O., From a Logical Point of View, second edition. CamBibliography ....................................................................................... 116 bridge: Harvard University Press, 1961. [72] Quine, W.V.O., Selected LogicofPapers, enlarged edition. New Working Together for the Well-being Migrants ........................... 119 York: Random Barry HallidayHouse, 1995. [73] Rav, Y., “A critique of a formalist-mechanist version of the justification of arguments in mathematicians’ proof practices”. Philospohia Mathematica, 3 (2007):1–30. [74] Rosental, C., “Apprendre `a voir apparaˆıtre des formes, des structures et des symboles: Le cas de l’enseignement de la logique a` l’universit`e”. Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

236 10

BIBLIOGRAPHY Table of Contents

In B. Lahire & C. Rosental, eds. La Cognition au Prisme des Sciences Bibliography 60 2008. Sociales,......................................................................................... 161–189. Paris: Editions des Archives Contemporaines, “Extensions of some theorems of G¨ odel and Church”. 4.[75] The Rosser, Ethics ofJ.B., Migration. Journalon of Recent Symbolic Logic, 1(3) (1936):87–91. Reflections Migration Policies and “Non-policies” in Italy and Europe ........................................... [76] Rotman, B., Ad Infinitum — the Ghost in Turing’s Machine: 61 an Essay Laura Zanfrini

in Corporeal Semiotics. Stanford: Stanford University Press, 1993. 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 [77] Rotman, B., Mathematics as Sign: Writing, Imagining, Counting. 4.2 Initiatives Governing Family and Humanitarian Stanford:for Stanford University Press, 2000. Migration: Labour Migration but not Workers’ Migration ............. 73 [78] de Saussure, F., Course in General Linguistics. New York: McGraw4.3 From Guest Workers to Unwelcome Guests .................................. 82 Hill, 1966. 4.4 Selective Policies and the Brain Drain............................................ 87 [79] Sperber, D., Le Structuralisme en Anthropologie. Paris: Editions du 4.5 Equal and Denied Opportunities ................................ 90 Seuil,Opportunity 1973. Bibliography ......................................................................................... 97 [80] Starobinski, J., Words upon Words: the Anagrams of Ferdinand de Saussure. New Haven: Yale University Press, 1979. 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Tasi´ Watter [81] c, V., Mathematics and the Roots of Postmodern Thought. Oxford: Oxford University Press, 2001. 5.1 State Interest and Responsibility their Citizens Living Abroad ........................................... 102 In P. [82] towards von Neumann, J., “The formalist foundations of mathematics”. 5.2 Applied Ethics 104Selected Benacerraf & .............................................................................. H. Putnam, eds. Philosophy of Mathematics —

Readings,Policy second 61–65. Cambridge: Cambridge 106 University 5.3 Migration andedition, Ethics ......................................................... Press, 1983. 5.4 Migration Policy in Colombia ...................................................... 108 [83] Wagner, R., “Mathematical marriages: intercourse between mathemat5.5 “Colombia nos une”...................................................................... 109 ics and semiotic choice”. Social Studies of Science, 32(9) (2009a):289– 5.6 Alianza País .................................................................................. 112 309. 5.7 Challenges .................................................................................... 114 [84] Wagner, R., “Mathematical variables as indigenous concepts”. InterBibliography 116 national ....................................................................................... Studies in the Philosophy of Science, 32(1) (2009b):1–18. [85] Wagner, R., for “For histories of Greek ........................... mathematics”. Science in Working Together thesome Well-being of Migrants 119 Context Barry Halliday(forthcoming). [86] Wahl, F., ed. Qu’est-ce que le Structuralisme?. Paris: Editions du Seuil, 1968. [87] Wittgenstein, L., Tractatus Logico-Philosophicus. London: Routledge and Kegan Paul, 1922. Also available online at http://www.kfs.org/ jonathan/witt/tlph.html Roy Wagner, S(zp, zp): Post-Structural Readings of Gödel’s Proof ©2009 Polimetrica International Scientific Publisher Monza/Italy

BIBLIOGRAPHY 10

237 Table of Contents

[88] Wittgenstein, L., Philosophical Investigations. New York: Macmillan, Bibliography 1953. ......................................................................................... 60 [89] Wittgenstein, L., Lectures on the Foundations of Mathematics. C. Di4. The Ethics of Migration. amond,on ed.Recent Chicago: The University Reflections Migration Policies of Chicago Press, 1975. and “Non-policies” in Italy and Europe ........................................... 61 revised [90] Wittgenstein, L., Remarks on the Foundations of Mathematics, Laura Zanfrini

edition. Cambridge: The MIT Press, 1978. 4.1 Restrictive Policies and Structural Demand for Immigrant Labour .. 65 4.2 Initiatives for Governing Family and Humanitarian Migration: Labour Migration but not Workers’ Migration ............. 73 4.3 From Guest Workers to Unwelcome Guests .................................. 82 4.4 Selective Policies and the Brain Drain............................................ 87 4.5 Equal Opportunity and Denied Opportunities ................................ 90 Bibliography ......................................................................................... 97 5. Colombia: Including Emigrants in Their Societies of Origin ....... 101 Urs Watter

5.1 State Interest and Responsibility towards their Citizens Living Abroad ........................................... 102 5.2 Applied Ethics .............................................................................. 104 5.3 Migration Policy and Ethics ......................................................... 106 5.4 Migration Policy in Colombia ...................................................... 108 5.5 “Colombia nos une”...................................................................... 109 5.6 Alianza País .................................................................................. 112 5.7 Challenges .................................................................................... 114 Bibliography ....................................................................................... 116 Working Together for the Well-being of Migrants ........................... 119 Barry Halliday

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