Possibility and Necessity in the Time of Peter Abelard 2021035289, 2021035290, 9789004470286, 9789004470460, 900447028X

Table of contents :
Contents
Acknowledgements
Introduction
1 A New Interest in Modal Logic
2 Early 12th-Century Sources on Modalities
3 Abelard’s Texts on Modalities
Part 1. Early 12th-Century Debates on Modal Propositions
Introduction to Part 1
1. The Received Views on Modalities
1 Necessity as Sempiternity and Immutability
2 Possibility as Potentiality
3 ‘One-Sided’ Possibility and Possibilities extra-actum
4 Absolute versus Temporally Qualified Modalities
2. The Grammar and Syntax of Modal Claims
1 What Is a Mode? Grammatical and Logical Perspectives on Modalities
2 Proper and Improper Modes
3 Adverbial and Nominal Modes
3. The Nature of Modalities and the Signification of Modal Terms
1 What Do Modal Terms Signify?
2 Do Modal Terms Refer to Things or to Propositions?
3 Possibility as Compatibility with Nature
4 Necessity as Inevitability and Immutability
Part 2. Abelard’s Modal Logic
Introduction to Part 2
4. Abelard on de re and de dicto Modalities
1 The de re/de dicto Distinction in the Dialectica
2 The Development of the Distinction in the Logica Ingredientibus
5. The Existential Import of Modal Propositions
1 The Existential Import of Propositions de puro inesse
2 The Existential Import in de rebus and de sensu Modal Claims
3 Existential Import and the Modal Square of Oppositions
6. The Logic of Modal Propositions
1 Abelard on the Syntactic Structure of de rebus Modal Propositions
2 Oppositions and Equipollences
3 Modal Principles of Inference, Conversions, and Syllogistics
7. Simple and Determinate Modal Propositions
1 Abelard on Temporally Qualified Modalities
2 On the Meaning of the dum-Clause
3 The Logic for Determinate Modal Propositions
4 Another Puzzle Raised by Determinate Modal Propositions
Part 3. Abelard on the Metaphysics and Epistemology of Modalities
Introduction to Part 3
8. Natures and Modalities
1 Two Primitive Concepts in Abelard’s Modal Language
2 Abelard on Natures and Nature
3 Abelard’s Modalities and Possible Worlds
9. Abelard on the Many Senses of Possibility
1 Any Man Can Be a Bishop: Possibility as Non-repugnancy with Nature
2 Humans Who Cannot Laugh and Uncoloured Bodies: Unrealizable but ‘Conceivable’ Possibilities
3 Amputees Can Walk and Crippled Men Can Fight: Abelard’s Distinction between Simple and Determinate Potencies
4 Might a Blind Person Have Been Able to See? Abelard on Past and Counterfactual Potencies
5 Dead Humans and Irrational Humans: Other Puzzling Cases of de re Possibilities
10. Necessity, Determinacy, and Contingency
1 Three Ways to Characterize Necessity
2 Determinacy and Contingency in Abelard’s Comments on De Interpretatione 9
3 Abelard against Logical Determinism
4 Abelard on Theological Determinism and the Dilemma of Divine Foreknowledge
Conclusion
Bibliography
Manuscripts
Primary Sources
Secondary Sources
Index

Citation preview

Possibility and Necessity in the Time of Peter Abelard

Investigating Medieval Philosophy Managing Editor John Marenbon

Editorial Board Margaret Cameron Thérèse Cory Nadja Germann Simo Knuuttila Martin Lenz Charles H. Manekin Christopher J. Martin

volume 16

The titles published in this series are listed at brill.com/imp

Possibility and Necessity in the Time of Peter Abelard By

Irene Binini

leiden | boston

Library of Congress Cataloging-in-Publication Data Names: Binini, Irene, author. Title: Possibility and necessity in the time of Peter Abelard / by Irene Binini. Other titles: Investigating medieval philosophy ; v. 16. Description: Leiden ; Boston : Brill, 2022. | Series: Investigating medieval philosophy, 1879-9787 ; volume 16 | Includes bibliographical references and index. | Contents: Introduction -- Early 12th-century debates on modal propositions. The received views on modalities; The grammar and syntax of modal claims; The nature of modalities and the signification of modal terms -- Abelard’s modal logic. Abelard on de re and de dicto modalities; The existential import of modal propositions; The logic of modal propositions; Simple and determinate modal propositions -- Abelard on the metaphysics and epistemology of modalities. Natures and modalities; Abelard on the many senses of possibility -- Conclusion. Identifiers: LCCN 2021035289 (print) | LCCN 2021035290 (ebook) | ISBN 9789004470286 (hardback) | ISBN 9789004470460 (ebook) Subjects: LCSH: Abelard, Peter, 1079-1142. | Modality (Logic) | Logic, Medieval. | Philosophy, Medieval. Classification: LCC B765.A24 B48 2022 (print) | LCC B765.A24 (ebook) | DDC 160–dc23 LC record available at https://lccn.loc.gov/2021035289 LC ebook record available at https://lccn.loc.gov/2021035290

Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill-typeface. issn 1879-9787 isbn 978-90-04-47028-6 (hardback) isbn 978-90-04-47046-0 (e-book) Copyright 2022 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Brill Nijhoff, Brill Hotei, Brill Schöningh, Brill Fink, Brill mentis, Vandenhoeck & Ruprecht, Böhlau Verlag and V&R Unipress. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Requests for re-use and/or translations must be addressed to Koninklijke Brill NV via brill.com or copyright.com. This book is printed on acid-free paper and produced in a sustainable manner.

To Andrea To Davide, who, when this book was started, was like Abelard’s ‘possible future son’ To our other little ones, who have remained in the realm of possibility

∵

Contents Acknowledgements xi

Introduction 1 1 A New Interest in Modal Logic 1 2 Early 12th-Century Sources on Modalities 2 3 Abelard’s Texts on Modalities 10

PART 1 Early 12th-Century Debates on Modal Propositions

Introduction to Part 1 14

1

The Received Views on Modalities 15 1 Necessity as Sempiternity and Immutability 19 2 Possibility as Potentiality 26 3 ‘One-Sided’ Possibility and Possibilities extra-actum 30 4 Absolute versus Temporally Qualified Modalities 33

2

The Grammar and Syntax of Modal Claims 45 1 What Is a Mode? Grammatical and Logical Perspectives on Modalities 45 2 Proper and Improper Modes 54 3 Adverbial and Nominal Modes 62

3

The Nature of Modalities and the Signification of Modal Terms 75 1 What Do Modal Terms Signify? 75 2 Do Modal Terms Refer to Things or to Propositions? 84 3 Possibility as Compatibility with Nature 90 4 Necessity as Inevitability and Immutability 103

PART 2 Abelard’s Modal Logic

Introduction to Part 2 118

4

Abelard on de re and de dicto Modalities 120 1 The de re/de dicto Distinction in the Dialectica 121

viii

Contents

2

The Development of the Distinction in the Logica Ingredientibus 130

5

The Existential Import of Modal Propositions 142 1 The Existential Import of Propositions de puro inesse 143 2 The Existential Import in de rebus and de sensu Modal Claims 148 3 Existential Import and the Modal Square of Oppositions 150

6

The Logic of Modal Propositions 157 1 Abelard on the Syntactic Structure of de rebus Modal Propositions 158 2 Oppositions and Equipollences 164 3 Modal Principles of Inference, Conversions, and Syllogistics 169

7

Simple and Determinate Modal Propositions 177 1 Abelard on Temporally Qualified Modalities 177 2 On the Meaning of the dum-Clause 182 3 The Logic for Determinate Modal Propositions 187 4 Another Puzzle Raised by Determinate Modal Propositions 194

PART 3 Abelard on the Metaphysics and Epistemology of Modalities

Introduction to Part 3 200

8

Natures and Modalities 202 1 Two Primitive Concepts in Abelard’s Modal Language 202 2 Abelard on Natures and Nature 206 3 Abelard’s Modalities and Possible Worlds 214

9

Abelard on the Many Senses of Possibility 230 1 Any Man Can Be a Bishop: Possibility as Non-repugnancy with Nature 235 2 Humans Who Cannot Laugh and Uncoloured Bodies: Unrealizable but ‘Conceivable’ Possibilities 240 3 Amputees Can Walk and Crippled Men Can Fight: Abelard’s Distinction between Simple and Determinate Potencies 248 4 Might a Blind Person Have Been Able to See? Abelard on Past and Counterfactual Potencies 255 5 Dead Humans and Irrational Humans: Other Puzzling Cases of de re Possibilities 261

Contents 

10

Necessity, Determinacy, and Contingency 271 1 Three Ways to Characterize Necessity 271 2 Determinacy and Contingency in Abelard’s Comments on De Interpretatione 9 276 3 Abelard against Logical Determinism 280 4 Abelard on Theological Determinism and the Dilemma of Divine Foreknowledge 294



Conclusion 308



Bibliography 311 Index 324

ix

Acknowledgements The research leading to this book originated during the time I spent as a PhD student at the Scuola Normale Superiore in Pisa. My first debt of gratitude is thus to Massimo Mugnai, who supervised my doctoral work, offering constant insight and support, and to all friends and colleagues from the Scuola ­Normale. I am deeply grateful to John Marenbon and Chris Martin, for guiding me through the fascinating subtleties of Abelard’s modal thought, and for their generous hospitality and kindness during my visiting periods in Cambridge and Auckland. I would also like to extend my gratitude to all Professors who have supervised my post-doctoral work: Anna Marmodoro at the University of Oxford; Nadja Germann at the University of Freiburg; Peter King in Toronto and Fabrizio Amerini in Parma, who, more than anyone else, has offered me valuable career advice and guidance during the last two years. This study could not have been done without the help of scholars who shared their unpublished and in-progress transcriptions of 12th-century logical sources with me. I especially would like to thank Yukio Iwakuma, Onno Kneepkens, Peter King and Chris Martin for giving me access to their in-progress editions and transcriptions of many of the sources that will be mentioned in the book. I owe more than an acknowledgment to Caterina Tarlazzi and Wojciech Wciórka, who have given me irrepleceable help with many of the transcriptions from manuscripts on which the following research is based, and who allowed this study to grow thanks to many conversations on 12th-century logic and the constant feedback that they have offered me. Finally, a sincere thanks to Bianca Bosman and Amanda George, who have proofread the manuscript, and to Marcella Mulder from Brill, for being a very thoughtful and supporting editor. I owe to my family – my parents Marina and Emilio, my parents-in-law Donatella and Pietro, and my husband Andrea – the time and the focus that I needed to complete this book during early motherhood first and a pandemic later. For all your support and help (and food), thank you.

Introduction 1

A New Interest in Modal Logic

Peter Abelard shares with many philosophers of his time a special interest in investigating the notions of possibility and necessity, and in providing them with a crucial role in logic, metaphysics, and theology. Although modalities had already been discussed by philosophers and logicians during the High Middle Ages, it is at the beginning of the 12th century that the analysis of modal propositions became a topic of central importance, for a number of reasons. One motive has to do with the changes in the logical curriculum established in the 11th century, which led logicians of this time to focus almost entirely on Boethius’ translations and commentaries on the Organon and on his logical monographs, after a progressive abandoning of other sources that had been influential during the 8th to 10th centuries.1 Of this new logical curriculum, several texts inspired – or better, required – a deeper reflection on modals. One was Aristotle’s De Interpretatione, two chapters of which were entirely devoted to modal logic and a further one to the nature of necessity and contingency. Another source was Boethius’ De Hypotheticis Syllogismis, which, building on the Greek commentary tradition, distinguished between different kinds of possibility and necessity. A third text was Aristotle’s Prior Analytics: even though logicians of the time were not directly acquainted with this work, they were aware that Aristotle described in it a system of modal and mixed syllogistics, and many of their reflections were driven by the aim to interpret modal propositions accordingly, making them suitable for use in syllogistic reasoning. A second reason why early 12th-century logicians emphasized the role of modalities was their interest in theories of conditionals and topical arguments, an interest inspired by Boethius’ monographs on the Topics. Following Boethius, they believed that the validity of an argument depended on some necessary connection holding between its premises and conclusion. Providing an analysis of the nature of necessity was then decisive to grounding their interpretation of loci. This is especially true for Peter Abelard, whose long discussion of conditionals in the Dialectica strongly relies on his reflection on the meaning of necessity and, in particular, on his understanding of necessity in terms of ‘immutability’. Abelard says that, indeed, the necessity 1 For a survey on the logical sources that were mostly influential in the High Middles Ages and on the ‘Boethian turn’ in logic taking place in the 11th and early 12th centuries, see (Marenbon 2008b). © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_002

2

Introduction

and ‘stability’ (firmitas) of a consequence consists in the immutable relation holding between two terms and between the nature of the things that these terms signify. As we will see, this understanding of necessity was very common in Abelard’s time and developed in a number of sources contemporary to his Dialectica. Finally, the interest of early 12th-century authors in the logic of necessity and possibility was driven by their desire to take a stance on the theological debates concerning God’s omnipotence and omniscience, which were raised in antiquity by Augustine and Boethius and further developed by late 11thcentury masters such as Anselm of Canterbury and William of Champeaux. Drawing once more on the legacy of Boethius, Abelard’s contemporaries felt encouraged to address these questions with a dialectical and analytical approach, which required them to engage in the definition of the notions of necessity, potency, and power and to provide a logical examination of them. Thanks to a deeper understanding of the nature of modal operators, Abelard and his contemporaries were able to deal with the theological issues related to divine omnipotence and omniscience by appealing to new dialectic tools, such as a syntactic and semantic analysis of the scope of modal terms and of temporally indexed modalities. 2

Early 12th-Century Sources on Modalities

The list of early 12th-century logical texts dealing with modalities and modal logic is extremely rich and varied, although difficult to manage in full since many of the relevant texts are still unedited and present uncertainties with respect to their authorship, dating, and circulation. In recent years scholars have made the effort to transcribe, edit, and catalogue this variegated material, preparing the ground for a systematic study of their content.2 However, 2 Major work in this field has been done by Yukio Iwakuma, who privately transcribed and generously shared with me and other researchers many of the logical texts to which I will refer in this book. Other important transcriptions and editions of early 12th-century logical material have been done recently, building on the existing work of De Rijk and Green-Pedersen, by several scholars, including E.P. Bos, I. Rosier-Catach, S. Ebbesen, A. Grondeux, H. Hansen, K. Jacobi, P. King, C.H. Kneepkens, C.J. Martin, J. Spruyt, C. Tarlazzi, and W. Wciórka. Apart from editions, logical texts from the 11th and 12th centuries have been catalogued in several contexts. Green-Pedersen has listed commentaries on Boethius’ De Differentiis Topicis in (GreenPedersen 1984). John Marenbon catalogued commentaries on Isagoge, Categories, and De Interpretatione in his ‘Working Catalogue’ in (Marenbon 2000b). He also offered a survey of early 12th-century logical texts in (Marenbon 2011). Other catalogues of commentaries

Introduction

3

interpreters have just begun to comprehend the elaborate architecture of early 12th-century logic and to unravel the system of interrelations existing among the various manuscripts, the texts they contain, and the theories offered in them. Apart from the works of Peter Abelard and a few other exceptions, sources from the first half of the 12th century concerning modal logic and theories of modalities have not yet been the object of careful study or of systematic comparison with Abelard’s modal thought.3 In Part I of this book I attempt to offer such a study and comparison, focusing on a number of problems concerning the syntax and semantics of modal propositions that were commonly debated by Abelard’s contemporaries. In Parts II and III I then turn to the details of Abelard’s own modal logic and theory of necessity, possibility, and contingency. Among all logical texts from the first half of the 12th century, we may identify four groups of sources containing discussions on modal logic: i. The larger group is constituted by the commentaries on De Interpretatione (catalogued by Marenbon as ‘H-commentaries’), where issues concerning modalities were usually debated in relation to Chapters 9 and 12–13. As Marenbon has pointed out, before the 11th century there was no proper Gloss Tradition for De Interpretatione,4 and although there are some individual manuscripts that contain glosses on it (one example is the 10th-century Leiden manuscript, which will be considered on pp. 108–9), they are very rare.5 In the 10th and early 11th centuries, commentaries on De Interpretatione were written by leading logicians such as Gerbert of Aurillac and Nokter Labeo, but it is only from the beginning of the 12th century that the number of surviving commentaries on the Aristotelian

on De Divisione, De Syllogismis Categoricis, and De Syllogismis Hypotheticis have been completed by Iwakuma but remain unpublished. Marenbon and Tarlazzi have recently published a study on 12th-century manuscripts containing logical material in (Marenbon and Tarlazzi 2018). 3 One important exception is the analysis of two anonymous treatises on modalities, M1 and M3, offered by Christopher Martin in (Martin 2016). For another introductory study of modal theories in unedited sources from the first half of the 12th century, see also (Binini 2019b) and (Binini 2020a). 4 With ‘Gloss Tradition’ is intended the tradition established in the 9th to 11th centuries of annotating manuscripts in the margins and between lines (Marenbon 2008b, p. 34). As Marenbon says, this tradition was very common in the High Middle Ages on logical sources such as Martianus Capella, the Categorie Decem, the Isagoge, while it is absent on the Categories and De Interpretatione. See on this (Marenbon 2008b, pp. 34–7). See also (Marenbon 1981); (Marenbon 2000a) and (Marenbon 2000b). 5 (Marenbon 2008b, p. 37).

4

Introduction

work rises significantly: Marenbon lists more than 20 of them, datable from 1100 to circa 1150, of both the literal and composite type.6 Of these, only some are relevant to our discussion, since not all surviving commentaries contain glosses on the relevant chapters of the Aristotelian work. Particularly important for early 12th-century theories of modalities are the two literal commentaries labelled H47 and H5,8 both traditionally considered early works by Peter Abelard, although this attribution has recently been criticized.9 Other important texts that are likely to be dated to the first quarter of the century (or at least before c.1120) are the unedited commentaries H9 and H11, the first of which contains a commentary on both Chapter 9 and 12–13 of De Interpretatione, while the second ends after discussing Chapter 10. The two texts are closely related, being very similar or even identical in some parts. Each is preserved in two manuscripts,10 which is quite uncommon for logical sources of this time (usually surviving in only one copy) and might be a sign that they were particularly influential on later authors.11 According to Iwakuma, the commentary on De Interpretatione labelled H9 is a revision of H11, and both are connected to William of Champeaux and his school.12 This attribution, although controversial,13 is in my view strengthened by the fact that in the Dialectica Abelard refers to some of the ideas invoked in 6 7 8

9 10

11 12

13

(Marenbon 2000b, pp. 116–22). Found in manuscript: Paris, Bibliothèque nationale de France, lat. 13368, fols 128r–144v. Edited in (Abaelard 1969a) and attributed by the editor Mario Dal Pra to Peter Abelard. Found in manuscript: Munich, Bayerische Staatsbibliothek, Clm. 14779, fols 44r–66r. This commentary is still unedited. I am very grateful to Yukio Iwakuma, who shared with me his transcription of H5. This set of glosses shows many similarities with H4, as Cameron and Martin have pointed out: see (Cameron 2011, pp. 655–8) and (Martin 2011, p. 607), although the Munich version is longer and more complex than the Parisian one (cf. Marenbon 2000a, pp. 47–8). See (Cameron 2011) and (Martin 2011). On the attribution of H5 to Abelard, see (Iwakuma 1999). H9: Orléans, Bibliothèque municipale, 266, pp. 5a–43a; Assisi, Biblioteca Conventuale Francescana, 573, fols 48rb–67vb. H11: Paris, BnF, lat. 13368, fols 225r–31r; Vatican City, ­Biblioteca Apostolica Vaticana, reg. lat. 230, fols 80r–7r. I am deeply grateful to C.H. Kneepkens, who gave me access to his in-progress transcription of H9. See (Marenbon and Tarlazzi 2018, p. 222). See (Iwakuma 1999) and (Iwakuma 2003). Margaret Cameron questions this attribution in (Cameron 2004). In this article Cameron also advances the proposal to momentarily abandon the effort of attributing early 12th-century logical texts to specific masters and to rather identify them using the common centre of their production (in this case, Notre Dame). The strategy of organizing this material by connecting each text to a school or a master may be, in her opinion, premature for logical commentaries datable to this period (Cameron 2004, p. 114). See, in particular (Marenbon 2008a, p. 77); (Jacobi 2011, pp. 267–70).

Introduction

ii.

14 15 16 17 18

19

5

H9 and connects them to his Master, commonly believed to be William of Champeaux.14 Whether it is by William’s school or not, H9 was most likely known by Abelard at the time in which he wrote the Dialectica, since he reports – and at times corrects – many of the ideas contained in it. Another commentary on De Interpretatione, labelled H8 in Marenbon’s catalogue, was written by Abelard probably in 1115–1120 and is included in the Logica Ingredientibus (H8 will henceforth be referred to as LI De Int).15 This commentary is of a composite type,16 meaning that Aristotle’s text is first discussed discursively, in long introductions that Abelard provides at the beginning of every chapter, and then literally, by means of a phrase-to-phrase commentary. I will return briefly to the content and dating of this text, which contains, together with the Dialectica, the core of Abelard’s views on modalities. A discussion on modal propositions is also included in the two commentaries H13 and H20, which are presumably datable to the second quarter of the century and are both preserved in the Orléans manuscript, which also contains H9.17 We then have two other commentaries on De Interpretatione containing a treatment of modals, labelled H17 and H15 (the last recently edited as the ‘Glossae Doctrinae Sermonum’),18 supposedly to be dated from the 1130s and whose authors both display partial knowledge of Abelard’s Logica Ingredientibus. Finally, topics concerning modalities are raised in the unedited ‘Summa Periermeneias’, catalogued as H21,19 probably dating from the mid-12th century but which seems more advanced than all the commentaries considered so far with respect to some of the ideas presented in it (for instance, the distinction between the de re and de dicto interpretation of modals). Apart from the ones on De Interpretatione, there are other commentaries that contain significant discussions on modalities. Within the corpus of See, for instance, the theory on modal conversions exposed in H9, which is discussed in Chapter 6. Edited by Geyer in (Abaelard 1927), and more recently re-edited by Jacobi and Strub in (Abaelard 2010b). References are to the Jacobi-Strub edition. See (Marenbon 2011, p. 185). H13: Orléans, Bibl. mun., 266, pp. 237–57; H20: Orléans, Bibl. mun., 266, pp. 257–63. See Anonymous, Glossae Doctrinae Sermonum, in (Abaelard 2010a). H15 is found in manuscripts: Paris, Bibliothèque nationale, lat. 15015, fols 180r–99r and Vienna, Österreichische Nationalbibliothek, cvp. 2486, fol. 6r (a short fragment). H17 is found in manuscript: ­Berlin, Deutsche Staatsbibliothek, lat. 624, fols 87v–96v. This dating is proposed by De Rijk in (De Rijk 1966). H21 is found in manuscript: Paris, Bibliothèque de l’Arsenal, 910, fols 83r–91r.

6

Introduction

the logica vetus, questions concerning the notions of potency and impotency were raised in Aristotle’s Categories and in Boethius’ commentaries on it, whereas issues about the modal relation holding between a substance and its properties were debated in Porphyry’s theory of separable and inseparable accidents included in the Isagoge. We therefore find some discussions on modal notions in early 12th-century commentaries on the Isagoge (catalogued as ‘P-commentaries’) and on the Categories (‘C-commentaries’). Among these, I will consider, in particular, the definitions of the term ‘necessarium’ presented in P14, P15, P16, and P17, all presumably dating from the first half of the 12th century,20 as well as the ‘Glossae Secundum Vocales’ (P11; henceforth: GSV)21 and the Logica Nostrorum Petitioni Sociorum (P12; henceforth: LNPS),22 both connected to the teaching of Peter Abelard. Abelard is also the author of a commentary on the Isagoge and the Categories (catalogued respectively as P10 and C10), which are part of the Logica Ingredientibus (I henceforth refer to these respectively as LI Isag and LI Cat).23 Moreover, the nature of possibility and necessity was discussed by Boethius in his De Hypotheticis Syllogismis,24 text that was also often glossed and commented upon during the 11th and 12th centuries in the so-called ‘SH-commentaries’. Particularly interesting are the discussions on modalities presented in SH2,25 which is found in the same manuscript as H5 and has some correlations with it, and in SH3 and SH4, preserved in the same MS Orléans, Bibl. mun. 266, which also contain many of the other logical texts listed here. iii. Another group of relevant sources are a number of short treatises surviving from the first half of the 12th century, which are entirely devoted to the discussion of modal propositions. Among these, there are two 20 21

22 23 24 25

P14: Paris, Bibliothèque nationale, lat. 17813, fols 1r–16v; P15: Dublin, Trinity College, 494, fols 113r–118v; P16: Munich, Bayerishe Staatsbibliothek, Clm. 14458, fols 83r–93r; P17: Paris, Bibliothèque nationale, lat. 3237, fols 125r–130r; ibid., lat. 3237, fols 123 r–124v. P11 is preserved in manuscript: Milan, Biblioteca Ambrosiana, M 63 sup., fols 73r–81v. It was edited in (Abelard 1933b) by Ottaviano. I am thankful to Peter King and Christopher ­Martin for giving me access to the in-progress edition that they are preparing of the ­Glossae Secundum Vocales and the Logica ‘Nostrorum Petitioni Sociorum’. This commentary is preserved in manuscript: Lunel, Bibliothèque municipale, 6, fols 8r–41r. It has been edited by Geyer as Logica ‘Nostrorum Petitioni Sociorum’ in (Abaelard 1933a) and attributed to Peter Abelard. LI Isag: ‘Glossae super Porphyrium’, edited in (Abaelard 1919); LI Cat: ‘Glossae super Categorias’, edited in (Abelard 1921). (Boethius 1969). SH2 is to be found in manuscript: Munich, Bay., Clm. 14779, fols 67v–86v; SH3 in Orléans, Bibl. mun., 266, pp. 118a–119b; SH4 in Orléans, Bibl. mun., 266, pp. 264a–276a.

Introduction

iv.

26

7

a­ nonymous treatises labelled by Iwakuma M1 and M3, both preserved in MS Orléans 266, with the first also to be found in MS Paris, BnF lat. 13368.26 The two texts are presumably from the same years in which Abelard wrote the Dialectica (1110–1115), and although there is no explicit mention of Abelard in them, the wording, examples, and issues that they discuss are very similar to the ones employed and considered in the Dialectica. Yet their authors seem to have no knowledge of the novelties introduced by Abelard in the Logica Ingredientibus. Both M1 and M3 mention contemporary masters, such as a certain ‘Magister W.’ (probably, William of Champeaux) and a ‘Magister G.’ or ‘Gos.’ (Joscelin of Soissons). The two treatises also have some similarities with the two commentaries H13 and H20, which are preserved in the same manuscript and seem to be connected to Joscelin’s school. A third anonymous treatise on modals is to be found at the end of Abelard’s Glossae on De Interpretatione in the Milan manuscript27 and was recently edited as ‘De Propositionibus Modalibus’ by Jacobi and Strub.28 This short treatise is probably to be dated after 1120, for the author shows some knowledge (at least partial) of Abelard’s commentary on De Interpretatione included in the Logica Ingredientibus. The treatise also reports ideas that are not Abelardian but seem to depend on the teaching of other masters. With respect to these, the De Propositionibus Modalibus presents some similarities with contemporary works connected to Joscelin’s school, such as M1, M3, and H20.29 Finally, a fourth text on modalities, which should be considered more as a collection of notes than an independent treatise, is preserved in the same manuscript that also includes Abelard’s De Intellectibus, placed right after it and copied by the same hand.30 This text includes an interesting discussion of modal propositions containing temporal clauses and other sorts of qualification, and its author is probably aware of the same discussion provided by Abelard in the Logica Ingredientibus. To conclude, several texts remain from the first half and the mid-12th century, which have the form of longer independent treatises.31 Among

M1 = Orléans, Bibl. mun., 266, pp. 166a–169a; Paris, BnF, lat. 13368, fols 175va–177ra. M3 = Orléans, Bibl. mun., 266, pp. 252b–257b. On these treatises see also (Martin 2016). 27 Milano, Biblioteca Ambrosiana M 63 sup., fols 44ra–72rb. 28 Anonymous, De Propositionibus Modalibus edited in (Abaelard 2010a). 29 See, for instance, the discussion on whether nominal modal terms should be taken as referring to words, understandings, or things, discussed in Chapter 3, Section 2 of this book. 30 Avranches, Bibliothèque municipale, 232, fols 68v–71v. 31 See on this (Marenbon and Tarlazzi 2018, pp. 226–8).

8

Introduction

these, the ones that contain a discussion on modalities are Garland’s Dialectica (whose authorship and dating are still controversial)32 and Abelard’s own Dialectica33 (written circa 1110–15). In the book I will also refer to some later treatises, such as the Introductiones Montane Maiores (parts of which are from the 1130s but whose discussion on modalities is probably no earlier than 1150),34 the Compendium Logicae Porretanum (mid-12th century),35 the unedited Ars Meliduna (written presumably between 1160 and 1175),36 and the Summa Dialectice Artis by William of 32

The authorship of this textbook is still a debatable issue. Iwakuma argued that the author should be identified with Gerlandus of Besançon, who died after 1148, and not with the earlier Garlandus, who was believed to be the author by De Rijk; see (Iwakuma 1992, pp. 47–54). Because of the uncertainty concerning the authorship, the dating of the Dialectica is still an open question. Marenbon suggests that the text could have been written in a time period going from the 1080s (or even earlier) up to the 1120s (Marenbon 2011, pp. 194–6). With respect to the theories of modalities presented in it, however, the text seems rather primitive when compared to other texts on modalities from the first two decades of the 12th century: no treatment of quantified modal propositions is offered, or any analysis of the semantic ambiguities related to the scope of modal operators, or a theory on the logical relationships holding between modal propositions with temporal determinations, all topics that are developed from the 1110s onward by Abelard and others. Based on this part of the book, I would then be inclined towards an early dating, not later than the 1110–1115. 33 (Abaelard 1970). 34 The Introductiones Montane Maiores are a collection of notes of logical content that, according to their editors, were produced by the school of the Montani, which was established on the Mont St Geneviève from the 1130s, along with other logical schools of the Nominales, Parvipontani, Meludinenses, and Porretani – (Bos and Spruyt 2017, p. x); but see (Iwakuma 2013, p. 29) for a challenge to the identification of Montani with Albricani. The Maiores are dominated by the teachings of Master Alberic of Paris, but they also inherit some theses from Abelard’s and Robert of Melun’s theories. References to Abelard in the past tense, along with other observations, led De Rijk to date the earlier parts of the Maiores between 1130 and 1140. However, the part of the tract that I will consider in this book – which contains an inquiry on modal propositions and on syllogismi incisi – was dated by De Rijk to a later period, probably no earlier than 1150. On the discussion concerning the dating of the Maiores, see (De Rijk 1966) and (Bos and Spruyt 2017, pp. xii– xiii). A critical edition of the text, preserved in manuscript Paris, Bibliothèque nationale, lat. 15141, fols 47ra–104ra, was recently published in (Bos and Spruyt 2017). On the Maiores and the school of the Montani, see (De Rijk 1966); (Iwakuma 2004); (Bos and Spruyt 2017, pp. ix–xliv). 35 The Compendium is edited in (Martin 1983). 36 The Ars is an unedited work by the school of Meludinenses and is preserved in manuscript Oxford, Bodleian Library, Digby 174, fols 211–241. Excerpts of it are in (De Rijk 1967, vol. I, pp. 292–390). The date of the Ars Meliduna is still very uncertain. On one occasion, De Rijk dated it as early as the mid-12th century (De Rijk 1982, p. 165), but, as Ebbesen noted, a more reasonable date seems to be around 1175. See on this (Ebbesen 2013, p. 70).

Introduction

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Lucca (?), supposedly written circa 1175–94.37 I will also mention a few other treatises whose dating is still uncertain but which are probably also written in the middle or second half of the 12th century, such as the Excerpta Norimbergensia38 and the Ars Burana.39 Many of the commentaries and treatises listed here are characterized by a number of features that, as Marenbon and Tarlazzi have noticed, are common to almost all logical texts from the first half of the 12th century.40 Apart from a few exceptions, these texts are preserved as unique copies in a single manuscript, and the few that are preserved in two manuscripts (H9, H11, H15, M1, and Abelard’ works) present significant differences in their two versions. These variances are a sign of the ‘fluidity’ of these texts,41 which are often the result of a ‘layered’ and constantly evolving composition, to which different authors could have contributed at different moments of time (or the same author at different stages of his career), so that the notions of ‘authorship’ and even of ‘same text’ are not always appropriate or applicable to them.42 Moreover, although many of these texts report references to masters of the time (such as William of Champeaux, Abelard, Alberic, or Joscelin), the texts themselves are generally anonymous, with the exception of Abelard’s works. As Marenbon has suggested, this anonymity should not be understood as if these texts’ authors are not yet identified but rather as an ‘essential anonymity’, in the sense that no single author can be pinpointed as being responsible for all the details of the theories reported in them or for a text’s many layers of composition.43 37 The Summa has been edited in (Guglielmo da Lucca 1975). The attribution of this text to William of Lucca is doubtful (Gastaldelli 1977); what is certain is that the author is a deferent follower of Peter Abelard and of the teaching of the Nominales. As its editor says, the Summa – which he dates between the 1175 and 1194 – seems to have had no circulation or influence outside the territory of Lucca (Guglielmo da Lucca 1975, p. 6). Nonetheless, the text is interesting, for it shows how some Abelardian theses survived (although at times with relevant modifications) in the second half of the 12th century. As Martin suggested, this text might be considered something of a ‘Compendium Logicae Nominalium’ (Martin 2001, p. 116). 38 Anonymous, Excerpta Norimbergensia in (De Rijk 1967, vol. II, pp. 109–41). 39 Anonymous, Ars Burana in (De Rijk 1967, vol. II, pp. 175–213). 40 On these characteristics, see (Marenbon and Tarlazzi 2018, pp. 221–6). 41 (Marenbon and Tarlazzi 2018, p. 222). 42 Cf. (Rosier-Catach 2011, p. xiii). On the notion of ‘layered text’ in early 12th-century texts, see (Marenbon 2008a, p. 67); (Rosier-Catach 2011, pp. xii–xvi); (Marenbon 2011, pp. 186–7). 43 (Marenbon 2011, p. 187).

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Another interesting feature noticed by Marenbon and Tarlazzi regards the manuscripts in which these texts are preserved, which usually contain not a single text but collections of logical works: for instance, MS Orléans 266 contains H9, M1, M3, H13, H20, SH3, and SH4; MS Munich 14779 contains H5 and SH2; MS Milan 63 includes Abelard’s Logica Ingredientibus and also the anonymous De propositionibus Modalibus; MS Paris BnF lat. 13368 contains M1, H4, and H11; and MS Berlin 624 includes Abelard’s glosses on De Interpretatione (=H8), H17 and SH1. It has been shown that logical manuscripts are also interrelated in such a way that they transmit similar collections of texts.44 3

Abelard’s Texts on Modalities

From this composite group of sources, Abelard’s Dialectica and his commentary on De Interpretatione stand out for the systematic approach and depth of insight with which modal notions are analysed. Within the Dialectica, modal propositions and their properties are discussed as part of the theory of categorical propositions, to which the second treatise is devoted. In Dial. 191–210, the author defines what ‘modes’ are and considers the morphological and syntactic features of the propositions containing them, insisting, in particular, on how to correctly construe negation and quantification in modal claims and on the semantic ambiguities raised by the scope of modal terms, or by their interaction with other logical operators, such as negation or temporal determinations. He also provides a scheme of the logical relationships occurring among modal claims, defining the rules of opposition and equipollence that govern their logic. Furthermore, Abelard devotes various passages to presenting his semantics for modal propositions and his interpretation of the meaning of necessity and possibility. Within the Dialectica, issues concerning modalities are also investigated in Dial. 210–221, where Abelard focuses on the connection between modalities and time and, in particular, asks how modal terms interplay with implicit temporal indexes in propositions de praeterito, de praesenti, and de futuro. The notion of possibility is further investigated within the treatise on qualities in Dial. 93–99, where Abelard discusses his theory of potencies and impotencies, while the notion of necessity has a crucial role in Abelard’s discussion of topical inferences in Dial. 253–413. As for the glosses on De Interpretatione, a discussion on modal propositions is carried out within the long introduction opening the commentary on 44

(Marenbon and Tarlazzi 2018, pp. 223–4).

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Chapters 12 and 13 (LI De Int. 391–433). Many of the topics raised in the Dialectica return here, such as the analysis of the relation between adverbial and nominal modes, the rules for construing negation and quantification in modal propositions, and the system of inferences and equipollences that are valid for them. Moreover, Abelard deals with modalities in his commentary on De Interpretatione 9 (LI De Int. 243–268), where he offers a detailed treatment of the notion of contingency and of the different sorts of necessity, a discussion that has many terminological and doctrinal similarities with the parallel analysis in Dial. 210–221. Indeed, despite a few differences, Abelard’s two logical works are very similar, both with respect to the problems that they consider and the order in which they are presented, and also with respect to the fundamental theoretical traits that they offer. This similarity seems to confirm the idea that the two works were written only a few years apart, probably in the second decade of the 12th century, with the Dialectica written circa 1110–1115 and the Logica a few years after that. The Logica might have been subject to revision or extension in the years from 1121 to 1127, when Abelard lived and lectured on logic in the ‘Paraclete’ Oratorium.45 Nevertheless, some discrepancies between the two Abelardian works might still be traced, and there is evidence that the theory presented in the Logica Ingredientibus is more mature than the one offered in the Dialectica, of which it corrects or improves a number of aspects. The main differences concern semantic issues such as the distinction between the de rebus and de sensu interpretations of modals (in particular, with respect to the problem of how de rebus and de sensu propositions are logically related to one another); the existential import of modal claims and also the semantic relation between necessity- and possibility-propositions. Moreover, in the Logica Ingredientibus the influence that the grammatical tradition had on the development of Abelard’s modal thought is much more evident: there is a stronger insistence on the linguistic and grammatical aspects of modes and modal propositions, such as the analysis of nominal claims as impersonal predications; questions about the lexical category to which modal terms belong; and issues concerning the twofold signification of modal terms, that is, their denotative aspects and the understandings that they generate in the mind of the hearer. 45

On the chronology of these two works, see, in particular, (Mews 1985, pp. 73–134); (Marenbon 1997, pp. 36–53); (Brower and Guilfoy 2004, pp. 6–8); (Jacobi and Strub 2010, pp. LXIII–IV).

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PART 1 Early 12th-Century Debates on Modal Propositions

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Introduction to Part 1 Part I of this book aims to present the logical and grammatical context in which Abelard’s modal theories originated, considering the debates on modalities that are put forward in published and unpublished treatises and commentaries of his time. I shall start by taking into consideration the sources on which Abelard and his contemporaries relied for construing their modal thought. Chapter 1 offers a survey of the ancient and early medieval paradigms that influenced 12th-century views on modalities, focusing, in particular, on their main source in this field, namely, Boethius. In Chapters 2 and 3 I will then proceed by identifying a number of questions and problems debated in sources of Abelard’s time, seeking to highlight the common elements that they share with respect to their wording, methods of analysis, and the authoritative texts to which they refer. I will also attempt to show that, despite a common background in their approach to modal propositions, and despite a number of common doctrinal elements that all these texts share, different positions were taken in answer to the problems raised by the analysis of modes. In particular, an intense debate was held on two aspects of modal logic. The first concerns the grammatical and syntactic structure of modal propositions, asking how this structure should be properly interpreted, which role the mode plays in it, and how this structure is related to that of non-modal categorical claims (Chapter 2). A second series of problems concerns the signification of modal terms such as ‘possible’ and ‘necessary’, asking whether these names have denotation or not, and whether they should be predicated of things or rather of propositional entities (Chapter 3). I will compare Abelard’s positions on these matters to the rival positions advanced by his contemporaries, and catalogue the arguments that were used in favour of different theories. As we will see, the majority of issues that are covered in Abelard’s works on modalities have a counterpart in contemporary sources, and many of the results that are usually recognized as Abelard’s main innovations in this field were already acknowledged and grasped by some of his contemporaries.

© koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_003

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The Received Views on Modalities Early 12th-century theories concerning the logic and nature of modalities stem from the interplay between different sources and traditions. As was mentioned in the Introduction, the main authority in this field was Aristotle’s De Interpretatione, filtered through Boethius’ translations and commentaries.1 In Chapters 12–13 of this work Aristotle aims to settle two main issues concerning modal propositions: (i) how the negative particle should be included in them in order to obtain their proper contradictory counterparts; and (ii) which logical relationships (contrariness, subalternation, equipollence) hold among possibility-, contingency-, impossibility-, and necessity-propositions. His analysis, like that of Boethius, is limited to the logic of singular or indefinite modal propositions. Early 12th-century logicians will extend this analysis by taking into consideration quantified modal claims. In De Interpretatione 12–13 Aristotle is also interested in defining the proper way to intend the term ‘possible’, which he takes as ambiguous, and its logical relation with the term ‘necessary’. In Chapter 9 of De Interpretatione, which famously focuses on future contingents and logical determinism, Aristotle advances some ideas concerning the nature of contingency and proposes a distinction between the modal status of present and past events (which he claims are in some sense ‘necessary’, on the basis of their having occurred in time) and that of certain future events, which may either occur or not occur. As we will see, all these topics insistently return in the discussions on modalities by Abelard and his contemporaries. Few other Aristotelian sources were available to early 12th-century logicians that might have contributed to shaping their modal thinking. It is still uncertain to what extent they knew the Prior Analytics and how they became acquainted with it. If there was any, their knowledge of this work was very limited, and they had no access to the details of Aristotle’s modal syllogistics (described in Chapters 8–22 of the first book) or to the definition of possibility advanced in Chapter 13 of the same book.2 Nevertheless, as I suggested in the Introduction, knowledge of the Prior Analytics, limited as it was, still had some 1 For Boethius’ translation of De Interpretatione, see (Aristoteles 1965, pp. 5–38). For Boethius’ commentaries, see (Boethius 1877; 1880). 2 Abelard was probably one of the first to have access to the Prior Analytics, but he did not know it in detail. See on this (Minio-Paluello 1954); (Minio-Paluello 1972, pp. 235–6); (Lagerlund 2017). © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_004

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role in shaping early 12th-century modal thought, for all authors of this time were aware that Aristotle used modal propositions to construe syllogisms and hence felt bound to provide an analysis of their syntax and logic compatible with this use – for instance, stating that modal propositions should be variable in quantity and that the same laws of conversion should be valid for them that are valid for other categorical claims. Also some passages from Aristotle’s Sophistical Refutations seem to have inspired early 12th-century modal thought, in particular, Aristotle’s views on the ambiguity of propositions such as ‘It is possible for someone who sits to walk’, which according to him could be read either in a divided sense (that is, as saying that someone who sits has the possibility of walking) or in a composite one (attributing the mode to the conjunction of two predicates, as in ‘someone who sits walks’).3 Abelard quotes this passage in his commentary on De Interpretatione (while no explicit mention of it is made in the Dialectica), and indeed almost all sources of his time, including the presumably earlier ones, such as H4, H5, and H9, take into consideration propositions in which two opposite terms (‘sitting’/‘standing’; ‘human’/‘dead’; ‘young’/‘old’) are said to inhere possibly in the same individual, and discuss their truth-value. Some other sources from the logica vetus, such as the Isagoge and the Categories, stimulated 12th-century logicians’ thoughts on the modal relations existing between a substance and its properties, as well as their views on the potentiae or impotentiae that substances have by virtue of their nature. Abelard and logicians of his time had no access to the other Aristotelian works devoted to modalities. In particular, they ignored the definitions of modal terms given in the Metaphysics and the modal discussions in the De Caelo and De Generatione et Corruptione, which were unavailable at the time. Apart from these logical sources, of crucial importance in shaping the analysis of modal propositions were Priscian’s Intitutiones Grammaticae and the tradition of commentaries known as the ‘Glosulae-complex’, a series of anonymous, ‘layered’ texts of grammatical content, including commentaries on Priscian and the Notae Dunelmenses, which were developed in the late 11th and early 12th centuries.4 Although important for many aspects of early 12th-­century logic (as several authors and in particular Irène Rosier Catach have recently shown), this grammatical background was especially relevant for discussions on modalities. As we will see in Chapter 2, the definition of 3 Cf. Soph. Ref., 166a23–28; Arist. lat. 9, 18–21. 4 For a survey on the Glosulae-complex, including a categorization of all manuscripts, dating, and hypothesis on authorship, see, in particular (Grondeux and Rosier-Catach 2011) and (Grondeux and Rosier-Catach 2017).

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‘mode’ itself, and the analysis of the role that modes play when included in categorical propositions, were based on Priscian’s theory of adverbs. Moreover, many debates involving modal propositions – such as the ones questioning the relation between adverbial and nominal modes – deeply depended on grammatical views connected to the Priscian tradition, which early 12th-century logicians tried to make compatible with the logical analysis of modals provided by Aristotle and Boethius. Also important for the development of early 12th-century modal thought were a number of theological sources and, in particular, some of Augustine’s works, such as his De civitate Dei, De dono perseverantiae, and De praedestinatione. These texts, together with Boethius’ De consolatione philosophiae, contributed to shaping early 12th-century views on contingency and free will, in particular, the theories on how to reconcile contingency with the Christian dogma stating the infallibility and completeness of God’s foreknowledge. It is also not clear whether more recent theological sources, such as the 11th-century works of Peter Damian and Anselm of Canterbury, influenced logicians of Abelard’s time, and to what extent. Some of the topics related to modalities that are treated by Peter Damian and Anselm bear a striking similarity to those that are discussed in early 12th-century sources. One of the most interesting parallels concerns the discussion of the ontological foundations of possibilities that Anselm advances in his Philosophical Fragments.5 This constitutes a major theme for Abelard’s contemporaries as well, some of whom rehearse the same examples and arguments already put forward by Anselm, as we will see in Chapter 3, Sections 1–3. Both Peter Damian and Anselm also discuss other logical and metaphysical issues that become key elements of 12th-century modal theories – for instance, the discrepancies between the grammatical and semantic form of modal claims and the proper/improper use of modal terms; the grounding of modalities in the natura rerum; and the relation between possibilities and potentialities. The direct or indirect influence of these authors on Abelard’s contemporaries, however, still remains to be established.6 Apart from the writings of Anselm and Peter Damian, the theological works written by William of Champeaux (now collected in the Sententiae)7 seem to have had an influence on Abelard’s views on God’s omniscience.8 5 See (Anselm of Canterbury 1969). 6 In Chapter 3, I will return to the relationship between certain problems Anselm raises in connection to modalities and their occurrence in the works of Abelard’s contemporaries. Some similarities between Anselm and Abelard on this matter were already noticed by Henry in (Henry 1967). 7 (Guillelmus Campellensis 1959). 8 See (Guilfoy 2012); cf. Chapter 10, Section 4 on this debate.

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We might then identify, among the many sources that inspired early 12thcentury debates on modalities: (i) a logical and Aristotelian tradition, mostly constituted by some chapters of De Interpretatione and other parts of the logica vetus; (ii) a grammatical tradition going back to Priscian; and (iii) a theological tradition inspired by Augustine and further developed by 11th-century theologians. Against this multifaceted background, however, we may still identify Boethius as the most important source on modalities for logicians of Abelard’s time – and as the main vehicle through which they became acquainted with ancient modal paradigms. In the era that has been defined ‘the Golden Age of Boethian logic’,9 the views on possibility and necessity presented in Boethius’ commentaries on De Interpretatione and in his treatise on hypothetical syllogisms10 had a most profound impact on both the terminology and the methods of analysis. Rather than presenting an independent and innovative account of modals, Boethius offered in his texts a composite theory, in which many elements coming from different modal paradigms are mixed together, and not always in a consistent way. Some of these elements will become central in early 12th-­century discussions of modalities, being either accepted and embraced by Abelard’s contemporaries or attacked and discarded in favour of new paradigms. In the following pages I offer a (far-from-exhaustive) account of Boethius’ modal theory, focusing mainly on the elements that early 12th-century authors inherited from him and incorporated in their discussion on possibility and necessity.11 In my view these elements may be summarized as follows: i. the connection between the notion of necessity and that of sempiternity and immutability. This connection will be incapsulated in the definition of necessity used most frequently by early 12th-century logicians, though alternative non-temporal characterizations will also be provided by ­Abelard and others; ii. the Aristotelian metaphysical view grounding all possibilities in the potencies or potentialities of things, that is, in the capacities, powers, or dispositions that substances have by virtue of some form or property embedded in them. As we will see in Chapter 3, this view will, in fact, be rejected by several 12th-century authors, Abelard included; iii. the definition of possibility as ‘one-sided possibility’, which contains necessity as one of its species; 9 10 11

(Marenbon 2008b, p. 20). (Boethius 1969). For a more detailed survey on Boethius’ modal account, see (Knuuttila 1993, pp. 45–62).

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iv. the existence of extra-actum potencies, which remain forever unrealized; v. the distinction between ‘absolute’ and ‘qualified’ modalities; and vi. the ‘modal asymmetry’ of time,12 that is, the idea that genuine possibilities must always refer to the future, while the present and past are necessary, at least in some ‘weak’ sense of necessity. This view on the modal status of time will be, in part, contested by Abelard, though it is accepted by many of his contemporaries. In this section I will briefly show how these elements were interpreted by Boethius, before investigating in Chapters 2 and 3 how early 12th-century authors incorporated and gradually transformed them into a new theory of modals. I shall set aside for the moment Boethius’ discussion of future contingents and indeterminism which, although extremely relevant for 12th-century theories on modalities, will be described in Chapter 10. 1

Necessity as Sempiternity and Immutability

At the beginning of his second commentary on Perihermeneias 12, Boethius states that if something is actually the case, and it exists in such a way that it will always be the same and never change, we say that it is ‘necessary’.13 The connection suggested here between necessity and sempiternity (or omni-temporality) returns in many other passages of Boethius’ commentaries. In these passages omni-temporality is used in three different ways: it may be attributed (i) to things themselves and their existence; (ii) to the properties of things and their sempiternal attachment to substances; or (iii) to propositions and their truth-values. In the first case substances are called sempiternal, inasmuch as they exist at every time, being ungenerated and incorruptible.14 These substances are also referred to as ‘incorporeal’ and ‘divine’ and are usually contrasted with mortal and corruptible beings, the existence of which is said to be ‘mutable’, for there are times in which they do not exist. In the second case sempiternity characterizes the relationship between substances and their properties, when these properties are attached to their bearer at every time 12 13 14

This expression is from (Zagzebski 2008). See (Boethius 1880, p. 383, 9–12): ‘si quid enim nunc alicui inest, hoc esse praedicatur, quod vero ita inest, ut semper sit et numquam mutetur, illud necesse esse dicitur, ut soli motus lunaeque cum terra obstitit defectus.’ See, for example, (Boethius 1877, p. 205, 13–5), where Boethius says that necessary are those things that are always in act and are therefore sempiternal: ‘necessaria sunt ea quae semper actu sunt.’

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and it is never the case that they do not inhere in them.15 Substances that are sempiternal in the first sense – that is, with respect to their existence – are also sempiternal in the second sense, because they have an ‘immutable nature’ and therefore retain the same properties at all times.16 Finally, Boethius attributes sempiternity to propositions the truth-value of which is not subject to variation in time. Propositions of this sort are the ones that are about sempiternal substances and their necessary properties, for instance, ‘God exists’, ‘God is immortal’, or ‘the Sun moves’.17 These are contrasted with propositions that are instead ‘unstable’ with respect to their truth and falsity, because the things they are about have a mutable and unstable nature.18 Knuuttila has interpreted the link between necessity and omnitemporality as an assumption of Boethius’ modal theory, which he used to provide an extensional or ‘statistical’ definition of the modal concept in terms of ­temporal moments. In the same way, he claims, this link was assumed without ­discussion in Aristotle, who – at least in some of his works – interpreted modal notions ‘as tools for expressing temporal or generic frequencies’.19 According to this interpretation, the equivalence between necessity and ­omnitemporality allows Boethius to spell out the signification of the modal notion in purely temporal and extensional terms, as what is actual (or what is true) at all times.20 15 16

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See (Boethius 1880, p. 384, 15–7): ‘necessitas enim non modo inesse vult aliquid, sed etiam inmutabiliter inesse, ut illud quod esse dicitur numquam esse non possit’. Boethius says that, while non-sempiternal things are contingently as they are, things that are sempiternal are necessarily what they are: ‘in mortalibus igitur rebus cum est aliquid et esse potest et ut sit non est necesse, in sempiternis autem quod est necesse est esse et quia est esse possibile est’ (Boethius 1880, p. 412, 5–7). In other passages Boethius admits that contingent and corruptible beings may also have some of their properties necessarily. He claims that, for instance, it is necessary that the fire is hot, or the snow cold, at least as long as fire and snow exist. I will return to this later in this section. See (Boethius 1880, pp. 186, 24–187, 2): ‘harum [i.e. categoricarum propositionum] autem quaedam sunt quae cum sempiterna significent, sicut hae res quas significant semper sunt et numquam a propria natura discedunt, ita quoque ipsae propositiones inmutabili significatione sunt: ut si quis dicat “deus est”, “deus inmortalis est”. hae namque propositiones sicut de inmortalibus dicuntur, ita quoque sempiternam habent et necessariam significationem.’ See (Boethius 1880, pp. 393, 29–394, 3): ‘quae non eodem modo dicuntur quemadmodum illae quae mutabilem naturam non habent, ut hae scilicet quas necessarias dicimus. Ut si quis dicat “solem moveri” vel “solem possibile esse moveri”, haec numquam ex veritate in falsitatem mutabitur.’ See also (Boethius 1877, pp. 124, 30–125, 14). (Knuuttila 1993, p. 3). (Knuuttila 1993, pp. 45–62). For the use of the statistical model in Aristotle and Boethius, see, in particular, (Hintikka 1973); (Knuuttila 2008; 2012).

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Rather than being an assumption of his system, however, Boethius’ link between necessity and omnitemporality is a consequence of another important element of his modal theory – as well as of Aristotle’s – namely, the connection between necessity and immutability. In Aristotle and Boethius, necessity is defined in terms of a lack of movement or lack of change, and the temporal characterization as sempiternity is a corollary of this definition. Because the characterization of necessity as immutability will be used extensively, not only in Boethius but also in early 12th-century texts (as will be described in Chapter 3, Section 4), it will be worth presenting it in brief here, in order to understand the origins of this terminology. In Aristotle’s Physics and Metaphysics the notion of possibility (or better, potentiality) is often defined in terms of change. A potency is, for him, a principle of movement or change that allows a substance to become different from how it actually is.21 Changes might occur with respect to the existence of substances, in which case we say that a substance comes to being through a movement of generation, or it passes from being to non-being through corruption; or they might occur with respect to their qualities (or other categories), in which case we say that a substance passes from having a certain quality to having the opposite one (e.g. from being white to being non-white). The movement that the substance undergoes while passing from one state to another consists in the (immediate or gradual) actualization of a potency. Without there being a precedent potency – which, as was said, is the principle of change – the process of change could not take place.22 Substances that possess a principle of change with respect to their existence or to some of their properties are considered by Aristotle contingent beings, that is, beings that are potentially otherwise than they actually are. These beings are movable or mutable, either in the sense that they may undergo generation and corruption or in the sense that they have different qualities at different times. On the other hand, substances that lack a 21

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See, for instance, Metaphysics V.12: ‘potency means a source of movement or change, which is in another thing than the thing moved or in the same thing qua other, e.g. the art of building is a potency which is not in the thing built, while the art of healing, which is a potency, may be in the man healed, but not in him qua healed. “Potency” then means the source, in general, of change or movement in another thing or in the same thing qua other, and also the source of a thing’s being moved by another thing or by itself qua other’ (transl. W.D. Ross). The same definition of potency is also to be found in Metaphysics IX.1; see (Aristoteles 1969). For the connection between the notion of change and modalities in Aristotle’s texts, see also: De interpretatione 13, 23a12–6; Metaphysics V.5, 1015b14–5, VI.1, 1026a11; IX.10, 1052a4; XII.6, 1071b5; XII.7, 1073a3–13; Nicomachean Ethics VI.1, 1139a7–8, VI.1, 14; VI.3, 1139b20 ff.; VI.4, 1140a1; Physics II.1, 193a26–7.

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principle of change with respect to their existence or their qualities are invariable in their nature and/or features.23 Things belonging to this last category, according to Aristotle, are the immaterial components of reality (for matter is what allows substances to change), belonging not to the sublunar world but to the celestial one. Because they lack potentiality, these substances are necessarily as they are, in the sense that it is impossible for them to be otherwise. We see then how the link between immutability and necessity emerges from Aristotle’s definition of potentiality in terms of change: necessary are those substances that are immutable with respect to their existence and properties, for they lack the potentiality (namely, the principle of change) that would allow them to be otherwise than they actually are. This link is to be found in the same terms in Boethius, who – exactly like Aristotle – delineates an ontology composed of mutable, material, and contingent beings, on the one hand, and immutable, necessary, and immaterial ones, on the other. We may then see how the link between omnitemporality and necessity, in turn, follows from defining necessity in terms of immutability: beings that are said to be ‘necessary’ because they lack mutability with respect to their existence, and which cannot therefore be the subject of generation and corruption, are sempiternal in the sense that they exist at every time. Similarly, beings that lack a principle of change with respect to one or some of their properties will have these properties in every time of their existence, and we say then that these properties belong ‘necessarily’ to them. Finally, propositions that are said to be ‘necessarily true’ because they are about immutable substances, (e.g. ‘the Sun exists’) or immutable properties of substances (‘the Sun is moving’) are also sempiternally true. It is significant to notice, thus, that the connection between modalities and time is not an assumption of the Aristotelian system but rather the consequence of his definition of modalities in terms of mutability and change. Although logicians at the beginning of the 12th century had no direct access to the texts in which Aristotle presented his definition of modalities in terms of change, they nonetheless inherited his explanation of necessity in terms of immutability and omnitemporality through Boethius. In many texts of this time, we find a definition of ‘necessary’ as ‘impermutabile’ or as ‘quod est in 23

See, for instance, Metaphysics V.5, 1015a34–1051b6, where Aristotle says that, among the many meanings of the term ‘necessary’, the principal and primitive meaning of the term is ‘that which cannot be otherwise than it is’ and all its other meanings are derived from this. Later in the same chapter Aristotle says that ‘necessary’ is primarily and in the strict sense what is ‘simple’, namely, what ‘does not admit of more states than one, so that it cannot even be in one state and also in another’ (transl. W.D. Ross).

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sempiterno actu’. Indeed, the connection between necessity and omnitemporality may also be found in earlier medieval sources from the 10th and 11th centuries, as will be shown in Chapter 3, Section 4. However, 12th-century logicians also put forward new characterizations of necessity, apparently unrelated to Aristotle’s modal metaphysics. To these new definitions, I will return in Chapter 3 and – more specifically to Abelard’s case – Chapter 10. In parallel to his definition of necessity in terms of sempiternity, Boethius also provides similar temporal characterizations of the other modal terms, in accordance with what has been called a ‘statistical’ or ‘frequency interpretation of modalities’. According to this paradigm, the notion of impossibility is connected to being never (true), whereas possibility is interpreted as expressing what is at least sometimes actual. Even though Boethius admits that there may be perpetually unactualized possibilities at the level of individuals (cf. Chapter 1, Section 3 below), at the level of species, and of natural kinds, he rather seems to assume that the predication of a certain possibility requires this possibility to be exemplified at least once in some members of a certain natural kind. As Knuuttila puts it, these sorts of ‘potency-type’ possibility ‘are taken to fulfil [a] criterion of genuineness’ by ‘prov[ing] their mettle through actualization’.24 Possibilities therefore occupy a sort of ‘middle ground’ between necessity and impossibility by virtue of them being sometimes actualized and sometimes unactualized. Boethius writes that: Things which neither always are nor always are not, but sometimes are and sometimes are not, have a certain cognation to contraries just because they at some time are and at some time are not. These are between necessary and impossible things.25 Knuuttila analyses in more detail the demarcation offered by Boethius between the predication of possibilities that refer to species or kinds, with respect to which no possibility remains perpetually unrealized, and possibilities that are instead predicated of individuals, which on the contrary ‘do not necessarily embody actualizations of all the possibilities belonging to their species’.26 I will return to these unrealized possibilities in Chapter 1, Section 3 below, and 24 25

26

See (Knuuttila 1993, pp. 46–7) on this. ‘Quaecumque neque semper sunt neque semper non sunt, sed aliquotiens sunt, aliquotiens non sunt, ea per hoc ipsum quod sunt et non sunt habent aliquam ad contraria cognationem’ (Boethius 1880, p. 237, 1–5), translated in (Knuuttila 1993, p. 47). For a similar view, Knuuttila also indicates passage 120, 24–121, 16 from Boethius’ first commentary on De interpretatione (Boethius 1877). (Knuuttila 1993, p. 47).

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I will point out how they will be particularly relevant for early 12th-century authors, who will make ample use of the concept of possibile extra-actum. As for the temporal characterization of modalities, Boethius’ definitions of necessity, impossibility, and possibility, in terms of what is always/never/sometimes actual, will have a long-standing impact on early medieval logicians. As Marenbon has pointed out, one of the first glosses that we have available on Aristotle’s De Interpretatione in the Latin medieval tradition, which seems to have been written in the 10th century and is preserved in manuscript Leiden, Bibliotheek der Rijksuniversiteit, Voss. lat. F. 70 (I) (s. x), fols 5”-9’, offers a discussion of modalities in which necessity, possibility, and impossibility are expounded in temporal terms. According to the author of these glosses, whatever necessarily is always is, and whatever is impossibly the case never is (‘Quidquid est quod impossibile est non esse, semper est. Quicquid impossibile est esse, semper non est’), whereas that which can possibly not be is not always the case, and that which can possibly be is not always not the case (‘Quicquid est quod possibile est non esse, non semper est. Quicquid est quod possibile est esse, non semper non est’).27 The non-sempiternity of contingent beings or states of affairs, the author continues, is justified by saying that things belonging to this category are mutable, for they may vary both with respect to their existence, through generation and corruption, and with respect to their properties (‘non semper est et non semper non est quicquid alicuius accidentis mutabilitate ita variatur ut de esse in non esse et de non esse in esse mutetur’). As Marenbon has remarked, the author’s division of modalities according to temporal concepts, which is certainly based on Boethius’ commentaries on De Interpretatione, echoes the ‘statistical interpretation’ of modality.28 Another 10th-century source, in which a similar connection is put forward between the notions of necessity/impossibility and those of invariability and omnitemporality, is Gerbert of Aurillac’s De rationali et ratione uti. Here, necessary beings are defined as those that are eternally in a certain state and cannot not be.29 I will return to these early medieval sources in Chapter 3, Section 4 below. In logical commentaries written at the turn of the 12th century the connection between the notion of necessity and that of eternality, omnitemporality, or immutability is still widely used. In Chapter 3, Section 4 below I show that 27 28 29

The full text of the gloss is transcribed in (Marenbon 2000a). (Marenbon 2000a, p. 30). See, for instance (Gerberto d’Aurillac 2007, p. 82): ‘Quae enim necessaria semper ex necessitate sunt, nec unquam non esse possunt’. See also p. 80, 7–10: ‘Quae necessaria sunt, inquit, in actu sunt, eo scilicet, quem relinquere nequeunt, ut coelum et sol proprium motum. Item quae necessaria sunt, sempiterna sunt.’

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many sources from this time period, such as the commentaries on De Interpretatione catalogued by Marenbon as H9 and H11, H4, and H5, as well as the commentary on De Hypotheticis Syllogismis SH2, all characterize necessity, at least with respect to some of its significations, in terms of invariability and sempiternity. Abelard too makes use of this characterization in his logical and theological works, as will be explained in Chapter 10. Much less frequent among early 12th-century authors, however, is the temporal characterization of the notion of possibility. In fact, almost all authors of Abelard’s time seem to reject Boethius’ suggestion that all possibilities – at least at the level of species – must actualize in some moment of time. On the contrary, in their reflections on modalities a prominent role is assigned to ‘extra-actum potencies’, namely, to potencies that remain unrealized, or which are entirely unrealizable, and yet remain real possibilities (see, in particular, Chapter 3, Section 3 and Chapter 9 below). Boethius’ classification of modalities in terms of frequency or time seems to be in the background of some ideas that return in the 11th and 12th century and will continue to be developed in later medieval logic, namely, the theory concerning the ‘modal matter’ of propositions.30 As Knuuttila has remarked, during the 13th century many authors gave their exposition of the standard square of opposition and of the rules of inference holding among categorical propositions on the basis of a distinction between the different ‘modal matters’ of these propositions, namely, based on whether these propositions were about necessary, impossible, or contingent things or states of affairs.31 This theory of modal matter, Knuuttila says, was based on Boethius’ works but may also be found in other authors belonging to the Greek commentary tradition, such as Ammonius.32 We already find the idea of distinguishing categorical propositions on the basis of their ‘modal matter’ in some sources written between the 11th and 12th centuries, such as the Dialectica of Garland and the Introductiones dialecticae secundum Wilgelmum, the latter of which preserves records of William of Champeaux’s teaching from the later 11th century.33 Both the Dialectica and the Introductiones present the logical relationships holding among categorical propositions by saying that these propositions are to be distinguished as being in three different ‘matters’ (in tribus materiebus), namely, ‘natural’ matter, ‘contingent’ matter, and ‘remote’ matter. Propositions that are ‘de naturali 30 31 32 33

I thank the anonymous referee for bringing this connection to my attention. Cf. (Knuuttila 2012, pp. 317–8); (Knuuttila 2017). Cf. (Knuuttila 2008, pp. 508–9). These are edited by Yukio Iwakuma in (Iwakuma 1993).

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materia’ are those that express a connection between two predicates which are related by some necessary link, such as ‘man’ and ‘animal’ in ‘every man is an animal’. As it is said in William’s Introductiones dialecticae, propositions of this sort are those in which the predicate inheres in the subject universally (praedicatum cuius inhaeret subiecto et omni […] inhaeret subiecto universaliter accepto). The reference to nature should be interpreted in the sense that a certain law of nature is expressed by propositions of this sort. Generally speaking, the notion of necessity will often be connected to the notion of nature by early 12th-­century authors, as we will see later in this volume (cf., in particular, Chapters 3.4, Chapter 8, and Chapter 10.1). Propositions that are ‘de contingenti materia’ are instead those such as ‘every man is white’, in which the predicate does inhere in the subject, but only in some cases and not universally. Finally, propositions ‘de remota materia’ have a predicate that in no way inheres in the subject (praedicatum cuius nullo modo convenit subiecto) and which thus expresses an impossible connection, such as ‘every man is a stone’. This distinction conveys an idea of what is contingent as what is actualized in at least some members of a species, and a parallel idea of necessity and impossibility as what is always or never actualized. 2

Possibility as Potentiality

According to Boethius, possibilities (possibilitates) are ontologically funded in the potencies or powers (potentiae, potestates) of things. In his longer commentary to De Interpretatione, Boethius says that the meaning of the term ‘possibile’ is derived from that of ‘potestas’,34 and this terminology is used diffusely within his two commentaries on the Aristotelian work. Boethius inherits this understanding of possibility from Aristotle, according to whom the term ‘potency’ refers to the ‘real powers or tendencies [of substances], the ends of which are either actual or non-actual at the moment of utterance’.35 According to Boethius, some of these potencies are actualized at some moment of time, having existed only potentially (potestate) in the substance. For instance, while I am writing, the potentia scribendi that existed in me in a latent, ‘inactivated’ state before I started to write comes to actuality, allowing me to perform this act.36 34 35 36

Cf. (Boethius 1880, p. 453, 15–6): ‘possibile a potestate traductum est’. (Knuuttila 1993, p. 46). (Boethius 1880, pp. 413, 1–2): ‘Ante enim quam scriberem erat mihi scribendi potentia sed ex potestate scribendi veni ad actum scribendi.’

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Potencies that may pass from a state of potentiality to one of actuality, and vice versa, are called by Boethius potencies ‘of both contraries’, that is, potencies that may evolve in the direction of actualization but that may also remain or return in a state of non-actuality. For instance, the fact that I have a potency to write, which may pass from being potestate to in actu, implies that I also have the potency of non-writing, so it would be true to say that it is both possible for me to write and not to write.37 Other potencies, on the other hand, are potencies for only one of the two contraries, for instance, the potency that fire has of being hot, which does not imply that the opposite property (being cold) is also possible for it. Potencies of this second sort, Boethius says, do not achieve actuality having been in a state of pure potency, because they have always been in act, at least as long as their bearer exists. Fire, for instance, does not become hot in actu after being so in potency but maintains its potency of being hot in actualization throughout its entire lifetime.38 Following Aristotle, Boethius calls those potencies that are of both contraries ‘rational’ and the ones that are of only one contrary ‘irrational’.39 There is for Boethius a third sort of potency, which always remain latent in things and are never actualized. These extra-actum possibilities – which will be central in early 12th-century modal theories – are, according to Boethius, real potencies existing in things, even though they remain perpetually unrealized. For instance, Boethius says that an infinite number exists in potency, since to any given quantity it is always possible to add another quantity, but never exists in act, because each actual number is finite.40 He also rehearses 37

38

39 40

See (Boethius 1880, pp. 412, 24–413, 10): ‘Huius autem non necessariae duae rursus partes sunt: una quae a potestate pervenit ad actum, altera quae semper actu fuit, a quando res illa quae susceptibilis ipsius est fuit. Et illa quidem quae a possibilitate ad actum venit utriusque partis contradictionis susceptibilis est, ut nunc ego qui scribo ex potestate ad actum veni et agens possum scribere. Ante enim quam scriberem erat mihi scribendi potentia sed ex potestate scribendi veni ad actum scribendi. Quare utraque mihi conveniunt et non scribere et scribere. Possum enim et non scribere, possum et scribere, quae est quodammodo contradictio. Atque ideo quaecumque ex potestate ad actum venerunt, ea et facere possum et non facere et esse et non esse, ut qui loquitur, quia antea potuit loqui quam loqueretur et nunc ideo potest loqui quia loquitur, et potest loqui et potest non loqui.’ See (Boethius 1880, p. 413, 10–9): ‘Alia vero quae numquam ante potestate fuit sed semper actu, a quando res ipsa fuit quae aliquid potestate esse diceretur, ad unam rem tantum apta est, ut ignis numquam fuit potestate calidus, ut postea actu calidus sentiretur, nec nix ante frigida potestate, post actu sed a quando fuit ignis actu calidus fuit, a quando nix actu frigida. Quocirca hae potentiae non sunt aptae ad utraque. Neque enim ignis frigus incutere nec nix calidum quicquam possit efficere.’ See, for example (Boethius 1880, pp. 446–7). See (Boethius 1877, p. 207, 1–11): ‘Alia vero sunt, inquit, quae actu quidem numquam sunt, semper autem sunt potestate, ut numerus infinitus quidem est, quod eum semper

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Aristotle’s example of a coat that has the potentiality to be cut but remains intact throughout its entire existence. In Boethius’ view, potencies may remain eternally unrealized either because of their very nature, as in the case of the infinite number, or because some external hindrance prevents their actualization, or again by virtue of an indeterministic element of chance that, according to Boethius, characterizes both the natural and the human world.41 Perhaps Boethius’ insistence on the existence of extra-actum possibilities was directed against deterministic definitions of possibility like the one given by the Megarian Diodorus Cronus, according to whom everything that is possible either is or will be the case, a definition that left no room for real possibilities that are never actualized in time.42 According to Boethius, latent and unrealized potencies are real constituents of things, in the sense that they have an ontological foundation in the substances to which they belong. He says, for instance, that even though a man is not actually performing an action at a certain moment of time, the potency to perform such an action is still present in him in that time.43 He also states that before a house was fabricated, the potency of it being built was already existent, and it is by virtue of this potency that we could have truly said ‘it is possible for the house to be’ even when the house did not exist.44 Potentialities

41 42

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44

in infinitum possis augere, sed actu infinitus non est. Quemcumque enim numerum sumpseris, actu finitus est; quemlibet enim numerum dicas, finita illum numerositas necesse est conplectatur, ut decem vel centum. Infinitus vero idcirco est potestate quod eum possis facere in infinitum concrescere, non tamen ut quilibet actu sit numerus infinitus.’ See also (Boethius 1880, p. 463, 11–3). See (Kretzmann 1985). According to what Boethius says in (1880, p. 234, 22–6), Diodorus Cronus defined ‘possible’ as ‘what either is or will be’ (quod aut est aut erit), ‘impossible’ as ‘what, being false, will never be true’, and ‘necessary’ as ‘what, being true, will never be false’. In (Alexander of Aphrodisias 1883, p. 184), Alexander confirms these definitions, stating that, according to Diodorus, if we assume that I am not, and never will be, in Corinth, then it would not be possible for me to be there. This understanding of possibility, according to which something is now possible if it is true at least once from now on, reflects a determinist view of reality, for it admits no possibility that is not actualized in time. On Diodorus’ modal views, see (Bobzien 1998, pp. 102–4). See, for example, the aforementioned passage from (Boethius 1880, pp. 412, 27–413, 2), where the author says that some possibilities come to act having existed in their subjects potestate only. Boethius talks as if the potency of writing were already present in (or possessed by) the subject before its actualization: ‘et illa [pars possibilitatis] quidem quae a possibilitate ad actum venit utriusque partis contradictionis susceptibilis est, ut nunc ego qui scribo ex potestate ad actum veni et agens possum scribere. Ante enim quam scriberem erat mihi scribendi potentia, sed ex potestate scribendi veni ad actum scribendi’ (my emphasis). See (Boethius 1877, p. 206, 23–7): ‘Quae actu sunt cum potestate, id est quae et actum habent et aliquando habuerunt potestatem, ut fabricata iam domus aliquando potuit fabricari et prius habuit potestatem secundum tempus, postea vero actum.’

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that are said to exist ‘before’ actualization are rather obscure entities, the ­ontological status of which is not clear in Boethius’ works. In particular, it is unclear whether they are present in things as some kind of form or property. Nevertheless, Boethius seems bound to admit the existence of these potencies because, given his equation between potencies and possibilities, he would not be able to admit the truth of propositions such as ‘it is possible for me to write’ or ‘it is possible for a house to be fabricated’ without admitting the corresponding potencies as existing in some sense. The ontological status of extra-actum potencies attributed to non-things was recognized as problematic by some authors in the early Middle Ages, such as Anselm of Canterbury. In his Philosophical Fragments Anselm asks in which sense some possibilities (potestates) are attributed to things that are non-existent, for instance, when we say that it is possible for a house to be prior to its existence.45 Some sophismata may be construed starting from this example, Anselm claims, because from the fact that a certain substance S does not exist, we may infer both that it is not possible for S to be and that it is not possible for S not to be, on the basis that no potency can be attributed to a non-existent object. Similarly, in his De Casu Diaboli Anselm considers whether we may say that it was possible for the world to exist before creation, since prior to that moment the world could have had no capability of either being or non-being. As was noticed by Knuuttila, the problems emerging in the analysis of these examples are related to a reading of possibilities as passive potencies embedded in a subject, an idea that was present in both Aristotle and Boethius but which begins to vacillate in Anselm’s reflection on modes.46 Problems related to the possibilities of non-things, and to the idea that things have the antecedent possibility of existing before their actual existence (‘prius potuerunt existere quam fuerunt’, as the author of H9 says47), insistently return in the works of Abelard and his contemporaries, who grasped how an understanding of all possibilities in terms of potencies ‘embedded in things’ may lead to dangerous ontological problems. The two examples employed by Anselm (the possibility that a house has of being fabricated before its actual existence and the possibility of the world to exist before its creation) are both 45

46 47

See (Anselm of Canterbury 1969, p. 341, 7–12): ‘Dicimus namque potestatem esse aliquando, in quo nulla est potestas. Nullus enim negat omne, quod potest, potestate posse. Cum ergo asserimus, quod non est, posse esse, dicimus potestatem esse in eo, quod non est; quod intelligere nequeo, velut cum dicimus domum posse esse, quae nondum est. In eo namque, quod non est, nulla potestas est.’ The example of the house seems to be based on Boethius’ mention of the potentiality of a fabricata domus to exist before its existence in (Boethius 1877, p. 206, 23–7). See on this (Knuuttila 2004, p. 119). See Orléans, Bibl. mun. 266, p. 39b.

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mentioned in some sources of the time, together with new examples involving the possibilities of chimaeras, goat-stags, or possible future humans.48 One strategy to account for problematic possibilities of this sort (which remarkably resembles the one advanced by Anselm in De Casu Diaboli) is proposed in Garland’s Dialectica, where it is said that some propositions such as ‘it is possible for birds to fly’ are true even though birds do not exist because it would be possible for God at any time to create them and make them fly.49 The possibilities of non-existent things would then be ontologically founded in God’s power. However, as far as I am aware, this is the only case in which this solution is used in early 12th-century sources. More often, the strategy of early 12th-century logicians to deal with problems of this sort is to reject Boethius’ idea that modal terms refer to something existing in things. As we will see in Chapter 3, Section 3, they opted instead for a ‘de-reification’ of the notion of possibility, according to which possibilities are not conceived as real constituents of reality, such as res or properties, but explained as relations of non-contradictoriness holding between certain predicates and the natural laws governing creatures. As we will see, in his Logica Ingredientibus Abelard pushes this de-reification further, saying that necessity and possibility are nothing other than ‘ways of conceiving things’ (see pp. 83–4). Despite inheriting important parts of modal logic and terminology provided in the De Interpretatione and Boethius’ commentaries, Abelard and other authors of his time seem inclined to abandon the metaphysical burdens related to the Aristotelian and Boethian ontology of potencies. I will return to this point in more detail in Chapter 3, Section 3. 3

‘One-Sided’ Possibility and Possibilities extra-actum

In De Interpretatione 12–13 Aristotle uses the term ‘possible’ (δυνατόν) – which he takes to be synonymous to ‘contingent’ (ἑνδεχόμενον) – in an ambiguous way: at times he uses it in the sense of two-sided possibility to refer to what is neither impossible nor necessary; and at other times he uses it in the sense of one-sided possibility, equivalent to ‘not-impossible’.50 Before concluding in De Int. 13, 6–11 that the term is equivocal and has two different meanings, Aristotle devotes a long discussion to the relationship between necessity and possibility, asking whether possibility-propositions follow or do not follow from 48 49 50

See Chapter 3, Sections 1 and 2 on these examples. (Garlandus Compotista 1959, p. 84, 21–3). This ambiguity in the use of the term ‘possible’ is also present in other texts of Aristotle, for instance, the Prior Analytics. On the ambiguity of Aristotle’s possibility, see (Hintikka 1973, pp. 27–9) and (Malink 2016).

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necessity-propositions. This question is raised by the fact that, if we understand ‘possible’ in the sense of one-sided possibility, everything that is necessary is also possible, and the inference from ‘it is necessary that p’ to ‘it is possible that p’ is always valid. If we take it instead as a two-sided possibility (what we would now call ‘contingency’), being necessary and being possible would be mutually exclusive. In his commentaries Boethius reports Aristotle’s arguments and follows him in calling ‘possible’ an ambiguous term.51 However, in his commentaries on De Interpretatione the understanding of the term as a one-sided possibility almost always prevails. Possibility is thus taken as the contradictory of impossibility,52 and necessity is said to be a sub-class or ‘species’ of the possible, namely, the part of possibility that is always in act. This reading of possibility will be very common in early 12th-century logic, where Aristotle’s notion of two-sided possibility disappears in favour of what is at times called ‘possibile largum’.53 The divisio of possibility that Boethius offers, which will often be rehearsed in early 12th-century commentaries on De Interpretatione, initially distinguishes between two ‘parts’ of the possible. First, possible is said of what is actually the case (quod iam est): Boethius calls this ‘possibile actu’ or ‘verum possibile’. Second, possible is what, though not actually being the case, can be (quod cum non sit esse potest): this is also called ‘possibile extra-actum’ or ‘forsitaneum possibile’.54 Within the first species of possibility, Boethius then distinguishes between (i) what is always in act (in sempiterno actu), which coincides with what is necessary, and (ii) what is presently in act, having been in potency, and may return to being extra-actum in the future. This second category of possibile actu is peculiar to mutable and corruptible beings, in which potency and actuality alternate. Boethius claims that, for what concerns contingent beings, every actuality is always preceded by a potentiality, while in the case of necessary and immutable beings, the act is never temporally preceded by potency. The second species of the possible, which includes things that are potentially though not actually the case, is itself divided into two categories: on the one hand, there are potentialities that will actualize in the future; on the other hand, there are potentialities that will never be in act but always remain in potestate. Boethius clearly admits the existence of potencies that are never realized (numquam actu) in several passages of his commentary, perhaps with 51

See (Boethius 1880, p. 455, 6–7): ‘possibilitas aequivoca est et multa significans.’ See also (Boethius 1877, p. 201, 26–7; 1880, p. 452, 21 ff.; 1880, p. 453, 13 ff). 52 Boethius says that ‘impossibile’ is the privatio of ‘possible’. See, for example (Boethius 1880, pp. 419, 20–4; 423, 23–5). 53 See H9: Orléans, Bibl. mun. 266, p. 38b. 54 For this division see (Boethius 1880, pp. 411 ff. and 454 ff).

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a critical intent against the definition of possibility given by Diodorus, as was said.55 The Diodorean characterization of possibility, which reduces the possible to what is actual at a certain – present or future – moment of time, is firmly rejected by Boethius, who fears its deterministic implications. Diodorus’ paradigm would indeed treat all events that do not happen in time as impossible, saying, for instance, that if a certain man will die at sea then it is impossible for him to die in any other way.56 Because of his indeterministic view of reality, Boethius instead wants to admit the existence of possibilities that never actualize, which he conceives – as we may infer from the examples he gives in his commentaries – as being of two different kinds: possibilities that could realize even though they never will (for instance, the potentiality a man has of walking even though he never walks)57 and possibilities that are, in principle, non-actualizable (such as the existence of an infinite number).58

figure 1 Boethius’ division of possibility, rehearsed in early 12th-century commentaries on De interpretatione 55 56 57 58

See (Boethius 1880, p. 234, 23–4). Cf. Section 2 in this Chapter. See (Boethius 1880, p. 235, 6–8): ‘Ille [Diodorus] enim arbitratus est, si quis in mari moreretur, eum in terra mortem non potuisse suscipere.’ See (Boethius 1877, p. 203, 19–22): ‘Nam et quae actu quidem non est, esse tamen poterit, ut homo cum non ambulat, ambulandi tamen retinet potestatem, non est eum impossibile ambulare.’ See (Boethius 1877, p. 207, 1–5): ‘Alia vero sunt, inquit, quae actu quidem numquam sunt, semper autem sunt potestate, ut numerus infinitus quidem est, quod eum semper in infinitum possis augere, sed actu infinitus non est.’ See also (1880, p. 463, 11–3): ‘Quasdam autem res esse in quibus sola potestas sit, numquam actus, ut numerus infinitus.’

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The division of possibility provided by Boethius is rehearsed by many authors in the early 12th century. In commentary H9, for instance, the anonymous author adopts the meaning of ‘possibile’ as one-sided possibility and distinguishes between ‘possibile quod est in actu’ (also called ‘verum possibile’) and ‘possibile quod non est in actu’ (‘possibile forsitaneum’). Among possibilities that are not in act, he admits the existence of some that are never actualized (numquam in actu). The first category is, in turn, divided into things that are in sempiterno actu and which are not preceded by an antecedent potentiality, and things that are in a transitory actuality and came to act from a precedent potestas (the author of H9 reports here Boethius’ example of a house that exists potentially before existing in act). A similar division of possibility may be found in the anonymous treatise M3, where again ‘possibile’ is divided into ‘actuale’ or ‘verum possibile’ and ‘possibile forsitaneum’, and the same terminology is advanced in commentaries H5, H4, in the Dialectica of Garland, and in Abelard’s literal commentary to De Interpretatione. 4

Absolute versus Temporally Qualified Modalities

Another aspect of Boethius’ theory that will deeply influence early 12th-­ century modal thought is his distinction between absolute and qualified (or conditioned) necessity and possibility. Qualified modalities are those in which a temporal determination is added to the modal term, as in ‘It is necessary for Socrates to read while he reads’ (Necesse est Socratem legere dum legit) or ‘It is possible for every man to have a heart as long as there are men’ (Possibile est omnem hominem habere cor quamdiu sunt). In early 12th-century logic, propositions with this structure are usually called ‘determinate’ or ‘composite’ modals. These usually include Boethius’ temporal determinations dum and quamdiu (or quando) but also cover other kinds of qualifications, such as the adverbs ‘in every time’ (omni tempore), ‘before’ (ante), and ‘after’ (postea), and the exclusive qualification ‘only’ (solum or tantum), which were not accounted for by Boethius. Extensive analysis of propositions of this sort is provided by Abelard and his contemporaries, who were deeply interested in their syntax and logic but also in the relevance of temporally qualified modals for philosophical discussions, such as the one on future contingents and divine foreknowledge (see Chapter 10.3–4). Boethius advances a distinction between absolute and qualified modalities in his treatise on hypothetical syllogisms, where he lists three different sorts of modal claim: i. propositions in which the modal term is predicated unqualifiedly (absolute) and without temporal determinations, as in ‘It is necessary for God

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to be immortal’ (Necesse est Deum esse immortalis) or ‘It is possible for a bird to fly’ (Possibile est avem volare). Boethius says that this is the usual and ‘proper’ way of interpreting modals; ii. temporally qualified propositions in which the dum-clause posits the existence or persistence of the modal clause’s subject, as in ‘It is necessary for Socrates to have a heart while he lives’ or ‘It is possible for Socrates to read as long as he exists’ (Necesse est Socratem habere cor dum vivit; Possibile est Socratem legere quamdiu permanet). Temporal qualifications of this sort will usually be referred to in 12th-century logic as determinationes extrasumptae; and iii. propositions in which a temporal clause is adjoined to the modal one, the predicate of which repeats the predicate included in the infinitive clause, as in ‘It is necessary for Socrates to sit while he sits’ (Necesse est Socratem sedere dum sedet). These temporal qualifications are called intrasumptae and, according to Boethius, are equivalent to the corresponding claims de puro inesse (e.g. ‘Socrates sits’).59

figure 2 Boethius’ distinction of different kinds of necessity and possibility in De ­Hypotheticis Syllogisms 59

‘Ea […] quae ex necessitate aliquid inesse designat, tribus dicitur modis. Uno quidem quo ei consimilis est propositioni quae inesse significat, ut cum dicimus, “Necesse esse Socratem sedere, dum sedet”. Haec enim eandem vim obtinet ei quae dicit: “Socrates sedet”. Alia vero necessitatis significatio est, cum hoc modo proponimus: “Hominem necesse est habere cor dum est atque vivit” hoc enim significare videtur haec dictio, non quoniam tamdiu eum necesse sit habere quamdiu habet sed tamdiu eum necesse est habere quamdiu fuerit ille qui habeat. Alia vero necessitatis significatio est universalis et propria, quae absolute praedicat necessitatem, ut cum dicimus: “Necesse est Deum esse immortalem” nulla conditione determinationis apposita. Possibile autem idem quoque tribus dicitur modis: aut enim quod inest possibile esse dicitur, ut: “Possibile est Socratem sedere, dum sedet” aut quod omni tempore contingere potest, dum ea res permanet

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Similar divisions between different kinds of necessity were already advanced in the Greek tradition of commentaries on Aristotle, to which Boethius is deeply indebted. The tripartite distinction proposed in De Hypotheticis Syllogismis essentially follows the one proposed by Theophrastus among three types of necessary proposition, even though, unlike Theophrastus, Boethius advances a threefold distinction not only for necessities but also for possibilities.60 According to what Alexander of Aphrodisias reports, ­Theophrastus divided necessity statements into: (i) unqualified or absolute necessity statements; (ii) ‘limited’ necessity statements, which express a conditioned (μετὰ διορισμοῦ) sort of necessity; and (iii) necessity propositions that are equivalent to simple (i.e. non-modal) assertions.61 A threefold division of necessity was also advanced in the works of Ammonius and Stephanus.62 Stephanus, for instance, divided necessities into absolute and hypothetical, the latter being predications that are necessary only as long as the predicate belongs to the subject, such as ‘Socrates is sitting of necessity as long as he is sitting’. Absolute necessities, in turn, are divided by him into two kinds: the necessary predications of sempiternal beings (‘God is of necessity good’); and the substantial predications of contingent beings, which are said to be necessary only under the condition that their subject exists.63

60 61 62 63

cui aliquid contingere posse proponitur, ut: “Possibile est Socratem legere quamdiu enim Socrates est”, legere potest; item possibile est quod absolute omni tempore contingere potest, ut avem volare’ (Boethius 1969, pp. 236–8). See on this (Thom 2003b, p. 38). This position held by Theophrastus is reported by Alexander of Aphrodisias in his commentary on Aristotle’s Prior Analytics. See (Alexander of Aphrodisias 1991, p. 36, 25–9) and (Alexander of Aphrodisias 1999, pp. 156, 29–157, 2). See also (Thom 2003b, p. 22). Cf. (Thom 2003b, pp. 21–36). For a discussion of the different sorts of necessity in the ancient commentators’ tradition, see also (Alexander of Aphrodisias 1999, pp. 148–52). See, for instance (Stephanus 2000, p. 158), quoted in (Thom 2003b, p. 36): ‘There is what is necessary absolutely and what is necessary hypothetically. We say that something is necessary hypothetically, so long as the predicate belongs to the subject. But the same things are capable also of not belonging, as that Socrates should be sitting or sleeping. So long as the sleeper sleeps, of necessity sleep belongs to him. The absolutely necessary is again twofold: it exists both in the case of eternal things and in the case of things that come to be and cease to be, when a substantial differentia of the thing that is subject is present. We say ‘substantial’ because in the case of the hypothetically necessary when the thing, that is, the predicate, is separated, for instance walking or sleeping, the subject is not destroyed, but here, for instance in the case of fire if the heat is separated it destroys the subject, that is, the fire. What is the necessity that is to be seen in the case of eternal things? For example, when we say ‘The Sun is of necessity in motion’, ‘God is of necessity good’. But in the case of things that come to be and cease to be, it is like this fire. Like the particular, we mean, and not the universal, since this particular fire comes to be and ceases to be, but the universal is always the same and does not cease to be.’

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A slightly different division between absolute and qualified modalities is presented by Boethius in his second commentary on Aristotle’s De Interpretatione, where he identifies two senses of necessity distinguishing predications that are ‘simply’ necessary, which seem to correspond to what he elsewhere calls ‘absolute’ necessities (e.g. ‘It is necessary that the Sun moves’), and those that are called necessary ‘qualifiedly’ or cum conditione (e.g. ‘It is necessary that Socrates is seated when he is seated’).64 In the passage from De Interpretatione 9, upon which Boethius is commenting (De Int. 9, 25–7), Aristotle himself suggests a similar distinction, speaking of things that are ‘simpliciter ex necessitate’ (ἁπλῶς εἶναι ἑξ ἀνάγκης) and things that are ‘necessario quando sunt’ (εἶναι ἑξ ἀνάγκης ὅτε ἔστι). Interestingly, while Aristotle in this context leaves the notion of simple necessity undefined (some commentators have proposed to read it as an atemporal necessity, or necessity ‘regardless of time’),65 Boethius characterizes it as a necessity ‘at all times’ (omni tempore) – an expression that will become very popular in the early 12th century.66 In his comments on De Interpretatione 9, the notion of a temporally conditioned necessity is used by Boethius to interpret Aristotle’s claim that ‘everything necessarily is when it is’,

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‘Duplex modus necessitatis ostenditur: unus qui cum alicuius accidentis necessitate proponitur, alter qui simplici praedicatione profertur. Et simplici quidem praedicatione profertur, cum dicimus solem moveri necesse est. Non enim solum quia nunc movetur sed quia numquam non movebitur, idcirco in solis motu necessitas venit. Altera vero quae cum conditione dicitur talis est: ut cum dicimus Socratem sedere necesse est dum sedet, et non sedere necesse est cum non sedet. Nam cum idem eodem tempore sedere et non sedere non possit, quicumque sedet non potest non sedere, tunc cum sedet: igitur sedere necesse est. Ergo quando quis sedet tunc cum sedet eum sedere necesse est’ (Boethius 1880, p. 241, 1–14). See (Von Wright 1984, p. 72). In an early 12th-century commentary to Boethius’ De Hypotheticis Syllogismis, labelled SH4 (Orléans, Bibl. mun. 266, pp. 264a–276a), the author puts forward an interesting doubt, namely, how to interpret the idea that absolute modalities must be taken ‘omni tempore.’ While considering Boethius’ example of absolute possibility provided in De Hypotheticis Syllogismis, that is, ‘it is possible for birds to fly’ (which Boethius expounds as ‘at all times it might happen that birds fly’), the author of SH4 wonders whether this must be interpreted as saying that there was not, and never will be, a moment in which birds cannot fly (‘sic nullum tempus est vel erit vel fuit in quo non sit vel erit vel fuit possibile aliquam avem volare’), or whether it must refer to future times only, saying that birds will be able to fly in any moment from now on (‘Vel dici potest de hac ave quae in omni futuro tempore possit volare’). He then adds that, independently of how we interpret Boethius’ ‘omni tempore’ determination, if we apply absolute modalities to contingent beings like birds, paradoxical consequences seem to follow, such as these being immortal, because a certain property is predicated as belonging to them at all times. I will return to this issue in the following pages.

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that is to say that once something has happened in time, the fact that it happened becomes unchangeable and therefore necessary. Boethius incorporates the principle of the fixity and necessity of the present and past in the modal views that he hands down to early medieval philosophers. He opposes this necessity to the unfixity and contingency of the future,67 but he also transmits the idea that the necessity characterizing present and past events is not an absolute and proper necessity but rather conditioned upon their having happened in time. Boethius was not particularly interested in the logic of temporally qualified modal claims: apart from establishing an equipollence between propositions such as ‘It is possible (necessary) for Socrates to sit while he sits’ and their correspondents de puro inesse, he drops any further analysis of the inference rules holding among simple and temporally qualified modal claims. Early 12th-century logicians, on the contrary, display a profound interest in the logical behaviour and philosophical relevance of temporally conditioned modalities. Analysis of this topic may be found in commentaries to Boethius’ monograph on hypothetical syllogisms (categorized as SH commentaries) and in the ones on Aristotle’s De Interpretatione (H commentaries), particularly in reference to Chapter 9, as well as in a number of treatises devoted to modalities, such as the two anonymous treatises M1 and M3,68 the brief treatise that follows Abelard’s De Intellectibus in MS Avranches, Bibl. mun., 232, Garland’s Dialectica, and Abelard’s logical works. The notion of temporal necessity was applied by Abelard’s contemporaries in the solution of two philosophical issues in particular. The first is a problem raised by the traditional connection between necessity and omnitemporality (see pp. 19–26 above) and consists in how to account for the necessary properties of contingent beings, that is, things that do not exist sempiternally. On the one hand, logicians of Abelard’s time take from Boethius the idea that no affirmation concerning contingent beings is necessarily true, for there are times in which it is false, namely, those times in which the subject does not exist.69 On 67

68 69

On Boethius’ views on the necessity of the past and the present, see (Knuuttila 1993, pp. 45–62). According to Knuuttila, the principles stating the unchangeability of present things and the necessity of the present were commonly accepted in ancient theories of modalities. Temporally qualified modals are here analysed in detail in M1: Orléans, Bibl. mun. 266, p. 168b; in M3: Orléans, Bibl. mun. 266, pp. 256a–257b. On the theory of temporally qualified modals in M1 and M3, see (Martin 2016, pp. 122–5). See, for instance (Boethius 1880, pp. 411, 27–412, 5): ‘Nam quod in sempiternis est esse possibile est, rursus quod est in mortalibus nec hoc a subsistendi possibilitate discedit sed tantum differt, quia id quod in aeternis est nullo modo permutatur et semper esse

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the other hand, Boethius admitted in other passages that contingent beings do have necessary properties, in the sense that they are invariable with respect to some of their features and lack the potentiality of being otherwise. For instance, he says that fire is necessarily hot and humans are necessarily mortal. In order to solve this issue, Abelard and other logicians apply the strategy of adding a temporal determination to modal clauses concerning contingent beings, saying, for instance, ‘Fire is necessarily hot as long as it exists’ (quamdiu est) or ‘It is necessary for every man to be mortal while there are men’ (dum homo est). In such cases, the span of time over which the modal term ranges is restricted to those moments in which the subject term is not empty, and so the propositions are necessary in the sense that they are true at all the times under consideration. This solution may be found in Garland’s Dialectica, who states that if we assumed any absolutely necessary proposition to be true about contingent beings such as Socrates or fire, we would end up with absurd consequences: if one says, for instance, that it is necessary for fire to be hot, it follows that it is impossible for it not to be hot, but this implies that it is impossible for fire not to exist, so that fire is sempiternal.70 In order to avoid sophismata of this sort, he continues, we should remember that necessary claims about contingent beings are always false in their absolute form and must be temporally qualified, saying, for instance, ‘it is necessary for Socrates to be an animal (or for the fire to be hot) as long as Socrates (or fire) exists’.71 Thus, Garland admits absolute necessities

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necesse est, illud vero quod in rebus mortalibus invenitur poterit et non esse et ut sit non est necesse. Ego namque cum scribo inest mihi scribere, quocirca et scribere mihi possibile est sed quoniam sum ipse mortalis, non est haec potestas scribendi necessaria: neque enim ex necessitate scribo. At vero cum caelo dicimus inesse motum, nulla dubitatio est quin necesse sit caelum moveri. In mortalibus igitur rebus cum est aliquid et esse potest et ut sit non est necesse, in sempiternis autem quod est necesse est esse et quia est esse possibile est.’ See (Garlandus Compotista 1959, p. 84, 25–33): ‘Nisi taliter determinetur “necessarium” et “possibile”, sophismata orientur inde. Verbi gratia: “Socrates est immortalis”. Utrum. Si non potest mori, est immortalis; sed non potest mori. Utrum. Si non potest non sedere, et non potest mori; sed non potest non sedere. Utrum. Si ex necessitate sedet, et non potest non sedere; sed ex necessitate sedet. Utrum. Si est vera ista propositio quae dicit: “necesse est Socratem sedere”, et ex necessitate sedet; si quis tibi istam propositionem concesserit sine determinatione, assume et regredere concludendo usque ad primam que in questione fuit.’ See (Garlandus Compotista 1959, p. 85, 3–9): ‘Quotienscumque aliquis fecerit tibi mentionem de necessario vel de possibili vel de contingenti, determinatum secundum quem modum acceperit. Nam si indeterminatum preterieris, inconveniens sepe inde habebis. Poterit enim tibi probari et hominem esse immortalem et ignem omni tempore durare ad similitudinem primi sophismatis. Si quis igitur tibi dixerit hominem ex necessitate esse animal et ex necessitate ignem calere, appone: “dum est homo” et “dum ignis calet”.’

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only when they are predicated of sempiternal beings, such as ‘it is necessary for God to be immortal’. Nonetheless, he still allows for predications about absolute possibility to be true even when they concern contingent beings: he states, for instance, that ‘it is possible for birds to fly’ is true absolutely – that is, at all times – because even when there are no birds it would be possible for God to create them and bring it about that they fly.72 Although this example was already present in Boethius, the justification appealing to God’s absolute power is added by Garland, who seems in this way to ontologically found the possibilities of non-existing things in God’s ability to bring them about.73 A similar point is raised in commentary SH2,74 where the terms necessarium and possibile are said to be ‘tribus modis’, either without determination and in the absolute sense or in connection with two possible temporal qualifications. Absolute necessity is here taken in the Boethian sense of necessity ‘at all times’ (which will be further explained in terms of inevitability)75 and is said to belong only to those beings that are immutable (‘quae non possunt permutari’), as opposed to determinate necessity, which may also be truly applied to mutable beings.76 In the Dialectica Abelard also limits the applicability of absolutely necessary propositions to sempiternal subjects, as do many other authors of the time. I will return to this in Chapter 3, Section 4, where I will investigate the early 12thcentury notion of ‘absolute necessity’. A second philosophical problem in which early 12th-century logicians applied the distinction between absolute and temporalized necessity is the interpretation of Aristotle’s idea that ‘whatever is necessarily is when it is’ (De 72 73

74 75 76

‘Item possibile est quod absolute omni tempore contingere potest, ut “possibile est avem volare”: licet enim avis omni tempore non sit, potest tamen contingere ut fiat a Deo et ut volet’ (Garlandus Compotista 1959, p. 84, 21–3). A slightly different position can be found in commentary SH4, where the author maintains that propositions about absolute possibility, such as ‘it is possible absolutely (= at all times) for birds to fly’ also raise paradoxical consequences when applied to contingent beings. See SH4: Orléans, Bibl. mun. 266, p. 270b and footnote 66, Chapter 1 on this. SH2: Munich, Bay., Clm. 14779, fols 67v–86v. This is a very common characterization of necessity, which we also find in several H commentaries, as will be explained in Chapter 3, Section 4. Although not explicitly stated in SH2, this may be inferred from the fact that the author says that absolutely necessary propositions about immutable beings entail – and are, in turn, entailed by – the corresponsing qualified necessities (e.g. the two propositions ‘it is necessary for God to be immortal’ and ‘it is necessary for God to be immortal while God exists’ are equipollent), while this is not the case for propositions concerning transient subjects, for the truth of ‘it is necessary for Socrates to be a man while Socrates exists’ does not entail that ‘it is necessary for Socrates to be a man’.

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Interpretatione 9, 19a23–4). The general attitude among authors of the time is to consider this as an improper and ‘harmless’ kind of necessity, conditioned upon the fact that certain events have already happened in time and are therefore now unpreventable. This allowed them to accept the ancient axiom of the necessity of the past and the present without admitting that past and present events are properly and unqualifiedly necessary, which would entail deterministic consequences. The author of H9, for instance, states that the necessity of which Aristotle speaks in this passage from De Interpretatione 9 is not simple or absolute necessity (which he characterizes as inevitability) but a conditioned necessity (or ‘necessitas modalis’), that is, the same kind of necessity that is included in claims such as ‘Socrates necessarily sits while he sits’, which amounts to saying nothing other than ‘Socrates sits’.77 He also says that everything that is present is necessary only ‘in respectu praesentis existentiae’, and this does not prevent it from being contingent in an absolute sense.78 Like the author of H9, other logicians of the time thought that Aristotle’s reference to the necessity of the present and the past could be interpreted as an improper kind of necessity. In commentaries of the time, absolute necessity is 77 See H9: Orléans, Bibl. mun. 266, p. 23a: ‘Postquam probaverat non omnia habere necessitatem determinati eventus, docet quod modalis necessitas inest rebus, scilicet quod quelibet res necessario est dum est; quod equivalet tamquam si diceretur simpliciter “est”. Illatio sic ab immediatis fit. Quandoquidem determinata necessitas non est rebus, ergo modalis est ibi, cum altera debeat ibi esse. Et hoc est: “Igitur quod est necesse est esse hoc modo quando est”, idest dum est, et quod non est necesse est non esse quando non est, idest dum non est.’ 78 H9: Orléans, Bibl. mun. 266, p. 22a: ‘Ergo non omnia sunt ex necessitate, idest non omnia habent determinatum eventum. […] quamvis removerit omnibus rebus [non] convenire necessitatem determinati eventus, tamen convenit bene presentibus rebus non inquantum fuerunt futura, sed in respectu presentis existentie ut Socrates sedens necessario sedet, idest ita sedet quod determinatum est eum sedere respectu presentis sessionis. Non autem omnibus presentibus rebus convenit hec necessitas determinati eventus inquantum aliquando fuerunt futura, quia dum non erant, determinatum esse in futuro non habebant. Et hanc sententiam explicat Aristotiles sic inferendo ab immediatis. Quandoquidem non omnia sunt ex necessitate determinati eventus, ergo presentia habent hanc necessitatem determinati eventus in respectu presentis existentie, cum alterum horum debeat esse. Et hoc est: “Ergo illud quod est, necesse est esse”, idest determinatum eventum habere, “quando est”, idest in eo respectu quod [corrected from quo] presentialiter existit. Et illud quod non est, necesse est non esse, idest determinatum est non esse quando non est in eo respectu quod [corrected from quo] presentialiter non existit. “Sed non omne quod est.” Quasi dicat: Quamvis hec necessitas existendi et non existendi conveniat rebus eo respectu quod [corrected from quo] presentialiter sunt vel non sunt, non tamen convenit eis absolute eadem necessitas, scilicet inquantum fuerunt futura. Et hoc est: Sed non omne quod est, necesse est esse absolute, idest aliqua sunt que non habent eventum determinatum inquantum aliquando fuerunt futura.’

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usually characterized in terms of ‘inevitability’ or ‘invariability’: things that are sempiternal and events that lack the possibility to change (‘nullo modo permutari possunt’) are said to be absolutely necessary, and the same applies to those propositions that talk about things and events of this sort. Events and propositions that are necessary in this first sense are contrasted with ‘determinate’ events and propositions, which – though not inevitable per se – are necessary because the cause of their happening (or of their truth) cannot be prevented or hindered (‘cuius causa non potest impediri’). Past and present events are usually said to be necessary in this second sense.79 Like in Boethius, the notion of temporally qualified necessity is used by early 12th-century authors to neutralize deterministic arguments like the ones raised in De Interpretatione 9 and those connected to God’s knowledge of the future. I will return to these arguments in Chapter 10 of this book. It may be worth noticing here, however, that although the distinction between absolute and qualified necessity that they employ was mainly based on Boethius texts, they might also have relied on other sources. Indeed, a similar discussion on two different senses of necessity can be found in some 11th-century theological works, in which authors such as Peter Damian and Anselm of Canterbury discuss the ‘factual’ or temporal necessity, according to which it is necessary for a certain event to happen when it happens, and oppose it to the proper and unqualified sense of the term ‘necessary’. In his Cur Deus homo Anselm famously distinguishes what he calls ‘necessitas praecedens’, or ‘efficiens’, which according to him is implicated in propositions such as ‘it is necessary for the sky to move’, from ‘necessitas consequens’, which is at stake when we affirm claims such as ‘you necessarily speak while you speak’. The first kind of necessity involves a certain natural constraint (‘violentia naturalis conditionis’), for things that are necessary in this sense have an efficient cause that forces them to be in a certain way. This is, for Anselm, the proper sense of necessity.80 What Anselm instead calls ‘consequent and not efficient necessity’ is not attributed by virtue of some constraint that forces things to be as they are but ‘caused by the actuality of things’81 and characterizes those events for which it is impos79 80 81

See Chapter 3, Section 4 and Chapter 10, Section 2 on this. On the early 12th-century notion of determinacy, see also (Binini 2019a) and (Binini 2019b). The early 12th-century characterization of necessity as what is ‘required or compelled by nature’ (explored in Chapter 3, Section 4) may be an echo of this Anselmian idea of necessity in terms of ‘natural constraint’. Cf. (Knuuttila 2004, p. 125). See Cur Deus homo II, 17 (Anselm of Canterbury 1946, vol. 2, p. 125): ‘Est namque necessitas praecedens, quae causa est ut sit res; et est necessitas sequens, quam res facit. Praecedens et efficiens necessitas est, cum dicitur caelum volvi, quia necesse est ut volvatur; sequens vero et quae nihil efficit sed fit, est cum dico te ex

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sible not to have happened once they have happened. This improper sense of necessity, Anselm says, is the one invoked by Aristotle in De Interpretatione 9 when he states that everything necessarily is when it is (‘Haec est illa necessitas quae, ubi tractat Aristoteles de propositionibus singularibus et futuris, videtur utrumlibet destruere et omnia esse ex necessitate astruere’). Like many 12th-century logicians, Anselm also says that everything that is necessary in the proper, unqualified sense is also necessary in the sense of sequent necessity, while the opposite inference is not valid (‘Sed ubicumque est praecedens necessitas, est et sequens; non autem ubi sequens, ibi statim et praecedens’). Anselm’s ‘consequent’ necessity resembles the notion of temporally qualified necessity that Boethius invokes while commenting on Aristotle’s view on the necessity of the present. However, Anselm distances himself from Boethius by remarking that improper necessity of this sort applies not only to events that are happening now, or have happened in the past, but to any tense and time, including the future. He claims that, with respect to consequent necessity, ‘whatever has been necessarily has been, whatever is, necessarily is and whatever will be necessarily will be.’82 Anselm seems then to reject Boethius’

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necessitate loqui, quia loqueris. Cum enim hoc dico, significo nihil facere posse, ut dum loqueris non loquaris, non quod aliquid te cogat ad loquendum. Nam violentia naturalis conditionis cogit caelum volvi, te vero nulla necessitas facit loqui. Sed ubicumque est praecedens necessitas, est et sequens; non autem ubi sequens, ibi statim et praecedens. Possumus namque dicere: necesse est caelum volvi, quia volvitur; sed non similiter est verum idcirco te loqui, quia necesse est ut loquaris.’ (Anselm of Canterbury 1946, vol. 2, p. 125): ‘Ista sequens necessitas currit per omnia tempora hoc modo: Quidquid fuit, necesse est fuisse. Quidquid est, necesse est esse et necesse est futurum fuisse. Quidquid futurum est, necesse est futurum esse.’ See on this (Holopainen 2006, p. 104). On the improper necessity of the future, see also Anselm’s De Concordia (Anselm of Canterbury 1946, vol. 2, pp. 250, 13–251, 2), where the distinction between antecedent and sequent necessity is applied to argue for the compatibility between the contingency of the future and divine foreknowledge. Future events, Anselm says, are necessary according to sequent necessity, that is, what will happen will happen necessarily. This, however, does not prevent many future events from being contingent, for they are not necessary in the proper sense: ‘Cum autem futurum dicitur de re, non semper res necessitate est, quamvis sit futura. Nam si dico: “cras seditio futura est in populo”, non tamen necessitate erit seditio. Potest enim fieri antequam sit, ut non fiat, etiam si est futura. Aliquando vero est, ut res sit ex necessitate quae dicitur futura; ut si dico cras esse futurum ortum solis. Si ergo cum necessitate pronuntio futurum de re futura: hoc modo seditio cras futura necessitate futura est, aut ortus solis cras futurus necessitate futurus est; seditio quidem quae non erit ex necessitate, sola sequenti necessitate futura asseritur, quia futura de futura dicitur. Si enim cras futura est, necessitate futura est. Ortus vero solis duabus necessitatibus futurus intelligitur, scilicet et praecedenti quae facit rem esse – ideo enim erit, quia necesse est ut sit – et sequenti quae nihil cogit esse, quoniam idcirco necessitate futurus est, quia futurus est.’

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views on the ‘modal asymmetry’ of time, according to which there is an opposition between the modal status of the present and the past, which are fixed and unchangeable from the present’s perspective, and the unfixity and ‘openness’ of the future. According to Anselm, events and propositions of all tenses may be contingent with respect to their efficient cause and necessary with respect to their actual happening at some point in time. In early 12th-century sources, we will see that the Boethian paradigm is prevalent in this respect, as authors of this time tend to apply the notion of temporally qualified necessity (which they also refer to as ‘determinacy’) only to the present and the past, and they never claim that the distinction between the two necessities may be applied to the future as well. Nonetheless, Boethius’ view on the modal asymmetry of time will start to be put into question by some authors of the time, and especially by Abelard, who advanced the idea that the present and past are also contingent and in no sense necessary (see Chapter 9, Section 4). A distinction between two senses of the term ‘necessarium’ similar to the one proposed by Anselm was advanced by Peter Damian (1007–1072) in his famous discussion on divine omnipotence. According to Damian, one kind of necessity, which he calls ‘necessity of nature’, is the one that governs the natural world by laws fixed by the creator, and which therefore establishes the limits of the possibilities and freedom of created beings. A second kind of necessity, which Damian refers to as a ‘dialectical necessity’, is the one according to which we say of something that has occurred that it occurred necessarily. This is because, according to the rules of dialectic, from the factuality of any statement one may infer its necessity,83 so that anything that is (or was or will be) true is in this sense necessarily true. Like Anselm’s sequent necessity, Damian’s dialectic necessity is conditioned upon a certain event having happened or upon a certain proposition being true in a definite moment of time. It is, however, a ‘harmless’ sense of necessity, because things that are called necessary in this sense are not inevitable per se and may still be considered contingent. Damian applies this notion in his defence of God’s omnipotence over events happening at all times: in his view, when someone tries to discard God’s omnipotence by saying that it is impossible for God to undo what is done, or that it is necessary for what has happened to have happened, these modal terms should be understood in the sense of ‘dialectic modalities’ and do not restrict God’s absolute power to bring about a different past. Moreover, Damian thinks, like Anselm, that the improper sense of necessity and impossibility should be 83

(Holopainen 2006, pp. 116–9).

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applied not only to the past but to all tenses, including the present and the future,84 so if one says that it is impossible for God to change the past by arguing that what has happened necessarily happened, then one should also admit that God cannot change the present or future either, for in the same sense it would be impossible for what is happening not to be happening and for what will happen not to happen in the future. Confusing ‘dialectic modalities’ and ‘natural modalities’ in this way would then endanger not only God’s power over the past but the entirety of his power, which would be absurd, according to Peter Damian. Even though both Anselm and Damian connect their notion of temporally qualified necessity to Aristotle’s discussion in De Interpretatione 9,85 displaying some knowledge of Boethius’ commentaries on it, the idea of distinguishing between two senses of necessity could also have been based on Augustinian sources, and particularly on the fifth chapter of De Civitate Dei, where Augustine also speaks of a sense of necessity ‘according to which we say it is necessary for something to be as it is, or happen as it does’ (‘necessitas secundum quam dicimus necesse esse ut ita sit aliquid vel ita fiat’), and says that necessity of this sort does not discard the existence of contingency or free choice, for it does not impose any genuine constraint upon things.86 Although it is still unclear whether these 11th-century theological discussions had any direct influence on early 12th-century logic, the interplay between Augustinian and Boethian sources that may be found in 11th-century theology also characterizes the logical conceptualization of modalities in the early 12th century. Despite the fact that the study of Aristotelian logic and of Boethius becomes predominant in the curriculum at the turn of the century, echoes of Augustinian views on modalities still remain in the background, as is evident, for instance, from the standard definition of necessity in terms of inevitability (see Chapter 3, Section 4 on this) or from early 12th-century debates on the compatibility between contingency, the fixity of God’s providential plan and the infallibility of his foreknowledge (see Chapter 10, Sections 3–4). 84

See (Holopainen 2006, p. 117). On Peter Damian’s use of modal terms, see also (Knuuttila 2004, pp. 115–8). 85 In De Casu Diaboli, Anselm refers to Aristotle’s dilemma in De Interpretatione 9 as ‘that very celebrated question’, suggesting that there was a lively debate on the topic among his contemporaries (Holopainen 2006, p. 104). 86 (Holopainen 2006, p. 111).

chapter 2

The Grammar and Syntax of Modal Claims 1 What Is a Mode? Grammatical and Logical Perspectives on Modalities Ancient modal theories such as the ones advanced by Aristotle or Boethius did not devote much space to reflect on what modal words are, on which is their proper classification with respect to the other parts of language, or on defining the syntactic and semantic role they perform when included in categorical propositions. Early 12th-century logicians, on the contrary – perhaps because of their deep sensitivity to the grammatical aspects of language – dedicated much thought to these matters, and these speculations had a profound impact on the logic and semantics they set up for modal propositions. The standard characterization of modes given by Abelard and logicians of his time is as follows: modes are the words that qualify (determinant) a simple predication, stating in which way (quomodo) what is signified by a predicate inheres in what is signified by the subject. Propositions in which modal terms are included, such as ‘Socrates reads well’ or ‘Socrates runs rapidly’, express a qualified inherence between two things and are usually contrasted with non-modal claims such as ‘Socrates reads’, which are called ‘simple’ or ‘de puro inesse’ because they affirm that a certain property is ‘unqualifiedly’ (simpliciter) conjoined to a certain substance.1 This definition of modes is advanced by Abelard in both the Dialectica and the Logica Ingredientibus, where he says that: both adverbs and nouns are said to be modes [modi], because they qualify the way [modum] of inherence or separation, as for instance when I say ‘Socrates reads well’, by means of ‘well’ I qualify the way in which the reading is conjoined to Socrates; or when I say ‘Socrates is possibly a bishop’, I do not state that being a bishop unqualifiedly inheres in Socrates, but possibly.2 1 The expression ‘de puro inesse’ comes from Boethius, who in his De Hypotheticis Syllogismis distinguishes between propositions ‘cum modo’ and propositions ‘praeter modum’, which are – he says – all those ones that ‘significant purum esse’. See (Boethius 1969, pp. 235–6). 2 See Dial. 191, 5–9: ‘Modi itaque dicuntur tam adverbia quam huiusmodi nomina quia modum inhaerentiae vel remotionis determinant, ut cum dico: “Socrates bene legit,” qualiter lectio Socrati cohaereat, per “bene” determino; vel cum dico: “Socrates possibiliter est episcopus”, episcopum quidem non simpliciter inhaerere Socrati, sed possibiliter propono.’ See also © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_005

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Modal words, Abelard also says, are the ones that could serve as proper answers to a ‘quomodo?’ question, that is, a question by means of which it is asked how or in which way the things signified by the proposition’s terms are conjoined or separated: Modes, from which some propositions are called ‘modal’, are properly said to be any of those adverbs which may be used as answer to a ‘in which way?’ question. As for instance if it is asked ‘in which way does he read?’, it would be legitimate to answer – with respect to the force of interrogation – that [he reads] ‘well’, ‘badly’ or ‘rapidly’. These adverbs, that qualify the inherence of a verb in modifying it, are properly said to be modes. (LI De Int. 392.22–27)3 As Abelard states in this passage, the words that may function as ‘inherencequalifiers’ are primarily adverbs, even though he admits that some nouns (such as ‘possibile’, ‘verum’, ‘necesse’, ‘bonum’) can be considered modes too, by virtue of the fact that they can be rephrased in an adverbial form and used to qualify a simple predication.4 According to Abelard, propositions de puro inesse are linguistically more basic than modal ones, and the latter are said to ‘descend’ from the former.5 The priority of simple claims to modal ones must be interpreted both as a syntactic priority, because the grammatical structure of modal claims is ‘composed’ of 195, 12–15: ‘Cum ergo dicimus: “Socrates est episcopus”, simplicem inhaerentiam episcopi ad Socratem ostendimus; cum vero “possibiliter” vel “necessario” adiungimus, non solum quod inhaereat, sed etiam qualiter inhaereat, aliquo modo inhaereat, et ita inhaereat.’ 3 ‘Modi autem, unde “modales” dicuntur propositiones, proprie adverbia sunt quaecumque in “quomodo?” responderi possunt. Ut, si quaeratur: “Quomodo legit?” licet responderi, quantum ad vim interrogationis pertinet: “Bene”, “Male”, “Celeriter”; haec itaque adverbia quae verbi inhaerentiam modificando determinant, proprie modi sunt’ (LI De Int. 392.22–27). On this point, see also the author of the Summa Dialectice Artis, a later 12th-century follower of Peter Abelard: ‘Modos vero illas adverbiales determinationes appellamus que ad interrogationem factam per “quomodo” vel per “qualiter” responduntur, veluti “bene”, “male”, “celeriter” et similia’ (Guglielmo da Lucca 1975, p. 103, §7.02). 4 See, for instance, LI De Int. 394.80–4: ‘Sicut autem Aristoteles adverbia modos appellat quaedam secundum sensum, ut “celeriter”, “necessario”, quaedam secundum positionem constructionis, sicut “possibiliter” vel “vere”, ita etiam nomina quae in sensum adverbii resolvuntur modos appellat, “necesse” scilicet, “possibile”, “verum” cum dicitur.’ 5 ‘Unde simplices ipsis modalibus, quasi compositis, priores sunt: ex ipsis modales descendunt et ipsarum modificant enuntiationem; in qua quidem modificatione tantum ab ipsis abundant et discrepant’ (Dial. 191, 23–6). See also (200, 20–2): ‘Et sunt quidem simplices natura priores quasi simplicia compositis; oportet enim prius inhaerentiam considerare quam modificare.’

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simple predications to which a certain modal term is adjoined, as well as a semantic priority, because simple predication is semantically the most primitive form of predication, and modal predication is derived from it. The characterization of modes provided by Abelard was indeed rather standard in sources from the early 12th century. We find it in similar terms in the commentary on De Interpretatione, catalogued as H9, where the author distinguishes between simple and cum modo propositions, saying that the latter express ‘in a qualified way’ what is stated simpliciter in the former. This is done by means of terms such as ‘well’, ‘truly’, ‘possibly’, or ‘necessarily’, which have the role of ‘modifying’ the way in which what is predicated is conjoined to the subject.6 The author goes on to say that what makes a proposition modal is not simply the fact that a modal term is included in it: in order for it to be properly modal, this term must perform the role of inherence-qualifier: We should consider that it is not whenever terms like ‘possible’, ‘necessary’ or some other of this sort are predicated that a proposition is called ‘modal’, but only when it states modally (cum modo) that something inheres in something else, that means, whenever [the mode] qualifies the inherence between things, as in ‘Socrates reads well’. Here, the mode qualifies the inherence of the reading in Socrates. In the same way, in ‘Socrates can read’ (Socrates potest legere) it is said that the reading is conjoined to Socrates not unqualifiedly, but potentially (potentialiter).7 An analogous point is made by Garland in the Dialectica, where he says that simple and modal propositions are distinguished by virtue of having a different intentio, inasmuch as simple categoricals state ‘that’ (quod) a certain predicate inheres or does not inhere in a subject, whereas modals state ‘in which way’ (quomodo) it inheres or does not inhere (‘alie intendunt ostendere quod praedicatum inhereat subiecto vel non inhereat, iste vero quomodo inhereat vel

6 See H9, Orléans, Bibl. mun. 266, pp. 33a–b: ‘Propositiones namque alie sunt de puro inesse et sine modo aliquid inesse enuntiant, ut “Socrates disputat”. Alie sunt que non simpliciter, sed cum modo aliquid enuntiant, ut “Socrates bene disputat” vel “Socratem possibile est disputare” […] Nam “bene”, “vere”, “possibiliter”, “necessario” et similia modi sunt in propositionibus, quia moderantur illud quod cum illis predicatur qualiter subiecto habeat coherere.’ 7 See H9, Orléans, Bibl. mun. 266, p. 33b: ‘Notandum autem quia non quotiens predicatur “potest”, “necessarium” vel aliquid tale modalis propositio vocatur, sed tunc tantum cum dicit aliquod alicui inesse cum modo, scilicet quotiens moderatur rerum coherentiam, ut “Socrates bene legit”: hic modus determinat coherentiam lectionis cum Socrate vel “Socrates potest legere”: hic non simpliciter, sed potentialiter dicitur lectio Socrati convenire.’

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non inhereat’).8 The modes ‘possibly’, ‘impossibly’, ‘necessarily’, and ‘contingently’ are therefore called by Garland ‘ways of inherence’ (modi inherentiae).9 Similar remarks can also be found in later sources from the second half of the 12th century, such as the Ars Meliduna, in which a proposition is said to be ‘modal’ if the inherence (cohaerentia) of its predicate in the subject is qualified by a mode;10 or the Excerpta Norimbergensia, in which the mode is said to express the quality of the predicate, either by determining a verb or an inherence between two terms;11 or again the Ars Burana, in which propositions are called modal when they include terms that modify (modificant, determinant) the inherence of a predicate.12 Early 12th-century sources, however, are usually ambiguous about whether modal terms act as qualifiers of the inherence between the subject and predicate or rather as qualifiers of the predicate itself and of the meaning expressed by the propositions’ verb. I will return to this later in this section. In the second half of the century, on the contrary, a debate emerges concerning this matter. 8 9 10

(Garlandus Compotista 1959, p. 81, 18–20). (Garlandus Compotista 1959, p. 82, 14). See Oxford, Bodl., Digby 174, fol. 228 va: ‘Modalis est illa propositio qua modificatur cohaerentia praedicati ad subiectum, ut “deum esse est necessarium”.’ For the same idea, see also fol. 228ra: ‘Modalis est illa [propositio] cuius praedicato determinatur modus cohaerendi ut “deum esse est necessarium”, vel consequendi ut “Socratem esse coloratum, si Socrates est albus, est necessarium”, quia enim modalis eiusdem praedicati ad subiectum modificat cohaerentiam, non tamen dico sui praedicati ad suum subiectum, sed cohaerentiam praedicati ad subiectum quam habet in subiecto implicitam.’ The author says that the (implicit) predicate and subject of a modal proposition are the same as the subject and predicate of the corresponding simple proposition. As we will see in C ­ hapter 2, ­Section 3, Abelard advances the same opinion in his works. It may be interesting to note that the author of the Ars Meliduna, differently from earlier logicians, distinguished between adverbs that determine the quality of an action (qualitas agendi), such as ‘well’ or ‘rapidly’, and those that determine the mode of inhering (modus cohaerendi), such as ‘possibly’, ‘truly’, or ‘necessarily’, stating that only the second should be considered modes. This distinction was never advanced in earlier sources, while it might have been the object of discussion in the second half of the century. See on this (Binini 2020a). 11 Anonymous, Excerpta Norimbergensia in (De Rijk 1967, p. 140): ‘Modalis est illa que habet modum in predicato. Modus est autem qualitas predicati, idest determinatio verbi, ut “male”, et huiusmodi adverbia, vel inherentie, ut “possibile”, “impossibile”, “verum”, “falsum” et similia. Cum enim dicimus: “homo bene currit”, “bene” adiunctum qualitatem predicati determinat.’ 12 Anonymous, Ars Burana in (De Rijk 1967, p. 207): ‘Modalis est illa in qua attribuitur predicatum subiecto cum determinatione, (ut) “Socrates necessario est homo”, “Socrates contingenter est albus”. Et dicuntur propositiones ille modales a modis qui in eis ponuntur, scilicet “possibile”, “impossibile”, “contingens”, “necessarium”. Modi autem dicuntur quia modificant, idest determinant, inherentiam predicati.’

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Some authors, such as that of the Summa Periermeneias, only speak of modes as qualifiers of the action (modus or qualitas actionis) expressed by the predicate term, without mentioning their use as inherence-qualifiers;13 others, such as the author(s) of the Ars Meliduna, disagree with this characterization, distinguishing between adverbs that determine the quality of an action ­(qualitas agendi), such as ‘well’ or ‘rapidly’, and those that determine the mode of inhering (modus cohaerendi), such as ‘possibly’, ‘truly’, or ‘necessarily’, ­stating that only the second should be considered modes.14 This discussion will be echoed in some 13th-century logical treatises, such as William of Sherwood’s works.15 Returning to the early 12th-century reading of modes, we should notice that, as a result of the standard characterization of modes as ‘inherencequalifiers’, affirmative modal propositions should always be taken to express a certain inherence between two terms, just as non-modal propositions do: indeed, how could a proposition state a ‘qualified’ relation between two things without stating that the two are also related simpliciter? This idea is explicitly advanced in some sources, such as the already mentioned commentary H9 and the treatise on modalities labelled M3, both claiming that propositions containing adverbial modes are similar to simple ones, in that they both express a relation of inherence between a subject and a predicate, a relation that is 13 14 15

Similar terminology may be found in sources of the same time, such as the Glossae Doctrinae Sermonum, which says that modes qualify the modus agendi vel patiendi (Anonymous, Glossae Doctrinae Sermonum, edited in Abaelard 2010a, p. 187). The relevant passage from the Ars Meliduna is quoted in footnote 29 of this Chapter. Cf. (Binini 2020a) on this debate. See, for instance (Guilelmus de Shyreswood 1966, pp. 41–2): ‘It should be noted, then, that adverbial modes can occur in discourse in two ways — viz., by determinating either the action itself of the verb or the inherence of the predicate in the subject. Take, for example, “Socrates is running contingently.” Here the word “contingently” can determinate the action as such, in which case the sense is “Socrates’s running is contingent” (cursus contingens est Sorti), and [the proposition] is not modal. Or it can determinate the verb itself in respect of (propter) its inherence [in] or composition [with the subject], in which case the sense is “the composition ‘Socrates is running’ is contingent.” In this case [the proposition] is modal, since [the adverb] determinates the action of the predicate in the subject. Here is a similar case: “the soul of Antichrist will necessarily be”; for if the [adverbial] mode determinates the action of the verb in respect of its composition, then [the proposition] is modal and the sense is “the composition ‘the soul of Antichrist will be is necessary,” which is false (et falsa). If, however, [the adverbial mode] determinates the verb’s action as such, then the sense is “necessary being goes together with the soul of Antichrist,” in which case it is not modal, and in which case it is true. And so also with respect to the other modes.’ For other examples of the 13th-century debate on this topic, and its connection to the development of the de re-de dicto interpretation of modals, see (Rivero 1974).

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unqualified in propositions de puro inesse and qualified in modal ones.16 Nonetheless, some authors of the time, Abelard included, raise doubts on this idea, for they think that there are many modal propositions, such as ‘Socrates is possibly a bishop’, that are true even though there is no actual relation between the things signified by predicate and subject. I will return to this later in this chapter. Another common point often recurring in sources of this time is that adverbial modes qualify the inherence between two things in the sense that they ‘modify’ (determinant, moderantur) the meaning of the verb to which they are attached, in the same way that adjectives qualify the signification of nouns. The author of M3, for instance, states that in expressions such as ‘rapidly runs’ the adverb functions as an ‘adiectivum verbi’, and it forms a single intellectus with the verb to which it is attached, just as adjectives do in expressions such as ‘homo albus’.17 The same view of adverbs is proposed by Abelard in Dial. 191, 12–518 and in LI De Int. 310, 73–619 and could be found in later sources such as the De Propositionibus Modalibus20 and the commentary H20.21 This reading is usually strengthened by an appeal to the authority of Priscian and to the commentary tradition on the Institutiones Grammaticae, to which early 12th-century logicians are so deeply connected. According to the analysis of adverbs provided by Priscian, the relation existing between adverb and verb is the same as the one found between adjective and substantive: the meaning of an adverb is ‘added’ to that of the verb that follows, so that the adverb ‘modifies’ the verb’s signification.22 In this analysis Priscian closely follows the grammatical tradition of his Greek predecessors, such as Apollonius and Dyscolus,

16 17

H9: Orléans, Bibl. mun. 266, pp. 33a–33b; M3: Orléans, Bibl. mun. 266, p. 252b. See M3: Orléans, Bibl. mun. 266, p. 253a: ‘Adiectivum enim et illud cuius est adiectivum faciunt unum intellectum ut “albus homo”, et adverbium verbi adiectivum esse videtur dicere Priscianus in Constructionibus’. 18 ‘Adverbia proprie modos dicimus et inde adverbia vocamus quia verbis adposita eorum determinant significationem, sicut adiectiva nomina substantivis adiuncta, ut cum dicitur: “homo albus”.’ 19 ‘Praeterea adverbium tunc proprie nominis sui etymologiam servat, cum ad verbum apponitur, quia adverbium quasi adiectivum verbi interpretatur.’ 20 Anonymous, De Propositionibus Modalibus in (Abaelard 2010a p. 231, 1–6): ‘Modalis propositio ex modo dicitur. Modus est adverbialis determinatio, quae ad interrogationem per “qualiter?” factam verbum modificare habet, ut “bene”, “prudenter”.’ 21 H20, Orléans, Bibl. mun. 266, p. 262b. 22 See (Keil and Hertz 2010, 15, 1, 1–17, 5, 37). On Priscian’s analysis of adverbs and their relation to adjectives, see also (Pinkster 2005, p. 37), (Luhtala 2005, p. 97) and (Kelly 2002, pp. 133 ff).

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and of some Stoics, who thought of adverbs as being ‘quasi adiectiva verborum’.23 Even though the idea that adverbs are added to verbs and modify their signification is rather vague and left unexplained in Greek and Latin grammatical sources, it is certainly to this idea that early 12th-century authors refer when they say that modes (which are for them primarily adverbs) act as qualifiers of a verb’s meaning or of the inherence between subject and predicate.24 Logicians of Abelard’s time were acquainted to this understanding of adverbs, not only through direct use of Priscian’s Institutiones but also through the so-called ‘Glosulae-complex’, a series of anonymous, layered texts of grammatical content, including commentaries on Priscian Maior and Minor and the Notae Dunelmenses, the earliest layers of which are to be dated to the late 11th century.25 In the Notae Dunelmenses we come upon the traditional definition of adverbs as modifiers of the meaning of verbs, which is also applied here to the particular case of the modal adverbs ‘possibiliter’ and ‘necessario’. The notion of ‘modification’ is rendered in Latin with the verbs moderari, determinare, and modificare, which are also usually employed in early 12th-century logical sources to describe the semantic role of modes when included in modal propositions.26 Moreover, in the Notae it is said that the characterization of 23 24

25 26

See (Keil and Hertz 2010, 2, 4, 16). Because for Abelard and his contemporaries the signification of modal adverbs can be associated with that of adjectives, we would expect them to endorse the view that all modes belong to the linguistic category of nouns, like other adjectives and adverbs do. However, at least in the Logica Ingredientibus, Abelard treats some modal adverbs – in particular, the alethic modes ‘necessarily’, ‘possibly’, ‘impossibly’ – as belonging to the category of indefinites, which includes terms that do not have a meaning on their own but only when taken in context (that is, they merely ‘co-signify’), just like conjunctions (e.g. ‘si’; ‘et’) and prepositions (e.g. ‘ad’, ‘de’). Abelard says that these adverbial modes (and their corresponding nominal forms) do not have a meaning on their own, as isolated from a context, insofar as they do not signify either things or accidents (that is, they do not have a signification in essentia or in adiacentia) but they merely co-signify (LI De Int. 407.412–408.425). This seems to have been a consolidated view in the early 12th century, for in other sources of Abelard’s time too, such as H9 and M3, we read that modal terms such as ‘possibly’ and ‘necessarily’ do not signify things or properties, and in this respect they differ from other nouns, adjectives, or derivative (sumpta) terms. I will return to this in Chapter 3, Section 1. For Abelard’s taxonomy of words and his distinction between linguistic categories, see Dial.118–140. For a discussion of these categories, see (Jacobi 1986, pp. 146 ff.); (Wilks 1998a, pp. 94 ff.). For Abelard’s idea that modal terms fall within the category of indefinites, see also (Nuchelmans 1973 pp. 139–44). For a survey on the Glosulae complex, including a categorization of all manuscripts, datings, and hypotheses on authorship, see, in particular (Grondeux and Rosier-Catach 2011) and (Grondeux and Rosier-Catach 2017). See the recent edition of the Notae Dunelmenses, in particular (Grondeux and Rosier-­ Catach 2017, volume II, pp. 394–7).

52 chapter 2 ‘verb-qualifiers’ applies not only to modal adverbs but also to modal nouns such as ‘possibile’ and ‘necesse’, which in claims like ‘necesse est Socratem legere’ are used as having an adverbial force (vim adverbiis), and as such they may also perform the role of qualifying the ‘act’ of the verb that follows them.27 This idea also has its justification in the teaching of Priscian, according to whom there are some nomina that can be used as having an adverbial status. Early 12th-century logicians, thus, are following a well-established grammatical – rather than logical – tradition when they argue that the semantic role of modal terms is that of qualifying the signification of a verb or the inherence between subject and predicate. This analysis of modes was probably successful in dialectical contexts because it allowed logicians to ‘reduce’ the syntax of adverbial modal claims to that of claims ‘de puro inesse’. This is because, according to this reading, propositions such as ‘Socrates runs rapidly’ or ‘Socrates is necessarily an animal’ have the same syntactic structure as propositions such as ‘Socrates runs’ or ‘Socrates is an animal’, with the only difference being that, while in the latter the relation between subject and predicate is stated unqualifiedly (simpliciter), in the former this relation is qualified by the mode, which modifies the predicate’s meaning. Simple and modal propositions remain alike in that they have the same subject and predicate and can be varied in quality and quantity in the same way, as shown in Table 1. Furthermore, even from a semantic point of view, simple and modal propositions are, in this way, interpreted within the same framework: in both cases, the meaning of the entire proposition is composed by conjoining the understanding (intellectus) generated by the subject with the one generated by the predicate, though keeping in mind that in the case of modal claims the meanings of adverb and predicate must first be united to form a single intellectus. This reading of modes, then, had the merit of maintaining a consistent and unitary theory of categorical propositions, with respect to both their syntax and their semantics. 27

(Grondeux and Rosier-Catach 2017, volume II, p. 378, 367–79): ‘Dicendum itaque, videtur “necesse” duplicem vim habere, scilicet vim nominis et vim adverbii. Ex vi nominis habet subicere rem suam et iungi intransitive cum substantivo. Ex vi autem adverbii habet modificare verbum, quod sequitur circa aliquid, ut cum dico “necesse est Socratem legere”, “necesse” quantum ad vim nominis nominativus est in hoc loco illius tertiae personae substantivi quae adiungitur sibi, scilicet “est”. Et rursus idem “necesse” acceptum in vi adverbii modus est actus huius verbi quod est “legere” circa hanc rem quae est “Socrates”, et ita bene potest stare constructio. Similiter si dicam “necesse est Socratem esse animal”, “necesse” determinat actum sequentis verbi, id est “esse”, qui actus est animal, determinat, dico, circa Socratem’ (my emphasis).

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The Grammar and Syntax of Modal Claims table 1  Early 12th-century analysis of adverbial modals

Structure of propositions de puro inesse (Omnis – Quidam) Sign of quantity

homo Subject

(non) Negation

est Copula

animal Predicate

Structure of propositions cum modo (Omnis – Quidam) Sign of quantity

homo Subject

(non) Negation

est Copula

animal necessario Predicate Mode Qualified Predicate

However, dialecticians of Abelard’s time came to realize that several problems were connected to this analysis. In particular, they were perplexed about whether all adverbial modes could be interpreted as verb- or inherence-qualifiers and, in particular, whether modes such as ‘possibly’, ‘impossibly’, or ‘falsely’ fit this characterization. If the role of these adverbs was indeed that of qualifying the meaning of a verb or its inherence in a subject, then every proposition containing these modes would express the existence of an actual inherence between the things signified by subject and predicate. This is because anytime it is true that ‘S is P in a certain way’, it must also be true that ‘S is P simpliciter’, as was mentioned earlier. But this does not seem right in the case in which the mode is an adverb such as ‘possibly’, ‘impossibly’, or the like, for propositions such as ‘S is (im)possibly P’ may be true even though the property of being P does not actually inhere in Socrates. How do these adverbs fit into the traditional framework then? In the next section I will focus on the debate that these ‘misbehaving modes’ generated among early 12th-century logicians, and on the distinction between proper and improper modes that some authors advanced in order to solve it. Before proceeding with the next section, we should clarify that, even though many sorts of adverbs and nouns were considered by early 12th-century logicians to be modes, logical sources of the time only focus on a limited number of modes, namely, the adverbs ‘possibly’, ‘contingently’, ‘impossibly’, ‘necessarily’, ‘truly’, and ‘falsely’, along with the respective nominal forms. Following Aristotle’s list of modes in De Interpretatione 12–13, Abelard and his contemporaries claimed that these are the only modes that are suitable for being arranged in

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a system of logical inferences and equipollence.28 Authors of the 12th century, then, do not seem to realize that there could be a modal logic with different modal operators besides the ones we would today call alethic modalities. The only exception to this view, as far as I know, is the author of the Ars Meliduna, who states that, to the ones that were traditionally considered ‘modes’ by Aristotle, two more terms might be added, namely, ‘certain’ (­certum) and ‘doubtful’ (dubium), perhaps envisaging – alone among his contemporaries – a possible use of modal logic to treat epistemic themes, a use that nevertheless he leaves unexplored.29 2

Proper and Improper Modes

The traditional idea that modes act as qualifiers of a verb’s meaning was often taken in correlation with Boethius’ view that the signification of a verb stated with a certain modal qualification (e.g. ‘to run rapidly’) is always ‘part’ of the signification of the same verb taken simpliciter (‘to run’).30 This part-whole 28

29

30

See Abelard’s Dial. 191, 37–192, 3: ‘Cum autem plures sint modi qui modales faciunt propositiones, horum naturam tractare sufficiat quorum propositiones ad se aequipollentiam habent, ut sunt: “possibile”, “contingens”, “impossibile”, “necesse”, quorum propositiones Aristoteles inde ad tractandum elegit quod ad se habeant aequipollentiam’; and LI De Int. 408.438–442: ‘Cum autem multi sint modi tam adverbiales quam casuales, hic tantum Aristoteles quatuor modorum propositiones diligenter exsequitur, contingentis scilicet, possibilis, impossibilis, necessarii, quae ad invicem maxime sunt affines et per omnes modos aequipollentes, sive de sensu sive de rebus expositae.’ The same idea may be found in many other sources of the time. I will return to this restriction in Chapter 8, Section 1. See Anonymous, Ars Meliduna in (De Rijk 1967, p. 332): ‘Et sunt modi qui propositionem faciunt modalem sex ab Aristotile assignati: “verum”, “falsum”, “possibile”, “impossibile”, “necessarium”, “contingens”. Quibus etiam addi possunt “dubium” et “certum”.’ The author of the Meliduna also claims that the other adverbs or nouns that were traditionally considered modes by Boethius (e.g. the adverb ‘rapidly’ in ‘Plato runs rapidly’) are not modes in the logical and usual sense, for they specify the quality of an action (qualitas agendi) rather than determining the way in which subject and predicate are conjoined (modus cohaerendi): ‘Boetius tamen modales appellat etiam istas: “Socrates legit bene”, “Plato currit celeriter”. Sed adverbia ibi posita magis determinant qualitatem agendi, idest qualiter legat vel currat, quam modum coherendi. Ergo modales eas fortasse dixit Boetius a qualitate sui predicati, quia scilicet in predicato verbum habent adverbio modificatum. Unde etiam in eis pars in modo predicatur. Sed frequens usus non recipit modales esse nisi que predictos contineant modos.’ See (Boethius 1990 II, 1189 B): ‘One can take parts and whole into account not only in substances but also in mode, times, quantities, and place. […] If something is put forth without qualification, it is a whole with regard to mode; if something is put forth with a qualification, it is a part with regard to mode.’ The translation is from (Stump 1978, p. 52).

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relation allows Boethius to establish a rule of inference deriving any unqualified verb from the same verb taken cum modo, by virtue of a locus a partibus. This means that anytime it is true that ‘S is P cum modo’, it is also true that ‘S is P’. Abelard reports Boethius’ rule of inference in both the Dialectica31 and the Logica Ingredientibus,32 and many references to the same idea (which either accept or refuse it) may be found in several sources of the time, such as M1 and M3, and later commentaries such as the Glossae Doctrinae Sermonum and H20.33 According to this view, applying a mode to a verb would result in ‘restricting’ this verb’s extension, which is compatible with the parallelism established by Priscian between adverbs and adjectives, for adjectives too generally ‘restrict’ the signification of the noun to which they are adjoined, making this noun applicable to fewer things. As was mentioned, however, this characterization raises some difficulties, because there seem to be a number of adverbs – traditionally counted as modes – that do not ‘qualify’ verbs in the sense of restricting their extension and delimiting one of their parts. The mode ‘possibly’, for instance, seems rather to ‘broaden’ the signification of the verb to which it is applied, because there are more things of which we could say, for instance, that they ‘possibly run’ than things that actually do run, as the authors of M1, M3, and H20 point out.34 For this reason, the mode ‘possibly’ does not seem to satisfy Boethius’ 31

‘Cum ergo dicimus: “Socrates est episcopus”, simplicem inhaerentiam episcopi ad Socratem ostendimus; cum vero “possibiliter” vel “necessario” adiungimus, non solum quod inhaereat, sed etiam qualiter inhaereat, aliquo modo inhaereat, et ita inhaereat. Ait in Topicis Boethius quod aliquid cum modo propositum pars accipiatur, et simpliciter acceptum totum intelligatur, ut: “cito currere” et “currere”: “currere” enim totum est, “cito currere”, autem pars; unde et dicitur quod “si cito currit, currit” sed non convertitur.’ (Dial. 194, 15–20) 32 See LI De Int. 392.39–46. 33 For references to this idea, see M1: Orléans, Bibl. mun. 266, p. 166b; M3: Orléans, Bibl. mun. 266, p. 253b; H20: Orléans, Bibl. mun. 266, p. 262b; Anonymous, Glossae Doctrinae Sermonum in (Abaelard 2010a, p. 187, 22–5). On the role of Boethius’ rule in M1 and M3, see also (Martin 2016, pp. 117–8). 34 See M3: Orléans, Bibl. mun. 266, p. 253a: ‘De modis adverbialibus faciunt quidam talem divisionem: Alii enim sunt modi vocis et sensus, alii vocis tantum; et qui vocis tantum, alii ampliant vocem, alii comitantur vocem, alii reducunt ad opposita. […] Ampliant vocem quibus adiunctis alicui voci, vox agit de pluribus cum illo modo quam per se, ut “possibiliter”. “Episcopatur” enim, vox ista, agit de episcopantibus tantum, sed “possibiliter episcopatur” et de episcopantibus et de non episcopantibus; nec concedunt sequi “si est episcopus possibiliter, tunc est episcopus”.’ See also M1: Orléans, Bibl. mun. 266, p. 166a: ‘Sed sciendum quod modi adverbiales alii sunt vocis tantum, alii tam vocis quam sensus. Ad quod videndum praenoscendum est quod alii modi restringunt verbalem, cui iunguntur, vocem; alii amplificant; alii permutant […] Illi ergo modi, qui verbum tantum ­restringunt,

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rule of inference, for although we may truly say that ‘Socrates possibly runs’, we cannot infer from this that ‘he runs simpliciter’. These difficulties are even clearer in the case of adverbial modes such as ‘impossibly’ or ‘falsely’, which, according to the authors of M1 and M3, neither restrict nor broaden but completely alter (permutant) a verb’s signification and ‘twist’ the understanding produced by it (intellectum detorquent).35 The term ‘truly’, which was usually counted as a mode in early 12th-century modal logic, also does not seem to satisfy the traditional characterization based on Priscian and Boethius, for even though the inference ‘If “S is truly P”, then “S is P”’ is valid, the signification of the qualified verb ‘truly P’ is not a proper part of the unqualified verb ‘P’.36 Among all the terms that were considered modes in early 12th-century modal logic, only one (the mode ‘necessarily’) seems to act as a proper qualifier of a verb in the sense of restricting its extension. All other modes – that is, ‘possibly, ‘impossibly’, ‘truly’, and ‘falsely’ – seem not to perform the same semantic role. Two different strategies were advanced by authors of this time to make these ‘deviant’ modes compatible with the traditional characterization given by Boethius and Priscian. On the one hand, some authors proposed to distinguish between ‘proper’ and ‘improper’ modes, where the first (e.g. ‘necessarily’) function as proper verb-qualifiers, while others (e.g. ‘possibly’) are modes with respect to their grammatical construction only, and not with respect to meaning. Abelard endorses this view, distinguishing between terms that are modes ‘quantum ad sensum’ and terms that are only modes ‘quantum ad enuntiationem’ or ‘secundum positionem constructionis’ (or also modes ‘in sensu’, as opposed to modes ‘in voce’).37 The latter are called modes because, when they pertinent et ad vocem et ad sensum, quia vocem pariter et sensum modificant. Restringendo namque vocem pauciora significare eam faciunt, ut “velociter currit homo”. Cum enim “currit” currentes omnes significet, “velociter currit” velociter tantum currentes demonstrat. Illi vero modi, qui vocis significationem ampliant vel ad alium intellectum detorquent, vocem tantum modificant, quia a sua eam significationem sive partim sive ex toto alienant. Quam enim vocem amplificant, aliud quodammodo significare compellunt, ut cum dico “rusticus episcopatur possibiliter”.’ 35 See M1: Orléans, Bibl. mun. 266, p. 166a. Abelard treats these two cases in Dial. 194, 37–195, 3 and LI De Int. 392, 33–7. 36 See on this Abelard’s Dial. 194, 34–7; LI De Int. 393, 63–394, 73. See also H20: Orléans, Bibl. mun. 266, p. 262b; M3: Orléans, Bibl. mun. 266, p. 253a. 37 LI De Int. 394.74–9: ‘Cum autem nec “vere” nec “possibiliter” quantum ad sensum modi sint, secundum tamen positionem constructionis Aristoteles modos ea appellat quia eundem locum in constructione possident, verbo adiecta, quem obtinent proprii modi. Quia, sicut dicimus: “Currit celeriter” (vel: “necessario”) ita etiam dicimus: “Currit possibiliter” (vel: “vere”) nil tamen in sensu modificantes, ut ostendimus.’ See also Dial. 194, 12–195, 10,

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are included in a categorical proposition, they have the same grammatical position that proper modes usually have, that is, they are attached to a verb if they have an adverbial form (as in ‘Socrates est episcopus possibiliter’), or they introduce an accusative infinitive clause if they have a nominal form (as in ‘Possibile est Socratem esse episcopum’). Although not differing from proper modes with respect to their grammatical construction, improper modes have a different semantic role, as they are not qualifiers of a verb’s meaning and they do not posit any actual relation of inherence between predicate and subject. Note that, as Abelard remarks in the Logica Ingredientibus, his distinction between proper and improper modes is meant to be applied to both adverbial and nominal modes.38 Abelard often refers, in his discussion of modal logic, to a distinction between the grammatical or surface structure (constructio)39 of modal propositions and their ‘deep’ structure, that is, what we would call today their logical form. The identification of these two levels of language is a crucial feature of Abelard’s logic, which enables him to distinguish between two different kinds of sentential well-formedness (congruitas) – namely, grammatical and semantic – and which is responsible for some of the more interesting novelties of

where Abelard says that improper modes are the modes ‘possibly’ (‘At vero “possibiliter”, si veritatem attentius inspiciamus, non est in sensu modus, sed in voce’), ‘truly’, and ‘falsely’ (‘Invenimus autem saepissime tales modos qui quidem quantum ad enuntiationem, non quantum ad sensum, modi vocantur, ut “vere” vel “falso”. Neque enim cum dicimus: “Plato vere est philosophus”, “vere” inhaerentiam philosophi determinat […] Non ergo “falso” inhaerentiam determinat, sed enecat’). ‘Necessarily’ is the only mode that is said to be proper (‘“Necessario” autem proprie modus videri potest, cum partem in natura faciat, ut scilicet “necessario esse hominem” pars sit in natura “esse hominem”. Unde si necessario est homo, consequitur ut sit homo; sed non convertitur’).’ 38 See LI De Int. 394, 86–90: ‘Et ita habemus quosdam modos adverbiales, quosdam casuales, et de utrisque quosdam proprie modos secundum sensum, quantum ad constructionem solam; nam “necesse” vel “necessario” proprie modi sunt, “possibile” vel “verum” siue eorum adverbia non ita.’ 39 Abelard uses two terms to refer to the syntactic structure of a proposition: one is ‘constructio’, which is used in this context and in several others devoted to modalities, and the other is ‘complexio’. The first term is related to the grammatical tradition: it is used by Priscian to refer to well-formed sequences of words (Keil and Hertz 2010 XVII, II, 108, 5–10; 108, 23-109-3) and is usually used by Abelard when referring to complete sententiae and their grammatical form (Jolivet 2000, p. 29) and (Valente 2015, p. 90). The term ‘complexio’ is used in dialectical contexts such as those devoted to the logical form of propositions when included in topical and syllogistic arguments, for example, Dial. 253, 31. This term is connected to a Boethian tradition. Boethius, for instance, uses ‘complexio’ to refer to the structure of propositions (complexio propositionum) or to the schemata for syllogisms (Boethius 1969, p. 2, 2–3) and (Boethius 2008, II passim).

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his modal system, such as the distinction between the de rebus and de sensu interpretation of modal claims, as we will see in Chapter 4. Abelard’s distinction between modes in sensu and in voce is rehearsed in later treatises, such as the De Propositionibus Modalibus, whose author follows Abelard’s terminology distinguishing between ‘proper’ and ‘improper’ modes (the latter are said to be modes ‘pro sola constructione’),40 and the Glossae Doctrinae Sermonum, where the author says that only some modes restrict the verb to one of its parts and determine the mode of inherence and noninherence, while others are called modes ‘tantum pro expressione facienda’.41 Also the author of the Summa Dialectice Artis, a devoted follower of Abelard, states that some nouns or adverbs (such as ‘possible’, ‘possibly’, or ‘falsely’) are called ‘modes’ only in an improper sense, as they do not function as qualifiers of an inherence.42 This same bipartition may also be found, attributed to ‘quidam’ (perhaps Abelard himself), in the treatises on modalities M1 and M3, where a distinction is proposed between adverbial modes that are ‘tam vocis quam sensus’ and modes that are ‘vocis tantum’. Modes that are called ‘tam vocis quam sensus’ modify both the wording and signification of the proposition in which they are applied, by restricting the verb’s extension and making ‘fewer things fall under its signification’.43 Modes that are ‘vocis tantum’, on the contrary, modify only 40

See Anonymous, De Propositionibus Modalibus in (Abaelard 2010a, p. 231, 7–12): ‘Modus alius proprie dicitur, modus alius improprie. Ille proprie dicitur modus, ex quo materialiter posito in propositione simplex potest inferri, ut ex ista “Socrates celeriter currit” potest inferri “Ergo Socrates currit”. Sunt autem alii qui hoc non habent, ut “falso”, “possibiliter”, “forsitan”, qui improprie et (pro) sola constructione modi dicuntur.’ 41 See Anonymous, Glossae Doctrinae Sermonum in (Abaelard 2010a, p. 187, 19–25): ‘Modi adverbiales sunt “bene”, “male”, “possibiliter”, “celeriter”, qui modi dicuntur adverbiales quia verbis adiciuntur ad modum agendi vel patiendi determinandum, et ad “Quomodo?” respondentur, faciuntque partem sub modo. Non tamen omnes: si enim dicatur “Socrates possibiliter legit”, non est pars ad “legere”, et vere similiter aliquando non facit partem in modo sed tantum pro expressione facienda apponitur.’ 42 See (Guglielmo da Lucca 1975, p. 102 § 7.02): ‘Sed modorum alii adverbiales, alii casuales dicuntur. Adverbiales quidem sunt illi quos supradiximus; casuales vero sunt ut isti: “possibile”, “impossibile”, “necesse” et similes: tamen non ita proprie modi ut predicti esse dicuntur, cum inherentiam verbi non modificent sicut illi; cum enim dicimus “Socratem legere est possibile” vel “Socrates legit possibiliter” seu “Socrates legit falso” non ostendimus ipsum aliquo modo legere vel ipsum carere lectione”. 43 See M1: Orléans, Bibl. mun. 266, p. 166a: ‘Illi ergo modi, qui verbum tantum restringunt, pertinent et ad vocem et ad sensum, quia vocem pariter et sensum modificant. Restringendo namque vocem pauciora significare eam faciunt, ut “velociter currit homo”. Cum enim “currit” currentes omnes significet, “velociter currit” velociter tantum currentes demonstrat’; M3: Orléans, Bibl. mun. 266, p. 253a: ‘Vocis et sensus modi sunt qui adiuncti

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the wording and not the meaning of the verb to which they are attached, and, rather than restricting the verb’s signification, they may broaden or completely transform it.44 After presenting this distinction, however, the authors of M1 and M3 seem to take a position against it. In fact, they maintain that every adverbial mode is a proper modifier of the adjoined verb’s signification, so that all are ‘tam vocis quam sensus’. As a consequence, they also maintain that Boethius’ rule of inference between a verb cum (adverbiali) modo and the corresponding unqualified verb is always valid, even in the case of adverbs such as ‘possibly’. They conclude then that any time it is true that ‘A peasant is possibly a bishop’, this means that ‘A peasant is a bishop in a certain way (hoc modo)’, therefore implying that ‘A peasant is a bishop simpliciter’. This opinion, antithetical to that of Abelard, is in M1 referred back to the authority of Master ‘Gosl.’, probably Joscelin of Soissons.45 The author of M1, however, still admits that a modal proposition such as ‘A peasant is possibly a bishop’ may be true, even though there is no actual inherence of the property of being a bishop in the subject, but this is only the case if we interpret this proposition figuratively, as if it were equipollent to the corresponding nominal form ‘it is possible for a peasant to be a bishop’ (Possibile est rusticum esse episcopum):

alicui voci faciunt eam agere de paucioribus, ut hic “Socrates bene legit” hae voces ad pauciores pertinent, quia de pluribus agit “legit” per se quam “bene legit” vel “male” vel “sapienter legit”, quia omnis bene legens est legens, sed non convertitur.’ 44 See M1: Orléans, Bibl. mun. 266, p. 166a: ‘Illi vero modi, qui vocis significationem ampliant vel ad alium intellectum detorquent, vocem tantum modificant, quia a sua eam significationem sive partim sive ex toto alienant. Quam enim vocem amplificant, aliud quodammodo significare compellunt, ut cum dico “rusticus episcopatur possibiliter”.’ M3: Orléans, Bibl. mun. 266, p. 253a: ‘Vocis tantum modi sunt qui vel ampliant etc. Ampliant vocem quibus adiunctis alicui voci, vox agit de pluribus cum illo modo quam per se, ut “possibiliter”. “Episcopatur” enim, vox ista, agit de episcopantibus tantum, sed “possibiliter episcopatur” et de episcopantibus et de non episcopantibus; nec concedunt sequi “si est episcopus possibiliter, tunc est episcopus”. Alii modi comitantur vocem, ut “vere”, quia quicquid vere est, est, et quicquid est, vere est. Alii reducunt ad opposita, ut “impossibiliter” et “falso”, quia si falso vel impossibiliter est lapis, non est lapis.’ It seems indeed that the authors of M1 and M3 are here presenting the same bipartition of modes endorsed by Abelard in the Dialectica, and we might suppose that he could indeed be the ‘quidam’ to whom they refer (although it could also be the case that they are referring to an older theory, then embraced by Abelard, but as far as I know there are no traces of it in earlier sources). 45 As Martin notes in (Martin 2016, p. 118), Joscelin is here referred to in the present tense.

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This proposition [namely, ‘a peasant is possibly a bishop’] could also be interpreted as if the mode – restricting the word ‘bishop’ – affected the proposition’s meaning, as if it said: ‘a peasant is a bishop in a certain way’. It would correctly follow from this that if someone is a bishop in a certain way (hoc modo), then he is a bishop. But Master Gosl. did not want to expound the mode in such a way, for he thought that [the proposition] ‘a peasant is possibly a bishop’ must be rather resolved into one having a nominal form, that is, ‘it is possible for a peasant to be a bishop’, and that it [should be understood] as having a figurative meaning. If the mode is expounded in this way, ‘being possibly a bishop’ does not imply ‘being a bishop unqualifiedly’, that is ‘being actually a bishop’.46 The same idea is presented in similar terms in M347 and also returns in other sources connected to the teaching of Joscelin, such as the commentary H20.48 According to early 12th-century logic, figurative propositions are those in which at least one word fails to bear its proper independent signification and acquires a special context-dependent meaning.49 In the case of a proposition such as ‘A peasant is possibly a bishop’ it is not clear which is the word undergoing this semantic shift, when the phrase is understood figuratively. One might argue that it is the predicate ‘bishop’, which, rather than standing for its direct signification (the property of being a bishop), may signify in this case a different property (e.g. the property of being a bishop possibly). More likely, though, it is the copula itself that changes its usual signification, for in this context 46 See M1, Orléans, Bibl. mun. 266, p. 166a–b ‘Potest tamen hoc tali modo intelligi, ut restringendo vocem iste modus ad sensum quoque pertineat, ac si diceret “rusticus episcopatur cum tali modo”. Ex hoc ergo bene sequitur quod “si episcopatur hoc modo, et episcopatur”. Sed m. Gosl. non vult hunc modum sic exponi, sed in casualem modum sic debere resolvi: “rusticus episcopatur possibiliter”, id est “possibile est rusticum episcopari”; et hoc figurato sensu; et sic iste modus expositus non infert episcopari sine modo, id est episcopari actualiter.’ 47 See M3, Orléans, Bibl. mun. 266, p. 253a: ‘Nos vero concedimus sequi: “si possibiliter episcopatur, id est si hoc modo episcopatur, et episcopatur”. Sed categorica non est vera “rusticus possibiliter episcopatur”, nisi figurative, scilicet possibile est [added between lines] rusticum episcopari.’ 48 See H20, Orléans, Bibl. mun. 266, p. 262b: ‘Ad hoc dicimus quod adverbii – quod vi, id est significatione, est adiectivum verbo – est determinare verbum; quod autem verbum adverbium determinet, non legi. Notandum est quod secundum hanc lectionem non sequitur, “si possibiliter episcopatur, et episcopatur” quod faceret ex proprio sensu. Vel possumus figuram [word is in the margin alia manu] facere, sic. “Rusticus possibiliter episcopatur”, id est “possibile est rusticum episcopari”.’ 49 On the notion of figurative meaning in early 12th-century logic, see (Rosier-Catach 1997) and (Wilks 1998b).

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it signifies not a relation of inherence but a relation of non-incompatibility between the property of being a bishop and the nature of the thing signified by ‘peasant’.50 An interesting aspect of the early 12th-century theory of figurativeness is that, when we consider figurative orationes, the usual rules of inference that are valid for propositions are not always preserved. Abelard, for instance, says that, although we should always be able to infer an unqualified noun from the same noun qualified by an adjective (e.g. ‘he is a white man’ implies that ‘he is a man’), when we consider a figurative proposition such as ‘This is an incomplete house’ we cannot infer from it that ‘This is a house’, because in the antecedent the term ‘house’ is used figuratively.51 This example is a good parallel to the case considered above, in which the proposition ‘A peasant is possibly a bishop’ is said not to imply that ‘A peasant is a bishop’, because the first is understood to have a figurative sense. Another interesting aspect to be noticed in the theory on modal claims put forward in M1 and M3 (and, albeit less clearly, in H20) is that their authors envisage an important distinction, both syntactic and semantic, between adverbial and nominal modal claims. According to their reading, affirmative adverbial claims always express a qualified inherence between two things and consequently posit the existence of an actual inherence between what is signified by the predicate and what is signified by the subject, just as affirmative simple propositions do. This was also endorsed in commentary H9, although the author did not elaborate on this point.52 Nominal claims, on the contrary, are said to be equivalent to figurative adverbial propositions: the mode included in them does not always have the role of qualifying a verb’s signification, and 50 51

This understanding of the notion of possibility will be investigated in Chapter 3, Section 3. See (Abaelard 1969b pp. 269–70) and (Abaelard 1987b pp. 159–60). The example is quoted in (Wilks 1998b, p. 175). 52 In H9 the author says that, while adverbial modals always express a ‘consignificatio’ or ‘cohaerentia’ between their predicate (qualified by the mode) and subject, nominal claims do not: ‘Sciendum quod duo genera modalium propositionum sunt. Unum quidem genus est cum aliquid cum modo predicatur. Et predicatum consignificat subiecto, alterum vero genus cum modus principaliter predicatur et primum quidem genus ad naturam simplicium accedit, quia et coherentiam predicati cum subiecto habent et sunt proprie universales, particulares, indefinite, singulares, et habent simplicem conversionem, ut “Socrates vere philosophus est”: hic “philosophus” cum “vere” predicatur et “Socrati” consignificat, et “ovum est animal possibiliter”: hic “animal” consignificat “ovo”, sed non per se, sed gratia “possibiliter”. […] Alterum vero genus modalium, scilicet ubi modus praedicatur tantum et “esse” et “non esse” subiciuntur, longe recedit a natura modalium. Cum enim dico “hominem esse animal possibile est”, hec vox, scilicet “possibile est” predicatur et “esse” ­subiectum, “homo” et “animal” determinationes, sed non est consignificatio inter predicatum et subiectum proprie”.’ In H9: Orlèans, Bibl. mun., 266, pp. 33a–b.

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they do not posit the existence of an actual inherence between two things. The semantics of nominal propositions, then, is essentially different from that of propositions de puro inesse and of adverbial modals. This theory contrasts with the reading proposed by Abelard and his followers. According to Abelard, adverbial and nominal claims, although different with respect to their grammatical structure, are alike with respect to their ‘deep structure’ and their meaning. Abelard insists that adverbial and nominal modes perform the same semantic role and that nominal propositions may be rephrased as having an adverbial form while preserving the same meaning, so it would be equivalent to say ‘a peasant is a bishop possibly’ and ‘It is possible for a peasant to be a bishop’. Generally speaking, logical sources of this time bear witness to a lively debate on the distinction between adverbial and nominal claims. This distinction was relevant to establishing the proper syntactic structure of modal propositions and identifying their subject and predicate, which in turn was of fundamental importance for determining how modal propositions should be negated and quantified, and consequently for arranging these claims in a system of logical inferences. In the next section I will focus on some major points emerging from this debate. 3

Adverbial and Nominal Modes

According to the Latin grammatical construction, a modal proposition may be construed either adverbially, as in ‘Socrates is necessarily a man’ (Socrates est homo necessario), or using a nominal mode followed by an accusative-infinitive clause, as in ‘It is necessary for Socrates to be a man’ (Necesse est Socratem esse hominem).53 Whether the difference between these two statements is merely 53

Translating these Latin nominal structures into English poses some difficulties. One possible option could be to translate them using a ‘that’-form, saying, for instance, ‘It is necessary that Socrates is a man’. This formulation, however, is usually associated with a de dicto reading of modal claims, which would be inappropriate in this context, because nominal propositions were thought by Abelard and early 12th-century logicians to be semantically ambiguous, allowing for either a de dicto or a de re interpretation (see ­Chapter 4 on the de re–de dicto distinction in Abelard and its 12th-century context). Another reason to avoid using the ‘that’-form to translate nominal claims is that, from the mid-12th century onwards, medieval logicians will introduce a distinction between the meaning of modal propositions formulated with an accusative infinitive construction and the meaning of the corresponding claims containing a ‘quod’ clause, such as ‘Possibile est Socratem sedere’ and ‘Possibile est quod Socrates sedeat’. This idea is advanced, for instance, in the logic of the Meludinenses. Indeed, uses of the ‘quod’ formulation are already common

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found at the level of grammar, or also at a semantic and logical level, was a matter of lively debate, of which we find traces in many early 12th-century sources devoted to modalities. Broadly speaking, two main positions might be identified in sources of the time. On the one hand, we have authors who think that adverbial and nominal claims only differ with respect to their ‘superficial’, grammatical structure but are the same with respect to their meaning and logical properties, so that we may always rephrase nominal claims into an adverbial form without altering their nature. This idea is suggested in some grammatical texts, such as the Notae Dunelmenses, in which it is stated that nominal modes such as ‘necesse’ and ‘possibile’ can be used as having the status of adverbs (vim adverbiis), so that these nomina in some cases have the same semantic role as their adverbial correspondents, even though they are grammatically different to them.54 As was mentioned in the previous section, Abelard too thinks that nominal modals might be ‘resolved’ or reduced to their adverbial counterparts while preserving the same meaning. Other logicians, such as Garland and the author of the Glossae Doctrinae Sermonum, probably endorsed a similar view, as we will show later in this section. On the other hand, authors such as those of H9, M1, M3, and H20 refer to the two categories of proposition as two different ‘kinds’ of modal (duo genera modalium),55 differing not only with respect to grammar but also with respect to their nature, meaning, and logical behaviour, so that a rephrasing of the latter into the former would be generally impossible (unless we take adverbial claims in a figurative sense, as was explained in the previous section). The debate on the relation between adverbial and nominal modals is particularly interesting for historians of logic, for it is intertwined with the discussion in early 12th-century logical texts, when authors want to make clear that modal propositions should be read de dicto and not de re (see pp. 85 ff. for this use in M3, H20 and De Propositionibus Modalibus). Because Latin claims containing a ‘quod’ construction would be naturally translated into English with a ‘that’-clause, it is important to use a ­different translation for Latin claims containing an accusative-infinitive structure. For these reasons, throughout the book I favour a translation of Latin nominal claims using the preposition ‘for’ followed by the subject term, as in ‘It is possible for Socrates to be a man’. This translation, which was also proposed by Martin in (Martin 2016), has the merit of being almost as flexible as the corresponding Latin expression, for it allows changing the order of the words by placing, for example, the mode at the beginning, in the middle, or at the end of the sentence, just as early 12th-century authors do. It is important, however, to keep in mind that modal propositions with this form must be taken as neutral with respect to the semantic level, in the sense that it could be interpreted either de dicto or de re. 54 See footnote 27, in this Chapter. 55 See M3, Orléans, Bibl. mun. 266, p. 252b; H9, Orléans, Bibl. mun. 266, p. 33a. In M3 this idea is referred back to the authority of Boethius.

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about whether nominal propositions such as ‘it is possible for Socrates to be a bishop’ should be read de re, that is, as saying that the property of being a bishop possibly inheres in the thing referred to by the subject ‘Socrates’, or de sensu (alternatively known as de dicto), as saying that the sensus of the simple proposition ‘Socrates is a bishop’ is possible. Abelard is usually credited with the identification, or at least with the first explicit systematization, of the de re-de dicto distinction,56 which is counted among the greatest achievements of his modal logic. However, a study of the many available sources on modalities from the first two decades of the 12th century reveals that this distinction was already recognized and discussed at the time in which Abelard wrote his Dialectica and Logica. This discussion often emerged from the analysis of syntactic aspects of nominal modal claims and their relationship with adverbial propositions.57 Adverbial modal claims were generally interpreted de rebus by Abelard and his contemporaries, as the modal adverb was generally conceived as a qualifier of the predicate’s meaning, as was seen in Section 1 of this Chapter. In propositions such as ‘Socrates is necessarily white’, for instance, the mode was read as having a narrow syntactic scope that includes the predicate term but not the subject. How nominal claims were interpreted, on the other hand, depended on the view one had concerning the relation between them and the corresponding adverbial propositions: authors who stressed the difference between adverbial and nominal claims, stating that the meaning of the latter is not reducible to that of the the former ones, tended to prefer a de sensu or de dicto reading of nominal claims, to differentiate their meaning from that of adverbial ones. On the contrary, authors such as Abelard, who thought of the difference between the two categories of modal as merely grammatical, opted for a de re interpretation of nominal modals, saying that even if they have an impersonal form with respect to their grammatical structure, their logical form is in fact personal and adverbial. I will return in Chapter 3, Section 2 and in 56

57

See, for example (Kneale and Kneale 1984), (Knuuttila 1993), (Dutilh Novaes 2004), for the attribution of the distinction to Abelard. Before Abelard’s logical texts started to be systematically studied, other medieval authors were thought to be the ‘inventors’ of the de rebus-de dicto distinction. Von Wright, for example, attributes this invention to Aquinas. See (Von Wright 1951) and (Uckelman 2008, p. 392, footnote 10) on this. On the origins of the distinction in the early 12th century, see (Martin 2016) and (Binini forthcoming). Differently from what Dutilh Novaes states in (Dutilh Novaes 2004, pp. 111–24), I claim that Abelard’s and other early 12th-century discussions of the de re/de dicto distinction are primarily syntactic and not semantic. Although authors of this time also took into account a number of problems concerning the signification of modal terms and the nature of modalities, their main interest was deciding how we should analyse the syntactic structure of modal claims and whether we can reduce their syntax and logical behaviour to that of simple categoricals.

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Chapter 4 to the origins and development of the de re/de dicto distinction in Abelard and his contemporaries. We should keep in mind, however, that the dispute presented in this section about the relation between adverbial and nominal claims was not merely a grammatical or a terminological debate; it was, in fact, at the core of early 12th-century reflections on the nature and logic of modalities. One thing upon which many authors agreed is that adverbial propositions are the ‘easy’ kind of modals and present ‘no ambiguity’,58 inasmuch as they are similar to non-modal claims with respect to many of their features. First, (affirmative) adverbial propositions, just like simple ones, always express a certain ‘coherentia predicati cum subiecto’, that is, a relation of inherence between what is signified by their predicate and subject. These subject and predicate are the same as the ones included in the simple propositions from which modals descend, and the modal term is read as a part of the predicate term, of which it qualifies the meaning (see Table 1, p. 53.). Second, adverbial claims are negated in the same way as propositions de puro inesse, by adding a negative particle to the proposition’s predicate (e.g. ‘Socrates currit necessario’ – ‘Socrates non currit necessario’).59 Third, their subject can be varied in quantity, being universal (e.g. ‘Every man is necessarily an animal’), particular (‘Some man is necessarily an animal’), indefinite, or singular. This variability in quantity is a significant feature, because it renders adverbial modals suitable for use in syllogisms, which is in line with what Aristotle states in the Prior Analytics. Finally, adverbial propositions resemble simple ones in that they share a similar logical behaviour: in particular, they follow the same rules for conversion.60 58

See, for example M1: Orléans, Bibl. mun. 266, p. 166a: ‘Modalium propositionum aliae sunt cum adverbiali modo, aliae cum casuali. Sed illae de adverbiali modo, quia parum distant ab illis de simplici esse, nullam habent ambiguitatem.’ 59 See LI De Int. 395, 106–9: ‘Cum adverbialem modum ponimus dicentes: “Socrates currit necessario” una tantum fit affirmatio et negatio sicut in simplicibus; sicut enim dicimus: “Socrates currit” (vel: “non currit”) ita: “Socrates currit necessario” (vel: “non currit necessario”).’ 60 With the exception of conversion by contraposition, on which some doubts were raised. Authors of H9, M1, and M3 think that conversion by contraposition is never valid for modal claims, because it is not allowed to ‘infinitize’ propositions. Garland also maintains that contraposition fails for modal propositions on some occasions, for when empty terms are included in them, the truth-value of two converted propositions is different, as in the case of ‘every man is possibly a substance’, which is true, and ‘every non-substance is possibly a non-man’, which is false because its subject is an empty term (Garlandus Compotista 1959, pp. 57, 20–63, 34). Abelard instead thinks that conversions of all kinds are valid for modals just as they are for simple propositions, and that the cases in which these laws fail in modal logic are also cases in which they fail in the logic of simple categoricals (for instance, when non-denotative terms are taken into consideration). See LI De Int. 400, 236–401, 249. I will return to Abelard’s views on conversions in modal logic in Chapter 6.

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These aspects of adverbial claims are listed in H961 and rehearsed almost verbatim in M362 and M1.63 Because of the ‘easiness’ of adverbial modals, the focus of early 12th-century logicians was the logic of nominal propositions, on which Aristotle had centred both his De Interpretatione and modal syllogistics. Propositions of this sort were already presented by Aristotle as positing a number of problems, the first of which is how they should be properly negated, that is, how the negative particle should be applied in them in order to obtain, from an affirmative 61 See H9: Orléans, Bibl. mun. 266, pp. 33a–33b: ‘Sciendum quod duo genera modalium propositionum sunt. Unum quidem genus est cum aliquid cum modo predicatur et predicatum consignificat subiecto, alterum vero genus cum modus principaliter predicatur. Et primum quidem genus ad naturam simplicium accedit, quia et coherentiam predicati cum subiecto habent et sunt proprie universales, particulares, indefinite, singulares, et habent simplicem conversionem, ut “Socrates vere philosophus est” hic philosophus cum vere predicatur et Socrati consignificat, et “ovum est animal possibiliter”: hic animal consignificat ovo, sed non per se, sed gratia possibiliter. Nam bene, vere, possibiliter, necessario et similia modi sunt in propositionibus, quia moderantur illud quod cum illis predicatur qualiter subiecto habeat coherere. Conversionem etiam simplicem habent, ut “omnis homo vere est albus”, “quoddam quod vere est album, est homo”. Sed conversionem per contrapositionem non habent, quia oratio non debet infinitari, converse vero modalium non debent dici modales nisi quando modus predicatur, modales enim ex modali predicatione dicuntur.’ 62 See M3: Orléans, Bibl. mun. 266, pp. 252b–253a: ‘Auctore Boethii in commento Periermenias, duo genera modalium propositionum novimus esse. Aliae enim sunt cum adverbiali modo, aliae cum casuali. Casuales modi sunt hi: possibile, contingens, impossibile, et necessarium. Adverbiales: bene, sapienter, velociter, et omnia qualitativa adverbia. Propositiones autem quae modos habent adverbiales cum illis de puro inesse in paucis differunt et in multis conveniunt. Sunt namque proprie universales, particulares, indefinitae, singulares affirmativae et negativae. Praedicatum quoque subiecto consignificat sicut in illis de puro inesse. Habent etiam converti simpliciter, ut ‘quidam homo bene legit’ ‘quidam bene legens est homo’, ‘nullus homo bene legit’ ‘nullum bene legens est homo’ vel ‘nullus qui bene legit, est homo’; et per accidens, ut ‘omnis homo bene legit’ ‘quidam bene legens est homo’. Per contrapositionem vero converti non habent, nulla alia causa impediente nisi quia oratio non infinitatur. Aristoteles hoc attestante Boethio dicit ‘albus asinus’ non possibile esse infinitari. Sequeretur enim ‘si hoc lignum est non albus asinus, tunc est asinus’. Quantitates autem habent proprie. Nam ‘omnis homo bene legit’ proprie est universalis, ‘quidam homo bene legit’ proprie paticularis. Et sic de ceteris.’ 63 See M1: Orléans, Bibl. mun. 266, p. 166a: ‘Modalium propositionum aliae sunt cum adverbiali modo, aliae cum casuali. Sed illae de adverbiali modo, quia parum distant ab illis de simplici esse, nullam habent ambiguitatem. sive per quantitatem seu per conversionem ad modum simplicium excepto quod conversionem per contrapositionem non habent, ut si dicam “omnis iustus bene vivit”, et faciam talem contrapositionis conversionem ‘omne non bene vivens est non iustus’, non recte facio, non quia si talis conversio fieret, a veritate rectae propositionis seu falsitate discreparet, sed quia oratio non potest infinitari. Nolunt auctores talem conversionem fieri.’

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modal proposition, the corresponding negative (and contradictory) one.64 According to Aristotle, the usual way of assigning negation in a proposition requires applying the negative particle to its predicate. But which term is the predicate in nominal modal claims? Taking a nominal proposition such as ‘It is necessary for Socrates to run’ (Necesse est Socratem currere), Aristotle first considers applying the negative particle to the verb ‘run’, which is the predicate of the corresponding simple and adverbial claims, in this way: ‘It is necessary for Socrates not to run’ (Necesse est Socratem non currere). He notices, however, that in this way we would not obtain a proper pair of contradictory propositions, for the two claims may be false at the same time.65 Therefore, Aristotle continues, the negative particle should be applied to ‘the other predicate’ included in the nominal claim, namely, the mode itself, in this way: ‘It is not necessary for Socrates to run’ (Necesse non est Socratem currere). Aristotle then states that the proper analysis of nominal modals is the one in which the modal term functions as predicate and the subject is the verb of the infinitive clause (or the entire infinitive clause), as shown in Table 2. table 2  The syntactic structure of nominal claims proposed by Aristotle

Structure of nominal propositions Necesse Predicate

(non) Negative operator

est Copula

Socratem

esse Subject

hominem

The Aristotelian solution to the problem of negation and his analysis of nominal claims were generally adopted without relevant changes in many early 12th-century sources. Some texts – such as H9, M1, M3, and Garland’s Dialectica66 – state that the subject of modal propositions is only the verb ‘esse’ of the infinitive clause and that the accusative terms ‘Socratem’ and ‘hominem’ are determinations of this subject. Other texts, such as H4, slightly adjust this analysis, saying that the subject of a nominal proposition is the entire phrase (tota oratio) of which the mode is predicated, so that in a proposition such as ‘Necesse est Socratem esse hominem’, ‘necesse’ would be the predicate and the

64 See De Interpretatione 12 (21a39–22a3). 65 See on this Dial. 192, 11–6. 66 H9: Orléans, Bibl. mun. 266, pp. 33a–33b; M1: Orléans, Bibl. mun. 266, p. 167a; M3: Orléans, Bibl. mun. 266, 253b; (Garlandus Compotista 1959, p. 80, 25–31).

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whole phrase ‘Socratem esse hominem’ the subject.67 The same idea is often found in later texts, such as the Glossae Doctrinae Sermonum,68 the Summa Dialectice Artis,69 the Introductiones Montane Maiores, and H21.70 This last reconstruction suggests that nominal claims do not share the same subject and predicate as the corresponding simple and adverbial ones. Rather, nominal modals would have an entire categorical proposition as their subject and affirm about that proposition that its meaning (sensus) is possible, impossible, or necessary.71 Such an analysis, however, contrasts with an assumption that was part of Aristotle and Boethius’ legacy on modal propositions, namely, that nominal modal claims can be used in syllogisms, and that, as such, they should be variable with respect to their quantity. Indeed, if the subject of a nominal proposition is an infinitive verb or an entire oratio, to which no sign of quantification can be added, then every nominal claim will be invariable in quantity and unfit for syllogisms.72 In order to unravel this difficulty, Abelard’s contemporaries made use of another aspect of Aristotle’s modal theory, namely that in nominal propositions two subjects and two predicates could be identified.73 In the proposition ‘Necesse est omnem hominem esse animal’, for instance, the proper or ‘principal’ 67 See H4: Paris, BnF, lat. 13368, fol. 151. 68 See Anonymous, Glossae Doctrinae Sermonum in (Abaelard 2010a, p. 216, 511–21). 69 See, in particular, (Guglielmo da Lucca 1975, 105, §7.07-08; 118, §7.43). 70 See H21: Paris, Arsenal, 910, fol. 88va: ‘Hic enim oratio ista [“possibile est Socratem legere”], “Socratem legere” subiectus terminus est, et “possibile” praedicatus.’ 71 As said in the Introductiones Montane Maiores, modes would then be determinations that qualify the truth or falsity of categorical propositions, that is, modal propositions would affirm that a certain categorical claim is possibly, necessarily, or impossibly true. See Anonymous, Introductiones Montane Maiores in (Bos and Spruyt 2017, 300, 10–2): ‘Secundum hoc dicit Aristotiles in categoricis modalibus subiciuntur esse et non esse, predicantur vero appositiones determinantes veritatem propositionum.’ This is, as far as I know, the only mention in sources from the first half of the 12th century in which modes are said to qualify the truth-value of propositions, being then ‘alethic modalities’ in the modern sense of the term. 72 Another problem that comes up in relation to this analysis is that if nominal propositions were understood in this way – with the mode as their predicate and an entire proposition as their subject – then these propositions would be ‘unsyllogistical’, not only because they would have no quantity but also because there would be no middle term in them grounding the validity of syllogisms. As far as I know, this objection is only raised in H21 while considering syllogismi incisi (see Paris, Arsenal, 910, fols 88va–88vb), while the other texts only seem to be concerned with the problem of quantity. 73 De Interpretatione 12 (21a39–22a3).

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terms are those signalled in Table 2, but there is also another pair of predicate and subject, which are the same as those of the non-modal proposition ‘Omnis homo est animal’. This distinction between two orders of terms in nominal claims returns in many treatises of the early 12th century, such as H9,74 H4, H5,75 M1, M3,76 and SH3,77 which usually speak of a ‘principal’ and a ‘secondary’ subject and predicate (see Table 3), as well as in many later sources, such as the Introductiones Montane.78 This distinction is also adopted by Abelard, but with an interesting twist. Rather than speaking of ‘principal’ and ‘secondary’ terms, Abelard distinguishes between the subject and predicate ‘according to the meaning’ (in sensu) and ‘according to the grammatical structure’ (quantum ad constructionis materiam). Abelard claims, in agreement with Aristotle and his contemporaries, that the mode is the predicate of nominal propositions,79 but only if we take into consideration their ‘surface’, that is, their grammatical constructio. If we look instead at their ‘meaning’ (sensus), we see that nominal claims have

74

H9: Orléans, Bibl. mun. 266, p. 33a. In H9 the author tries to reconcile Aristotle’s idea that the mode is the principal predicate of nominal modals (‘modus principaliter predicatur’) with the views of Boethius, who also assigned quantity to nominal claims. According to him, two strategies have been proposed to reconcile these two views. One consists in saying that the quantity of modal propositions depends on the signum applied to the subject’s determinatio; and the other proposes that there are two predicates and two subjects in modal claims of this sort and that the proposition’s quantity depends on the signum that is applied to its ‘secondary subject’. The exact same view is rehearsed in M3, whose author explicitly says that the second strategy – distinguishing principal and secondary terms – is more convincing than the first. 75 See H4: Paris, BnF, lat. 13368, fol. 114va; H5: Munich, Bay., Clm. 14779, fols 60r–60v. 76 See M1: Orléans, Bibl. mun. 266, 167a; M3: Orléans, Bibl. mun. 266, p. 253b. 77 SH3: Orléans, Bibl. mun. 266, p. 119a. 78 See Anonymous, Introductiones Montane Maiores in (Bos and Spruyt 2017, p. 300, 18–28), where the author rehearses the idea that, if the subject and predicate of nominal modal claims were considered with respect to grammar, then these propositions would not be suited for syllogisms, for they would have no quantity: ‘Et in hoc videtur tamen esse contra Aristotilem qui dicunt “homo est albus” subicitur res, in “possibile est hominem esse album”, “hominem esse album” subicitur, predicatur “possibile”; et in hoc assignat differentiam modalis et simplicis categorice. Et nos dicimus quod in utraque idem subicitur. Sed cum Aristotiles assignavit “esse” et “non esse” subiecta, respexit ad verborum ordinem – scilicet esse hominem est possibile –, non tamen negavit res subici. Sed ratione atque auctoritate cogimur Aristotilem, qui facit sillogismos mixtos quod dicamus in huiusmodi propositionibus subici verba et propositiones universales. Aliter enim non essent sillogismi quos Aristotiles ponit syllogismos.’ 79 See, for example, Dial. 191, 34–6.

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table 3  Principal and secondary terms in nominal modals

Principal terms (Abelard: terms secundum constructionem) Secondary terms (Abelard: terms secundum sensum)

Necesse

(non)

Predicate

Negation Copula Determination Subject Determination of the subject of the subject In other (later?) sources: Subject

Qualifier of the predicate (or the inherence)

est

Omnem hominem

Quantified subject

esse

Animal

Copula Predicate

the same terms as the correspondent simple claim (see Table 3). This position is supported in both the Dialectica80 and the Logica.81 The ‘real’ form of nominal propositions would be made explicit if we ‘resolved’ them into an adverbial form, for example, rephrasing ‘it is necessary for every man to be an animal’ into ‘every man is necessarily an animal’. Abelard considers the adverbial structure as the primitive and more appropriate form of modal claims. This is because the adverbial constructio more closely ‘mirrors’ the real structure (what we would call the ‘logical form’) of modal predications, inasmuch as it is adverbs that we properly understand as modes.82 Abelard’s distinction between a proposition’s grammatical and semantic structure (which we also encountered in Chapter 2, Section 2, when referring to modes secundum constructionem and secundum sensum) is a distinguishing feature of his approach to the analysis of natural language, through which Abelard aims to capture what we would today call the ‘logical form’ of a sentence, or in other words its ‘underlying’ form, as opposed to its ‘surface’ structure. 80

Dial. 191, 26–30: ‘Cum autem in sensu modales cum simplicibus eosdem retineant terminos, in his tamen modalibus quae casuales habent modos, quantum ad constructionis materiam alii considerantur termini, ut cum dicimus: “possibile est Socratem episcopum esse”, “esse” quidem subicitur, et modus ipse, id est “possibile”, praedicatur.’ 81 LI De Int. 396, 124–42. 82 See Dial. 191, 11–5: ‘Resolvuntur enim huiusmodi nomina in adverbia, quae videlicet adverbia proprie modos dicimus et inde adverbia vocamus quia verbis adposita eorum determinant significationem, sicut adiectiva nomina substantivis adiuncta, ut cum dicitur: “homo albus”.’

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The idea that the ‘real’ form of a sentence is not always what it appears, and that it may be made explicit by a proper paraphrase or reformulation of that sentence, often occurs in Abelard’s logic.83 As far as I know, the same distinction between the structure in sensu and the structure secundum constructionem is not to be found in other sources from Abelard’s time but only in later texts that are, to some extent, familiar with Abelard’s teaching, such as the Glossae Doctrinae Sermonum, the Introductiones Montane, or the Summa Dialectice Artis. The author of the De Propositionibus Modalibus, who was certainly acquainted with (parts of) the Logica Ingredientibus, mentions Abelard’s distinction between the analysis in sensu and secundum constructionem but is, to my knowledge, the only author who explicitly rejects it, on the basis that no other predicate or subject should be identified in modal propositions other than, respectively, the mode and the verb of the infinitive clause. This was probably due to his preference for the de dicto reading of modals, as I argue elsewhere.84 83

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See on this (Iacona 2018, pp. 6–7). On Abelard’s notion of logical form, see also (Martin 2004). It would be interesting, but outside the scope of this book, to follow the developments of Abelard’s distinction between the ‘surface’ and the ‘underlying structure’ of modal propositions as it survives in sources from the second half of the century and later on in the 13th century. As I show in (Binini 2020a), in the mid-12th century there are several authors who adopt this distinction, such as the authors of the Introductiones Montane Maiores and of the Summa Dialectice Artis. In the 13th century several logicians also make use of the same distinction, for instance, William of Sherwood and Thomas Aquinas, as shown in (Rivero 1974). Abelard was probably not the first medieval logician to notice how, in natural language, surface grammar does not always mirror the logical form of sentences. A similar idea had already emerged, for instance, in Anselm of Canterbury’s semantics, where a distinction is proposed between the ‘proper’ (logical) and ‘improper’ (that is, dependent on the ordinary usage of language) forms of an utterance, together with the idea that the grammatical structure of a proposition could, at times, be misleading, in that it does not necessarily mirror its ‘real’ form. On this see, in particular (Henry 1982, pp. 141–2). Henry refers, as a paradigmatic example of Anselm’s approach, to his treatment of the pseudo-name ‘nothing’ and, more generally, to his treatment of empty and negative names. According to Henry, Anselm’s distinction between the apparent and the logical form of propositions emerged as a consequence of the ‘rivalry between logic and grammar which was a pervasive feature of Anselm’s intellectual context’. In Henry’s view this rivalry is strikingly similar to the 20th-century contrast between the ‘logical’ form of an utterance and its ‘apparent logical’ form, so that, he says, ‘it is not only “­Russell’s merit” (as Wittgenstein put it) but also Anselm’s to have shown that the apparent logical form of the proposition need not be its real form’ (Henry 1982, pp. 141–2). From the little we have seen of Abelard’s analysis of modal claims so far, we already know that he too deserves part of this merit. See Anonymous, De Propositionibus Modalibus, in (Abaelard 2010a, pp. 234, 88–235, 117): ‘Sunt tamen quidam qui eas alia praedicata et alia subiecta habere dicunt, scilicet secundaria, sicut istam “Socratem esse hominem est possibile” “esse” dicunt habere prin-

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By stressing the contrast between the proposition’s constructio and its sensus, Abelard sets the stage for his idea that adverbial and nominal claims, despite their apparent differences, are really the same with respect to their meaning. In the Dialectica he insists that nominal propositions can unproblematically be translated or ‘reduced’ to the corresponding adverbial forms, so it would be equivalent to say that ‘It is possible for Socrates to be a bishop’ and ‘Socrates is a bishop possibly’ (Dial. 191, 1–20). The reducibility of nominal modals to the corresponding adverbial form was also maintained by other authors of Abelard’s time, as in the Dialectica of Garland,85 and in later sources such as the Glossae Doctrinae Sermonum86 and the commentary H21.87 We read in M3 that a similar position was also endorsed by a certain ‘Magister W.’ (perhaps, William of Champeaux), according to whom the meaning of every nominal claim should be expounded by means of an adverbial constructio, so that the meaning of ‘it is possibile for Socrates to be a man’ would be the same

cipale subiectum, “possibile” vero principale praedicatum et “Socratem” et “hominem” secundarium subiectum et secundarium praedicatum. […] Dicunt ergo, cum universales et particulares possint fieri, signum universalitatis et particularitatis ad aliud subiectum oportere addi, cum ad esse poni non possit, et ita alia subiecta dicunt ibi esse. Aliunde etiam hoc confirmant, ex conversionibus scilicet quae ab Aristotele fiunt, sicut “Possibile est hominem esse animal”, “Possibile est animal esse hominem”. Aristoteles etiam facit incisos syllogismos ita: “Possibile est omnem hominem esse animal et Socrates est homo, ergo possibile est Socratem esse animal”, quos dicunt non posse esse alicuius figurae, nisi sint ibi alia subiecta et alia praedicata quam “esse” et “possibile”, cum “possibile” et alii modi non possint subici. Nos autem dicimus quod non sunt ibi alia subiecta vel praedicata nisi verba et modi. Quod autem dicit Boethius, quod possunt fieri universales et particulares, sic intelligimus: universales et particulares vocat non quod habeant signum universalitatis et particularitatis additum ad subiecta, sed quod agunt de quantitate omnium vel nonnullorum. […] De incisis syllogismis dicimus quod nullius figurae sunt et tamen firmae complexionis.’ See (Binini 2020a) on this. 85 See (Garlandus Compotista 1959, pp. 81, 30–82, 1). The agreement between Abelard and Garland concerning this point was signalled in (Martin 2016, pp. 116 ff.). It is not clear, however, whether Garland admits that every nominal proposition is suitable for such rephrasing or that just some of them are. The only example he provides concerns propositions about necessity, which are, in this respect, less problematic than propositions about possibility or impossibility. 86 See Anonymous, Glossae Doctrinae Sermonum, in (Abaelard 2010a, p. 188, 26–9): ‘Nominales vero modi sunt “possibile”, “necessarium”, “contingens”; qui verbis semper adiunguntur ut adverbiales, ut “Socratem legere est possibile”, et in adverbiales resolvuntur ut “possibile est Socratem legere”, id est Socratem legit possibiliter.’ 87 See H21: Paris, Arsenal, fol. 88rb: ‘Modi quoque possunt dici, quia quaedam ex illis propositionibus, in quibus ponuntur resolvuntur in illas quae habent modos adverbiales. Sic ista “possibile est Socratem disputare” in istam “Socrates disputat possibiliter”, et ista “necesse est Socratem legere” in istam “Socrates legit necessario”.’

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as ‘Socrates is possibly a man’.88 All these sources suggest, then, that adverbial and nominal modals, despite being different with respect to their grammatical structure, are in fact equivalent with respect to their meaning (and, as a consequence, with respect to their truth-value). This idea is strongly opposed in other authors, such as M1 and M3. The author of the former says that, if such a reduction of nominals into adverbials were in fact possible, then they would not be two different kinds of modal (duo genera modalium) but merely two kinds of linguistic expression (duo genera locutionis), and this would be contrary to what the authorities say.89 Moreover, he thinks that there are many cases in which the adverbial and the corresponding nominal modals have a different truth-value, so that the meaning of one cannot be reduced to the meaning of the other. A proposition such as ‘Socrates is possibly a bishop’, for instance, cannot be true unless there is an actual relation of inherence between Socrates and the property of being a bishop, while this is not the case for the nominal proposition ‘it is possible for Socrates to be a bishop’, which can be true even though Socrates is not a bishop in act. The same idea is also defended in M1, where it refers to the teaching of Joscelin of Soissons.90 Moreover, the author of M3 points out that there are many nominal claims that are true even though they are about non-existent things, for instance, ‘It is possible for a chimaera not to be a goat-stag’ or ‘It is possible for the world to be created’, uttered before the existence of the world. The corresponding adverbial claims would instead turn out to be false according to his reading, for their subject term would fail to denote. The semantic difference between adverbial and nominal claims, which results in a different logical behaviour of the two kinds of proposition and makes it impossible to reduce the latter to the former, was also stressed in the early commentary H9, where adverbial and nominal claims are again presented as duo genera modalium and are said to have different features in both their syntactic and semantic form.91 Early 12th-century sources on modalities are, then, split with respect to their account of the relation between adverbial and nominal modals. According to 88 See M3: Orléans, Bibl. mun. 266, p. 254b: ‘M. vero W. dicebat communem esse sensum omnium modalium cum casuali modo quod per illas cum adverbiali modo exponi debeant, sicut haec: “Socratem esse hominem est possibile”, id est “Socrates est possibiliter homo”.’ Unfortunately, M3’s report is too concise to be sure of what exactly the author had in mind and whether his idea coincided with that later defended by Abelard. I briefly deal with this question in (Binini forthcoming). See also (Martin 2016, pp. 118 ff.) on this. 89 M3, Orléans, Bibl. mun. 266, p. 254b. 90 M1, Orléans, Bibl. mun. 266, pp. 166a–166b. 91 See H9, Orléans, Bibl. mun. 266, pp. 33a–33b.

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some authors, amongst whom Abelard, the distinction between adverbials and nominals is only at the propositions’ superficial and grammatical level but does not affect their meaning. Other authors, perhaps those connected to the teaching of Joscelin of Soissons (M1; M3; H20), suggest instead that the difference between the two kinds of modal is not limited to their grammatical structure but has to do with their nature and signification and also affects their logical properties. We will see how the position that these authors took concerning the relation between adverbial and nominal claims is reflected in their views about the proper interpretation of the scope of nominal modes, namely, whether these modes should be understood de sensu or de re (cf. Chapter 4 of this book). Apart from these discussions on the syntax and grammatical structure of modalities, early 12th-century authors also considered a number of problems related to the signification of nominal modal terms and the nature of modalities. A surprisingly consistent and unitary theory of modals emerges from sources of the time, a theory that – though based for the main part on Aristotelian and Boethian sources – is yet different in important aspects from the received modal paradigms. These early 12th-century debates on the nature of possibility and necessity will be investigated in the next chapter.

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The Nature of Modalities and the Signification of Modal Terms 1

What Do Modal Terms Signify?

Apart from their concern for the syntactic structure and logical properties of modal propositions (seen in Chapter 2), 12th-century logicians were interested in the signification of modal terms and developed a theory – partly new and partly based on ancient paradigms – about how the notions of possibility and necessity should be properly interpreted. There are two main questions related to this subject that often return in sources of the time. A first doubt that is put forward is whether or not modal terms have denotation, that is, whether there is some existing res to which they refer. Specifically, Abelard’s contemporaries were interested in whether modal terms denote a form or a property existing in things, so when we say ‘It is possible for Socrates to be a man’, what we mean is that a certain possibilitas or potentia inheres in Socrates. A second doubt rehearsed in several sources asks what is said to be ‘possible’ or ‘necessary’ in nominal propositions such as ‘It is possible for every man to be an animal’: is the modal term attributed to things (men and animals) and their possibilities, or is it rather attributed to the simple proposition ‘every man is an animal’ and to what this proposition says, that is, to its propositional dictum? As we will see, the two questions are closely related, and the answers that are advanced to solve them seem to be driven by a common intent, which is shared by many authors of the time despite their doctrinal differences. This shared intent is what we may call a ‘de-reification’ of modal terms, that is, the elaboration of a theory in which modal terms are not analysed by reducing them to real constituents of ontology, such as properties or forms embedded in things. In fact, early 12th-century logicians wanted to speak about things having certain possibilities or necessities without committing to the existence of either modal properties or these properties’ bearers, and in order to do so they unanimously ruled out the idea that modal nouns denote something existing in substances. Even authors who embraced a de rebus reading of modalities, like Abelard, still insist that modal terms do not signify properties that things have but are rather used to express relations holding between certain linguistic items (predicates or sentences) and the nature of things. With respect to this, we could perhaps say that the early 12th-century approach to modalities is a deflationary one, © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_006

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which avoids identifying the signification of modalities in some real, existing metaphysical item. As was seen on p. 29, concerns about the ontological foundation of possibilities were already present in the works of Anselm of Canterbury, who wondered how the reading of possibilities in terms of potencies, inherited by Aristotle and Boethius, could be compatible with attributing possibilities to non-existing things, such as the possibility of a house to be fabricated before its actual existence or the possibility of the world to exist before its creation. In early 12th-century logical sources, examples concerning the modalities of nonthings such as chimaeras, goat-stags, or future beings are multiplied, highlighting their authors’ interest in the ontology of these modalities. In this and the following section we shall see how, in order to speak freely about the modalities of non-things and about extra-actum possibilities, logicians of Abelard’s time abandoned the metaphysical burden connected to the Aristotelian and Boethian reading of possibilities in terms of active or passive potencies possessed by a subject, in favour of a new reading of modalities.1 Let me start by explaining in more detail what Abelard and authors of his time answered to the first question considered above, namely, whether modal terms denote some property or form existing in a substance.2 A discussion of this topic may be found, with a strikingly similar terminology, in the anonymous texts H9 and M3, in Abelard’s Dialectica, and in his later Logica Ingredientibus. All of these sources provide a unanimous negative answer to the question, stating that there is no form or property to which modal terms refer. In fact, they claim that such an interpretation of modal terms would lead to absurd consequences, such as the truth of conditionals like ‘if nothing exists, then something exists’.3 1 For a survey of the Aristotelian and Boethian reading of possibilities as potencies, see Chapter 1. 2 Their answer to the second question, whether modal terms refer to things or to the dicta of propositions, will be analysed in Section 2 of this Chapter. 3 For Abelard, and probably also for other authors of his time, the question of whether or not modal terms such as ‘possibile’ and ‘necesse’ have any denotation arises as a consequence to the categorization of these terms as ‘indefinite words’, namely, as words that, instead of having signification on their own, merely co-signify within a linguistic context. As was said in footnote 24 in Chapter 2, Abelard associates nominal modes with words such as conjunctions (et, si) or prepositions (e.g. de), that, ‘uttered in isolation, […] have a signification which is vague and undetermined: the hearer’s mind is kept in suspence about that to which they are attached. Only when the open places by which they are accompanied have been filled is their imperfect and indefinite signification rendered precise and definite’ (Nuchelmans 1973, p. 140). As Nuchelmans notes, at Abelard’s time different views were advanced by grammarians and logicians concerning the signification of indefinite terms, both with respect to their denotation and with respect to the understanding they cause in the hearer’s mind. Abelard

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The author of H9 – who might have been the source of Abelard’s and M3’s discussion of the problem – provides the following reductio argument in support of this view. He first assumes that (i) ‘nothing exists’ and then considers the proposition (ii) ‘It is not possible for Socrates to be a stone’, which he seems to take as true even in the given situation in which there is no existent thing – and in which, thus, also Socrates does not exist. From (ii) it follows, by virtue of the rules of equipollence holding among modal claims, that (iii) ‘It is impossible for Socrates to be a stone’. Now, if we interpret the modal term ‘impossible’ as if it signified a property of impossibilitas (or any other property) existing in Socrates, we would have it that (iv) ‘Socrates has an impossibility’ and therefore that (v) ‘Socrates exists’. This is impossible, because it contradicts the premise (i). According to the author, the fallacy lies in the wrong interpretation of the term ‘impossible’ in (iii), which should not be interpreted as positing the existence of a certain property in Socrates. This is true, he continues, of all modal terms, which ‘nichil ponunt in rebus de quibus agitur in propositionibus illis’, that is, they do not posit the existence of anything in the substances about which modal propositions are. According to H9, this is true not only of nominal modes but also of adverbial ones. Just as the nominal proposition ‘It is possible for William to be a bishop’ (Possibile est Vuilelmum esse episcopum) does not affirm that a certain property of possibilitas inheres in the subject, in the same way the corresponding adverbial claim ‘William is a bishop possibly’ (Vuilelmus est episcopus possibiliter) does not express the inherence of the property of being a bishop in the subject, but it simply ‘predicates’ this property of him.4 famously states that words of this sort have no signification but ‘unite significant sounds by inclining the mind to a certain mode of conceiving’ (Nuchelmans 1973, p. 141). The same idea is applied by Abelard within his discussion of the signification of nominal modes (see later in this section at p. 83). 4 See H9: Orléans, Bibl. mun. 266, pp. 37a–37b: ‘Notandum etiam quod iste voces “possibile”, “necessarium” et alii modi qui predicantur, nichil ponunt in rebus de quibus agitur in propositionibus illis. Si enim ponerent, sequeretur: “si nichil est, aliquid est” hoc modo. Verum est enim “si non est possibile Socratem esse lapidem, tunc impossibile est Socratem esse lapidem”. Et si quia non est possibile Socratem esse lapidem, impossibile est Socratem esse lapidem, et quia non est possibile Socratem esse lapidem, Socrates habet impossibile, et ita Socrates est. Et si quia non est possibile Socratem esse lapidem, Socrates est, et quia nichil est, Socrates est – ab antecedenti, quia si nichil est, Socrates non est; si Socrates non est, non habet possibile, et ita non est possibile eum esse lapidem. Quare si nichil est, aliquid est. Quare dicendum est quod [quando] “possibile” et “impossibile” “necessarium esse” in modalibus predicantur, significant “possibile” et “impossibile” et “necessarium” non ponunt circa res de quibus in modalibus, ut etiam quando dicimus ‘quilibet est episcopus possibiliter’, ‘episcopus’ episcopium significat. Sed non est in eo, et predicatur tantum de eo’. On the last part of this passage, cf. the parallal fragment in the Assisi manuscript of H9 (Assisi, Bibl. Franc. 65rb), which

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For this reason we should say that, when ‘possible’, ‘impossible’ and ‘necessary’ are predicated in modal claims, they signify possibility, impossibility and necessity, but they do not posit the existence of anything in the substances about which modal proposition are. In the same way, also when we say: ‘William is a bishop possibly’, ‘bishop’ signifies being a bishop, but [being a bishop] is not posited as existing in William, it is only predicated of him. [my emphasis] A very similar view is maintained in the treatise on modalities labelled M3. Like that of H9, the author of M3 asks whether the existence of any property is predicated by means of nominal modes (‘videamus utrum aliqua proprietas per modalia nomina ponatur’) and states that many paradoxical consequences would follow if we interpreted modalities in this way, such as ‘if nothing exists, a chimaera exists’. This is shown by proving that ‘if no chimaera exists, then something exists’, which is equivalent to the former conditional by contraposition. Let us assume – the author begins – that the antecedent is true, and that therefore (i) ‘no chimaera exists’. Consider now the proposition (ii) ‘it is possible for a chimaera not to exist’, which the author of M3 seems to take as true on the basis of (i). If we interpret the mode ‘possible’ as positing the existence of a form of possibilitas in something, from (ii) it would follow that (iii) ‘there is the possibilitas that a chimaera does not exist’ (‘possibilitas non existendi chimaeram est’), and so we would have that (iv) ‘something exists’, namely, the form of possibility itself. We would have then proved that ‘if no chimaera exists, then something exists’, which is equivalent to the paradoxical ‘if nothing exists, a chimaera exists’.5 Clearly, this argument retraces the one put forward in H9. M3 also includes another sort of argument to undermine the idea that modal nouns posit the existence of some properties or forms in things. These arguments are meant to d­ iffers quite consistently and on which the following translation is based: ‘Quare dicendum est quando (corrected from: quod) “possibile” et “impossibile” et “necesse” in modalibus predicantur, quod significant (corrected from: significant quod) possibilitatem et impossibilitatem et necessitatem, sed non predicantur circa res de quibus agitur in propositionibus modalibus. Ut etiam quando dicimus “Vuilelmus est episcopus possibiliter”, “episcopus” episcopum significat, sed non in Vuilelmo, et predicatur tantum de eo’. I am very grateful to Wojciech Wciórka for pointing out the differences between the two manuscripts on this point and discussing them with me. 5 See M3: Orléans, Bibl. mun. 266, p. 254b: ‘Investigato sensu modalium, videamus utrum aliqua proprietas per modalia nomina ponatur. Si enim per ea aliquid ponitur, multa sequentur inconvenientia. Quorum unum est: “Si nulla res est, tunc chimaera est”. Quia si chimaera non est, aliqua res est. Quod sic probatur. Si chimaera non est, possibile chimaeram non esse, et ita possibilitas non existendi chimaeram est, et sic aliqua res est.’

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show that the absurd conditionals ‘if it does not exist, then it exists’ (si non est, est), and ‘if it will exist in the future, then it exists now’ (si erit, est), follow from such an interpretation of modal nouns. Assume, for instance, that Socrates will exist at some future time. From this it follows that ‘it is possible for Socrates to exist’. But if we interpret modal nouns as referring to some form inhering in Socrates, we should admit that Socrates already has this form in the present moment, and therefore Socrates already exists in the present (otherwise he could not be the bearer of any form). We have then inferred the absurd claim ‘if Socrates will exist, then Socrates exists now’.6 Having offered this and other arguments, the author of M3 concludes that ‘clearly many inconveniences follow if we admit that the existence of something is posited by modal words’ (haec et plura alia inconvenientia, si per modales voces aliquid ponatur, sequi manifestum est). Arguments of this second sort are interesting because they clearly point out that, according to the author of M3, nominal modal claims such as ‘it is possible for Socrates to exist’ have no existential import, and their truth not only does not posit the existence of any property in Socrates but also does not posit the existence of Socrates himself. The same view seems to be endorsed, albeit only implicitly, in H9’s arguments, where propositions such as ‘it is not possible for Socrates to be a stone’ were said to be true even when Socrates does not exist. As we will see shortly, in the Dialectica Abelard also assumes that nominal claims have no import, explicitly saying that there are many true modal claims about non-existent beings, such as ‘It is necessary for chimaeras not to be goat-stags’ or ‘It is possible for my future son to exist’.7 Although early 12th-century authors do not justify the truth of these modal propositions explicitly, the reasoning behind their view might be the assumption that whatever is actually the case in a certain moment of time is also possibly the case. Because it is actually the case that chimaeras are not goat-stags, we may validly infer that ‘it is possible for chimaeras not to be goat-stags’, even if chimaeras do not exist. Similarly, because a certain state of affairs will become 6 See M3: Orléans, Bibl. mun. 266, p. 254b: ‘Et aliud “si non est, est”, hoc modo. Si non est, possibile est non esse; et sic possibilitas est; et sic aliquid est. Item, “si erit, et est”, sic. Si Socrates erit, possibile est esse Socratem; et sic Socrates habet possibilitatem existendi; et ita est. Item “si non est, non possibile est esse”, quia si est possibile esse, et est. Si Socratem esse est possibile, Socrates habet possibilitatem existendi; et ita possibilitas est in Socrate; et ita est. Quare si possibile est esse, et est. Quare “si non est, non est possibile esse”. Haec et plura alia inconvenientia, si per modales voces aliquid ponatur, sequi manifestum est.’ 7 Abelard changes his view in the Logica Ingredientibus, where he instead takes all modal claims – adverbial and nominal ones – as having an implicit import. See on this (Binini 2018). I will return to this in Chapter 5.

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actual in some future time, for example, that Socrates will exist, it must be possible (now) for it to happen. The implicit principles justifying this reasoning may be formalized in the following way: i. ii.

pt = now → ◊t p; pt’ ≥ t = now → ◊t p.8

The first principle, according to which we can infer possibility from actuality, can be traced back to the authority of Aristotle and Boethius. Boethius, for instance, says that ‘being possibly the case’ always follows from ‘being actually the case’, for everything that actually is also can be (‘rursus omne esse sequitur posse esse. Quod enim est et potest esse’9). According to him, this can be proven by considering the evident principle, which is equipollent to (i) by contraposition, stating that ‘if something cannot be the case, then it is not actually the case’ (‘nam si esse non posset, sine ulla dubitatione nec esset’10). This idea returns in many early 12th-century sources, whose authors state that whatever is true, or whatever is in actu, is also possible. Being actually true is usually seen as one species of the possible, also called ‘verum possibile’ or ‘possibile actu,’ which is contrasted with what is possible but – temporarily or permanently – unrealized (see Chapter 1, Section 3 on this). The second principle, stating that whatever will be the case in some future time is (now) possible, might be seen as an extension of the first, which passes from considering what is the case in the present moment to considering what is the case at any moment in time from now on. Many authors of the time think that what will be the case in the future constitutes a species of the possible. Abelard too holds in the Dialectica that ‘whatever is future is possible’ (quod futurum est, possibile est).11 Returning to the question of whether modal nouns denote a property of things, arguments analogous to those used in H9 and M3 are also advanced in Abelard’s Dialectica, and again the similarity between the three texts in both the terminology and the line of reasoning is evident. Rehearsing verbatim the 8

9 10 11

The formula ‘pt = now → ◊t p’ should be read as saying: ‘If proposition p is true at time t (which is the present time), then it is possible at t that p is true.’ The second formula ‘pt’ ≥ t → ◊t p’ says instead that ‘if proposition p is true at a time t’, which is later than t, then it is possible at t that p is true’. Written in this way, the two formulations presuppose a de dicto reading of possibility. This might not be exactly in line with the principles that early 12th-century logicians had in mind, which were probably ambiguous with respect to the scope of modalities. (Boethius 1880, p. 385, 3–4). See (Boethius 1880, p. 385, 3–5). Dial. 196, 7–8.

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same quaestio used in M3, Abelard asks ‘whether any property is predicated by means of modal terms, as some people want’ (utrum aliqua proprietas per modalia nomina, ut quidam volunt, praedicaretur). It is not clear who are the quidam defending the idea that the predication of modal nouns amounts to a predication of properties, and claiming, as Abelard reports shortly after this, that by means of the names ‘possible’ and ‘necessary’ a property of possibilitas or necessitas is predicated. It is unlikely that these quidam are contemporaries of Abelard, since, as we have seen, there seems to be a shared rejection of this view in sources of the time. More likely, Abelard refers here to ancient modal theories, perhaps to Boethius or Aristotle himself. This seems to be confirmed by what he says in the Logica Ingredientibus, where he explicitly distances himself from Aristotle’s understanding of modalities on this point, claiming that Aristotle interpreted necessity and possibility as kinds of form belonging to substances and understood the term ‘possibile’ as if it were ‘a name of things’ (nomen rerum), that is, a name that refers to the possibilitates or potestates existing in substances: Note that from the words of Aristotle, when he speaks of ‘possibilities’ (potestates), it seems that in the name ‘possible’ he understands a certain form, that is, a certain potency or possibility, when he posits such name in modal propositions – which seems to make [this name ‘possible’] a name of things (nomen rerum). We have rejected this position above. We, on the contrary, do not understand any form when speaking of ‘possibility’ or ‘necessity’, but we expound [these terms] according to the meaning of modals.12 As will become clear, the exposition ‘according to the meaning of modals’ is the one in which the term ‘possible’ expresses a non-incompatibility with nature (non repugnantia naturae), whereas ‘necessary’ is predicated of something that nature requires (natura exigitur). Returning to the Dialectica, Abelard argues for the idea that modal nouns do not signify forms by stating that, if this were the case, all modal propositions concerning non-existent beings would be false, while in fact there are many such propositions that are true, for instance, ‘it is possible for my future son to exist’ or ‘it is necessary that chimaeras are not human’. By means of 12 See LI De Int. 472, 613–9: ‘Nota etiam quod ex verbis Aristotelis, cum ait “potestates”, videtur ipse in hoc nomine “possibile”, quod etiam nomen rerum facere videtur, potestatem sive possibilitatem, quandam formam, intelligere, cum ipsum in modalibus propositionibus ponit; quod supra negavimus. Nos tamen, cum dicit “potestatem” vel “necessitatem,” nullas intelligimus formas sed iuxta sensum modalium omnia exponimus.’

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propositions of this sort, he continues, nothing is predicated of future sons or chimaeras, which – being non-existent – could not bear any property or accident. Rather, Abelard says, the term ‘possible’ must be understood in terms of ‘what is compatible with nature’, and ‘necessary’ must be understood as ‘what natures requires’ or ‘imposes.’ We shall now investigate whether any property is predicated by means of nominal modes, as some people want. They say that by the noun ‘possible’ a possibility is predicated, and a necessity by the noun ‘necessary’, as if when we say ‘it is possible (or necessary) for Socrates to be’ we would attribute a certain possibility or a certain necessity to him. But this is false. There are many affirmations of this sort that are true even though they are about non-existent things, which – being non-existent – admit no property of accidents. Indeed, what does not exist cannot bear anything existent. Of this sort of modals [namely, nominal modals], the following are true: ‘it is possible for my future son to exist’, ‘it is possible for a chimaera not to exist’ or ‘it is necessary for chimaeras not to be human’; nonetheless, nothing is taken to be attributed to non-existing things by means of these propositions, but – as said above – by means of ‘possible’ is expressed what is compatible with nature, by means of ‘necessary’ what [nature] requires or imposes.13 Abelard continues along the same lines as H9 and M3, saying that if we understood modal terms as signifying properties, impossible consequences would follow, such as ‘if it will exist, then it exists now’ or ‘if it does not exist, then it exists.’ The argument provided is exactly the same as the one found in M3. Some ontological and semantic worries related to the signification of modal nouns are presented again in the Logica Ingredientibus, where Abelard repeats the idea that nominal modes have no denotation, an idea that he now enriches with new details. While seeking an answer to the question of what modal 13

Dial. 204, 1–12: ‘Nunc autem utrum aliqua proprietas per modalia nomina, ut quidam volunt, praedic[ar]etur, persequamur. Aiunt enim per “possibile” possibilitatem praedicari, per “necesse” necessitatem, ut, cum dicimus: “possibile est Socratem esse vel necesse”, possibilitatem aut necessitatem ei attribuimus. Sed falso est. Multae verae sunt affirmationes huiusmodi etiam de non-existentibus rebus, quae, cum non sint, nullorum accidentium proprietates recipiunt. Quod enim non est, id quod est sustentare non potest. Sunt itaque huiusmodi verae: “filium futurum possibile est esse”, “chimaeram possibile est non esse”, vel “necesse est non esse hominem”; nihil tamen attribui per ista his quae non sunt, intelligitur, sed, ut superius dictum est, per “possibile” id demonstratur quod natura patiatur, per “necesse” quod [dicit] exigat et constringat.’

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terms signify when they are included in nominal propositions, Abelard affirms three things. First, nouns such as ‘possible’ or ‘necessary’ neither have denotation (nominatio) nor signify forms (‘nec res aliquas nominando contineant nec formas determinent’). Second, modal nouns of this sort have no signification of their own but merely ‘co-signify’. With respect to this point, modes resemble other parts of language that have no signification in isolation from a context, for instance, the conjunction ‘if’ (si). Third, he thinks that, rather than generating a definite image or understanding in the intellect, modal terms convey a certain ‘way of conceiving’ the things of which they are predicated (modus concipiendi circa res subiectae orationis’). Since [the modal nouns] ‘possibile’ and ‘necessary’ are not derivative (sumpta)14 expressions, and they neither contain any thing by denoting it nor do they determine any form, it should be asked what it is that they signify. Indeed, when it is said ‘It is possible for what is not to be’, or ‘it is necessary for God to exist’ or again ‘it is necessary for chimaeras not to exist’, we do not intend it in the sense that certain forms exist in these things. We say that in propositions of this sort [the terms] ‘necessary’ and ‘possible’ co-signify rather than having a signification of their own, because nothing is understood in them unless they are applied to the phrase (oratio) that is the subject. And therefore, these terms express a way of conceiving the things of which the subject phrase is about, just as an interposed verb or the conjunction ‘if’ (which expresses a necessity of conjunction) would do. And, just like in the case of these last expressions no image is raised in the understanding, but by means of the verb or the conjunction the mind captures a certain way of conceiving those things that are adjoined to them, the same happens for the terms ‘possible’ and ‘necessary’. And here with ‘necessary’ is meant what is inevitable, with ‘possible’ what is not repugnant to nature.15 14 Abelard’s nomina sumpta are those concrete names that are taken or derivate from the abstract corresponding name, such as ‘white’ from ‘whiteness’. On Abelard’s treatment of nomina sumpta and on the translation of this technical term, see (Jolivet 2000, pp. 107–8), and (Marenbon 1997, pp. 140–1). 15 See LI De Int. 407, 412–408, 425: ‘At vero cum “possibile” vel “necessarium” sumpta non sint nec res aliquas nominando contineant nec formas determinent, quid significent quaerendum est; non enim, cum dicitur: “Id quod non est possibile est esse” vel: “Deum necesse est esse” vel: “Chimaeram necesse est non esse” quasi formas aliquas in rebus accipimus. Dicimus itaque necessarium sive possibile in huiusmodi enuntiationibus magis consignificare quam per se significationem habere; nil quippe in eis est intelligendum nisi subiectae orationi applicentur, et tunc modum concipiendi faciunt circa res subiectae

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The reading of modalities exposed here, as having entirely no ontological correlate but instead as mental attitudes that incline the mind to certain ‘ways of conceiving’ things,16 might be seen as the culmination of the process of ­de-reification of modalities mentioned earlier. At the end of the passage we once again encounter the idea that the term ‘possible’ should be understood in terms of ‘what is not incompatible with nature’ – an idea which was already present in the words quoted above from the Dialectica. The term ‘necessary’, on the other hand, is defined here as ‘inevitable’, which is elsewhere interpreted as ‘what [nature] requires or imposes’. These definitions of modalities return in many sources of the time. In Chapter 3, Sections 3 and 4 I shall consider these characterizations more closely and give a detailed analysis of the understanding of possibility and necessity that they represent. But first, we should take a look at the second question that early 12th-century authors raised concerning the signification of modes, namely, whether these modes refer to propositional entities or to things themselves. 2

Do Modal Terms Refer to Things or to Propositions?

Although many sources of the time agree that nominal modes do not denote properties existing in things, they advance divergent opinions on how these modes should be properly interpreted. In particular, part of the debate focuses on what item do modal terms refer to, that is, what is said to be ‘possible’ or ‘necessary’ in nominal modal propositions. Two alternative interpretations are outlined in answer to this question: possibility and necessity either refer to the things (res) that the modal proposition is about, or they refer to the propositional entities (sensus or dicta) of which modes are predicated. This part of the early 12th-century debate on modalities is particularly interesting because it contributes to preparing the grounds for identifying and developing the de re-de sensu interpretation of modal claims.17 Although Abelard’s logical works are perhaps the first in which this distinction is systematically investigated and

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orationis sicut facit verbum interpositum vel coniunctio “si”, quae ad necessitatem copulat; ac, sicut in istis nulla imagine nititur intellectus sed quendam concipiendi modum anima capit per verbum vel per coniunctionem circa res earum vocum quibus adiunguntur, ita per “possibile” et “necessarium”. Et est hoc loco “necessarium” pro inevitabili, “possibile” quasi non repugnans naturae.’ On the notion of consignificatio in Abelard and in the grammatical tradition of the late 11th century Glosulae on Priscian, see (Rosier-­Catach 2003). On Abelard’s use of the expression ‘modus concipiendi’ with respect to modal terms and other indefinite terms, see (Nuchelmans 1973, pp. 141–2). See on this (Binini forthcoming).

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theorized (as we will see in Chapter 4 of this volume), the syntactic and semantic ambiguity of modal claims is acknowledged and debated in many other texts that can be dated to the early 12th century, which shows that Abelard was not the only logician interested in the topic. A discussion of this issue may be found in the anonymous treatise M3, in which the author considers the proposition ‘it is possible for every man to be an animal’ and asks what is said to be possible by this claim, whether it is the words (voces) composing the proposition, the understandings (intellectus) generated by these words, or rather the things (res) that these words signify.18 The author rapidly discards the idea that it is words or understandings that are called ‘possible’ or ‘necessary’, because if this were the case propositions such as ‘it is possible for every human to be a stone’ would be true, since the words included in them and the understandings generated by these words are possible. For the same reason, we cannot even say that it is the things denoted by the words ‘human’ and ‘stone’ that are possible in the sense that their existence is possible, or we would end up with the same problematic consequence.19 And yet, M3 reports, some people still interpret modal terms as referring to things (res) in a different sense. They take a proposition such as ‘For every human it is possible to be an animal’ to mean that ‘things have the possibility that every human is an animal’ (‘res habent possibilitatem quod omnis homo sit animal’). The modal term would then be interpreted as pointing out a certain feature or possibilitas that things ‘possess’. This interpretation, however, is incorrect according to the author of M3, for it fails to account for the many cases in which modal claims are true despite them dealing with non-existent subjects. If the term ‘possible’ referred to things and the possibilitates they possess, how could a modal proposition such as ‘it is possible for a chimaera not to be a goat-stag’ be true, when neither chimaeras nor goat-stags exist? And how could the modal claim ‘it is possible for the world to be made’ (­ possibile mundum fieri), uttered before the creation of the world, be true, if in the assumed situation no res whatsoever exists?20 And yet, both propositions are true, according to the author of M3: 18 See also (Martin 2016, p. 120) on this. 19 See M3 Orléans, Bibl. mun. 266, p. 254b: ‘Quaeritur quem sensum habeant istae modales et quid dicant. Cum enim dicimus “omnem hominem esse animal est possibile”, quid dicimus esse possibile: sive has voces seu intellectum seu res quae significantur ab his vocibus? Si dicimus vel res vel voces vel intellectus esse possibiles, iam vera erit “omnem hominem esse lapidem est possibile”, quia talis intellectus est possibilis vel istae voces sunt possibiles vel homo et lapis res quae hic significantur sunt possibiles.’ 20 Note that this example is the same as the one used by Anselm in his De casu diaboli, where he is also interested in investigating the ontological foundations of possibilities

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There are some who expound [nominal propositions such as] ‘for every man to be an animal is possible’ in this way: ‘things have the possibility that every man is an animal’. But this cannot be right. Indeed, it is true that ‘for chimaeras not to be goat-stags is possible’. [To which] we say: How would things have the possibility that chimaeras were not goatstags? After all, there are no things having that possibility, because neither chimaeras nor any other such thing exists. And yet the proposition is true. In the same way, if before the creation of the world one said: ‘It is possible for the world to be made’, this proposition would be true, but which things would have the possibility of the world being made, if nothing whatsoever existed? Thanks to this and many other examples, it can be shown that their exposition [of modals] is incorrect.21 Having dismissed the idea that modal nouns should be taken as referring to res and to the way things are, the author of M3 offers his own interpretation, according to which modal terms are applied to the sense (sensus) of the nonmodal propositions of which they are predicated, so that in a proposition such as ‘it is possible for Socrates to read’ what is said to be possible is the sensus of the non-modal claim ‘Socrates reads’: It seems to us that the sense (sensus) of nominal modals should be expounded in a different way: when we say ‘for Socrates to be a man (or to read) is possible’, we do not affirm that Socrates or his reading or these words or these understandings are possible, but that the sense (sensus) [of this proposition] ‘Socrates reads’ is possible, that is, it is possible that (quod) Socrates reads. This is what you should respond to those who interrogate you on the meaning of modal claims.22 and wonders how we could speak about the possibilities of things before their actual existence. Anselm solves this puzzle by grounding the possibility of the world to exist before its actual existence in the power of God, saying it would be possible for God to create it. Similar questions concerning the ontological correlate of possibilities return in Anselm’s Philosophical Fragments. See pp. 28 ff. on this. 21 See M3: Orléans, Bibl. mun. 266, p. 254b: ‘Sunt qui exponant ita ‘Omnem hominem esse animal est possibile’: res habent possibilitatem quod omnis homo sit animal. Sed hoc nihil est. Vera est enim ‘chimaeram non esse hircocervum est possibile’. Dicemus: quomodo [corrected from: dicemus modo quod] res habent possibilitatem quod chimaera non sit hircocervus, quippe nullae res habent illam possibilitatem, quia neque chimaera neque alia, tamen vera est illa propositio. Item antequam mundus fieret, si diceretur ‘possibile mundum fieri’, vera esset talis propositio; sed cum nulla res esset, quae res habebant possibilitatem ut mundus fieret? His et multis aliis exemplis nulla esse ostenditur illa expositio.’ 22 See M3: Orléans, Bibl. mun. 266, p. 254b: ‘Nobis autem aliter videtur exponendus sensus modalium: cum dicimus “Socratem esse hominem” vel “Socratem legere est possibile”, non

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The only argument given in favour of the proposed ‘de sensu’ interpretation appeals to the truth of modal propositions dealing with non-existent things, which, as we have seen in the last section, was accepted by many logicians of this time. However, the preference for this interpretation of modes is also in line with many other aspects of the modal theory outlined in M3, which were discussed in Chapter 2, having to do not with the signification of modal claims but with their syntactic structure and their relation with the corresponding simple and adverbial forms. As we have seen, the author of this treatise affirms that the mode functions as the predicate in nominal modals and that the subject is the entire proposition to which the mode is applied. Moreover, he states that nominal propositions are not always reducible to an adverbial form, for some may be true even though the corresponding adverbial claims are false (see Chapter 2, Sections 2 and 3 on this). All of these features are compatible with the de sensu reading of nominal modal claims that M3 is proposing here. The same question raised in M3 about the sensus of modal claims may be found in similar terms in other sources of the time, such as H20 and De Propositionibus Modalibus. The commentary on De Interpretatione labelled H20 – which has many doctrinal similarities with M3, is found in the same manuscript, and is also probably connected to the school of Joscelin of Soissons – proposes almost verbatim the wording and solution already seen in M3: the author rules out the view that modal nouns refer to the words, understandings, or things included in modal propositions and states that a modal claim such as ‘It is possible for Socrates to read’ (Possibile est Socratem legere) must be expounded as meaning that the content (sensus) of the proposition to which the modal term is adjoined is possible, as if it said: ‘It is possible that Socrates reads’ (Possibile est quod Socrates legat).23 This ‘quod-clause’, which we already encountered in M3, is here used to disambiguate the structure of infinitive accusative modal claims and to point out more clearly that the sentence must be understood de sensu and not de rebus. The treatise De Propositionibus Modalibus (which is probably a later source, since its author displays dicimus vel quod Socrates sit possibilis vel lectio Socratis vel quod voces vel intellectus sint possibiles, sed hunc sensum: “Socratem legere” esse possibile, id est possibile est quod Socrates legat. Et hoc respondeat qui de sensu modalium inquiretur.’ 23 See H20, Orléans, Bibl. mun. 266, pp. 262b–263a: ‘Cum enim dicimus “omnem hominem esse possibile est”, quid dicimus esse possibile? Vel has voces dicimus esse possibiles, vel intellectus vel res. Si vel res vel intellectus vel voces dicimus possibiles, iam vera erit “hominem esse lapidem possibile est”. Res enim et voces et intellectus possibiles sunt. Nobis videtur sensus sic exponendus. Cum dicimus “Socratem legere possibile est”, non dicimus quod Socrates sit possibilis vel lectio Socratis vel voces vel intellectus, sed hunc sensum, scilicet sensum huic adiunctum possibile esse, id est possibile est quod Socrates legat.’

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some knowledge of Abelard’s Logica Ingredientibus, or at least of parts of it) also points out that modal nouns should refer not to things, words, or understandings but to what is proposed by a sentence, so the proposition ‘it is possible for Socrates to read’ is taken to mean ‘it can happen that Socrates reads’ (ita contingere potest quod Socrates legat), while the proposition ‘it is necessary for God to live’ is interpreted as saying ‘it is actually the case that God lives and it cannot be otherwise’ (ita est quod deus vivit et aliter esse non potest).24 Notice that the first example is the same as the one already found in M3 and H20. Differently from these sources, though, the author of DPM also adds an example considering a proposition about necessity. In both examples we see the same use of the ‘quod-form’ that was already present in M3 and H20. Apart from these three sources, we have other evidence for the preference of some 12th-century authors for the de sensu interpretation of nominal modals. It is, however, an indirect testimony, reported by Abelard as the position of his magister. According to what Abelard says in a well-known passage of the Dialectica, his Master’s reading of modal claims highly resembles the one put forward in the texts we have just seen, for he thinks that modal claims are related to (or better ‘descend from’) the corresponding simple ones by virtue of the fact that they deal with their content (sensus), so when we say ‘It is possible for Socrates to run’ (Possibile est Socratem currere) what we mean is that ‘It is possible what (quod) this proposition says: ‘Socrates runs’’:25 It is our Master’s view that these [i.e. nominal modal propositions] descend from simple claims in such a way that they are about their sensus, as when we say: ‘it is possible (or necessary) for Socrates to run’, we would affirm that it is possible or necessary what is said by this proposition ‘Socrates runs’.26 24 See Anonymous, De Propositionibus Modalibus, in (Abaelard 2010a, p. 233, 76–82): ‘Quaeritur quid dicatur esse possibile vel necesse in huiusmodi propositionibus, utrum res vel voces vel intellectus. Dicimus quod nec hoc nec illud dicitur esse possibile vel necesse, sed hoc proponitur per istam “Possibile est Socratem legere”, quoniam ita contingere potest quod Socrates legat. Sic et ista “Necesse est deum vivere” hoc proponit, quoniam ita est quod deus vivit et aliter esse non potest.’ 25 Notice that, in all the sources seen so far in this section, the authors say that modal claims must refer to the sensus of propositions, but no one mentions dicta or uses a ‘de dicto’ terminology. Abelard is the only author (apart from later sources such as H21, the Introductiones Montane or the Ars Meliduna) who uses the expressions de sensu and de dicto interchangeably when talking about the interpretation of modal claims. 26 Dial. 195, 12–5: ‘Est autem Magistri nostri sententia eas ita ex simplicibus descendere, quod de sensu earum agant, ut cum dicimus: “possibile est Socratem currere vel necesse”, id dicimus quod possibile est vel necesse quod dicit ista propositio: “Socrates currit”.’

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As is known, Abelard attacks this position, advancing several arguments to prove its inconsistency.27 In both the Dialectica and the Glossae on De Interpretatione he argues for the opposite opinion, namely, that the proper understanding of modal claims is the one in which modes refer to the things themselves that the corresponding simple propositions are about, and not to their propositional content. According to his interpretation, modal propositions must thus be taken ‘de rebus’.28 As was the case for the other authors seen so far, in Abelard there is also a correspondence between what he thinks is the proper interpretation of the signification of modal terms and his reconstruction of the syntactic structure of modal propositions. As seen in Chapter 2, Sections 2 and 3 above, Abelard thinks that nominal claims are reducible to an adverbial and personal form, since, although impersonal with respect to their grammatical structure, they are in fact adverbial in meaning. Moreover, he claims that propositions such as ‘Possibile est Socratem esse hominem’ have the same subject and predicate in sensu as the corresponding simple and adverbial claims ‘Socrates est homo’ and ‘Socrates est homo possibiliter’, so that the three sentences all talk about the same things. What does Abelard intend when he says that modal terms must be understood de re or de rebus, that is, as referring to things rather than propositional items? Certainly, he does not intend that modal terms denote some property or form inhering in substances, for we have seen in Chapter 3, Section 1 that he strongly rejects this reading of modes – just as some of his contemporaries do. Rather, Abelard explains his de rebus interpretation saying that propositions about possibility should be understood as pointing out what is not incompatible with the nature of things (or with nature in general), while propositions about necessity should be understood as pointing out what the nature of things requires and compels. These definitions of modal notions may be found in a great number of other sources devoted to modalities that are contemporary to Abelard. In the next sections, I will consider some of these sources and explain how this understanding of modalities originated and developed in the early 12th century. 27 28

Abelard’s position on the de re-de sensu distinction will be investigated in more detail in Chapter 4. Dial. 200, 12–20: ‘Sed, ut quidem praediximus, non placet nobis ita modales ex simplicibus descendere propositionibus, quod de sensu ipsarum agant, sed de rebus ipsis de quibus illae simplices, sicut et illae faciunt modales quae adverbiales habent modos, in quas istae quae casuales habent, resolvuntur. Sunt enim, ut dictum est, eiusdem sensus ut “omnis homo possibiliter est albus” et “omnem hominem possibile est esse album”; sic itaque ex simplicibus modales descendere concedimus, quod cum modo de iisdem rebus enuntiant, de quibus illae simpliciter proponebant.’

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Possibility as Compatibility with Nature

In his commentaries on De Interpretatione Boethius claims that modal propositions about possibility and contingency should not be evaluated ‘ex eventu’, in the sense that their truth-value does not depend on the states of affairs that are actually occurring in the present circumstances, or on the ones that occur in other moments of time. The meaning of a proposition such as ‘it is possible for p to happen’, he says, is not affected by the fact that what is affirmed by p does, or will, take place.29 In modern terms a similar idea is expressed by saying that modal operators are not truth-functional, that is to say, the truthvalue of a modal clause does not depend on the truth-value of the (non-modal) sentences that compose it. In the Dialectica Abelard raises a similar point when speaking of propositions about possibility. He insists that the truth of these propositions does not depend on what is actually the case and claims that a proposition such as (*) ‘It is possible for Socrates to be a bishop’ may be true even though Socrates is presently not a bishop and never will be one (cf. ­Chapter 9, Section 1 for a discussion of this example). But if not on the basis of actual or future events, how should propositions of this sort be evaluated? According to Abelard, what is needed in order for a possibility-proposition such as (*) to be true is a ‘non-incompatibility’ relation (non repugnantia) between what is expressed by the predicate, ‘being a bishop’, and the nature of the thing denoted by the subject, Socrates.30 If there is no incompatibility between the two, we say that it could happen that Socrates is a bishop, because the nature of Socrates would allow it to happen (‘natura rei non repugnaret ad hoc ut contingat, sed patiatur contingere’):31 29

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See (Boethius 1880, pp. 383, 16–384, 3): ‘Quod enim posse esse vel contingere dicitur, nondum quidem est, sed esse poterit. Sive autem eveniat sive non eveniat, quia tamen esse potest, contingens vel possibilis dicitur propositio. Non enim ex eventu diiudicantur huiusmodi propositiones, sed potius ex significatione hoc modo: si quis enim dicat posse cras esse circenses, possibilis est contingensque adfirmatio. Quod si cras sint circenses, non tamen aliquid est actu propositionis contingentis vel possibilis permutatum, ut necesse fuisse videatur, quod illa possibiliter promittebat. Quod si rursus non sint circenses, omnino nec sic aliquid permutatum est, ut necesse fuisse non esse circenses videatur. Non enim (ut dictum est) secundum eventum ista iudicantur, sed potius secundum ipsius propositionis promissum.’ Subject and predicate here are intended as what early 12th-century logicians usually called the ‘secondary terms’ of modal propositions, and what Abelard called the subject and predicate ‘according to the meaning’ (in sensu), not those according to the grammatical structure. See pp. 68 ff. on this. Notice that what is at stake in this passage is the relation between a property expressed by the predicate and the specific nature of an individual (the substance denoted by the

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‘Possible’ and ‘contingent’ mean the same thing. For we do not take here the term ‘contingent’ as meaning what actually happens, but what can happen, even if it should never happen, so long as the nature of the thing is not incompatible with its happening, but instead allows it to happen. For instance, when we say that ‘It is possible for Socrates to be a bishop’, this is true even though he never is one, since his nature is not incompatible with being a bishop. We may assess [such non-incompatibility] from other individuals of the same species, who we see actually participate in the property of being bishops. For indeed, whatever actually happens in one individual, we consider that the same can happen in every individual of the same species, because they are all of a same nature.32 This passage from the Dialectica draws attention to several interesting aspects of Abelard’s understanding of possibility. First, it shows that, like many of his contemporaries, Abelard is committed to the existence of unrealized possibilities, that is, possibilities that are never actualized in time and are then always extra-actum. As we have seen in Chapter 1, Boethius extensively talked about unrealized possibilities in his commentaries on Aristotle, and his terminology was employed by early 12th-century logicians, who used it to interpret Aristotle’s references to ‘pure potencies’ in De Intepretatione 9 and 13.33 Second, Abelard embraces a view according to which all individuals belonging to the subject). At other times in Abelard’s texts, and also in other sources contemporary to him, possibility is evaluated in terms of a non-incompatibility relation between a predicate and ‘Nature’ taken in general, considered perhaps as the ‘sum’ of all individual natures, or the general complex constituted by all natural laws. I will return to this later in this section. 32 ‘“Possibile” quidem et “contingens” idem prorsus sonant. Nam “contingens” hoc loco quod actu contingit accipimus, sed quod contingere potest, si etiam numquam contingat, dummodo natura rei non repugnaret ad hoc ut contingat, sed patiatur contingere; ut, cum dicimus: “Socratem possibile est esse episcopum”, etsi numquam sit, tamen verum est, cum natura ipsius episcopo non repugnet; quod ex aliis eiusdem speciei individuis perpendimus, quae proprietatem episcopi iam actu participare videmus. Quicquid enim actu contingit in uno, idem in omnibus eiusdem speciei individuis contingere posse arbitramur, quippe eiusdem sunt omnino naturae’ (Dial. 193, 31–194, 5). See also Dial. 193, 19–23: ‘Cum ergo dicimus: “Socrates est episcopus possibiliter” et verum enuntiamus, quomodo per “possibiliter” inhaerentiam episcopi ad Socratem determinamus, cum ipsa omnino non sit? Nullo enim modo proprietas episcopi Socrati laico cohaeret. Nec “posse cohaerere” dicendum est “cohaerere”.’ 33 Aristotle deals with unrealized possibilities in Chapter 9 of the De Interpretatione, where he claims that a proposition such as ‘It is possible for this cloak to be cut up’ should be considered true even if the cloak will never be cut up (see De Interpretatione 9, 19a12– 22). The idea of unrealized possibilities again returns at the end of De Interpretatione 13,

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same natural kind are ‘of the same nature’ (eiusdem naturae) and which, by virtue of having the same nature, also have the same possibilities: what is possible for one individual must also be possible for all other members of the same species, since, according to his definition, possibility depends (exclusively) on what nature allows. Finally, the passage could be read as a sketchy epistemology of possibility: Abelard says that we know (or that we are entitled to believe) that it is possible for a subject to have a certain property because we have experience of other individuals – which are of the same nature as the subject under consideration – having that property in act. Empirical experience seems then to be treated by Abelard as a ‘good guide to possibility’ (or, at least, a partial guide to it), for the knowledge of possibility is obtained, as Knuuttila has remarked, ‘through inductive abstraction’ on what has been exemplified either by a single substance or by the other individuals belonging to the same natural kind.34 All these aspects deserve further analysis, which I will deal with in Part II of this book (see, in particular, Chapters 8 and 9). For the moment, I shall focus instead on Abelard’s definition of possibility as ‘non-incompatibility with nature’ and compare it with similar characterizations that are used in sources from the first half of the 12th century. Evidence of this interpretation of possibility is quite widespread in Abelard’s texts on modalities. The definition often occurs in the Dialectica, where what is possible is also defined in terms of what ‘nature allows’ (natura patitur or permittit),35 and in the Logica Ingredientibus, where possibility is conceived in conformity with what is allowed or permitted by the nature of a thing (‘secundum hoc quod natura rei quoquo modo permittit’).36 Dispositions and dispositional terms, such as ‘fragile’, ‘durus’, ‘frangible’, and the like, which are taken by Abelard to refer to a certain subject’s passive possibilities or aptitudes, are also

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where Aristotle divides possibilities into those that will actualize at some point in time and those that will always remain pure potencies. See (Knuuttila 1993, p. 91). See, in particular, in Dial. 196–8 and 200–4. The same idea is rehearsed in Dial. 98, 16–8 (‘Nullam formam in nomine “potentis” intelligamus, sed id tantum quod naturae non repugnet; in qua quidem significatione nomine “possibilis” in modalibus propositionibus utimur’), Dial. 176, 27–31 (‘Haec igitur: “quidam homo non est homo”, idest “quaedam res quae est animal rationale mortale, non est animal rationale mortale vel animal simpliciter”, semper falsa est; est enim omnino impossibile quod ipsa dicit nec ullo tempore contingere potest nec eius exemplum natura patitur’) and Dial. 385, 3–5 (‘Potentiam enim et impotentiam secundum naturam accipimus, ut id tantum quisque possit suscipere quod eius natura permittit, idque non possit quod natura expellit’). See, for example, LI Cat. 124, 33–7 (‘Potentia quoque cum dicitur posse inesse alicui, talis est sensus quod eam subiectam habere queat, hoc est naturae eius non repugnat, ut habeat’); LI De Int. 266, 541–5; 408, 426–7; 414, 568–415, 594.

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characterized by the author in terms of nature and what is (more or less) likely to happen in conformity with the nature of the thing (‘secundum facilitatem naturae’).37 Abelard’s definition of possibility rests on the two basic concepts of repugnancy and nature, and we should say something more here about what logicians of his time intended by these two concepts. The first is often used in 12th-century logical sources, either in the sense of general oppositio or in the more specific sense of contradictoriness between linguistic items, such as terms or propositions. The term ‘repugnantia’ was already used by Boethius with the same meaning. ‘Repugnant’ terms are those that cannot be simultaneously predicated of the same subject, for instance, ‘black’ and ‘white’,38 or ‘man’ and ‘donkey’, whereas repugnant propositions are those that cannot be true or false simultaneously, such as ‘every man is just’ and ‘not every man is just’.39 Apart from these uses, Abelard and his contemporaries also use the notion of (non) repugnantia to intend a relation that might occur between a certain property (or the term expressing this property) and nature. They say, for instance, that having a certain property is repugnant or non-repugnant to the nature of an individual, to the nature of a species or kind, or to ‘Nature’ in general, as we will see in this section. It is more difficult to distinctly point out what early 12th-century authors intended when speaking about the natures of things. Indeed, nowhere is a clear theorization of natura provided, either by Abelard or his contemporaries, although authors of this time attempt various characterizations of this concept. Some early 12th-century texts connected to the teaching of Abelard, such as the Logica Nostrorum and the Glossae Secundum Vocales (P11 and P12 in Marenbon’s catalogue), affirm that nature is that in which many res come 37 See Dial. 28–32; Dial. 425, 37–6.18; LI De Int. 255, 312–22. Although general or simple possibilities are defined by Abelard only in terms of a subject’s nature, aptitudes and dispositions are defined in terms of the subject’s nature plus some other conditions, such as the subject’s physical constitution or the external circumstances. Consequently, whereas all subjects that have the same nature are taken by Abelard to have all the same possibilities, they might not have the same dispositions or the same aptitudes, for their physical constitution or the circumstances they are in differ. For a more detailed comparison between simple possibilities and aptitudes, see Chapter 9. 38 See, for example Dial. 174, 25–8: ‘Ea namque opposita contraria definiunt quae prima fronte sibi opponuntur, hoc est quae maxime sibi repugnant, velut album et nigrum, quae nullo modo eidem simul inesse possunt.’ 39 See, for example Dial. 173, 28–32: ‘Quae [propositiones] vero contradictoriae sunt atque inter se verum falsumque semper dividentes, contradictionis oppositione sibi repugnant, ut “omnis homo iustus est”, “non omnis homo iustus est” et rursus “nullus homo iustus est”, “quidam homo iustus est”; sic etiam singulares “Socrates est iustus”, “non est Socrates iustus”.’

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together (convenire in natura) and by virtue of which they are said to be ‘the same’ (idem) with respect to genus or species. Just as Abelard does in some passages of the Dialectica,40 these texts tend to speak of natures as referring not to individuals but to natural kinds, talking, for instance, of ‘natura animalis’ or ‘natura hominis’. The idea of explaining nature in terms of the similitudo existing between things is based both on Porphyry’s claim that ‘a species collects many into a single nature’41 and Boethius’s definition of nature as ‘the likeness of the things that come into being’ (similitudo rerum nascentium),42 which is reported in the Logica Nostrorum, in the Glossae Secundum Vocales, and in the Sententie Secundum Magistrum Petrum. In this last anonymous source the author quotes Boethius, saying that: nature is ‘the likeness of things that come into being,’ as though to say explicitly that the same things are of one nature that are similar to one another by natural activity. Accordingly, we call the name ‘man’ a nature, which is naturally common to many things in virtue of its single imposition, due to the fact that they are naturally similar to one another in that each of them is a rational mortal animal.43 In other passages the Sententie present an understanding of nature that is slightly different from the traditional views, for the author states that not only those individuals that are alike with respect to their species or genus, but also those that are similar with respect to some accidental forms are ‘of a same 40 See e.g. Dial. 198, 2; 255, 10; 281, 24–5; 302, 25. 41 See Isagoge 3 12, 15–7. 42 See (Boethius 1847, p. 166A). As King notices, Abelard also cites Boethius as claiming that nature is ‘similitudo rerum nascentium’ (see, for instance, LI Cat. 278, 16–20 and LI De Int. 33, 190), but what Boethius, in fact, says is that nature is ‘ipsa nimirum similitudo nascentium’, though King points out that ‘rerum’ for ‘nimirum’ would be an easy mistake to make (King 2004, p. 115, note 58). King also remarks that Abelard – and we may add, his contemporaires as well – silently ‘passed over Boethius’s four ‘official’ definitions of ‘nature’ given in Contra Eutychen 1’, probably because they are less suitable for use for their interpretation of nature. 43 See Sententie super mag. Petrum in (Minio-Paluello 1958, pp. 115, 28–116, 7), translated in (King 2004, p. 82): ‘Naturam quippe Boetius dicit “similitudinem rerum nascentium”, ac si aperte dicat easdem res esse unius naturae que operatione nature similes sunt ad invicem. Unde hoc nomen quod est “homo” nature dicimus, quod ex una ipsius impositione commune est naturaliter multis rebus secundum hoc quod invicem sibi naturaliter sunt similes (in eo scilicet quod unaquaeque earum sit animal rationale mortale); hoc vero nomen “Socrates” personae potius dicimus quam nature, quia per ipsum discretio personae monstratur, non convenientia multarum rerum quibus datum sit secundum similitudinem alicuius naturae.’

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nature’. He admits, for instance, that there is a nature of women (natura sexus muliebris)44 and a nature of aquatic beings (natura aquatici elementi).45 As was said, in early 12th-century texts we encounter mentions of not only the nature of individuals or the nature of natural kinds, such as the natura Socratis or natura animalis, but also ‘Nature’ in a more general sense, called ‘natura rerum’ or simply ‘natura’. What they seem to intend with this notion is the totality of the laws governing the natural world, which God had established with creation and which is exemplified by what the different individual natures of substances require or are (in)compatible with. In this sense, natura is said to be the object of scientia physica46 and concerns the ‘origin and genesis of all things.’47 This idea is also invoked in other sources, such as the De Propositionibus Modalibus, where it is said that with the term natura we intend the first creation of things (‘Natura autem dicitur prima rerum creatio’),48 or the Summa Dialectice Artis, where the author says that nature is ‘physica illa quam Deus in re posuit’. From what we gather from the use of this notion in Abelard’s own works (to which I will return in more detail in Chapter 8, Section 2), the nature of a substance is conceived as a bundle of properties – for Abelard, individual entities – that are essential to that substance, namely, that inhere in it not accidentally but substantially. The division between accidental and substantial forms is traditionally specified, following the Porphyrian terminology, in terms of (in)separability: substantial or essential to an individual are those properties that cannot be separated from it without its substance being destroyed.49 By contrast, an accidental form is, in Abelard’s words, ‘a form that can be both present and absent in the subject matter without destruction of the latter, i.e. in such a way that in the situation in which it would arrive or depart it would

44 (Minio-Paluello 1958, p. 118). 45 (Minio-Paluello 1958, p. 119). 46 Abelard’s Dial. 286, 31–5; cf. also the Logica Nostrorum in (Abaelard 1933a, p. 506, 19–20) 47 Cf. Logica Nostrorum in (Abaelard 1933a, pp. 513, 21–514, 6): ‘Et haec quidem sententia Platoni imputatur, quod scilicet genera et species, huiusmodi conceptiones, νοῦς (id est divinae menti) attribuit, ideo fortasse quod formas exemplares habuerit Deus in mente ad quarum similitudinem dictus est. Postea operari res ipsas, quae a generalibus et specialibus nominibus appellantur. Hae quippe res operibus naturae, non artificis consistunt. Quae conceptiones recte Deo attribuuntur, cuius hae effectus sunt, quem hoc in loco naturam vocamus, id est originem et nativitatem omnium.’ 48 Anonymous, De Propositionibus Modalibus, in (Abaelard 2010a, p. 66). 49 For the distinction between substantial and accidental forms in Abelard, see, in particular (Wciórka 2008, pp. 161–81). I will return to this distinction and Wciórka’s interpretation in Chapter 8.

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not be necessary that the subject matter should be destroyed because of it in the nature of its substance, that is, exit a general or specific status’.50 The nature of Socrates, thus, would be constituted by Socrates’ substantial forms, such as his (particular) rationality, mortality, animality, and by many other forms that are inseparable from him and of which we may not be aware.51 Given this understanding of natures, a property P is said to be ‘non-repugnant’ with the nature of an individual S if there is no relation of contradictoriness between being P and any of the properties that constitute the nature of S. When this is the case, Abelard says that the nature of S ‘allows’ or ‘tolerates’ (patitur; permittit; non expellit) p. As could easily be seen, the notion of repugnantia employed in this definition is itself defined in modal terms. This is because the notion of repugnancy is spelled out in terms of contrariness and contradictoriness, which are, in turn, defined in terms of (im)possibility: two sentences are contraries if they cannot simultaneously be true, and they are contradictories if they cannot simultaneously be true or false. This is why King claims that Abelard merely proposes an ‘analysis’ of modal concepts and not a ‘reductive elimination’ of them.52 It may also seem that the notion of nature itself is intrinsically tied to a modal characterization, because the distinction between essential and accidental forms – on which the notion of nature is based – rests, in turn, on the ideas of separability and inseparability: part of the nature of a substance are those properties that cannot be separated from it. In Chapter 8, however, where I consider Abelard’s idea of nature in more depth and try to provide an interpretation of the essentialist framework on which it is based, I claim that the notion of nature is for Abelard more fundamental than the modal notions of necessity and possibility. Indeed, nature is treated by him as a primitive notion, which is used as the (metaphysical and conceptual) ground for modalities, as the source of all modal truths. Apart from Abelard’s texts, the definition of possibility in terms of ‘nonrepugnancy with nature’ may also be found in many other sources of the time, 50 See LI Isag. 92, 9–14; the translation is from (Wciórka 2008, p. 171). 51 Abelard insists that, generally speaking, we are usually ignorant about natures and about what constitutes them. Most of the time we are, in fact, not able to specify which are the substantial forms of the different individual substances we have experience of. In Dial. 286, 31–287, 1 Abelard states that it is not the aim of the logician to investigate the nature of things, but that studying natures and their causes is the purpose of physica, that is, natural philosophy. Other remarks about our ignorance of natures are also to be found in LI De Int. 252, 211–2 and 254, 275–7. I will return to how we should interpret Abelard’s claims on this ignorance about nature in Chapter 9. On this, see also (King 2004, pp. 81 ff.) and (Marenbon 1997, p. 117). 52 Cf. (King 2004, p. 116).

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such as commentary H9, Garland’s Dialectica, treatise M3, and the De Propositionibus Modalibus, as well as several other commentaries on the Categories and Boethius’ De Topicis Differentiis.53 In Garland this characterization comes up in connection with the discussion of possibilities extra-actum. Having distinguished between potencies that are currently actualized and those that are unactualized, Garland says that the second category also includes possibilities that are always extra-actum and remain thus ‘pure potencies’ or ‘solae potentiae.’ This divisio accurately follows Aristotle’s distinction at the end of De Interpretatione 13 as well as the division made by Boethius of the many species of the possible.54 What Garland adds to this traditional division is the example he gives of possibilities that are always extra-actum: he says that a proposition such as ‘it is possible for Garland to be a bishop’ is true even though Garland will never be a bishop in act, inasmuch as there is no incompatibility between the nature of the subject and the property of being a bishop.55 Affinities with Abelard’s view expounded in the passage from the Dialectica quoted at the beginning of this section (Dial. 193, 31–194, 5) are evident, as both authors make use of the same example (someone who is not a bishop in act but for whom it is still possible to be a bishop) and invoke a definition of possibility in terms of non-repugnancy with nature in order to justify the existence of eternally unrealized possibilities.56 This particular characterization of possibility might have been developed in the early 12th century precisely to account for extra-actum possibilities, that is, to provide a definition that allowed us to separate what is possible from what is actual at a certain moment in time. The connection between this definition of possibility and the analysis of extra-actum potencies is also evident in other texts, such as the commentary H9, in which the ‘non-repugnancy with nature’ terminology emerges in a similar context. While commenting on Aristotle’s division between the many species of the possible, the author of H9 also distinguishes between possibilities in actu and possibilities extra-actum, and within the first category he further distinguishes possibilia that are now in act and have always been so, and those that have been actualized after being existent in potency at an earlier time. 53 54 55 56

For the use of this terminology in Garland’s Dialectica and in M3, see also (Martin 2016). See Chapter 3, Section 3 on this. See (Garlandus Compotista 1959, pp. 83, 35–84, 1): ‘Potentia vero extra actum quam effectus non consequitur, est illa cui nec natura repugnat nec tamen umquam erit, ut cum dico: “possibile est Iarlandum fieri episcopum”, numquam tamen episcopus erit.’ The similarity between the positions of the two authors has already been highlighted in (Thom 2003a), (Thom 2003b, p. 49) and in (Martin 2016). Notice that, differently from Abelard in the Dialectica, Garland does not speak here of the nature of a thing but of nature in general.

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Rehearsing an example already used by Boethius, he claims that a house now existing in act was already existing potestate, as an extra-actum potency, before it was fabricated.57 But in what sense did the house already exist in potency before its actualization? Does this mean that things have a certain ontological status as extra-actum possibilities before becoming actual? The author seems to answer in the negative, claiming that these things are said to exist in potency before their actualization only in the sense that there is no incompatibility between their being and the nature of things (‘prius potuerunt existere quam fuerunt et ita quod natura non repugnat’). At the end of the passage, the author of H9 also takes into account extra-actum possibilities that are never realized in time, and he provides an example similar to the one used by Abelard and Garland concerning the possibility of a peasant to be a bishop or a king.58 Although very brief, H9’s mention of this ‘non-repugnancy’ paradigm is intriguing, for it suggests that this particular definition of possibility was invoked to avoid concerns about the ontological status of the unactualized possibilities attributed to non-existent things. Interestingly, the same example considered in H9 (the house existing in potency before its actualization), which was taken from Boethius’ commentary on De Interpretatione,59 was already presented as problematic by Anselm of Canterbury in his Philosophical Fragments, where Anselm asks in which sense some potencies (potestates) are attributed to things that do not exist, for instance, when we say that a house has the potency of being while it still does not exist.60 As Anselm suggests, the 57 For the same example, see (Boethius 1877, p. 206, 23–7). 58 See H9: Orléans, Bibl. mun. 266, p. 39b: ‘Possibilia alia sunt in actu, alia numquam in actu. Subdividit ea etiam que sunt in actu, sic: quod alia sunt in actu sine precedente potestate, ut divine substantie, alia vero sunt in actu cum precedente potestate, idest prius habuerunt potestatem quam actum, ut fabricata domus. […] “Que”, scilicet ea que sunt in actu, “priora sunt” et digniora scilicet potestatibus natura, idest per naturam ipsius actus. Actus namque natura et dignitate precedunt solas potestates, sed vera sunt posteriora in tempore(?) ipsis potestatibus. Potestas namque, ut dictum est, eos actus secundum tempus precedit. Vel sic. “Quae priora sunt natura”, idest naturaliter, prius potuerunt existere quam fuerunt et ita quod natura non repugnaret; tempore vero, idest secundum tempus existendi actu, sunt posteriora se ipsis quantum ad hoc quod natura prius potuerunt existere. Alia vero numquam sunt, sed potestate sola, ut quod rusticus fiat episcopus vel rex’ (my emphasis). 59 (Boethius 1877, p. 206, 23–7). 60 See (Anselm of Canterbury 1969, p. 341, 7–12): ‘Dicimus namque potestatem esse aliquando, in quo nulla est potestas. Nullus enim negat omne, quod potest, potestate posse. Cum ergo asserimus, quod non est, posse esse, dicimus potestatem esse in eo, quod non est; quod intelligere nequeo, velut cum dicimus domum posse esse, quae nondum est. In eo namque, quod non est, nulla potestas est.’ See p. 29 on this and other Anselmian examples.

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admission of these possibilities is controversial, because no potency can be said to be embedded in a non-existing substance. As we have already seen in Chapter 3, Section 1, concerns about the ontological status of modalities were widespread among logicians of Abelard’s time, who were interested in talking about possibilities without committing to a special ontology of modal forms or to the existence of the things of which possibilities were predicated. The understanding of possibility in terms of nonrepugnancy with nature could have provided them with an easy way to speak about the possibilities of non-existing things while avoiding the ontological commitment that was instead enclosed by the Aristotelian and Boethian reading of possibilities in terms of potencies. Another source that suggests a connection between the definition of possibility as non-incompatibility with nature and concerns about the ontological status of possibilities is M3. As was said in Chapter 3, Section 1, the author of M3 rejects the idea that modal terms signify or denote properties existing in substances, because he thinks that propositions such as ‘it is possible for Socrates to be an animal’ are true even though Socrates does not actually exist and cannot therefore bear any property. Having presented the many difficulties that would follow from an interpretation of possibilities as forms existing in things, the author mentions a strategy designed by a certain ‘Master W.’ to expound the signification of modes without reifying them. According to W.’s interpretation, he says, the claim ‘It is possible for Socrates to be an animal’ should be expounded ‘in a negative sense’ (in negativo sensu), as meaning: ‘It is not repugnant to the nature of the thing that Socrates is an animal’ (Socratem esse animal est possibile, id est non repugnat natura rei Socratem esse animal).61 Using this negative definition of possibility, ‘M.W.’ was able to speak about the possibilities of Socrates without positing the existence of special modal forms inhering in him. This is because, by affirming that it is possible for Socrates to have certain properties, he only means that no relation of incompatibility exists between the nature of things and the fact that Socrates is an animal.62 61 See M3, Orléans, Bibl. mun. 266, p. 255a: ‘Investigato sensu modalium, videamus utrum aliqua proprietas per modalia nomina ponatur. Si enim per ea aliquid ponitur, multa sequentur inconvenientia. […] Item si non est, non possibile est esse, quia si est possibile esse, et est. Si Socratem esse est possibile, Socrates habet possibilitatem existendi; et ita possibilitas est in Socrate; et ita est. Quare si possibile est esse, et est. Quare si non est, non est possibile esse. Haec et plura alia inconvenientia, si per modales voces aliquid ponatur, sequi manifestum est. Unde m. W. exponebat eas in negativo sensu, ut istam: “Socratem esse animal est possibile”, id est non repugnat natura rei Socratem esse animal.’ 62 This brief passage from M3 suggests, thus, that the negative formulation in terms of ‘non-repugnancy’ was probably relevant to this characterization of possibility, and

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Apart from the Dialectica of Garland, the commentary H9, and the treatise M3, the terminology of ‘non-repugnancy with nature’ also returns in other sources of Abelard’s time. One interesting mention of it may be found in a commentary on Boethius’ De Topicis differentiis catalogued as B8,63 in a passage in which the author discusses Boethius’ claim that ‘it is impossible for Daedalus to fly’ because Daedalus lacks the proper forma naturalis that would allow him to have wings.64 In B8 various interpretations of this passage are listed, attributed to many different ‘quidam’.65 The interpretation preferred by the author is the one that understands Boethius’ forma naturalis not as a property that Daedalus has but as the structure (compositio) of Daedalus, that is, the special arrangement of bodily parts that he has by virtue of his nature. This natural structure, the author says, is repugnant to having wings and therefore also to flying, and this is the reason why it is impossible for Daedalus to perform this action. We say, then, that it is not possible for Daedalus to fly because this would be repugnant to his natural form (‘Vere Daedalus non potuit volare, quia naturalis forma illius repugnavit’). The same terminology occurs, though very briefly, in commentary B9, in which the forma naturalis in question is interpreted as a property that Daedalus has, his ‘Dedalitatem’, and not as his natural structure.66 Even though neither the author of B8 or B9 are particularly interested in further investigating the nature of impossibility, it is interesting that in both commentaries the explanation that is offered of it is formulated in terms of what is repugnant with the nature of a thing. Another mention of the connection between possibility and the ‘nonrepugnancy with nature’ terminology could be found in the commentary on the Categories catalogued as C27,67 where the author presents the notion of ‘natural potencies and impotencies’ (potentiae et impotentiae naturales) and describes natural potencies as the ones that individuals have by virtue of their nature and not by virtue of having acquired them through practice or experience. A natural potency is, for instance, the one that some human beings t­herefore we should be careful in preserving it by translating non repugnantia as ‘nonincompatibility’ rather than ‘compatibility’ with nature. 63 B8: Vatican City, Bibl. Vat., reg. lat. 230, fols 72ra–79vb; Orléans, Bibl. mun. 266, pp. 43a– 74b; Paris, Arsenal 910 fols 105ra–120vb. References are to the Orléans manuscript. 64 See (Boethius, 1990, 1189 D-1190 A): ‘Ab eo quoque quod cuiuslibet forma est, ita non potuisse volare Dedalum, quoniam nullas naturali forma pennas habuisset. Maxima propositio: tantum quaeque posse quantum forma naturalis sua permisit. Locus a forma.’ 65 See B8: Orléans, Bibl. mun. 266, p. 63a. 66 B9 is found in Ms Orléans, Bibl. mun. 266, pp. 205a–229b. References are to p. 225b. 67 C27: Milano, Archivio Capitolare della Basilica Ambrosiana, fols 1ra–15rb. An edition may be found in (Sirtoli 2016).

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have to run, which they do not possess ‘per applicationem’, because they have exercized it, but because nature has provided them with the proper physical structure allowing them to run ‘with ease’ (facile).68 In this context, the author claims that, although it is not true that ‘every human being has the natural potency to run’ (because not everyone has the proper physical form allowing him or her to run ‘with ease’), it is still true that ‘it is possible for every human being to run’, because, he explains, ‘the nature of no human is incompatible with running’ (‘nullius enim hominis natura cursui repugnat’). The author suggests a distinction between what is possible for a certain individual, which he defines as everything that is not repugnant with its nature and is common to all individuals of the same species, and the natural potencies that this individual has, which depend on its nature but also on other conditions, for instance, its physical constitution (‘Et attende quod, cum omnis homo possit currere, nullius enim hominis natura cursui repugnat, non tamen omnis homo naturalem habet potentiam’).69 This distinction between possibility and potency (which we will also find in Abelard, and on which C27 probably relies as its main source) is intriguing, for it highlights an important consequence of the early 12th-century definition of possibility: because logicians of this time used non-incompatibility with nature as the only criterion for delimiting what is possible for a substance, it follows that a substance’s possibilities will not depend on any factor that is external to its own nature. In particular, the possibilities of things are entirely independent upon their physical conformation or on external circumstances. We will have, thus, that, as the author of C27 states, for every human it is possible to run even though some cannot actually do it, because their physical shape or the external conditions prevent them from running. A similar idea returns 68

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The use of this terminology of ‘potentia naturalis’, based on Boethius’s translation and commentary on the Categories, is quite common in early 12th-century sources, mainly in the ‘C commentaries’, that is, the commentaries on the Categories. Abelard also makes use of this notion, introducing interesting innovations to the traditional view, as we will see in Chapter 9. According to Boethius’s reading of Aristotle, a natural potency is the ability to do or to undergo a certain action ‘easily’ (facile), which we attribute to things on the basis of their nature and physical constitution, regardless of whether the ability has ever actually been manifest in its bearer. For instance, if we see men of a strong constitution, we may call them ‘pugilists’ (pugillatores) even though they have never practised fighting and had no experience of it, that is, not because they have ever fought but because they would be able to do it (‘non in eo quod iam sint pugiles sed eo quod esse possint’). The same is the case for other terms denoting natural abilities, such as ‘runners’ (cursores), ‘healthy,’ ‘sick,’ ‘hard’, or ‘soft’, which are attributed secundum potentiam vel impotentiam naturalem and not on the basis of an actual event. See (Boethius 1847, 244A–245D). A similar idea will also return in Abelard’s theory of potentiae, as we will see in Chapter 9.

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in Abelard’s Dialectica, where the author insists that it is possible for a blind man to see or for an amputee to walk, on the basis that there is no incompatibility between walking or seeing and the nature of human beings.70 As a result both Abelard and the author of C27, then, are obliged to elaborate on another notion of possibility alternative to generic non-incompatibility with nature – which is that of ‘potentiae naturales’ in C27 and of ‘potentiae determinatae’ in Abelard – in order to capture those possibilities that are effectively ‘open’ to individuals, that is, what individuals are genuinely able to do or become. Another consequence of the definition of possibility as non-incompatibility with nature is that, provided that the nature of a substance remains the same through its entire lifetime, what is possible for an individual does not change in time. Possibilities, thus, cannot be lost or acquired. The notion of possibility emerging from this definition is therefore quite abstract, unrelated to how individuals are able to act and to what can actually happen to them. This was pointed out by Thom,71 who suggested a comparison between Abelard’s notion of possibility as non-incompatibility with nature and the definition of the possible invoked by the Stoic philosopher Philo. From what we know from Boethius and other sources, Philo claimed that external circumstances have no role in delimiting what is possible for an individual, and that it would be possible, for example, for straw to burn even when it rests at the bottom of the ocean.72 According to Philo’s definition, ‘a proposition is possible which is capable of truth according to the proposition’s own nature’, and impossible is ‘that which, according to its own nature, can never be capable of truth.’73 Little is known about what Philo really had in mind when giving these definitions of modalities, and it is unlikely that he could have inspired early 12th-century logicians on this topic, since they knew of his modal theory only the rather obscure report in Boethius’ commentary on De Interpretatione. Yet some elements of Philo’s definition indeed resemble the conception of possibility that Abelard and other authors of his time wanted to capture with the 70 71 72 73

On this, see also (Knuuttila 1993, p. 90) and (Martin 2001). See for example (Thom 2003b, p. 51). See (Alexander of Aphrodisias 1883, p. 184, 6–10). In the same passage Alexander reports that the Philonian criterion for possibility is the ‘suitability of the subject’. This is what Boethius reports about Philo’s definition of modalities: ‘Philo says that is possible which is capable of truth according to the proposition’s own nature […] In the same way Philo defines that which is necessary as that which, being true, as far as itself is concerned, can never be capable of falsehood. That which is non-necessary he determines as that which, as far as itself is concerned, is capable of falsity; and that which is impossible as that which, according to its own nature, can never be capable of truth’ (Boethius 1880, p. 234, 10–21; translated in Bobzien 1998, p. 108).

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‘non-incompatibility with nature’ paradigm. Both definitions are ‘essentialist’ and ‘conceptual’ in spirit, and as such very distant from Aristotle’s view of possibility, which was based on what is potential (and therefore, actualizable) for individuals.74 4

Necessity as Inevitability and Immutability

One of the definitions of ‘necessity’ that more frequently returns in early 12th-century sources is the one that equates necessity with ‘unavoidability’ (inevitabilitas). This is how Abelard characterizes necessity in the Logica Ingredientibus75 and the Dialectica, where he states that this is the usual and proper signification of ‘necessarium’.76 As Tarlazzi has shown, defining the necessary as inevitabile is very common in contemporary commentaries on Porphyry’s Isagoge, where a division of the term ‘necessary’ is usually provided that distinguishes its three meanings: necessarium as ‘useful’ (pro utile), as ‘companion’ or ‘friend’ (pro amicus seu familiari), and as ‘unavoidable’ (pro inevitabile).77 The latter is usually said to be the proper meaning of the term, as it denotes what is necessary per se and not in relation to something else.78 Tarlazzi tracked down this tripartition down in the early 12th-century commentaries P14, P15, P16, and P17, and in the slightly later commentaries P19 and P25 (c.1130s–1140s). A similar terminology is also proposed in P20 (probably from the late 1130s), limited to the two senses pro inevitabile and pro utile.79 Although having a slightly different t­ripartition of 74 See (Bobzien 1998, p. 109). 75 See LI De Int. 407, 412–408, 425. 76 See Dial. 194, 7–8: ‘“Necessarium” autem id dicit quod ita sit et aliter esse non possit. Hoc loco “necessarium” idem accipiatur quod “inevitabile”; quae quidem consueta et propria significatio est “necessarii”.’ See also Dial. 272, 11–2. 77 (Tarlazzi forthcoming). 78 See, for instance, P14 (Paris, BnF, lat. 17813, fol. 1vb: ‘Necessarium autem tribus dicitur modis: scilicet pro amico seu familiari, unde Tullius “suis quisque necessariis adesse cogetur”; alio modo accipitur pro utili, tertio pro inevitabili. Pro amico accipi hic non potest, sed pro inevitabili vel pro utili, quia scientia harum rerum ad praedicamenta et ad alia inevitabilis est et utilis, sine qua illa non possunt sciri. Quia tamen proprie inevitabile in se aliquid dicitur, utile vero respectu alterius, convenientius accipitur hic necessarium pro utili quam pro inevitabili, cum hic quod dicitur necessarium non in se ipso consideratur sed ad aliud refertur.’ Commentary P16 does not use the exact same tripartition, and it has ‘pro simplici necessario’ instead of ‘pro inevitabile’, but it later suggests that this simple necessity should be read as inevitabilitas (Munich, Bay., Clm. 14458, fol. 84rb). 79 P20: Wien, VPL 2486, fols 45ra–60vb. The discussion of necessary is on fol. 45 vb.

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the significations of necessarium, the characterization of necessity as unavoidability is also advanced in the Glossae Secundum Vocales (P11)80 and the Logica Nostrorum,81 also belonging to the commentary tradition on the Isagoge, and to other sources of the time, such as the treatise on modalities labelled M1.82 According to Tarlazzi, some of the meanings of necessarium used in these texts were common even in earlier glossed manuscripts of Isagoge, which had Boethius’ second commentary on Porphyry as their common source. For instance, she notices that ‘necessarium’ is already glossed with ‘utilitas’ in the 10th and 11th centuries.83 However, as far as I know, the association of necessity with ‘unavoidability’ (inevitabilitas) has no correspondents in earlier glosses on the logica vetus and starts to be used as a standard definition of necessity only in the first years of the 12th century.84 Given that the glossing of necessity as unavoidability is so widely used in logical commentaries of Abelard’s time – not only in the commentaries on Porphyry but also in those on De Interpretatione and Boethius’ De Hypotheticis Syllogismis, as we will see – one might wonder where this definition comes from and what these authors had in mind when speaking of inevitabilitas. The association of necessity with unavoidability does not seem to come from Boethius’ own commentaries on the Isagoge, although, as was said, these were the main source on the signification of ‘necessarium’ for the aforementioned P-commentaries. In a passage from his second commentary Boethius proposes a divisio of the meanings of the Greek term ‘ἀναγκαῖον’ (necessarium), saying that it may be taken both in the sense of ‘utilitas’ and in the sense of ‘necessitas’. Boethius does not specify any further what he means by this second sense, but he offers one example for it, saying that in this sense we say 80 See Glossae Secundum Vocales: Milano, Biblioteca Ambrosiana, M63 sup., fol. 73vb: ‘Sunt autem necessarii tres consuetae significationes, cum scilicet modo pro inevitabili ponitur ut “Necesse est substantiam non esse qualitatem”, modo pro utili ut “Necesse est me ire ad forum”, modo pro determinato ut “Necesse est hominem quandoque mori”.’ 81 See (Abaelard 1933a, p. 510, 25–9): ‘Sunt autem huius vocabuli necessarium tres consuetae significationes: pro inevitabili scilicet ponitur, ut “necesse est Deum esse immortalem”; modo pro utili, ut “necesse est me ire ad forum”; modo pro determinato, ut “necesse est hominem mori quandoque”.’ 82 See Orléans, Bibl. mun., 266, p. 169a. 83 See Vercelli, Biblioteca Capitolare S. Eusebio, CXXXVIII (143), fol. 1va; Venice, Biblioteca Nazionale Marciana, Lat. Z. 497 (=1811), fol. 107ra. Cf. (Tarlazzi forthcoming) on this. 84 Tarlazzi reports that the understanding of necessity as inevitability occurs in Munich, Bay., Clm. 4621, fol. 80v, where it is said that ‘necessarium duobus modis accipitur, pro inevitabili et pro utili....’ The text has been dated to the 11th century by Iwakuma, but the dating is not certain, and it might in fact be postponed to the early 12th century. See (Tarlazzi forthcoming).

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that ‘it is necessary for the sun to move’.85 The term ‘inevitability’ as a synonym of necessity, however, is not used in this passage. Nor does the association of necessity with inevitability ever occur in his other logical works, and although the terms ‘inevitabilis’ and ‘inevitabiliter’ are used twice in the Consolatio, it is never explicitly associated with necessity as one of its definitions.86 Where should the origins of this understanding of necessity be traced back to, then? Perhaps, an Augustinian influence may be behind the 12th-century use of this term. In his De Libero Arbitrio Augustine uses the term ‘unavoidable’ three times in modal contexts, associating it once with the divine providence and twice with the notion of necessity, which he characterizes as ‘inevitabilis and fixa necessitas’. These last two occurrences are from a discussion with which early 12th-century logicians were well acquainted, namely, the discussion of how God’s infallible knowledge that someone will sin is compatible with the fact that he or she will sin out of choice and not out of ‘unavoidable necessity’.87 An echo of this Augustinian discussion might then be in the 85

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(Boethius 1906, pp. 149, 10–151, 9): ‘NECESSARIUM in Latino sermone, sicut in Graeco “anagkoion”, plura significat. Diversa enim significatione Marcus Tullius dicit necessarium suum esse aliquem atque nos cum nobis necessarium esse dicimus ad forum descendere, qua in voce quaedam utilitas significatur. Alia quoque significatio est qua dicimus solem necessarium esse moveri, id est necesse esse. […] namque, ut dictum est, necessarium et utilitatem significat et necessitatem.’ Only once is the term ‘inevitabile’ used in connection with necessity – not as an explication of the modal term but as a sort of intensification of it, in the expression ‘inevitable necessity’ – in Boethius’ first commentary on De Interpretatione: ‘Syllogismus autem huiusmodi est: si omnis affirmatio vera est aut falsa definite et eodem modo negatio, eveniet ut omnia inevitabili necessitatis ratione contingent.’ In the Consolatio the term ‘inevitabilis’ or ‘inevitabiliter’ is used twice in contexts that are indeed connected to some notion of necessity, but no explicit association between necessity and inevitability is made. For the first occurrence, see § 3.2.4.14–5 in (Augustine 2010, p. 75), translated by Peter King: ‘Since these things are so, it perplexes me beyond words how it could happen that [1] God has foreknowledge of everything that will happen, and yet [2] we do not sin by any necessity. Anyone who said that something can turn out otherwise than God previously foreknew would be trying to destroy God’s foreknowledge with his senseless irreligiousness. Consequently, God foreknew that a good man was going to sin. Anyone who allows that God has foreknowledge of everything that will happen must grant me this. Thus if this is the case, I do not say that God would not make him – for He made him good; nor could any sin of his harm God, Who made him good; instead, He showed His own goodness in making him, even showing His justice in punishing him and His mercy in redeeming him – I do not say, therefore, that God would not make him, but I do say this: Since God had foreknown that he was going to sin, it was necessary that what He foreknew would be the case would happen. So how is the will free where such unavoidable necessity is apparent (ubi tam inevitabilis apparet necessitas)?’ For the second occurrence, see §3.3.6.21 in (Augustine 2010): ‘Surely what perplexes and upsets you is how these two claims are not opposed and inconsistent: [1] God foreknows everything that will be; [2]

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b­ ackground of the early 12th-century use of inevitabile as one meaning for necessarium while glossing the Isagoge. The commentaries on Isagoge considered above do not usually elaborate on the notion of necessity as inevitability. On the contrary, this notion is more closely looked at and examined in other early 12th-century texts that deal with the nature of modalities and, in particular, in the commentaries on De Interpretatione 9 and 12–13 (H-commentaries) and those on Boethius’ De Hypotheticis Syllogismis (SH-commentaries). Looking at these sources, we may identify two senses in which the ‘inevitability’ associated with necessity is intended: in the first sense, inevitable is what is ‘immutable’ (impermutabile), and cannot be otherwise than it is, and is therefore also omni-temporally as it is (sempiternus); in the second, inevitable is what is ‘absolutely’ and ‘unconditionally’ necessary, as opposed to what is necessary in a determinate way, that is, only under certain circumstances. These two senses are at times intertwined, since absolute necessity is, in some cases, equated with immutability and sempiternity. In commentary H9, which is probably one of the older sources, the different meanings of necessarium are considered while glossing De Interpretatione 9. Here, the author distinguishes between five uses of the term: (i) ‘unavoidable’, as when we say ‘it is necessary for God to be immortal’;88 (ii) ‘determinate’, as in ‘it is necessary for humans to die’; (iii) ‘modal’, for example, ‘it is necessary for a man to live while he lives’; (iv) ‘useful’, as in ‘it is necessary to go to the forum; and (v) ‘appropriate’, as when we say ‘it is necessary to go to the church’.89 We may set aside the last two senses of the word, since they are not relevant here, and focus on the first three. Inevitable necessity is at times also called ‘necessitas simplex’ or ‘absoluta’ in H9, and is usually expounded in terms of sempiternity. As the author says, things that are sempiternal are said to have ‘simple necessity in their being, because they are in a certain way and it is impossible for them to be otherwise’ (‘dicuntur habere simplicem necessitatem in suo esse, We sin not by necessity but by the will. For if God foreknows that someone is going to sin, you say, it is necessary that he sin; but if it is necessary, then there is no choice of the will in his sinning, but an unavoidable and fixed necessity (inevitabilis et fixa necessitas) instead’ (my emphasis). 88 Necessity is also equated with inevitability in H9’s commentary to Chapter 12 of De Interpretatione, where the author considers the signification of modal terms when used in modal logic and says: ‘Necessarium autem hic accipitur inevitabile’ (Orléans, Bibl. mun. 266, p. 33b). 89 See H9: Orléans, Bibl. mun. 266, p. 18b: ‘Necesse enim aliud inevitabile ut Deum esse immortalem, aliud determinatum ut hominem mori, aliud modale ut hominem vivere dum vivit, aliud utile ut ire ad forum aliud conveniens ut ire ad ecclesiam. Potest enim dici necessarium equivocum ad omnia illa.’

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quia ita sunt ut dicuntur et aliter esse non possunt’).90 A proposition such as ‘Socrates is a substance’, for instance, is said to be of this sort, because what it says cannot be false and is therefore true necessarily.91 In his commentary on De Interpretatione 13 the author again repeats that what is impossibly otherwise than it actually is is ‘sempiternal’ and ‘immutable’ with respect to its being or to some of its properties. Fire, for instance, is sempiternal and cannot change with respect to the property it has of being hot; similarly, the sky is sempiternally moving and cannot vary from being in motion (immutari non potest).92 Later in the same discussion, the author again stresses the connection between necessity and sempiternity or immutability, saying that things that are necessary are always in act, and things that are always in act are sempiternal (‘Ea namque que necessaria sunt, semper actu sunt; sed que actu semper sunt, sempiterna sunt’). On several occasions the author of H9 contraposes inevitable necessity with ‘determinate’ or ‘modal’ necessity, supposedly in the sense that – while what is inevitable is necessary and immutable at all times – what is determinate is immutably true only as long as a certain condition is satisfied, that is, only in a certain period of time or given certain assumptions. This clarifies why he thinks that propositions such as ‘God is immortal’ are inevitably necessary, while propositions such as ‘humans are mortal’ are only determinately so: this is because the second proposition is immutably true only as long as humans exist.93 He also suggests that the distinction between absolute and ­determinate (or ‘modal’) necessity is at the core of Aristotle’s solution to the

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H9: Orléans, Bibl. mun. 266, p. 22b. See the incipit of H9’s commentary on De Int. 9: ‘Res ergo quedam sunt que a sempiterno et a proprio esse numquam discedunt, et dicuntur habere simplicem necessitatem in suo esse, quia ita sunt ut dicuntur et aliter esse non possunt, ut “Socrates necessario est ­substantia”. Ista propositio, que huiusmodi rem enuntiat, ut “Socrates est substantia”, dicitur habere necessariam veritatem, non quod semper propositio fiat, sed cum fit, potest esse non vera’ (Orléans, Bibl. mun. 266, p. 17b). See Orléans, Bibl. mun. 266, p. 38a: ‘Ille quidem que sunt in sempiterno actu valet alterum tantum et hoc est scilicet “Quemadmodum dictum est, ut ignem non est possibile calefacere et non calefacere”, sed alterum tantum, idest calefacere. Et ne videretur hoc tantum esse in igne, ideo subdit “ut quecumque”, vel talia possibilia, “semper agunt”, idest in sempiterno actu sunt, non possunt esse et non esse circa eundem actum. Ea enim que in sempiterno actu sunt, ab eo quod sunt, immutari non possunt, ut celum, quoniam semper movetur, a motu immutari non potest’ (my emphasis). The distinction between absolute and temporally determined modalities, very common in early 12th-century sources, was inherited from Boethius, who advances it both in his commentary on De Interpretatione 9 and in De Hypotheticis Syllogismis. For Boethius’ view on this matter, see Chapter 1, Section 4.

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problem of logical determinism in De Interpretatione 9:94 what Aristotle meant when affirming that ‘whatever is necessarily is when it is’ should be interpreted in the sense of determinate or modal necessity, not of unavoidability, as saying that present events are not inevitable per se, although the fact that they are happening now makes it impossible for them not to happen now. The necessity of present (and past) events, thus, is not absolute but conditioned upon their having happened in a certain moment of time. Like the author of H9, many other logicians of the time claimed that every proposition about the past and present is determinately necessary because it is now fixed and unpreventable, though not necessary in the proper sense (unavoidable). I will return to this in Chapter 10, Section 2. The connection between the notion of necessity and that of immutability and omni-temporality has its roots in ancient theories: it was maintained by Aristotle and stressed in several passages of Boethius’ commentaries on De Interpretatione, as was seen in Chapter 1.95 Through Boethius, this connection was then inherited by early medieval logicians and influenced Latin medieval modal thought long before the 12th century. In his survey of early medieval glosses on Aristotle,96 Marenbon draws attention to the only known commentary on De Interpretatione from before 1100 (probably from the 10th century),97 preserved in manuscript Leiden, Bibliotheek der Rijksuniversiteit, Voss. lat. F. 70 (I) (s. x), fols 5”-9’, which contains a discussion on modalities. While glossing the ninth chapter of De Interpretatione, the author offers a temporal definition 94 See H9: Orléans, Bibl. mun. 266, pp. 22b–23a: ‘Et in contradictione [c. 9, 19 a 278]. Quod invenit in rebus, adaptat propositionibus, quia sicut quedam res habent necessitatem determinati eventus, non tamen simplicem necessitatem, ita et propositiones de huiusmodi rebus habent determinatam veritatem, non tamen inevitabilem. Et hoc est: “Et in contradictione est eadem ratio”. Removet a quibusdam rebus inevitabilem necessitatem secundum esse per se vel non esse per se. Modo vero attribuit omnibus rebus communiter eandem necessitatem secundum esse vel non esse sub disiunctione; quod sic dicit “Omne quod est, necesse est inevitabiliter vel esse vel non esse”. Et eodem modo: “Futurum necesse est vel esse vel non esse futurum, non tamen dividentem ”, quasi dicat: Quamvis omne futurum necesse sit vel esse vel non esse futurum, tamen dividentem, idest hominem accipientem alteram partem illius disiunctionis, non est dicere necessario, idest inevitabiliter alterum futurum, et de tali futuro dat exemplum ibi: “Dico autem” etc.’ Notice that the use of ‘inevitabile’ in the discussion on De Interpretatione 9 was not present in Boethius’ commentaries on the same work, while the notion of ‘determinate’ or ‘definite’ necessity was. 95 On Boethius’ view, see Chapter 1.1. On the link between necessity and omnitemporal actuality in ancient sources, see, in particular (Knuuttila 1993, pp. 1–18 and pp. 45–62). For Boethius, see, in particular (Boethius 1880, pp. 236, 5–237, 9). 96 See (Marenbon 2000a). 97 See (Marenbon 2000b, p. 83).

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of modal terms, saying that whatever necessarily is always is, and whatever is impossibly the case never is (‘Quidquid est quod impossibile est non esse, semper est. Quicquid impossibile est esse, semper non est’). Likewise, that which can possibly not be is not always the case, and that which can possibly be is not always not the case (‘Quicquid est quod possibile est non esse, non semper est. Quicquid est quod possibile est esse, non semper non est’). The text continues by saying that the first two modalities – necessity and impossibility – are defined on the basis of eternity (aeternaliter) , while the other two – possible actuality and possible not actuality – are defined on the basis of occurrence in time (temporaliter). As Marenbon notices, the glossator also says that the first two modalities happen by ‘simple necessity’, while the other two happen by contingency (‘Sunt itaque duo contingentia, quoniam eveniunt utrumlibet. Duo vero superiora ex simplici necessitate et numquam possunt contingere’).98 The non-sempiternity of contingent beings is justified by saying that things belonging to this category are mutable, for they may vary both with respect to their existence, through generation and corruption, and with respect to their properties (‘non semper est et non semper non est quicquid alicuius accidentis mutabilitate ita variatur ut de esse in non esse et de non esse in esse mutetur’). Another 10th-century logical source in which the concept of necessity is related to those of immutability and omnitemporality is Gerbert of Aurillac’s De rationali et ratione uti. Here, necessary beings are defined as those that are eternally in a certain state and cannot be otherwise than they are.99 Despite lacking doctrinal innovations, both Gerbert’s treatise and the Leiden gloss are interesting for the history of modalities, for they both show that early medieval logicians were familiar with the connection between necessity and sempiternity or immutability and applied these notions in their reading of Aristotle’s De Interpretatione. Many of the points raised in H9’s discussion on necessity as inevitability return in other texts of the same period. Terminology similar to the one that is used in H9 may be found, for instance, in commentary H11, which is closely related to H9. The author is commenting on De Interpretatione 9 and considers Aristotle’s dilemma, according to which, if we admit that every proposition is true or false, then everything would happen out of necessity. Here, the author says, necessity is understood as the lack of chance and free will. However, he 98 99

The full text of the gloss is transcribed in (Marenbon 2000a). See, for instance (Gerberto d’Aurillac 2007, p. 82): ‘Quae enim necessaria semper ex necessitate sunt, nec unquam non esse possunt.’ See also p. 80, 7–10: ‘Quae necessaria sunt, inquit, in actu sunt, eo scilicet, quem relinquere nequeunt, ut coelum et sol proprium motum. Item quae necessaria sunt, sempiterna sunt.’

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goes on, the term ‘necessarium’ is usually understood in a different way, and he distinguishes three senses that it may have: (i) absolutely and inevitably necessary, which is said of what is always in a certain way and can never be otherwise, as when we say ‘God is immortal’; (ii) determinately necessary, as, for example, in ‘this man will die’; and (iii) modally necessary, as in ‘it is necessary for this man to be mortal as long as he exists or lives’.100 The division among the three senses of necessity (inevitabile-determinatummodalis) is the same as the one presented in H9, and the examples used are also the same as the ones used in the Logica Nostrorum and similar to those in Glossae Secundum Vocales.101 Moreover, in this brief passage the author of H11 explicitly equates the notion of inevitability with that of absolute necessity, which he explains as being sempiternally and immutably in a certain way (‘necessarium absolutum et inevitabile, illud scilicet quod dicitur semper ita est et nunquam aliter esse potest’).102 The two commentaries H4 and H5 connect the notion of inevitable necessity not with that of sempiternity but rather with that of immutability.103 In the latter we find a division of the meanings of ‘necessary’ into three senses: (i) unavoidable (inevitabile); (ii) determinate (determinatus) ; and (iii) consequent 100 See H11, Paris, BnF, lat. 13368, fols 229vb–230ra: ‘Solet autem aliter accipi necessarium, scilicet necessarium absolutum et inevitabile, illud scilicet quod [non] dicitur semper ita est et nunquam aliter esse potest, ut est deum esse immortalem. Vel necessarium pro determinato, ut est hunc hominem mori. Determinatum enim est quod hic homo aliquando morietur. Vel etiam accipitur necessarium modale, ut est hunc hominem necessarium esse mortalem dum est atque vivit.’ 101 Note that the proposition ‘Necesse est hominem mori’, which is used in H9, H11, LNPS, and GSV, as an example for determinate necessity, is instead used in H4 and H5 as an example for inevitability, or absolute necessity. 102 Another passage at the beginning of H11’s discussion on De Interpretatione 9 shows the connection between inevitability or ‘simple’ necessity and sempiternity. Here, the author advances a tripartition among res (things, events) and propositions, saying that those things that are sempiternal and immutable with respect to their nature – such as God – are said to have ‘simple necessity’; while those that are immutable only as long as they exist (quamdiu sunt in ea natura ex necessitate sunt) – like human beings are necessarily mortal as long as they exist – are not said to have simple necessity but only ‘necessitas quamdiu’. Then we have a third category of res, which have neither simple nor quamdiu necessity, for instance, the fact that Socrates walks. The same tripartition, the author continues, may be advanced for propositions, some of which are sempiternally true and are therefore said to be simply necessary, others are only necessary quamdiu, while others again are capable both of being true and of not being true. There is an almost identical passage in H9 (Orléans, Bibl. mun. 266, p. 17b). 103 This was also suggested in H9 and H11, which equated simple necessity with what ‘immutari non potest’, but it remained in the background, in favour of the explication in terms of sempiternity.

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(consequens) . The third meaning is an addition – to my knowledge peculiar to only H4 and H5 – to the standard list of meanings of necessarium used in early 12th-century commentaries. The author of H5 adds an explanation of the three meanings, saying that inevitable is said of what cannot change in any way (‘inevitabile est quod nullo modo potest permutari’), for instance, when we say ‘it is necessary for humans to die’ or ‘for the sun to rise’. Determinate is said of that whereby the cause cannot be prevented by chance or free will, even though this cause is not per se immutable (‘determinatum necessarium est cuius causa non potest impediri per casum vel per utrumlibet […] licet possit permutari’). Necessary in this second sense is the truth-value of present and past propositions such as ‘Socrates is white’, since the cause of their truth or falsity can no longer be prevented. Only future events may be prevented from happening. Finally, necessary consequens is said on the basis of the relation existing between an antecedent and a consequent: if we say, for instance, that ‘if Socrates is a man, necessarily he is an animal’, this necessity concerns not what is said by the consequent per se but the relation between it and what is said by the antecedent (more precisely, the relation between being a man and being an animal).104 The author concludes by saying that whatever is inevitable is also necessarium determinatum and necessarium consequens, but the opposite is not the case.105 104 See H5, Munich, Bay., Clm. 14779, fol. 51r: ‘Necessarium aliud inevitabile, aliud determinatum, aliud consequens, id est conveniens. Inevitabile est quod nullo modo potest permutari, ut “necesse est hominem mori”, “solem oriri”. Determinatum necessarium est cuius causa non potest impediri per casum vel per utrumlibet, ut propositionibus de praesenti et de praeterito est determinata veritas, id est determinatum necessarium, quarum causa non potest impediri per casum vel per utrumlibet, ut in hac propositione “Socrates est albus” est determinata veritas, cuius causa, id est albedo inhaerens subiecto, non potest impediri, licet possit permutari. Impediri enim tantum dicimus de rebus futuris. Consequens necessarium est quod consideratur in propositionibus secundum modum actionum ipsarum propositionum. Modum actionis ipsarum propositionum dicimus cohaerentiam terminorum, sive cohaereant permutabiliter sive impermutabiliter, ut in hac propositione quae dicit “si Socrates est homo, necessario est animal” ponitur necessarium consequens, id est conveniens, et non necessarium inevitabile, quia, cum animal sequatur ad hominem est necessario, non sequitur impermutabile consequens, quia animal potest permutari circa idem subiectum; sed, cum dicimus “si Socrates est homo, necessario est substantia”, hic ponitur necessarium consequens et impermutabile, quia substantia ita cohaeret subiecto ut non possit separari. Et nota quia consequens necessarium, id est conveniens, continet [continet] inevitabile necessarium et determinatum. Continetur etiam necessarium inevitabile a determinato necessario; sed non continetur ab illo necessarium determinatum, quia, quicquid est inevitabile necessarium, est indeterminatum et consequens, sed non convertitur.’ 105 Interestingly, the author adds that, although ‘Socrates is an animal’ is here called necessary consequens (since animal necessarily follows from man), it is not necessary in the sense of inevitable or immutable, because the same subject can change with respect to

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The same terminology explaining absolute necessity in terms of immutability may be found in a commentary on Boethius’ De Hypotheticis Syllogismis, catalogued as SH2, which is preserved in the same manuscript as H5 and which comes immediately after it. In this commentary we find the standard distinction between two senses of necessarium, which might be taken ‘pro determinato’ or ‘pro inevitabile.’ The latter meaning is associated with what is also called ‘necessitas absoluta’, which refers to what is necessary unqualifiedly and omni tempore and is proper of those things that ‘non possunt permutari’. The example given of such necessity is the proposition ‘it is necessary for Socrates to be a substance’, which is expounded as saying: ‘Socrates is immutably a substance’ (Socrates impermutabiliter est substantia).106 The commentary on De Interpretatione H4 also presents many similarities with H5, including a similar list of the meanings of necessarium, at the beginning of its discussion on De Interpretatione 9. Without going into the details of these meanings, we may just say that the author of H4 does not use the term ‘inevitable’ but rather speaks of ‘simple’ necessity, and like H5 explains this in terms of immutability (pro impermutabile) and in opposition to determinate necessity. Just as his contemporaries, the author uses this distinction to support the idea that present and past propositions are necessary only in the second sense, for not all of them are immutable per se.107 the property it has of being an animal. If we say instead that ‘if Socrates is a man, necessarily he is a substance’, the consequent ‘Socrates is a substance’ is both necessary consequens and necessary impermutabile, because the property of being a substance cannot be separated from its bearer, and so the subject is immutable with respect to it. This is interesting because it suggests that a certain subject may remain the same (idem) despite a variation of its ‘substantial’ forms (e.g. animality). The author of H5 seems to claim that, on the contrary, the property of being a substance is entirely inseparable from its bearer, namely, that the subject would not remain the same were it to lose it. As we will see in Chapter 9, Section 5, Abelard will defend a similar position, claiming that there may be identity and individuality independently of (at least some) differentiae. On Abelard’s view on identity and persistence with respect to substantial forms, see also (Binini 2020b). 106 Like the author of H5 and H4 (but differently from several other commentaries on De Interpretatione such as H9, H11, and Abelard’s own glosses on De Interpretatione), the author of SH2 admits that we could properly attribute absolute necessity to non-sempiternal beings, like in this case saying that Socrates is necessarily (namely, inevitably or immutably) a substance. For SH2’s treatment of necessity as immutability, see Munich, Bay., Clm. 14779, fols 74r–74v. 107 See H4, Paris, BnF, lat. 13368, fol. 134va: ‘Multis modis accipitur “necesse”. Accipitur enim pro consequenti, ut in hac consequentia “si albus est, necesse est”, id est consequens est, ut habeat albedinem. Accipitur etiam pro impermutabili, ut “necesse est (pro impermutabile est) hominem mori, solem oriri”. Dicitur quoque “necesse” determinatum, ut in propositionibus singularibus et contradictoriis agentibus de praesenti et de praeterito, necesse est, id et determinatum, alteram esse veram, alteram falsam; et istud est determinatum

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The understanding of necessity as ‘inevitability’ and the explication of this in terms of immutability and sempiternity may also be found in Abelard’s Dialectica, where Abelard says that inevitabile is the usual and more proper meaning of necessarium.108 Abelard returns to this in his treatise on topical arguments, where (using very similar words to the ones seen in H9) he says that ‘necessary is taken as unavoidable, namely as that the act of which is sempiternal, either with respect to being or non being’. Being sempiternal, what is necessary cannot be otherwise than it actually is, so that when it is it cannot not be, and when it is not, it cannot be.109 The connection between necessity and sempiternity is repeated in Dial. 279, 13–4, where Abelard says that: ‘Whatever is necessary is sempiternal and has no beginning’ (Quod autem necessarium est, sempiternum est nec principium novit). As in H9 and other treatises of this period, in the Dialectica Abelard also associates necessity with immutability (incommutabilitas), saying that necessary are those things that cannot change and those propositions the truth-value of which remains unvaried at all times.110 The connection between necessity and sempiternity or immutability is less frequently used in the Logica Ingredientibus, although it is mentioned in two passages.111 In Chapter 10 I suggest that Abelard might have consciously abandoned the temporal characterization of necessity in this later work, because he necesse quod non potest impediri per casum vel per utrumlibet.’ For the connection of ‘impermutability’ with ‘simple’ necessity, see also fol. 137ra: ‘Sed hoc non possumus dicere quod omne, quod est, necesse est esse simpliciter, nec omne, quod non est, necesse est non esse simpliciter, id est impermutabiliter ita quod habeat impermutabilem necessitatem’; ‘Si necesse est esse simpliciter, id est impermutabiliter, necesse est esse determinate; sed non convertitur.’ 108 See Dial. 194, 7–9: ‘Hoc loco “necessarium” idem accipiatur quod “inevitabile”; quae quidem consueta et propria significatio est “necessarii”.’ 109 See Dial. 272, 11–5: ‘Necesse autem hic quod inevitabile dicitur accipimus, cuius quidem sempiternus est actus, sive circa esse sive circa non esse, id est cum sit, non potest non esse, vel cum non sit, non potest esse, nec in esse vel in non esse principium habuit, sed semper vel est ita vel non est.’ 110 See, for instance, Dial. 282, 20–2: ‘necessitas aut(em) determinata et incommutabilis veritas eius consistit, unde non alia firma est cuiuslibet ostensio nisi quae necessitate fulcitur’; 279, 10–3: ‘Cum ita per “est” verbum “animal” “homini” copulatur, actus tantum eius inhaerentiae demonstratur; cum vero per “si” conditionem idem eidem coniungitur, incommutabilis consecutionis necessitas ostenditur’; 282, 27–9; 282, 30–3; 284, 2–3. 111 See LI De Int. 428, 962–3, where Abelard says that ‘Si enim necesse est, incommutabiliter verum est’; and LI De Int. 13, 472, 620–30: ‘Disposuit superius ita ordines modalium quod propositiones de “necessario” ultimas collocavit. Nunc autem ostendit eas naturaliter debere praeponi caeteris propositionibus, quia scilicet res de quibus verae sunt propositiones “necessarii”, priores sunt tam natura quam dignitate caeteris rebus; quippe res, quae necessariae sunt, sempiterne sunt et principia aliarum rerum, ut Deus et mens ex ipso nata, quae eterna sunt’ (my emphasis).

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had envisaged a number of logical problems connected to it, which would put at risk his system of logical inferences for modal propositions. The explication of the necessity of propositions in terms of their omnitemporal and immutable truth has an important consequence for the logic of modalities, namely, that only those propositions the subject of which is a sempiternal thing are properly necessary. This is because every proposition, including a non-sempiternal subject, such as ‘fire is hot’ or ‘Socrates is human’, turns out to be false at times in which their subject is non-existent and therefore is not true at all times. From what we have seen so far, some of the authors who connected necessity with omnitemporality, like those of commentaries H9 and H11, only admitted propositions about sempiternal beings as necessarily true or false (such as ‘God exists’ or ‘God is immortal’), while they thought that propositions about contingent beings could only be necessary in the sense of determinate necessity, that is, only if a temporal condition is added to them (as in ‘every human is an animal as long as humans exist’).112 In his Dialectica Garland also states that necessary propositions about contingent beings can only be true if we add a temporal determination to them, saying, for instance, ‘It is necessary for fire to be hot as long as there is fire’, and he contrasts this sort of determinate necessity with absolute modal propositions such as ‘It is necessary for God to be immortal’.113 A similar idea can also be traced down in later sources, such as H13, where the author says that we may have absolutely necessary propositions only concerning necessary things, while propositions such as ‘Men are mortal’ can be called necessary only in the sense of determinate necessity, such as saying that every man is mortal as long as there are men.114 Other early 12th-century authors, on the contrary, seem to admit that proposi112

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See also Chapter 1, Section 4 on this. See H9: Orléans, Bibl. mun. 266, p. 17b: ‘Sunt quedam res que in aliqua natura cum simplici necessitate non perdurant, sed tamen quamdiu sunt, in ea natura ex necessitate sunt, ut res hominis non cum simplici necessitate est mortalis. Sed tamen eum esse mortalem necesse est, quamdiu est. Ita etiam propositio de huiusmodi re ut “homo est mortalis” dicitur necessario vera, quamdiu est res illa de qua agit. Hec ita est vera, que agit de re quod necessario est in illa proprietate, quamdiu ipsa est.’ (Garlandus Compotista 1959, pp. 84, 25–85, 9). It might be interesting to notice that the author of H13, despite rehearsing the standard distinction between absolute and determinate necessity while commenting on the ninth chapter of De Interpretatione, does not define absolute necessity in terms of immutability or sempiternity, like the majority of other sources do, rather saying that absolutely necessary is that the contradictory of which cannot be true. Examples of such absolutely necessary propositions are the usual ‘God is immortal’ but also ‘Man is not a stone’ and ‘Chimaeras are not goat-stags’. The latter two propositions, despite being about non-sempiternal beings, are still absolutely necessary because their dividens is false ­omnitemporally.

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tions about contingent beings can also be absolutely necessary, for instance, those of H4 and H5, who provide the claims ‘it is necessary for humans to die’ and ‘it is necessary for the sun to rise’ as examples of absolute necessities. In the Dialectica Abelard very clearly states that necessity can only be attributed to sempiternal things, and that even propositions predicating the essential properties of a contingent subject, such as ‘Socrates is a body’ (which, he says, were considered necessary by his Master), are not necessary because there are times in which they are false, namely, before Socrates was created or after he dies: But according to this reading, the proposition ‘It is necessary for Socrates to be a body’ would be true because, Socrates being a body, he cannot exist without body. But it seems to me that such a proposition is entirely false, although our Master was pleased with it. This sort of necessity may happen only in things that are sempiternal. In fact, it is not always the case that Socrates has a body, because before he came into existence, he was not a body: since he was entirely non-existent, he could not have been a body. It seems to me that the term ‘necessary’ should be expounded in the following way: what is of necessity in such a way that it cannot be otherwise, namely, what cannot not be, like for instance ‘God is immortal’: he is immortal in such a way that he cannot be otherwise, that is, it cannot happen that he is not immortal. Whereas, speaking of Socrates, it could happen of him that he is not a body, and indeed this will happen: once he will be dead, it will be true to say that ‘it is not the case that Socrates is a body’, just as this was true before Socrates’ creation.115 Abelard concludes that necessity can only be attributed to things the existence of which is not preceded by non-existence, such as God, and that,

115 See Dial. 200, 36–201, 12: ‘Sed sic vera erit haec propositio: “necesse (est) Socratem esse corpus”; cum enim sit corpus, non potest existere sine corpore. Atque falsa mihi omnino videtur illa propositio, quamvis Magistro nostro placeat. In his enim quae sempiterna sunt, solis necessitas ista contingit. Socrates autem semper corpus non habuit, quia, antequam esset, non erat corpus; cum enim omnino non esset, corpus esse non poterat. Videtur itaque mihi sic exponendum “necessarium” quod illud ex necessitate est (illud) quod ita est illud quod non potest aliter esse, idest non potest non esse, ut Deus necessario immortalis est; sic enim est immortalis quod non potest aliter esse, idest non potest contingere ut non sit (im)mortalis. At vero de Socrate potest contingere quod non sit corpus, quia adhuc continget quod non erit corpus; mortuo enim Socrate verum erit dicere quia non est Socrates corpus, sicut et antequam crearetur, verum erat.’

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concerning things that are not sempiternal, we can never say that nature requires them to be a certain way.116 The fact that many early 12th-century logicians avoid attributing necessity to contingent beings, however, leads to a serious difficulty, because the standard rules of equivalence between modal propositions no longer seem to hold. If we consider a proposition such as ‘it is necessary for Socrates to be human’, saying that it is false on the basis of the fact that there are times in which Socrates does not exist, this other proposition saying ‘it is not possible for Socrates not to be human’ should also be false, since according to the standard rules the two should be equipollent. The latter proposition, however, seems to be true both when Socrates exists and when he does not exist. The equipollence between ‘it is necessary for S to be P’ and ‘it is not possible for S not to be P’, then, is endangered by the standard characterization of necessity as omnitemporal and immutable truth. Although this problem is never explicitly raised by Abelard’s contemporaries, Abelard seems to be aware of it in the Logica Ingredientibus, where he also offers a possible solution, claiming that the rules of equipollence holding among necessity and possibility propositions are only valid under certain conditions, namely, only as long as all the terms included in modal propositions actually refer to some existent being, and thus no empty term is included in them. I will return to this problem, and to the role that existential import has in Abelard’s modal system, in the next part of the book, which is devoted to the details of Abelard’s semantics and logic for modal propositions. 116 See Dial. 201, 1–7: ‘In his itaque solis necessitas contingit quorum existentiam vel actum potestas non praecessit, ut in Deo; neque prius potuit Deus immortalis esse quam fuit. Quaecumque igitur vel aliquando non fuerunt aliquod vel aliquando non erunt, non sunt ex necessitate illud. Si enim umquam fuerunt vel erunt sine eo, non exigit illud ex necessitate natura.’

PART 2 Abelard’s Modal Logic

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Introduction to Part 2 Having investigated Abelard’s and his contemporaries’ definitions of modes and their analysis of the syntactic structure of modal propositions in Part I, in the second part of this book I focus on Abelard’s modal theory by taking into consideration its logical core, namely, the system of relations of opposition and equipollence that he establishes among propositions about possibility, impossibility, and necessity. To describe the logical behaviour of modal propositions, we first need to examine Abelard’s distinction between two possible expositions of modal terms, de re and de dicto (or de sensu). The identification of these two possible readings of modals is considered one of the greatest achievements of Abelard’s work, and perhaps the one that had the longest-lasting impact on the history of logic. In the Dialectica and the Logica Ingredientibus Abelard uses this distinction as the basis for his modal semantics and theory of modalities. In Chapter 4 I focus on this distinction by bringing attention, first, to the way in which Abelard elaborates on it in the Dialectica, and second, to how the same distinction is further developed and perfected in the Logica Ingredientibus. In Chapter 5 I pass to describe Abelard’s views on the existential presupposition of modal propositions and suggest that – at least in the Logica Ingredientibus – Abelard interprets all de rebus propositions about possibility and necessity as having an implicit import. Thus, he thinks that it is a necessary condition for the truth of propositions such as ‘it is possible for my son to be alive’ or ‘it is necessary for all men to be animals’ that their subjects’ referents exist. This seems to go against an opinion that was commonly accepted by Abelard’s contemporaries, which Abelard himself endorses in the Dialectica, namely, that modal terms may be truly predicated of non-existent or future subjects (cf. Chapter 3, Sections 1 and 2 on this). With respect to this point, Abelard’s two logical works differ significantly, and the author’s change of mind might have been due to a further development of his de rebus/de sensu distinction in the Logica. In the same Chapter I also claim that in the Logica Ingredientibus Abelard was aware of some difficulties emerging from attributing existential import to modal propositions, and that, accordingly, he decided to restrict the validity of his modal system to propositions that do not contain non-denoting terms. In Chapter 6 I expound the system of logical relations between modal propositions, as described by Abelard in the Dialectica and the Glossae on De Interpretatione. Abelard conceives of his modal logic as an extension of his ‘classical’ logic (viz., the logic of propositions de puro inesse), in the sense that © koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_007

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every logical rule that he takes as valid for non-modal propositions is preserved in the logic of modal ones. In particular, according to Abelard, the rules of conversions and of syllogistic inferences that are valid for simple categorical predications are also valid for de re modal propositions. New principles and rules are also added to describe the logical relations between modes. Some of these are represented by means of modal squares of opposition, which Abelard provides for both singular and quantified modal propositions. Chapter 7, which concludes the second part of the book, presents Abelard’s logic for modal claims containing temporal qualifications, such as ‘It is possible for Socrates to sit while (dum) he is a man’. Abelard refers to these claims as ‘determinate’ or ‘composite’ modals, as opposed to ‘simple’ ones. Although Abelard’s interest is mainly directed to temporal determinations, introduced by the adverbs ‘while’ (dum, cum), ‘as long as’ (quando, quamdiu, quotiens), or ‘in every time’ (omni tempore), in the Logica Ingredientibus he also considers other sorts of qualification, such as the spatial qualification ‘where’ (ubi) or the exclusive determination ‘only’ (solum, tantum). To temporally qualified modals, Abelard devotes a long and intricate discussion both in the Dialectica and the Glossae on De Interpretatione. His aim is first to investigate the syntactic structure of propositions of this sort and to list the various possible ways in which they can be interpreted, and then to establish a system of logical rules relating determinate modal propositions to simple modal ones and to propositions de puro inesse. In this discussion of determinate claims Abelard reveals rigorous and sophisticated care in distinguishing the different scopes and semantic roles that can be attributed to the linguistic items composing modal propositions, such as the temporal adverb, the modal term, and the other logical connectives that might be included in them, in particular, the negative operator ‘non’.1 Abelard also takes into account some sophismata that are raised by propositions containing temporal qualifications. In particular, he considers some absurd consequences that might be derived from the apparently innocuous claim that it is possible for Socrates to sit at every time at which he lives (Possibile est Socratem sedere omni tempore vitae suae), which, according to some people, entails that Socrates is at the same time both sitting and not sitting. 1 See also (Martin 2016) on this.

chapter 4

Abelard on de re and de dicto Modalities An account of Abelard’s achievements in the field of modal logic must include some discussion of his distinction between de rebus and de sensu (better known today as de re/de dicto) modalities, one of Abelard’s major logical accomplishments. Abelard designed this distinction to unveil a semantic ambiguity hidden in propositions containing nominal modes, such as ‘It is possible for someone who is standing to sit’ (Possibile est stantem sedere). In propositions of this sort, the modal term might be interpreted as having either a narrow or a wide scope, namely, as predicating a possibility either of a certain thing (res) – the person who is actually standing – or of a certain propositional content (sensus, dictum) – the one signified by the non-modal sentence ‘Someone who is standing sits’. In the first case we say that the mode is de re or de rebus, whereas in the second we say that it is de sensu or de dicto. Even though, as was argued in Chapter 2, Abelard may not have been the first medieval author to reflect on the ambiguity of modal terms and to identify two senses in which they could be understood, he is the first to develop and systematize this semantic ambiguity into a sophisticated theory on the scope of modal terms, a theory that he initially presents in the Dialectica and then enriches with new details in the Logica Ingredientibus. Abelard’s sensitivity to the ambiguities of linguistic constructions, and particularly to the ambiguities concerning the scope of logical connectives, constitutes one of the core features of his approach to logic. His texts on modalities are rich in discussions concerning the scope of different logical elements, such as the negative particle, temporal indexes, quantifiers, and modes themselves. Abelard’s reflections on these matters are based on his usual demarcation – which he is perhaps the first in the history of logic to delineate with such clarity and perspicuity – between the grammatical, syntactic structure of propositions, on the one hand, and their semantic structure, on the other. Abelard often stresses that the ‘surface’ structure of modal claims (their constructio or complexio, as he calls it) does not necessarily mirror their meaning (sensus), namely, what we would today call their ‘deep structure’ or ‘logical form’. We have already encountered Abelard’s distinction between these two levels of analysis – secundum constructionem and secundum sensum – in Chapter 2 of this volume, and, as we will see, the same distinction returns within Abelard’s reflection on the structure of de re and de dicto modals.

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In this chapter I will first retrace some of the main features of Abelard’s analysis of de rebus and de sensu modalities in the Dialectica (Chapter 4, Section 1) and the Logica Ingredientibus (Chapter 4, Section 2). As we will see, the two Abelardian texts differ quite consistently with respect to this matter, testifying an evolution in Abelard’s modal thought. In both works, however, Abelard is consistent in preferring the de re reading and in maintaining that modality is primarily a ‘mode of being’, in the sense that modal propositions tell us something about things themselves and their natures, and only indirectly do they apply to propositions and their sensus. 1 The de re/de dicto Distinction in the Dialectica A distinction between de re and de dicto modalities is already advanced by Abelard in the Dialectica, albeit in a less definite and refined way than in the Logica Ingredientibus. The two possible interpretations of modal terms arise from Abelard’s reflection on how modal propositions are derived from the corresponding simple ones. Considering the relationship between a proposition such as ‘It is possible for an S to be P’ and the corresponding de puro inesse ‘S is P’, Abelard identifies two possible answers to the question of how the latter descends from the former: either the modal proposition is about the same things that the simple proposition is about, so that both have the same subject and predicate and both affirm something concerning the things signified by these terms; or the modal proposition is about the simple proposition itself or, more precisely, about the content (sensus) expressed by it. In the first case we say that the modal proposition is de re (or de rebus), inasmuch as it deals with the same res as the corresponding simple proposition. In the second case we rather say that the modal proposition is ‘de sensu simplicis’, so that the mode is understood as having a wider scope, which applies to an entire propositional content.1 In the Dialectica Abelard affirms that only the first is a correct reading of modal propositions. The alternative interpretation is attributed by Abelard to his Master, who is said to hold a view according to which modal claims are ‘de sensu simplicium’, so that when we say ‘It is possible for Socrates to run’, we are affirming that what is said by the proposition ‘Socrates runs’ is possible.2 In the 1 For a similar account on how the de rebus/de sensu distinction is presented in the Dialectica, see also (Marenbon 1991). 2 ‘Restat autem nunc qualiter modales propositiones ex simplicibus descendant confiteri. Est autem Magistri nostri sententia eas ita ex simplicibus descendere, quod de sensu earum

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discussion that follows Abelard critiques the de sensu exposition of modals by saying that it is an improper interpretation and posits a number of semantic problems, eventually leading his Master to an inconsistent position. Whether Abelard does in fact succeed in proving the inconsistency of the de sensu interpretation is questionable, and I will return to this issue below. Before we do this, it could be useful to go briefly through the objections that Abelard raises against his Master’s opinion. Four objections are presented, which are first listed altogether in Dial. 195, 15–26 and then more extensively explained one by one in Dial. 195, 26–198, 11. First, Abelard says that if modal propositions are interpreted de sensu, then all the rules of conversion – both simple and by contraposition – should be valid for them. However, it was the opinion of his Master that conversions are not to be maintained in modal propositions as they are in simple ones. But these two assertions – that modal propositions must be read de sensu and that conversions are invalid – are incompatible, according to Abelard. The position held by his Master would thus be incoherent. The relation between modalities de re and de dicto and the validity of conversions was animatedly debated by Abelard’s contemporaries, and I will return to this at the end of this section. Abelard’s second objection states that, if modal propositions are expounded de sensu, some propositions that should be considered true – and that his Master held as true – turn out to be false. For example, the following proposition: ‘For every man it is possible to be a non-man’ (Possibile est omnem hominem esse non hominem) is true according to Abelard, presumably on the basis that each thing that is now a man will become a non-man in the future, once dead. However, if we interpret it as saying: ‘What is said by this proposition “Every man is a non-man” is possible’, the proposition is evidently false. Another example offered by Abelard is the proposition ‘For every man it is possible to be dead’ (Omnen hominem possibile est mortuum esse), which again should be taken as true but is, in fact, false de sensu.3 If one interprets the latter ­proposition de agant, ut cum dicimus: “possibile est Socratem currere vel necesse”, id dicimus quod possibile est vel necesse quod dicit ista propositio: “Socrates currit”’ (Dial. 195, 11–5). 3 ‘Restat autem nunc post conversiones ut ostendamus secundum eorum expositionem eas falsas quas veras aestimant, ut istam: ‘possibile est hominem mortuum esse”, sic scilicet expositam: “possibile est quod haec propositio dicit: homo est mortuus.”’ Abelard has some difficulties trying to justify that (*) ‘For a man it is possible to be dead’, although false de sensu is true de rebus. This is because he interprets the de rebus reading in terms of non-incompatibility with the nature of a thing, so that the proposition would mean ‘Being dead is not incompatible with the nature of a man’. It seems, however, that ‘being dead’ is in fact incompatible with the nature of any substance who is actually a man, for such a nature requires being animate as an essential form. Abelard’s argumentation for the truth of (*) rests on the

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sensu, Abelard claims, one says that the content of this proposition ‘A man is dead’ is one among all the things or events that are possible, or, in other words, that the two predicates ‘man’ and ‘dead’ may simultaneously attach to the same subject. This is certainly false, for being a man requires being alive, and it is therefore impossible for someone who is a man to be dead at the same time.4 On the other hand, Abelard continues, other modal propositions that are commonly taken as false would be true de sensu, such as ‘For no man is it possible to be white’. Abelard interprets this proposition de rebus as: ‘The nature of no man is compatible with being white’, which would intuitively be false, whereas, according to his Master’s de sensu reading, the proposition says ‘What this proposition states “no man is white” is possible’ or ‘It might be the case that whiteness inheres in every man’ (Posset omni homini contingere albedo), which is true.5 Thus, the de sensu exposition leads, according to Abelard, to a misleading attribution of truth and falsity. This objection might seem inconclusive, since Abelard only appears to point out that the de re and de sensu interpretations return different truth-values, while giving no justification as to why the de sensu semantics would be, per se, inappropriate. It should probably be read as an ad hominem objection, accusing the Master of holding an interpretation of modals according to which the very same propositions that he considers true should rather be taken as false, and vice versa. As we will see later in this section, in the commentary H9 (but also to some extent in the treatise M3) we indeed find a treatment of modals that presents inconsistencies of this sort. idea that, although it is true that a man cannot be dead, we might consider the thing that is actually a man (id quod est homo) not as a human but as a mere corporeal substance. If we attend to this substance as a body, we might truly affirm that there is no incompatibility between its corporeal nature and the property of being dead (Dial. 196, 29–197, 31). I will offer a detailed analysis of this passage in Chapter 9, Section 5. 4 Dial. 196, 32–197, 2: ‘Si enim possibile est quod illa dicit propositio, possibile simul mortuum et hominem cohaerere, quod quidem falsum est, cum ex natura oppositionis alterum non possit pati alterum. Neque enim homine[m] vivente in eodem existere possunt, quippe cum “mortuum” “vitam” non perferat, nec homine[m] mortuo, quippe cum “hominem” “mors” non patiatur. Quia ergo nec homine vivente nec mortuo nec etiam antequam homo crearetur, natura hominem et mortuum patiatur, numquam simul ea patitur. Nullo itaque modo videtur vera haec propositio: “possibile hominem mortuum esse”, ut scilicet de sensu simplicis exponatur.’ 5 ‘Nunc autem monstremus eas quae falsae sunt, veras esse, vel quae negativae sunt, affirmativas esse secundum supradictam expositionem, ut istam: “nullum hominem possibile est esse album”. Haec enim secundum eos ex ista descendit: “nullus homo est albus”, et de sensu illius agit, ita scilicet quod dicit: “possibile est esse illud quod ipsa dicit”. Sed iam vera est, si i[s]ta exponatur, et affirmativa de non esse. Posset enim omni homini contingere albedo, sicut et omni animali sanitas’ (Dial. 197, 32–8).

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In the passages containing Abelard’s second objection to his Master’s theory, we find a brief explanation of what Abelard means by ‘de rebus’ and ‘de sensu’ in the Dialectica. A proposition about possibility is true de rebus when the predicate term is not incompatible with the nature of the thing signified by the subject term. A proposition such as ‘It is possible for every man to be white’, for instance, is true de rebus if being white is compatible (or ‘not repugnant’, as Abelard says) with the nature of humans, that is, if it does not contradict any of the substantial properties that are essential to human beings.6 On the contrary, the de sensu reading of the same proposition is explained by Abelard with two different characterizations. On the one hand, the modal proposition is true de sensu if what is said by the corresponding proposition de puro inesse is possible (‘Possibile est quod illa propositio dicit’; ‘Possibile est esse illud quod ipsa dicit’), or, in other words, if what the simple proposition affirms ‘might be the case’ or ‘could happen’ (contingere posset). On the other hand, Abelard also says that a proposition such as ‘It is possible for an S to be P’ is de sensu if the subject S is possibly P while remaining S (e.g. some man is possibly dead while remaining a man). To this alternative characterization of the de sensu interpretation, Abelard will often resort in the Logica Ingredientibus as the ‘per compositionem’ or ‘per coniunctionem’ reading of modals. Abelard often oscillates between these two interpretations of de sensu, even though they do not completely converge, as we will clarify in Chapter 4, Section 2. A third objection raised by Abelard to his Master’s exposition of modals concerns the proper interpretation of the quality of propositions, that is, whether they are affirmative or negative. Abelard states that if modal claims are taken de sensu, some negative propositions appear erroneously to have an affirmative structure, such as (again) ‘For no man is it possible to be white’ (Nullum hominem possibile est esse album). Abelard thinks that this is properly a negative universal claim, while interpreted de sensu it would be an affirmative proposition de non esse.7 Finally, Abelard’s last – and perhaps more perspicuous – objection to the de sensu analysis is that if modal propositions were read in this way then they would not be ‘modal’ at all, but rather propositions de puro inesse, for they would affirm that a certain predicate (the modal term) is predicated unqualifiedly of a certain subject, namely, the essentia of the proposition that functions

6 On the idea of possibility as non-incompatibility with nature, see Chapter 3, Sections 3 and Chapter 9 of this volume. 7 See footnote 5 in this Chapter for the relevant passage in the Dialectica.

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as subject.8 As was explained in Chapter 2, Section 1, early 12th-century authors thought that, in order for a proposition to be considered modal, it must express a qualified inherence between two things, and the modal term should have the role of indicating in which way (quomodo) the predicate term is conjoined to the subject term. Abelard claims that if one expounds the claim ‘For no man is it possible to be white’ to mean ‘What is said by this proposition is possible: “No man is white”’, then the proposition asserts the unqualified conjunction of the predicate ‘possible’ to the sensus of this proposition ‘No man is white’, so the proposition would in fact be de puro inesse. This latter is perhaps the most powerful among Abelard’s four objections against the de sensu reading, since the characterization of ‘modal’ on which it is based indeed seems to be a standard and well-established opinion of his time, and was rehearsed in many important sources on modalities, including commentary H9, which allegedly reports the theories of William of Champeaux, the ‘Master’ to whom Abelard is referring in the Dialectica. Among these four objections, the first one – concerning the validity of conversions in modal logic – deserves closer attention, and I will focus on it in what remains of this section. As we have already seen, Abelard argues that if someone reads modal propositions de sensu, he or she must also consent to the validity of simple conversion and conversion per contrapositionem in modal logic. However, since Abelard’s Master does not want to admit that these are valid, his position is inconsistent. Again, note that this objection is not against the de sensu interpretation in itself but only against the compatibility between such a de sensu interpretation and the denial of the validity of conversions. Abelard has an argument to demonstrate that all de sensu modals are convertible. More precisely, the argument shows that conversions are valid for modal propositions as long as they are valid for their corresponding simple ones. This last caveat is important, since Abelard thinks that in the case of simple propositions there are also cases in which conversions fail (see Chapter 6, Section 3). Consider now a pair of de puro inesse propositions, ‘p’ and ‘q’, where ‘q’ is obtained by conversion from ‘p’. Propositions ‘p’ and ‘q’ are equipollent. Appealing to the principle stating that anytime what is said by one of two equipollent propositions is possible, what is said by the other one is also possible,9 8 ‘Nec iam etiam modalis appellari potest, sed simplex, quia simpliciter possibile attribuit subiectae propositionis essentiae. Unde nec ulla est ibi modificatio rerum inhaerentiae, quippe nec de rebus agitur, sed de sensu propositionis. Quare, quoniam in vi modi non est “possibile”, modalem non facit propositionem’ (Dial. 198, 3–8). 9 ‘Cum enim possibile sit esse quod dicit una aequipollentium, possibile est esse et quod alia proponit; et de impossibili similiter, et necessario’ (Dial. 195, 35–7). The same goes for impossibility and necessity.

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Abelard claims that whenever we have a pair of equipollent simple propositions, their corresponding modal propositions must also be equipollent. So, for instance, the following are valid: i. ii.

Every man is an animal ⇔ every non-animal is a non-man ⇒ ◊ (every man is an animal) ⇔ ◊ (every non-animal is a non-man). No man is a stone ⇔ no stone is a man ⇒ ◊ (no man is a stone) ⇔ ◊ (no stone is a man).

Abelard takes this as proof that conversions are also valid for modal propositions, when interpreted de sensu, because whenever their corresponding simple propositions are equivalent by virtue of conversions, the modal propositions de sensu are also equipollent.10 He claims that his Master is therefore wrong in rejecting the validity of conversions for de sensu propositions.11 Abelard goes on to examine some alleged counter-examples to the validity of conversion in de sensu modal claims, probably the ones proposed by his Master as proof of such invalidity, for instance, the pair: (1.a) ‘For every man it is possible to be a stone;’ (1.b) ‘For every non-stone it is possible to be a non-man.’ Abelard says that his Master takes (1.a) to be false and (1.b) to be true, and he justifies the truth of (1.b) with an argument a partibus, by dividing the term ‘every nonstone’ into its two ‘parts’ (the first including all the non-stones that are men and the second all the non-stones that are non-men) and then arguing for the truth of ‘It is possible for every non-man to be a non-man’ (which is evident) and that of ‘It is possible for every man to be a non-man’, which seems to be based on the aforementioned principle, according to which whatever will happen in the future is possible (‘Quod enim futurum est, possibile est; aliter enim futurum non esset, nisi scilicet possibile esset; neque enim futurum est quod natura non patitur’, Dial. 196, 5–9). Abelard replies to this counter-example by saying that, if we understand modal propositions de sensu, proposition (1.b) must also be false, for it is not 10 11

Notice, however, that, even though we accept Abelard’s reasoning, the modal propositions considered in (i) and (ii) would indeed be equipollent, but not by virtue of conversions. ‘Miror, inquam, cum modales de sensu simplicium agere faciat, non de rebus ipsis de quibus simplex agit, cur non in istis, sicut in simplicibus, conversiones omnes recipiant. Neque enim secundum eorum expositionem conversiones in istis magis deficiunt quam in illis nec, si sensum suae expositionis attendant, unam veram in conversionibus et aliam falsam, sicut aestimant, invenient; quod tam in conversione simplici quam in conversione per contrapositionem licet inspicere’ (Dial. 195, 28–196, 1).

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possible that what this proposition says happens: ‘Every man is a non-man.’ He also maintains that the only case in which the two propositions are not equipollent is when one or more of the terms included in (1.a) or (1.b) are empty (namely, when they fail to refer) or ‘universal’ (namely, when they refer to everything that exists). However, the same failure of conversion is also detected for propositions de puro inesse, and it is not specific to modal propositions. For example, also in the case of the two simple propositions ‘Every man is a stone’ and ‘Every non-stone is a non-man’, conversion rules fail in a situation in which there are no men. As a consequence, Abelard claims that when we consider the validity of conversions, both in simple and modal propositions, we have to posit the condition that all the terms present in converted propositions are neither empty nor ‘universal’. If this condition is granted, the two propositions (1.a) and (1.b) are equivalent and both false, and therefore they do not constitute a counter-example to the validity of conversions (see on this also LI De Int. 400, 240–401, 249). Abelard also considers other counter-examples, which involve conversions simplex and per accidens rather than per contrapositionem. In the following four pairs of propositions, it is the opinion of Abelard’s Master that one side is true and the other false (Dial. 196, 22–24). Abelard answers that, if we read modal propositions de sensu, in all these pairs the converted propositions have the same truth-value and are thus equipollent to their rectae counterparts: (2.a) (2.b) (3.a) (3.b) (4.a) (4.b) (5.a) (5.b)

‘For no blind man is it possible to see.’ ‘For no one who sees is it possible to be blind.’ ‘For no dead [thing] is it possible to be a man.’ ‘For no man is it possible to be dead.’ ‘For every man it is possible to be dead.’ ‘For some dead [thing] it is possible to be a man.’ ‘For no body is it necessary to be a man.’ ‘For no man is it necessary to be a body.’

As I have argued elsewhere (see Binini forthcoming), some of the examples attributed by Abelard to his Master coincide with the ones advanced in the commentary H9, where the anonymous author argues for the invalidity of conversions for nominal modal claims by advancing the following cases: (1.a) (1.b) (4.a) (4.b)

It is possible for every man to be a stone – FALSE. It is possible for every non-stone to be a non-man – TRUE. It is possible for every man to be dead – TRUE. It is possible for some dead to be a man – FALSE.

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(5.a) For no body is it necessary to be a man – TRUE. (5.b) For no man is it necessary to be a body – FALSE.12 The author of this commentary13 seems not to distinguish clearly between modalities de re and de sensu, providing an analysis of modals that incorporates elements of both readings. For instance, his justification of the truth of (4.a) seems to be based on an intuitive de rebus reading in which the possibilities of a thing are interpreted in terms of the potentialities of ‘becoming’ ­something else. Other aspects of the treatment of nominal modals in H9 suggest instead that the author had an inclination for a de sensu reading, for instance, his denial that nominal claims could be generally translated into an adverbial form. If the position advanced in H9 is indeed the one criticized by Abelard in the Dialectica (or at least connected to it), the ambiguities and incongruities present in this anonymous commentary with respect to the de re/de sensu interpretation of nominal modals would reinforce what Abelard says about the fact that in his time some people – his Master among them – held inconsistent views on modalities, claiming that modal claims had to be understood ‘de sensu simplicium’ and yet maintaining the truth of propositions such as ‘It is possible for every man to be a non-man’.14 Another analysis of the validity of conversions in modal logic is advanced in the anonymous treatise M3, presumably written in the same years as the ­Dialectica or slightly later. We have already come across this treatise in Chapters 2 and 3 of this volume, as this is one of the most important sources on modalities from Abelard’s time, discussing both the syntactic structure of modal propositions and the signification of possibility and necessity. As was suggested in Chapter 3, Sections 1 and 2 above, the author of M3 displays some acknowledgement of the de re/de dicto distinction and considers this distinction within his discussion of modal conversions, a discussion that it is interesting to compare with the one provided by Abelard and by the author of H9. Without going into the details of such a discussion here,15 I will simply say that M3 agrees with Abelard in claiming that propositions such as ‘It is possible for every man to be a non-man’ or ‘It is possible for every man to be dead’ are false when taken de sensu, and therefore he considers them equipollent with their converted form. 12 See H9, Orléans, Bibl. mun. 266, p. 33b. Cf. (Binini forthcoming). 13 As was said, Iwakuma proposed that H9 was written by someone connected to the teaching of William of Champeaux, which would coincide with the identification of Abelard’s Master in William, if the position of H9 is indeed the one targeted in the Dialectica. 14 See Dial. 195, 12–9. 15 For a detailed analysis and comparison of the three texts, see (Binini forthcoming).

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This is because he takes the de sensu as a sort of per compositionem reading (just as Abelard does in the Logica, as we will see), in which two incompatible predicates are said to possibly inhere at the same time in the same subject. However, M3 disagrees with Abelard in maintaining that conversions are not generally valid for modal propositions. The author offers other examples in which they fail, such as the pair: (6.a) It is possible for every young to be old – TRUE. (6.b) It is possible for some old to be young – FALSE. It is not clear why the author takes the first to be true, given the per compositionem interpretation that he endorses elsewhere. As I have argued in (Binini forthcoming), perhaps the author of M3 is still driven by a residual understanding of possibilities in terms of potentialities, according to which what is possible for a substance is defined on the basis of what might be actualized in some future moment of its life. Even though Abelard does not consider the very pair (6.a)–(6.b) in his treatment of conversions, he presents a similar case when considering the pair (2.a) ‘For no blind man is it possible to see’ and (2.b) ‘For no one who sees is it possible to be blind’. Abelard believes that both propositions in this pair are false when taken de sensu and true de rebus, so they would not be a counter-example to the validity of conversions in modal logic, as was said. He seems therefore to disagree with the author of M3 with respect to these cases, although their position is similar with respect to others. To sum up, in the Dialectica Abelard claims that the validity of conversions must always be granted if modal claims are interpreted de sensu and that it would be incoherent to maintain a de sensu reading, on the one hand, and the invalidity of conversions, on the other. On this basis, he accuses his Master of holding an inconsistent view of modals. Let us remember again that this objection is not effective in refuting the de sensu reading per se but only points out the incompatibility between endorsing the de sensu interpretation as the allencompassing way of construing modal propositions with nominal modes and the refusal of their convertibility. Abelard’s critique is more intelligible if we read it within its context, a context involving a dispute on modal conversions, the echoes of which we find in other sources of the time. Modal conversions seem to have been used by authors from the early 12th century to uncover the difficulties and ambiguities hidden in nominal modal claims, and their analysis is closely tied to the development of the de re/de sensu distinction. In the Logica Ingredientibus Abelard ‘softens’ the radical critique against the de sensu reading that he had offered in the Dialectica, as he is ready to admit de sensu as a legitimate interpretation of (at least some) modal propositions.

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Nevertheless, he still takes the de rebus exposition as the most proper and basic interpretation of modes, either adverbial or nominal. Of the four objections to the de sensu reading that he had listed in the Dialectica, only one will survive, namely, the idea that de sensu propositions are not, strictly speaking, ‘modal’. In the Logica Abelard also elaborates further on what he means when saying ‘de re’ and ‘de sensu’, and he famously connects this distinction with the Aristotelian distinction between ‘per divisionem’ and ‘per compositionem’ interpretation. 2

The Development of the Distinction in the Logica Ingredientibus

The passage with which Abelard introduces the de rebus/de sensu distinction in the glossae on De Interpretatione is one of the most famous and quoted passages of Abelard’s logical works. Here, Abelard explicitly presents the de rebus/ de sensu pair as identifying a semantic ambiguity of nominal modal claims, and he then establishes the truth conditions for the same proposition – ‘It is possible for he who stands to sit’ (Possibile est stantem sedere) – with respect to both expositions. Abelard, however, does not present the distinction as his own but refers it back to Aristotle’s Sophistical Refutations, where the Philosopher talked about a compound and a divided reading of modals: Videntur autem duobus modis exponi posse, veluti si dicam: Possibile est stantem sedere. Ut enim docet Aristoteles in Sophisticis Elenchis, alius est sensus per divisionem alius per compositionem: per compositionem vero est si stare et sedere simul in eodem subiecto coniungat, ac si dicamus: ‘Possibile est stantem sedere manentem stantem’ id est: sedere simul et stare, ac si dicamus: ‘Possibile est ita contingere ut haec propositio dicit “Stans sedet”’ quod est omnino falsum quia iam duo opposita simul inesse eidem possent; et tunc quidem possibile quasi ad integrum sensum propositionis applicatur, ac si dicatur: ‘Possibile est evenire ut haec propositio dicit “Stans sedet”’. Si vero ita accipiatur quod is qui stat possit sedere quandoque, non coniungimus tunc opposita, et ad rem ipsam, non ad propositionem, possibile referimus dicentes rem quae stat posse quandoque sedere, non posse contingere ut dicit propositio Stans sedet. (LI De Int. 401, 250–64) The proposition ‘It is possible for he who stands to sit’ is said to be true de rebus if the predicate term ‘sit’ is compatible with the nature of the thing signified by the subject, which is indeed the case for the proposition under example. Conversely, the truth conditions for the corresponding de sensu proposition are given with respect to two different paradigms. First, a de sensu proposition is

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true if what is said by the predicate is compatible with some property that the subject actually has, and according to which it is characterized, for example, as ‘standing’. Because ‘sitting’ and ‘standing’ are incompatible properties, which cannot be simultaneously predicated of the same subject, the proposition under example is false de sensu. Second, a de sensu possibility-proposition is true if the corresponding claim de puro inesse ‘can be’ or ‘can happen’. Again, because it could not happen that ‘Someone who stands sits’ were true, the modal claim is said to be false de sensu. This last characterization of the de sensu reading involves the application of the modal term to a propositional dictum and could also be exposed by means of a phrase such as ‘the following is possible (or could happen): that he who is standing sits’ (‘Possibile est ita contingere ut haec propositio dicit “Stans sedet”’). The first of these expositions, however, does not seem to be completely de sensu. Instead, it almost amounts to a sort of de re reading, in which a combination of properties is assessed, as if it were said: ‘he who is standing can sit while standing’ (stans potest sedere manens stans). Following Aristotle, Abelard classifies this last de sensu exposition as a ‘per compositionem’ or ‘per coniunctionem’ reading, as opposed to a ‘per divisionem’ one. From what Abelard says in this passage, he seems to take these two expositions of de sensu as coincident and thus to equate the de dicto reading with the per compositionem one. In the example used, the two readings are in fact identical and return the same truth-value, but there are examples – some of which are considered by Abelard in the Logica – in which the two do not converge. It is not clear whether Abelard was aware that his per compositionem is only one out of several possible de sensu readings, as Knuuttila has suggested,16 or whether instead he fails to recognize any de sensu interpretation other than the per compositionem one. I will return to this point at the end of this section. Differently from what he does in the Dialectica, in the Logica Ingredientibus Abelard does not argue against the validity of the de sensu interpretation per se, claiming that it is an incorrect understanding of modalities. Rather, he underlines that the de rebus and de sensu are two alternative and legitimate expositions of modals but that we should carefully distinguish between the two in order to avoid sophismata resulting from the ambiguous scope of the modal term. Although the de sensu reading is not rejected as incorrect, Abelard still points out that the de rebus reading is the more proper and fundamental understanding of modal propositions. We may identify three arguments for the priority of the de rebus reading over the de sensu one: i. First, propositions understood de sensu are not, strictly speaking, modal propositions but are in fact predications de puro inesse. As was said in the previous section, this objection rests on the idea – commonly accepted 16

See (Knuuttila 1993, pp. 86–7).

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by early 12th-century authors – that modal terms act as inherence qualifiers, a role that they can perform by virtue of the fact that, when adjoined to a certain verb, they ‘modify’ its meaning by adding a certain qualification to it. As I argued in Chapter 2, to justify this particular reading of adverbs, authors of the time appealed to Priscian’s idea that adverbs qualify (moderant) the meaning of verbs just as adjectives do with nouns, as if they were ‘adiectiva verborum’. ii. Second, de sensu modal propositions do not have any quantity; in other words, they are neither universal, particular, indefinite, nor singular. The quantity of nominal modals was a common object of discussion in early 12th-century logic, which stimulated the analysis of these propositions’ syntactic and semantic structure, as I argued in Chapter 2.1 of this ­volume.17 iii. Third, de sensu modal propositions are impersonal constructions, and therefore they lack the possibility to convert. This third point may sound odd, as in the Dialectica Abelard argues precisely for the opposite view, saying that de sensu modal propositions allow for the same conversion rules that are valid among simple propositions. This point, however, rests on a reflection concerning the impersonality of propositions, which was not present in the Dialectica, and it is possible that Abelard developed this line of thought later on and that it contributed to changing his views on the de re and de sensu interpretations.18 The first objection is the same as the one that Abelard proposes in the Dialectica against his Master, and I will not return to it here. The second and third objections, on the other hand, are worth exploring in a little more detail, as they allow us to connect Abelard’s reflection on modalities with parallel discussions raised in contemporary sources. As was already remarked in Chapter 2, several sources from the first decades of the century express an interest in analysing the syntactic structure of propositions containing nominal modes, and particularly in identifying which terms are subject and which predicate in propositions of this sort. On the basis of what Aristotle said in De Interpretatione concerning the proper way to negate modals, some authors proposed reading the modal term ‘possible’ as the predicate in propositions such as ‘It is possible for every man to be an animal’ (Possibile est omnem hominem esse 17 18

For a more detailed analysis, see also (Binini forthcoming). All three objections are briefly sketched in the following passage: ‘At vero, cum de sensu propositionis exponuntur, proprie modales non sunt, nec universales vel particulares vel indefinitae vel singulares, nec ideo simplicium conversiones retinent; tunc enim quasi totius propositionis sensus subiectum est et modus simpliciter praedicatur; nec est personalis enuntiatio ullo modo sed impersonalis, ideoque conversione caret proprietas constructionis’ (LI De Int. 402, 273–8).

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animal). Based on the same passages of De Interpretatione, authors of Abelard’s time also embraced the idea that the subject of nominal modals would thus be the verb included in the infinitive accusative clause (esse) or rather the entire oratio (omnem hominem esse animal), of which the modal term is predicated (see Chapter 2, Section 1 of this volume). This analysis is mentioned in several sources, such as Garland’s Dialectica, the anonymous commentaries H9, H4, and H5, and the treatises on modalities M1 and M3, as well as later sources such as the Glossae Doctrinae Sermonum (H15), the Introductiones Montane Maiores, and the Summa Periermeneias (H21). In many of these texts, however, this reading is presented as problematic. Their authors say that such an analysis would make nominal propositions invariable with respect to quantity, because no sign of quantification could be added to their subject term. Lacking quantity, these propositions would thus be ‘unsyllogistical’, because in order to be included in syllogisms every proposition should be either universal or particular. The objection raised by Abelard in the Logica concerning the lack of quantity of de sensu propositions, an objection that many other logicians of his time raise with him, is more profound than it might seem at first sight. It has to do with the possibility of construing syllogisms using modal propositions, a possibility that Aristotle had envisaged when proposing his syllogismi incisi, and to which logicians of Abelard’s time wish to adhere. As Abelard had said in a preceding passage of the Logica, we may solve this issue if we analyse the structure of modal propositions such as ‘It is possible that every man is animal’, not according to their grammatical construction but according to their meaning, taking ‘every man’ as subject and ‘animal’ as predicate. In this way we could construe syllogisms of different figures.19 This solution, however, would not be viable if one interpreted modal propositions de sensu, for according to this exposition the proposition would be impersonal, and its subject could not be quantified. The de sensu reading of modalities therefore seems inappropriate for modal syllogistics.20 19

20

LI De Int. 399, 198–203: ‘Cum itaque Aristoteles figuras in his quoque syllogismis servet et ipse primam figuram diffiniat in qua medius terminus subicitur et praedicatur, secundam in qua tantum praedicatur, tertiam in qua tantum subicitur, oportet nos ad subiectum secundum sensum respicere, non constructionis, alioquin nulla esset figura.’ Many authors in the first half and in the mid-12th century agree with Abelard on this point, believing that Aristotle’s modal syllogistics is valid only if we interpret modes de re. A similar idea is supported, for instance, by the authors of the Introductiones Montane Maiores, of the Summa Periermeneias (H21), and of De Propositionibus Modalibus. Furthermore, the author of the later Ars Meliduna, who favours the de dicto as the proper interpretation of modes, acknowledges that the invariability in quantity of these modals renders them unusable for syllogisms and proposes that Aristotle’s syllogismi incisi are

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Abelard’s objections concerning the invariability in quantity of de sensu modal propositions, and the invalidity of their conversions, are connected to his idea that propositions of this sort have an impersonal construction, which in some cases cannot be reduced to a personal form. Indeed, a relatively extensive part of Abelard’s treatment of de sensu modalities in the Logica is dedicated to his theory of impersonal sentences (LI De Int. 404, 326–408, 437), a theory of which there is no trace in the Dialectica. A sentence has a personal construction or intent when its terms are suitable to refer to something that exists.21 Some propositions, such as ‘Evenit Socratem currere’ (It happens that Socrates runs) or ‘Ventum est ecclesiam’ (which might be translated into ‘There was an arrival at the church’), include terms that do not signify personally, and therefore cannot be rephrased into a personal form. Of this sort are also modal propositions that are grammatically construed using nominal modes followed by an infinitive clause, such as ‘It is obligatory for Socrates to read’ (Oportet Socratem legere) or ‘It is necessary for Socrates to read’ (Necesse est Socratem legere). In the Logica Abelard formulates a distinction between two ways in which propositions of this sort are said to be ‘impersonal’: only with respect to their grammatical structure or with respect to both grammar and meaning. Of the first kind are those propositions that, despite having an impersonal syntactic form, are really personal in meaning and can thus be rephrased into a personal construction (see LI De Int. 402, 273–86). The grammatically impersonal proposition ‘It is obligatory that Socrates reads’ and ‘There was an arrival at the church’, for instance, could be translated into the personal claims: ‘Socrates must read’ (Socrates est oportunus ad legendum; LI De Int. 403, 301– 4) and ‘Some people arrived to the church’.22 The same may be said for many modal propositions, including nominal modes, which, despite their syntactic difference, are the same in meaning as the corresponding adverbial forms. The impersonal ‘It is possible for Socrates to read’ (Possibile est Socratem legere), for instance, has the same meaning as ‘Socrates possibly reads’ or ‘Socrates can read’ (Socrates legit possibiliter; Socrates potest legere). The possibility to reformulate impersonal propositions of this sort as having a personal intent and form allows Abelard to admit that these propositions may also be varied with respect to quantity (being universal, particular,

21 22

in fact not real syllogisms but arguments of apparent syllogistic form. (See Binini 2020a on this). For this characterization, see (Wilks 2008, p. 107); for a presentation of Abelard’s theory of personal and impersonal construction and its background, see also (Jacobi 1985, pp. 30–40); (Nuchelmans 1973). Cf. (Wilks 1998b, p. 107).

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indefinite, or singular) and suitable for conversion. Differently from what he said in the Dialectica, however – where he suggested that all nominal propositions could be rephrased as having an adverbial, personal meaning – in the Logica Abelard proposes that some nominal modals are ‘entirely impersonal’ with respect to both grammar and meaning, and as such they have no quantity and completely lack the capability to convert, either simply or by contraposition. Examples of such propositions are those that include non-denoting subjects (e.g. ‘Necesse est chimaeram non esse qualitatem’; ‘Necesse est chimaeram non esse’) and other nominal claims such as ‘It is possible for that which is not to be’ (Id quod non est possibile est esse). Abelard explicitly says that propositions of this sort cannot be rephrased as having a personal construction (‘Nullam personalem resolutionem habent’) because their terms do not have a personal intent and they do not name any thing (LI De Int. 403–5). Modal claims of this sort can only be interpreted de sensu. However, Abelard still denies that this de sensu exposition should be read as if the modal term functioned as predicate inhering in a propositional dictum, and as if the latter were conceived as a thing. As Nuchelmans has convincingly argued, Abelard’s analysis of the impersonality of propositions such as ‘Possibile est Socratem legere’ rests fundamentally on the idea that accusative-infinitive phrases such as ‘Socratem legere’ should not be read as names of some sort, namely, as expressions that signify in nominando and of which the modal term would be predicated. Abelard does indeed recognize, as Nuchelmans says, ‘the strong temptation to construe the complement of [the modal term] as a sort of naming expression which requires a thing as its denotatum’.23 Still, he resists this ‘temptation’ and thinks that instead the accusative-infinitive phrase should be understood as having a verbal force, as if it were said, for example, ‘Potest contingere, ut Socrates legat’. This is probably because he denies the existence of propositional entities such as dicta, which would be the ontological correlate of accusative-infinitive phrases, if these were taken as names. As Nuchelmans remarks, Abelard’s analysis of impersonality is construed, in fact, as ‘a very ingenious antidote against confusing the dictum with a thing’.24 Interestingly, whereas Abelard suggested in the Dialectica that all de sensu propositions admitted conversions in all circumstances in which they were 23 24

A similar analysis of impersonal, and more specifically, modal, predication is offered, for instance, in the Ars Meliduna, whose author propends to a de dicto reading of nominal modes. See (Nuchelmans 1973, pp. 153–4). For a discussion of Abelard’s analysis of impersonality in the Logica Ingredientibus, and its relation to Abelard’s denial that dicta are res, see (Nuchelmans 1973, pp. 139–64).

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valid for propositions de puro inesse, in the Logica Ingredientibus he refutes that de sensu propositions are convertible at all, unless they are reduced to a personal grammatical form. The proposition ‘It is possible for every man to be white’, interpreted de sensu – that is, as having the mode functioning as predicate and an entire proposition as subject – is in fact equipollent to ‘It is possible for everything which is not white to be a non-man’, but their equipollence is not by virtue of conversion (LI De Int. 404, 326–9). The Logica Ingredientibus disagrees then with the Dialectica, both in the idea that there are nominal modal propositions that are entirely impersonal and cannot be interpreted de rebus, and in the idea that conversions are invalid for de sensu modal propositions, at least for those that cannot be reformulated in a personal construction. Another element that distinguishes the Logica Ingredientibus from the Dialectica is Abelard’s attempt to establish a logical relation of inference between de sensu propositions and their de rebus counterparts. This topic is developed in LI De Int. 416, 618–421, 751. Here, Abelard defends the idea that any de sensu possibility-proposition entails the corresponding de rebus one, whereas the opposite inference is not valid. This inference is based on Abelard’s interpretation of the de sensu reading as a per compositionem or per coniunctionem exposition. According to this exposition, as was said in the beginning of this section, a proposition such as ‘It is possible for an S to be P’ would be interpreted as ‘The thing that is S can be P while remaining S’. This is true if three criteria are satisfied: that S exists, that being S is compatible with being P, and that being P is compatible with the nature of the thing that is ‘S’ in the actual situation. If we take the de sensu interpretation in this sense, as per compositionem, Abelard says, anytime we have it that a de sensu proposition is true, its corresponding de rebus form is also true. Per compositionem possibilities are therefore a sort of proper subset of de rebus possibilities, and, in this sense, we might say that Abelard’s de sensu reading, reinterpreted as the compound reading it is in the Logica Ingredientibus, is in fact a special form of the de re interpretation. This is because Abelard interprets propositions such as ‘It is possible for S to be P’ as if their subject term ‘S’ were somehow split into two parts, one of which posits the existence of the thing that is ‘S’ and leads us to take the nature of this res into consideration, and the other of which posits the qualification ‘while remaining S’, which we have to combine with the predicate term ‘P’ in order to evaluate their compossibility. The first element of which the subject is composed remains outside the scope of the modal term. This becomes clearer when we read what Abelard says next. Having stated the general rule of inference according to which all de sensu possibilities infer their de rebus counterparts, Abelard proceeds to consider some possible counter-examples that may be advanced against it, namely,

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cases of possibility propositions that are true de sensu but false de rebus. He acknowledges two such cases: (a) ‘It is possible for every substance to be a spirit’; and (b) ‘It is possible for my son to be alive’ (uttered in a situation in which the speaker has no sons):25 It is argued to the contrary that, although it is possible that all substances are spirits (namely, it is possible that things happen as this proposition says: ‘Every substance is a spirit’, because it could happen that there are only spirits, and then this proposition would be true: ‘Every substance is a spirit’), nevertheless it is not true de rebus that every substance could be a spirit. And now, while I don’t have a son, the proposition de sensu saying that ‘It is possible that my son is alive’ seems to be true, in the sense that it is possible that it happens as this proposition says: ‘My son is living’, because perhaps it will be indeed be so, but the proposition de rebus saying that ‘My son can be alive’ is not true, because through the subject term ‘my son’ I suppose that my son exists and I connect ‘can be alive’ with the subject as if he were existent […] For this reason, it seems that de sensu affirmations about possibility do not entail de rebus affirmations, nor vice versa. And perhaps it would not be a problem if no entailment relation were there. Abelard, however, proceeds by stating that if we interpret the de sensu interpretation properly, we see that every de sensu affirmation about possibility does in fact entail its corresponding de rebus counterpart. What he calls the ‘proper de sensu reading’ is the per compositionem one. On such an interpretation, both (a) and (b) are false de sensu, just as they are de rebus, and thus they do not constitute a counter-example to the general rule of inference established above. Proposition (a) is false per compositionem, not because ‘being a substance’ and ‘being a spirit’ are opposite predicates but because the predicate ‘being a spirit’ 25

‘Sed opponitur quod, si possibile est omnem substantiam esse spiritum, id est possibile est ita evenire ut haec propositio dicit “Omnis substantia est spiritus”, quippe posset contingere ut soli spiritus essent et tunc vera esset haec propositio “Omnis substantia est spiritus”, nec tamen ideo verum est de rebus quod unaquaeque substantia possit esse spiritus. Sed et, cum nullum filium habeam, propositio vera videtur de sensu quae ait “Possibile est filium meum vivere”, id est “Possibile est ita evenire ut haec propositio dicit ‘Filius meus vivit”’, quia adhuc fortasse ita continget; nec tamen vera est de rebus quae ait “Filius meus potest vivere”, quippe per subiectum quod est “filius meus” positionem existentiae filii mei facio et quasi ipsi exsistenti “posse vivere” copulo. [...] Ideoque nec affirmationes “possibilis” de sensu videntur inferre affirmationes de rebus, sicut nec e converso. Ac fortasse nil obest si nulla sit inferentia’ (LI De Int. 417.634–418.653).

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is incompatible with the nature of some of the things that are currently substances. On the other hand, proposition (b) is false per compositionem because it fails to satisfy the presupposition of existence that is implicitly carried by the subject term ‘my son’, which is a non-denoting term in the actual situation. From Abelard’s analysis of these two propositions interpreted per compositionem, it is clear that he intends the proposition’s quantification, as well as the existential import posited by the proposition’s subject, as falling outside the scope of the modal operator, even in the case of the de sensu interpretation. The domain of individuals over which the quantifier in (a) ranges is that of actual substances, not of possible ones. Thus, the proposition’s truthvalue depends on the natures that substances have in the actual situation, and because some of these natures are incompatible with being spirits, (a) turns out to be false both when taken de re and when taken de sensu (intended as per compositionem). Expounded de sensu per compositionem, the meaning of these two propositions is the following: (a*) Every (actually existing) substance can be a spirit while remaining a substance. (b*) My son (who actually exists) can be living while remaining my son. Interpreted in this way, the two propositions evidently entail their de rebus counterparts, which are: ‘Every (actually existing) substance can be a spirit’ and ‘My son (who actually exists) can be living’.26 26 See LI De Int. 418, 653–420, 713 on this: ‘Si bene tamen attendamus qualiter de sensu eas esse dicamus, videntur semper illae de sensu inferre illas de rebus. Quod enim diximus, eas modo accipi de sensu modo de rebus, idem est quod Aristoteles per coniunctionem et divisionem accipit; ut cum dicimus “Possibile est stantem sedere” vel “non sedere”, si de sensu accipimus, tale est ut dicamus “stans potest sedere manens stans” vel “potest non sedere manens stans”; ex quibus, si concedantur, potest inferre simpliciter quod et potest sedere et potest non sedere. Quare, si quis de sensu ita accipiat “Possibile est omenm substantiam esse spiritum” vel “filium meum vivere”, falsae sunt, et ex eis necessario illae de rebus sequuntur quae etiam falsae sunt. Cum enim de sensu per coniunctionem accipiuntur, talis est: “Omnis substantia potest esse spiritus manens substantia” et “Filius meus potest vivere manens filius meus” unde possibile simpliciter sequitur. [...] Quotiens vera est affirmatio de possibili de sensu accepta, ut expositum est, hoc est per coniunctionem sumpta, vera est de rebus, simpliciter scilicet intellecta; sed non convertitur, ut ostendimus. Si quis autem opponat quod “Diem crastinam possibile est esse” vel “filium meum, cum nondum si pater”, hae propositiones, de sensu verae sunt sed non de rebus, fallitur; si enim de sensu accipiatur “Dies crastina potest esse”, tale est per coniunctionem quod possit esse manens dies crastina, quod falsum est; tamen verum est quod diem crastinam possibile est esse; nam, licet non sit dies crastina, sub hoc tamen nomine iam manet et si de ea non praedicetur. Ideoque nam vere dici potest et “Dies crastina erit” et “Possibile est ipsam esse”. At vero non ita “Filius meus erit” vel “filium meum possibile est esse” vera est,

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Because, according to Abelard, the presupposition of existence in an affirmative categorical is posited by the subject term (cf. Chapter 5), the fact that this term is outside the scope of the modal operator makes it so that (a*) and (b*) cannot be true per compositionem unless their subject has an existing referent in the actual situation. The signification of the two terms ‘every substance’ and ‘my son’ included in the two per compositionem modals is the same as the one they have in the corresponding simple claims ‘every substance is a spirit’ and ‘my son lives’. To use Abelard’s way of formulating the de re/de sensu distinction, we might say that (a*) and (b*) are still de re in the sense that they are about the same things that the corresponding propositions de puro inesse are also about. As Knuuttila also suggests,27 it thus seems that Abelard’s per compositionem reading is in fact subsumed under his de rebus reading. This was noticed by Thom as well, who suggests that this explanation of the per compositionem reading may indicate ‘a desire on Abelard’s part to assimilate de sensu propositions with his preferred de rebus model and a reluctance on his part to acknowledge them as exhibiting a genuinely distinct form’.28 Another possible reading of (a) and (b), corresponding more closely with what we today call de dicto, is the one whereby the modal operator has a wider scope that also includes existential presupposition and quantification. In this case the domain of possible individuals does not necessarily coincide with the actual one, and we may truly affirm that (a**) ‘A situation is possible in which all existing substances are spirits’ or (b**) ‘A situation is possible in which I have a living son’. As I said at the beginning of this section, it is not clear whether Abelard entirely acknowledged the distinction between this de dicto reading and the one that he calls de sensu per compositionem. Certainly, he did not explicitly point out that per compositionem is just one possible reading de sensu, and he never considers systematically de sensu sentences without existential import or ranging over a domain of individuals different from the actual one. Whether or not the domain of individuals involved in de sensu modal propositions coincides with the actual one became a matter of debate in the mid12th century, perhaps under the influence of some passages from the Logica Ingredientibus. In the Introductiones Montane Maiores, for instance, the author seems to accept both the de rebus and de sensu readings as correct and consistent interpretations of modals, although he denies that the latter could be used in syllogisms. Unlike Abelard, he maintains that there are some modal

27 28

quippe nondum cadit sub oratione subiecta; ideoque neque de rebus haec modalis vera est neque de sensu.’ Cf. (Knuuttila 1993, p. 86). (Thom 2003b, p. 46).

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propositions, for example, ‘It is possible for every animal to be a man’, that are true interpreted de sensu, even though they are false de rebus.29 Interpreted de sensu, this proposition means that ‘It is possible what this proposition says “every animal is a man”’ (Possibile est quod ista dicit ‘omne animal est homo’). By taking this to be true, the author of the Maiores seems to hold an interpretation of de sensu that is different from Abelard’s per compositionem, in which the quantified subject, ‘every animal’, denotes other individuals than the actual existing animals. Because the part of the Maiores that discusses modalities was presumably written no earlier than 1150,30 it is likely that their author knew Abelard’s position on de sensu in the Logica Ingredientibus and was perhaps directly confronting it. A similar position is reported in the Glossae Doctrinae Sermonum (H15, in Marenbon’s catalogue), an anonymous commentary on De Interpretatione that is presumably connected to the teachings of Alberic and was probably written between 1130 and 1140. According to the author, it is the opinion of some that modal propositions such as ‘It is possible for every man to be white’ should be interpreted as saying that ‘What this proposition says is possible: “every man is white”’, the truth of which is justified with the idea that ‘It might happen that only white men will exist’ (Potest contingere quod soli homines albi erunt). The author points out that this claim should not be exposed as if the quantified term ‘every man’ referred to the things that are men in act; rather, this term is included in the scope of possibility, in this way: ‘It is possible of everything which is a man that it be white’ (Et non exponunt secundum ea quae sunt in actu, sed dicunt totum debere sic exponi: ‘possibile est de omni eo quod est homo quod ipsum sit album’).31 More clearly than the Maiores, the author of the Glossae suggests that if we interpret such propositions such as de sensu, the domain of objects is ampliated by the term ‘possible’. 29 See Anonymous, Introductiones Montane Maiores in (Bos and Spruyt 2017, p. 301, 25–31): ‘Si enim de sensu exponeretur, iam minime sequeretur, quamvis vera sit ista propositio de sensu exposita “sed omne animal esse hominem est possibile”, quia possibile est quod ista dicit “omne animal est homo”, et cum ea vera sit assumptio haec “sed omnis asinus est animal”. Non tamen sequitur “omnem asinum possibile est esse hominem”. Si vero prima de rebus exposita vera esset, necessario sequeretur; sed falsa est de rebus. Falsum enim est “omne animal possibiliter fit homo.”’ 30 See (De Rijk 1966, pp. 1–57); (Bos and Spruyt 2017, pp. xii–xiii). Cf. also (Binini 2020a) on the relation between the Maiores and Abelard. 31 Anonymous, Glossae Doctrinae Sermonum, in (Abaelard 2010a, pp. 218, 605–219, 611): ‘Sunt autem qui huiusmodi propositiones accipiant, scilicet “Possibile est omnem hominem esse album”, id est “possibile est quod dicitur hac propositione: Omnis homo est albus”, quia leviter potest contingere quod soli homines albi erunt, nec tamen tunc significabit aliud. Et non exponunt secundum ea quae sunt in actu, sed dicunt totum debere sic exponi: “possibile est de omni eo quod est homo quod ipsum sit album.”’

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In neither of these two works, however, is the distinction between the de sensu and the per compositionem reading of modals explicitly demarcated and systematized. As far as I know, the only source from the mid-12th century that seems to differentiate between the de dicto reading, on the one hand, and the per compositionem, on the other, is the anonymous commentary on De Interpretatione labelled H21, also called ‘Summa Periermeneias’ by its author. Although interpreting the compound reading as Abelard does in the Logica, that is, as if per compositionem possibilities were a subset of divided possibilities and only involved the domain of actually existent objects, the author used the de dicto interpretation to consider situations in which the domain of objects differs from the actual one.32 Summing up, the distinction between de rebus and de sensu modalities in the Logica Ingredientibus is proposed as a distinction between two alternative – but equally valid – interpretations of modal propositions. Differently from the Dialectica, Abelard does not polemically refer to the de sensu interpretation as an inconsistent reading held by his Master, and although he still maintains a preference for modalities de rebus, he also suggests that there are nominal propositions that can be interpreted only de sensu. These are propositions that are entirely impersonal and which therefore cannot be rephrased as having an adverbial and personal construction. As was shown in Chapter 2, the relation between adverbial and nominal modals was a matter of lively debate in logical sources from the early 12th century, and it is significant that Abelard – who first identified the difference between the two kinds of modal merely as a matter of their grammatical construction – arrived through his reflection on impersonal sentences in the Logica at a very different position, according to which adverbial and nominal modals differ more profoundly, not only grammatically but also with respect to their logical form and meaning. Although he admits that the de sensu interpretation is a valid reading of modals, Abelard points out that there are difficulties connected to this interpretation, for instance, their lack of quantity and their unsuitability for conversion. As we saw, these objections to the de sensu reading were common in Abelard’s time, and they were raised especially in the context of considering the suitability of nominal modal propositions for use in syllogisms. Like many other medieval logicians, Abelard thus holds that Aristotle’s modal syllogistics is valid only when read de re. As we have also seen, Abelard’s discussion on the relation between de sensu and de rebus possibilities encouraged him to consider issues concerning the existential import of modal propositions, a problem that he undertakes in a sophisticated – and probably unprecedented – way. This topic will be the subject of the next chapter. 32

See (Binini 2020a) on this.

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The Existential Import of Modal Propositions Before considering the rules of inference governing the logic of modal propositions, something should be said about how Abelard deals with existential import and empty terms within his modal system. The issue is not unproblematic, because Abelard’s position on the topic is not always consistent.1 His two main logical works – the Dialectica and the Logica Ingredientibus – differ considerably on this matter, which indicates a development in Abelard’s thought. Moreover, Abelard seems to have been torn between different, conflicting views concerning the attribution of modalities to non-things: on the one hand, he follows his contemporaries in admitting that we can truly predicate possibilities about things that do not exist or will exist in the future, inasmuch as the predication of modal terms does not amount to an attribution of properties to such things (cf. Chapter 3, Section 1 in this volume). On the other hand, the idea of ascribing modalities to non-things seems incompatible with the modal semantics that Abelard comes to refine in the Logica Ingredientibus, according to which modalities should essentially be interpreted de re. Finally, in the Logica Abelard envisages a number of logical problems that would follow from admitting empty terms in modal propositions, problems that essentially emerge when looking at modal claims within the wider framework of Abelard’s logic for categorical propositions, and particularly in connection with his treatment of negative categoricals. As we saw in Chapter 3, logicians of Abelard’s time had a significant interest in the modalities of non-things and were generally inclined to admit the predication of the modal noun ‘possibile’ of statements concerning non-existent items, such as future or even impossible substances. In the Dialectica Abelard explicitly affirms that:

1 So far only a few scholars have addressed the problem of existential import in Abelard’s modal logic. Paul Thom (2003b) has suggested that all de rebus propositions have existential import, according to Abelard. However, he does not go into the details of this assumption and does not explain how Abelard’s system of equivalences and oppositions can be valid in spite of this. Other interpreters, such as Michael Astroh and Roberto Pinzani, recognize that there are problems connected to the existential presupposition in Abelard’s modal propositions and admit that the problem requires further discussion, which, however, they do not undertake; cf. (Astroh 2001) and (Pinzani 2003). I have explored the question of existential import in Abelard’s modal logic in some depth in (Binini 2018). © koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_009

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there are many [modal nominal] affirmations that are true even though they are about non-existent things […]. Of this sort of modals, the following are true: ‘it is possible for my future son to exist’, ‘it is possible for a chimaera not to exist’ or ‘it is necessary for chimaeras not to be human’.2 The idea that modalities could be truly attributed to non-existent things was commonly brought up to justify the thesis that modal terms such as ‘possible’ and ‘necessary’ do not signify forms or properties inhering in substances (cf. Chapter 3, Sections 1–2 above). In the Logica, as we will see, Abelard argues instead for the opposite view, namely, that no modal proposition is true unless its subject term denotes something that exists in the actual situation. Besides, Abelard states that the laws of inference and equipollence between modal propositions are only valid under the condition that all terms included in them have an existing referent. The modal system advanced in the Logica, thus, is only meant to work for propositions whose subject terms actually denote. Abelard arrives at the point of modifying the views he previously defended in the Dialectica concerning existential import in modal logic after considering some problems connected to the scope of modal terms and to the logical relationship between possibility and necessity, as we will see. Before delving into the problem of existential import in modal logic, in the following section I briefly present the way in which Abelard deals with this issue in his logic of non-modal propositions. 1

The Existential Import of Propositions de puro inesse

There are two main places where Abelard considers the question of the existential presupposition of simple categorical propositions: when offering his theory of negation (Dial. 173–84); and when discussing Boethius’ rule of conversion by contraposition (LI De Int. 400, 240–401, 249). On these two occasions Abelard opts for two different solutions to overcome the problems raised by empty terms in categorical logic. In this section I will try to retrace 2 Dial. 204, 1–12: ‘Multae verae sunt affirmationes huiusmodi etiam de non-existentibus rebus, quae, cum non sint, nullorum accidentium proprietates recipiunt. Quod enim non est, id quod est sustentare non potest. Sunt itaque huiusmodi verae: “filium futurum possibile est esse”, “chimaeram possibile est non esse”, vel “necesse est [chimaeram] non esse hominem”; nihil tamen attribui per ista his quae non sunt, intelligitur, sed, ut superius dictum est, per “possibile” id demonstratur quod natura patiatur, per “necesse” quod [dicit] exigat et ­constringat.’

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both solutions and consider whether either is applicable in the case of modal propositions. Regarding simple propositions, Abelard’s idea – not unusual among medieval logicians – is that all affirmative propositions carry an implicit presupposition of existence, while the corresponding negative propositions do not. Affirmative propositions such as ‘Socrates is a stone’ or ‘Every man is an animal’ must thus be read as saying: ‘Socrates, who exists, is a man’ and ‘Men exist and everyone of them is an animal’. In a situation in which there are no men (e.g. before creation, as Abelard often says), both propositions would turn out to be false. Although this seems to be Abelard’s usual interpretation of affirmative categoricals de puro inesse, there are nevertheless a few passages that could be problematic for this interpretation, since they suggest that some affirmative propositions might in fact be true even if their subject term is empty. For instance, Tweedale notices that Abelard takes propositions such as ‘The chimaera is a chimaera’ to be true.3 Also some other propositions, such as ‘Homer is a poet’, ‘A chimaera is thinkable’, and ‘The chimaera does not exist’, are considered true by Abelard in some passages of the Dialectica (e.g. Dial. 135, 9–138, 26; 162, 16–8; 167, 6–169, 28). As Jacobi has shown, however, Abelard justifies the truth of these propositions by saying that they are translatable into a different structure, which would include a denoting subject. The proposition ‘Homer is a poet’, for instance, might be rephrased into a sentence about an existing poem written by Homer (Dial. 135–6; 168, 11–7). The proposition ‘A chimaera is thinkable’, on the other hand, is translated into a sentence about a person who imagines a chimaera (Dial. 136, 32–6; 168, 21–5). In this way, Abelard attempts to justify the intuitive truth of some propositions whose implicit import is not satisfied.4 That for Abelard implicit import is included in all affirmative propositions de puro inesse seems thus established on good grounds. What about negative categoricals? In the Dialectica Abelard famously distinguishes between two ways of negating a proposition such as (a) ‘Socrates is a stone’. The negative particle can either be applied to the copula, as in (a*) ‘Socrates is not a stone’ (Socrates non est lapis), or it can be applied to the entire affirmation, as in (a**) ‘It is not the case that Socrates is a stone’ (Non Socrates est lapis). Abelard calls the first negatio separativa or remotiva and says that its semantic role is to separate the subject from the predicate, that is, to indicate that the things signified by these two terms are not actually conjoined. On the other hand, the author 3 See (Tweedale 1976, p. 336). 4 Cf. (Jacobi 1986, pp. 157–8).

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refers to the second sort of negation as negatio extinctiva or destructiva, saying that its semantic function is to destroy or extinguish the entire sense of the proposition to which it is applied.5 Separative and extinctive negation behave differently with respect to existential import. Consider again proposition (a). According to Abelard, there are two conditions that must be satisfied for it to be true: first, that the subject term ‘Socrates’ does not fail to denote; and second, that the things signified by the subject and the predicate are actually conjoined. Consider now (a*), the meaning of which could be made explicit by saying: ‘Socrates, who exists, is not a stone’. Again, we have two conditions for the truth of proposition (a*): that the subject term is not empty, and that the things signified by subject and predicate are actually separated. In proposition (a**), instead, the negative particle is applied propositionally, so that both the connection between subject and predicate and the existential import fall within its scope, as if it were said: ‘It is not the case that: Socrates, who exists, is a stone.’ This is true either when Socrates does not exist or when he exists but the property of being a stone does not inhere in him. Having an empty subject is thus a sufficient condition for the truth of negative propositions of this sort.6 Abelard’s theory on the existential import of these claims is derivable from his discussion of negation in Dialectica 173–184, where he argues, against Boethius, that the proper negation of a universal proposition such as ‘Every man is an animal’ (Omnis homo est animal) would then be ‘Not every man is an animal’ (Non omnis homo est animal), and not, as Boethius proposed in his commentary of De Interpretatione, the particular proposition ‘Some man is not animal’ (Quidam homo non est animal). This last proposition, where negation is posited separatively, contains an implicit import and would thus have the same truth-value as the universal affirmation in a situation in which men do not exist. For this reason, Abelard insists that only the negatio exstinctiva can 5 On Abelard’s theory of extinctive negation, see, in particular, (Martin 1991) and (Martin 2004b). As Martin has argued, Abelard seems to conceive of extinctive negation as a truthfunctional propositional operator. This is because extinctive negation is applied to an entire proposition and renders a proposition as its value. Also, extinctive negation might be iterated or combined with other connectives: for instance, we may apply an extinctive negation to a proposition that already includes a separative negation, for example, by saying ‘It is not the case that some man is not an animal’ (Non quidam homo non est animal), or we may formulate a sentence that contains a double extinctive negation, such as ‘It is not the case that not every man is an animal’ (Non non omnis homo est animal). On this point, see (Martin 2004b, p. 167). 6 On the different behaviour of separative and extinctive negation with respect to existential presupposition, see also (Wilks 2008, pp. 108–9).

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be used to create a proper relation of contradictoriness between quantified propositions, because it is only by means of propositional negation that we obtain, from any affirmative claim, its proper dividens. As is well known, Abelard’s distinction between two sorts of negation impacts his formulation of the traditional square of oppositions. Criticizing the square offered by Boethius, Abelard suggests a new formulation of it, which he considers a more accurate interpretation of Aristotle’s position in De Interpretatione, where both the negative universal proposition and the negative particular are formulated using external negation (this new square is represented in Figure 3). We might alternatively represent Abelard’s system of inferences between affirmative and negative categoricals by means of a ‘rectangle of oppositions’, which takes into consideration the relations between separative and extinctive negation, as Martin has proposed.7

figure 3 Abelard’s reformulation of the square of opposition 7 See (Martin 2004b, p. 168). Even if Abelard is very clear in saying that affirmative universal propositions must be negated by applying an extinctive negation to their whole content, he is less explicit about the proper way of negating particular affirmatives such as ‘Quidam homo est albus’. In a passage he suggests that their proper contradictory would be the negative universal proposition ‘Nullus homo est albus’, which, as he states, must be understood as having exactly the same meaning as ‘Non quidam homo est albus’, because the term ‘nullus’ in fact includes an extinctive negation (Dial. 177, 24–36). In other places, however, Abelard s­ uggests

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By resorting to extinctive negation and to the attribution of existential import to affirmative claims only, Abelard was able to provide a system of inferences for propositions de puro inesse, whose validity is also preserved when empty terms are included. Even in a situation in which a term fails to denote, propositions would still maintain the same relations of contradiction, contrariety, and subalternation.8 Another place where Abelard confronts the problem of existential presupposition within categorical logic, as was mentioned, is when he deals with Boethius’ rules for conversion by contraposition. According to Boethius, a proposition such as (b) ‘Every man is an animal’ is equipollent to (b*) ‘Every non-animal is a non-man’, and the two should thus have the same truth-value in all possible situations. If we evaluate them in a situation in which there are no men, however, we see that, whereas (b) is false, because its implicit import is not satisfied, (b*) turns out to be true, for everything that exists is a non-man in such a situation. The presence of empty terms, then, seems to put contraposition at risk, for a proposition that contains an empty subject is not generally equipollent with its converse. Abelard’s proposal as a way out of this difficulty is to restrict the validity of conversion by contraposition, which he still maintains as a rule of inference in his logic, but only under the conditions that all terms included in propositions actually denote.9 Abelard is not the only logician of his time to notice the problems raised by admitting Boethius’ conversion by contraposition, once taken in a pair with empty terms. We may also find traces of this idea in Garland’s Dialectica (57, 20–63, 34), where Garland notices that it would be problematic to admit conversions for propositions containing terms that are predicable of everything that exists (such as ‘substantia’), for these would convert into propositions containing non-denoting terms (‘non-substantia’). The rules of conversion by contraposition do not seem to hold for propositions of this sort, Garland says. It is not clear, however, whether Garland thinks that propositions containing empty names are non-significant propositions, since they contain parts that fail to refer, or that they are significant but false. For Abelard, propositions that contain empty terms are certainly significant – for terms have signification even if they do not have a referent – but they are false if their quality is affirmative. that propositions introduced by ‘nullus’ must be interpreted separatively or ‘remotely’ (e.g. Dial. 174, 18–23). 8 For a discussion of Abelard’s square (in opposition to the one of Boethius), see (Wilks 2008, pp. 108–9) and (Martin 2004b). 9 Cf. also (Binini 2018) on this.

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Summing up, we have seen that on the two occasions where he considers the existential import in categorical propositions, Abelard advances two different strategies to deal with the problem of empty terms. The first is to say that the satisfaction of an implicit existential presupposition is a necessary condition for the truth of affirmative propositions but not for the truth of negative ones, if negation is applied properly – that is, extinctively. This move allows him to maintain the system of inferences summarized by the traditional square of opposition and to extend its validity to propositions that contain empty terms (which could not be done in Boethius’ logic). The second strategy is to restrict the validity of certain logical rules (e.g. conversions) to those propositions that do not contain empty names. In the following sections we will see that Abelard resorts to both of these strategies when dealing with existential presuppositions in modal logic. 2

The Existential Import in de rebus and de sensu Modal Claims

In a famous passage from the Logica Ingredientibus Abelard states that the proposition ‘It is possible for my son to live’ (Possibile est filium meum vivere), although possibly true de sensu, is false de rebus if the speaker has no sons, because by positing the subject term ‘my son’ we are implicitly also positing the existence of the thing to which the term refers: The proposition ‘It is possible for my son to live’—which means ‘It is possible for what this proposition says, “My son lives”, to happen’—seems to be true de sensu even if I have no sons, because it might be the case that this will indeed happen. However [the proposition] that says: ‘My son possibly lives’ is not true de rebus, because by means of the subject term I presuppose the existence of my son, and I conjoin it to the predicate ‘possibly lives’ as if my son were existing. Furthermore, when I say ‘my son does not live’, using a separative negation, we do not admit that this is true, because by means of the term that is the subject—namely, ‘son’—a presupposition [of existence] has been made, and I separate [the predicate] ‘live’ from the subject, who is posited as existing. Therefore, when [my son] does not exist, the proposition [‘my son does not live’] is false. From this it follows that the affirmative claim ‘my son possibly lives’ seems to be even more false, when taken de rebus.10 10

LI De Int. 417, 639–50: ‘Sed et, cum nullum filium habeam, propositio vera videtur de sensu quae ait: “Possibile est filium meum vivere” id est: “Possibile est ita evenire ut haec

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The passage evidently shows that Abelard interprets affirmative de rebus propositions about possibility as having import. Interestingly, he also claims that the presupposition of existence included in de rebus modal claims is posited by the subject term itself, and not by the copula that connects it to the predicate (‘per subiectum quod est “filius meus” positionem existentiae filii mei facio’). What Abelard thinks about de sensu modal propositions is not clear. At times he says that there are de sensu claims about possibility that remain true even if their subject is empty, as in the passage just quoted, and in some passages of the Dialectica (e.g. 204, 1–17). At other times he states that de sensu claims must also fulfil an existential assumption in order to be true (LI De Int. 419, 702–420, 714), and he reinforces this idea by claiming that every de sensu possibility proposition entails the corresponding de rebus one. This ambiguity perhaps has to do with the fact that Abelard is not always consistent in his analysis of de sensu modalities, which he understands at times according to a per compositionem reading and at other times according to what we now call a de dicto reading (cf. Chapter 4, Section 2 of this volume). Nevertheless, because the logical system of inferences and equipollences that Abelard provides for modal propositions is restricted to de rebus modalities, we might here set aside the problems of de sensu modal claims and focus our analysis exclusively on de rebus ones. That de rebus propositions about necessity also require the satisfaction of an implicit import in order to be true is implied by many passages from both the Dialectica and the Logica Ingredientibus. We may infer this from Abelard’s repeated assertions that propositions about necessity can only be true if their subject term refers to a sempiternal being, such as God (e.g. Dial. 193, 26–9; 195, 7–8; 201, 2–9; 201, 12–7). This assumption is related to Abelard’s idea that a proposition about necessity is true only if it is sempiternally true (see Dial. 272, 10–5; 278, 20–2; 279, 10–3; 282, 25–33, cf. Chapter 3, Section 4 and Chapter 10, Section 1 of this volume). Because a proposition such as ‘Every man is an animal’ turns out to be false when men do not exist, Abelard insists that the corresponding modal proposition ‘It is necessary for every man to be an animal’ is generally false. On the contrary, a proposition such as ‘God is immortal’ is sempiternally true, and therefore it is true to affirm that ‘It is necessary for propositio dicit ‘Filius meus vivit’”, quia adhuc fortasse ita continget; nec tamen vera est de rebus quae ait: “Filius meus potest vivere” quippe per subiectum quod est “filius meus” positionem existentiae filii mei facio et quasi ipsi existenti posse vivere copulo. Unde nec, cum dico: “Filius meus non vivit” faciens negationem separativam, pro vera eam recipimus quia in subiecta oratione, filii < mei > scilicet, positio facta est et ab eo quasi existente vivere separo; ideoque, cum non existat, falsa etiam est negatio. Ex quo multo magis falsa videtur affirmatio quae dicit filium meum posse vivere, cum de re ipsa accipitur.’

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God to be immortal’. If affirmative propositions about necessity must have a sempiternal subject in order to be true, then these propositions evidently turn out to be false when their subjects are non-denoting terms. If this is the case, then all affirmative propositions about necessity are taken to have import, just like de rebus affirmative propositions about possibility. 3

Existential Import and the Modal Square of Oppositions

Abelard is consistent in presenting, in both the Dialectica and the Logica Ingredientibus, the same schemes of logical rules for de re modal propositions. He begins by listing all possible forms of singular and quantified propositions and establishing the orders of equipollence for both. After that, Abelard arranges a scheme of logical relations of contradictoriness, contrariness, and subalternation, first for singular claims and then for quantified ones. For the sake of simplicity, I will only consider here singular modal propositions, but the same conclusions may be drawn for particular and universal claims. There are four forms of modal proposition with the same singular subject and the same mode: a. b. c. d.

‘It is possible for Socrates to be white’ (Possibile est Socratem esse album). ‘It is possible for Socrates not to be white’ (Possibile est Socratem non esse album). ‘It is not possible for Socrates to be white’ (Possibile non est Socratem esse album). ‘It is not possible for Socrates not to be white’ (Possibile non est Socratem non esse album).

These four forms generate four orders of equipollence, representing the logical relations that different modes have to one another, as shown in Figure 4. All propositions belonging to the same order are equipollent to one another, whereas the relations among the four orders are that of contradictoriness (first to third order; second to fourth order), contrariness (third to fourth), subcontrariness (second to first), and subalternation (fourth to first and third to second).11 As will be argued in more detail in Chapter 6, the system of logical relations presented by Abelard for propositions of this sort is valid, or, more precisely, valid as long as the terms contained in modal propositions are not empty. But consider now a situation in which Socrates does not exist and notice how, in 11 Cf. Dial. 199; LI De Int. 475–8 and 491–7.

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figure 4 The orders of equipollence for singular modal propositions

such a situation, some of the logical relations stated in the square would still be valid, while others would not. Let us consider first the pair of contradictory propositions (1.a) ‘It is possible for Socrates to be white’ and (3.a) ‘It is not possible for Socrates to be white’. Although Abelard is not explicit about how negation should be interpreted in modal propositions, as we will see in the next chapter, we may suppose that he intended the negative particle included in (3.a) as an extinctive negation, in conformity with his general theory of negation presented in the Dialectica. This would preserve the validity of Abelard’s relations of contradiction between modal claims because, according to this interpretation of ‘non’, the existence of the subject is a necessary condition for the truth of affirmative propositions, whereas it is sufficient for the truth of negative propositions that the subject does not exist. In the situation under scrutiny, in which the term ‘Socrates’ is empty, proposition (1.a) would thus be false and proposition (3.a) true. The relation of contradictoriness between (1.a) and (3.a) is then preserved, even when the subject term is empty, and the same is the case for all contradictory pairs stated in the square, since in all pairs we will find that one proposition is affirmative (and thus false) and the other negative (and thus true in the given situation), provided that we take negation extinctively.12 12

Abelard never explicitly says that negation should be interpreted in this way while giving his orders of opposition and equipollence for modal claims. Indeed, he does not mention the distinction between separative and extinctive negation at all in his treatises on modalities, and there are some passages from the Dialectica that may lead us to think that

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Consider now the relations of equipollence between possibility and impossibility that are offered in Abelard’s square. The two propositions (3.a) ‘It is not possible for Socrates to be white’ and (3.b) ‘It is impossible for Socrates to be white’ are said by Abelard to be equivalent. As such, they should have the same truthvalue in all possible situations. A doubt arises at this point: should we consider proposition (3.b) to be an affirmative proposition, as its grammatical structure would suggest, or is it instead a negative one? If (3.b) is affirmative, it would be a necessary condition for its truth that the subject term ‘Socrates’ were not empty. On the contrary, the non-existence of Socrates would be sufficient for the truth of proposition (3.a), which is certainly negative. If, as a general rule, we were to interpret all impossibility-propositions as affirmative propositions, it would follow that all given equipollences between possibility and impossibility fail. There is a way, however, to overcome this difficulty and preserve the equipollence between possibility and impossibility propositions. The solution consists in saying that propositions about impossibility such as (3.b) are in fact negative, despite their grammatical structure. Although Abelard does not adopt this reading explicitly, to support it we may appeal to his distinction between interpreting propositions according to their linguistic structure (secundum constructionem) and according to their meaning (secundum sensum).13 Moreover, the interpretation of (3.b) as negative is justified by Abelard’s usual definition of ‘impossible’, which, as he states, signifies nothing other than ‘not possible’.14 If we take literally this idea that impossible and not possible are the same in meaning, the two propositions (3.a) and (3.b) above would have entirely the same meaning and, as such, would be unrestrictedly equivalent. The same solution might also be applied to justify the equipollence between propositions (1.a) ‘It is possible for Socrates to be white’ and (1.b) ‘It is not impossible for Socrates to be white’. According to the reading I have just proposed, proposition (1.b) should be interpreted as containing – with respect to meaning, even if not grammatically – a double negation, so that it should be read as saying: ‘It is not the case that: it is not possible for Socrates to be white’. Abelard explicitly admits, at least in one passage, the equivalence between an affirmative proposition and the double negation of the same proposition,15 and so again propositions (1.a) and (1.b) would result in being equipollent in all possible situations, even those in which their subject term is empty. Notice,

13 14 15

he in fact interpreted negation separatively and not extinctively. I will return to this in Chapter 6. Cf. Chapter 2, Sections 2. and 3 on this distinction. See, for example, Dial. 194, 5–6; LI De Int. 395, 97–9 and 417, 632–3. See on this Dial. 179, 20–6; the passage is commented on by Martin in (Martin 2004b, p. 167).

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however, that the equipollence between (1.a) and (1.b) should be considered not as a proper mutual inference but as a mere ‘concomitance’ (comitatio, in Abelard’s terminology),16 for the two propositions have the same truth-value in all possible situations but do not have the same meaning. The relation between propositions (3.a) and (3.b) would instead be a semantic relation of mutual inference and not just an equipollence. Just like the relations of contradictoriness, then, the rules of equipollence between the possibility and impossibility described in Abelard’s modal square would also remain valid if empty terms were admitted. This is not the case, however, for the logical relations established between propositions about possibility, such as (1.a), and those about necessity, such as (1.c), ‘It is not necessary for Socrates not to be white’. In such pairs we have one side that is affirmative and the other negative, which, as was said, proves problematic when we take into account empty terms. Given the interpretation of negation adopted so far, if we consider a possible situation in which Socrates does not exist, we will have it that proposition (1.a) is false and (1.c) true. Generally speaking, if the subject term has no existing denotatum, all the aforementioned pairs, (1.a)– (1.c), (2.a)–(2.c), (3.a)–(3.c), and (4.a)–(4.c), would have one side that is true and the other that is false, and they would not be equipollent.17 I believe that Abelard, at least when writing the Logica Ingredientibus, was aware of this difficulty, and for this reason he proposed to restrict the validity of his modal system to only those situations in which the things referred to by the subjects of the propositions (actually) exist. There is one passage from Abelard’s Glossae that supports this interpretation, a passage in which Abelard clearly states that the equivalence between necessity and possibility (or necessity and impossibility) holds only insofar as non-denoting terms are not taken into account. After presenting the schemata of equipollence and opposition for modal claims, Abelard first claims that all listed equipollences between possibility and necessity should be conceived not as proper consequences (consequentiae) but as rules of concomitance (comitationes). This is because when we logically connect propositions about possibility and necessity, like (1.a) and (1.c), we are 16

17

According to Abelard, two propositions are ‘naturally concomitant’ if they have the same truth-value in every possible situation. For a proper consequentia or inferentia between two propositions, Abelard requires something more, namely, a semantic relation between two propositions, such as that the meaning (sensus) of the consequent is contained within the meaning of the antecedent. For this distinction, see (Martin 2004b). On the relationship between inferentia and comitatio in Abelard’s modal logic also, see (Thom 2003b). The same problem is raised by quantified modal propositions such as ‘It is necessary for every man to be an animal’ and ‘It is not possible for every man not to be an animal’.

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positing not a semantic relation between their meaning but a logical relation between these propositions’ truth-values. This idea is advanced in opposition to the theory of others, who maintain, on the contrary, that whenever two modal claims are said to be equipollent, they must also have the same meaning. Instead, Abelard stresses that propositions such as ‘It is possible for S to be P’ and ‘It is not necessary for S not to be P’ (and similarly their opposites, ‘It is not possible for S to be P’ and ‘It is necessary for S not to be P’) are only equipollent inasmuch as they are always true or false together, but there is no semantic relation of containment between their meanings (LI De Int. 411, 502–18). At this point in the Logica Abelard pauses to consider the logic of quantified modal propositions (414, 545–416, 610) and the inferential relations between de rebus and de sensu claims (416, 619–420, 723), an issue that leads him to return again to the question of existential import and the validity of the modal square of oppositions. In the passage that follows he states not only that the equivalence between propositions about possibility and necessity should be conceived as a mere concomitance and not as a proper consequence, but also that this concomitance is valid only under the assumption that the subject terms included in modal propositions are not empty: But it seems to me that such equipollences among modal propositions maintain their validity only under the condition that the thing [signified by] the subject term exists – for example, only while Socrates exists […] As long as Socrates exists, when the proposition ‘It is not possible for Socrates to be white’ (or ‘It is impossible for Socrates to be white’) is true, then the proposition ‘It is necessary for Socrates not to be white’ is also true, and vice versa. Since we want to understand the proposition ‘It is necessary for Socrates not to be white’ as having the intent of an affirmative categorical proposition, it is necessary, for it to be true, that there is something falling under the term that is the subject, as we recalled above. […] We concede that propositions that are different in meaning are also equipollent, in the sense that none can be true or false without the others—given that the things [they talk about] subsist. (420, 733–421, 751)18 18

‘Sed videntur nobis huiusmodi aequipollentiae modalium propositionum tantum aequipollentiam custodire re subiecti termini permanente, velut tantum dum Socrates permanet, sicut et illae quarum aequipollentiam superius ascripsit praedicato per finitum et infinitum variato. Quamdiu itaque Socrate permanente vera est: “Non possibile est Socratem esse album” (vel: “Impossibile est”) vera est etiam quae ait: “Necesse est Socratem non esse album” et e converso. Cum enim velimus in vi affirmativae categoricae accipere: “Necesse est Socratem non esse albedinem” oportet ad hoc ut verum sit rem manere sub subiecto vocabulo, ut supra meminimus. Si vero in sensu aliarum accipiamus, ut quidam

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Abelard states here that propositions about possibility and necessity are equipollent only under the condition that their subject exists, and this restriction is the result of the fact that these propositions are different in quality, so that whereas affirmative modal propositions must satisfy an existential import in order to be true, negative propositions do not. These remarks about the restricted equipollence between possibility and necessity highlight an important aspect of the way these two modes are related in Abelard’s theory of modality, an aspect to which I will return again in ­Chapter 8. According to Abelard, certain logical relations connecting the two modes ‘possible’ and ‘necessary’ may be established, but this should not be taken as if the meaning of one mode were spelled out in terms of the other. In other words, although he thinks that we may establish a logical relation between the two modalities, no semantic relation between possibility and necessity can be provided. This is in line with Abelard’s (earlier) claim that between possibility and necessity propositions there is only a mere concomitance or equipollence but not a relation of proper inferentia. As I will argue in Chapter 8, this also means that both ‘possible’ and ‘necessary’ should be taken as primitive modes in Abelard’s modal system and that the two cannot be inter-defined. This is not the case for the relation between the other modes, namely, possibility, impossibility, and contingency. Indeed, Abelard explicitly suggests that the two modes of impossibility and contingency can both be defined in terms of possibility, because ‘contingent’ has the same meaning as ‘possible’, and ‘impossible’ means nothing other than ‘not possible’ (cf. Dial. 194, 5–6; LI De Int. 395, 97–9; LI De Int. 394, 92–395, 95). These three modal terms are thus treated as inter-definable, and indeed it seems that the mode ‘possible’ could be taken as the primitive notion from which the other two are derived. On the contrary, Abelard never conceives of the relation between possibility and necessity as a sort of interdefinability. The fact that, in his view, the equipollence between possibility and necessity propositions is only maintained under certain conditions, and not unrestrictedly, confirms the peculiar character of the relation between these two notions in Abelard’s theory. I conclude this chapter by pointing out that Abelard’s awareness of the problems raised by the presence of empty terms in logic is remarkable. In noticing volunt, erit negativa in sensu: “Necesse est Socratem non esse albedinem” sicut illae et ita semper vera est cum illis. Sunt enim quidam qui omnes propositiones eiusdem ordinis in eodem sensu accipi volunt ut mutuas ad invicem consequentias habeant, alioquin ex negativa in sensu sequeretur saepe affirmativa, quippe in eodem ordine negativae affirmativis adiunguntur. Nos vero in diverso sensu eas quoque concedimus aequipollere ita ut rebus permanentibus nulla possit esse vera vel falsa sine aliis.’

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these difficulties, and in trying to provide a logical system that could take into account non-denoting terms, Abelard goes far beyond not only Boethius but also his contemporaries. Although it is true that in some sources from his time (e.g. in the Dialectica of Garland) there is some acknowledgement of the puzzles raised by empty terms for the validity of some logical rules, these are only sketchy remarks, not comparable to Abelard’s highly sophisticated discussion. Abelard’s conclusions on existential import in modal logic, however, seem, to a certain extent, to clash with what he endorses concerning the logic of categoricals de puro inesse. Whereas Abelard was able, with his reformulation of Boethius’ square of opposition, to provide a non-modal logic that would preserve its validity in the presence of non-denoting terms, he was unable to do the same for the logic of modal propositions. Empty terms, which Abelard struggled to take into account within his non-modal system, are thus ultimately excluded from his modal logic. In the next chapter I will consider in more depth the logical system that Abelard provides for propositions about possibility, impossibility, and necessity. I will return to the analysis of Abelard’s modal squares for singular and quantified modal propositions, and I will complement this with an account of his theory of modal conversions and modal syllogistics.

chapter 6

The Logic of Modal Propositions In both the Dialectica and the Logica Ingredientibus Abelard considers the logical relationships describing the behaviour of singular and quantified propositions about possibility, impossibility, necessity, and contingency. As mentioned earlier, the system of rules he designs is meant to apply to de rebus modal propositions only, and not to de sensu ones, as Abelard maintains that the de rebus reading is the appropriate and more fundamental understanding of modalities. The logical system that Abelard proposes for modal propositions presents a level of sophistication and originality unprecedented in early medieval discussions on modalities. Abelard is the first (known) medieval author to consider in such detail the logic of quantified modal claims and to delve into the difficulties raised by the use of negation, of temporal determinations, and of the existential presupposition in modals. In this and the following chapters I focus on the system of logical inferences, opposition, and equipollence arranged by Abelard for singular and quantified modal propositions, and I describe the analysis that he provides of modal conversions and syllogistics. Chapter 6 is limited to the logic of ‘simple’ nominal modals, such as ‘It is possible for Socrates to be a man’, whereas Chapter 7 investigates Abelard’s logic for temporally qualified modal propositions, for example, ‘It is possible for Socrates to be white while being a man’. In the following pages modal propositions are formulated grammatically as having a nominal construction. The standard form that Abelard uses is the one that places the subject (in the accusative case) before the nominal mode, which is, in turn, followed by an infinitive clause, such as ‘Socratem possibile est esse album’ or ‘Omnem hominem possibile est esse album’. As I have done in earlier chapters, I will translate these expressions as follows: ‘it is possible for Socrates to be white’ and ‘It is possible for every man to be white’.1 As was said in Chapter 2, logicians from the early 12th century focus their analysis on modal propositions having this structure, rather than considering their adverbial counterparts. In this respect they follow Aristotle’s example in De Interpretatione, where the philosopher states that nominal modals present more problems than adverbial ones with respect to their construction and logical 1 On the reasons for this English translation, see footnote 53, Chapter 2 above. © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_010

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properties. Abelard’s logic too is centred on propositions containing nominal modes, even though he believes that the adverbial structure would ultimately be more appropriate, insofar as it more closely mirrors the ‘deep’ structure of modal claims, which are for him fundamentally de rebus. Abelard believes, however, that nominal propositions are generally reducible, or translatable, into their adverbial counterparts, so that the difference between adverbial and nominal claims is merely at the grammatical level, and not at the semantic one. This idea is based on his analysis of the syntax of nominal modals, to which the next section is devoted. 1

Abelard on the Syntactic Structure of de rebus Modal Propositions

There are two points upon which Abelard insists in the Dialectica concerning the relation between simple and modal propositions: first, the latter are derived from the former; and second, modals differ from propositions de puro inesse only with respect to the way in which the inherence is asserted: while simple propositions assert some inherence unqualifiedly (simpliciter), modal propositions assert the same inherence cum modo (see Chapter 2, Sections 1–2 on this). This means that modal propositions do not differ from simple ones with respect to the things they deal with, for, in fact, simple and modal propositions are used to express something about the same things. Concerning the first point, Abelard says that propositions de puro inesse are prior to and more basic than modal ones and that modals ‘descend’ from them.2 The priority of simple claims may be interpreted both as a syntactic priority – namely, the grammatical structure of modal claims is ‘composed’ of a simple predication to which a certain modal term is adjoined – and as a semantic priority, in the sense that the meaning of modal propositions is construed by qualifying the inherence signified by the corresponding simple claim. The other point on which Abelard insists is that modal propositions and the corresponding simple ones are about the same things, and thus they include the same subject and predicate. In the Dialectica the relation between the two 2 See Dial. 191, 23–6: ‘Unde simplices ipsis modalibus, quasi compositis, priores sunt: ex ipsis modales descendunt et ipsarum modificant enuntiationem; in qua quidem modificatione tantum ab ipsis abundant et discrepant.’ Another passage in which Abelard refers to this priority of simple propositions over modal ones is Dial. 200, 20–2, where he says: ‘Et sunt quidem simplices natura priores quasi simplicia compositis; oportet enim prius inhaerentiam considerare quam modificare.’

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statements ‘S is P’ and ‘It is possible for S to be P’ is located precisely in this sharing of terms. With respect to this point, Abelard says, the grammatical construction of nominal modals might be misleading. Nevertheless, with respect to their sensus, propositions such as ‘It is possible for an S to be P’ have entirely the same meaning as their adverbial counterparts, such as ‘S is possibly P’.3 In order to support this view, Abelard appeals to a distinction between two levels of modal proposition: that of the grammatical, ‘surface’ structure, and that of their (deeper) meaning (cf. Chapter 2, Section 2–3 above). With respect to grammar, in a nominal proposition such as ‘It is necessary for every man to be animal’ (Necesse est omnem hominem esse animal), the mode functions as predicate, whereas the subject is the infinitive verb ‘esse’, and the two accusative terms ‘omnem hominem’ and ‘animal’ are determinations of this subject. With respect to the meaning, however, the subject and predicate terms are the same as the corresponding simple proposition ‘Every man is animal’, and the mode functions as a qualifier of the inherence between predicate and subject (or, alternatively – Abelard is not always clear on this – of the meaning of the predicate).4 I have shown in Chapter 2 that many contemporaries of Abelard offer a similar distinction between two orders of terms in nominal propositions, although they usually talk of ‘principal’ and ‘secondary’ predicate, and they do not explain this distinction – as Abelard does – in terms of a discrepancy between grammar and meaning. Having determined which terms are the subject and which the predicate in modal propositions, Abelard considers the problem of how modal propositions should be properly negated, that is, how the negative particle should be applied in order to obtain, from an affirmative modal proposition, its corresponding 3 This is what Abelard holds in the Dialectica (e.g. Dial. 193, 11–7). In the Logica Abelard thinks that the reducibility of nominal modals to adverbial ones is still possible in general and that the de rebus interpretation is still the most proper reading of nominal modes. However, he has lost confidence in the idea that all nominal modals may be rephrased as having a personal construction, for he acknowledges that there are some propositions that are impersonal with respect to both their grammar and meaning. Propositions of this sort can only have a de sensu interpretation, and they therefore have a different semantic relation to the propositions de puro inesse from which they derive. I explained this point in Chapter 4, Section 2. Abelard, however, is not interested in the logic of these purely de sensu propositions, and he restricts his system to those propositions that can be interpreted either de rebus or de sensu per compositionem, as I have argued in Chapter 4. 4 Cf., for instance, Dial. 191, 26–30: ‘Cum autem in sensu modales cum simplicibus eosdem retineant terminos, in his tamen modalibus quae casuales habent modos, quantum ad constructionis materiam alii considerantur termini, ut cum dicimus: “possibile est Socratem episcopum esse”, “esse” quidem subicitur, et modus ipse, id est “possibile”, praedicatur.’ The same idea is then repeated in the Logica Ingredientibus (e.g. LI De Int. 396, 124–42).

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table 4  Abelard's analysis of modal propositions' terms, with respect to grammar and meaning

Terms ‘secundum constructionem’ Terms ‘secundum sensum’

Necesse est

Omnem hominem

esse

Animal

Predicate

Determination of the subject

Subject

Determination of the subject

Qualifier of the predicate

Quantified subject

Copula

Predicate

negative one. The problem of assigning negation to modal propositions is inspired by what Aristotle says in De Interpretatione (12, 21a39–22a3), and indeed Abelard’s treatment of this topic quite closely follows Aristotle’s proposal, which was also adopted by Boethius and by Abelard’s contemporaries. According to Aristotle, the usual way of assigning negation in a proposition is by applying the negative particle to the term that functions as predicate. Because in nominal modal propositions there are two terms possibly functioning as predicates, there are also two different ways of assigning negation in them: either we appose the negative particle to the term that is the predicate in the infinitive clause, or we attach negation to the modal term, that is, to the grammatical predicate. Aristotle argues that, if we apply negation in the first way, we do not obtain a proper relation of contradiction between affirmation and negation, because two propositions such as ‘It is possible for Socrates to be white’ and ‘It is possible for Socrates not to be white’ might be simultaneously true. The proper way of assigning negation in nominal modal propositions must therefore consist in applying the negative particle to the mode itself, saying, for example, ‘It is not possible for Socrates to be white’. Abelard closely rehearses Aristotle on this point, by stating that negation must be applied to the term that is the predicate secundum constructionem, that is, with respect to the grammatical construction. Although Abelard’s answer is not per se original, it is still interesting to compare his approach to the problem of applying negation in modal propositions with his general theory of negation, which he deals with in Dial. 173–184.5 5 I have summarized the main points of Abelard’s theory of negation in Chapter 5, Section 1. For a general interpretation of this theory and a comparison with Boethius’ understanding of negation, see (Martin 2004b, pp.158–92).

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What Abelard says about negating modal claims seems, in fact, to conflict with the idea that he advances elsewhere, namely, that in order to obtain the correct relations of contradictoriness the negative particle must always be applied not to the proposition’s predicate or copula but rather to the entire propositional content. As mentioned in Chapter 5 above, Abelard distinguishes between two kinds of negation, which he calls ‘separative’ and ‘extinctive’ (or ‘destructive’). He says that to properly negate a proposition means to obtain its corresponding contradictory proposition, that is, to obtain another proposition that is never simultaneously true or false with the first. Contradictory p ­ ropositions are also called ‘dividentes’, inasmuch as they ‘divide’ truth-values among them. Abelard thinks that for each proposition there is always one, and only one, proposition that is its proper dividens (Dial. 173, 23–5). In opposition to the tradition of Aristotle and Boethius, who said that negation must always be applied either to a predicate or a copula, Abelard argues in the Dialectica that the only correct way to negate a categorical proposition is by means of extinctive negation, which destroys the whole meaning of the affirmation to which is applied (Dial. 178, 28–32; 180, 2–3), and he maintains this for both singular and quantified categorical propositions (Dial. 179, 34–180, 13). According to Abelard, the extinctive use of the negative particle is not only to be applied to simple categorical claims, but to claims of any sort, and therefore, we would suppose, also to modal ones. However, Abelard is not always consistent in applying this theory, and, in particular, he seems not to apply it to modal claims. In fact, in his treatises on modals Abelard seldom mentions the distinction between separative and extinctive negation, rather arguing that, in nominal modals the negative particle should be applied to the proposition’s predicate, as was said. This may lead us to think that, when we consider propositions such as ‘Non possibile est Socratem esse album’, the negative particle must be conceived as a separative negation and not as an extinctive one. Evidence for this interpretation is provided by at least one passage from the Dialectica, where Abelard says that in propositions of this sort the negative particle ‘separates’ the predicate (namely, the modal term) from the subject, which is identified with the verb of the infinitive clause.6 Another passage that goes in the same direction is Dial. 199, 13–4, where Abelard argues for the validity of the inference ‘If it is not possible for Socrates not to be white, it is possible for Socrates to be white’. If the negative particle included in the antecedent were interpreted extinctively, the

6 See Dial. 192, 26–8: ‘Oportet enim ut in istis negatio praedicatum removeat, modum scilicet, ab eodem subiecto, sive scilicet “esse” sive “non esse”.’

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inference would turn out to be invalid, because if Socrates did not exist, the antecedent would be true and the consequent false.7 Nevertheless, the terminology Abelard uses in other passages suggests that, at the time in which he wrote his analysis of modal propositions, he had already developed his theory of extinctive negation. For instance, he says that when the negative particle is placed before an affirmative proposition, as in ‘Non possibile est Socratem esse lapidem dum est lapis’, the negation could (and should, if we want the modal square of opposition to be valid) be applied to the whole sense of the proposition that it precedes, in order to ‘extinguish’ this sense.8 A similar position is held in LI De Int. 432, 1073–83, where again Abelard claims that in determinate modal propositions the pre-posed negation could be interpreted as removing the entire content of the proposition to which it is applied (‘totum auferat’). It is then plausible that Abelard had already developed his distinction between separative and extinctive negation before construing his logic of modalities. If this is the case, why did he not make consistent use of extinctive negation in his treatise on modals? Abelard’s statement that in modal propositions negation must be applied to the predicate, so as to separate it from the subject, might be explained by his wish to remain faithful to the Aristotelian position in De Interpretatione 12, where Aristotle says that, in any given proposition, the negative particle must always be attached to the term that is the predicate. Another possible answer could be that, when initially presenting his logical system for modal propositions, Abelard did not feel the need to distinguish between different sorts of negation because he did not take into consideration cases in which the semantics of negative propositions are relevant, such as cases concerning non-denoting terms. It was indeed the problem of empty terms that led him to develop his theory of extinctive negation in the first place (cf. Chapter 5, Section 1 above). What we may conclude, aside from speculation, is simply that textual evidence is controversial on how Abelard interpreted negation in his modal logic. If we want to read Abelard charitably, however, and make his discussion about negation in modal claims consistent with his general theory, we should interpret propositions such as ‘Non possibile est Socratem esse album’ 7 Cf. Chapter 5, Section 1 for the semantics of negative propositions. 8 See Dial. 208, 30–209, 11: ‘Sed contra dico quia, si aequipollentias servare volumus, oportet in negativis non modum, sed cum determinatione ipsa removeri. Cum ergo dicimus: “si falsa est Socratem esse lapidem dum est lapis, tunc vera est non possibile est Socratem esse lapidem dum est lapis”, per negativam particulam totum propositionis sensum exstinguimus, idest ipsum praedicatum cum determinatione ipsa removemus.’ (my e­ mphasis)

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and ‘Non necesse est Socratem esse album’ as if negation were applied extinctively, namely, as saying ‘Non: possibile est Socratem esse album’. This also allows us to preserve the validity of the relations of contradictoriness and opposition that Abelard establishes between modals, as was seen in Chapter 5, Section 2.9 Having settled the issue concerning the quality of modal propositions, we should say something about their quantity. According to the usual framework adopted by early 12th-century logicians, the quantity of a proposition depends on its subject term. As was seen in Chapter 2, Section 2 of this volume, many authors of Abelard’s time interpreted nominal modals as if their subject were the verb of the infinitive clause to which the mode is attached, or alternatively the entire phrase (oratio) of which this mode is predicated. They observe that this subject is invariable in quantity and therefore question the suitability of claims of this sort for use in syllogisms or conversions. Some authors conclude that, in fact, nominal modal propositions cannot be properly used in modal syllogistics and do not follow the standard rules of conversions, and more generally that they do not behave logically like their adverbial counterparts (see Chapter 2, Section 3). Abelard also notices that if we take into consideration the term that is subject ‘with respect to grammar’, modal propositions would be invariable in quantity (LI De Int. 397, 168–398, 174). However, he claims that in nominal modals quantity should always be assigned on the basis of the term that is the subject with respect to meaning (see LI De Int. 398, 174–188; Dial. 193, 6–13), which is in fact variable, being universal (e.g. ‘For every man it is possible to run’), particular (‘For some man it is possible to run’), indefinite,10 or singular (Dial. 192, 31–3; LI De Int. 398, 174–7). The variation of nominal modals according to quantity and quality provides us, for each modality, with a list of four singular modal propositions and eight quantified modal propositions. The meaning of these de rebus modals is interpreted by Abelard on the basis of a ‘nature-based’ modal semantics, according to which a proposition such as ‘It is possible for every (some) man to be white’ (Omnem/quendam hominem possibile est esse album) is taken to mean

9

10

Another controversial issue is whether the negation in modal propositions de non esse, such as ‘Possibile est Socratem non esse album’, is separative or extinctive. Again, Abelard never makes his opinion clear on this point in either the Dialectica or the Logica Ingredientibus. Wciórka convincingly argues, however, that in this case negation should also be interpreted extinctively in order to preserve the validity of Abelard’s system (Wciórka 2012, pp. 70–89). Abelard will later say that all indefinite propositions are equivalent to particular ones, so we can ignore them when dealing with quantified modal logic.

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‘Every (some) man has a nature that is not incompatible with being white’. This semantics will be explored in detail in Part III of this book. The logical relations of opposition and equipollence between singular and quantified modals are offered by means of different squares of opposition, which will be considered in the next section. 2

Oppositions and Equipollences

Let us first consider various sorts of modal proposition, varied with respect to mode (possible, contingent, impossible, necessary), subject (de esse, de non esse), quality (affirmative and negative), and quantity (singular, particular, universal). There are, for each mode, four singular modal propositions and eight quantified ones. The orders of equipollence between propositions of different modalities are based on the schematic orders of inference provided by Aristotle in De Interpretatione 12 and 13, which are: Possibile est esse – Contingit esse – Non impossibile est esse – Non necesse est non esse; Possibile est non esse – Contingit non esse – Non impossibile est non esse – Non necesse est esse; Non possibile est esse – Non contingit esse – Impossibile est esse – Necesse est non esse; Non possibile est non esse – Non contingit non esse – Impossibile est non esse – Necesse est esse. (cf. LI De Int. 409, 459–410, 471) After rehearsing Aristotle’s orders of equipollence among modes, which do not take quantification into consideration, Abelard moves on to consider the various combinations of mode, quality, and quantity, varying propositions first for singular subjects and then for universal and particular ones. Beginning with singular modal propositions, Abelard establishes the four orders of equipollence and a modal square of opposition, represented in Figure 5 (see Dial. 198, 35 ff.; LI De Int. 409, 459–410, 475). Propositions belonging to the same order are equipollent to one another. Moreover, propositions of the first order are contradictories to those of the third, and the same relations of contradictoriness hold between the second and the fourth order (Dial. 199, 4–5 and LI De Int. 411, 491–4). Propositions in the third and fourth orders are instead in a relation of contrariness: in other words, they can be simultaneously false but not simultaneously true. Subcontrariety holds between propositions in the second and first order, which cannot

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figure 5 The square of opposition for singular modal propositions

be simultaneously false, although they can be simultaneously true (see LI De Int. 411, 494–7). Finally, a sort of subalternation may be established between propositions of the fourth order with respect to those of the first, and between propositions in the third with respect to those of the second. In both cases the first entail the latter, but this implication is not convertible. Abelard gives a justification for this last rule of subalternation: his argument rests on the principle, repeated in both the Dialectica and the Logica, that if two propositions ‘p’ and ‘q’ are equipollent, everything that is implied by ‘p’ is also implied by ‘q’, and anytime ‘p’ follows from another proposition, ‘q’ also follows from that proposition.11 Abelard is consistent in presenting, in both the Dialectica and the Logica Ingredientibus, the same schemes of rules. However, only in the Logica does he explicitly set these rules in the form of a square of oppositions resembling the one commonly given for propositions de puro inesse. Whereas there are four types of singular modal proposition, and consequently four orders of equipollence, quantified de rebus propositions are doubled in number and thus arranged within eight orders of equipollence (Dial. 199, 25; LI De Int. 412, 518–413, 538). The following rules of equipollence 11

‘Sunt enim omnes cuiuslibet ordinis propositiones ad se aequipollentes; quicquid autem ad unam sequitur aequipollentium, et ad aliam; vel ad quodcumque una sequitur, et alia.’ (Dial. 199, 5–24; the same principle is stated in LI De Int. 410, 475–8).

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are established for quantified modalities (Dial. 202, 30–203, 4; LI De Int. 411, 478–491): 1. possibility and impossibility propositions are equipollent when they have the same subject, same quantity, and same quality; 2. possibility and necessity propositions are equipollent when they have a different subject, the same quantity, and the same quality; 3. impossibility and necessity propositions are equipollent when they have a different subject, the same quantity, and the same quality. Here, the subject is taken with respect to the grammatical construction, that is, as the infinitive verb included in the nominal clause (‘esse’ or ‘non esse’). As was said, the quality of a proposition is determined by its being affirmative or negative; the quantity is determined by the term that is subject secundum sensum (as we may note from the rules above, equipollent propositions always have the same quantity). Given these eight orders of equipollence, Abelard says in the Logica Ingredientibus, it is not difficult to determine the rules of contradictoriness, contrariness, subcontrariness, and subalternation that are valid among them, since the relations between quantified modals are the same as those stated for singular propositions (LI De Int. 413, 540–414, 544).12 He then leaves these rules implicit, but for the sake of clarity we can try to make them explicit: i. there is a relation of contradictoriness between the first and seventh order, between the third and fifth order, as well as between the second and eighth order, and between the fourth and sixth order; ii. there is a relation of contrariness between the first and third order, and between the second and fourth order; iii. there is a relation of subcontrariness between the fifth and seventh order, and between the sixth and eighth order; iv. there is a relation of subalternation between the first and fifth order, and between the third and seventh order; as well as between the second and sixth order and between the fourth and eighth order. Figures 6 and 7 represent the two squares of opposition containing quantified modal propositions de esse and de non esse. 12

Martin correctly points out that the ‘similarity’ between singular and quantified modals in this respect should be interpreted in the sense that the same schemes of contrariness, contradictoriness, and so on, may be established between the eight different orders, and not in the sense that the inferences between the four orders of universally quantified modals (and, independently, of particular ones) retrace those of singular modals (Martin 2001, pp. 122–3). This way of identifying a similarity between the logic of singular and quantified modals, Martin remarks, is also invoked and explained in more detail in the Summa Dialectice Artis some decades later (Martin 2001, pp. 114 ff.).

figure 6 The square of oppositions for quantified modals I

figure 7 The square of oppositions for quantified modals II

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Some scholars have claimed that, even though Abelard was able to establish, for any two quantified modal propositions, what the logical relation holding between them was, he was unable to provide general rules of equipollence and inference for quantified modal propositions, and had thus failed to provide a proper modal system of inferences and oppositions.13 It is clear from both the Dialectica and the Logica Ingredientibus, however, that Abelard made an effort to organize all singular and quantified modal propositions into a general scheme of relations, and he seems to have consciously put all these relations into three different squares of opposition (one for singular claims, one for quantified de esse claims, and one for quantified de non esse claims). Although Abelard never represented these squares by means of a diagram, his schemes of modal inference were commonly used as a sketch for later discussions about the logical system of modal propositions.14 As Martin has pointed out,15 Abelard’s inferential system for de rebus modal propositions is indeed a valid system and ‘perfectly correct’. It is important to remark, however, that its validity depends on the acceptance of two conditions. First, the equipollences between modal propositions are understood in the sense of mere concomitance (comitationes) and not as proper consequentiae, which means that propositions are said to be equipollent insofar as they have the same truth-value in every possible situation, and not in the sense that the meaning of one is reducible to that of the other. In my view this caveat is a direct result of Abelard’s idea that no semantic relation of interdefinability may be established between possibility and necessity, although the two modes are logically relatable.16 Moreover, Abelard thinks that there can be no proper inference between propositions having a different quality. The second condition that must be granted to validate the rules of inference stated above is that all terms included in modal propositions are non-empty, that is, that all terms refer to some existent item. If this condition is not satisfied, the equipollences between necessity and possibility propositions will not be valid, according to Abelard. This is because affirmative de rebus propositions are always taken as including an implicit import, which must be satisfied in order for the propositions to be true, whereas negative claims do not, as was 13 14 15 16

Cf. (Knuuttila 1993, p. 88). See also (Thom 2003b, pp. 54–5). (Lagerlund, 2000 p. 37). (Martin 2001, p. 123). See, for instance, LI De Int. 411, 502–412, 508: ‘Inferentiam autem ubique accipimus in naturali comitatione, quia scilicet ita adiunctae sunt propositiones ut non possit evenire ita ut una dicit quin etiam contingat ita ut alia proponit. Si enim secundum consequentiam inferentias pensaremus, fortassis falleretur, cum videlicet una propositio alterius in se sententiam non contineat, ut: “Necesse est esse” cum inferat: “Possibile est esse” sensum eius non videtur continere.’

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argued in Chapter 5. Therefore, Abelard’s modal logic only works within the domain of actually existent things. 3

Modal Principles of Inference, Conversions, and Syllogistics

Apart from the logical relationships established by the three modal squares considered above, Abelard accepts other inferential principles as valid for modal propositions. One is the commonly acknowledged ‘ab esse ad posse’ principle, according to which if something is actually the case, then it is also possibly the case (see, for example, Dial. 204, 20–1). We have seen this principle at play in some arguments concerning the nature of modals advanced by Abelard and his contemporaries in Chapter 3. To this, Abelard adds the principle according to which, from a necessity proposition, we may always infer the corresponding proposition de puro inesse. By virtue of the transitivity of entailment, we may then also establish the inference from a necessity proposition to the corresponding possibility proposition, which is also included in the squares of opposition presented above: i. ‘Socrates is white’ ⇒ ‘It is possible for Socrates to be white’. ii. ‘It is necessary for Socrates to be white’ ⇒ ‘Socrates is white’. iii. ‘It is necessary for Socrates to be white’ ⇒ ‘It is possible for Socrates to be white’. These principles, which establish a sort of hierarchy among modes and are also known as laws of modal subordination, were already accepted by Aristotle and Boethius. Another principle that Abelard admits in his modal logic is the one stating that, if the antecedent is possible or necessary, the consequent is also possible or necessary. Moreover, if the consequent is impossible, the antecedent is impossible (see, for example, Dial. 202, 6–8). These last rules of inference, however, are taken by Abelard as being valid for de sensu modal propositions, but they cause some difficulties when applied to de rebus ones. As we will see, Abelard warns against the applicability of these rules to de rebus modalities in his solution to a theological puzzle concerning God’s foreknowledge and contingency (see Chapter 10.4). I therefore give here only a de sensu formulation of these principles: iv. (p ⇒ q) ⇒ (◊ p ⇒ ◊ q) v. (p ⇒ q) ⇒ (□ p ⇒ □ q) vi. (p ⇒ q) ⇒ (∼◊q ⇒ ∼◊p)

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As was said, Abelard also admits the standard modal rules according to which:

vii. ‘It is possible for Socrates to be white’ ⇔ ‘It is not necessary for Socrates not to be white’. viii. ‘It is necessary for Socrates to be white’ ⇔ ‘It is not possible for Socrates not to be white’. These, however, should be considered not as definitional inferences but as mere equipollences in the sense of what Abelard calls ‘natural concomitance’, and their validity is restricted to cases in which we presuppose that all terms included in modal propositions actually denote. As was seen in Chapter 4, Abelard and his contemporaries animatedly discussed the validity of conversions for nominal modal propositions, and they held very different positions on the topic. Abelard seems to admit that the rules of conversions are always valid for de rebus modal claims – or, more precisely, they are valid in all those cases in which the corresponding de puro inesse propositions also convert. Abelard places restrictions on the validity of conversions in both simple and modal categoricals with respect to those cases in which empty terms are included. He excludes that certain laws (e.g. contraposition) are valid when the terms included in the simple or modal propositions fail to denote.17 Traces of the same idea are also found in Garland’s Dialectica (57, 20–63, 34), as we have shown in Chapter 5, Section 1. Apart from this limitation, Abelard holds that singular and quantified de rebus modal propositions convert by conversio simplex, per accidens, and per contrapositionem, just like their counterparts de puro inesse. Hence, modals ‘preserve the nature of simple propositions with respect to conversions’ (modales simplicium propositionum naturas in conversionibus custodiunt), provided that we analyse the structure of nominal modals with respect to their meaning and not their grammatical construction.18 He therefore admits the following inference per contrapositionem: ix. ‘For every man it is possible to live’ ⇔ ‘Everything for which it is not possible to live is not a man’. ‘Omnem hominem possible est vivere’ ⇔ ‘Omne quod non est possible vivere est non homo’.

He notices, however, that although the two are equipollent, inasmuch as they have the same truth-value in the same situations, the converted proposition is 17 Cf. LI De Int. 400, 29–401, 249. 18 See LI De Int. 399, 204–6.

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not modal like its antecedent, for it asserts an unqualified predication between its predicate ‘non-homo’ and the quantified subject ‘omne quod non est possible vivere’. In order to understand this conversion, we need to understand the mode as part of the subject in the converted proposition and as part of the predicate in the propositio recta.19 On the basis of a similar analysis, we may also admit the following inferences simplices or per accidens:

For every man it is possible to run ⇔ Something for which it is possible to run is a man. ‘Omnem hominem possible est currere’ ⇔ ‘Quiddam quod possible est currere est homo’. xi. For no body is it necessary to be a man ⇔ Nothing for which it is necessary to be a man is a body. ‘Nullum corpus necesse est esse hominem’ ⇔ ‘Nil quod necesse est esse hominem est corpus’. xii. For no body is it necessary to be a man ⇔ Not everything for which it is necessary to be a man is a body. ‘Nullum corpus necesse est esse hominem’ ⇔ ‘Non omne quod necesse est esse hominem est corpus’. x.

Abelard remarks that in all these cases nominal propositions should be read de rebus, namely, as if they were equipollent to the corresponding adverbial propositions, so that ‘For every man it is possible to run’ is the same as ‘Every man can run’, and ‘For no body is it necessary to be a man’ equates to ‘Nobody is necessarily a man’. He therefore concludes that nominal claims of this sort convert just like their adverbial counterparts and that we should interpret the mode as part of the propositions’ predicate (or of the subject, in converted ones).20

19

20

In (Thom 2003b, pp. 57–8) Paul Thom observes that if we instead take the predicate in the usual sense of Abelard’s semantics, that is, as excluding the mode, the usual laws of ­conversions do not hold: ‘Given that for Abelard in genuinely modal propositions the predicate excludes the mode’, he says ‘we might describe his position as stating that modal propositions, qua modal, do not convert. They convert only by virtue of the fact that, when their predicates are seen as including a mode, they instantiate non-modal forms.’ LI De Int. 400, 223–6: ‘Quippe tantundem valet: “Omnem hominem possibile est currere” quantum: “Omnis homo potest currere”, et: “Nullum corpus necesse est esse hominem” quantum: “Nullum corpus est necessario homo”. Unde istae quoque sicut illae converti possunt et, cum in praedicatis sint secundum sensum “posse vivere” vel “esse hominem necessario”, haec tota in subiectis secundum conversionem poni convenit.’

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Abelard’s analogy between the behaviour of adverbial and nominal modals with respect to conversions becomes significant when we consider it within the context of early 12th-century reflection on modalities. Many authors of Abelard’s time, in fact, admitted that conversions were valid only for adverbial modal categoricals, claiming that their nature is similar to that of proposition de puro inesse by virtue of sharing the same subject and predicate and of their variability in quantity. They rather denied that these features apply to nominal modals, attributing to them ‘a different nature’ and thus considering adverbial and nominal ‘two different kinds of modalities’ (duo genera modalium; cf. Chapter 2 on this). Abelard insists, on the contrary, that the difference between adverbial and nominal only amounts to a grammatical or syntactic difference, while in fact they have the same meaning and also the same logical properties.21 Abelard also considers the use of nominal modal propositions in syllogistics in both the Dialectica (Dial. 245–9) and the Logica (LI De Int. 398–9). Both discussions are relatively concise and show that Abelard had very limited knowledge of the Prior Analytics. Abelard focuses his discussion on the so-called syllogismi incisi,22 namely, syllogisms that include both modal and de puro inesse propositions. For instance, in the Logica Abelard discusses the following syllogistic forms:23 It is possible for every animal to move, But every man is an animal, Therefore, it is possible for every man to move. [Barbara MXM] For no stone is it possible to live, But for every man it is possible to live, Therefore, no man is a stone. [Cesare LMX] For no body is it necessary to be white, But every swan is a body, Therefore, for no swan is it necessary to be white. [Celarent MXM]24 21 22 23 24

I have discussed this topic in more detail in (Binini forthcoming). The expression ‘syllogismi incisi’ is employed in the Logica Ingredientibus (LI De Int. 487, 25–38) but not in the Dialectica. On the use of syllogismi incisi in 12th-century logic, see (Minio-Paluello 1954, pp. 211–31). For Abelard’s use of modal syllogisms, see, in particular (Thom 2003, pp. 58–63). As Thom remarks, Abelard also accepts Barbara LXL and Celarent LXL; see (Thom 2003b, p. 59).

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The Dialectica also includes other syllogisms, for example: For everything that is just it is possible to be good, Every virtue is just, Therefore, for every virtue it is possible to be good. As Thom has noted, Abelard offers no proof for these arguments. However, on the basis of his nature-based semantics, the validity of each may be easily proved, as well as other syllogisms, the validity of which follows as a corollary. Among these, Thom lists: Darapti MXM; Baroco MLX and LMX; Bocardo LXL and MXM; Ferio LXL; Datisi MXM; Festino MLX and LMX; Disamis LXL and MXM; Darii LXL and MXM; Camestres LMX and MLX; Ferison MXM and LXL; Ferio MXM; Cesare MLX; and Datisi LXL. Apart from mixed syllogisms, Abelard also considers a few syllogisms that are entirely modal, such as: For everything for which it is possible to die it is possible to live; For every man it is possible to die; Therefore, for every man it is possible to live. Arguments such as this, Abelard claims, were admitted by Aristotle and used in the argumentation that he included in the De Interpretatione (Dial. 246, 3–22). Within Aristotle’s framework this should be a valid argument in the first mode of the first figure. Abelard, however, rebuts arguments of this sort, which are composed of modal propositions only, as only apparently syllogistic, because their premises are not connected by a middle term. Take, for example, the first premise of the aforementioned argument: ‘For everything for which it is possible to die it is possible to live’ (Omne quod possibile est mori possibile est vivere). The subject secundum sensum of this proposition is ‘that for which it is possible to die’ (illud quod possibile est mori). In order to have a proper syllogism in the first figure, the subject of the first premise should function as predicate in the second premise. The second premise should then be the following: ‘Every man is that for which it is possible to die’, and the proper conclusion ‘Therefore, for every man it is possible to live’. However, the resulting syllogism would not be entirely constituted by modal propositions, because the second premise is in fact de puro inesse, insofar as the predicate ‘that for which it is possible to die’ is unqualifiedly predicated of every man:

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For everything for which it is possible to die it is possible to live; Every man is that for which it is possible to die; Therefore, for every man it is possible to live.25 With this and other examples, Abelard argues that modal propositions can only be used in mixed syllogisms and that no proper syllogism is entirely modal. Despite not being syllogisms, however, these latter arguments ‘hold maximum probability’, even though they do not have the necessary validity that would be granted by syllogistic figures (Dial. 247, 26–28; cf. Thom 2003b, p. 62). Based on what Abelard said in the Dialectica, we can conclude that the subject and predicate of modal propositions used in syllogisms are to be understood secundum sensum, and not secundum constructionem. This is in line with his idea that Aristotle’s syllogistics must be read de rebus, an idea that was quite common in the early 12th century, as we will see. The same view is repeated in the Logica Ingredientibus, where Abelard says that in order to preserve figures, we have to consider subject and predicate in meaning and not in grammar (oportet nos ad subiectum sensus respicere, non constructionis, alioquin nulla esset figura, cf. LI De Int. 399, 201–3). The same, Abelard maintains in the Logica, should be done when we apply conversions to modal propositions (LI De Int. 399–400). On such a de re interpretation the mode is taken as being part of the predicate term, as its qualification (cf. also Chapter 2 on this). In the decades following Abelard’s Logica Ingredientibus, many logicians took into consideration the use of nominal modal propositions for the construction of syllogisms. Indeed, as I have argued elsewhere,26 whereas early 12th-century texts on modal logic were mainly dedicated to issues emerging from the reading of De Interpretatione 12 and 13 – namely, negation, the relation between necessity and possibility, and the validity of modal squares – texts later than the 1130s mainly revolve around the suitability of modal propositions for use in syllogisms. The main questions that are put forward ask 25 See Dial. 246, 23–3: ‘At vero mihi hi non esse syllogismi videntur qui ex solis modalibus compositi sunt, quorum primae propositiones medio termino non connectuntur. Cum enim dicitur: “omne quod possibile est mori, possibile est vivere”, “illud quod possibile est mori” subiectum est in sensu, sicut “homo”, cum dicitur: “omnem hominem possibile est vivere”. Tale est enim: “omne illud quod possibile est mori, id est omnem illam rem quam mori contingit, possibile est vivere”. Si ergo in secunda propositione ipsum praedicaretur hoc modo: “sed omnis homo est illud quod possibile est mori”, “ergo omnem hominem possibile est vivere” recte in syllogismo per primam figuram conclusisset. Sed iam secunda propositio simplex esset, in qua “illud quod possibile est mori” simpliciter de homine praedicatur.’ 26 See (Binini 2020a).

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which interpretation of modes (de re or de dicto), of the syntax of modal claims and of conversion laws, would be best for preserving the validity of Aristotle’s system in the Prior Analytics. The general idea advanced in texts of this time is that modal syllogisms can only be preserved if modes are interpreted de re and if modal propositions are expounded according to an in sensu analysis, which does not coincide with their grammatical structure. The main arguments used in support of this view are that de dicto propositions would be invariable in quantity and that syllogisms including de dicto claims would have no middle term grounding the validity of the argument. De dicto propositions are then considered by many authors to be ‘unsyllogistical’. This position may be found, for instance, in the Introductiones Montane Maiores and in the ‘Summa Periermeneias’ (commentary H21). Other authors still claim that we cannot have proper syllogisms if modals are expounded de dicto, but suggest that perhaps the modal and mixed ‘syllogisms’ put forward by Aristotle in the Prior Analytics are still valid arguments, even though they only have an apparent syllogistic structure. Another option mentioned by the author of the Ars Meliduna is that of construing modal syllogistics only with adverbial, and not nominal, modals.27 Also, in the treatise on modalities that is found in the same Ambrosian manuscript that contains Abelard’s Logica, edited as ‘De Propositionibus Modalibus’,28 the anonymous author reports the position of ‘quidam’, ­according to which 27

MS Oxford, Bodl., Digby 174, fol. 228vb: ‘Nam modales, licet non sint nisi singulares, tamen aequipollent universalibus vel particularibus in syllogizando, et assignantur tunc aliter termini propositionum, aliter syllogismorum qui ex eis fiunt; etenim syllogismus eosdem habet terminos cum eo qui ex eis de inesse contexitur. Vel, quod verius, potest dici quod orationes illae non sunt syllogismi, immo argumentationes falsae, sed propter formam syllogisticam quam habere videntur vocat eos syllogismos. Aut ne auctori in aliquo contrarii videamur, dicemus eum id intellexisse de illis quae modos habent adverbiales a nominibus inflexos; illae enim syllogisticae sunt ut “omnis homo necessario est animal”, sed “omne risibile necessario est homo”, ergo “omne risibile necessario est animal”.’ 28 Anonymous, De Propositionibus Modalibus, in (Abaelard 2010a, pp. 234, 88–235, 117): ‘Sunt tamen quidam qui eas alia praedicata et alia subiecta habere dicunt, scilicet secundaria, sicut istam “Socratem esse hominem est possibile” “esse” dicunt habere principale subiectum, “possibile” vero principale praedicatum et “Socratem” et “hominem” secundarium subiectum et secundarium praedicatum. […] Dicunt ergo, cum universales et particulares possint fieri, signum universalitatis et particularitatis ad aliud subiectum oportere addi, cum ad esse poni non possit, et ita alia subiecta dicunt ibi esse. Aliunde etiam hoc confirmant, ex conversionibus scilicet quae ab Aristotele fiunt, sicut “Possibile est hominem esse animal”, “Possibile est animal esse hominem”. Aristoteles etiam facit incisos syllogismos ita: “Possibile est omnem hominem esse animal et Socrates est homo, ergo possibile est Socratem esse animal”, quos dicunt non posse esse alicuius figurae, nisi sint ibi alia subiecta et alia praedicata quam “esse” et “possibile”, cum “possibile” et alii modi

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modal propositions are said to be suitable for syllogisms because their subject and predicate are understood in a way other than the grammatical construction suggests. The position targeted here seems to be Abelard’s, which relies on the distinction between the reading secundum sensum and secundum constructionem of modal propositions. The thesis expressed in De Propositionibus Modalibus, contrary to this Abelardian distinction, is that no other predicate and subject should be identified in modal propositions other than, respectively, the mode and the verb of the infinitive clause. Modal nominal propositions, the author continues, could still be used in syllogisms, but these would be of no figure, and yet they would maintain their validity. Apart from the modal squares of opposition and modal syllogistics, Abelard and his contemporaries also devoted detailed discussions to the logic of determinate modal propositions, namely, propositions in which the modal term is indexed by means of a temporal qualification. Their logic is explored in the next chapter.

non ­possint subici. Nos autem dicimus quod non sunt ibi alia subiecta vel praedicata nisi verba et modi. Quod autem dicit Boethius, quod possunt fieri universales et particulares, sic intelligimus: universales et particulares vocat non quod habeant signum universalitatis et particularitatis additum ad subiecta, sed quod agunt de quantitate omnium vel nonnullorum. […] De incisis syllogismis dicimus quod nullius figurae sunt et tamen firmae complexionis.’

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Simple and Determinate Modal Propositions 1

Abelard on Temporally Qualified Modalities

Abelard concludes his discussion of the logic of modalities by considering qualified modal propositions, which he refers to as ‘determinate’ or ‘composite’ modals, as opposed to ‘simple’ ones. Although Abelard’s interest is mainly directed towards the temporal qualifications introduced by the adverbs ‘while’ (dum, cum), ‘as long as’ (quando, quamdiu, quotiens), ‘in every time’ (omni tempore), ‘before’ (ante), and ‘after’ (postea), he also briefly considers other sorts of determination, such as the spatial qualification ‘where’ (ubi) or the ­exclusive ‘only’ (solum, tantum). His main focus, however, is on those modal claims that contain a ‘dum’ determination, such as ‘It is necessary for Socrates to read while he reads’ or ‘It is possible for Socrates to sit while he stands’. To them, Abelard devotes a long and rather intricate discussion in both the Dialectica (206, 7–210, 180) and the glosses on De Interpretatione (LI De Int. 422, 778–432, 1085). Determinate modal propositions are generally construed, grammatically, as having the following structure: (i) a modal term usually in the nominal form (possibile, necesse), which may or may not be preceded by an extinctive negation; (ii) an accusative-infinitive clause, varying in quality and quantity, whose predicate may be in the present, future, or past tense; and (iii) a categorical proposition governed by a temporal adverb (‘dum’, ‘quamdiu’, etc.), which again may be affirmative or negative, and whose predicate may be in the present, past, or future tense. Abelard’s aim is, first, to investigate the syntactic structure of propositions of this sort and to list the various ways in which they can be interpreted, as we will see in Chapter 7, Section 2. Having considered all possible interpretations, Abelard establishes a system of logical rules relating determinate modal propositions to simple modal ones, as well as to propositions de puro inesse. This system displays Abelard’s rigorous and sophisticated treatment of the different scopes and semantic roles that may be attributed to the syntactic components of modal propositions, such as temporal indexes, modal terms, quantitative, and negative operators. In Chapter 7, Section 3 I retrace some of the most relevant details of Abelard’s analysis.1 Finally, Abelard 1 An analysis of Abelard’s system for determinate propositions was also proposed by Martin in (Martin 2016, pp. 125–32), who also puts it within the contexts of early 12th-century © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_011

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takes into account some sophismata raised by temporally indexed modalities. In particular, he considers the absurd consequences that might be derived from the apparently innocuous claim that ‘It is possible for Socrates to sit at every time of his life’ (Possibile est Socratem sedere omni tempore vitae suae). I shall analyse this ­controversial claim and Abelard’s solution to the puzzles related to it in Chapter 7, Section 4. Abelard is not the first author in the history of logic to consider the combination of modality and temporal operators. A brief analysis of modal propositions containing dum-clauses had already been advanced by Boethius in his treatise on hypothetical syllogisms.2 There, Boethius distinguished between three sorts of modal: i. propositions in which the modal term is predicated unqualifiedly and omnitemporally (absolute), as in ‘It is necessary for God to be immortal’ (Necesse est Deum esse immortalis) or ‘It is possible for a bird to fly’ (Possibile est avem volare); ii. temporally qualified propositions in which the dum-clause posits the existence or persistence of the modal clause’s subject, as in ‘It is necessary for Socrates to have a heart while he lives’ or ‘It is possible for Socrates to read while he exists’ (Necesse est Socratem habere cor dum vivit; Possibile est Socratem legere quamdiu permanet); and lastly, iii. propositions in which a temporal clause is adjoined to the mode, the predicate of which is the same as the predicate in the infinitive clause, as in ‘It is necessary for Socrates to sit while he sits’ (Necesse est Socratem sedere dum sedet). As Thom notes, in his second commentary on De Interpretatione Boethius presents a similar division of the different kinds of necessity, distinguishing between necessities that are ‘simple predications’ (e.g. ‘It is necessary that the Sun moves’), which seem to correspond to what elsewhere he calls absolute necessities, and those that are ‘put forward with the necessity of some accidental characteristic’ (e.g. ‘It is necessary that Socrates is seated when he is seated’), which correspond to conditioned necessities.3 As was already said in Chapter 1, Section 4, Boethius was not particularly interested in the logic of temporally qualified modal claims. Apart from establishing an equipollence between propositions such as ‘It is possible (necessary) for Socrates to sit while he sits’ and their correspondents de puro inesse d­ iscussions on the same topic. My analysis is partly built on that of Martin, and extends or complements it with new details. 2 (Boethius 1969, p. 236–8). 3 (Thom 2003b, p. 38).

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‘Socrates sits’, he does not delve into further analysis concerning their logical behaviour. Early 12th-century logicians, on the contrary, display a profound interest in the logic and philosophical relevance of temporally conditioned modalities. Determinate modal claims were vigorously debated by some of Abelard’s contemporaries at the beginning of the 12th century, as is witnessed by some treatises on modalities of the time, such as Garland’s Dialectica and the two anonymous treatises M1 and M3.4 Garland’s analysis of determinate modal claims is very concise, mostly retracing the distinction already made by Boethius between three different sorts of necessity and possibility-statement. Like Boethius, Garland distinguishes between two sorts of determinate claim: those in which the determining clause and the modal clause have the same predicate (e.g. ‘It is necessary for Socrates to sit while he sits’), which he takes to be equipollent to the corresponding non-modal claims; and those in which the determining clause posits the existence of the modal clause’s subject (‘It is necessary for Socrates to be a man while Socrates exists’). In the two treatises M1 and M3 the analysis of temporally qualified claims is developed in more detail, taking into account many of the questions that Abelard is also interested in, such as the different possible interpretations of determinate modal claims, the role of negation, and the question of whether the usual rules of equipollence and opposition that hold between simple modal propositions also hold for determinate ones. Apart from these sources, a discussion of determinate modals is also advanced in a number of anonymous commentaries on Boethius’ monograph on hypothetical syllogisms (categorized as SH commentaries) and in the ones on Aristotle’s De Interpretatione (H commentaries), particularly in reference to Chapter 9, as well as in the brief treatise on modals that follows Abelard’s De Intellectibus in MS Avranches, Bibl. mun., 232. I offered a more detailed (though far from exhaustive) description of Boethius’ views and the early 12th-century discussions on temporally qualified modals in Chapter 1, Section 4. Abelard follows Boethius in giving a threefold distinction for possibilityand necessity-claims, although the tripartition he uses is slightly different from the one advanced in De Hypotheticis Syllogismis. Apart from the category of unqualified modal claims, Abelard identifies two different categories of determinate modal proposition: those that are qualified intrinsically; and those that are qualified extrinsically. A qualification is intrinsic (intrasumpta determinatio) if the verb stated in the determining clause is the same as the one included in the infinitive clause, as in the modal proposition ‘It is possible for Socrates to 4 Cf. (Martin 2016, pp. 115–25).

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read while he reads’ (Possibile est Socratem legere dum legit).5 On the contrary, the qualification is extrinsic (extrasumpta) if the verb in the infinitive clause differs from that included in the determining clause, as in ‘It is possible for Socrates to read while he sits’ (Possibile est Socratem legere dum sedet), or if the same predicate is repeated but varied in quality, as in ‘It is possible for Socrates to read while he does not read’ (Possibile est Socratem legere dum non legit). Differently from Boethius and from other early 12th-century logicians, Abelard does not use extrinsic qualifications to posit the existence of a subject but rather to express the (in)compossibility between two predicates. Whereas for Abelard the predicate of an extrinsic temporal determination might be any sort of predicate different from the one included in the infinitive clause, Boethius, Garland, and other known authors of the time only consider as ‘extrinsic’ those determinations in which the predicate is a verb such as existere, persistere, vivere, as in the two propositions ‘It is necessary for a man to have a heart while he lives’ (Necesse est hominem habere cor dum vivit), or ‘It is possible for Socrates to read while he exists’ (Possibile est Socratem legere dum permanet). According to their analysis, the function of the determining clauses in these cases is to restrict what is said by the modal claim to those times in which the subject term in fact exists. Propositions of this sort are contrasted with unqualified or ‘absolute’ modal propositions, such as ‘It is necessary for God to be immortal’, in which the mode is said to refer to all times (see C ­ hapter 1, Section 4 for more details). According to Garland, for instance, if one wants to formulate a true necessity proposition whose subject is a contingent being – namely, an individual or a species that does not exist sempiternally – one can only do so by means of 5 In the glosses (LI De Int. 421, 758–422, 774) Abelard insists that, in the case of intrinsic determinations, the infinitive clause and the determining clause must have not only the same predicate but also the same subject. According to Abelard, even when the subject term of the dum-clause is not explicitly stated, if the determination is intrasumpta we should always understand the dum-clause as if a relative pronoun ‘ipse’ were implicitly contained as its subject, in order to grant the identity between the subject of the infinitive clause and the subject of the temporal clause. Abelard thus states that, for instance, the proposition ‘It is possible for a certain man to run while running’ (Possibile est quendam hominem currere dum currit), in which the temporal clause has no explicit subject, must be taken as saying ‘It is possible for a certain man to run while he himself is running’ (Possibile est quendam hominem currere dum ipse currit) and not as saying ‘It is possible for a certain man to run while some man (quidam homo) runs’. Such a requirement is given only for modal propositions containing intrinsic determinations, which may suggest that Abelard would allow, in the case of extrinsic determinations, that the subject of the determining clause and that of the infinitive clause be different, as in ‘It is possible for Socrates to run while Plato sits’ or ‘It is necessary for every man to be rational while some animal is irrational’. Abelard, however, never explicitly considers examples of this sort, and we therefore limit our discussion to determinate modal propositions in which the infinitive clause and temporal clause share the same subject.

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a determinate modal claim. Every absolute necessity proposition about nonsempiternal beings will, in fact, turn out to be false. This is because an absolute necessity proposition such as ‘It is necessary for S to be P’ can only be true if it is impossible that ‘S is not P’, that is, if there is no possible situation or no possible time in which it is not the case that ‘S is P’. But since the proposition ‘S is P’ is false in those situations in which the subject S does not exist, if S is not a sempiternal being there will be times in which the claim is false and therefore ‘S is P’ would not be necessary. Unqualified necessity propositions with nonomnitemporal subjects are therefore always false. A determinate proposition such as ‘It is necessary for S to be P while S exists’, on the contrary, is true if it is impossible for S not to be P only in those times and in those situations in which S actually exists.6 Garland deals with this problem in Dial. 84, 25–85, 9, where he claims that, if we admit that unqualified necessity propositions about contingent beings are true, absurd conclusions might be drawn from them. If, for instance, someone affirms absolutely that ‘Socrates necessarily sits’ or ‘Fire is necessarily hot’, he or she might be forced to conclude that Socrates is immortal or that fire exists sempiternally.7 Garland’s solution to the problem is that absolute claims concerning the necessary properties of contingent beings are always false, and they must thus be temporally qualified by means of an extrinsic determination if one wants to avoid absurd conclusions.8 Extrinsic temporal determinations are then used by Garland and other contemporaries – and probably by Boethius too, even though he is not always explicit on this – as devices allowing them to formulate true necessity 6 See Chapter 1, Section 4 of this volume for a more detailed analysis of this topic. 7 Suppose, for instance, that (a) ‘Socrates necessarily sits’ (Necesse est Socratem sedere or Socrates ex necessitate sedet) were true. It would follow that (b) ‘For Socrates it is impossible not to sit’ (Socrates non potest non sedere), namely, that there is no possible situation or time in which ‘Socrates does not sit’ is true. Thus, there would also be no possible situation in which Socrates is dead, because if such a situation were possible, then the claim ‘Socrates does not sit’ would be true in it. If (b) were true, then, it would also be true that (c) ‘For Socrates it is impossible to die’ (Socrates non potest mori), which entails the absurd claim (d) ‘Socrates is immortal’ (Socrates immortalis est). Garland seems here to implicitly assume that the affirmative proposition ‘Socrates sits’ has an implicit existential import, so that it can only be true when Socrates exists, while the negative proposition ‘Socrates does not sit’ does not have such an import, so it turns out to be true even if Socrates does not exist, for instance, in those times in which he is dead. 8 See (Garlandus Compotista 1959, p. 85, 3–9): ‘Quotienscumque aliquis fecerit tibi mentionem de necessario vel de possibili vel de contingenti, determinatum secundum quem modum acceperit. Nam si indeterminatum preterieris, inconveniens sepe inde habebis. Poterit enim tibi probari et hominem esse immortalem et ignem omni tempore durare ad similitudinem primi sophismatis. Si quis igitur tibi dixerit hominem ex necessitate esse animal et ex necessitate ignem calere, appone: “dum est homo” et “dum ignis calet”.’

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propositions concerning contingent beings.9 Abelard, on the contrary, is not interested in such a use of extrinsic determinations. Even though he is also concerned about the problems raised by the equipollence between (a) ‘It is necessary for S to be P’ and (b) ‘It is not possible for S not to be P’ in the case that ‘S’ refers to a non-sempiternal being, he does not solve these problems by resorting to dum-qualifications. Rather, he employs extrinsic determinations for different purposes, such as to explore the relations of compossibility and incompossibility between predicates, that is, to investigate which predicates are possibly or necessarily predicated simultaneously of the same subject. This will become clear in the next sections. 2

On the Meaning of the dum-Clause

Having distinguished between intrinsic and extrinsic qualifications, Abelard moves on to consider the meaning and logical properties of determinate modal propositions, focusing especially on those containing the temporal adverb ‘dum’. As he claims in both the Dialectica and the Logica, a temporal clause introduced by ‘dum’ always has a twofold role: (i) it posits the existence of a specific (present, past, or future) moment in time; and (ii) it states that a certain predication is true at that time. The temporal proposition ‘while Socrates sits’ (dum Socrates sedet), for example, is taken by Abelard to mean ‘A certain time t exists, such that Socrates sits at t’. According to Abelard, when the predicate of the dum-clause is in the present tense, the existential assumption made by the dum qualification refers to the present. Conversely, if the predicate of the dum-clause is in the past or future tense, the ‘dum’ refers to some past or future moment (LI De Int. 426, 892–6). There are some passages, however, in which Abelard seems to think that even if the verb in the dum-clause is in the present tense, the ‘dum’ might refer to some moment in time other than the present. For example, when Abelard considers in LI De Int. 425, 860–77 the proposition ‘It is possible for Socrates to sit while he sits and does not sit’ (Possibile est Socratem sedere dum sedet et non sedet), he claims that there are two ways in which this proposition might 9 Both Boethius and Garland do allow for absolute claims about possibility concerning nonomnitemporal beings, such as ‘It is possible for a bird to fly’ (Possibile est avem volare). For Garland, this proposition is omni-temporally true because it is true even in those times in which birds do not exist, insofar as it is possible for God to create them and to make things so that they can fly: ‘Item possibile est quod absolute omni tempore contingere potest, ut “possibile est avem volare”: licet enim avis omni tempore non sit, potest tamen contingere ut fiat a Deo et ut volet’ (Garlandus Compotista 1959, p. 84, 21–3).

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be interpreted: either we take the temporal adverb ‘dum’ in the determining clauses ‘dum sedet’ and ‘dum non sedet’ as referring to the present time, or we take one of the two as referring ‘indifferenter’ to a certain moment that does not necessarily coincide with the present.10 We should note, however, that Abelard proposes this second interpretation only within his solution to a sophisma raised by determinate modals such as ‘It is possible for Socrates to sit at any moment of his life’ (more on this in Chapter 7, Section 4). The tenseless or ‘indifferent’ interpretation of dum-qualifications that he suggests in this context might thus be an ad hoc way out of the argument, and it does not represent the usual interpretation that Abelard gives of temporal clauses in the present tense. In particular, the option of interpreting the dum-clause ‘indifferenter’ is only available when we have a conjunction of dum-conditions, as in ‘dum sedet et non sedet’, in which case Abelard admits that we may read one of the two temporal qualifications tenselessly as referring to all times and the other as referring to the present. Having considered the meaning of the dum-clause, Abelard claims that a modal proposition containing a temporal qualification cannot be true unless its determining proposition introduced by the dum is also true. Therefore, affirmative determinate modal propositions always entail their determining propositions, so that, for instance, the proposition ‘It is possible for Socrates to read while he reads (or while he lives)’ entails that ‘Socrates reads (lives)’.11 This rule of inference is reported by Abelard as common opinion (LI De Int. 422, 780) and was indeed generally accepted in early 12th-century discussions on determinate modalities. Abelard, however, acknowledges some exceptions to this rule. First, he thinks that the inference is invalid when the temporal clause introduced by ‘dum’ falls within the scope of a negative particle (I consider this case below). Second, the rule is invalid when the temporal clause’s predicate is stated in a tense other than the present. Therefore, it is not possible to 10

11

Abelard makes the same point in Dial. 209, 23–35, where he considers the proposition ‘Possibile est Socratem legere quando legit et quando non legit’. In this case Abelard also says that the two temporal determinations ‘quando legit’ and ‘quando non legit’ can either be interpreted as referring both to the same present time or as referring to ‘any time’ (omnis temporis accipiuntur). In the Dialectica and the Glossae Abelard proposes this interpretation of the temporal clause ‘dum sedet et non sedet’ while trying to solve a puzzle raised by the admittance of modal propositions with universal temporal qualifications, such as ‘It is possible for Socrates to sit in every moment of his life’. I will return to this puzzling case in Chapter 7, Section 4. ‘Cum enim determinatio tempus ponat in quo aliquid contingere dicitur, non potest ipsa vere copulari nisi contingeret quod in ea contingere dicitur. Quomodo verum esset “Possibile est me legere dum lego” vel “ubi lego” nisi tempus vel locus contingant in quibus legam?’ (LI De Int. 422, 785–9).

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infer, from the truth of a determinate proposition such as ‘Necesse est Socratem sedisse dum non sedit’, the truth of ‘Socrates non sedit’; nor is it possible to infer from ‘Necesse est Socratem sessurum esse dum non sedebit’ the truth of ‘Socrates non sedebit’. This is because by means of the temporal clauses ‘dum non sedit’ and ‘dum non sedebit’ is posited the existence of an indefinite but particular moment in time at which Socrates was sitting or at which Socrates will sit. However, by means of the simple propositions ‘Socrates non sedit’ and ‘Socrates non sedebit’, it is said that at every past time or at every future time it is the case that Socrates does not sit at that time. Abelard makes this point in the Logica, but not in the Dialectica, where temporal propositions whose tense is other than the present are not considered.12 Abelard moves on to consider the various meanings of modal propositions containing dum-qualifications, stating that a proposition such as (*) ‘It is possible for he who is standing to sit while he stands’ (Possibile est stantem sedere dum stat) could be expounded in two different ways: 1. 2.

There exists a time t (=now) such that ((this person stands at t) and (it is possible for this person to sit)). There exists a time t (=now) such that (For this person, who is standing at t, it is possible to stand and sit at t).

In the first case we have a temporal hypothetical proposition, in which the ‘dum’ only works as a temporal qualification; in other words, it merely has the role of positing the existence of some moment in time in which the predication ‘this person stands’ is true. What the proposition says according to this first sense is that there is a time in which the subject ‘stantem’ actually stands and it is (unqualifiedly) possible for this subject to sit. The proposition is hypothetical because it is a conjunction of two distinct propositions: a simple proposition (‘This person stands at t’) and a modal proposition (‘It is possible for this person to sit’). If both conjuncts are true, then the entire proposition is true.

12

‘Cum enim dicitur “dum non sedet sedebit”, in “dum non sedet” praesens positio fit temporis in quo non sedet, ac si poneretur iam contingere illud tempus in quo non sedet, quod contingere non potest nisi simul vera sit haec proposition “Non sedet”. Cum vero dicitur “sedebit dum non sedebit” tale est ac si diceretur “sedebit dum contingit tempus in quo non sedebit”; sed non ideo vera haec propositio “Non sedebit”, quae omni tempore sedere removet; cum enim multa sint futura, non est verum quod, si non sedebit in eo futuro, non sedebit. At vero, cum unum sit praesens, oportet ut, quicquid non sedet in praesenti, quotiens in significatione praesentis tantum profertur, quotiens itaque determinatio praesentis supponitur verae modali et non removetur determinatio, oportet propositionem quae ad determinationem pertinent veram esse’ (LI De Int. 427, 915–28).

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In the second case we have a modal categorical proposition, in which the ‘dum’ qualification has the role of not only positing the existence of a time in which this person actually stands but also of conjoining the predicate of the infinitive clause with the predicate of the temporal clause, in order to form a compound predicate ‘stare et sedere’, which is said to be possible for a certain subject. According to this interpretation, the proposition says that there is a time t (the present) in which the subject actually stands, and it is possible for the subject to simultaneously stand and sit at t.13 As Martin has shown, the same distinction between these two possible interpretations of determinate modal claims is also proposed in the Orléans treatises M1 and M3. In both treatises this latter reading is proposed as the proper interpretation of propositions of this sort.14 If we interpret determinate modals as either temporal hypotheticals or modal categoricals, the qualifying clause ‘dum stat’ posits the existence of a time in which the subject is actually standing, and therefore the determinate modal proposition ‘It is possible for he who is standing to sit while he stands’ entails its determining proposition, ‘He who is standing stands’. For this reason, the temporally qualified proposition ‘It is possible for he who is standing to sit while he stands (dum stat)’ is not equipollent to the simple de sensu modal claim ‘It is possible for he who is standing to sit while standing (manentem stantem)’, because whereas it is a necessary condition for the truth of the first that the subject is actually standing, this is not the case for the latter (LI De Int. 424, 831–42). According to Abelard, the former proposition tells us something about what is presently the case, while the latter (the de sensu one) does not assert anything concerning the actual state of affairs, but only has to do with possibilities and compossibilities. In the glosses (LI De Int. 428, 957–69) Abelard advances a further interpretation of determinate modal claims. He states that a proposition such as ‘It is necessary for someone to stand while he stands’ (Necesse est stantem stare dum stat) may be interpreted in the two senses mentioned above – namely, as a temporal hypothetical or as a modal categorical – but it could also be interpreted in a third sense, where the determination introduced by ‘dum’ is applied to the modal term itself, as a ‘determinatio necessarii’. The three senses thus distinguished by Abelard are the following: 1. Temporal hypothetical: There exists a time t=now such that ((this person stands at t) and (it is necessary for this person to stand)). 2. Modal categorical: There exists a time t=now such that (it is necessary that (this person, who is standing at t, stands at t)). 13 14

For the twofold interpretation of determinate modal claims, see Dial. 206, 23–37 and LI De Int. 424, 819–48. (Martin 2016, pp. 123 ff.).

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3.

Determination of the mode: There exists a time t=now such that (it is necessary at t that (this person, who is standing at t, stands at t)). Abelard claims that the proposition is only true when interpreted in the third way. Proposition (1) is false because standing is not a necessary predication of the subject, presumably because it is not required by his or her nature or because the subject is a contingent being. (2) would only be true, Abelard says, if the simple proposition ‘This person stands while he stands’ were immutably true (‘Si enim necesse est, incommutabiliter verum est’: LI De Int. 428, 962–3), which is not the case. Also, in the case of proposition (3), the meaning of the modal term ‘necessity’ is spelled out in terms of immutability. However, since in this case the mode itself is determined, for proposition (3) to be true it is not necessary that the simple proposition ‘This person stands while he stands’ be immutably true at all times. What is required is its immutable truth within the limited span of time in which the subject actually stands.15 Abelard suggests that the third possible exposition of determinate modal claims, in which the temporal qualification is applied to the mode, is suitable for propositions about necessity but not for propositions about possibility (LI De Int. 428, 969–429, 981). The reason seems to be that while ‘necesse’ is a proper mode, or a mode in sensu (namely, it properly functions as a qualification of the inherence or of the predicate to which it is applied, cf. Chapter 2, Section 2), ‘possibile’ is only improperly said to be a mode, since it is a mode with respect to grammar only and not with respect to meaning. Because ‘necesse’ (or ‘necessario’) properly functions semantically as a qualifier, it can itself be qualified in turn, so that when we say ‘Socrates necessarily stands while he stands’ we are temporally determining the mode, therefore positing the qualification of a qualification. Since ‘possible’ does not have the same qualificatory role, it cannot be temporally qualified (cf. LI De Int. 429, 978–81). Apart from temporal propositions introduced by ‘dum’, Abelard also considers modal propositions in which a quamdiu-clause or a quotiens-clause is included. These determinations, however, are not scrutinized in any depth. 15

‘Nunc autem determinationes necessarii consideremus. Cum dicitur “necesse est hunc stare dum stat” constat modalem veram esse, non temporalem. Sed, si iuxta expositionem possibilis hanc determinatam de necessario exposuerimus, non minus falsa erit quam temporalis, ut scilicet ita dicamus necesse est ita evenire ut dicit haec propositio “Hic stat dum stat”. Si enim necesse est, incommutabiliter verum est; sed, cum iste non steterit, ex toto falsum est dicere “Hic stat dum stat”. Restat tertius sensus qui verus est, quando ipse modus, scilicet necesse, determinatur ac si ita dicatur “Iste stat necessario dum stat”, hoc est “Stat ita quod non potest non stare retinendo stationem quam habet”; et in hac quidem expositione determinatio quae est “dum stat” est modi praedicati qui est “necesse”’ (LI De Int. 428, 957–69).

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Differently from propositions introduced by ‘dum’ or ‘cum’ (translated here as ‘while’), a temporal clause introduced by ‘quamdiu’ (‘as long as’) does not have the role of positing the existence of some moment in time in which a certain state of affairs actually occurs, but rather of stating that a certain predication is possible or necessary during all those times in which the subject has a certain property or is in a certain state, even if this is not the case at the present time. The proposition ‘It is possible for Socrates to sit as long as he lives’, for instance, differs from ‘It is possible for Socrates to sit while (dum) he lives’, because it is a necessary condition for the truth of the second, but not of the first, that Socrates actually sits (Dial. 208, 7–11). Because a quamdiu determination does not posit the existence of a single time but refers to every time in which a certain predication is the case, Abelard classifies it as a ‘universal determination’. 3

The Logic for Determinate Modal Propositions

Having considered the possible interpretations of modal claims that contain temporal qualifications, Abelard establishes a number of rules to describe their logical behaviour, relating them to both simple modal propositions and propositions de puro inesse. As we have already seen, Abelard accepts as valid the inferential rule according to which we can infer from a determinate modal claim its determining proposition. Boethius says in De Syllogismis Hypotheticis16 that determinate modal propositions with intrinsic determinations not only infer their determining propositions but are in fact equipollent to them. According to him, propositions such as (a) ‘It is necessary for Socrates to read while he reads’ and (b) ‘It is possible for Socrates to read while he reads’ are equipollent to the non-modal proposition (c) ‘Socrates reads’. This is not the case for determinate propositions with extrinsic determinations, which infer their determining clause but are not inferred by them. In the Dialectica (207, 29–208, 4) Abelard considers Boethius’ idea, noticing, however, that if we admit the equipollence between both (a) and (c) and between (b) and (c), we should admit that (a) and (b) also have the same truth-value, by virtue of the transitivity of equipollence (Dial. 207, 16–8). This is problematic since Abelard does not accept that propositions about necessity can be inferred from propositions about possibility. He then states that, although it is true to say that (a), (b), and (c) have the same truth-value in every possible situation, and they are then in a relation of ‘concomitance’ (comitatio) to one another, no mutual ‘inference’ may be established among 16

(Boethius 1969, p. 236).

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them.17 Although Abelard does not explicitly specify this, the equipollence (i.e. concomitance) between proposition (c) and proposition (a) only holds if (a) is understood as a modal categorical and not if it is understood as a temporal hypothetical. In the Logica, though not in the Dialectica, Abelard also considers whether any logical relationship between determinate and simple modal propositions can be established. He claims that any affirmative determinate proposition about possibility implies the corresponding simple modal one, while the converse inference is not valid. From the fact that ‘It is possible for Socrates to read while he reads’ it follows that ‘It is possible for Socrates to read’, but not vice versa. As far as propositions involving necessity are concerned, Abelard establishes the opposite inference, namely, that every affirmative simple proposition about necessity implies a corresponding determinate proposition. For instance, if ‘It is necessary for Socrates to read’ is true, then ‘It is necessary for Socrates to read while he reads’ or ‘It is necessary for Socrates to read while he sleeps’ are also true, but the converse inferences are not generally valid. This is because, according to Abelard, it is possible to infer a determinate necessity from an unqualified one, but a simple necessity is never entailed by the corresponding qualified one. Once the relations between determinate simple modals and propositions de puro inesse are established, Abelard asks whether the relations of equipollence and opposition that were stated for simple modal claims – the ones summarized in Chapter 6, Section 2 – are also valid for determinate modals. He affirms that if determinate claims of this sort are interpreted correctly, their logical behaviour can be properly described by the same modal squares of opposition that he established for unqualified modal claims. In order to show how this is the case, however, we first need to consider determinate modal propositions containing negations and analyse the interaction between the scopes of the negative particle, the modal term, and the temporal qualification in propositions of this sort. 17

‘Sunt igitur aequipollentes “possibile est Socratem legere dum legit” and “necesse Socratem legere dum legit”, quod omnino mihi pro falso constat, sicut et de modalibus cum extrasumptis determinationibus, veluti istae: “possibile est Socratem sedere, dum est homo” et “necesse est Socratem sedere dum est homo”; illa enim vera est, haec falsa. Similiter et istae cum determinationibus intrasumptis, si proprietatem modorum attendamus, non aequipollent. Neque enim “possibile” “necessarium” infert, sed ab eo infertur. Quamvis ergo una numquam sine alia ita reperiatur, gratia scilicet identitatis terminorum, quantum tamen ad complexionem et naturam modorum cassa est et in his consecutio “possibilis” ad “necessarium”. Aequipollentiam ergo, secundum Boethium, comitationis concedimus in istis, non inferentiae’ (Dial. 207, 24–36).

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With respect to the grammatical structure, there are three different ways in which a negative particle can be applied in a determinate modal proposition: it can be included in the temporal clause, as in (1) ‘It is possible for Socrates to sit while he does not sit’ (Possibile est Socratem sedere dum non sedet). Alternatively, it can be applied to the verb in the infinitive clause, in which case we have affirmative modal propositions de non esse, as in (2) ‘It is possible for this stone not to be a man while it is a man’ (Possibile est hunc lapidem non esse hominem dum est homo). Finally, it can be applied to the term that is the predicate with respect to the grammatical structure, that is, to the modal term itself, in which case we have a negative modal proposition such as (3) ‘It is not possible for Socrates to be a stone while he is a stone’ (Non possibile est Socratem esse lapidem dum est lapis). Abelard does not discuss the first case at length, because he seems to find it unproblematic. His main interest is directed towards propositions such as (2) and (3). When dealing with the case of determinate modals de non esse, Abelard distinguishes between three different ways in which they can be interpreted (cf. LI De Int. 422, 789–97; 430, 1028–47). Just like determinate modal propositions de esse, these propositions can be understood as temporal hypotheticals or as modal categoricals. Furthermore, depending on the scope that we attribute to the negative particle, they can be taken as negative modal claims, if the dum-determination is included within the scope of the negation, or as affirmative modal claims, if the dum-determination is external to the scope of negation. Proposition (2), for instance, can be understood in one of the three following ways (LI De Int. 422, 789–97 and 430, 1028–47): (2.a) There exists a time t=now such that: ((this stone is a man at t) and (it is possible for this stone not to be a man)). In this case the dum-qualification only has a temporal meaning, and the proposition is then considered a temporal hypothetical. As is the case for the other temporal hypothetical propositions, (2.a) implies its determination ‘This stone is a man’. Since this is false, the entire temporal hypothetical turns out to be false. We might also consider proposition (2) as a modal categorical in which the negative particle is applied to both the infinitive clause and also to the temporal clause, so that the modal term ‘possible’ refers to the whole sense of a negative claim, as if it said: (2.b) There exists a time t=now such that: (it is possible that this is not the case (this stone, which is a man at t, is a man at t)). According to Abelard, interpreted in this way, the proposition is true, for there is indeed a possible situation in which it is false that ‘This stone, that is actually a man, is a man’. In (2.b) the temporal determination is part of the scope of the

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negative particle, or, as Abelard says, the negative particle ‘intercepts’ (intercipit) the temporal clause. Because the dum-determination is included in the scope of negation and is then removed by means of the ‘non’ particle, we cannot infer the determining clause, ‘This stone is a man’, from proposition (2.b). Finally, we may consider proposition (2) as an affirmative modal categorical in which the negative particle is only applied to the predicate of the infinitive clause, not including the temporal determination within its scope: (2.c) There exists a time t=now such that: (it is possible that (this stone, which is a man at t, is not a man at t)). Proposition (2.c) is a modal categorical proposition in which the mode ‘possible’ refers to the whole sense of a proposition constituted by an affirmative claim (‘This stone is a man at t’) and by a negative claim (‘This stone is not a man at t’) and says there is a possible situation in which the following proposition is true: ‘There exists a time t in which this stone is a man and is not a man’. This, Abelard says, is entirely false. Because in (2.c) the temporal qualification is external to the scope of negation, it is valid to infer from (2.c) that ‘This stone is a man’ (LI De Int. 431, 1028–49). We shall now consider the case in which the negative particle is attached to the predicate of the modal proposition, that is, to the modal term itself. In LI De Int. 431, 1061–432, 1085 Abelard considers the following proposition: (3) ‘It is not possible for Socrates to be a stone while he is a stone’ (Non possibile est Socratem esse lapidem dum est lapis). There are again three possible ways in which the proposition can be interpreted.18 It can be interpreted as an affirmative hypothetical proposition (3.a), as a negative hypothetical proposition (3.b), or as a negative modal proposition (3.c): (3.a) There exists a time t=now such that: (Socrates is a stone at t) and (it is not possible for Socrates to be a stone). (3.b) It is not the case that (there exists a time t=now such that: (Socrates is a stone at t) and (it is possible for Socrates to be a stone)). (3.c) It is not the case that (it is possible that (there exists a time t=now such that: Socrates, who is a stone at t, is a stone at t)). In propositions (3.b) and (3.c) the negative particle is interpreted as an extinctive negation; in other words, it applies to the whole sense of the propositions following it.19 Because in both cases the temporal determination is included within the scope of negation, it is not possible to infer from (3.b) and (3.c) that ‘Socrates is a stone’, which does correctly follow from (3.a). 18 19

Cf. (Martin 2016, pp. 131–2). (Martin 2016, p. 132).

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The problem concerning the proper way of interpreting negation is related to the question of whether the logical rules of opposition and equipollence that are valid for simple modal propositions are also valid for determinate modal ones. Abelard reports in Dial. 208, 21–209, 11 one puzzling argument, by means of which some (quidam) aim to show that admitting the usual equipollence rules for determinate modal claims would lead to absurd conclusions and that we should therefore hold these rules as invalid. Martin has shown that this argument, which he refers to as ‘the Equipollence Argument’,20 is also discussed in the anonymous treatises M1 and M3 on modalities. The solution proposed by both Abelard and the authors of these treatises rests on their analysis of the scope of negation. They state that if the negative particle included in determinate claims is interpreted correctly, the logical rules represented in the modal squares of oppositions are in fact valid for determinate modal propositions, just as they are for simple modal ones. What follows is a reconstruction of the ‘Equipollence Argument’, as Abelard presents it in the Dialectica. As was said above, it is generally admitted as a valid principle that from a determinate modal claim we may infer its determining proposition. We may then admit as true that (a) ‘If it is possible for Socrates to be a stone while he is a stone, then Socrates is a stone’. By contraposition, it follows that (b) ‘If Socrates is not a stone, it is not possible for Socrates to be a stone while he is a stone’. Let us posit as true that (c) ‘Socrates is not a stone’. From (b) and (c) follows (d) ‘It is not possible for Socrates to be a stone while he is a stone’. According to the rules of equipollence represented by the modal square of opposition, (d) should be equipollent to (e) ‘It is impossible for Socrates to be a stone while he is a stone’, which, in turn, is equipollent to (f) ‘It is necessary for Socrates not to be a stone while he is a stone’. From this, it is inferred that (g) ‘Socrates is a stone’. But this, Abelard says, is impossible, for it contradicts the initial hypothesis (c). Abelard’s way out of the argument consists in specifying the scope of the negative particles in propositions (d), (e), and (f). According to him, proposition (f) is equipollent to the other two only when interpreted as saying (f*) ‘It is necessary that this is not the case: Socrates is a stone while he is a stone’, that is, only if the modal term ‘necesse’ is excluded from the scope of the negative particle and if the negation’s scope includes both the predicate of the infinitive clause and the temporal determination.21 The negative particle in propositions (d) and (e) must instead be interpreted extinctively; in other words,

20 (Martin 2016, pp. 130–2). 21 Cf. Dial. 209, 5–8 and 209, 2–3: ‘Per negativam particulam similiter et esse lapidem cum determinatione ipsa denegamus’.

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it must extinguish the whole modal proposition, including the temporal determination,22 so that their meaning would be: (d)=(e) ‘It is not the case that (It is possible for Socrates to be a stone while he is a stone’). If the negation is interpreted in this way, the three propositions are indeed equipollent. From their equipollence, however, no absurd conclusion is derived, for the temporal determination ‘while he is a stone’ in (f) is included within the scope of the negative particle, and so the inference from (f) to (g) is not authorized. Because it rests on this illegitimate inference, the puzzling argument is, according to Abelard, fallacious. In the Dialectica Abelard thus concludes that the rules of equipollence and opposition represented by the modal squares correctly describe the logical behaviour of determinate modal claims, once granted that all propositions containing negative particles are interpreted in such a way that the negation also includes the temporal clause within its scope. In the Logica Ingredientibus Abelard proposes a similar solution to the same puzzle. Again, he is concerned about the equipollence between the three propositions ‘It is possible for Socrates to be a stone while he is a stone’, ‘It is impossible for Socrates to be a stone while he is a stone’, and ‘It is necessary for Socrates not to be a stone while he is a stone’ (LI De Int. 431, 1050), for this last proposition seems to imply that ‘Socrates is a stone’, which is absurd. And again, he thinks that the solution to the puzzle lies in revealing the semantic ambiguity hidden in these propositions, which depends on the scope of the negative operator. The analysis provided in the glosses is slightly different from that in the Dialectica, though, for in the latter Abelard distinguishes between all the possible interpretations of determinate claims, including negation, whereas in the Logica Abelard aims to show that the equipollence rules of modal propositions should be maintained independently of how propositions are interpreted (LI De Int. 431, 1050–432, 1085). The fact that the standard equipollences of modal claims are valid for propositions containing temporal qualifications does not imply that they are also valid for any sort of determination. In the Logica Ingredientibus Abelard briefly considers two other kinds of qualification – introduced by the adverbs ‘solum’ and ‘tantum’, which will be translated here as ‘only’ – that might be included 22

Dial. 208, 32- 209, 3: ‘Per negativam particulam totum propositionis sensum exstinguimus, idest ipsum praedicatum cum determinatione ipsa removemus’ and again ‘Totum propositionis sensum privare et exstinguere debemus’.

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in simple or modal claims, as in ‘This only is Socrates’ (Iste tantum est Socrates) or (a) ‘For Socrates only is it possible to be a man while he is a man’ (Possibile est solum Socratem esse hominem dum est homo). Abelard asks whether the standard equipollences that are valid for simple modal propositions, and which he had also just shown as valid for temporally determinate ones, are also preserved for propositions containing a solum or tantum determination. These equipollences, in fact, seem to fail for propositions of this sort. Consider, for instance, proposition (a), stating that Socrates is actually a man and that he is the only thing for which it is possible to be a man. This proposition, Abelard says, is clearly false, as there are many things for which it is possible to be a man. If the standard rules of equipollence were valid, proposition (a) should be equipollent to (b) ‘For Socrates only it is not impossible to be a man while he is a man’ (Non impossibile est solum Socratem esse hominem dum est homo), which should, in turn, be equipollent to (c) ‘For Socrates only it is not necessary not to be a man while he is a man’ (Non necesse est Socratem solum non esse hominem dum ipse est homo). One might think, however, that while propositions (a) and (b) are false, proposition (c) is true, and therefore the usual equipollence rules seem to fail. Abelard says that perhaps this is not incongruous, for even when tantum and solum are included in propositions de puro inesse, many inference rules that are usually valid seem to fail. It is not the case, for instance, that ‘If this one only is Socrates, then this one only is a man’ (Si iste tantum est Socrates, iste tantum est homo), or that ‘If it is not the case that this one only is a man, then this one only is a non-man’ (Si non hoc solum est homo, hoc solum est non-homo). Therefore, it does not sound too problematic that the usual modal inferences do not work for propositions containing ‘solum’ and ‘tantum’. Nevertheless, Abelard suggests a possible way to maintain the usual modal inferences in propositions of this sort. Abelard’s justification for how these equipollence rules are supposed to work is, however, not entirely clear to me. He seems to propose that since the three propositions (a*) ‘Possibile est Socratem esse hominem dum est homo’, (b*) ‘Non impossibile est Socratem esse hominem dum est homo’, and (c*) ‘Non necesse est Socratem non esse hominem dum ipse est homo’ are equipollent to each other, and since the adverb solum, once included in them, maintains the same meaning in all, then the three propositions (a), (b), and (c) should also be equipollent. This reasoning is not really convincing, because the fact that the determination ‘solum’ has the same meaning in the three propositions, and that the corresponding undetermined propositions are equipollent to one another, does not per se guarantee that propositions (a), (b), and (c), in which a solum determination is included, are in turn equipollent. Perhaps, what Abelard wants to

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suggest here is that we must be careful to interpret propositions (a), (b), and (c) in the same way, that is, as being either all de rebus or all de sensu. In his explanation he indeed seems to suggest that the three propositions must all be taken de rebus. According to the de rebus interpretation, the three propositions have the following meaning: (a) ‘Socrates, and only he, has a nature which is compatible with being a man, while he is a man’; (b) ‘Socrates, and only he, has a nature which is not incompatible with being a man, while he is a man’; (c) ‘Socrates, and only he, has a nature which does not require that he is not a man, while he is a man’. If interpreted in this way, all propositions are false, and so they can correctly be considered equipollent. If instead they were interpreted as being de sensu (e.g. ‘The following is possible: that only Socrates is a man while being a man’), the three propositions would all be true and would also maintain their equipollence. The initial puzzle concerning the equipollence between (a), (b), and (c) therefore seems to result from the fact that while (a) and (b) were interpreted de rebus, proposition (c) was interpreted de sensu and as such taken as true. Having solved – or having attempted to solve – the puzzle concerning the determinations ‘solum’ and ‘tantum’, Abelard is able to conclude that the rules of equipollence and opposition represented by the modal squares are valid not only for simple modal propositions but also for all determinate ones. This confirms what was said above, namely, that Abelard’s logic for nominal modal claims (interpreted de rebus) could be seen as an extension of his logic for categoricals de puro inesse, except for the restriction that he poses on the denotation of terms. 4

Another Puzzle Raised by Determinate Modal Propositions

Both in the Dialectica (209, 12–210, 18) and in the glosses on De Interpretatione (425, 860–428, 956), Abelard presents a puzzling argument that arises when we consider propositions containing universal temporal qualifications, such as: ‘It is possible for Socrates to sit in every time of his life’ (Possibile est Socratem legere omni tempore vitae suae). According to the opinion of some, reported by Abelard in the Dialectica and the Logica, propositions of this sort lead to paradoxical consequences. For instance, it (allegedly) follows from the given example that there is a moment of time in which Socrates simultaneously sits and does not sit. This is a reconstruction of the argument as presented by Abelard. Suppose that the following proposition is true: (1) ‘It is possible for Socrates to sit in every moment of his life’ (Possibile est Socratem sedere omni tempore vitae suae).

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Indeed, there is nothing in the nature of Socrates that compels him to stand, which seems to justify the truth of (1). From (1) it is possible to infer, by virtue of a locus a toto, that (2) ‘It is possible for Socrates to sit while he sits and does not sit’ (Possibile est Socratem sedere dum sedet et non sedet). This move is justified by saying that if there is some property that is possibly predicated of a subject in every time of its existence, then it could also be predicated of the same subject in each part of this time (‘quicquid enim convenit alicui in omni tempore aliquot, convenit ei in qualibet parte illius temporis’ Dial. 109, 19–21). Proposition (2) should be read as the conjunction between two propositions: ‘(It is possible for Socrates to sit while he sits) and (It is possible for Socrates to sit while he does not sit)’. From this conjunction both conjuncts follow, namely, that (3) ‘It is possible for Socrates to sit while he does not sit’ (Possibile est Socratem sedere dum non sedet) and (4) ‘It is possible for Socrates to sit while he sits’ (Possibile est Socratem sedere dum sedet). Because from determinate propositions of this sort one might always infer the temporal clause introduced by dum, we now have that (5) ‘Socrates does not sit’ and (6) ‘Socrates sits’ and thus their conjunction (7) ‘Socrates sits and does not sit’, which is absurd. Abelard’s first reply to the argument is to point out that we should disambiguate the determinate propositions (2), (3), and (4), which, as was seen earlier in this chapter, can be understood either as temporal hypotheticals or as modal categoricals. Abelard thinks that the argument is plausible only if they are understood as temporal hypotheticals.23 Although Abelard’s answer is laid out differently in the two works, there is one point that both the Dialectica and the Glossae locate as the reason for the invalidity of the argument, which has to do with the meaning of proposition (2) ‘Possibile est Socratem sedere dum sedet et non sedet’. If we expound (2) as a temporal hypothetical, the dum-clause has the role of positing the existence of a specific time in which the determination is true, that is, a specific time in which Socrates sits and a specific time in which Socrates does not sit. If we take these two times as both referring to the present, as if we said: 23

‘Illud etiam notandum quod, cum dicitur: “si possibile est eum sedere omni tempore vitae suae, possibile est eum sedere dum non sedet”, aliter probabilis non est nisi illud “dum” in vi temporis acceptum coniungat, ac si diceretur “Possibile est ipsum sedere eo tempore ­existente in quo non sedet” sicut existente crastino tempore vel alio in quo non sedet praesentialiter, cum tempus nondum sit; et tunc illud “dum” ad existentiam temporis tantum applicatur. Si vero non solum vim temporis habeat, verum etiam coniunctionis, tale est ac si diceretur “Possibile est sedere et non sedere dum non sedet”, id est “Permanente iam tempore in quo non sedet, possibile est ita contingere ut dicitur in hac propositione ‘Socrates sedet et non sedet”’; si enim vim determinationis temporalis recte ­attendamus, ut propositio quae in ea est inferri possit, oportet nos facere in ipsa determinatione quidem positionem temporis quo non sedet’ (LI De Int. 425, 878–426, 891).

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(2.a) ‘There exists a time t=now such that (Socrates sits at t) and (Socrates does not sit at t) and (it is possible for Socrates to sit)’, then the proposition will evidently be false, because two incompatible predicates are attributed to Socrates simultaneously. If this is the case, Abelard claims, the argument fails because proposition (2) does not follow from (1) by virtue of an a toto inference, since a time t in which Socrates both sits and does not sit does not exist, and therefore t is not a part of ‘omnis tempus vitae Socratis’.24 There is yet another way in which we can interpret proposition (2), that is, as if the two predicates ‘sedet’ and ‘non sedet’ in the temporal qualification were referring not to the present moment only but ‘indifferenter’ to any time in Socrates’ life. We can, for example, take the predicate ‘non sedet’ to refer to the present time and the predicate ‘sedet’ to refer to some past or future time, so that the meaning of proposition (2) would be: (2.b) ‘There exists a time t=now, and there exists a time t’, such that ((Socrates sits at t’) and (Socrates does not sit at t) and (it is possible for Socrates to sit))’. No absurd conclusion is entailed by (2.b), for although we are still concluding that Socrates both sits and does not sit, the two predicates refer to two different moments in time.25 However, Abelard seems unsatisfied with this first solution, and in both the Dialectica and the Logica he goes on to say that, even if we understand proposition (2) in the sense of (2.b), namely, as a temporal hypothetical proposition in which the two predicates refer to different moments in time, the inference from (1) to (2.b) is still illegitimate, so that the invalidity of the 24

25

‘Sed dico illam consequentiam omnino falsam: si possibile est eum legere omni tempore vitae suae, tunc legit quando legit et quando non legit, si in “legit” praesens tempus et in affirmatione et negatione attendatur. Tempus enim in quo praesentialiter legit et in quo praesentialiter non legit, non sunt partes temporis. Neque enim simul existere possunt tempus in quo praesentialiter legit et in quo praesentialiter non legit, sicut nec ipse simul legere et non legere potest’ (Dial. 209, 23–30); ‘Ad quod respondendum est quod, si sedet et non sedet praesentis tantum sint designative cum de Socrate stante agimus, non procedit, cum videlicet tempus in quo praesentialiter sedeat numquam contingat’ (LI De Int. 425, 866–9). ‘Si vero “sedere” indifferenter utamur pro omni tempore et “non sedere” pro praesenti et de eo loquamur qui aliquando sedet et modo non sedet, satis concedendum videtur a toto, quod videlicet, cum sit possibile eum sedere omni tempore vitae suae, possibile sit sedere dum sedet et rursus possibile sit sedere dum non sedet. Quod si inferatur “Ergo sedet et non sedet”, non est inconveniens, cum sedet indifferenter acceptum sit omnis temporis, ac si diceretur “Sedet nunc vel sedit olim vel sedebit”, et “non sedet” praesentis tantum sit temporis’ (LI De Int. 425, 869–877).

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argument lies not in the ambiguity of (2) but primarily in the incorrect inference of (2) from (1). Abelard’s dissatisfaction with this inference derives from the idea that, while by means of proposition (1), a certain possibility is ascribed to a subject, by means of the determinate proposition (2), or any other temporal hypothetical proposition of this sort, we predicate an actualization of such possibility at a certain moment of time. But, as Abelard says in the Dialectica, we are never entitled to infer an actuality from the ascription of a possibility. The fact that we can derive proposition (2) from (1) might have some validity by virtue of the way things actually are, he says. Nevertheless, it does not count as a proper inference, because it does not necessarily follow from the fact that Socrates has a possibility that this possibility is realized at some moment of time. This point is rehearsed insistently by Abelard both in the Dialectica26 and in the Logica.27 26

27

In the Dialectica the author insists that, although the two propositions might be true together, and are actually true together, the locus a toto must not be accepted because it requires inferring an actuality from a potency. See Dial. 209, 35–210, 18: ‘Mihi autem nullo modo hic locus a toto necessitate videtur tenere, sed semper constantia egere, ut etiam cum dicimus de Socrate etiam legente: “si possibile est Socratem legere omni tempore vitae suae, tunc possibile est legere dum legit” ac scilicet “cum tempus in quo legit, sit pars vitae illius”. Alioquin sequeretur quod si possibile eum legere omni tempore vitae suae, tunc legit, quod nullo modo de eo vivente, legente sive non legente, consequitur. Neque enim potentia actum inferre potest. Sed [si] diceretur quod et ista: “si possibile est eum legere omni tempore vitae suae, tunc cum legit et cum non legit” in hac sequitur constantia quod tempus in quo legit et in quo non legit sit pars vitae illius. Sed tunc falsum erit antecedens et “legit” et “non legit” omnis sunt temporis. Locum vero a toto omnino calumniari hic oportet, etiamsi tempus in quo legit sit pars. Sed si possibile est eum legere omni tempore vitae suae, tunc possibile est eum legere dum legit, quia omne tempus vitae illius et illud in quo legit sine lectione potest esse.’ In the Logica Abelard says that, although the inference from (1) to (2.b) is a valid inference ex actu – that is, because of the way things actually are, (1) and (2.b) are true together – it is nevertheless not a valid inference ex natura, and only consequences ex natura must be accepted as proper consequences. Because, according to Abelard, it is sufficient for the validity of an argument that its consequence is always true together with the premises given the way things actually are, the derivation a toto of (2.b) from (1) can be considered a valid argument. However, because this inference is not necessarily valid, it cannot be considered a true consequence: ‘Sed profecto hi, qui omnes argumentationes in consequentias veras transferunt, poterunt fortasse eam recipere, ut dictum est, si sola positio temporis fiat, non coniunctio propositionum. Quod si procedatur hoc modo “Si possibile est eum sedere dum permanent tempus in quo stat, ergo stat”, et ita per medium inferatur quod, “si possibile est hunc sedere omni tempore vitae suae, ergo stat”, concedunt fortassis hanc quoque consequentiam gratia termini et per dissimilitudini medii termini resistunt, cum prior consequentia sit ex actu, secunda ex natura. Nos autem huiusmodi consequentias actuales nullo modo recipimus etsi argumentationes de his factas non reprobemus’ (LI De Int. 427, 938–428, 852).

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Abelard’s insistence that some possibilities exist and are ascribable to things even though they are never actualized in time, is in line with what he claims in many passages of the Dialectica and the Logica concerning unrealized and unrealizable possibilities. We have already come across the views of Abelard and his contemporaries on extra-actum possibilities in Chapters 1 and 3. In the third and last part of this book, which is dedicated to Abelard’s theory of the metaphysics and epistemology of modalities, I will return to this topic in more detail, showing how Abelard’s definition of possibility is fundamentally designed to distinguish the realm of possibility from that of actuality and actualizability.

PART 3 Abelard on the Metaphysics and Epistemology of Modalities

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Introduction to Part 3 The last part of this book is dedicated to Abelard’s theory on the nature of modalities, and to the questions he raises concerning how we may come to know that something is possible or necessary. In Chapter 8, I first argue that ‘possible’ and ‘necessary’ are both primitive concepts in Abelard’s theory, and that although one could establish a logical relation between propositions including these two modes (a relation that Abelard labels ‘comitatio naturalis’), these propositions bear no proper relation of inferentia, because the meaning of the term ‘possible’ cannot be reduced to that of ‘necessary’, and vice versa. In the same Chapter, I also provide an analysis of another concept that has a central role in Abelard’s modal theory, namely, the concept of natura rerum. As is known, Abelard and many of his contemporaries define both possibility and necessity in terms of nature, stating that possible is what is compatible (non repugnant) with the nature of a thing and necessary is what is required or compelled by such nature. On the basis of the analysis of nature and of the relation between natures and modalities provided in Section 8.2, the final Section of Chapter 8 offers a reassessment of Abelard’s modal views by stressing the difference between his interpretation of modalities and the one that is at play in some contemporary models, such as that of possible worlds, a model that defines the truth conditions of modal claims by appealing to a spectrum of situations alternative to the actual one. I argue that, on the contrary, Abelard believes that the truth conditions of all modal claims only depend on actual objects and on the natures that these objects have in the actual situation. Chapter 9 catalogues and investigates the different senses that Abelard attributes to the term ‘possible’, by analysing the rich constellation of examples concerning possible entities or possible states of affairs that the author discusses in his logical works. I move from famous cases that have already been the object of scholarly debate – such as the possibility of any human to be a bishop, the possibility of a blind man to see or that of an amputee to walk – to other examples that are still in need of careful examination – such as that of men being unable to laugh, of bodies being without colour, or the possibility of humans to be dead or irrational. Each of these examples is connected to a special sense of possibility, and yet this variety of uses is not symptomatic of an inconsistency or heterogeneity in Abelard’s thought, for all these senses could be referred back to the standard definition of possibility as non-incompatibility with nature, which is consistently held by Abelard to be the proper and basic interpretation of the modal term. Despite presenting some minor © koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_012

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internal discrepancies, thus, I believe that Abelard’s overall reflection on possibility is quite uniform and coherent. This might be better appreciated if we compare his view on possibility with that on necessity, which suffers instead from the lack of a univocal definition and from the compresence of conflicting tenets, which render Abelard’s overall understanding of necessity somehow unstable, as I argue in Chapter 10. In this final Chapter, I first list and explore the different definitions of necessity that Abelard provides in the Dialectica and the Logica Ingredientibus, and I relate them to the context of early 12th-century debates on necessity, determinacy, and future contingents. I then proceed to examine in detail how Abelard applies his reflections on necessity within his discussion of logical determinism (in particular, in connection to the analysis of Aristotle’s dilemma presented in De Interpretatione 9) and of theological determinism (specifically, in relation to the problems raised by the infallibility of God’s foreknowledge).

chapter 8

Natures and Modalities 1

Two Primitive Concepts in Abelard’s Modal Language

As we saw in Chapter 2, the usual characterization of modes given by early 12thcentury authors is meant to apply to all sorts of adverbs that, when added to categorical propositions, function as either inherence- or predicate-qualifiers.1 According to Abelard and his contemporaries, all terms such as ‘rapidly’, ‘well’, ‘useful’, and ‘right’ (as well as their nominal counterparts) are modes, insofar as they determine a predication de puro inesse and transform it into a qualified one. However, in the logical discussion of modal propositions, Abelard – and generally all authors of his time – limits himself to considering only the six modal terms discussed by Aristotle in De Interpretatione 12–13, namely: ‘possible’, ‘contingent’, ‘impossible’, ‘necessary’, ‘true’, and ‘false’. To these modes we refer today as alethic modalities.2 Abelard follows Aristotle in the justification offered for this restriction, saying that only these six modes, differently from other modal terms, maintain mutual relations of equipollence, so that their logical behaviour can be arranged into a system of logical inferences.3 1 As was said on pp. 47 ff. above, neither in the texts of Abelard nor in those of his contemporaries do we find a clear distinction between the use of modes as inherence-qualifiers or as predicate-qualifiers. Logicians of this time seem to use the two characterizations interchangeably and contrast them with the alternative ‘de dicto’ interpretation of modes, where the modal term is in the predicate position and attached to an entire propositional content. We begin to find evidence of an ongoing reflection on the distinction of modes as verb-qualifiers and as inherence-qualifiers in the second half of the 12th century, for instance, in the Ars Meliduna. The author of this treatise remarks that, on the basis of what Boethius had said, all propositions that include an adverb that qualifies the predicate, including, for example, ‘well’ or ‘rapidly’, are traditionally considered ‘modal’. However, he points out that there is a distinction between terms that modify the ‘quality of the action’ (qualitas agendi) expressed by the predicate, such as ‘well’ and ‘rapidly’, and terms that modify the ‘way of inherence’ (modus cohaerendi) of the predicate in the subject, such as ‘possible’ and ‘necessary’. The author of the Ars recognizes only the latter as proper modes. This distinction is then rehearsed in 13thcentury sources, such as William of Sherwood’s discussion on modalities (cf. footnote 15, Chapter 2). 2 One notable exception in the second half of the 12th century is the Ars Meliduna, whose author considers whether terms such as certum and dubium may also be considered modes (see footnote 29, Chapter 2). 3 Abelard defends this view in both the Dialectica (Dial. 191, 37–192, 3) and the Logica Ingredientibus (LI De Int. 408, 438–42). © koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_013

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On closer inspection, we may say that Abelard’s modal language is in fact constituted only by two primitive modes, namely, ‘possible’ and ‘necessary’. This is because, on the one hand, Abelard denies that ‘true’ and ‘false’ are modes in the same sense as the others are,4 and, on the other hand, he affirms that the meanings of both ‘contingent’ and ‘impossible’ are reducible to that of ‘possible’ (reducuntur ad sensum possibilis, cf. LI De Int. 394, 92–395, 95). This is because ‘contingent’ has ‘entirely the same meaning as possible’ and ‘impossible’ is a mere negative form (abnegativum) of possibility, meaning nothing other than ‘not possible’ (Dial. 194, 5–6; LI De Int. 395, 97–9). Because of the interdefinability between possibility, contingency, and non-impossibility, Abelard explicitly states that Aristotle’s modal language can be rephrased as consisting of only two modes, namely, ‘possible’ and ‘necessary’ (LI De Int. 394, 92–395, 95). We might be tempted to take this a step further, saying that these two last modes are also definable in terms of one another and, as such, in principle reducible to a unique, primitive modal term. Paul Thom, for instance, suggested this idea, saying that Abelard takes possibility-propositions as the primary case, with impossibility- and necessity-propositions regarded as secondary.5 Abelard’s logic, however, does not permit this reduction to a single modal term. Even though he accepts the standard inference rules between possibility and necessity, saying, for example, that ‘S is necessarily P’ is equipollent to ‘S is not possibly not-P’, he nevertheless insists that the meanings of the two modes cannot be spelled out by reducing one to the other. He thinks that the relation one may establish between possibility and necessity is not a semantic relation of inter-definability but only a logical relation holding between the truth-values of modal propositions. Using his words, we may say that between possibility- and necessity-propositions there is only a relation of concomitance (comitatio) and not of proper inference (cf. Chapters 5 and 6 on this). Furthermore, Abelard claims that the logical relation between the two modal terms is not generally valid but holds under limited conditions, namely, 4 Abelard’s consideration of these last two modes’ logical behaviour is rather limited, for he only states a few inferences that relate these modes to the other alethic modalities: for example, he says that the modal proposition (a) ‘Socrates is truly a bishop’ entails (b) ‘Socrates is possibly a bishop’ (stating in this way a form of the ab esse ad posse principle) and that the same proposition (a) logically follows from (c) ‘Socrates is necessarily a bishop’ (ab necesse ad esse principle). He also says that proposition (d) ‘Socrates is impossibly a bishop’ entails (e) ‘Socrates is falsely a bishop’. Apart from stating these logical inferences, Abelard dedicates some lines of the Dialectica to the examination of the meaning of these two modes (Dial. 204, 18–206, 6). This discussion has no counterpart in the Glossae. 5 (Thom 2003b, p. 52).

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that all terms making up modal propositions are non-empty.6 If this condition is not met, even the comitatio between possibility- and necessity-propositions generally fails. This restriction imposed by Abelard on the logical relation between the two modal terms is further evidence of the irreducibility of the two, because it shows that there are cases in which the two are unrelatable, even from a purely logical point of view. To represent Abelard’s modal system, then, we need to posit two modes as primitive, ‘possible’, and ‘necessary’, In this third part of the book I will investigate the meanings that Abelard attributes to these two terms and his reflections upon the nature and epistemology of possibility and necessity. Abelard’s analysis of the nature of modals incorporates traditional aspects with innovative views. A large part of Abelard’s reflection on possibility, for instance, is driven by his interest in unrealized possibilities and in the attribution of possibilities to non-things or future things, an interest that – as we have seen in Part I of this book – he shares with other logicians of his time. Although based on ongoing discussions, Abelard brings the debate about unrealized possibilities to a new level of sophistication, exploring many cases in which possibilities might be attributed to things even when remaining perpetually unactualized and only ‘counterfactually’ possible. Like his contemporaries, Abelard also engages in the debate concerning puzzling possibilities, such as the possibility of a blind man to see or of a standing person to sit, possibilities that, as we will see, were discussed animatedly at the beginning of the 12th century. Abelard enters this debate throwing an entirely new light on these cases by analysing these puzzling modal propositions through new logical devices such as the de re/de dicto distinction or his distinction between many senses of sameness and difference. Another element that Abelard inherits from traditional discussions on modalities are the standard characterizations of possibility and necessity in terms of, respectively, non-incompatibility with the nature of things and immutability or sempiternity. As was shown in Chapter 3, Section 3, the definition of possibility on the basis of natures was already in use before Abelard. We find it, for instance, in the commentary H9 and in Garland’s Dialectica, as well as several other sources from the beginning of the 12th century. According to Peter King, such a characterization has its origins in Boethius, who saw ‘possibilities [as] rooted in the individual’s matter and nature’ and who also refers to ‘the Peripatetic view of possibility as depending on the nature of the

6 Cf. Chapter 5, Section 3. For a more detailed discussion of this point, see (Binini 2018, pp. 13–5).

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thing’.7 It is only from the beginning of the 12th century, however, that the idea of non-repugnancy with nature starts to be systematically used in modal logic and theories, often in connection with the justification of possibilities that are not followed by actualization. The temporal characterization of necessity may also be traced back to Boethius (and indeed, to Aristotle himself and other ancient sources) and was echoed in modal discussions from the 10th and 11th centuries, as well as early 12th-century sources (cf. Chapter 3, Section 4 above). Even though ­Abelard – especially in the Dialectica – also makes an appeal to this characterization of necessity in terms of time, he seems to progressively abandon it in the Logica, in favour of a new definition of the term, which, like that of possibility, is given on the basis of natura rerum. According to this definition, necessary is that which is ‘required’ or ‘compelled’ either by the nature of a thing or a species or by nature in general (quod natura exigit or compellit). Abelard’s new definition of necessity, which returns in both the Dialectica and the Logica Ingredientibus, as well as his later texts, will then be adopted by other authors connected to his teaching, such as those of the Logica Nostrorum and the Glossae Secundum Vocales, the De Propositionibus Modalibus,8 and the Summa Dialectice Artis.9 By providing the definitions of all modal terms on the basis of natura rerum, Abelard gives rise to a systematic modal semantics based on the notion of nature, according to which being possible equals being non-incompatible (or non-repugnant) to the nature of a thing, being impossible means being contradictory to such a nature, and being necessary is equivalent to being required by the nature of a substance. These three definitions constitute the core of what I will call Abelard’s ‘nature-based modal semantics’. Because the notion of natura is at the heart of his semantics, I should say something about Abelard’s theory of natures and the role that this notion plays in his essentialist metaphysics, before delving into Abelard’s many senses of ‘possibility’ and ‘necessity’. I will do this in the next section. In the last section of this chapter I will then turn to some considerations of Abelard’s modal semantics in its ‘fourth dimension’,10 that is, in relation to contemporary views on the metaphysics of modalities. 7 (King 2004, p. 116, n. 62). 8 Anonymous, De Propositionibus Modalibus, in (Abaelard 2010a, p. 233, 64–6): ‘De sensu. Modi isti diverso habent sensus. Possibile tantum valet quantum: natura patitur, impossibile: natura repugnat, necesse: natura exigit. Natura autem dicitur prima rerum creatio.’ 9 (Guglielmo da Lucca 1975, pp. 105–6 §7.09). 10 (Marenbon 2013a).

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Abelard on Natures and Nature

As was said in Chapter 3, even though early 12th-century authors often appeal to the notion of ‘natura rei’ (or ‘rerum’) in logical contexts and elsewhere, they seldom provide a systematic theorization of it. This might be because, as Marenbon has remarked, the terminology of natures, as well as the ontology presupposed by it, were commonly accepted by early 12th-century logicians as undiscussed assumptions, of which no clarification or justification was required.11 It was then taken for granted by authors of this time that individual substances have a nature and that, by virtue of such a nature, they may be classified into natural kinds and categorized as animals, humans, donkeys, water, wood, and so on. Such a classification is not conventional or minddependent but grounded on the nature of things. They also took it as a given that individuals belonging to the same natural kind are ‘alike’ with respect to their substantial properties and can therefore be characterized as being ‘of the same nature’ (eiusdem naturae). Furthermore, Abelard and logicians of his time generally assume that the natures of things can be described in terms of genus-­differentiae definitions and ordained hierarchically following the socalled Porphyrian tree. In logical sources of this time we encounter mentions not only of the nature of individuals (e.g. natura Socratis) or of natural kinds (natura hominis, natura animalis) but also of ‘Nature’ in a general sense, referred to as ‘natura rerum’ or simply ‘natura’. As was said in Chapter 3, Section 3, natura in this sense is taken as the totality of the laws governing the natural world, which God had established with creation and which are exemplified by what the different individual natures of substances require or are (in)compatible with. Natura is also said, by Abelard and others, to be the object of scientia physica, having to do with the ‘origin and genesis of all things’.12 In respect to his nominalist ontology, Abelard conceived of the nature of a substance as a ‘cluster’ or ‘bundle’ of particular differentiae, that is, as the collection of individual forms that inhere substantially – namely, not accidentally – in a bearer. Whereas accidental properties are extrinsically related to the substances to which they are attached and are thus ‘separable’ (either de facto or conceptually) from them, the properties that constitute a thing’s nature make 11

For this and other assumptions in Abelard’s and his contemporaries’ philosophy, see, in particular (Marenbon 1997, pp. 104; 117–23); (King 2004, pp. 81 ff.). 12 See Dial. 286, 31–5 and the Logica ‘Nostrorum’ in (Abaelard 1933, p. 506, 19–20; 514, 5–6). According to some scholars, natures were interpreted in early 12th-century texts as ‘ideas existing in the mind of God’. On this, see, for instance, (Rosier-Catach 2007).

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up what we would call its ‘essence’, or its ‘internal structure’, as Martin puts it.13 The nature of Socrates, for instance, is constituted by his individual rationality, mortality, animality, bipedality, and by many other forms that are essential to him and of which we have no knowledge. Nature in this sense is also called the ‘substantia’ or ‘constitutio’ of a thing. Scholars have attributed either a ‘loose’ or a ‘strict’ understanding of natures to Abelard. According to the former, the nature of a thing would not be only constituted by its substantial or ‘essential’ features but also by properties that, despite being accidental, are inseparably linked to their bearer, such as propria. Martin, for instance, includes inseparable accidents in the constitution of Abelard’s natures.14 King too suggests that ‘Abelard often uses the word “nature” loosely to cover more than the individual’s substantial forms, instead capturing the typical material organization, behaviour patterns, way of life, and so on’.15 We should say, however, that at least in logical contexts – and particularly where he is discussing modalities – Abelard is careful to always use ‘nature’ in the strictest sense, excluding from it everything that is accidental. In this sense the possession of propria and of inseparable accidents, like the ability to laugh for humans, is considered extrinsic from nature’s requirements. As Abelard says in his commentary on Porphyry, the nature of humans would in fact ‘permit’ (pateretur) that they are without the ability to laugh, because the form of risibilitas is not part of their nature (see LI Isag. 90, 39–91, 16; cf. Chapter 9, Section 2 of this volume). In logical contexts, then, Abelard seems to assume that the only properties that are included in a subject’s nature are its generic form and differentiae. As Abelard says multiple times in the Dialectica (e.g. Dial. 188, 14; 194, 5; 211, 26–7; 228, 3; 385, 6; 426, 5; 582, 19), different particular individuals can be ‘of the same nature’ (eiusdem naturae). This use of ‘sameness’ in relation to natures has led some interpreters to wonder whether or not this notion puts the consistency of Abelard’s nominalism at risk. Is Abelard, by appealing to sameness in nature, implicitly reinserting a universal into his ontology? Authors such as Spade and Panaccio,16 and more recently Marenbon,17 have indeed considered a realist interpretation of Abelard’s natures, whereas others have offered a ‘deflationary’ reading of this notion, so to speak, according to which Abelard’s natures are nothing other than individuals themselves and would therefore 13 14 15 16 17

See (Martin 1992, p. 112). (Martin 2001, p. 111). (King 2004, p. 81). (Spade 1980) and (Panaccio 2009). (Marenbon 2015, pp. 44 ff.).

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pose no threat to his irrealist ontology.18 This last view finds evidence in what Abelard claims, for instance, in De Intellectibus, where he states that ‘no nature subsists indifferently’, but like all other things that exist, natures too exist as personally discrete and numerically one.19 As King points out, Abelard also expresses the same sentiment in other passages, for instance, LI Isag. 24, 17–20. Also in his theological writings, Abelard seems to appeal to a similar view, according to which affirming that two individuals are ‘of a same nature’ is entirely compatible with the particularity and discreteness of these individuals. In both the Theologia Summi Boni and the Theologia Christiana, Abelard famously engages in a long discussion to explain how the three persons of the Trinity – Father, Son, and Spirit – are called ‘the same’ despite being different, and he suggests that this case is analogous to that of two members of the same species, Socrates and Plato, who are simultaneously ‘different’ and ‘the same’. Socrates is said to differ from Plato both personally and numerically (‘alius personaliter’; ‘diversus numero’), in the sense that their essentia is particular and discrete. However, the two men are not different substantially (substantialiter) because they are ‘of the same nature’ (eiusdem naturae), meaning that they are not different with respect to any of their substantial properties (nulla substantiali differentia disiuncti sunt).20 Being the same in nature is then associated by Abelard with the idea of being the same substantialiter and of having the same differentiae. Socrates would be of ‘the same nature’ as Plato in the sense that Plato’s nature, like that of Socrates, is constituted by a (discrete, particular) form of rationality, mortality, and so on, but there is nothing that the two subjects ‘share’ ontologically or which is present in both as a universal. As noted by Marenbon, however, the problem about how to explain this sameness in differentiae remains, given that for Abelard all forms are individual and discrete.21 What does it mean for Plato and Socrates to both have a rationality, albeit a distinct one? Does this analysis conceal an idea of type-differentiae, and how would Abelard explain the relation of ‘sameness’ between particular discrete rationalities? Many interpretations have been suggested on this matter, and I will not discuss them here.22 In the analysis that I propose in the next section of this chapter I will, however, insist that for Abelard natures have the same primitive ontological status that Abelard appoints to 18 19 20 21 22

In particular (King 2004) and (King 2018). (Abaelard 1994, pp. 72–4, § 75–6), quoted in (King 2004, p. 115). See e.g. (Abaelard 1969b, pp. 223–4) See (Marenbon 2008c; 2015). Marenbon (2015) offers a beautiful and clear reconstruction of the several readings that have been given of Abelard’s nominalism with respect to the notion of ‘natura’.

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particular substances, to which they are in fact identical, both numerically and essentially. Abelard’s natures are immutable, both in the sense that the substantial forms constituting them do not vary through time and in the sense that individuals cannot vary with respect to their nature.23 This implies that categorical propositions stating something about the nature of things, for example, ‘Socrates is a man’, ‘Socrates is rational’, or ‘men are animals’, are always and necessarily true, at least as long as their subject term refers to something that actually exists. Hypothetical propositions whose truth is grounded in the nature of things, such as ‘if it is a man, it is an animal’, ‘if it is a body, it is corporeal’, are eternally true, even at those times in which the things they talk about are non-existent. Natures are also immutable in the sense that the ‘number’ of natural kinds is invariable, namely, there cannot be more or fewer natural kinds, or different ones, than the ones that actually exist in our reality. The natures that were ordained by God during the secondary creation are, in fact, all the natures that exist now and will exist in the future.24 As other scholars have pointed out, Abelard thinks that we are often in the dark about what constitutes the nature of a thing, and most of the time we are not able to specify the substantial forms of the different individual substances that we have experiences of. In the Dialectica (286, 31–287, 1) he states that, in fact, it is not the aim of the logician to investigate the nature of things but that studying natures and their causes is the purpose of physica. Other remarks about our ignorance of natures are also to be found in the Logica Ingredientibus, for instance, in the many passages in which Abelard insists on 23

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Abelard in fact admits that, in some sense, a certain substantia might subsist as ‘the same’ despite having a different nature, as I will argue in Chapter 9, Section 5. He says, for instance, that one individual res that is actually a human could have (or might have had) different substantial properties than the ones it actually has. Abelard also insists, especially in De Intellectibus, that there is more than one nature associable with each substance, an idea that may sound puzzling given the ‘essentialist’ framework that he endorses. The modal relation between individual substances and their nature, however, should be understood in the context of Abelard’s theory of individuality and of the many senses of difference and sameness. I will return to this topic in Chapter 9, Section 5. On this, see also (Binini 2020b). Abelard says that all species together with their essential features have already been determined by God, and it would be false to say about species that do not exist, such as chimaeras or goat-stags, that they might exist someday: ‘Nam coniunctionis actum in quibusdam cognovi et chimaeram vel hircocervus amplius, ut esse possint, seminaria in rerum natura non habere ex illa dei creatione, quae die septimo specierum omnium formas complevit, in quibus seminaria futurorum posuit, ut iam amplius nullam novam speciem crearet’ (LI De Int. 249, 157–62).

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the distinction between what is ‘determinate’, that is, knowable on the basis of nature, and what is ‘certain’, namely, actually known by someone (see, for example, LI De Int. 252, 211–2 and 254, 275–7).25 Whether the number of stars is even or odd, Abelard claims, rehearsing Boethius, must certainly be determinate with respect to the nature of things, and yet it is actually unknown – and perhaps, in principle, forever unknowable – to us. At the same time, Abelard takes for granted that we do have epistemic access – however limited – to the nature of some things, and that in a number of cases we are in fact able to discern between the properties that constitute the nature of an individual and properties that do not. He generally accepts the list of generic and specific forms traditionally attributed to substances by authoritative sources, in particular, those summarized in the Porphyrian tree. In some cases, however, he hints at the fact that the traditional attribution of essential properties raises problems. Paradigmatic is his reflection on the property of bipedality and on whether or not it is constitutive of human nature.26 Despite these problematic cases, however, Abelard admits that we do have a partial grasp on natures and that natures are the sources of knowledge that allow us to establish the truth of certain propositions, such as conditionals and modal claims.27 As I will remark below, he is also open to admitting that we have a ‘negative’ knowledge of natures; that is, in many cases we can be sure about what is non-incompatible with the nature of a thing or with nature in general. This knowledge generally comes from our experience and sense-perception. For instance, from the fact that we see that a certain individual manifests a property in act, we infer that such a property is not incompatible with its nature or with the nature of any other individual belonging to the same natural kind (I will return to this in Chapter 9, Section 1). Knowledge of this sort is, we would say using a modern terminology, an a posteriori metaphysical necessity, because it concerns an essential truth that is nevertheless epistemically contingent and comes to knowledge through factual evidence. In De Intellectibus Abelard suggests that we have knowledge of natures not only in some limited cases, but that any knowledge we possess is also related to the discretion of some nature, because the process of understanding is always 25 26 27

On our ignorance of natures in Abelard’s theory, see also (King 2004, pp. 81 ff.) and (Marenbon 1997, p. 117). On the distinction between determinacy and certainty, also rephrasable as knowability and actual knowledge, see also (Binini 2019). See (Martin 2001); (Martin 2004a). See, for example, Dial. 255, 13–7: ‘Cum enim dicimus: “si est animal, est animatum,” quantum quidem ad rerum naturam quam novimus, de veritate consequentiae certi sumus, quia scilicet animal sine animato non posse subsistere scimus, non quidem ad complexionem inferentis.’ See also Dial. 284, 26–9.

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related to considering an object with respect to (one of) the nature(s) that it has. As Margaret Cameron recently remarked,28 for Abelard nature ‘poses a constraint on human understanding’, in the sense that we are able to understand a certain object and reason about it only by focusing on (or paying attention to) its nature(s), that is, only by considering this individual as having, for example, a human nature, an animal nature, a bodily nature, and so on. A similar idea was also highlighted on multiple occasions by Irène Rosier Catach, who writes that, according to Abelard’s theory of cognition, the human mind is characterized by the ability of the understanding (intellectus) to ‘disentangle’ or ‘discriminate between the various properties of a thing’, distinguishing those that constitute its nature and those that do not, and then to focus on certain properties by disregarding others.29 The understanding’s capacity to discern is then connected to its ability to differentiate between what constitutes a nature and what does not. It is natures, then, that set the limits of our ways of conceiving, just as they set the metaphysical limits of what is possible, or not possible, for a substance.30 Although I will not delve into the role of natures in Abelard’s theory of mind or in his semantics, it is nevertheless important to remark upon the centrality of natures in various areas of Abelard’s philosophy, and to appreciate how the appeal to this notion provides coherence and cohesion to different parts of his thought, from his metaphysics of modalities to his semantics and theory of understanding. To use Cameron’s words again, ‘the consistency with which Abelard saw nature as constraining the modes of reality, our understanding, and even our linguistic meaning is [...] remarkable. It displays a finely tuned awareness of the implications of Aristotelian isomorphism connecting reality, understanding and language’.31 I will return to this in the Conclusion of the book, where I will defend the idea that Abelard’s theory of modalities is highly consistent, both in itself and within his general philosophy. Returning to the investigation of what Abelard’s natures are, I would like to dedicate some space in this section to one last question, namely: How does Abelard interpret the relation between natures and modalities? The question might seem somehow redundant, especially given what was stated above, that is, that Abelard defines modal notions in terms of natures and construes his 28 29 30 31

See (Cameron 2020, p. 374). See e.g. (Rosier-Catach 2017, p. 253). (Cameron 2020, p. 374–80). With respect to this we may venture to say, following Cameron’s and Rosier’s reflections, that for Abelard the domain of intelligibility coincides with that of possibility, so that what is intelligible is possible and what is possible is intelligible. (Cameron 2020, p. 385).

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modal semantics on the basis of this notion. This suggests that natures are, for him, conceptually prior to modalities, and indeed, that he attempted to use natures to perform a ‘reduction’ of modal notions.32 Although this may seem obvious and well established, my impression is that previous studies did not fully appreciate the consequences, within Abelard’s theory of modality, of the priority of natures over necessity and possibility, a priority that is both conceptual – natures are primitive notions upon which modal notions are construed – and metaphysical – natures are the metaphysical grounds and the epistemic sources of modal truths. Stressing this anteriority of natures over modalities, in my view, might be helpful when reconsidering some aspects of Abelard’s modal theory in a new light.33 From a metaphysical point of view, Abelard’s natures are, as was said, clusters of particular properties that inhere in individual substances. But, as Abelard himself remarked, we should not ‘reify’ natures by making them something that can be considered an entity in itself, different in some respect from the individual to which is connected. Natures, thus, should not be interpreted as ‘parts’ or ‘constituents’ of individual things, although we may say that the individual ‘has’ a certain nature. Nor would it be correct to say that natures are the ‘internal structure’ of substances, if we intend such a structure in a componential sense. Interpreting natures as parts or components, in fact, would make them different, at least numerically, with the substance with which they 32

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One objection comes easily to mind at this point: Does Abelard not also define nature(s) in modal terms? His characterization of the distinction between ‘essential’ (substantial) and accidental properties seems in fact given, as it traditionally was given, in terms of (in)separability: accidental are those properties that can be separated from their bearer, either de facto or in reason, without the subject being destroyed, whereas substantial properities are those that inhere inseparably in their bearer. On the modal characterization of Abelard’s notion of accident, see also (Wciórka 2008). However, despite this apparent circularity, it still seems to me that Abelard treats natures as primitive notions, which are anterior to the logical concepts of possibility and necessity. We may appreciate this if we consider that natures play a substantial role, not only in Abelard’s theory of modalities but in many other areas of his philosophy, from semantics, to psychology, and even theology. This suggests that natures are conceptually more fundamental than modalities, since they have a more extensive philosophical and explanatory role. A similar ‘switch of perspective’ on the relation between modalities and essences has proven useful in contemporary debates on the metaphysics and epistemology of modalities, especially following the works of Kit Fine and Jonathan Lowe, to whom I owe some of the ideas and terminology that I use here to interpret Abelard. Fine famously suggested that essences are the ‘starting point in explaining matters concerning modalities’ (Borghini 2016, p. 161), and that ‘it is preferable to try to explicate the notions of metaphysical necessity and possibility in terms of the notion of essence, rather than vice versa’ (Lowe 2012, p. 934).

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are associated. But Abelard insists, as we saw earlier, that natures are the individuals, both essentially (namely, they are the same essentia or concrete thing) and numerically (that is, there is only one thing, for example, Socrates, and not two, for example, him and his nature). This is made clear by Abelard in De Intellectibus, where he claims that the ‘bodily essence’ (corporea substantia) of this body is nothing other than this body itself, just as the human nature in this man, which is Socrates, is the same as Socrates. More generally, Abelard clarifies that natures are ‘nothing other’ (nihil aliud) than their ‘bearers’ and are entirely identical to them.34 From a metaphysical standpoint, then, Abelard’s natures share the same primitive status that he notoriously attributes to the basic components of his ontology, namely, individual substances. How do natures serve as ‘metaphysical support’ for modal truths? As we have already seen in Chapter 3, Sections 1–3 above, Abelard denies that modal terms such as ‘possible’ and ‘necessary’ denote some property or form existing in things, and therefore that modal claims such as ‘it is possible for Socrates to be white’ are true on the basis of a (categorical or dispositional) property that Socrates possesses, such as the property of being ‘possibly white’. Even when he speaks of potencies or abilities, such as the possibility to walk or run easily (cf. Chapter 9, Section 3), Abelard thinks that there is no form possessed by a subject by virtue of which we can say that he or she is able to walk in a certain way.35 Rather, Abelard thinks that the truth of claims such as ‘it is possible for Socrates to be white’ or ‘it is possible for every human to walk’ depends on the fact that there is no incompatibility between the property expressed by the predicate (‘white’, ‘walk’) and the nature of the subject (‘Socrates’, ‘every man’). Incompatibility, as was said in Chapter 3, Section 3, is interpreted here in terms of contradictoriness. The absence of contradictoriness between what is included in a substance’s nature and certain predications that we may put forward about this substance is, so to speak, the ‘truth-maker’ that renders possibility-predications such as these true rather than false. For necessity-predications natures also play the same role of truth-making. The truth of propositions such as ‘it is necessary for Socrates to be a rational’ or ‘it is necessary for all stones to be corporeal’ depends on whether the property expressed by the predicates (‘rational’, ‘corporeal’) is, or is not, constitutive of 34

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(Abaelard 1994, pp. 72–4; §74–75): ‘nulla est natura quae indifferenter subsistat, sed quaelibet res, ubicumque est, personaliter discreta est atque una numero reperitur. Corporea quippe substantia in hoc corpore, quid est aliud quam hoc corpus? vel humana natura in hoc homine, hoc est in Socrate, quid aliud est quam ipse? Nihil utique aliud sed idem penitus essentialiter.’ See also (Martin 2001, p. 105) and (Binini forthcoming) on this.

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the nature of the thing to which the subject refers, that is, on whether being rational or being corporeal constitutes the nature (or, ‘is required’ by the nature) of Socrates or of stones. Because all modal concepts are, for Abelard, reducible to either possibility or necessity, we can infer that natures ground all modal truths. For him, the evaluation of modal predications is always made on the basis of both natures and of what stands in a relation of non-contradictoriness or inclusion with respect to them. This idea is important in relation to another issue that has been amply debated by commentators of Abelard’s modal theory. For Abelard, the truthmakers of modal predications – what renders possibility- and necessity-propositions true or false – are entities that belong to the actual world and actual history: they are the natures of things and, thus, the individuals themselves that currently exist. Particular substances, with their existence as members of natural kinds, establish the ranges and limits of what is possible and what is not. Even though Abelard is more than happy to admit possibilities that are, and remain perpetually, unactualized, and even though he in fact insists that what is possible cannot be judged on the basis of what becomes actual at some point, he still maintains that the grounds or sources of modalities are identifiable with concrete existing entities – and, in addition, with the way we understand and conceive of these entities, attending to them with respect to some of their properties. It is important to keep this in mind when we attempt to read Abelard’s modal theory through models that invoke alternative, counterfactual situations, such as the model of possible worlds. Models of this sort, in fact, aim to assign the truth conditions of modal predications by recurring to situations that are different from the actual one and, in some cases, also to counterfactual individuals that do not exist in the actual world. This way of interpreting modalities might be in contrast with Abelard’s intent, for he in fact seems to construe his ‘realm’ of possibilities and necessities starting from entities (individuals, natures) that exist in the actual world, and to which modal truths can always be retraced. In the following section I will say something more about the appropriateness of the possible-worlds model for interpreting Abelard’s modalities. 3

Abelard’s Modalities and Possible Worlds

Since Abelard’s modal theories first came to light, scholars have held contrasting views on whether contemporary models – in particular, that of possible worlds, which defines the truth conditions of modal claims by appealing to a

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spectrum of situations alternative to the actual one – could be appropriately invoked to clarify and systematize Abelard’s ideas on possibility and necessity. The semantics of possible worlds, considered in its intuitive core and deprived of any technical or formal characterization, requires that modal propositions such as ‘it is possible that p’ and ‘it is necessary that p’ are evaluated on the basis of what is true or actual in ‘worlds’ or situations alternative to the actual one. The analysis of modalities that this model proposes is captured by two principles that are usually called ‘Leibnizian biconditionals’, which equate possibility to being true (or actualized) at at least some possible worlds, and necessity as being true (or actualized) at all possible worlds. This analysis owes its appeal to the fact that it allows modal logic to ‘regain extensionality’ in a sense,36 for it offers an extensionally defined system of situations over which the modes ‘possible’ and ‘necessary’ would range as ‘quantifiers’ of some sort.37 This semantics also connects the meaning of possibility to that of being actual in a certain situation, capturing an intuitive idea of possibility as related to actualizability conditions: being possible, in this sense, means being actualizable given certain circumstances, a certain history, a certain set of natural laws that might even be different from the actual ones. Apart from its use as a formal, technical device in modal logic, the semantics of possible worlds has been often invoked by contemporary philosophers in debates concerning the metaphysics and the epistemology of modalities, as a model which could also be fruitfully applied in the analysis of the nature of possibility and necessity and of the meaning of modal language, in answer to questions like: ‘What is it that makes propositions about necessity and possibility true?’, and ‘What do we intend when we say that something is necessary or possible?’. With respect to these questions, however, the notion of ‘possible worlds’ has been used in a number of different ways and significations. In particular, it has been the matter of animate debate what kind of entities exactly possible worlds would be, and which is the ontological status of objects and states of affairs taking place at worlds different from the actual one. A survey of the many philosophical positions on this issue is outside the scope of this book, but it might be helpful to briefly recall some of the main positions that have been advanced with respect to these questions, before starting to 36 37

See (Menzel 2017) for this formulation. As Christopher Menzel (2017) puts it, ‘possible worlds raised the prospect of extensional respectability for modal logic, not by rendering modal logic itself extensional, but by endowing it with an extensional semantic theory — one whose own logical foundation is that of classical predicate logic and, hence, one on which possibility and necessity can ultimately be understood along classical Tarskian lines’.

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consider the semantics of possible worlds in relation to the modal thought of Peter Abelard.38 According to a famous and highly disputed position first proposed by David Lewis in his On the Plurality of Worlds (1986), the entities to which we refer with the label ‘possible worlds’ are real, concrete entities, whose ontological status is similar to the one appointed to the actual world. These worlds are infinite in number, spatio-temporally ‘independent’ and causally disconnected from one another. Despite their mutual independence, however, different worlds – or parts of these worlds – may present similarities to each other and to our actual world, similarieties that allow us to ‘confront’ events taking place at different worlds. As is known, the position championed by David Lewis, also known as ‘(extreme) modal realism’ or ‘concretism’, has prompted many criticisms and challenges, going from ‘incredulous stares’, as it were, to philosophical positions offering less ontologically ‘robust’ readings of possible worlds, some of which are, for instance, those falling under the labels of ‘abstractionism’, ‘ersatzism’ or ‘modal fictionalism’. Other criticisms of Lewis have instead gone in the direction of rejecting the idea of possible worlds altogether, aiming to substitute the terminology connected to this semantics with an analysis of modalities funded on different grounds. These are the so-called theories of ‘new actualism’ (or ‘hardcore actualism’), including for instance ‘dispositionalism’ and ‘new essentialism’. Abstractionist theories of possible worlds aim to provide some sort of ontological reality to worlds alternative to the actual one by defining them as abstract objects, such as (maximally consistent) sets of propositions or states of affairs, or as abstract, either linguistic or non-linguistic, representations of the many ways in which the actual world might have been. These representations may be seen as recombinations of existing objects or features of the actual worlds or alternatively as ‘pictorial’ representations, based on images rather than on language. These views of possible worlds as abstract entities are also called at times ‘ersatzist’ theories of possible worlds, as they tend to see possible worlds as having a ‘surrogate’ (from the German, ersatz) status with respect to the actual world, which is seen as ontologically privileged. Theories falling under the label of ‘modal fictionalism’ also make use of the terminology of possible worlds to analyse the modal concepts of possibility and necessity, allowing that we can meaningfully speak of possible entities and hypothetical scenarios, even though they take these as merely fictional entities,

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For a clear introduction to contemporary debates on the nature of possible worlds, see for instance (Borghini 2016).

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which can be conveniently invoked in philosophical discourse without necessarily entailing any serious ontological commitment to their existence. Even though they do it in very different ways and with different ontological inclinations, all the theories that have been briefly (and, no doubt, superficially) expounded so far share a common sentiment, namely that the semantics of possible worlds, apart from being a powerful formal device applicable in modal logic, can be appropriately invoked also in discussions concerning the nature of modalities and the meaning of modal language, to provide a definition of what it means to be possible or necessary and to explain or justify the attribution of truth values to modal propositions. After all, this is what a semantics, if we take the term seriously, should do. This common sentiment has been challenged by a number of scholars in recent literature. Many philosophers interested in the nature and epistemology of modalities have criticised the idea that modal terms like ‘possible’ and ‘necessary’ can be fruitfully explained in terms of alternative, counterfactual worlds or states of affairs. According to them, a more appropriate way to analyse modalities is by ‘grounding’ modal concepts on entities or features that belong to the actual world, such as existing objects or actual properties belonging to them. Because of their rejection of possible-worlds terminology and the preminence given to the actual world in the interpretation of modal language, proponents of these theories have been categorized as ‘new actualists’, or also as ‘hardcore actualists’.39 As Borghini has put it, ‘all the proposals falling under the label of new modal actualism share two important tenets. First, these theories deny that possible worlds provide a viable analysis of modal sentences’, because they do not accept the so-called Leibnizian biconditionals as offering a good definition of modal terms. Second, ‘new modal actualists aim to substitute talk of possible worlds with talk of modalities that are possessed by individuals’. The leading idea motivating these two tenets is that possibility and necessity are ‘rooted’ in the ways objects actually are, and that therefore the truthmakers of modal language must be looked for within the actual world, rather than by extending our search to alternative, counterfactual situations – independently of whether these alternative situations are real, abstract or fictional entities. Therefore, although accepting that possible worlds might be ‘a useful formal device in modal logic’ and in other formal contexts, new actualists think that ‘they have little to do with the metaphysics of modality’,40 because ‘what makes modal propositions true are irreducibly modal features of the 39 40

Cf. (Vetter 2011, p. 742); (Borghini 2016, p. 158); (Contessa 2009). (Vetter 2011, p. 742)

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actual world (such as laws of nature, dispositions or essences)’.41 Moreover, proponents of this view believe that ‘reversing the direction of explanation’, by defining possibility and necessity in terms of alternative notions like essences or dispositions rather than vice versa, may have a number of explanatory benefits, both because it would allow us to have a finer grained exposition of modalities than the one that is obtained thanks to the possible worlds semantics, and because we already have independent reasons to include notions such as essences, natural laws or dispositions in ‘our inventory of reality’.42 In what follows, I advance the idea that Abelard is in many ways very close to the positions of ‘new actualism’ or ‘hardcore actualism’ summarized here, in the sense that he shares some of the leading ideas characterising these positions, namely: i. the meaning of modal terms ‘possible’ and ‘necessary’ is not fully captured by an ‘extensional’ analysis such as the one expressed by the Leibnizian biconditionals; ii. the truth makers of modal propositions are to be identified as features and objects belonging to the actual world; iii. it is better to characterize modalities on the basis of other notions (namely, the notion of natures) rather than vice versa. 41 42

(Contessa 2009, p. 342). See e.g. (Borghini 2016, p. 159): ‘The new modal actualist denies that our approach to the [question: * What does it take for a certain situation to be possible?*] should start from necessity and possibility: instead, she suggests that we start from alternative notions— such as dispositions, essences, or other modal properties—which we already have reason to include into our inventory of reality. Thus, instead of talking about possible worlds, the new modal actualist will carry forward a theoretical analysis of possibility founded on one (or more) of these alternative notions; necessity and possibility will have to be explained in terms of those notions.’ See also (Contessa 2009, pp. 349–50, for a similar analysis: ‘Consider now . It seems reasonable to think that, if such a proposition has a truthmaker, its truthmaker(s), like the truthmaker for , should somehow involve the teacup. So, for example, a hardcore actualist would think that its truthmaker is something along the lines of the state of affairs the teacup’s being fragile, or the state of affairs the teacup’s being made of porcelain (assuming that its being made of porcelain is the causal basis of its fragility) or a (non-transferable) dispositional trope, or …. Independently of how they fill the details of the story in, hardcore actualists agree that the truth of is no less rooted in the way the teacup actually is than the truth of . As far as I can see, the pull of this intuition is one the main reasons behind hardcore actualism (and, I suspect, that denying this intuition was one of the main reasons why Lewis was so often treated to the incredulous stare). Truths about how the world could possibly be are no less grounded in the concrete, actual world than truths about how the world actually is.’

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This, I think, may lead us to reconsider the appropriateness of the possibleworlds semantics for interpreting Abelard’s modal thought, even though several scholars in the past have tried to read Abelard otherwise. I should point out, however, that rather than settling the question, my aim here is simply to open some new questions and offer a new way of looking at texts. According to some interpreters, at least in some passages Abelard did in fact think of possibilities in counterfactual terms similar to the ones at play in the possible-worlds model. Evidence for this is mainly to be found in Abelard’s explicit acceptance of synchronic modalities, such as the possibility that someone has of being seated in the very moment in which he is standing, or the possibility that someone who is now blind has to (presently) see. Synchronic modalities of this sort seem difficult to justify if we restrict the evaluation of modal propositions to the actual history and to the states of affairs that occur in it. For this reason, both Weidemann and Jacobi interpreted Abelard by appealing to possible worlds or possible histories, as did Simo Knuuttila on some occasions, although he believed that Abelard was not always consistent on this point.43 There are other pieces of evidence which would go in the direction of this interpretation, such as Abelard’s admission that both past and present events are contingent, and that because things might have gone differently from how they actually did, God could have had a different knowledge of them. Moreover, as Martin has pointed out in some of his articles, when discussing unrealized possibilities such as the one that a blind man has to see, Abelard justifies these possibilities by providing a counterfactual exposition of them, saying for instance that it is now possible for a blind man to see because things might have gone so that this person had never lost the ability to see, which he has in fact lost in the actual history. In his article ‘Abelard’s concept of possibility’ (1991), however, Marenbon remarked that caution should be paid when attributing a possible-worlds framework – however historically rephrased – to Abelard. There seem in fact to be, in Abelard’s views, elements that are in contrast to the idea that modal propositions should be evaluated on the basis of this model. One of these elements is Abelard’s preference for a de rebus exposition of modalities, and for a modal paradigm that is based on the notion of ‘possibility-for’, rather than of ‘possibility-that’. As Marenbon explains, Abelard seems inclined to accept that there could be alternative possible life-stories for existing individuals, but not alternative possible worlds or counterfactual states of affairs. Moreover, the admittance of counterfactual events or states of affairs seems to be in contrast 43

See (Weidemann 1981), (Jacobi 1983), (Marenbon 1991), (Knuuttila 2012) on this debate.

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with the nominalist ontology defended by Abelard, that excludes events, states of affairs and propositional entities like dicta from the catalogue of existing things. The vocabulary of possible worlds and alternative situations, however, has continued to be attributed to Abelard by several scholars in recent studies.44 It is important to return to the issue of Abelard and possible worlds, especially now that Marenbon’s critiques have found echoes in the studies of other scholars, who have defended the view that many medieval modal theories, which had been interpreted in terms of possible worlds in the past, cannot in fact be appropriately understood on the basis of this semantics. Robert Pasnau, for instance, recently claimed that pre-modern philosophers ‘often seek to restrict their modal thinking in ways that are surprising from our current vantage point’, generally limiting their attention to ‘a small modal space’, coinciding with the actual world and the actual course of history.45 The perspective from which the truth of modal statements is assessed would thus be, according to Pasnau, different in medieval and contemporary authors: medieval authors would in fact ‘prescind from the wide-open modal space of all possible words’ to which we are nowadays used, a modal space that is ‘overabundant’ for the purposes they had in mind when discussing modalities.46 Let me return now to some of the reasons why some interpreters have read Abelard as a supporter of the possible-worlds semantics. According to a traditional view, ancient and early medieval theories of modalities read possibilities ‘diachronically’, that is, as evolving through time. According to this modal paradigm, which, as Knuuttila has often remarked, was inherited by medieval authors from ancient modal theories,47 incompossible antecedent possibilities – such as that someone will be standing and not standing at some time t – may exist simultaneously with respect to some future moment in time. However, once the moment t has become present and one of the two possibilities has actualized, the alternative unrealized possibility ‘vanishes’, and the unactualized course of affairs that it represents has stopped being genuinely open. At time t, then, it would be false to say that the subject – who is actually ­standing – still retains the possibility of being sitting, because the actualization of this latter possibility would raise a contradiction with what has in fact 44 45 46

47

See e.g. (Pinzani 2003, pp. 189–92); (Martin 2001, pp. 110–1); (Martin 2004a, p. 181). Cf. (Pasnau 2020). Cameron too has recently suggested that Abelard ‘is committed to a one-world theory of modality, rendering any possible-worlds-style interpretation of his philosophy inappropriate’ (Cameron 2020, p. 370). However, she does not offer evidence for this claim other than what was already put forward by Marenbon in 1991. Cf., for example (Knuuttila 2017).

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actualized. According to this diachronic model, the range of possibilities that are predicable of a certain subject varies depending on time and on the actual circumstances unfolding in time. Singular alternative possibilities that refer to the future exist until the realization of a certain course of action has taken place. Once one alternative has realized, the incompossible possibility, instead of remaining counterfactually possible as an unrealized potency, stops existing as a real possibility. There are some elements in Abelard’s philosophy that have led commentators to believe that he would not endorse this diachronic paradigm. First, he explicitly accepts unrealized possibilities on many occasions and indeed insists on the idea that we may predicate possibilities of a substance even though this substance in fact manifests an incompossible property during its entire lifetime. For instance, Abelard believes that we may truly attribute to Socrates the possibility of being a bishop, even though Socrates is, and will remain, a layman as long as he exists. Because for Abelard everything that is actualized is also possible, this means that he takes two incompossible possibilities – that of being a layman and that of being bishop – as truly predicable of Socrates in every moment in which he lives. As Strobino and Thom have recently pointed out, this example alone would be sufficient to commit Abelard to the existence of simultaneous alternative possibilities.48 But there are also other passages in which Abelard more explicitly declares that certain possibilities are attributable to a substance in those very moments in which the contrary possibilities are manifest in act. For instance, he says that a man who is blind still has the ‘simple possibility’ to see, in the sense that, like other individuals like him, he might have maintained the potency of sight that he has in fact lost. In his analysis of this example Christopher Martin noted that Abelard does not treat the blind man’s possibility to see as referring to some moment in time other than that in which the man is actually blind, as the diachronic model would require. On the contrary, he claims that ‘it might have been the case that this person who has become blind sees, even at that very time in which he remains blind’ (Posset enim contingere, ut is qui caecus factus est, videret hoc etiam tempore quo caecus permanet). As Martin points out, unrealized possibilities of this sort are justified by Abelard in counterfactual terms: Abelard suggests that the actual course of events, which has led to the manifestation of a certain event in the present, could have happened otherwise, leading to an entirely different state of affairs, for example, 48

(Strobino and Thom 2016, p. 360).

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one in which the one who is blind preserved his or her genuine ability to see. Abelard’s treatment of the blind man’s case would then be clear evidence of his acceptance of ‘alternative histories’ and ‘counterfactual situations’.49 In Chapter 9, Section 4 below I will return to Abelard’s exposition of the blind man’s case and parallel it with similar examples that Abelard provides. We will see that, in all these examples, Abelard admits that certain ­possibilities – which he calls ‘simple possibilities’ – can be predicated of a substance entirely independently of their actualizability conditions, as timeless possibilities that belong to things solely by virtue of their nature. The invariability in time of Abelard’s possibilities, and their independence from any factor extrinsic to ‘natures’, seem to place Abelard’s modal views very far from the diachronic model, which defines the range of possibilities that are attributable to a certain subject as depending on both time and the actual circumstances unfolding in time. Another element of Abelard’s modal paradigm that seems compatible with synchronic possibilities, as was said, is his idea that both present and past events are contingent. Abelard explicitly claims this in his Glossae on De Interpretatione 9, where he says that if we consider two contradictory propositions de praeterito or de praesenti, such as ‘I sat’ and ‘I did not sit’, although their disjunction is now necessary, neither of the two disjuncts is necessary in itself (LI De Int. 248, 130–4). Moreover, even though Abelard characterizes the present and past as ‘determinate’, applying a standard terminology inherited from Boethius and widely used by his contemporaries, he never defines determinacy in modal terms, as if it were a species of necessity, which is done instead by many authors of his time. Indeed, as King has noticed, on several occasions Abelard rather emphasizes that necessity and determinateness differ (e.g. LI De Int. 284–5).50 This is interesting because it suggests that Abelard consciously refused to attribute necessity of any sort to the modal status of the present and the past, as would be required by a diachronic reading of possibilities. There is, then, ample evidence for ascribing to Abelard an understanding of possibilities as synchronic. We should now ask whether the acceptance of these synchronic possibilities necessarily goes hand in hand with the acceptance of a possible-worlds framework, or whether we could make room for possibilities of this sort within the limits of a ‘smaller modal space’, as Pasnau puts it, which coincides with the actual world.

49 50

See (Martin 2001, p. 110–1). See (King 2004, p.117, n. 67). I will return to this point in Chapter 9, Section 4 and Chapter 10, Sections 2–4 below.

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Marenbon’s reasons for rejecting the ascription of ‘possible worlds’ to Abelard – a notion that he wishes to substitute with that of ‘possible life histories’ – are based mainly on two pieces of evidence. The first is a passage extrapolated from Abelard’s discussion on ‘determinate’ modal propositions, namely, statements in which modalities are indexed with temporal references, such as ‘it is possible for Socrates to read while he reads.’ As we saw in Chapter 7, Section 4 above, in both the Logica and the Dialectica Abelard considers a sophistical argument that, starting from the truth of (*) ‘it is possible for Socrates to read in every time of his life’ (Possibile est Socratem legere omni tempore vitae suae), derives the truth of the conjunction (**) ‘it is possible for Socrates to read while he reads and it is possible for Socrates to read while he does not read’, and then argues that a contradiction follows from this conjunction, namely, that Socrates simultaneously reads and does not read. Although Abelard rejects the argument as sophistical, Marenbon notes that he does in fact believe that admitting proposition (**) to be true would lead to a contradiction, and he therefore argues that (**) is false, while holding (*) as true. According to Marenbon, the reason is that the truth of (**) would entail that there is at least one moment in time in which the subject actually reads and one in which he actually does not, and it would be false to say that the subject has the possibility to read in that very moment in which he actually does not read. Marenbon then concludes that by rejecting the truth of (**) Abelard would be rejecting ‘possibility-that (i.e. sentential, situational) counterfactuals’, namely, the existence of alternative simultaneous states of affairs. As was seen in Chapter 7, Section 4 above, however, Abelard’s reasons for rejecting the entailment from (*) to (**) have nothing to do with diachronic versus synchronic possibilities. Rather, what Abelard wishes to point out is that from modal propositions that express a purely possible inherence, such as (*), we are never entitled to infer the predication of an actual inherence, an inherence that (**) posits by virtue of its temporal determination ‘dum (non) legit’. Abelard declares in the Dialectica (210, 8) that it is always wrong to infer an actuality from a possibility (neque enim potentia actum inferre potest),51 because from the fact that a possibility is predicated of Socrates, it does not follow that this possibility is realized in some moment of his life. Rather than being evidence of Abelard’s rejection of synchronic possibilities, then, Abelard’s argument should be read as a further insistence on his part on the idea that possibilities may be predicated of things even in those times in which they are not actualized, and that the attribution of these possibilities is entirely 51

The details of Abelard’s argument are explained in Chapter 7, Section 4 above.

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independent of what is actual for the subject in some moment – and indeed in the subject’s entire lifetime. The second piece of evidence provided by Marenbon against the acceptance of ‘possible-worlds’ (namely, alternative states of affairs) in Abelard has to do with some theological tenets of his thought, according to which there could only be one providential plan established by God, inasmuch as God ‘cannot do anything other than what he actually does’.52 However, Marenbon also notes that, when considering the matter of theological determinism in the Dialectica and the Logica Ingredientibus, Abelard admits that ‘things could happen otherwise than God has foreseen’ (possibile est rem aliter evenire quam Deus providit). Even though Abelard warns the reader against interpreting this as an admittance of the existence of alternative states of affairs, he still remarks that the actual course of history is contingent and might not have occurred as it actually did.53 This is in line with other passages where Abelard attributes contingency to past and present events (cf. Chapter 9, Section 4 for more details on this interpretation). Abelard, then, seems to accept genuine counterfactuality, both in the sense that some possibilities are attributable to things although they remain perpetually unrealized – insofar as they are not contrary to these things’ natures – and in the sense that some of the actual states of affairs are contingent, that is, they have the possibility of not being or not having been. Still, one might argue that Abelard’s synchronic unactualized possibilities do not necessarily go hand in hand with the admittance of what we would call ‘possible worlds’. The apparatus of possible worlds, as was mentioned, owes its intuitive appeal to the ‘regained extensionality’ that it provides for modal logic, based on the idea that certain events or properties, which are not manifest in the actual situation or in the actual course of history, are possible insofar as they are actualized in at least one possible situation. This characterization of possibility parallels a concept of necessity as what is true, or actualized, in every possible situation. In what follows, I bring to attention two aspects of Abelard’s modal views that seem to be in contrast to this core intuition. The first concerns his admittance that certain properties (namely, inseparable accidents) belong to their bearers at every possible situation, even though they are not necessary properties of these bearers. The second concerns Abelard’s refusal to admit the truth of any modal proposition that is not about actually

52 53

See (Marenbon 1991, p. 606); cf. (Abaelard 1969b, p. 358, 417 ff.). Abelard’s arguments for compatibility between the infallibility of God and the existence of contingency will be presented in Chapter 10, Section 4 below.

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existing individuals and the natures they currently have – in other words, his refusal to admit modal truths concerning counterfactual individuals. Let us begin with the first point. Abelard accepts the traditional distinction between the substantial and accidental properties of things, and he believes, with Porphyry, that some properties, despite accidental, are yet de facto inseparable from their bearers. These ‘inseparable accidents’ are, for instance, the ability to laugh for men or the property of being coloured for any corporeal substance. Like Porphyry, Abelard believes that there is no ‘actualizable situation’ (or, we could say, no ‘possible world’) in which bodies lack colour and men are unable to laugh, and yet he declares that having colour is not necessary for a body – or that a body could be (posse esse) without colour – because such a property does not constitute the nature of bodies. Abelard argues for this idea in his commentary on Isagoge included in the Logica Ingredientibus, where he claims, first, that propria are not part of the nature of their subject, because they are in some sense separable from it, namely, separable ‘quantum ad naturam rei’ (LI Isag. 90, 10); and, second, that this ‘conceptual separability’ entails some sort of possibility. Here Abelard advances the idea that when we say that something ‘might be’ (posse esse), this can be interpreted in two senses: according to the first, we say that it is impossible for a man to be without the ability to laugh, because ‘it could not happen in act’ that there is a man who is unable to laugh. According to the second sense, however, Abelard admits that ‘it might be’ that a man is without one of its propria (‘alio modo contingere potest hominem posse esse sine proprio’), because human nature does not require the possession of these properties (‘non ex eo quod est homo exigere proprium’).54 According to this second sense, he continues, it is true to affirm that the nature of humans ‘would allow’ the absence of risibilitas (‘bene natura hominis pateretur ipsum esse sine risibilitate’; LI Isag. 90, 39–91, 3) and that ‘a man might be without the ability to laugh’ (homo posse esse sine risibili; 91, 27–32).55 The ideas that Abelard expresses in these passages are in line with his usual definitions of possibility and necessity, according to which necessary is what is ‘required by’ or ‘contained in’ the nature of a thing, and possible is everything that is not incompatible with such a nature. They are also in line with what Abelard argues in his discussion of topics in the Dialectica, where he famously 54

55

‘Sed licet homo non possit esse sine risibilitate quodammodo, quia videlicet non potest contingere, ut homo sit et non risibilis, alio tamen modo contingere potest, ut voluit Porphyrius hominem posse esse sine proprio, ut videlicet negative intelligatur sic: non ex eo quod est homo, exigere proprium’ (LI Isag. 91.11–16, my emphasis). I will analyse these passages in more detail in Chapter 9, Section 2.

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proposes a division between two senses of necessity (cf. Dial. 283, 37–284, 6). In one sense, he suggests there, we may say that there is a necessary link between two predications such as ‘x is P’ and ‘x is Q’ because one cannot be the case without the other – or, as he puts it,56 because there is no possible situation in which one is true and the other is false. According to another, stricter, sense of necessity, the two predications are necessarily linked only if being P requires (exigit) being Q, that is, if being Q is included in the nature of P. The first connection is exemplified by the relation holding between the predication of a substantial term and its inseparable accidents, for example, ‘x is a human’ and ‘x is able to laugh’ or ‘x is a body’ and ‘x is coloured’. The second is instead exemplified by the relation holding between a substantial term and the properties that are part of its essence or nature, such as ‘x is a human’ and ‘x is animate’.57 Abelard thus admits that there is a sense of necessity according to which something is not necessary although it is actualized in all possible situations, for example, the fact that a body is coloured.58 This seems to correspond to the sense of possibility identified in Abelard’s reflection on propria in the Logica Ingredientibus, according to which something is possible though entirely not actualizable. These senses of possibility and necessity, evidently, cannot be captured by an extensional definition such as the one given in terms of possible worlds or alternative situations. This model is in fact not sufficiently finegrained to grasp the distinction between what is ‘essential’ (that is, necessary 56 57

58

(Martin 2004b, p. 181). ‘There seem to be two kinds of necessity of consecution. A broader kind, which is found where the antecedent cannot hold without the consequent. Another narrower kind, where not only can the antecedent not be true without the consequent but also of itself requires (exigit) the consequent. This latter necessity is the proper sense of consecution and the guarantee of immutable truth. As, for example, when it is said “if something is human, then it is an animal,” human is properly antecedent to animal since it of itself requires animal. Because animal is contained in the substance of human, animal is always predicated with human.’ Cf. Dial. 283, 37–284, 6, translated in (Martin 2004b, p. 181). Martin (2004b) famously argued that this distinction, which is presented by Abelard as a distinction between two senses of necessity, should in fact be rephrased as a distinction between a criterion of necessity, which Martin spells out as inseparability in every possible situation, and a criterion of relevance, which requires something stronger than necessity, namely, conceptual inseparability. I believe, however, that we should take literally Abelard’s idea that the second criterion also expresses a sense of necessity, one that perhaps cannot be explained in terms of actualizability in possible situations but which is nevertheless conceived as a modal criterion by Abelard. As we will see in Chapter 10, the characterization as what is required by a thing’s nature is, in fact, Abelard’s principal definition of necessity. Martin himself points out that, according to Abelard’s second sense of necessity, as what is required by the nature of a thing, what is necessary and what is actualizable in every possible situation do not coincide.

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in the stricter sense, as what nature requires) and what is merely inseparable in act. By using actualizability in all or some possible situations as the defining criterion for Abelard’s modalities, we would thus end up disregarding an important distinction of Abelard’s modal paradigm, which also relevantly impacts other parts of his logic, for example, his theory of conditionals. One might argue that these cases involving propria are in fact ‘borderline cases’, which are part of the metaphysical baggage inherited by Abelard from authorities but which should not be taken as exemplificatory of his modal views. This might be true, but I believe instead that Abelard’s reflection on inseparable accidents and their modal status is paradigmatic of the way in which he generally thinks of possibility: for Abelard, possibility cannot be characterized in terms of actualizability or actualizability conditions, and he insists on this idea at length throughout his entire modal theory, as we will see in Chapter 9. This idea of possibility is, in my view, diametrically opposed to the core intuition that lies at the basis of possible worlds, which, as was said, relies on the idea that to be possible means to be actualizable given certain (actual or counterfactual) conditions. A second piece of evidence suggesting that Abelard’s modal thought does not match with modern possible-worlds semantics is connected to his reflection in the Logica Ingredientibus on the distinction between de re and de sensu modalities. As was said in Chapter 4, Section 2, in the Logica Abelard considers the relation between possibility-propositions interpreted de sensu and their de re counterparts. He reports the opinion of some according to whom propositions such as (*) ‘it is possible for every substance to be a spirit’ are false de rebus, because being a spirit is incompatible with some of the things that are actually substances, but true de sensu, inasmuch as a situation in which all existing substances are spirits is possible.59 Abelard, however, does not share this opinion and suggests that the de sensu reading that it makes use of is incorrect. According to his re-definition of de sensu as per compositionem, Abelard says 59

‘Sed opponitur quod, si possibile est omnem substantiam esse spiritum, id est possibile est ita evenire ut haec propositio dicit “Omnis substantia est spiritus”, quippe posset contingere ut soli spiritus essent et tunc vera esset haec propositio “Omnis substantia est spiritus”, nec tamen ideo verum est de rebus quod unaquaeque substantia possit esse spiritus. Sed et, cum nullum filium habeam, propositio vera videtur de sensu quae ait “Possibile est filium meum vivere”, id est “Possibile est ita evenire ut haec propositio dicit ‘Filius meus vivit”’, quia adhuc fortasse ita continget; nec tamen vera est de rebus quae ait “Filius meus potest vivere”, quippe per subiectum quod est “filius meus” positionem existentiae filii mei facio et quasi ipsi exsistenti “posse vivere” copulo. [...] Ideoque nec affirmationes “possibilis” de sensu videntur inferre affirmationes de rebus, sicut nec e converso. Ac fortasse nil obest si nulla sit inferentia.’ (LI De Int. 417, 634–418, 653)

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that the correct de sensu interpretation of (*) is the following: ‘Every substance is possibly a spirit while remaining a substance’ (Omnis substantia potest esse spiritus manens substantia); and he maintains that this is false, just as it would be when interpreted de re. Why is the proposition false per compositionem? Not because ‘being a substance’ and ‘being a spirit’ are opposite predicates, but because the predicate ‘being a spirit’ is incompatible with the nature of some of the things that are currently substances. This is because, in Abelard’s per compositionem reading, the subject ‘every substance’ picks out the res that are substances in the actual situation, and the modal proposition is thus evaluated as true or false on the basis of the nature of these substances.60 In the Logica, thus, Abelard denies that in either de re or de sensu (per compositionem) propositions the quantifier may range over a domain of individuals different from the actual one. The truth conditions of all modal claims thus depend on actual objects and on the natures that they have in the actual situation. Abelard does acknowledge a de sensu reading of modals in which the subject term is itself included in the scope of the modal operator, but he thinks that this purely impersonal reading is not an admissible interpretation of modal claims. He excludes from his modal logic any predications in which modalities are not ‘grounded’ on actual things but concern impersonal states of affairs (see Chapter 4, Section 2 on this). This is particularly interesting when we consider that, in Abelard’s times, there were authors who instead admitted that de sensu propositions such as ‘it is possible for every animal to be a horse’ were both sound and true, because they interpreted it as saying: ‘A situation is possible in which all existing animals are horses’. The anonymous authors of the Introductiones Montane Maiores and the Glossae Doctrinae Sermonum, for instance, both accept this reading, as I argued in Chapter 4, Section 2.61 Abelard’s refusal to take into consideration counterfactually possible individuals seems to clash with a model of alternative ‘worlds’ or situations, which are not prevented from being populated by different objects. As Marenbon (1991) put it, although moving from a different perspective, this seems to confirm that Abelard thought more in terms of ‘alternative life stories’ (to which I may add, ‘of actually existing things, seen in terms of their actual nature’) than in terms of ‘alternative situations.’ It is true, though, that Abelard admits – at least in the Dialectica, even though he denies it in the Logica – that true predications could be advanced concerning non-existent beings, and indeed, as was said in Chapter 3, the 60 61

For the analysis of Abelard’s per compositionem exposition in the Logica Ingredientibus, see Chapter 4, Section 2 of this volume. On this, see also (Binini 2020a).

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attribution of possibilities and necessities to non-things was a common trait of early 12th-century discussions on modals. However, this may not be too problematic for my interpretation, that is, for the idea that the truth-makers of Abelard’s modal propositions are always entities – individual substances and their natures – that exist in the actual world. This is because Abelard claims that when we understand or think something about non-existing res, such as chimaeras, laughing stones, or future days, we always think of them in connection with certain properties and a certain nature – a nature that actually exists. For instance, when we reason about a centaur, we understand it as an animal, or as corporeal, or sensitive, or more generally as a res. We cannot understand any non-thing, or reason about it, unless by attending to a certain nature in it, and the nature that we attend to is always an actually existing nature, such as human or animal or bodily nature.62 Abelard’s claims in the Dialectica about the attribution of modalities to non-things, then, may still be read as if the source of their truth were the natures existing in the actual situation. The issues raised by attributing modalities to non-things, however, are entirely overruled in the Logica Ingredientibus, where, as was said, Abelard only admits actual things as subjects of both de re and de sensu modal predications. I hope to have offered some new elements (although certainly not conclusive or exhaustive ones) that may contribute to reconsidering the attribution of the possible-worlds semantics to Abelard. I have suggested that this semantics is not appropriate to capturing some aspects of his modal thought and that we should rather read him as an ‘actualist’ about modalities, namely, as ontologically founding modal truths in the actual world and in its actual inhabitants. With this interpretative model in mind, I now set out to dedicate the next two chapters of this book to the details of Abelard’s metaphysics of possibility (Chapter 9) and necessity (Chapter 10). 62

See, for instance, LI De Int. 29, 96–102: ‘Est autem ratio potentia discernendi, id est attendendi et deliberandi apud se aliquid quasi in aliqua natura vel proprietate consistens, veluti si quis rem aliquam vel in eo quod est res, vel in eo quod est substantia vel corporea vel sensibilis vel colorata penset, vel quasi in aliqua natura vel proprietate excogitet ipsam, etsi ipsa non sit, sicut hircocervus vel dies crastina vel lapis risibilis.’ On this, see also (Abaelard 1994, p. 90, § 95) and (Abaelard 1994, p. 28, § 6): ‘At vero intellectus esse non potest, nisi ex ratione aliquid iuxta aliquam naturam aut proprietatem attendatur, etiam si sit intelligentia cassa. Quippe cum centaurum sibi animus confingit tamquam animal partim ex homine partim ex aequo compositum; itaque animalis naturam, ac per hoc corporis sive substantie, attendere eum necesse est. Et cum hominis et equi quasi partes quasdam sibi iunctas consideret, et humani quoque et equini corporis non pretermittit proprietatem.’

chapter 9

Abelard on the Many Senses of Possibility Like his contemporaries, Abelard offers, in both the Dialectica and the Logica Ingredientibus, a definition of the possible as what is not incompatible with nature (non repugnans naturae, cf. Chapter 3, Section 3). According to this definition, possible is everything that does not contradict (in Abelard’s words, that is not repugnant to) the features constituting the natures of individual substances. Such a characterization – based on the two notions of non-contradictoriness, on the one hand, and of nature(s), on the other – appeals to some sort of metaphysical coherence or metaphysical compatibility holding between certain predications and the intrinsic ‘essence’ of things. By grounding possibilities exclusively on natures, Abelard’s definition disregards other criteria that one might see as relevant for capturing an intuitive idea of possibility, such as the physical conditions of individuals, the suitability of external circumstances, and, more generally, any condition that is extrinsic to the individual essences. For Abelard, however, these ‘extrinsic’ criteria are not pertinent for demarcating the boundaries of what is, or is not, said to be ‘possible’ for a thing. The domain of possibility outlined, thus, is broad enough to include ‘pure’ possibilities, namely, possibilities that remain eternally unrealized as a result of external hindrances or unfavourable circumstances. So, for instance, Abelard takes it as true that Socrates is possibly a bishop, even though he never was, and never will be, one, because there is nothing in the nature of Socrates that would prevent him from having such a property. Although the available sources from the early 12th century show that many logicians of this time wanted to take unrealized possibilities into account, referring e.g. to laymen being possibly bishops (cf. Chapter 3, Section 3), Abelard pushes his account of unrealized possibilities far beyond that of his contemporaries, stating that, on the grounds of the same account of possibility, we should also admit, for example, that it is possible for someone who lacks feet to run, because this would not be incompatible with his or her nature. His modal paradigm also includes possibilities that, despite having been genuine potentialities in the past, have become unrealizable after a certain moment in time, such as the possibility for someone who has lost his or her sight to regain it. At other times, Abelard stretches the boundaries of the possible to include possibilities that are not only unrealized but in principle unrealizable, such as the possibility of individuals to lack one of their inseparable accidents, for example, that of corporeal substances to be without colour or that of human © koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_014

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beings to lack the ability to laugh. Even though properties of this sort attach to their bearers in such a way that in no realizable condition are separated from them, they are not part of their bearers’ natures and are therefore ‘conceptually separable’. Thus, they do not inhere necessarily in substances, and it would in some sense be possible for substances not to have these properties. Abelard therefore seems to count as possibilities even states of affairs that are in fact entirely unactualizable. The domain of possibilities resulting from this definition is so broad that it may seem to delineate an abstract and ungenuine sense of the possible, which fails to capture what is effectively ‘open’ for an individual, that is, what the individual is concretely able to do or become. We should add that Abelard, starting from his nature-based definition of possibility, also provides other characterizations of the modal term that seek to grasp a narrower – and perhaps more intuitive – sense of the word, according to which possibilities coincide with the concrete potentialities (in Abelard’s words, the ‘natural potencies’) of things, which are grounded on some specific nature but also on the physical, contingent features of individuals. Some of the various senses that Abelard attributes to the term ‘possible’ have been explored by Christopher Martin, who identifies, among others, a definition of the word pointing at the set of possibilities that are open to an individual in the future, given its history up to a certain moment in time. Another Abelardian sense of ‘possible’, according to Martin, demarcates what was compatible with the nature of an individual in its past, but which is no longer realizable for him or her. A third use of the term refers to what is actualizable for an individual, not by virtue of his or her own nature but rather thanks to some extrinsic (e.g. divine) intervention.1 The catalogue of things that Abelard takes as ‘possible’ is indeed considerably varied. In this chapter I retrace some of his many uses of the term by analysing the rich constellation of examples that he discusses in his logical works. I will move from famous cases that have already been debated by scholars – such as the already mentioned possibility of Socrates to be a bishop, or that of a blind man to see – to others that are still in need of careful examination – such as that of humans to be unable to laugh, or that of humans to be dead or irrational. Table 5 presents some of these examples – each connected to a special sense of possibility.2 1 See (Martin 2004a) on these senses. 2 Senses (vii) and (viii) have already been analysed in Chapters 3–5, and I will not return to them in this chapter. See, in particular, Chapter 3, Sections 1–3 for the discussion of the possibilities of non-existent or future things in Abelard and his contemporaries. See Chapter 5

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table 5  Abelard’s senses of possibility

Senses of ‘possibility’

Abelard’s examples

(i)

e.g. it is possible for Socrates to be a bishop

possible is everything that is not incompatible with the nature of an individual substance (ii) possible is that which – despite being unactualizable – might be conceived without (conceptual) contradiction

e.g. it is possible for a blind man to see

Possibilities of opposite predicates Possibilities of non-existing things

e.g. it is possible for someone who is standing to sit at the same time at which he/ she is standing (vi) possible is what is compatible e.g. it is possible for the with the body or the corporeal substantia that is now substantia of an individual Socrates to be dead; it is possible for that which is a human to be irrational (vii) possible is any state of affairs e.g. it is possible that that might happen in the future my future son will be alive (viii) possible is what might happen e.g. it is possible that given a different domain of all existing substances things are spirits

Unrealized and unrealizable possibilities

(iii) possible is what is actually realizable for an individual, given its physical constitution and/or the external circumstances (iv) possible is everything that – despite being unactualizable given the actual circumstances – could have happened had things occurred otherwise (v) possible is that which can be predicated synchronically of a subject who manifests the opposite property in act

e.g. a body might be without colour; a human might be without the ability to laugh e.g. for any man it is possible to run, but not every man can run ‘with ease’

Areas of interest in Abelard’s modal thought

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I will argue that this variety of uses is not symptomatic of an inconsistency or heterogeneity in Abelard’s thought, for the majority of these senses (with the exception perhaps of the last two, which Abelard eventually excludes from his modal thought) may be referred back to the broader sense of possibility as non-incompatibility with the nature of existing things, which is consistently held by Abelard to be the proper and basic interpretation of possibility. The significations of ‘possible’ evoked in (ii)–(vi) may then be subsumed under the broad sense of possibility defined by (i). Despite presenting some minor internal discrepancies, then, I believe that Abelard’s overall reflection on possibility is quite uniform and coherent. This might be better appreciated if we compare his view on possibility with that on necessity, which suffers instead from the lack of a univocal definition and from the compresence of conflicting tenets, which render Abelard’s overall understanding of necessity somehow unstable, as will be explained in Chapter 10. In the present chapter I also suggest that Abelard’s various examples about what is, or is not, possible may be gathered into three macro-areas that reflect Abelard’s main interests on possibilities, areas around which his modal thought was developed. The first is that of unrealized and unrealizable possibilities, which has been mentioned many times already (see, in particular, Chapters 3 and 8 of this volume) and which is exemplified by cases such as Socrates being possibly a bishop, humans being possibly unable to laugh, and blind men who possibly see. All of these cases are expressions of Abelard’s analysis of the demarcation between the domain of the actual and that of the possible. This area also includes Abelard’s reflections on the distinction between the general possibilities and the concrete potentialities of things, and on the development of possibilities through time (diachronic versus synchronic possibilities). A second main area of Abelard’s reasoning on possibility has to do with puzzling possibilities such as those that attribute opposite features of the same being, for instance, the possibility of a standing person to sit or that of a human to be dead. Examples such as these were discussed animatedly by Abelard’s contemporaries, who considered them within their analysis of the validity of conversions for modal propositions. As we saw in Chapter 4, Section 1, some early 12th-century logicians, like the authors of the commentary H9 or of the treatise on modalities M3, took conversions as being invalid for nominal modal on the problem of existential import in Abelard’s modal logic, and on the change occurring between the Dialectica and the Logica on this matter. See Chapter 4, Section 2 for Abelard’s consideration of cases in which possibilities are evaluated over a domain of objects different from the actual one, an idea that he in fact rejects in the Logica Ingredientibus.

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propositions, on the grounds that, whereas it is true that, for example, ‘It is possible for every man to be a cadaver’ or ‘It is possible for every young to be old’, their converted forms, ‘It is possible for a cadaver to be a human’ or ‘It is possible for every old to be young’, are false. The discussion of these cases was also linked to the fallacy per compositionem/per divisionem, with which logicians became acquainted around the 1110s–1120s thanks to the initial circulation of Aristotle’s Sophistical Refutations. Abelard also devotes much thought to the discussion of these cases, the analysis of which is connected to the development of his de re/de dicto distinction. Finally, a third central issue in Abelard’s theory on possibility is that which concerns possibilities of future things, such as the possibility of a future child to exist, or the modalities ascribed to non-existing, counterfactual individuals, such as the possibility of an alternative situation in which all existing substances are spirits. The discussion of these examples is triggered by Abelard’s reflection on purely impersonal modalities, the use of which would allow us to extend the range of admitted possibilities to those that have no corresponding subject in the actual situation. As was said in Chapter 3, many contemporaries of Abelard were interested in ascribing possibilities to non-existent or future things, and indeed they seem to accept true modal propositions about non-things as admissible. I have also explained how Abelard, though willing to admit the predication of modalities about non-things and future things in the Dialectica, denies that modal propositions of this sort could be true in the Logica, so that he restricts his modal language and semantics to the domain of things that actually exist. As Knuuttila put it, Abelard envisages the possibility to speak about modalities ‘as item[s] of the domain of non-things, consisting of the natures of things, assertoric contents of propositions and other intelligible matters which in some way determine the order of existing things without being part of it’.3 Nevertheless, Abelard eventually refrains from this idea, stating that impersonal and purely de dicto predications are not, properly speaking, ‘modal’. I have already analysed the issues related to the modalities of non-things in Chapter 4, Section 2 and Chapter 5, Section 2–3, and I will not return to them in this chapter. In what follows I rather focus on Abelard’s theory of unrealized and unrealizable possibilities (Chapter 9, Sections 1–4), as well as his analysis of the puzzling cases in which incompatible predicates are said to possibly inhere in the same subject (9.4–9.5).

3 (Knuuttila 1993, p. 95).

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1 Any Man Can Be a Bishop: Possibility as Non-repugnancy with Nature In a well-known passage from the Dialectica Abelard claims that the modal proposition ‘Socrates is possibly a bishop’ (Socrates est episcopus possibiliter) is true even though Socrates never was a bishop and never will be one. The truth of this proposition is justified by invoking the view that what is possible for a certain subject is everything that is non-repugnant to this subject’s nature. According to this characterization, many states of affairs that never occur are included among possibilities, for there are indeed many things that are compatible with the nature of a subject and that nevertheless are never actualized at any moment of this subject’s existence. Abelard presents this idea in Dialectica 193–4, while addressing the problem of how to give the truth conditions for sentences concerning possibilities, necessities, and impossibilities. With respect to these conditions, he remarks, modal sentences differ from simple categorical ones: while the latter are made true by virtue of the actual inherence of a certain property in a subject – and false when this is not the case – modal sentences are not said to be true or false by virtue of an actual inherence or separation between things. The modal sentence ‘Socrates is possibly a bishop’, for instance, is true, not by virtue of the predicate being in some way (quomodo) conjoined to the subject, but rather by virtue of the fact that being a bishop is not incompatible with the nature of Socrates (and of any other human). Abelard invokes this view against those who interpreted modal propositions (at least in their adverbial form) as always entailing the existence of an actual inherence between what is expressed by their predicate and subject terms, an inherence that would be qualified by means of the modal adverb. As was said in Chapter 2, some of Abelard’s contemporaries held this view, such as the authors of treatises M1 and M3, and perhaps also that of commentary H9. Abelard, on the contrary, claims that both adverbial and nominal propositions about possibility may be true even though there is no actual connection between their predicate and subject, because what is expressed by modals does not depend on what is, or is not, the case, but rather on (in)compatibility relations holding between certain predicates and the nature of things: When we say: ‘Socrates is a bishop possibly’ and we assert that this is true, in which way do we modify, through [the mode] ‘possibly’, the inherence of being bishop in Socrates, given that there is no such inherence? In no way, in fact, does the property of being a bishop cohere with Socrates, who is a layman. But when we say that [a certain property] might cohere

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(posse cohaerere), we are not saying that it also does cohere. […] ‘Possible’ and ‘contingent’ mean the same thing. For we do not take here the term ‘contingent’ as meaning what actually happens, but what can happen, even if it should never happen, so long as the nature of the thing is not incompatible with its happening, but instead allows it to happen. For instance, when we say that ‘It is possible for Socrates to be a bishop’, this is true even though he never will be so, since his nature is not incompatible with being a bishop. We may evaluate [this non-incompatibility] from other individuals of the same species, who we see actually participate in the property of being bishops. For indeed, whatever actually happens in one individual, we consider that the same can happen in every individual of the same species, because they are all of the same nature.4 Similarly, the modal proposition ‘It is impossible for Socrates to be a stone’ is true not by virtue of the fact that being a stone never inheres in Socrates but because the nature of Socrates is not compatible with being a stone (Dial. 193, 25–6). As was discussed in Chapter 3, Section 3, examples like the ones provided by Abelard were amply discussed by his contemporaries. We find similar cases in the Dialectica of Garland, the commentary H9, as well as the treatises M1 and M3, plus some other commentaries on De Interpretatione or on Boethius.5 The references to unrealized potencies that we find in these sources are probably motivated by the need of early 12th-century logicians to interpret and comment upon the modal theory developed by Aristotle in De Interpretatione. At the very end of Chapter 13, Aristotle provides a list of things that are possible, including what he calls ‘pure potencies’, namely, possibilities that are never followed by actualization. Aristotle also deals with unrealized possibilities in 4 See Dial. 193, 19–194, 1: ‘Cum ergo dicimus: “Socrates est episcopus possibiliter” et verum enuntiamus, quomodo per “possibiliter” inhaerentiam episcopi ad Socratem determinamus, cum ipsa omnino non sit? Nullo enim modo proprietas episcopi Socrati laico cohaeret. Nec “posse cohaerere” dicendum est “cohaerere” […] “Possibile” quidem et “contingens” idem prorsus sonant. Nam “contingens” hoc loco [non] quod actu contingit accipimus, sed quod contingere potest, si etiam numquam contingat, dummodo natura rei non repugnaret ad hoc ut contingat, sed patiatur contingere; ut, cum dicimus: “Socratem possibile est esse episcopum”, etsi numquam sit, tamen verum est, cum natura ipsius episcopo non repugnet; quod ex aliis eiusdem speciei individuis perpendimus, quae proprietatem episcopi iam actu participare videmus. Quicquid enim actu contingit in uno, idem in omnibus eiusdem speciei individuis contingere posse arbitramur, quippe eiusdem sunt omnino naturae; et quaecumque uni communis est substantia, et omnibus; alioquin specie differrent quae solis discrepant accidentibus.’ 5 Cf. also (Thom 2003b) and (Martin 2016) on this.

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Chapter 9 of the De Interpretatione, where he claims that a proposition such as ‘It is possible for this cloak to be cut up’ is true even if the cloak will never be cut up. On the basis of these Aristotelian passages and of Boethius’ commentaries on them, early medieval thinkers were inclined to include an account of extra-actum possibilities within their modal views, and I have suggested in Chapter 3, Section 3 that the definition of possibility in terms of non-incompatibility with nature might have developed precisely to overcome ontological problems connected to the admittance of possibilities of this sort. Several interesting consequences follow from the criterion of ‘natural suitability’ with which Abelard illustrates the possible in the aforementioned passage of the Dialectica. First, the possibilities of an individual are ‘immune to change’,6 in the sense that they cannot be either acquired or lost. Because the nature of a substance is invariable in time, the range of possibilities that depend on such a nature are also not subject to temporal variation. Abelard’s naturebased definition therefore offers a ‘static’, rather than dynamic, account of the possible. Second, because all individuals belonging to the same natural kind are ‘of the same nature’, as Abelard remarks, what is possible for an individual is also possible for all other members of the same species. Abelard rehearses this idea in a number of passages of the Dialectica, such as the following: What we see as actually occurring in one of the particulars, we believe that the same might occur (posse contingere) in every other individual of the same species. Indeed, we intend ‘potency’ and ‘impotency’ with respect to nature, so that any substance could receive only what its nature allows, and could not receive what its nature repels. Because all particular things having the same species are of a same nature (whence it is also said that the species itself is the entire substance of individuals), they are all the same with respect to the potencies and impotencies that they admit.7 The idea of different individuals being of the same nature (eiusdem naturae) – and consequently having the same possibilities – is used insistently by Abelard in the Dialectica (e.g. Dial. 188, 14; 194, 5; 211, 26–7; 228, 3; 385, 6; 426, 5; 582, 19), although it has no parallel in the Logica Ingredientibus. Similar expressions 6 Cf. (Knuuttila 1993, p. 90). 7 See Dial. 385, 1–8: ‘Quod enim in uno particularium videmus contingere, id in omnibus eiusdem speciei individuis posse contingere credimus; “potentiam” enim et “impotentiam” secundum naturam accipimus, ut id tantum quisque possit suscipere quod eius natura ­permittit, idque non possit quod natura expellit. Cum autem omnia eiusdem speciei particularia eiusdem sint naturae unde etiam dicitur ipsa species tota individuorum substantia esse, idem omnia recipere potentia sunt et impotentia.’

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may be found in some of Abelard’s later texts, such as the Theologia Summi Boni and the Theologia Christiana.8 What Abelard says in Dial. 193–4 concerning the signification of the term ‘possible’ is also interesting when one seeks to understand his views on modal epistemology, in particular, his theory on how we know (and how we can justify our belief) that something is possibly predicated of a thing. According to Abelard, the perception of the actual world guides us to the knowledge of not only realized but also unrealized possibilities. This is because our perception that some property actually inheres in an individual of a certain species grounds not only our knowledge that this individual is possibly a bishop (on the basis of the principle that what is actual is also possible) but also our knowledge that being a bishop is possible for all individuals that are of the same species, insofar as they all have the same nature, and therefore the same possibilities and impossibilities. From what we perceive as actual in one subject, then, we derive some knowledge about what is possibly predicated of the other subjects with the same nature. Nevertheless, perception – or ‘inductive abstraction’, as Knuuttila has called it9 – is neither a complete nor infallible guide to the knowledge of natures and possibilities. This depends on the fact that not all the possibilities of a thing are manifested through the individuals of a species. Indeed, as I suggest in the next section, there are some possibilities that are in principle non-actualizable in any member of a species but which are still possible for them, such as the possibility of human beings not to be able to laugh or that of corporeal substances not to have a colour. The fallibility and incompleteness of our epistemological access to possibilities also depends on the limits of our access to natures themselves. As was said in Chapter 8, Section 2, Abelard often states that we are largely ignorant about the properties that constitute natures, in the sense that ‘we often do not know what differentia distinguishes members of one species from members of another species belonging to the same genus’.10 Therefore, most of the time we are not able to say what counts as essential and what counts as accidental for different individuals. What Abelard admits is, so to speak, a ‘negative knowledge’ of natures, in the sense that from what we see actualized in a thing we infer that certain properties or behavioural patterns are not incompatible with the nature of this thing and of other things of the same kind.11 8 9 10 11

See, for example, (Abaelard 1969b, p. 223–4). See (Knuuttila 1993, p. 91). See (Marenbon 1997, p. 119). On ignorance of natures, see also Chapter 8, Section 2 and, in addition, (King 2004, p. 81 ff); (Marenbon 1997, p. 117); (Binini 2021).

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In a famous passage from the Dialectica Abelard states that, in fact, it is not the aim of the logician to investigate natures, and that studying natures and their causes is rather the purpose of ‘physics’, that is, what we would call natural philosophy. He does nevertheless recommend to logicians and natural philosophers – who are both interested in natures, even if for different purposes – to take each other’s achievements into consideration.12 As was said in Chapter 8, however, despite the fallibility and incompleteness of our epistemological access to natures, Abelard seems bound to admit that, in many cases, we do have some grasp of the natures of things – albeit limited and imperfect. This is repeated often by Abelard in his discussion of topical inferences, where he says that, on some occasions, we are certain about the truth of a conditional because of our knowledge of the nature of the things referred to by the propositions’ terms.13 Even though we are not able to entirely and infallibly discriminate between the essential and accidental properties of things, according to Abelard, we still know something about the range of their possibilities – either thanks to our senses, which allow us to perceive what is actually manifest in a species’ members and so to exclude that certain things are incompatible with their nature, or through reason, which acquires knowledge of things by attending to their nature. As Noël has suggested, the typical behaviours of individuals allow us to obtain some understanding of their natures, and “since behaviors unfold in time, getting to know a thing is always a gradual process”, open to flaws and errors. Similarly, our cognition of the unrealized possibilities of things is a gradual, cumulative process, based on our sense of perception and on the capacity of reason to identify natures.14 As I suggest in the following section, however, Abelard also seems to admit other possibilities that are entirely inaccessible to our knowledge through this sort of ‘inductive abstraction’, since they are confined to a realm of non-realizability. 12

13

14

‘Hoc autem logicae disciplinae proprium relinquitur, ut scilicet vocum impositiones pensando quantum unaquaque proponatur oratione sive dictione discutiat. Physicae vero proprium est inquirere utrum rei natura consentiat enuntiationi, utrum ita sese, ut dicitur, rerum proprietas habeat vel non. Est autem alterius consideratio alteri necessaria. Ut enim logicae discipulis appareat quid in singulis intelligendum sit vocabulis, prius rerum proprietas est investiganda. Sed cum ab his rerum natura non pro se sed pro vocum impositione requiritur, tota eorum intentio referenda est ad logicam’ (Dial. 286, 31–287, 1). See, for example, Dial. 255, 13–7: ‘Cum enim dicimus: “si est animal, est animatum,” quantum quidem ad rerum naturam quam novimus, de veritate consequentiae certi sumus, quia scilicet animal sine animato non posse subsistere scimus, non quidem ad complexionem inferentis.’ See also Dial. 284, 26–9. (Noël 2018, p. 54).

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2 Humans Who Cannot Laugh and Uncoloured Bodies: Unrealizable but ‘Conceivable’ Possibilities According to the nature-based semantics that Abelard proposes, a modal predication such as ‘It is possible for an S to be P’ is true if being P is not in contradiction to any predication constituting S’s nature. Natures are also used by Abelard to define the semantics of necessity propositions such as ‘S is necessarily P’, which, according to Abelard, is true if, and only if, P is ‘required’ (exigitur) by the nature of S, that is, if being P constitutes S’s nature as one of its substantial forms. In this sense, it is necessary, for example, that a certain man is animal or mortal. As we have seen in the last section, these modal definitions permit us to make room for unrealized possibilities such as that of any human to be a bishop. In the next two sections of this chapter (3 and 4) we will see that, according to the same view, Abelard is able to extend the range of the possible to possibilities that have an even higher degree of unrealizability, such as that of a blind person to see or of an amputee to walk. In this section I first show that, according to Abelard’s modal paradigm, we are also allowed to admit possibilities that are in principle unactualizable, such as the possibility that something is a man despite being unable to laugh or that something is a body although lacking colour. Generally speaking, Abelard’s modal characterization permits that it is in some sense ‘possible’ for any individual substance to be without its inseparable accidents. This idea is defended by Abelard in his commentary on the theory of propria presented by Porphyry in the Isagoge. As is known, Porphyry defined propria as inseparable accidents, namely, as those properties that – although not constituting the essence or nature of their subjects – are nevertheless in act inseparable from them. Standard examples given by Porphyry are the ability to laugh for men or blackness for crows or Ethiopians. These properties are inseparable in the sense that there is no realizable situation in which the subject does not have them: it would not be possible, for example, for a man to exist who is in act unable to laugh. However, when taken in pair with the definition of ‘accident’ as a property that can either belong or not belong to the subject without it being destroyed (praeter subiecti corruptione), Porphyry’s definition of propria seems at first sight to be somewhat oxymoronic. In which sense do these properties accidentally belong to their subjects while at the same time being inseparable from them? The solution proposed by Porphyry to reconcile these two conflicting characterizations of propria – as both inseparable and accidental – was to consider these properties, although inseparable in act, as separable ‘in reason’ from their subjects, in the sense that they could

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be ‘conceived’ (subintelligi in the Latin translation) as separated from them.15 Essential properties, on the contrary, are those that are inseparable both in act and in mind, so that a situation in which they do not belong to their subjects would not only be unrealizable but also inconceivable. In his Glossae on Porphyry Abelard compares Porphyry’s treatment of propria with the one Boethius gives in his De Divisione. There, Boethius argues against Porphyry that some propria, such as the ability to count or to learn geometry with respect to humans, are not separable from their subjects in any sense, either in act or in the mind. This is because, even though they are not a part of humans’ substantia and they do not constitute their nature, it is still the case that if these properties were to be separated from their bearers, these subjects would not persist as humans (si haec possibilitas ab homine seiungatur, homo ipse non permanet).16 Boethius’ position echoes – though it does not explicitly mention – Aristotle’s admittance of necessary or per se accidents, namely, properties that do not constitute the essence of a thing but which are nevertheless necessarily predicated of it. Examples of such accidents given by Aristotle are the property of triangles to have the sum of interior angles equal to two right angles,17 or the property of swans and snow to be white. Alexander of Aphrodisias also admitted inseparable accidents, advancing as an example – again – the property of being white for swans and snow.18 However, in Alexander’s and (presumably) also in Aristotle’s theory, each necessary connection holding between a substance and its inseparable accidents is caused by some features that belong to the essence of the thing. The whiteness of snow, for instance, despite not itself being part of snow’s nature, is still caused by some material properties that constitute such a nature and/or follow from it. Inseparable accidents, then, would be necessary by virtue of being grounded in the nature of things.19 15

16

17 18 19

The relevant passage for this thesis is the incipit of Isagoge V (in the Latin translation): ‘Accidens vero est quod adest et abest praeter subiecti corruptionem. Dividitur autem in duo, in separabile et in inseparabile; namque dormire est separabile accidens, nigrum vero esse inseparabiliter corvo et Aethiopi accidit (potest autem subintellegi et corvus albus et Aethiops amittens colorem praeter subiecti corruptionem).’ This is what Boethius says on this in De Divisione: ‘Aliud rursus est quod ratione separari non possit, quod si separatum sit species interimatur, ut cum dicimus inesse homini ut solus numerare possit vel geometriam discere. Quod si haec possibilitas ab homine seiungatur, homo ipse non permanet; sed haec non statim earum sunt quae in substantia insunt, nam non idcirco homo est quoniam haec facere potest, sed quoniam rationalis est atque mortalis.’ (Boethius 1998, p. 20) See e.g. Metaphysics 5, 30, 1025a30–2; Prior Analytics 1.3 643a27–31. Cf. (Alexander of Aphrodisias 2001, pp. 50–1). See (Malink 2005, p. 125). For such an interpretation of Aristotle, according to which all necessary properties of a thing are grounded in their essence, see also (Charles 2000, p. 203).

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It is not clear whether Boethius also adheres to this view, taking properties such as the ability to do geometry or to count as inhering necessarily (but accidentally) in a subject by virtue of being grounded on the essence of humans and thus following from that essence. There are no clear elements in Boethius’s works to acribe this interpretation to him, even though he might have had something of this sort in mind. Abelard, on the other hand, explicitly opposed the view that the inseparable accidental properties of a thing follow from this thing’s nature or from its substantial properties. In his treatise on topical inferences, he repeatedly states that conditionals such as ‘If it is a body, it is coloured’ or ‘If it is a man, it is able to laugh’ are not true, since what is expressed in the antecedent and consequent are not related by the necessary semantic connection that is needed to ground the truth of conditionals. Conditionals of this sort are contrasted against others in which antecedent and consequent are related by a connection of ‘conceptual inseparability’, a connection that grounds their perpetual truth because what is said in the consequent is ‘required’ or ‘compelled’ by what is said in the antecedent (as in, for example, ‘If it is a body, it is corporeal’ or ‘If it is a man, it is an animal’). This is what Abelard maintains, for instance, in one passage of the Dialectica: When it is proposed: ‘if it is a body, it is corporeal’, ‘if it is a body, it is coloured’, although it is the same substance of the body (eadem corporis substantia) that is both corporeal and coloured, and although everything that happens to be coloured is also corporeal, and vice versa, so that there is no diversity (distantia) between the substance which is informed by colour or constituted by corporeity with respect to their res, still the former enunciation happens to be true, and the latter false, according to the fact that the substance of body is considered in different ways: in the first case, it is considered as something informed by corporeity, in the second, as something informed by colour. Of these two forms, the first inheres in the body substantially, the second accidentally. Because the form of corporeity inheres substantially in the body, this form is understood (intelligitur) in the very name of the substance, so that when it is said that any given thing is a body, it is also proposed that it is a corporeal substance, but not that it is coloured; since every bodily substance might remain intact without colour (quippe absque colore omni substantia corporis integra posset consistere). Because ‘coloured’ designates the substance of body by virtue of an accidental form – a form without which any thing

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might persist in its nature of body, whereas ‘corporeal’ does so by virtue of a substantial form, a form without which in no way the substance of body can persist or be conceived, the second conditional lacks the necessity which the first holds.20 According to Abelard, thus, the predication of an inseparable accident does not validly follow from the predication of the substance to which the accident belongs. I have italicized a few expressions in which Abelard suggests that, in some sense of the expression ‘might be’ (possit esse), it is true to say that a corporeal substance might be without colour – and more generally, without one of its inseparable accidents – because the substantia that is the body could remain intact (possit consistere integra) without any of its accidental features. On the other hand, Abelard states that the same substantia cannot be deprived of one of its substantial forms and still remain the same, and that indeed it cannot even be conceived of without those forms. This is exactly what Abelard also suggests in his commentary on Porphyry’s Isagoge, as we will see 20 See Dial. 285, 18–286, 1: ‘Cum enim proponitur: “si est corpus, est corporeum”, “si est corpus, est coloratum”, quamvis eadem corporis sit substantia, quae et corporea est et colorata, et quicquid coloratum esse contingit, et corporeum, et econverso, ut iam nulla sit in re distantia inter substantiam quae colore formatur aut corporeitate constituitur, –– illam tamen enuntiationem veram esse, hanc vero falsam esse contingit, secundum id quod diversis modis substantia corporis accipitur; hic quidem secundum id quod corporeitate, ibi vero secundum id quod colore formatur. Quarum quidem formarum haec secundum substantiam, illa vero secundum accidens inest corpori. Quia vero corporeitatis forma substantialiter corpori inest, in substantiae ipsius nomine ipsa quoque intelligitur et, cum corpus quidlibet esse dicitur, corporea substantia esse proponitur, sed non colorata; quippe absque colore omni substantia corporis integra posset consistere. Quia ergo coloratum ex accidentali forma substantiam corporis designat, sine qua quidem forma quaelibet res in natura corporis omnino possit consistere, corporeum vero ex substantiali, praeter quam nullo modo substantia corporis vel intelligi potest, haec consecutio necessitate, quam illa tenet, privatur’. For a similar position, see also Dial. 334, 31–335, 2: ‘Licet autem eadem res per “animal rationale mortale” et per “homo” praedicetur, quia tamen illam esse diversis modis demonstrant, non est consequentia, sicut nec ista: “si est corpus, est coloratum”. Licet enim essentia illa quae per “coloratum” attribuitur, | eadem cum illa sit quae per “corpus” ponitur, tamen quia aliunde a “colorato” quam a “corpore” nominatur – ex adiacentia scilicet coloris, absque quo omnino corpus posset consistere, quippe eius est fundamentum – omni profecto necessitate consequentia illa destituta est’; and Dial. 350, 6–15: ‘Nulla itaque consequentia ex natura simpliciter paritas vera potest ostendi, sed fortasse ex prietate paritatis naturalis. Sed et fortasse hoc falsum est. Nam quis hanc necessariam recipiat: “si est corpus, est coloratum”, quippe corpus est coloris fundamentum et absque colore omnino consistere potest? Sed nec ista: “si est homo, est risibilis” necessaria potest dici, secundum id quod Porphyrius speciem proprio priorem naturaliter appellat, cum videlicet proprium in specie posterius fieri dicit.’

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further on in this section. The sense of possibility that is at play in these passages, h ­ owever, needs to be specified, and I will return to this point. Another ­expression that deserves attention, for Abelard seems to use it in a technical sense, is the ‘substantia corporis’, which I have translated as ‘substance of the body’. Abelard uses similar expressions in other passages on modalities that have long puzzled interpreters, and I will discuss it in more details in Section 5 of this chapter. In the commentary on the Isagoge that is included in the Logica Ingredientibus, Abelard aims to reconcile the diverging opinions of Porphyry and Boethius on the inseparability of propria, by saying that their controversy depends on an ambiguity in the terminology.21 There are in fact, Abelard says, two ambiguities in Porphyry’s and Boethius’ discussions: the first concerns the notion of ‘separability in mind’, while the second concerns the very notion of ‘what possibly is’ or ‘might be’. As for the first ambiguity, Abelard says that ‘separability in mind’ could be interpreted in two ways: with respect to our human mental abilities or with respect to ‘the nature of things’. While Porphyry adopts the latter interpretation, Boethius uses the term in the first sense. As for the second ambiguity, Abelard says that there are two ways in which something ‘might be the case’: in the first sense, it is not possible for something to be without one of its propria, because it cannot happen that something exists as separated from them. Boethius, who uses this sense of possibility, is therefore right to deny that it is possible for a subject to lack an inseparable accident. There is, however, also another, ‘weaker’ sense of ‘being possibly the case’, with respect to which we can truly say that ‘it might be that a subject is without a proprium’ (e.g. for a body to be without colour; for a human to be unable to laugh). This is due to the fact that inseparable accidents are not required (exiguntur) by the subject’s nature, and they are thus not connected to their bearer with the necessary tie that links a substance to its essential properties. Here is a more detailed outline of Abelard’s reasoning. Abelard begins by stating that Boethius acknowledges propria as accidents. He therefore admits that these properties are not part of the nature of their subject. Because, he continues, the nature of a thing is anterior or prior to its accidents, it must be true that accidents are in some sense separable from the substance, for there could be no priority without separability. However, because propria are in some

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The reconciliation is, however, unbalanced on the side of Porphyry, because Abelard says that Boethius’ position is not only contrary to the one held by Porphyry but also inconsistent in itself: ‘At vero hoc loco Boethius tam sibi ipso quam Porphyrio contrarius esse videtur’ (LI Isag. 90, 5–7).

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sense separable from their subject, and because they clearly are not separable in act, the only way in which they are separable is separability ‘in reason’.22 How are we to interpret this notion of ‘rational separability’? There are, Abelard says, two possible interpretations: in the first sense, ‘separable in reason’ is what we, as rational human agents, are able to ‘picture in our reason’ as separated. This is what Abelard calls separability in reason ‘quantum ad discretionem hominum’. This is not the sense in which propria are separable, and Abelard denies that we could in fact imagine a man who is unable to laugh, or that in general we could have images of any substance as being without its inseparable accidents. This is because our mental activity is very much influenced by our sense experiences, so that our imagination is limited and governed by what we have perceived as happening in act. Because, in his commentary, Boethius intends the separability in mind with respect to our discernment, he is then right to deny that the ability to laugh or count is separable in reason from humans. The second sense in which the separability in reason can be interpreted, the one that Abelard attributes to Porphyry, has nothing to do with our imaginative capacities, but rather concerns the natures of things and the possibility to discriminate between properties that constitute a nature and properties that do not. This is Abelard’s separability quantum ad naturam rei.23 According to Abelard, this ‘conceptual separability’, or separability quantum ad naturam rei, entails some sort of possibility (or more precisely, a certain way in which things ‘might be’), and Abelard insists on this in a few passages from his commentary on propria.

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‘Sed si, ut ipse ait Boethius, accidentia sunt propria, quomodo saltem ratione separari non possunt, quae natura separari permittit? Sicut et ipse Boethius ibidem in ipsis Divisionibus glaucitatem oculorum a subiecto ratione dividit, Porphyrius nigrum a corvo. Praeterea ipse Porphyrius ad differentiam proprii et speciei in sequentibus dicit, quod ante subsistit species quam proprium, proprium vero posterius fit in specie. Quomodo autem ante est quam proprium in natura, si non possit ab ea proprium saltem ratione separari?’ (LI Isag. 90, 10–8). ‘Sed sciendum est quod duobus modis “separari ratione” accipitur, scilicet vel quantum ad discretionem hominum vel quantum ad naturam rei. Quantum autem ad naturam Porphyrius dicit speciem priorem esse proprio, Boethius vero quantum ad discretionem nostram dicit potentiam numerandi vel discendi geometriam ratione non separari ab homine.’ (LI Isag. 90, 19–24) Notice that, in De Intellectibus, Abelard does in fact admit that human reason has the capacity to discriminate between those properties that constitute the nature of a thing and those that do not. See on this Chapter 8, Section 2 above. On Abelard’s theory of the intellect with respect to the discretion of natures, see, in particular (Rosier-Catach 2017) and (Cameron 2020).

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In one passage he says that the nature of humans ‘would allow’ the absence of risibilitas (‘bene natura hominis pateretur ipsum esse sine risibilitate’) because this capacity does not constitute its essence. But this is precisely the way in which Abelard defines possibility within the semantics presented above: possible is that which is allowed by the nature of a thing (i.e. that which ‘natura permittit’, or ‘natura patitur’).24 Abelard then goes on to distinguish between two senses of ‘what might be’ (posse esse): in the first sense, it is impossible for a man to be without the ability to laugh, because it could not happen in act that there is a man who is unable to laugh. In another sense, however, Abelard admits that it might be the case that a man could be without this ability (‘alio modo contingere potest hominem posse esse sine proprio’) because it is not required by its nature to have this property (‘non ex eo quod est homo exigere proprium’).25 Finally, Abelard explains that the expression ‘what might be’ (posse esse) is ambiguous and susceptible to being interpreted in two different ways. Again, the distinction between two senses is made, on the one hand, in terms of what is realizable or what could happen, and, on the other hand, in terms of what is required or not required by the nature of something. Abelard calls the latter sense a ‘negative interpretation’ of the possible, which he thinks comes into play when Porphyry states that substances possibly lack their propria: What is meant by saying: ‘a man might be without the ability to laugh’ can be interpreted in two different ways: either as that, by virtue of being a man, does not require being able to laugh, which is true in conformity with Porphyry’s exposition, or as saying that a man could exist in such a way that he is unable to laugh, which Boethius correctly negates, since it is false. But there is no contradiction with Porphyry, because Porphyry would accept this ‘might be’ in a negative sense, whereas Boethius would negate this interpreting it in a positive sense.26 24

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‘[Propria] in natura rei iuxta eundem Boethium et Porphyrium separabilia sint, quia videlicet bene natura hominis pateretur ipsum esse sine risibilitate, quippe ea substantiam eius non constituit sicut rationalitas et mortalitas nec per eam natura hominem facit sicut per illas’ (LI Isag. 90, 39–91, 3, my emphasis). ‘Sed licet homo non possit esse sine risibilitate quodammodo, quia videlicet non potest contingere, ut homo sit et non risibilis, alio tamen modo contingere potest, ut voluit Porphyrius hominem posse esse sine proprio, ut videlicet negative intelligatur sic: non ex eo quod est homo, exigere proprium’ (LI Isag. 91, 11–6, my emphasis). ‘Quod itaque dicitur homo posse esse sine risibili, duobus modis accipi potest, scilicet vel quod ex eo quod homo est, non exigat risibile, quod verum iuxta acceptionem Porphyrii, vel quod homo possit esse ita, quod non sit risibilis, quod quia falsum est, bene Boethius

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Here and in the previous passages what ‘might happen’ seems to be understood in a first sense as some sort of realizability or actualizability: it is impossible that a man is without the ability to laugh because such a situation could under no circumstances occur. In the second sense possibility is instead understood negatively, in terms of non-incompatibility with a thing’s nature. If some property is not required (exigitur) by the nature of a thing, it is not a necessary one, and therefore the contrary property is possible. Interestingly, in the Dialectica Abelard proposes a distinction between two senses – or two ‘degrees’ – of necessity that retraces the one that he has just proposed about ‘what might be’. I will return to this distinction in Chapter 10, Section 1. We should note, however, that, contrary to what he does with ‘necessarium’, Abelard never explicitly refers the ambiguity to the term ‘possibile’ itself; rather, it is the expression ‘posse esse’ that he characterizes as ambiguous. From what John of Salisbury claims in the Metalogicon, it seems that, in the second half of the 12th century, a similar distinction between the meanings of ‘possible’ and ‘contingent’ had become common. John suggests that the term ‘possible’ was usually taken to include unactualizable cases, such as those of substances that are possibly without their inseparable accidents (e.g. it would be possible for an Ethiopian to be white or for a swan to become black), whereas if someone were to say publicly that these cases were also ‘contingent’, he continues, they would be judged ‘out of their head’: At present, we by no means consider ‘contingent’ equivalent to ‘possible’, although this is the meaning Aristotle seems to have attributed to it in his treaties on modals. While it is ‘possible’ for the Ethiopian race to become white, and the species we know as swans to become black, neither of these is ‘contingent.’ If one were to assume that these things are contingent [contingere], simply because they are possible, and were publicly to assert this, on the authority of Aristotle, but in opposition to the evident way in which the public use the terms, he would evidently be out of his head, or at least a bit tipsy.27 It is notable that Porphyry – or any other author before Abelard, as far as I know – did not draw a connection between the notion of ‘what can be conceived’ (subintelligi potest) and what ‘might be’ (posse esse). Abelard seems to be the first to establish a link from conceivability to a certain broad sense of

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negat. Nec contrarius Porphyrius, cum Porphyrius “posse esse” negative accipiat, Boethius affirmative acceptum removeat’ (LI Isag. 91.27–32, my emphasis). (John of Salisbury 2009, pp. 169).

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possibility. Nevertheless, as was said earlier, Abelard does not use ‘conceivability’ in this context as an epistemological notion, that is, as referring to the ability possessed by a rational agent to unite or separate concepts in the mind. On the contrary, because for Abelard the capacity we have to conceive or imagine depends on what we have experience of through senses, conceivability in this sense would not be a good guide to possibility, at least according to what he says in this part of the Logica. The commentary on Porphyry’s treatise on propria is not the only place where Abelard treats statements about possibility as ambiguous and susceptible to being evaluated as both true and false, depending on the meaning we attribute to the modal term. In the next section I consider other possibilitypropositions that Abelard considers to be in need of disambiguation, such as ‘It is possible for an amputee to walk’, ‘It is possible for a crippled man to fight’, and ‘It is possible for a blind man to see’. 3 Amputees Can Walk and Crippled Men Can Fight: Abelard’s Distinction between Simple and Determinate Potencies Modern interpreters of Abelard’s modal thought have already brought attention to some examples, reported in both the Dialectica and the Logica Ingredientibus, where Abelard claims that it is possible for someone who is crippled to fight and for someone who has lost his legs to walk or run (mancus potest pugnare; possibile est curtatum ambulare).28 The truth of these propositions is justified by resorting to the usual definition of possibility as metaphysical coherence between the predication of a certain property and the nature of substances: we know that the abilities to fight and to run are compatible with the nature of humans because we observe some humans who manifest the abilities in act. Because, as we have seen in Chapter 9, Section 1, nature is the same in any member of a species, we may infer that every human possesses these potencies, even those who have lost (or never had) the physical appropriate conditions that would render them actualizable. Potencies such as these, which belong to a subject by virtue of mere compatibility with its nature (secundum hoc quod natura rei permittit, cf. LI Cat. 229, 25), are also called by Abelard ‘simple’ potencies (potentiae simplices). They are possibilities in the ‘abstract’ and notional sense that was exposed at the beginning of this chapter, a sense that, as we have seen, includes states of 28

For an analysis of these cases, see, in particular, (Martin 2004a). Other comments on these examples are to be found in (Knuuttila 1993, p. 90), (Thom 2003b, p. 50).

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affairs that remain unrealized or which are in fact unrealizable given the circumstances in which they are predicated. Abelard contrasts simple potencies with ‘determinate’ ones. With the notion of determinate potencies, Abelard wishes to capture a more concrete and genuine sense of possibility, according to which what is possible is what is actualizable and concretely open for an individual to do or become. According to this second sense, it would not be true to say, for instance, that an amputee possibly walks or runs, because – having lost the physical conditions to actually do so – the amputee has also lost the relevant determinate potency. Abelard’s distinction between simple and determinate potencies (where the latter are also called ‘aptitudes’ – aptitudines) is to be found within his discussion of ‘natural potencies and impotencies’ (potentiae et impotentiae naturales),29 which are possibilities and impossibilities that belong to substances by virtue of nature and not by being acquired through some sort of learning or experience.30 In the Dialectica (96, 17–99, 24) Abelard presents simple potencies as those that belong ‘simpliciter’ to their owners, which he divides into those that are required by the nature of a thing, inasmuch as they constitute its substantia, and those that are simply compatible with such a nature. The former are, for instance, the potency that human beings have to be rational and mortal31 or the potency that honey has to be sweet.32 These are actually manifest in their bearers and, as Abelard says, inhere substantially in them in such a way that they ‘occupy their entire nature’ (naturam totam occupant). Simple potencies that are not required but merely compatible with the nature of their owners, on the other hand, are, for example, the potency that human beings have to run or to fight. Potencies of this sort are not always manifest but nevertheless belong to all members of a species and are invariable through time and circumstances. Indeed, Abelard claims that perhaps these potencies also inhere 29

See, in particular, Dialectica 96–9; 384–9; 391–2; LI Isag. 96–109; LI Cat. 122–39; 223–51; 259–85; LI De Int. 265, 516–9. 30 The use of this terminology of ‘potentia naturalis’, based on Boethius’ commentary on the Categories, is quite common in early 12th-century sources, mainly in the C commentaries. For some details on this notion, see footnote 68, Chapter 3. 31 ‘Sunt autem aliae potentiae vel impotentiae quae naturae propriae sunt, non aptitudinis, in eo scilicet quod non solum eas natura contulit, verum etiam eas exigit, ut rationalitas, irrationalitas, mortalitas, immortalitas, quae speciei cui insunt, naturam totam occupant nec ei per accidens, sed substantialiter insunt. Omnes enim homines rationales sunt vel mortales, sed non omnes salubres vel pugillatores dicuntur; unde haec per accidens inesse clarum est’ (Dial. 96, 34–97, 3). 32 See Dial. 99, 21–4.

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in their subjects substantially, rather than accidentally (Dial. 97, 5–6), since they also exclusively depend on a substance’s nature. This observation, though brief, is interesting, for it suggests that, for Abelard, the predications of simple possibilities with respect to each individual are necessary. We would therefore have that, if it is possible for Socrates to, say, run, it is also necessary that this is possible. Abelard does not elaborate further on the possibility to iterate modal operators in this way, but he seems to have at least contemplated such a possibility. Determinate potencies, on the other hand, belong to their owners accidentally and contingently. They include the abilities – or inabilities – to actively perform an action or the dispositions to passively undergo a change, such as the potencies to fight and run well, to be easily broken or cut, or to be inclined to good or bad health.33 Although, like simple ones, determinate potencies also depend on the nature of their owners (it is a necessary condition for having an aptitude that it is not incompatible with one’s nature), their possession depends on other conditions too, such as the physical conditions of the individual and perhaps – Abelard is not clear on this point – the external and contingent circumstances that the individual is in.34 For this reason, whereas 33

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See, for example, Dial. 97, 4–14: ‘Neque enim cursor aut pugillator a simplici potentia currendi vel pugnandi (quae enim fortasse substantialiter insunt), nominantur, immo a potentia pugnandi facile vel currendi leviter. Potentiarum itaque vel impotentiarum huiusmodi aliae sunt ad aliquid facile faciendum, ut potentiae vel impotentiae facile pugnandi vel currendi, aliae non ad patiendum facile, sed magis ad resistendum facile, ut “sanativus” dicitur eo quod possit non facile infirmari, idest resistere vehementer infirmitati, ac vix eum contingat infirmari, “aegrotativi” vero aecontrario dicuntur, ex impotentia scilicet eiusdem, per quod videlicet non queant facile resistere infirmitati. “Durum” quoque dixit secundum potentiam non facile secari, hocest secundum id quod facile sectioni resistat; “molle” vero secundum impotentiam eiusdem, de eo scilicet quod non possit non facile secari, idest facile resistere sectioni.’ It is not clear whether the possession of a determinate potency is also dependent on the external circumstances in which the subject is. Paul Thom, in (Thom 2003b, p. 51), seems to think that external circumstances could prevent a subject from having a certain determinate potency. Thom alludes here to the Stoic problem, reported by Alexander of Aphrodisias, concerning whether chaff that is in the depths of the sea still has the possibility to burn. He says that, according to Abelard’s understanding of possibility, it would be true to say that chaff has the simple potency to burn – insofar as it is compatible with its nature: ‘Chaff at the bottom of the ocean has precisely the same nature as chaff on dry land.’ But chaff does not have the determinate (Thom says, the ‘concrete’) potency to burn because of the external circumstance in which it finds itself. This concrete possibility is prevented by an external circumstance and not by an inappropriate physical constitution of the chaff. Thom here suggests that, for Abelard, the possession of determinate (concrete) potency is not only dependent on the nature and physical constitution of a thing, but also on other external contingent conditions, which are independent of the thing

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every member of a certain species has the same simple potencies, not everyone has the same determinate potencies. Not every human being, for instance, has the determinate potency to fight easily – only some do. More precisely, only human beings that have a particular, and similar, physical constitution have this aptitude, for instance, those who have the appropriate flexibility of arms and legs.35 Within his analysis of determinate potencies, Abelard raises a concern about the ontological status of certain potencies, such as the disposition to be easily sick (aegrotativum), the act of which seems to be a negative state of affairs (not being healthy). Admittance of potencies and impotencies of this sort is problematic, for it seems to bind us to admit that everything that is not healthy – even stones or things that do not exist – has the corresponding potency. However, Abelard claims that this concern only arises if we maintain that the predication of a potency amounts to the predication of a certain property or form in a bearer. If this were the case, the attribution of an inability or a negative disposition would correspond to the predication of a negative property. But, Abelard claims, we should not understand the term ‘possible’ or ‘potent’ as referring to some property or form inhering in a thing. As was made clear in Chapter 3 of this book, the predication of modal terms does not amount to an attribution of properties, according to Abelard and some of his contemporaries (see Chapter 3, Section 1 on this).36 A distinctive mark of determinate potencies, which differentiates them from simple ones, is that they are attributed to a subject accompanied by a certain qualification, expressed by an adverb: we say, for instance, that someone has the ability to run rapidly or to be easily broken. We might even say that

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itself. However, as far as I know, Abelard never provides examples of such a situation, that is, of a situation in which a subject is prevented from having a determinate potency because of some external factor. ‘Alia enim est potentia pugnandi simpliciter, quae omnibus aequaliter inest hominibus, alia potentia pugnandi facile secundum flexibilium membrorum aptitudinem, quae non omnibus inest’ (LI Cat. 229, 25–7). A similar formulation may be found in Dial. 96, 32–3. ‘Unde potius potentiae non facile aegrotare actus erit de non esse: unde ipsa est potentia quod non facile aegrotare dicitur; hunc autem, cum sit de non esse, non necesse est potentiae suae universaliter supponi, ut scilicet dicamus omne quod non facile aegrotat, potentiam ad non aegrotandum facile habere, id est sanativum esse; quippe iam lapis ipse et quaecumque et non sunt, aegrotativa dicerentur! Sic quoque et potentiae non esse album, cum sit actus non esse album, ipsi tamen universaliter subdi non potest, ut videlicet dicamus omne quod non est album potentiam illam habere, sed fortasse ita: “potens non esse album”, ut nullam formam in nomine “potentis” intelligamus, sed id tantum quod naturae non repugnet; in qua quidem significatione nomine “possibilis” in modalibus propositionibus utimur’ (Dial. 98, 7–18).

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these adverbs introduce a factor of ‘gradability’ in the attribution of determinate potencies. Differently from simple potencies – which, as we have seen, are the generic possibilities of a thing – potencies of this sort admit degrees: things might be more or less breakable, more or less inclined to remain in good health, or more or less agile in fighting or walking.37 Abelard expounds this idea in the Dialectica, where he says that different subjects cannot be compared with respect to their natural simple potencies (e.g. humans with respect to rationality or the ability to laugh), while we might allow a comparison with respect to their abilities or dispositions, saying, for instance, that a man is more or less strong than another one, or that a certain body is more resistant or less fragile than another. These comparisons depend on the fact that the abilities and dispositions of things are of different degrees, and these degrees depend on factors having to do with the physical constitution of their bearers (e.g. the suitability of their limbs or the density of their parts). Simple potencies, on the contrary, are not gradable, since they only depend on the nature of things, and individuals of the same species are entirely alike with respect to them.38 Moreover, differently from simple possibilities, determinate potencies do not omnitemporally belong to their subjects: even if a human being has the ability to fight easily at a certain time of life, this does not necessarily mean that he or she has this potency at every time in which he/she exists, for a 37

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This element of gradability is a feature that is also seen as relevant for defining powers or potentialities in some contemporary theories of modalities, and it is used, for example, to differentiate potentialities from possibilities. Cf., in particular, (Vetter 2018, p. 281): ‘Potentialities come in degrees: some glasses are more fragile than others, and some of us possess the ability to play the piano to a much greater degree than others. Moreover, those degrees are contingent: a given glass might have taken a little crack and thus been more fragile than it is; had I practised the piano more when I was a child, I would now possess the ability to play it to a much greater degree.’ ‘Quae enim secundum naturam potentiae sunt, comparari non possunt, sed fortasse illae quae sunt aptitudinis, secundum quod et potentior et facilior hic homo illo dicitur et durius hoc corpus illo, quod scilicet facilius possit sectioni resistere. Quas enim natura infert potentias aequaliter, sicut natura ipsa, omnibus inest, ut rationalitas singulis hominibus. Quae vero habitudinis sunt, comparantur; prout enim quidam melius vel peius dispositi sunt, magis vel minus potentes dicuntur, et magis aptus hic ad currendum vel ad pugnandum quam ille dicitur secundum membrorum aptitudinem, vel magis durus secundum partium densitatem. Has itaque potentias habitudinis, non naturae, quae accidentales sunt, nihil prohibet comparari. Sed hae quidem quae in naturam substantiae veniunt, sub comparatione non cadunt, ut rationale, risibile. Ac si haec per accidens homini inesse dicatur, quae propria est, illa vero substantialiter, quae maior est, nec tamen multo rationabilius hanc accidentibus hominis quam illam aggregant, cum utramque natura conferat. Quod enim natura exigit, separari non patitur et quod ipsa requirit, deesse non potest.’ (Dial. 426, 1–17)

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change in the physical conditions may result in losing an ability or disposition (e.g. amputation of a leg may result in losing the potency to run easily). That determinate potencies can be lost because of a change in physical conditions is explicitly remarked upon by Abelard in De Intellectibus, where he considers the relation between rationality (rationalitas) and reason (ratio) and says that it is analogous to the relation between the simple potency to run and the determinate potency to run easily. Whereas rationality and the simple potency to run belong to subjects solely by virtue of nature and independently of actual manifestation, reason and the ability to run easily only belong to those subjects who exercise these potencies in act and without the physical impediments that may be derived by age or a bodily deficit.39 Although Abelard admits that it is possible for an individual to lose one of its determinate potencies, it is not clear whether he would also admit that potencies of this sort can be gained or acquired. As far as I know, he never contemplates cases in which determinate potencies are acquired, so that their bearer comes to have them from a certain moment on. Nevertheless, Abelard’s theory does not explicitly exclude cases of this sort. Anyhow, what is certain is that Abelard interprets determinate potencies as dynamic, constantly evolving possibilities, delineating a flexible spectrum of the possible, which may ‘shrink’ and perhaps also ‘widen’ depending on contingent circumstances such as the physical suitability of substances and, perhaps, the presence or absence of external hindrances. This dynamic model contrasts with the one that is proposed for generic, species-wide possibilities, which are, as was said, atemporal and ‘immune to change’.40 Abelard thinks that when we talk about an individual’s capacities in our everyday language, we usually refer to possibilities in the sense of the determinate potencies of a subject, that is, to what a subject is genuinely able to do or become and to what is actualizable for it (LI Cat. 229, 34–6; see also Dial. 97,

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‘Non idem vero est rationalitas quod ratio: illa quippe omnibus angelicis et humanis spiritibus inest, ex qua rationales dicti sunt; haec vero quibusdam tantum solis scilicet, ut diximus, discretis. Tantum itaque inter rationalitatem et rationem differre arbitror, quantum inter potentiam currendi et potentiam facile currendi, ex qua cursores Aristoteles appellat secundum membrorum flexibilium aptitudinem. Quicumque igitur spiritus ex natura propria discernere potest, rationalitatem habet. Rationem vero ille solus qui hoc facile exercere valet, nulla aetatis imbecillitate remoratus aut inconcinnitate complexionis sui corporis ex qua perturbationem aliquam trahat, ut insanus aut stultus fiat’ (Abaelard 1994, p. 30, §8–9). For the use of this last expression and some notes on the atemporality of Abelard’s possibilities, see (Knuuttila 1993, p. 90).

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17–8).41 However, Abelard believes that the proper and fundamental sense of possibility is the one referring to simple potencies and based on metaphysical coherence. Determinate potencies constitute a subset of the wider range of possibilities that is delineated by Abelard’s definition of the possible in terms of non-repugnancy with nature. Paul Thom characterized Abelard’s distinction between simple and determinate potencies as a distinction between ‘abstract’ and ‘concrete’ possibilities.42 The characterization that I have advanced in this section is that between the (metaphysical, natural) possibilities and the potentialities of a thing. Abelard’s determinate potencies, in fact, have several features that usually characterize our idea of potentiality, as opposed to that of possibility. I have tried to expound these features in this section, but it might be useful to sum them up here. First, determinate potencies are defined by giving the conditions of their actualizability: the possession of such a potency is connected to the possibility to manifest this potency in act, whereas simple potencies are somewhat independent of their realizability and of realizability conditions. Second, determinate potencies are identified at the level of individuals, whereas simple potencies are identified at the level of species and natures. Third, determinate potencies admit degrees, whereas species-possibilities are not gradable. Fourth, determinate potencies are dynamic and subject to variation, depending on both time and contingent factors, whereas simple potencies are unchangeable and unrelated to any factors other than specific natures. We do not know whether Abelard’s distinction between a broad sense of possibility and a stricter sense of potentiality or potency had any influence on later authors. As far as I am aware, this distinction returns in at least one source, a commentary on the Categories (C27),43 in which the author evokes Abelard’s theory of potentiae et impotentiae naturales and describes natural potencies as those that individuals have by virtue of their nature. He also distinguishes potencies from possibilities, saying that even though it is false that ‘every human being has the natural potency to run’ (because not everyone has the proper physical form allowing him or her to run ‘with ease’), it is still true that ‘it is possible for every human being to run’, because, he explains, ‘the nature of no human is incompatible with running’ (‘nullius enim hominis natura cursui repugnat’).44 The author retraces Abelard’s distinction between what is possible for a certain individual, which is defined in terms of non-repugnancy with 41 42 43 44

Cf. (Martin 2001, p. 102) on this point. (Thom 2003b, p. 51). C27: Milan, Archivio Capitolare della Basilica Ambrosiana, M2, fols 1ra–15rb. See Milan, Bas. Ambr., M2, fols 10va–10vb.

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nature and is a species-wide possibility, and the natural potencies that this individual has, which depend on its nature but also on other conditions, for instance, its physical constitution. In the next section we will see how the contrast between simple and determinate potencies is applied by Abelard to another case, that of a blind man who is said to ‘possibly see’. This case is used by Abelard to further investigate the relation between possibilities, potentialities, and time. 4 Might a Blind Person Have Been Able to See? Abelard on Past and Counterfactual Potencies By resorting to the distinction between simple and determinate potencies, and to his definition of simple possibility as non-incompatibility with nature, Abelard justifies the truth of other puzzling propositions, such as the one asserting the possibility of a blind man to see. Like the cases that were the subject of the previous section (‘It is possible for an amputee to walk’ or ‘for a crippled man to fight’), and like other cases that Abelard takes into consideration in other parts of his work (e.g. ‘It is possible for someone who is standing to sit’), the blind-man example is also a case in which two incompatible properties are said to inhere possibly in the same subject. It is Abelard himself who draws an analogy between the following three examples: i. It is possible for a blind man to see; ii. It is possible for an amputee to walk; iii. It is possible for someone who is standing to see; saying that they should be treated according to a similar exposition (LI Cat. 274, 7–14) and claiming that they are all ambiguous and could be either true or false depending on how they are interpreted. It is true, for instance, to say that a man who is blind still has the ‘simple possibility’ to see, in the sense that, similarly to other individuals like him, he might have maintained the ability of sight that he has in fact lost. It is false, on the contrary, to say that one person could regain actual sight having lost it. Similarly, Abelard takes it as possible for the amputee to have feet – not in the sense that he or she might recover them, but in the sense that he might have had them; and for a man who is now standing to sit in the very present moment in which he stands, although he cannot simultaneously be standing and sitting: We therefore concede that he who is blind might see simpliciter, because he might see in such a way that he might never had acquired blindness, as

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other [humans] do, although it is not possible for him to see after becoming blind. Similarly, we concede that an amputee might have two feet, but not that he might acquire them after he had lost them, namely, he might not recover them. And we also concede that he who is standing might sit in the present, but not that he might sit while he stands, that is, not in the sense that he could be both standing and sitting. (LI Cat. 274, 7–14)45 The parallel established by Abelard between these three examples is not immediately evident. It is clear that all propositions considered have a similar form, in which two opposite properties are predicated of the same thing. However, it is not equally clear how the amputee and the blind-man cases could be appropriately analysed by means of the per divisionem/per compositionem analysis that Abelard provides to deal with the standing-sitting case (cf. Chapter 4, Section 2 on this analysis). In fact, there is at least one relevant difference between the latter example and the two former ones: we could say that a man who is actually standing possibly sits, inasmuch as sitting is realizable for him at some other ( future) time, posterior to the moment of predication. Abelard himself appeals to this justification in his analysis of the example, as we will see shortly. Nevertheless, we cannot say that an amputee possibly walks or a blind man possibly sees in the sense that, although not having these properties in act, these may actualize at subsequent moments of his life. In fact, the abilities of seeing and walking, once lost, are lost forever, according to Abelard. What Abelard has in mind while establishing the parallel between the three cases is probably that, when we evaluate claims having the form ‘It is possible for an S, who is actually not-P, to be P’, we should always distinguish carefully between the broad, species-wide notion of possibility that is based solely on the subject’s nature – what Abelard here calls ‘simple’ ascription of possibility, which could be construed as a per divisionem possibility – and the notion of possibility that has to do with what is actualizable for an individual given its actual attributes and circumstances, which he construes here as a sort of per compositionem possibility. Another question raised by Abelard’s defence of the truth of propositions (i)–(iii) has to do with whether Abelard expounds the possibilities in question 45

‘Concedimus itaque eum qui caecus est, posse videre simpliciter, quia si videre posset, ut numquam habuisset caecitatem, sicut ceteri faciunt, posse autem eum videre, postquam caecus est, non est possibile. Sic curtatum concedimus posse habere duos pedes, sed non posse habere, postquam amiserit, hoc est non posse recuperare pedes; et stantem concedimus sedere in praesenti, sed non posse sedere dum stat, in eo scilicet quod possit habere stationem et sessionem’ (LI Cat. 274, 7–14).

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diachronically or synchronically. If the former were the case, when affirming that ‘It is possible for an S, who is actually not-P, to be P’, Abelard would take the possibility of not being P as referring to a time other than the one in which S is actually P. In the latter case, Abelard would instead take the possibility of not being P as attributable to S at the very same time in which S is P. table 6  The distinction between diachronic and synchronic possibilities

Diachronic:

It is possible for S, who is P at time t, not to be P at time t’, where t’ differs from t. Synchronic: It is possible for S, who is P at time t, not to be P at t.

As some scholars have noted, in some passages Abelard speaks as if he has the first interpretation in mind. When he deals with the standing-man case in the Logica Ingredientibus, for instance, he claims that the correct interpretation of the proposition ‘It is possible for someone who is standing to sit’ is that in which the possibility to sit refers to the ability of the subject to be sitting ‘quandoque’, namely, to manifest the relevant property in act at some time other than the present. This formulation suggests, according to some interpreters,46 that the possibility in question is to be read diachronically. As Marenbon has pointed out, such a diachronic interpretation of modalities might have been inspired by the ancient modal paradigms with which Abelard was acquainted. Both Aristotle and Boethius, in fact, are usually interpreted as holding a diachronic view of possibility. Knuuttila too interprets Abelard as following a diachronic paradigm for possibilities in this case, a paradigm that would be based on the model offered by Boethius and would exclude synchronic alternatives.47 Such a diachronic interpretation of possibilities also seems to have been endorsed by some of Abelard’s contemporaries. As was seen in Chapter 4, Section 1, some logicians of Abelard’s time discuss modal propositions similar to (i)–(iii). The analysis of these cases was brought up within the debate concerning the validity of conversions for nominal modal claims, and it reveals that at least some contemporaries of Abelard understood modalities according to a special diachronic model similar to the one offered by Boethius, in which possibilities refer to some future time and ‘vanish’ once the contrary state of affairs has realized. According to this view one could say, for instance, that it 46 47

Cf. (Marenbon 1997, p. 222). Cf. (Knuuttila 1993, p. 95).

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was antecedently possible for someone to both sit and not sit at the present time, but the possibility of sitting disappears when, in the present, the subject in question actually stands. The author of M3, for instance, maintains that ‘It is possible for every young man to be old’ and ‘for every child to be a young man’, but he does not allow that from these one could infer the converted forms, namely, ‘It is possible for some old man to be young’ and ‘It is possible for a young man to be a child’. Although he does not offer a justification for this claim, he seems to rely on an intuitive understanding of modalities according to which the spectrum of possibilities that are open to a subject becomes progressively narrower with time, because some of the facts that were possible antecedently to a certain moment become impossible once the opposite state of affairs has occurred.48 In the Dialectica (Dial. 196, 15–28), Abelard reports the opinion of some, according to whom two propositions such as ‘For no one who sees is it possible to be blind’ and ‘For no one who is blind is it possible to see’ fail to convert – presumably on the basis that the first is false, because certain people who actually see may become blind in the future, and the second true. This analysis of conversions, rejected by Abelard in the Dialectica, seems to go hand in hand with an interpretation of possibilities in terms of diachronic potentialities, according to which what is possible for a substance is defined on the basis of what might be actualized in some future moment of its life. As Martin has noted, however, Abelard’s exposition of the blind man’s case suggests another interpretation, namely, that he is thinking of possibilities of this sort synchronically.49 To understand this, we should see this case in connection with Abelard’s theory of habitus and privatio, a connection that helps us to reveal his thoughts on the association between possibility and time. Following Aristotle, Abelard specifies that any subject who is susceptible to having a certain habitus (e.g. having sight, having hair) is also susceptible to being deprived of it and acquiring the corresponding privatio instead (becoming blind or bald). The turning of a habitus into the corresponding privatio is, according to Abelard, an irreversible state: there is no possibility for the former habitus to be restored. This means that once a man has become blind, there is no chance for his sight to be reinstated and no chance that he might 48 49

For a modern characterization of this diachronic model, see, for example, (Von Wright 1984, pp. 96–103). I offer an analysis of the relevant discussions in M3 and in H9 in (Binini forthcoming). On the distinction between diachronic and synchronic modalities, see, in particular, (Von Wright 1984). For the use of this distinction in understanding medieval interpretations of modality, see (Knuuttila 1993). For the specific case of Abelard’s theory, see (Martin 2001) and (Martin, 2004b).

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actually see again.50 It is crucial to stress this point because it entails that, when Abelard states that it is indeed possible for someone who is blind to see, he does not mean that the possibility to regain sight at some future time is an open, genuine chance for the subject. Once lost, the ability to see, intended as a genuine potentiality, is lost forever. Nevertheless, Abelard maintains that the (simple) possibility to see is still predicable of the blind person secundum naturam, namely, by virtue of the relation of non-repugnancy between sight and the nature of the thing: Any man, even the one who is blind, has the possibility to see. For indeed, his nature would surely allow that during his lifetime he would have beared vision and preserved it throughout his entire life, so that blindness would never occur in him. What we see to possibly occurring in one of particular [substances], we believe that the same might occur in all individuals of the same species. This is because we intend ‘potency’ and ‘impotency’ with respect to nature, so that any thing might bear only those [properties] that its nature permits, and cannot bear those that its nature rejects. Because all particular things of a same species are of a same nature – whence it is said that the species is the entire substance of individuals –, they all admit the same potencies and impotencies.51 As Martin has pointed out, referring to a parallel discussion of this example in the Logica Ingredientibus, Abelard emphasizes that the possibility of the blind man to see does not refer to a time other than that in which the man is actually blind. Rather, Abelard states that ‘It might be that a person who has become blind sees, even at that very time in which he remains blind’ (Posset enim contingere, ut is qui caecus factus est, videret hoc etiam tempore quo caecus permanet):

50 51

On this see, for example, Dial. 384, 28–30: ‘Cum autem de habitu transitus fiat in privationem, de privatione in habitum impossibile est fieri regressionem.’ ‘Quilibet enim homo, etiam ille qui caecus est, possibilis est videre. Bene enim tota eius natura pateretur ut et tempore suo visionem suscepisset et eam in vita sua custodisset, ut numquam in eo caecitas conti[n]gisset. Quod enim in uno particularium videmus contingere, id in omnibus eiusdem speciei individuis posse contingere credimus; ‘potentiam’ enim et ‘impotentiam’ secundum naturam accipimus, ut id tantum quisque possit suscipere quod eius natura permittit, idque non possit quod natura expellit. Cum autem omnia eiusdem speciei particularia eiusdem sint naturae – unde etiam dicitur ipsa species tota individuorum substantia esse –, idem omnia recipere potentia sunt et impotentia’ (Dial. 384, 2–385, 8).

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Whence we concede that all men are able to see, even those who are blind, but nevertheless that there may be no revision from privation to habit. For it might have fallen out, that he who has been made blind, would have seen even at this time at which he remains blind, in such a way, that is, that he never would have been blind, and there would have been no regression. But it is entirely impossible that someone who is blind, or anyone else, might see after he is blind, that is, that after he has become blind he might recover his vision. We concede thus that someone who is blind might, without qualification, see, because he might have seen in such a way that he never became blind, just as other do. For him to be able to see after he is blind is, however, not possible. Thus, we concede that an amputee might have two feet, but not that he might have them after he has lost them, that is, not that he might recover his feet; and we concede that a standing man might sit at the present moment, but not that he is able to sit, while he stands, in such a way, that is, that he is able to be both sitting and standing.52 As Martin has argued, simple unactualized possibilities, such as the one that the blind man has to see, are justified by Abelard in counterfactual terms.53 Suggesting that the actual course of time is somewhat contingent, Abelard claims that some things might have gone otherwise than they actually did, resulting in alternative present states of affairs – or more precisely, as Marenbon has suggested, alternative life histories. For instance, events could have gone in such a way that the person who is actually blind never lost his or her sight but preserved a genuine ability to see (Posset enim contingere, ut is qui caecus factus est, videret hoc etiam tempore quo caecus permanet, ita quidem, ut numquam habuisset caecitatem). Martin interprets this passage as a sign that,

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‘Unde omnes homines concedimus posse videre, etiam eos qui caeci sunt, nec tamen regressionem posse fieri de privatione ad habitum. Posset enim contingere, ut is qui caecus factus est, videret hoc etiam tempore quo caecus permanet, ita quidem, ut numquam habuisset caecitatem atque nulla esset regressio. Sed hoc omnino impossibile est, ut is qui caecus est, vel quislibet alius possit videre, postquam caecus est, hoc est praecedente caecitate reperiret visionem. Concedimus itaque eum qui caecus est, posse videre simpliciter, quia si videre posset, ut numquam habuisset caecitatem, sicut ceteri faciunt, posse autem eum videre, postquam caecus est, non est possibile. Sic curtatum concedimus posse habere duos pedes, sed non posse habere, postquam amiserit, hoc est non posse recuperare pedes; et stantem concedimus sedere in praesenti, sed non posse sedere dum stat, in eo scilicet quod possit habere stationem et sessionem’ (LI Cat. 273, 39–274, 10, translated in Martin 2001, p. 110). Cf. (Martin 2001, p. 110).

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in Abelard’s modal theory, contingency must refer not only to the future but also to the present and the past. There are also other hints in Abelard’s texts that he considered the present and the past as contingent. In his commentary to De Interpretatione 9, for instance, he claims that if we consider two contradictory propositions de praeterito or de praesenti, such as ‘I sat’ (or ‘I sit’) and ‘I did not sit’ (‘I do not sit’), their disjunction is necessary, but neither of the two disjuncts is necessary in itself (LI De Int. 248, 130–4). Moreover, although Abelard conforms to the standard characterization of present and past events as ‘determinate’, as all early 12th-century authors do, he refuses the Boethian definition of determinacy as a kind of necessity, and he provides an alternative, epistemological definition of this concept, which has no modal implications (cf. Chapter 10, Section 2). The issue of the necessity versus contingency of the present and the past was animatedly debated in the early 12th century, and there are other logicians – the most explicit being the anonymous author of the commentary H20 – that insist instead that all propositions about the past are ‘absolutely’ necessary, just as propositions such as ‘God is immortal’ are.54 5 Dead Humans and Irrational Humans: Other Puzzling Cases of de re Possibilities As explained in the previous sections, the proper and primary sense in which Abelard understands the terms ‘possible’ and ‘impossible’ is that of (non-) incompatibility or (non-)repugnancy between a certain predicate and the nature of a thing. On the basis of these nature-based definitions, propositions such as ‘It is possible for this man to be irrational’ or ‘This human can be dead’ should turn out to be false, insofar as the nature of humans, according to the standardly accepted Aristotelian and Porphyrian framework, requires animation and rationality as essential forms. It is puzzling, thus, to read how Abelard, in both the Dialectica and the Logica, argues for the possibility of humans to be dead (Dial. 196, 29–197, 31) or irrational (LI Isag. 92, 21–33). These examples have puzzled commentators, and their consistency with Abelard’s overall modal semantics must be justified. As I hope will become clear, Abelard’s statements must be interpreted by relating them to his theories of identity and individuality, as well as to his ideas on the multiplicity of natures that are associable with the same individual res. 54

See (Binini 2019) on early 12th-century discussions on determinacy and necessity with respect to the present, past, and future events.

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An analysis of the ‘dead humans’ case is presented by Abelard in the Dialectica, in connection with his critique of the de sensu interpretation of modal propositions. Here, Abelard claims that it was the opinion of his Master (very likely, William of Champeaux)55 that nominal modal propositions such as (i) ‘It is possible for a human to be dead’ (Possible est hominem mortuum esse) should be expounded de sensu. Abelard also claims that his Master took nominal modals of this sort not to convert salva veritate. He thought that, in fact, while (i) is true, its converted (ii) ‘It is possible for a dead thing to be a man’ is false, presumably on the basis that in (i) there is a reference to a state of affairs that will happen in the future, while (ii) refers to a state of affairs that cannot actualize. Many examples of this sort were discussed by contemporaries of Abelard, as was mentioned in Chapter 4, Section 1.56 Abelard thinks that these two commitments – the de sensu reading of nominal modals, on the one hand, and the refusal of conversions, on the other – are incompatible and thus render his Master’s modal theory inconsistent. To show this, he aims to demonstrate that all conversions are valid for de sensu modalities, and that, in particular, the two propositions (i) and (ii) have the same truth-value (viz., false) when taken de sensu. According to Abelard’s explanation of the de sensu reading, proposition (i) is true de sensu if what is said by the corresponding simple proposition, ‘a man is dead’, is possible. However, because being dead and being human are repugnant to each other, there is no possible situation in which they are both predicable simultaneously of the same subject, so (i) is false de sensu, just like its converted (ii).57 After saying this, Abelard goes on to state that, however, if we interpret (i) in the proper way – namely, de re – the proposition turns out to be true. This is not in the sense that ‘It is possible for a human being to die’ or ‘to be dying’ (Possibile est hominem mori), but in the sense that ‘The individual substance which is actually a human can be dead’ (Id quod est homo potest mortuum esse). Abelard claims that there is, in fact, no incompatibility between the individual thing 55 56

57

This identification seems to be well established, although Martin challenges it in (Martin 2016). I have argued in (Binini forthcoming) that the analysis of conversions and their validity was at the basis of the identification of the de re/de dicto distinction, and that the position that Abelard attributes to his Master is very similar to the one endorsed by the anonymous author of commentary H9. ‘Restat autem nunc post conversiones ut ostendamus secundum eorum expositionem eas falsas quas veras aestimant, ut istam: “possibile est hominem mortuum esse”, sic scilicet expositam: “possibile est quod haec propositio dicit: ‘homo est mortuus’”. [...] Nullo itaque modo videtur vera haec propositio: “possibile hominem mortuum esse”, ut scilicet de sensu simplicis exponatur’ (Dial. 196, 29–197, 2).

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that is now a human – meaning, the corporeal substantia actually informed by human nature – and the property of being dead. I will quote this example in full, as the context in which it is formulated is important for its comprehension: In no way does the proposition ‘It is possible for a man to be dead’ appear true, if exposed as being about the sense of a simple proposition (de sensu simplicis). When we expose it de rebus, however, it does seem true, as saying that: ‘It is possible for a man to be dead’, namely, ‘that which is man (id quod est homo) can be made dead’. But I say [this] because ‘being made dead’ is not the same as ‘dead’; ‘being made dead’ is the same as ‘being dying’, not ‘dead’. ‘Dying’ and ‘dead’ are in fact opposite to each other, for ‘dying’ is a name for the living, since indeed one cannot be dying if one does not live. It seems thus that [it would be true to say] that ‘it is possible for a man to die’, from whence we also say that men are mortal, but not that ‘it is possible for a man to be dead’. […] we cannot admit that those [properties] that the nature of a thing does not demand might inhere in this same thing, but we can only admit those whose coming up are not contrary to the nature of such a thing. We may thus admit that this body could be dead, although [this body] is a human, if we take into consideration only the property [it has] of being a body, but not its being a human. For indeed, ‘dead’ is not repugnant to ‘body’, but to ‘human’. […] And indeed, being dead will never inhere in a human, neither when this human exists nor when he does not exist; which is evident, since the two are incompatible. Nevertheless, this body, which is human, will be dead, because given that we attend to it as a body, it is not repugnant to ‘dead’. Therefore, just as we admit this [i.e. that ‘body’ is not repugnant to ‘dead’], because this body will indeed be dead, in the same way we also accept that being dead is possible for this body, but not for this human, although the human is the body. For it is one thing to consider in this subject the simple nature it has as a body, and another to consider in the same subject its properties as a human. For with respect to the substance which is a human [substantia quae homo est], once the human will be destroyed [this substance] will still remain a body, but it will not remain a human.58 58

‘Nullo itaque modo videtur vera haec propositio: “Possibile hominem mortuum esse”, ut scilicet de sensu simplicis exponatur. Cum vero de rebus exponitur, vera videtur hoc modo: “Possibile est hominem esse mortuum”, idest id quod est homo, potest mortuum fieri. Sed dico quia fieri mortuum non est esse mortuum; fieri enim mortuum, mori est; non mortuum esse. “Moriens” autem et “mortuum” adversa sunt; “moriens” enim viventis

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In this passage Abelard invokes a de re reading of modal claims in which possibilities refer to individuals, not as members of the natural kind to which they actually belong but as mere bodies, individual corporeal substances. Abelard calls this reading ‘de rebus’, but it does not coincide with his standard de re interpretation, according to which the truth-value of a modal proposition is established on the basis of the actual specific nature of a substance. According to this alternative de re reading, the notion of possibility is still spelled out in terms of compatibility (non repugnantia) with nature, but the nature under consideration is the one of the same substances considered as a body – or as a mere substantia. Abelard justifies the claim ‘this substance that is human can be dead’ by saying that, after all, ‘this human’ and ‘this corporeal substance which is actually a human’ both refer to the same res, although one might attend to this res in different ways, considering it alternatively as a body or as a human being. These two different ‘perspectives’ that we might have while attending to the same substance allow us to attribute to it a different range of modal properties, for, although it is impossible for this individual, considered as a human, to be dead, it is nevertheless possible for this same thing, considered as a corpus or a substantia quae homo est, to be dead. It might be useful to read this passage in connection with what Abelard states in De Intellectibus concerning the multiplicity of natures that are associable with each substance. In a number of passages in this work, Abelard advances the idea that we might consider things as having a different nature, depending on which of their properties we pay attention to.59 These assertions might be puzzling if we take them coupled with Abelard’s essentialist framework, that is, with his idea that every individual substance has a nature consisting

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nomen est: neque enim moritur nisi vivens. Videtur ergo possibile hominem mori, unde mortalis dicitur, sed non mortuum esse. [...] Ea ergo quae natura rei non exspectat, non possumus confiteri posse illi inesse, sed quae tantum in esse advenientia naturam rei non expellunt. Possumus itaque hoc corpus, quod tamen homo est, confìteri posse mortuum esse, si corporis proprietatem tantum attendamus, sed non hunc hominem. “Corpori” enim “mortuum” non repugnat, sed “homini”. [...] At vero mortuum numquam homini inhaerebit: neque enim ipso existente neque non existente; quod quidem patens est, cum videlicet alterum non patiatur alterum. Sed tamen hoc corpus, quod homo est, mortuum erit; quippe ut “corpus” acceptum “mortuo” non repugnat. Sicut ergo fatemur quia hoc corpus erit mortuum, sic et recipimus quia possibile est hoc corpus esse mortuum, sed non ideo hominem, quamvis tamen et hoc corpus homo sit. Aliud est enim corporis simplicem attendere in eo naturam, aliud hominis proprietatem in eodem considerare. Secundum namque substantiam quae homo est, remanebit homine in se destructo, non tamen homo’ (Dial. 196, 29–197, 31). Cf. also (Noël 2021) and (Binini 2021) on this.

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in a bundle of properties that are entirely inseparable from it, and that each individual belongs to a certain natural kind by virtue of such a nature. This essentialist picture does, in fact, suggest that the association between each individual and its nature is univocal and necessary. And yet, the idea that more than one nature can be attributed to a certain substance – and that the nature that is associated with it may depend on how we pay attention to this substance with our understanding – is remarked upon by Abelard several times. In De Intellectibus Abelard claims that our intellect always understands a certain thing by taking into consideration only ‘some of its natures and properties’ and by disregarding others.60 He also observes that, when we attend to a certain corporeal thing, we may consider it as a member of a natural species, therefore attributing a certain specific nature to it; or rather we may consider it in its pure and simple nature of a body. For instance, the same thing can be considered a man, a white thing, a hot thing, and so on, or it can simply be considered as ‘this body’ (hoc corpus), discarding its other ‘innumerable natures and properties’.61 A similar point is also made by Abelard in the Logica Ingredientibus,62 where he claims that the intellect always c­ onsiders 60

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‘Uterque autem intellectus, tam abstrahens scilicet quam substrahens, aliter quam res se habet concipere videtur, cum videlicet utroque res coniunctas divisim intelligo, que divisim non subsistunt; modo videlicet solam materiam per se, modo solam attendendo formam; praeterea nemo, cum aliquam rem attendit, eam excogitare sufficit secundum omnes naturas eius aut proprietates sed secundum aliquas tantum. Cum itaque rem quamlibet secundum aliquas tantum naturas eius vel proprietates attendimus, ipsa autem res non secundum eas tantum quas consideramus sese habeat profecto aliter quam ipsa sit eam consideramus’ (Abelard 2004, p. 72; my emphasis). ‘Verbi gratia hoc corpus et corpus est, et homo, et calens, et candidum, et innumeris aliis naturis vel proprietatibus subiectum; et aliquando tamen ipsum in eo tantum quod corpus est attendo, non in eo quod homo est, vel quod calet, vel quod albet; et sic in singulis rebus quas intellectus noster percipit, aliquam tantum que illis rebus insunt, non omnia, attendit’ (my emphasis). See also: ‘Praeterea cum quislibet corpoream naturam simpliciter ac pure concipit, in eo scilicet tantum attendens quod est corporea, id est corpus, aut quamlibet naturam ut universalem capit, hoc est indifferenter absque ulla scilicet personali discretione eam attendit, profecto aliter eam intelligit quam subsistat. Nusquam enim ita pure subsistit sicut pure concipitur; sed ubicumque sit innumeras, ut dictum est, aut naturas aut proprietates habet quae minime attenduntur; et nulla est natura quae indifferenter subsistat, sed quaelibet res, ubicumque est, personaliter discreta est atque una numero reperitur’ (Abelard 2004, pp. 72–4; my emphasis). LI De Int. 36, 259–62: ‘Ubi vero attendit naturam aliquam rei vel in eo quod res est vel ens vel substantia vel corpus vel alba vel Socrates, intellectus dicitur, cum quidem de confusione, quae imaginationis erat, ad intellectum per rationem ducitur.’ See also LI De Int. 29, 96–102 on the same idea: ‘Est autem ratio potentia discernendi, id est attendendi et deliberandi apud se aliquid quasi in aliqua natura vel proprietate consistens, veluti si quis rem aliquam vel in eo quod est res, vel in eo quod est substantia vel corporea vel sensibilis

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a thing by focusing on some of its natures, attending to it as either a res or an existent thing (ens), a substance, a body, a white thing, or as Socrates. The fact that we might attend to things in different ways and understand them as having a different nature on the basis of these acts of attentio seems to be at the basis of what Abelard says in the Dialectica about the same thing having different possibilities and necessities, depending on whether we take it as a human or as a body that is human. The peculiar reading of the notion of possibility that is at play in this section of the Dialectica might also be helpful when interpreting what Abelard says in some passages of the Logica Ingredientibus, where he claims that the individual thing that is now a human might have had other substantial forms or a different nature than the ones it actually has: An accident (that is, an accidental form) is a form that can inhere or not inhere in a subject without this subject being corrupted. [...] Note that when it is said: ‘can inhere or not inhere without the corruption of the subject’, this is valid also for substantial forms. Just as rationality inheres in this human and he is not corrupted on account of it, in the same way this human might be without [rationality] in such a way that he would not be corrupted. For it could happen that this substance of a human (haec substantia hominis) was never rational and so it would never be corrupted on account of rationality, since it never had it. It could also happen that [this substance of a human] was without [this form of rationality], in such a way that it had another form instead, and never this one, and so it would not be corrupted on account of it. It follows from this that ‘inhere and not inhere’ are to be understood not in the divided sense, but in the compound one, in the sense that this subject might either have or not have this form, that is to say it could change with respect to this form without corruption, so that even if the subject has [this form] in one moment and then loses it, it would not be substantially corrupted.63

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vel colorata penset, vel quasi in aliqua natura vel proprietate excogitet ipsam, etsi ipsa non sit, sicut hircocervus vel dies crastina vel lapis risibilis.’ LI Isag. 92, 9–33: ‘Accidens, hoc est accidentalis forma, est ea forma quae subiectae materiae potest et adesse et abesse praeter corruptionem ipsius [...] Nota etiam, quod ait: abesse et adesse praeter subiecti corruptionem, hoc substantialibus quoque formis conveniat. Sic enim rationalitas adest huic homini, ut non corrumpatur, et sic posset hic homo sine ea esse, ut ideo non corrumperetur. Posset enim contingere, ut haec substantia hominis numquam rationalis fuisset, ideoque numquam corrumperetur propter rationalitatem, cum eam numquam habuisset. Posset etiam fortassis contingere, ut sic ista careret,

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In this passage, to which Marenbon has drawn attention, Abelard claims that not only can accidental forms be separated from their bearers without corruption, but substantial forms are also in some sense ‘separable’ from their bearer, to which they are attached only contingently. If, for instance, a certain form of rationality that actually inheres in this human were to be separated from it, the subject would not be corrupted on account of it. This is because the same thing that is actually informed by a certain form of rationality might have had another rationality instead of this one – or perhaps no rationality at all. So, the loss of that particular form would not lead to its corruption, because it never had it. What is puzzling in this passage is that, according to what we have seen so far about Abelard’s essentialism and modal theory, being rational is something that is required by the nature of humans, and it should thus be impossible for a human to be without this property. How can Abelard claim, then, that ‘This human might be without rationality’ or that ‘It could happen that this substance of a human was never rational’ (‘Hic homo posset esse sine [rationalitate]’; ‘Posset enim contingere, ut haec substantia hominis numquam rationalis fuisset’)? Once more, these claims are understandable if we acknowledge that it is ‘this substance of a human’ (haec substantia hominis) – and not ‘this human’ – that Abelard is saying is separable from its actual rationality and therefore possibly irrational. This passage, and the one from the Dialectica quoted above, may thus be seen in parallel. In both, Abelard distinguishes between an individual substance seen as a member of a certain kind, with its own specific nature and inseparable forms, and the same individual considered as a mere corporeal substantia, which resists the loss of its substantial forms and may undergo substantial changes while remaining ‘the same’, either through time or counterfactually. Depending on how we attend to the subject – as a member of a species or as a mere body – we attribute different possibilities and impossibilities to it. The fact that it is possible for this bodily substance that is actually human to be dead or irrational does not imply that it is possible for this human to be irrational or dead. quod aliam rem habuisset et nunquam istam et ideo numquam per istam corrumperetur. Unde divisim non est accipiendum adesse et abesse, sed coniunctim ita scilicet, quod ipsum subiectum possit formam istam et habere et non habere, id est secundum eam permutari praeter corruptionem, ut videlicet cum prius habeat ac postea amittat, non sit substantialiter corruptum.’ Translation of the central passage (p. 92, 24–9) is taken from (Marenbon 2008c, p. 90). For a careful analysis of this passage, see (Marenbon 2008c).

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The use of expressions such as ‘id quod est homo’ or ‘haec substantia hominis’, which I have emphasized in the texts quoted above, are crucial for the interpretation of these texts, since these terminological devices are used by Abelard to signal that he is ‘switching the perspective’ on the subject, so to speak, and passing from talking about a human being and his or her possibilities to talking about the corporeal substance that is human and its possibilities. The same linguistic tools are used by Abelard in other contexts, especially when he presents his well-known theory of the many senses of sameness and difference. As is known, Abelard acknowledges many different ways in which two things are considered ‘the same’. In particular, he accepts that two things may be the same essentially and numerically, while differing with respect to their properties or definition.64 One such case is the famous example of the wax and the image made of wax: although an image and the wax of which it is made are the same in their essentia, and also the same in number (for there is one thing and one thing only that is this wax and this waxen image), the two have different properties, because the image has the property of being made material, while the wax has no such property.65 Other similar examples, listed by Wilks66 and well known to scholars, are that of the vox and the sermo, which are the same res but of which only the first has the property of being predicable of many, or 64

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The notion of ‘essential’ sameness can be understood in light of the 12th-century use of the word essentia as meaning ‘existing thing’ or ‘concrete thing’; see (King 2004, p. 86). According to Abelard, two things, A and B, are essentially the same when they are not two things but rather one, or when they have the same material parts. Tullius and Cicero, or this ensis and this mucro, are the same in this sense. Essential sameness is closely connected, although not coincident, to ‘numerical sameness’. Things that are essentially the same are also numerically the same, although the reverse is not always the case, for, according to Abelard, two things (e.g. myself and my own arm) might have different material parts – and therefore a different essentia – and yet not differ in number. For a survey of Abelard’s notions of sameness, see (King 2004, pp. 86–92). Things that are essentially or numerically the same can still be different in property or different in definition. A famous Abelardian case is that of an image made of wax and the matter out of which the image is composed: although this wax and this image are numerically and essentially the same (since there is only one res, or one ‘concrete thing’, that is both the image and the wax), they still have different properties, for example, the image is made material while the wax is not. See on this (Abaelard 1969b, pp. 317–8). See, for example, this passage from Abelard’s Theologia Christiana, quoted and translated in (Wilks 1998a, p. 370): ‘Some things are essentially the same which are nonetheless distinguished by their properties [...] For example, in this wax image, the wax is numerically the same “as the image”, that is, the matter and what is made material “are the same”; however, the material and what is made material do not share their properties, since the material itself of the wax image is not what is made material.’ (Wilks 1998a, p. 366).

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that of the three persons of the Trinity, who are simultaneously the same but differing in properties (e.g. the Son is generated, while the Father is not). As Wilks remarks, Abelard states that, although it would be false to say, for instance, that ‘The wax is made material’ or that ‘The Father is generated’, we may still truly say that ‘That which is (id quod est) the wax is made material’ or that ‘That which is the Father is generated’. This is because the ‘id quod est’ phrasing – along with other phrases that Wilks labels ‘essential-predication locutions’ – indicates that the copula is used to express an essential predication (that is, it affirms an identity between the res referred to by the subject and that referred to by the predicate) rather than an adjacent predication, that is, an attribution of a property.67 Similarly, Abelard states in a passage of the glosses on De Interpretatione that propositions such as ‘This man will be a cadaver’ or ‘This cadaver was a man’ are true if we intend them as saying ‘That which is a man will be a cadaver’.68 Abelard’s analysis of these cases may shed some light on the puzzling passages on modalities that were quoted above, in which Abelard claimed that even though it is false that ‘This human can be dead’ or ‘irrational’, we may still admit it as true that ‘That which is this human can be dead (or irrational)’. This is because, with the latter formulation, we are not attributing the possibility of being dead to the human itself; rather, we say that this human being, actually informed by animality and rationality, and this corporeal substance, the nature of which is compatible with being dead or irrational, are the same res. If we read the passages on modalities in this light, we see that Abelard’s perplexing examples about dead humans and irrational humans are just special cases of two things being essentially the same while different in properties.69

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The distinction between essential predication and adjacent predication is a fundamental element of the strategy that Abelard uses to solve these puzzling cases. This distinction is presented and investigated in (Wilks 1998a, pp. 366–70). As Wilks puts it, to read a sentence as involving an essential predication is simply to attribute to the predicate the role of being the name of something. For instance, if we take a sentence such as ‘Socrates is white’, and we take the predication as being an essential one, we intend that the two terms ‘Socrates’ and ‘white’ both denote a thing and that what the predicate denotes is identical to what the subject denotes. To read a sentence as an adjacent predication, by contrast, is to read the predicate as corresponding to some inhering form. If we read ‘Socrates is white’ in this way, the subject term ‘Socrates’ is still taken to denote a substance, but the predicate ‘white’ corresponds to whiteness, and what the proposition claims is that the form referred to by the predicate actually inheres in the thing denoted by the subject, as if we had said, ‘Whiteness inheres in Socrates’. LI De Int. 100, 206–7. I discuss this parallel in more detail in (Binini 2020b).

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The two passages from the Dialectica and the Logica Ingredientibus quoted above also bring to light a feature of Abelard’s ontology that had already been remarked upon by several commentators, namely, that the connection between a certain individual substance and the substantial forms that inhere in it is somewhat contingent. As Marenbon has shown,70 within Abelard’s ontology any given form – both accidental and substantial – might have gone to a different particular substance than the one to which it has in fact become attached. Even though the properties that constitute a thing’s nature are essential to it, still it is in some sense possible, according to Abelard, for the thing not to have them and to have other properties instead. This is in the sense that the same forms that are attached to a certain individual substance in the actual history might have gone to a different substance, and other forms might have attached to this one. With respect to this point, some commentators have characterized Abelard’s ontology in terms of a trope theory, where accidents and differentiae exist and are individuated independently from the substances that are their bearers in the actual situation.71 The contingent relation existing between individual properties and their individual bearers is consistent with Abelard’s theory concerning the individuality and identity of things: according to him, all existing things are individuated in themselves, so that their being individual does not depend on something other than their own existence. In particular, substances are not individuated by the substantial properties that characterize them in the actual situation or by the nature that we attribute to them. Rather, the individuality of both substances and forms is, for Abelard, primitive and irreducible. 70 71

See (Marenbon 1997, p. 119). See in particular (Martin 1992); (Marenbon 2008c); (Noël 2021).

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Necessity, Determinacy, and Contingency 1

Three Ways to Characterize Necessity

Throughout the preceding chapter I have tried to show that, despite putting into play different senses of possibility and potentiality, Abelard was able to offer a consistent and quite homogeneous theory of the possible, taking possibility fundamentally in terms of non-incompatibility between certain predicates and the nature of things. As was shown in Chapter 3, Section 3, the definition of possibility in terms of non-repugnancy with nature was quite standard in logical sources of Abelard’s time, and many authors at the beginning of the 12th century appealed to it in order to justify unactualized possibilities and the attribution of possibilities to non-things. Even so, we should grant Abelard the merit of using this standard definition to structure a sophisticated doctrine of possibility and potentiality, a doctrine that aimed to explain in terms of nature not only unactualized but also unactualizable possibilities, past possibilities, and even counterfactual ones. The same coherence and homogeneity of intent cannot be found, on the contrary, in Abelard’s treatment of necessity. This is primarily because Abelard provides multiple definitions of the modal term – some new, others taken from traditional sources – that are not always consistent with one another and therefore instill an element of instability into his modal theory and logic. In this section I will list and explore the definitions of the concept that Abelard provides in his logical works and relate them to the context of early 12th-century debates on necessity, determinacy, and future contingents. In Chapter 10, Sections 2–4 I will then go on to examine how Abelard applies his reflections on necessity within his discussions on logical and theological determinism. We could derive (at least) three different characterizations of the concept of necessity on the basis of Abelard’s works: i. Necessary as what is sempiternally and immutably true, or that the contrary of which is omnitemporally false; ii. necessary as what is inevitable, that is, what is in a certain way and cannot be otherwise (or cannot not be); iii. necessary as what is required or compelled by the nature of a thing, or by nature in general. As we saw is Chapter 3, Section 4, the first two characterizations are often presented as a pair by authors of Abelard’s time, who – like Abelard – tend to © koninklijke brill nv, leideN, 2022 | DOI:10.1163/9789004470460_015

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associate the idea of necessity with that of unavoidability (inevitabilitas) and omnitemporality, as well as with the impossibility of being otherwise. This ‘inevitable necessity’ was also referred to as simple or absolute necessity, in contrast with a determinate or conditioned one (see Chapter 1, Section 4 and Chapter 3, Section 4 on this opposition). In Chapter 3, Section 4 I listed various sources in which the ancient link between necessity and sempiternity or immutability is rehearsed, among which are the commentaries on De Interpretatione H11, H9, H4, and H5 and the commentary on Boethius’ De syllogismis hypotheticis SH2.1 In the Dialectica Abelard says that the understanding of the necessary as ‘inevitable’ – namely, as that which ‘is in a certain way and cannot be otherwise’ – is the proper and more usual signification of the modal term (consueta et propria significatio est ‘necessarii’, Dial. 194, 7–9). A similar connection between necessity and inevitability is proposed by Abelard in the Logica Ingredientibus2 and in his Theologia Scholarium.3 In another passage of the Dialectica4 Abelard expounds this inevitability in both temporal terms, as what ‘does not have a beginning’ and is perpetually as it is, and in terms of the impossibility of its contrary, as what, when it is, cannot not be.5 In this work Abelard makes ample use of the temporal characterization of necessity as sempiternal act or sempiternal truth (incommutabilis veritas, see, for example, Dial. 278, 21; 284, 3; 340, 25). This characterization is in line with his insistence, in the same work, on the fact that necessity can only be properly predicated of sempiternal beings, and not of transient ones,6 a thesis that was also defended by some of his contemporaries. Both the temporal characterization and that of the impossibility of being otherwise are exemplified in a passage from the Dialectica, where Abelard claims that a proposition such as (*) ‘It is necessary for Socrates to be a body’ is false, contrary to what his Master endorsed, because there are times in which it would be false to say that ‘Socrates is a body’, namely, those in which Socrates 1 See Chapter 1, Section 1 for the use of this interpretation of necessity in Aristotle and Boethius. 2 LI De Int. 407, 412–408, 425. 3 (Abaelard 1987a, 3, 101; 3, 107). 4 See Dial. 272, 11–2, cf. also 279, 13–14. 5 ‘Necesse autem hic quod inevitabile dicitur accipimus, cuius quidem sempiternus est actus, sive circa esse sive circa non esse, id est cum sit, non potest non esse, vel cum non sit, non potest esse, nec in esse vel in non esse principium habuit, sed semper vel est ita vel non est.’ We cannot but notice the similarity between Abelard’s words and those put forward by the author of the commentary H9, who, as well as saying that what is necessary must be understood as inevitable (Orléans, Bibl. mun. 266, p. 33b), also states that: ‘Res ergo quedam sunt que a sempiterno et a proprio esse numquam discedunt, et dicuntur habere simplicem necessitatem in suo esse, quia ita sunt ut dicuntur et aliter esse non possunt.’ 6 See, in particular, Dial. 193, 26–9; 195, 7–8; 201, 2–9.

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does not exist. As with any other proposition concerning transient beings, (*) does not satisfy the sempiternity criterion, nor that of the impossibility of being otherwise, as Abelard says in the Dialectica: Sed sic vera erit haec propositio: ‘Necesse (est) Socratem esse corpus’; cum enim sit corpus, non potest existere sine corpore. Atque falsa mihi omnino videtur illa propositio, quamvis Magistro nostro placeat. In his enim quae sempiterna sunt, solis necessitas ista contingit. Socrates autem semper corpus non habuit, quia, antequam esset, non erat corpus; cum enim omnino non esset, corpus esse non poterat. Videtur itaque mihi sic exponendum ‘necessarium’ quod illud ex necessitate est (illud) quod ita est illud quod non potest aliter esse, idest non potest non esse, ut ‘Deus necessario immortalis est’; sic enim est immortalis quod non potest aliter esse, idest non potest contingere ut non sit (im)mortalis. At vero de Socrate potest contingere quod non sit corpus, quia adhuc continget quod non erit corpus; mortuo enim Socrate verum erit dicere quia non est Socrates corpus, sicut et antequam crearetur, verum erat. In his itaque solis necessitas contingit quorum existentiam vel actum potestas non praecessit, ut in Deo; neque (enim) prius potuit Deus immortalis esse quam fuit. Quaecumque igitur vel aliquando non fuerunt aliquod vel aliquando non erunt, non sunt ex necessitate illud. Si enim umquam fuerunt vel erunt sine eo, non exigit illud ex necessitate natura. (Dial. 200, 36–201, 17)7 It is particularly within Abelard’s theory of conditionals that the connection between necessity and time assumes a central role.8 Abelard believes that the 7 For a similar claim, see 202, 19–25: ‘Et similiter videtur in istis aequipollentia sicut in singularibus; sed in neutris concedimus. Neque enim cum necesse sit Socratem non esse equum, necesse est esse non-equum. Si enim necesse esset esse non-equum, sempiternum esse et semper verum. Sed antequam esset Socrates vel postquam morietur, falsum est dicere: “Socrates est non-equus”, ut in tractatu affirmationis et negationis ostendimus. Id etiam in universalibus fallit.’ For the idea that only sempiternal beings may be the subject of true necessity claims, see also Dial. 193, 26–9: ‘Aut qualiter “necessario” inhaerentiam hominis determinat, cum nullam habeat ad aliud ex necessitate inhaerentiam […]? Nulla enim res homo est ex necessitate’ and Dial. 195, 7–8: ‘Si actum rei consideremus, nihil esse hominem necessario inveniemus.’ Other mentions of these definitions of necessity may be found, for example, in Dial. 194, 7; 221, 12–3; 461, 7. 8 On Abelard’s theory of conditionals, a theory that he presents in the Dialectica and in his commentary on Boethius’s De topicis differentiis, the most thorough analysis still remains the one proposed by Martin in (Martin 2004b, pp. 126 ff.), although Martin limits his analysis to the theory provided by Abelard in the Dialectica.

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truth-value of consequentiae such as (i) ‘If something is a man, it is an animal’ or (ii) ‘If every human is an animal, then every human is animate’ is immutable and sempiternal, as well as being independent of the actual existence of the (contingent) things that the propositions are about. This sempiternity of truth assures, according to him, the proper necessity of the consecution and therefore grounds the ‘stability’ (firmitas) of non-syllogistic consequences of this sort (see, for example, Dial. 282, 25–33 and Dial. 160, 17–21). According to Abelard, the validity of consecution in conditional propositions such as (i) and (ii) is granted by the relation of necessity holding between antecedent and consequent, necessity that is, in turn, grounded on the fact that the habitudo between what is expressed in the antecedent and in the consequent is immutable, because it is founded on the nature of things (ex rerum natura).9 Abelard believes that ‘the truth of consecution lies in necessity’ (Dial. 271) and that this necessity is needed to guarantee the sempiternity and immutability of truth.10 Notice that Abelard, in this part of the Dialectica, agrees with his contemporaries by calling this concept of necessity as sempiternity ‘simple’ necessity (see, for example, Dial. 284, 10–1). The connection between necessity and sempiternity or immutability, which was so significant in the Dialectica, seems to fade into the background in the Logica Ingredientibus. It is true that Abelard still provides a characterization of necessity in temporal terms in one passage of his literal commentary to De Interpretatione (LI De Int. 472, 620–30), and he also says in another passage that ‘if something is necessary, then it has incommutable truth’ (LI De Int. 428, 962–3). Nevertheless, he seems to appeal to this idea much less frequently than he did in the Dialectica. Whether this reveals a substantial doctrinal change in Abelard’s understanding of necessity is hard to establish, since Abelard never explicitly signals that he has changed his mind on this matter. And yet, it is interesting that, in the Logica Ingredientibus Abelard points out a number of logical difficulties connected to the existential import of modal claims and to the logical relation between possibility and necessity, difficulties that are also related to the traditional equation of necessity with sempiternity. One of these concerns is the standard laws of equipollence between possibility and necessity propositions. Abelard is inclined to admit the laws according to which 9 10

See, for example, Dial. 254, 31–255, 11; cf. (Martin 2004b, p. 172) on this. As Martin clarifies, this necessity criterion, inspired by Boethius, was not uncontroversial, and some of Abelard’s contemporaries did in fact favour a criterion of probability or plausibility to it (Martin 2004b, pp. 176–7). As Martin puts it, Abelard’s true conditionals are those that are based on a law of nature (lex naturae exigunt, see Dial. 280, 13 ff.), a law which holds eternally and independently of the existence of the things the conditionals are about (2004, p. 180).

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what is necessarily the case is equivalent to what is not possibly not the case, but he realizes that problems arise when we only admit true necessary propositions about sempiternal beings. In fact, when we consider a proposition such as (i) ‘It is necessary for every man to be an animal’, this proposition turns out to be false (because the claim de puro inesse ‘Every man is an animal’ is false when men do not exist), whereas its supposed equipollent (ii) ‘It is not possible for every man not to be animal’ is true in any situation – both when men exist (since being animal is part of their nature) and when men do not exist (since the implicit import included in its contradictory ‘It is possible for every man not to be animal’ is not satisfied). In order to preserve the logical relation between the possibility and necessity, Abelard would need to admit the truth of (i), despite the fact that this truth is not sempiternal. To maintain the system of logical inferences between modal propositions, Abelard might then have decided to abandon the characterization of necessity as omnitemporal truth. A confirmation of this is perhaps the fact that, in the Logica, Abelard provides examples of true necessity propositions about contingent beings, which he had denied in the Dialectica. Moreover, we have already seen in Chapters 5 and 8, Section 1 that Abelard explicitly states in the Logica that between necessity and possibility a logical relation of equipollence might be established, although this cannot be intended as a semantic relation. This is because, for Abelard, the meaning of one modal concept cannot be expressed by means of the meaning of the other. He seems thus to also put into question the second characterization of necessity listed above, according to which that which is necessary is what ‘cannot be otherwise’. The third definition of necessity provided by Abelard is that which is given in terms of nature, where what is necessary is characterized as what ‘nature requires or compels’ (natura exigit or compellit). In this sense, necessity may be properly attributed not only to sempiternal beings but to all substances, including contingent creatures, natural elements, and even things that do not exist. What is predicated as necessary for these creatures are the essential properties that inhere in them, that is, the substantial forms that constitute their nature. As was mentioned in Chapter 3, Section 4, to my knowledge, this last definition of necessity was not used by Abelard’s contemporaries, even though they made use of the parallel definition of possibility in terms of nature. The new characterization of necessity might have been created by Abelard with the intention of providing all definitions of modal terms on the basis of natura rerum. The Abelardian definition of necessity as ‘what nature requires’ may instead be found in a number of later sources, whose authors were acquainted

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with Abelard’s works, such as the Logica Nostrorum and the Glossae Secundum Vocales, as well as the De Propositionibus Modalibus11 and the Summa Dialectice Artis.12 Among the traditional views on modalities that Abelard and his contemporaries inherited from ancient sources, there was also a distinction between two different ‘degrees’ of necessity, absolute or simple necessity, on the one hand, often glossed as inevitability and sempiternity, and determinate or conditioned necessity, on the other. This last sense was often used either in the attribution of necessary properties to contingent beings (as opposed to sempiternal ones) or to characterize the asymmetry between the modal status of past and present events – which, having happened, are now unchangeable and unpreventable and therefore determinately necessary – and that of the future, which is, on the contrary, open and ‘indeterminate’, and therefore properly contingent. Abelard also appeals to the traditional distinction between determinacy and indeterminacy in his discussion of future contingents, where he tries to defend the idea that present and past events are determinate but not necessary in any relevant sense. As in many other contexts, Abelard incorporates the traditional views on future contingents but re-elaborates them into an insightful new theory. Nonetheless, as I argue in the next sections, some problems remain unsolved in Abelard’s defence of indeterminism, and the solutions he proposed against logical and theological determinism are not always convincing. 2 Determinacy and Contingency in Abelard’s Comments on De Interpretatione 9 The existence of contingent events – that is, of events that are equally apt to happen or not to happen in time – is taken by Abelard as an evident and indubitable feature of the way things are. According to him, contingency characterizes both the natural world, inasmuch as some natural events are not the outcome of a chain of natural causes but happen by chance, and the human world, in the sense that some events that take place are the result of human free will and unconstrained deliberation. Generally speaking, Abelard holds that it is possible for some facts and events to be otherwise than they actually 11 Anonymous, De Propositionibus Modalibus, in (Abaelard 2010a, p. 233, 64–6): ‘De sensu. Modi isti diverso habent sensus. possibile tantum valet quantum: natura patitur, impossibile: natura repugnat, necesse: natura exigit. Natura autem dicitur prima rerum creatio.’ 12 (Guglielmo da Lucca 1975, pp. 105–6 §7.09).

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are and that there are many alternative ways in which things could have been or might evolve in the future. While defining contingency, Abelard quite closely follows the terminology and distinctions expounded by Boethius in his two commentaries on Periermeneias. What Abelard adds to Boethius’ picture is a particular attention to the ontological correlates of terms such as ‘contingent’ and ‘chance’. In the glosses on De Intepretatione, for instance, he says that the term ‘utrumlibet’, which is used to refer to those events that might happen ‘in both ways’ – that is, either happen or not happen – is imposed on things or events not by virtue of a certain property that they have, but rather by virtue of a common cause (‘non ex proprietate aliqua datum, sed ex causa communi inventum’), that is, by virtue of the fact that these events are equally apt to actualize or not. This remark on the signification of the modal term ‘contingent’ is in line with something that Abelard also states concerning the terms ‘possible’ and ‘necessary’, namely, that these words have no denotation in themselves and do not refer to a certain res or to some property existing in things.13 Because the use of the term ‘contingent’ does not amount to an ascription of properties or to the nomination of a res, Abelard holds that this term may be properly used to refer to either existent or non-existent things, saying, for instance, that some events that will never take place are contingent. This allows him to talk about the contingency of events that remain perpetually unrealized (and which are therefore nonexistent) and also releases him from ontological commitments on the status of eventus when discussing the logic of future propositions. Following Boethius, in the Dialectica Abelard divides contingency into three ‘species’: chance (casus), free will (liberum arbitrium), and natural disposition (facilitas naturae). A similar distinction may be found in several commentaries on De Interpretatione from the first decades of the 12th century. ‘Chance’ is, for Abelard, a name that refers to events that are unexpected (inopinati eventus), not in the sense that we cannot foresee them but in the sense that they are unpredictable by nature (‘inopinatus non quantum ad actionem nostrae cognitionis sed quantum ad naturam’). Events that happen by chance may be the outcome of either natural causes or actions performed by rational agents, when they are not preceded by any deliberation, judgement, or hope to obtain the outcome that they in fact lead to. For instance, it is said of a man who finds a buried treasure while ploughing a field that he has found the treasure ‘by chance’, because the action leading to the discovery was undertaken to obtain a different outcome than the one it actually gets (Dial. 215, 9–15; LI De Int. 256, 13

Abelard says that, because of this, modal terms count as ‘indefinite terms’; see footnote 3, Chapter 3.

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332–257, 349). ‘Free will’ (liberum arbitrium) is a name for events that are efficiently caused by our own action, the achievement of which is preceded by (i) the will (voluntas) to obtain a specific result and (ii) a certain judgement of the mind (iudicio mentis). An event is the result of free will if in the agent achieving it there is a conjunction of will and mental deliberation, together with an absence of external constraints that would prevent him or her from obtaining that result. Finally, the term ‘facilitas naturae’ refers, according to Abelard, to the natural disposition that some things have to bring about certain events, even though their happening is not required or forced by nature. For example, a glass has a natural disposition to break, by virtue of which it is called ‘breakable’ (Dial. 215, 28–32; LI De Int. 256, 318–9). The analysis of contingency that Abelard proposes in the Logica Ingredientibus is slightly different from the one proposed in the Dialectica. Rather than following Boethius’ division of contingency into chance, free will, and natural disposition, in the Logica Abelard only says that contingent events might have three possible efficient causes: they might happen by virtue of nature (ex natura), by virtue of human action (ex nobis), or by virtue of a conjunction of the two.14 As some commentators have noticed, Abelard thinks that contingency should refer not only to future events but also to present and past events, for even if these have already happened, things might also have occurred in some other way. For instance, Abelard thinks that even if it is now true that Socrates is sitting, we might still say that it is possible now for him not to sit, for things might have gone in such a way that Socrates were presently standing (see Chapter 9, Section 4).15 Given Abelard’s acceptance of the contingency of the present and past, it might be puzzling to read that he also accepts – in line with his contemporaries – a traditional distinction demarcating the determinacy of all present and past events from the indeterminacy of future contingent ones. Like the majority of early 12th-century logicians, Abelard holds that the truth-value of present and past propositions is always definite or determinate, whereas some future propositions (those de futuro contingenti) are true or false only indefinitely, because the event to which they refer is still indeterminate.16 In texts from Abelard’s time all authors invoked a similar distinction in their 14 15 16

For a more detailed analysis of Abelard’s definition of contingency, see (Binini 2019b). See, in particular, (Knuuttila 1993); (Martin, 2004a); (Martin 2001) and (Knuuttila 2010). For the distinction between the diachronic and synchronic paradigm of modalities, see (Von Wright 1984). Although Abelard speaks interchangeably of the (in)determinacy of events, propositions, or truth-values, it seems that for him it is events that are the proper bearers of determinacy and indeterminacy, while propositions are said to be determinate or indeterminate only on the basis of the event to which they refer. See on this (Lewis 1987, pp. 84–7).

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reflection on Aristotle’s dilemma posed in De Interpretatione 9, making use of the notions of (in)determinate events, (in)determinate propositions, and (in) determinate truth and falsity. They inherited this distinction from Boethius, who rather spoke of the definiteness and indefiniteness of events and of their truth values, as we will see in Chapter 10, Section 3. Abelard’s attribution of determinacy to every event that has occurred in the past or the present, however, does not imply that he also attributes necessity to them. In fact, while many contemporaries of Abelard defined determinacy as a special sort of necessity – saying that determinate are those events which, though not being inevitable or absolutely necessary per se, are unavoidable from the present perspective17 – Abelard opted for a different characterization of the notion of determinacy, which is given not in modal but in epistemological terms. He claims that those events are ‘determinate’ that are ‘knowable on the basis of themselves’ (‘ex se cognoscibilis’), which may be the case: (i) either on the basis of their existence, that is, by virtue of the fact that they have happened in a certain moment of time (‘cognoscibilis ex existentia sui, cognoscibilis ex actu’); or (ii) on the basis of nature, by virtue of the fact that they are instantiations of a natural law (‘cognoscibilis ex natura’). A similar definition is embraced by the authors of commentaries H9 and H11, which, as was seen, are probably important sources for Abelard’s Dialectica. The accessibility to knowledge associated with the notion of determinacy, as Abelard insistently specifies, must be understood as knowability ‘in principle’, and not in terms of actual knowledge. There are, in fact, many events that are knowable but not known, such as whether the number of stars is even or odd, as Abelard says, rehearsing Boethius. In parallel, there are also events that are actually known but not knowable ex se, for instance, the truths that we know on the basis of divine prophecy, which may concern future events that are indeterminate in their nature. For Abelard, then, the determinacy of past and present events derives from their capability of being known, and not from their modal status. In this respect, he seems to be in opposition to the opinion of other logicians of his time, who 17

A modal definition of determinacy is used, for instance, in commentaries H5, H13, and H20, where necessity is divided into several species, among which are ‘absolute’ necessity and ‘determinate’ necessity. As was seen in Chapter 3, Section 4, absolute necessity is usually characterized in terms of inevitability or invariability: things that are sempiternal and events that lack the possibility to change (‘nullo modo permutari possunt’) are said to be absolutely necessary, and the same applies to those propositions that talk about things and events of this sort. Events and propositions that are necessary in this first sense are contrasted with ‘determinate’ events and propositions, which – though not inevitable per se – are necessary because the cause of their happening (or of their truth) cannot be prevented or hindered (cf. H5: Munich, Bay., Clm. 14779, fol. 51r: ‘cuius causa non potest impediri’). Past and present events are usually said to be necessary in this second sense.

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instead followed Boethius in claiming that all past and present events are necessary, even if only in a weaker and conditioned sense of necessity. Abelard’s refusal to explicitly attribute necessity to the present and past, however, does not safeguard him from the challenges posed by deterministic arguments. In particular, Abelard’s acceptance of the traditional view, according to which every present and past event is determinate – in combination with his defence of the principle of bivalence – exposes him to the risk of logical determinism. Abelard considers three different but related arguments for logical determinism, all connected to the dilemma of future contingents presented by Aristotle in De Interpretatione 9. In the following section I will explore these arguments and their ancient roots, and I will then present the responses advanced by Abelard against them. 3

Abelard against Logical Determinism

In De Interpretatione Aristotle advances a number of logical principles that, in his view, capture the nature of assertoric propositions. One of these is the principle of bivalence, according to which every proposition has exactly one truthvalue, either true or false. As is well known, however, the validity of bivalence is put into question in Chapter 9 of De Interpretatione, where Aristotle considers future contingent statements such as ‘There will be a sea battle tomorrow’, and asks whether the present assignation of a specific truth-value to them would lead to the conclusion that the corresponding future events are presently bound to happen or not to happen. Even though Aristotle clearly rejects determinism as an absurd position in De Interpretatione 18b26–19a22, the solution he advances against the deterministic dilemma is notoriously obscure. In particular, it is not clear whether Aristotle decides to reject the validity of bivalence for future contingent propositions or whether he maintains unqualified bivalence and argues instead for the compatibility between this principle and the existence of contingent events. Setting aside the problem of which is the correct interpretation of Aristotle’s text, I shall focus here on the interpretations that have been given of this chapter of De Interpretatione by medieval authors in the early 12th century, and on the commentary tradition on which these interpretations were built. Generally speaking, up to Abelard’s time three main lines of solution had been advanced to address the dilemma posed by De Interpretatione 9 and its future sea battle.18 According to a first interpretation, Aristotle would end up 18

See, in particular (Gaskin 1995, pp. 12–7) and (Sharples 2009, pp. 208–9) on this.

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rejecting general bivalence and saying that future contingent propositions are neither true nor false. This solution – at times referred to as the ‘Standard interpretation’ of Aristotle’s dilemma – seems also to have been the oldest interpretation on record.19 As Boethius reports,20 the Stoics thought that this was indeed Aristotle’s way out of the dilemma, a way out that they rejected by opting instead for maintaining general bivalence and embracing determinism.21 As Simplicius states in his commentary on Aristotle’s Categories,22 some Peripatetics also interpreted the Aristotelian argument in De Interpretatione 9 as if a qualification of bivalence were required. A second interpretation of De Interpretatione 9 seeks instead to maintain the compatibility between bivalence and contingency by attributing to Aristotle the view according to which the actual truth of future statements does not entail their necessary truth. This view is usually referred to as the ‘non-standard interpretation’ of Aristotle23 and involves no qualification of the principle of bivalence. According to the proponents of this solution, Aristotle’s aim is to point out that the fatalist argument is based on some confusion concerning the use of the notions of necessity and truth. In particular, Aristotle claims that the principle according to which, of every pair of contradictory statements, necessarily one is true and the other is false is not to be confused with the principle stating that, of every such pair, one member is necessarily true and the other is necessarily false. In other words, the modal operator of necessity cannot be distributed over disjunction. Among ancient philosophers this solution was maintained by the Academic Sceptic Carneades, as Cicero reports in his De Fato.24 The idea that the necessity of a disjunction does not entail the necessity 19 20

21 22 23 24

See (McKim 1972, p. 81); (Kretzmann 1987, pp. 24–5); (Sharples 2009, p. 209). ‘Now some people – the Stoics among them – thought that Aristotle says that future contingents are neither true nor false. For they interpreted his saying that nothing [of that sort] is disposed more to being than to not being as meaning that it makes no difference whether they are thought false or true; for they considered them to be neither true nor false [in Aristotle’s view], but falsely’ (Boethius 1880, p. 208, 1–4, translation by N. Kretzmann). See, for example (Cicero 1968, pp. 20–1); (Bobzien 1998, pp. 59–86). (Simplicius 1907, p. 407, 6–13). See e.g. (McKim 1972, pp. 83–4). See (Sharples 2009, p. 209). Some modern commentators have also attributed this solution to Aristotle. This second interpretation is mainly based on a famous passage from Aristotle’s De Interpretatione 9, where the Philosopher distinguishes between the necessity that things have to be as they are while they are, from the ‘unqualified’ necessity of being in a certain way (De Interpretatione 19a23–6). Anscombe and others take this passage as an indication that Aristotle aims to solve the puzzle by distinguishing between truth and necessity, and by claiming that the necessity of the event is a different issue

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of either disjunct is worth mentioning here, because it will also be employed by Abelard in his commentaries on De Interpretatione 9, as we will see. Finally, a third way out of the dilemma attributed to Aristotle in late antiquity was proposed by Boethius in his commentaries on Aristotle. Boethius reads Aristotle as maintaining that, even though every proposition is either true or false, not all propositions are determinately true or false, because some have a truth-value that is presently indefinite or indeterminate. Specifically, Boethius holds that present and past propositions are always ‘definitely true’ or ‘definitely false’, whereas future contingent propositions are true or false only ‘indefinitely’, inasmuch as the event to which they refer is not yet fixed.25 This solution, which became standard in early 12th-century discussions on De Interpretatione, was probably common even before Boethius, and we find it in similar terms, for instance, in Ammonius.26 Most likely, this was in fact the usual interpretation of Aristotle’s text in earlier Greek commentaries on De Interpretatione 9, now lost.27 Boethius’ stance on the truth-value of future contingent propositions is that the principle of bivalence is generally valid for them, and that the deterministic consequences of this principle could be avoided by appealing to a distinction between definite and indefinite truth, as appears clearly in this and other passages: It is necessary that either the affirmation be true or the negation, but not that either of them be definitely true, the other definitely false. For if someone else denies what we say: – ‘Alexander is to be bathed’ – and says ‘Alexander is not to be bathed’, it is indeed necessary that this whole [state of affairs] come about – that either he is bathed or that he is not bathed – and it is necessary that one be true and the other false: either the affirmation, if he has been bathed, or, if he has not been bathed, the negation. But it is not necessary that definitely the affirmation be true, because in cases of this sort the negation could come about; but neither is it ever definite that the negation be true ([and] the affirmation false), from the analytical necessity involved in the definition of the term ‘true’ (Sharples 2009, p. 210). 25 For Boethius’ distinction between definite and indefinite truth-values, see (Boethius 1877, pp. 106, 30–107, 6; 108, 2–5; 122, 26–123, 10 and 124, 8; Boethius 1880, pp. 208, 7–18; 219, 5–17 and 246, 12–13). Boethius’ position is analysed in (Knuuttila 2010, pp. 77–80). 26 Ammonius claims that all pairs of contradictory future sentences divide the two truth-­ values, not in a definite way but in an indefinite one (Seel 2001, p. 234); see also (Sorabji 1998). 27 (Ebbesen 2009, p. 29).

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because the negation can fail to come about. Accordingly, as regards the whole contradiction it is of course necessary that one be true, the other false. But that one be definitely true, the other definitely false – as is the case regarding things that are past and those that are present – is not possible in any way.28 What Boethius means by ‘(in)definite truth’, however, is far from clear. According to some modern interpreters, Boethius would be affirming that, in pairs of contradictory future propositions such as ‘Alexander will be bathed’ and ‘Alexander will not be bathed’, truth and falsity are not yet definitely distributed between the two contradictories, and so the two propositions would be ‘true or false’ only in a disjunctive way.29 This interpretation of Boethius’ words was also advanced by some early 12th-century authors, according to whom future contingent propositions are indefinite in the sense that they are merely ‘disjunctively true-or-false’. The author of the Editio super Aristotelem De interpretatione (commentary H4, in Marenbon’s catalogue), for instance, interprets Boethius’ position in this way, as Knuuttila has shown.30 He affirms that, while both present and past propositions have determinate truth or falsity and are also disjunctively true-or-false (‘sub disiunctione et determinatam habent veritatem et falsitatem’), future contingent claims are true or false only under disjunction (‘sub disiunctione tantum’). The exact same idea is supported by the author of commentary H5.31 This is also the opinion offered by Garland in his Dialectica, where he claims that future contingent propositions cannot be counted among true propositions or false ones. Rather, they belong to a special category of their own, the category of propositions that are ‘either-true-orfalse’ (‘vel verae vel falsae’).32 Of course, this interpretation of Boethius’ distinction between definite and indefinite truth amounts to a rejection of general bivalence, for indeed it assigns to future contingent propositions a third truth-value (‘true-or-false’), which does not coincide with any of the two traditional ones, ‘true’ and ‘false’.

28

29 30 31 32

See Boethius 1877, pp. 106, 30–107, 16; translated in Kretzmann 1987. Other passages in which Boethius advances this idea are: (Boethius 1877, pp. 108, 18–26; 125, 20; 1880, p. 204, 8–25); see also (Boethius, 1877, pp. 109, 9–17; 110, 28–112, 4; 114, 8–24; 208, 7–23; 211, 26–213, 4; 219, 5–17). See (Knuuttila 2010) on this. Among interpreters that have supported this interpretation, Knuuttila mentions (Frede 1985); (Craig 1988); (Gaskin 1995); (Kretzmann 1987). (Abaelard 1969a, pp. 100, 13–19 and 112, 7–113, 3); cf. (Knuuttila 2010, pp. 81–2). See Munich, Bay., Clm. 14779, fol. 51r. (Garlandus Compotista 1959, p. 74, 19–31).

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If this were indeed Boethius’ position, his interpretation of Aristotle would entail a qualification of bivalence, after all. Another possible interpretation claims that, according to Boethius, future contingent propositions are not definitely true or false because their truthmakers are not yet determined, but nevertheless they are still either simpliciter true or simpliciter false in the present moment. This second reconstruction of Boethius involves no qualification of the principle of bivalence, for it admits that all propositions, including future ones, either fall within the category of true propositions or fall into the category of false ones.33 As Knuuttila notices, this seems to also have been Abelard’s own interpretation in the Dialectica and the Glossae, where he maintains that – although future contingent propositions have an indeterminate truth-value34 – they should still be counted as true or false simpliciter. 35 The same view is endorsed by some other 12th-century commentators. According to the author of H9, for instance, when we say that a proposition is (in)determinately true, this signifies that ‘It is true in such a way that it deals with an (in)determinate event’.36 The same formulation can also be found in other commentaries, such as H11, H13, and H20. Like Abelard, the authors of these texts admit a valid inference between ‘being (in)determinately true’ (or ‘false’) and ‘being true’ (‘false’) simpliciter. Despite this multiplicity of interpretations, Boethius’ strategy of distinguishing between definite and indefinite truth-values was widely influential on early 12th-century commentaries on De Interpretatione, and we find appeals to it in every known discussion of the topic from Abelard’s time. Like Boethius, Abelard’s contemporaries argued for the compatibility between the existence

33

Among modern commentators, this interpretation was supported by, for example, Mignucci, Seel, and others. This interpretation of Boethius and Ammonius is advanced, for instance, in (Mignucci 1987); (Mignucci 1998); (Seel 2001); (Beets 2003). 34 See, for instance, Dial. 210, 34–211, 5 and 211, 28–32; LI De Int. 246, 69–71 and 250, 171–81. Not only does Abelard embrace this idea, he also attributes this solution to Aristotle himself: see LI De Int. 245, 59–246, 71. 35 Dial. 211, 28–32: ‘Sicut autem eventus contingentis futuri indeterminatus est, ita et propositiones quae illos eventus enuntiant indeterminate verae vel falsae dicuntur. Quae enim verae sunt, indeterminate verae sunt, et quae falsae, indeterminate falsae sunt secundum indeterminatos, ut dictum est, eventus quos pronuntiant’. And 213, 17–20: ‘“Amplius si est album nunc, inquit Aristoteles, verum erat dicere prius quoniam erit album”; quare omnia futura, antequam praesentia sint, vere possunt praedici quia futura sunt, licet nondum nobis determinatum sit quod futura sint.’ Cf. (Knuuttila 2010, p. 83). 36 See H9 (Orléans, Bibl. mun. 266, p. 18a): ‘Notandum autem quod cum dicimus propositionem determinate vel indeterminate veram nichil aliud est dicere quam vera est et ita quod agit de determinato vel indeterminato rei eventu.’

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of future contingent events and the validity of bivalence and excluded middle, principles that they take to hold for assertoric propositions in any tense. Abelard’s general answer to the arguments of logical determinism may be summarized as follows. First, Abelard claims that the principle of bivalence holds unqualifiedly, and therefore every proposition has either the truth-value true or the truth-value false. He recognizes no other truth-values beyond these two. In particular, Abelard explicitly argues against the position that future contingent claims are neither true nor false, and he also does not embrace the idea that some propositions are only disjunctively true-or-false. Apart from bivalence, Abelard also accepts the law of excluded middle, according to which, of every pair of contradictory statements, ‘p’ and ‘not-p’, it is necessary that exactly one is true and the other false. This law is taken to hold unrestrictedly and unqualifiedly for all propositions, independently of their modal status and tense. The general validity of excluded middle, however, does not entail any deterministic consequences because, as Abelard says, it is not valid to infer from the necessity of a disjunction the necessity of its disjuncts. Abelard also thinks, following Boethius, that future contingent propositions, although being presently true or false, are only indeterminately so. This is because their truth-maker (that is, the eventus rei to which they refer) is not yet determinate, where determinate is taken to mean ‘knowable by virtue of its having happened in time, or by virtue of nature’ (Dial. 211, 28–32). Abelard not only embraces this idea but attributes it to Aristotle himself (LI De Int. 245, 59–246, 71). Nevertheless, even if the future statements ‘p’ and ‘not-p’ are only indeterminately true or false, the proposition that says ‘Necessarily: either p or not-p’ is not only true but also determinately true (Dial. 212, 36–213, 3). Finally, in answer to a specific argument for determinism (the third among the ones that I will consider below), Abelard points out that it might be possible for a future proposition to be determinate without the corresponding future event also being determinate. For example, we might indeed say that propositions such as ‘Socrates will eat tomorrow’ are determinate, according to the fact that this proposition is presently either true now or it is false, but this does not necessarily entail that the future event that Socrates will eat tomorrow is also determinate. This last point may sound perplexing, and I will consider it more carefully below. In the Dialectica and the Logica Ingredientibus Abelard considers three different arguments that someone might advance against the compatibility between unqualified bivalence and contingency. Of these, the third one is, in my view, the strongest and most innovative, and perhaps the most interesting as well, since it is related to the distinction between determinate and indeterminate truth-values – a distinction that, as we saw, was meant to solve the

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issue of determinism and which instead ended up raising new deterministic consequences. The first of Abelard’s three arguments37 aims to show that, since future propositions do not have a determinate truth-value, they do not have a truthvalue at all, that is, they are neither true nor false. This entails that the disjunctive proposition ‘p or not-p’ also cannot be true, since its truth-value should result from that of its components. The argument thus challenges both general bivalence and the law of excluded middle. Abelard only mentions this argument briefly in the Dialectica,38 where he reports the idea of ‘some’ according to whom future contingent propositions such as ‘p’ and ‘not-p’ are not proper dividentes and do not constitute a contradictory pair, for neither of them is true, inasmuch as neither of them is determinate.39 The same idea is presented again later in the Dialectica (213, 3–10) and also appears once in the Glossae on De Interpretatione.40 Abelard replies to this argument in two steps: first, he states that having a determinate truth-value is not a necessary condition for having a truth-value tout-court. Some propositions might be true or false even if only indeterminately. This answer relies on the definition that Abelard gave of determinacy. An event is determinate, according to him, if it is ‘per se knowable’, that is, if it can produce knowledge about itself (‘notitiam de se conferre potest’). Abelard says that we are not allowed to infer, from the fact that it is impossible for us to know which is the truth-value of a proposition, that this proposition is neither true nor false, because we should be careful in distinguishing the knowability of truth from truth itself. People who propose this idea, according to Abelard, make reality depend on knowledge or ignorance, which is entirely wrong.41 37 Cf. Dial. 210, 31–211, 1; 212, 36–213, 28 and LI De Int. 245, 59–66. 38 Dial. 210, 31–211, 1. 39 ‘Contradictio [enuntiationum de futuri contingenti] quibusdam non videbatur posse fieri, hocest affirmatio et negatio dividentes, eo scilicet quod nulla propositio de huiusmodi futuro vera videtur; pro eo videlicet quod, dum adhuc futurum est, non sit eventus rei determinatus. Nulla enim vera videbatur posse dici propositio nisi quae determinate esset vera, et falsa similiter, ut sunt omnes illae de praesenti vel praeterito et necessario futuro vel naturali.’ 40 ‘Quoniam autem propositiones de praesenti et praeterito, quaecumque verae sunt vel falsae, determinate verae sunt vel falsae, nulla autem veritas vel falsitas contingentis futuri determinata erat, plerique propositiones de contingenti futuro veras vel falsas omnino esse denegebant, eo videlicet quod ea, quam habent, veritas vel falsitas eis nondum aperiri posset. Unde non ita proprietatem contradictionis recipiebant in propositionibus de futuro huiusmodi sicut in praesenti et praeterito’ (LI De Int. 245, 59–66). 41 ‘[Propositiones de futuro contingenti] dividentes esse denegebant, cum neutram illarum veram vel falsam dicerent, eoquod determinate quae vera vel falsa esset, nescirent. Cum

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Second, Abelard claims that certain propositions, such as future contingent ones, have a truth-value, even if only an indeterminate one. Therefore, they may also be put in a proper relationship of contradictoriness with other propositions or constitute true disjunctive claims such as ‘p or not-p’. Abelard attributes this solution to Aristotle himself, who assigns truth and falsehood equally to all propositions, although truth is not determinate in all of them.42 In conclusion, Abelard claims that even if a future contingent proposition ‘p’ is only indeterminately true or false, the disjunctive proposition ‘p or not-p’, as well as the state of affairs to which it refers, is nevertheless determinately true. According to Abelard, thus, the determinacy of a composite proposition does not depend on the determinacy of its components.43 Abelard then presents a second argument that could be advanced against the validity of what he calls the ‘proprietas contradictionis’ – that is, the principle according to which, in any pair of contradictory propositions, one and only one of them is true – when applied to future contingent propositions. The argument44 is in the form of a reductio and quite closely retraces Aristotle’s own dilemma in De Interpretatione 9. It aims to show that, if we admit that it is necessarily the case for any pair of contradictory propositions ‘p’ and ‘not-p’ that either ‘p’ is true or ‘not-p’ is true, it follows that either what is said by ‘p’ is necessarily the case or that what is said by ‘not-p’ is necessarily the case. If this is so, the events signified by ‘p’ and ‘not-p’ necessarily occur or do not occur, and therefore they would not be contingent but rather determined. This would lead to the destruction of contingency and, in particular, to the destruction of human deliberation (consilium) and actions (negotium). But since it is evident that there are some events that are brought about by human beings’ deliberation and free actions, the premise included in the argument must be false. The argument then concludes that the aforementioned principle concerning

enim neutram per se veram esse vel falsam recognoscerent, neutram veram esse vel falsam volebant; ac si minus, aliquid eorum quae propositiones dicunt, in re esset vel non esset propter eorum cognitionem vel ignorantiam, secundum quae scilicet ipsae propositiones verae esse vel falsae dicendae sunt. Si enim ita est ut propositio dicit, vera est; si autem non, falsa, sive haec nobis cognita sint sive non’ (Dial. 212, 36–213, 11). 42 See LI De Int. 246, 69–71: ‘Quorum errorem postea [Aristoteles] corriget veritatem vel falsitatem omnibus aequaliter assignans, licet non sit in omnibus determinata.’ 43 ‘Cum autem propositionum de contingenti futuro nulla sit vera vel falsa determinate, omnium tamen dividentium determinatum est et necesse alteram veram et alteram falsam, cuiuscumque sint temporis, ut sunt illae et quae de futuro contingenti fiunt, veluti istae: “Socrates hodie leget”, “Socrates hodie non leget”’ (Dial. 212, 36–213, 3). 44 This second argument is considered in Dial. 213, 29–214, 25 and 219, 25–222, 25; LI De Int. 245, 1–246, 71.

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contradictory pairs does not hold unrestrictedly, and, in particular, it does not hold for future sentences. Abelard’s reply to this argument is quite well known. His solution consists in saying that the principle in question (in the Latin translation of Aristotle’s text, that omnium affirmationum et negationum necesse est alteram esse veram et alteram falsam) is ambiguous and could be read as having two different senses (Dial. 219, 32–6). In order to explain this ambiguity, Abelard resorts to an analogy with another Aristotelian principle concerning contraries, which says that, of any pair of contrary predicates, such as healthy and non-healthy, it is necessarily the case that one inheres in a substance while the other does not inhere (De Interpretatione 17b26 ff.). This claim, Abelard states, should not be taken as saying that, of the two contraries, one and the same always inheres in the substance and the other always does not inhere in it; rather, it must be taken as saying that, necessarily, one or the other of the two inheres and one or the other of the two does not inhere. Similarly, it is not the case that, of every pair of propositions ‘p’ and ‘not-p’, one and the same proposition is necessarily true and the other is necessarily false, but that, necessarily, one or the other of the two is true and one or the other of the two is false. The ambiguity seems to lie in the use of the term ‘altera’, which could be understood either as picking one of the two propositions rigidly (one and the same proposition is necessarily false) or as picking, indifferenter and sub disiunctione, one proposition or the other. In the latter case, Abelard says, the term ‘altera’ must be read in the sense of ‘alterutra’. If we read the principle in the first sense, as saying that for every pair ‘p’ and ‘not-p’ ‘it is necessary that p is true or it is necessary that not-p is true’, the principle is false. If, instead, we read it in the second sense, as saying that ‘it is necessary that indifferently one of p or not-p is true’, the principle is true.45 That this was also Aristotle’s own solution to the problem, Abelard claims, is clear from what he says about the distinction between absolute and conditional 45

‘Potest autem et vere et falso accipi, sicut et illud quod in tractatu oppositorum de eisdem affirmationibus et negationibus dixit, alteram scilicet semper esse veram et alteram falsam, veluti istarum: “Socrates est sanus” et “Socrates non est sanus”. Si enim ita intellexeris quod uni et eidem semper verum inhaereat, falsum est, cum potius neutra illarum veritatem custodiat, sed modo vera sit eadem, modo falsa. Si vero ita sumpseris ut “alteram” non circa una tantum teneas, sed indifferenter accipias ac si dicas “alterutram”, verum est. Semper enim alterutra vera est, hocest semper ita se habet quod vel haec vel illa vera est. Haecque Aristotelis acceptio exstitit, cum scilicet ait alteram semper esse veram et alteram falsam, ut illud scilicet “alteram” dividue sumeret ac si “alterutram” diceret. Sic quoque et hoc loco, cum ait alteram necesse est esse veram et alteram falsam.’ (Dial. 219, 36–220, 12)

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necessity, that is, between things that are unqualifiedly (simpliciter) necessary from things that ‘necessarily are when they are’.46 Because, Abelard continues, we are never entitled to infer an absolute necessity from a conditional one, we are also not entitled to infer from the fact that it is conditionally necessary that either ‘p’ is true or ‘not-p’ is true the fact that one of ‘p’ and ‘not-p’ is absolutely necessary (or, we might say, we are not entitled to infer from the necessity of a disjunction the necessity of either disjunct). This second argument, then, is sophistical according to Abelard, because it is based on a semantic ambiguity. If the logical principle that is at stake is taken in its proper sense, as saying ‘Necessarily: p is true or not-p is true’, then it is true, but it would not follow from it that either ‘p’ or ‘not-p’ are necessary in themselves. Finally, Abelard devotes a long part of his work to a third deterministic argument,47 which runs as follows: if we accept both the validity of bivalence and the idea that propositions about the present or the past are determinately true or false, then we end up saying that all propositions – even future contingent ones – should have a determinate truth-value. The interesting aspect of this argument is that it explicitly targets the traditional distinction between determinate and indeterminate truth, which, as was said, was accepted by many 12th-century logicians as a way out of logical determinism. This new deterministic argument, however, aims to demonstrate that distinguishing between determinate and indeterminate events is a useless move, because, from accepting the determinacy of the past and the present, the determinacy of all future propositions necessarily follows – and consequently also the determinacy of all future events. Let us see why. This new version of logical determinism is based on the idea that for any future contingent proposition, for instance, ‘Socrates will eat tomorrow’, it is possible to formulate a present (or past) proposition that predicates the truth or the falsity of the former proposition, as in ‘That Socrates will eat tomorrow is (was) true’. This present proposition must have a determinate truth-value, insofar as: (i) every present and past event is determinate, and (ii) bivalence holds, namely, every proposition is either presently true or presently false. But if ‘That Socrates will eat tomorrow is true’ is determinate, it seems that the 46

‘Sic quoque et hoc loco, cum ait alteram necesse est esse veram et alteram falsam, quod quidem ipse manifeste in sequentibus in solutione huius argumentationis declaravit, cum ait: “igitur esse quod est, quando est, et non esse quod non est, quando non est, necesse est; sed non omne quod est necesse est esse nec quod non est necesse est non esse; non enim idem est omne quod est esse necessario, quando est, et simpliciter esse ex necessitate”.’ (Dial. 220, 11–7) 47 Cf. Dial. 212, 10–23; LI De Int. 252, 215–253, 241.

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future event to which it refers should also be presently determinate. And since one could construct a similar argument for every future proposition, we may conclude that no future event is indeterminate and contingent. As far as I know, no exact parallel of this argument is found in Boethius or other pre-Abelardian commentaries on De Interpretatione, although we do find a concise version of it in the commentary H9, which also offers a solution that seems similar to that proposed by Abelard. Among all three arguments that Abelard considers concerning logical determinism, this seems to be the one that troubles him the most, and to which he dedicates the greatest attention. However, both the exact structure of the argument and Abelard’s answer to it have been a matter of debate.48 The argument posits four different entities, two propositions, and two events: – A future contingent proposition (p) = ‘Socrates will eat’; – a future event (π) = that Socrates will eat, which is the referent of proposition (p); – a present proposition (q) = ‘that Socrates will eat is true’; – a present event (χ) = that truth inheres in proposition (p); which is the referent of proposition (q). In the Glossae Abelard presents the argument with the following words (I have added the labels ‘p’, ‘q’, ‘χ’, ‘π’ to help the reader identify which proposition or event Abelard is talking about): Yet with regard to certain present and past propositions, a question remains whether they are definite, that is definite in nature, since these propositions cannot be known but on the basis of some future indeterminate event. As when it is said: (p) ‘Socrates will eat,’ certainly this proposition is already presently true or false, and this other proposition that says (q) ‘“that Socrates will eat” is true’ is a proposition about the present and therefore it is already either determinately true or determinately false, at least by virtue of the nature of (χ) the present inherence of truth or falsity that it has. But if (p) ‘Socrates will eat’ is determinately true, it is also determinate (π) that Socrates will eat, for just as the truth of propositions depends on the events of things, so also the knowledge of these propositions’ truth and falsity must be obtained from the knowledge of the events. For indeed it is impossible to know that a proposition is true without knowing that what it says is the case, since it is certain that the 48

See, in particular (Normore 1982, pp. 362–3); (Lewis 1987). In what follows I retrace the interpretation that I have offered, in more detail, in (Binini 2019b).

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proposition cannot be true but by virtue of the fact that what the proposition says really occurs.49 According to my reconstruction, the argument initially assesses the determinacy of the proposition (q), which is a proposition de praesenti, on the basis of the fact that it corresponds to a present event (χ) that is determinate. This first passage may already sound troubling. Why does Abelard not escape the deterministic conclusions of the argument by challenging the determinacy of (q), namely, by saying that the eventus to which (q) refers is not a present event but rather a future one? This would seem to be a viable option for him, as Normore has noted, since Abelard admits, at least in the Logica Ingredientibus, that there are propositions in the present tense that are nevertheless de futuro contingenti and therefore have only indeterminate truth.50 Abelard’s acceptance of unqualified bivalence, however, commits him to the idea that every proposition, including the ones that are indeterminately true, such as (p), is also true simpliciter. This means that, in the present moment, a future proposition such as (p) either has the property of being true or has the property of being false. Thus, either there presently is an eventus consisting of the inherence of truth in (p) or there is not such an event. Since this is a present event, it must be determinate on the basis that it is happening now. Assuming, for the sake of argument, that (p) is presently true, the present event (χ), consisting in the inherence of truth in (p), must be determinate, as must the present-tensed proposition (q), because every proposition that refers to a determinate event is itself determinate. Abelard is then bound to accept the determinacy of (χ) and (q), and he infers from it that the future proposition (p) must also be determinate, by virtue of an

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LI De Int. 250, 182–251, 196: ‘De quibusdam tamen praesentibus sive praeteritis restat quaestio, utrum definita sint, ⟨scilicet⟩ in natura, cum ⟨non⟩ nisi per futura indeterminata sciri queant. Veluti cum dicitur: “Socrates comedet” haec propositio iam profecto praesentialiter est vera vel falsa, et haec propositio quae dicit: “‘Socrates comedet’ vera est” de praesenti est et ideo iam vel determinate vera est vel determinate falsa saltem in natura praesentis inhaerentiae veritatis vel falsitatis quam habet. At vero si Socrates comedet est vera determinate, oportet et determinatum esse, quod Socrates comedet, quia sicut veritas propositionum ex eventu rerum pendet, ita et cognitionem veritatis vel falsitatis ex cognitione eventuum necesse est haberi. Impossibile enim est cognosci veram esse propositionem ita, ut nesciatur, quod ita sit, ut ipsa dicit, cum videlicet certum sit eam non aliunde veram esse nisi ex eo quod ita dicit enuntiando, sicut in re est’. Propositions of this sort are, for instance, ‘Socrates is the name of the man who will eat tomorrow’, or ‘I see a man who will eat’; see LI De Int. 251, 196–204. See (Normore 1982, pp. 362–3) on this.

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implicit principle according to which determinacy is always preserved in valid inferences. He says in the Logica: But there are some who say that (p) ‘Socrates will eat’, which is perhaps presently true, is determinately true with respect to the truth itself, i.e. with respect to [the] property [of being true] that it presently has, for indeed the event (χ) consisting in the present inherence of this property to proposition (p) is determinate, and [the proposition (p)] itself is already now determinately true.51 Once he has accepted the determinacy of (χ), (q), and (p), however, Abelard blocks the chain of entailments constituting the argument, stating that even though (p) is taken to be determinate – even if only in a weak sense, as we will see – it would not be right to infer from this that the future event (π), to which (p) refers, is also determinate. His way out of the dilemma, thus, consists in admitting that a proposition could be determinate without the corresponding event being determinate as well. Abelard also adds that there is a terminological ambiguity hidden in the argument, and that there are, in fact, two ways in which a proposition is said to be determinate. One is with respect to the determinacy of the event to which it refers (quantum ad eventum), and the other is with respect to the present inherence of truth in it (quantum ad praesentem et determinatam inhaerentiam veritatis), that is to say, with respect to the property that it presently and determinately has of being true or false. Proposition (p) is determinate in the second sense but not in the former one.52 51

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LI De Int. 252, 215–20: ‘Sunt autem qui dicunt quod “Socrates comedet”, quae fortassis praesentialiter vera est, determinate vera est quantum ad veritatem ipsam, scilicet proprietatem quam praesentialiter habet, quippe determinatus est eventus proprietatis praesentialiter rei inhaerentis, et ipsam iam determinate veritatem habet.’ LI De Int. 252, 220–5: ‘Sed licet determinate vera dicatur propositio quantum ad praesentem et determinatam inhaerentiam veritatis, quantum tamen ad eventum, quem loquitur indeterminatum, indeterminate vera est. Et hoc loco Aristoteles determinate vel indeterminate veras vel falsas propositiones dicit quantum ad eventus, scilicet determinatos vel indeterminatos, quos proponunt.’ A similar distinction between two senses of determinacy may be found in the commentary on De Interpretatione 9 preserved in H9. While discussing a version of this same argument, the author of H9 claims that when we say that ‘Socrates will sit’ is indeterminately true, this means that it is true in such a way that it deals with an indeterminate event. When instead we say that ‘Socrates will sit’ is determinately true, this means that truth inheres presently – and so determinately – in it. In the first case, indeterminacy refers to the event, and in the second one determinacy refers to the truth. See H9 (Orléans, Bibl. mun. 266, p. 18a): ‘Attende ergo quod ubi dicitur “‘Socrates

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Having distinguished between the two senses of determinacy, Abelard concludes by saying that the deterministic argument is also based on a further confusion between the two notions of determinacy (that is, knowability) and certainty (namely, actual knowledge). In the case of certainty, Abelard claims, we would indeed be allowed to infer the certainty of a future event (π) from the certainty of the present proposition (q), but this inference is not valid for determinacy. Whence, if this consequence is to be admitted: ‘If (q) “Socrates will eat” is true, then (π) Socrates will eat’, and the antecedent is certain, then the consequent will also be certain. But perhaps it is not the case that if the antecedent is determinate, then the consequent is also determinate, because the present event (χ) [to which (q) refers] is knowable in itself, but the future contingent event (π) is not.53 Having presented this way out, Abelard concludes his defence of the compatibility between unqualified bivalence and the existence of future contingent events. As I have tried to show, his solutions are based on examination of the concept of determinacy – a concept that he inherits from Boethius, which was in fact widely used by his contemporaries – but which Abelard reshapes in order not to be entrapped in fatalist consequences. On the one hand, he does so by providing a definition of this notion in terms of knowability or accessibility to knowledge, instead of using the traditional modal characterization of determinacy as a species of necessity. On the other hand, he distinguishes between two different senses in which a proposition is said to be determinate, of which only one implies the determinacy of the corresponding event. As I have argued elsewhere, Abelard’s way out of this last deterministic argument, and generally his treatment of the meaning of ‘determinacy’, seem flawed and raise more problems than they actually solve. For instance, it is not clear in which sense some propositions can be said to have a determinate truth-value while being at the same time contingent. Furthermore, while Abelard’s notion of determinacy quantum ad eventum seems to have some sort

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sedebit’ est vera indeterminate”, hoc est dicere vera est, ita quod agit de indeterminato eventu rei. Quando vero dicitur “‘Socrates sedebit’ est vera determinate”, hoc est dicere veritas presentialiter et ideo determinate inest ei, ut in una indeterminatio ad eventum, in alia determinatio ad veritatem referatur.’ LI De Int. 252, 236–253, 241: ‘Unde et si talis consequentia recipiatur: “Si ‘Socrates comedet’ est vera, Socrates comedet” et certum sit antecedens, certum erit et consequens. Sed non fortasse, si determinatum sit antecedens, et consequens, quia praesens eventus ex se cognoscibilis est sed non ita futurus contingens.’

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of philosophical relevance, his weaker notion of determinacy quantum ad praesentem inhaerentiam veritatis seems to be an entirely ad hoc notion, which the philosopher brings up in order to escape determinism but which has no other role in his theory of contingent propositions. We should appreciate, however, that, in addition to the acute (although perhaps, ultimately unconvincing) reasoning with which he tries to defeat logical determinism, Abelard’s commentary on De Interpretatione 9 also offers a novel and sophisticated piece of applied modal logic. Within this discussion Abelard employs several tools and techniques that he developed through his reflection on modal propositions, such as the analysis of the scope of modes with respect to other logical operators. Abelard also seems to treat the terms ‘determinate’ and ‘certain’ as if they were modal operators of some sort, an idea that, to my knowledge, was not common at the time, although it might be an anticipation of later developments in medieval epistemic logic. In the next section, which concludes this book, we will see how Abelard also confronts some problems of theological determinism by resorting to the logical apparatus that he had developed within his modal logic. 4 Abelard on Theological Determinism and the Dilemma of Divine Foreknowledge As we have seen, Abelard devotes a long discussion to the problem of logical determinism and to the puzzles raised by the application of bivalence and excluded middle to future contingent propositions. In addition to these problems, Abelard and other logicians contemporary to him also discuss a number of arguments for theological determinism, related to the compatibility between the admittance of contingency and the infallibility of God’s foreknowledge. Within his commentary on Chapter 9 of De Interpretatione, Abelard reports the opinion of some who have tried to demonstrate the necessity of every event happening in time by appealing to God’s providence or predestination. They affirm that since God has already established a providential plan and knows everything that will happen in the future, things cannot but happen in conformity to his knowledge, which is infallible, and to his providential plan, which is unchangeable (‘secundum eius providentiam, quae falli non potest, et institutionem praedestinationis, quae mutari non potest’).54 A consequence of 54

‘Sunt autem nonnulli, qui nil utrumlibet appellent nec aliqua futura contingentia dicant, sed omnia quae eveniunt ita ut eveniunt ex necessitate evenire. Quod ex dei providentia sive praedestinatione conantur ostendere. Aiunt enim, quod deus, qui in sua providentia

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this, they go on, is that everything is predetermined by God, who would then be chargeable for all good and bad things that come about (‘omnium bonorum laudem vel malorum culpam in auctorem omnium refundebant’). Humans would therefore be relieved of the responsibility for their own actions. This opinion, Abelard says, is execrable, not only with respect to the Christian religion but also with respect to natural reason, and, in addition, to Peripatetic philosophy (LI De Int. 259, 402–4). Abelard strongly rejects the idea that the infallibility of God’s knowledge and the fixedness of God’s providential plan necessarily entail the absence of contingency and free will. Before investigating the fallacies in this fatalistic argument, he delves into a terminological clarification, defining what is intended by the terms ‘providence’ (providentia, vis providentiae) and ‘predestination’ (vis praedestinationis).55 The term ‘providentia’, he says, refers to God’s knowledge of future events (praescientia futurorum; see, for example, LI De Int. 259, 404–260, 410). This consists in the simultaneous knowledge of every singular state of affairs that takes place in the future, a knowledge that God possesses ‘before’ these events take place (simul singula praescivit, antequam eveniret). This knowledge includes not only the good things, which are efficiently brought up by God, but also the evil ones – for which we humans, not God, are responsible (‘est providentia non solum praescientia bonorum, quae ex eo procedunt, verum etiam malorum, quae a nobis fiunt’). ‘Praedestinatio’ instead has the same signification as fate (fatum or fatatio); in other words, it refers to the events that God established to happen in history and which are brought about by him: ‘praedestinatio idem esse quod fatum, id est fatatio, videtur, quando videlicet bonum quod providet stabiliendo mente disposuit, ut eveniat, quando ipse voluerit’. In contrast to providence, which was said to be the knowledge of both good and bad things, predestination includes

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falli non potest, omnia ab aeterno providit et pradestinavit ita evenire ut eveniunt, et tunc evenire quando eveniunt; quare secundum eius providentiam, quae falli non potest, et institutionem praedestinationis, quae mutari non potest, necesse est singula ita et tunc evenire ut eveniunt et quando. Et ita omnia sub necessitate costringunt, ut nullatenus vitari possit, quin eveniant, sicut eveniunt et quando’ (LI De Int. 259, 388–98). The same problem is posed in Dial. 217, 19–22: ‘Cum enim ab aeterno Deus omnia futura esse, sicut futura erant, providerit, Ipse autem in dispositione suae providentiae falli non possit, necesse est omnia contingere sicut providit; si enim aliter contingere possent quam lpse providerit, possibile esset Ipsum falli.’ This distinction is proposed only in the glosses on De Interpretatione 9, and not in the Dialectica, where Abelard only speaks of providentia or divine foreknowledge and never of predestination.

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good things only. Following Augustine, Abelard thinks that predestination is nothing other than ‘praeparatio beneficiorum dei’. The distinction between providence and fate had, in fact, already been proposed by Boethius,56 to whom Abelard makes direct reference in LI De Int. 261, 425–44, saying that he took ‘providentia’ as divina ratio and ‘fatum’ as the divine dispositio of events that take place in the world of moving things (rebus mobilibus dispositio). Abelard notes that there is an ambiguity in Boethius’ words, because he presents foreknowledge and predestination as simultaneously different and the same. According to Abelard, it is correct to consider the two as essentially the same and to say that both God’s providence and predestination are nothing other than God himself. This is because, he states, it is somehow improper to distinguish among different attributes of God, given that God’s nature is simple and indivisible.57 However, the two are also considered to be different from the point of view of human beings, because the two names are assigned according to a different causa impositionis.58 Having distinguished between foreknowledge and predestination, Abelard insists that neither impose any necessity on things, for by means of foreknowledge God knows whatever will be, including future contingent events, but knows them as contingent and not as necessary. Similarly, predestination

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This distinction already had a long history before Boethius: see (Sharples 2009, p. 214) on this point. As Sharples notes, the distinction ‘became particularly significant in the Platonist tradition of which Boethius is part, where it was emphasized not only that fate is the working-out of the providential plan in space and time, but that rational human souls can rise above the level of fate’. The topic was debated, for instance, in Plotinus, Proclus, Calcidius, and Augustine. See (Cicero 1991, pp. 29–31) and references there. For Abelard’s discussion of God’s simplicity, see, in particular, LI De Int. 262, 455–263, 485. ‘Quae quidem verba habent ambiguitatis, cum scilicet modo idem fatum et providentiam vocat, modo diversa. Sed cum in deo nil sit aliud ab ipso nec aliud sit sapientia eius vel providentia vel praedestinatio (id est fatalis stabilitio) eius, quam ipse, recte idem essentialiter dixit; quia vero homines nomina tam creatori quam creaturis aliunde providentem, aliunde fatalem dixerunt, recte secundum diversas vocabulorum causas diversa fatum et providentiam dixit, sicut aliud risibile esse, aliud navigabile esse dicimus, cum tamen idem sit penitus navigabile et risibile, ac est tale, ac si dicatur quod aliud sonat “risibile” aliud “navigabile” secundum diversas impositionis causas. Sic et deus et providentia dicitur ex eo quod providet et praescit, et fatum ex eo quod stabilit et disponit in creaturis. Nec ullae sunt proprietates, quas in deo intelligamus, dum eum providentem vel fatalem dicimus vel scientem vel intelligentem vel bene agentem, sed more humano loquentes simplicem eius essentiam et in se omnino invariabilem pro his, quae per eum invariabilem varie fieri contingunt et varie a nobis exscogitantur, variis designamus nominibus’ (LI De Int. 261, 444–262, 462).

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does establish what will take place in the future but, again, not as taking place necessarily.59 Moreover, Abelard recalls Boethius’ analogy between God’s knowledge of the future and our own knowledge of present facts. Just as when I see someone walking in front of me, and I know that he or she is walking, this does not imply that he or she is walking necessarily, so it is not right to infer from the fact that God already knows that I will be walking or that I will sin that I do so out of necessity.60 Although Abelard does not explicitly mention the Boethian view that God’s knowledge is not, strictly speaking, foreknowledge, we might infer that he endorsed it too, given his insistence that God knows all events simultaneously (omnia simul praescivit, see, for example, LI De Int. 264, 508; 259, 407). As Marenbon suggests is the case for Boethius, the metaphysical ground on which Abelard bases the idea that God knows future events, just as he knows past and present events, seems not to be his eternity or atemporality but rather his simplicity and the consequent immutability of his knowledge.61 After considering the signification of providence and fate, Abelard passes to the analysis of an ‘astute but sophistical’ argumentation (callida sed cavillatoria argumentatio), demonstrating the inadmissibility of contingency on the basis of the infallibility of God’s knowledge. According to this argument, if we admit that it would be possible for things to happen otherwise than they in fact do happen, we would also be admitting that they happen otherwise than God knows them, and therefore that God’s knowledge is fallible. But since it is impious to attribute fallibility to God, we are forced to conclude that it is impossible for things to happen otherwise, and therefore that everything necessarily happens as it actually does. 59

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‘At vero, cum provideat vel praedestinet futura, neque providentia eius neque praedestinatio necessitatem rebus infert. Providet enim futurum fieri, sed non ex necessitate fieri; stabilit futurum, ut fiat, sed non ut ex necessitate fiat. Sic enim providet et stabilit futura, sicut sunt eventura, ut scilicet sic eveniant ut possint etiam non evenire. Quippe sic eventura sunt ut possint etiam non evenire.’ (LI De Int. 264, 491–7) And: ‘Sic ergo integre providentiam eius consideremus, quae omnia simul praescivit, quae ad meum actum sive possibilitatem pertinebant, et ita me ambulare modo et simul modo posse non ambulare providit, secundum eius providentiam et me ambulare contingit et posse non ambulare quia utrumque in eius providentia aequaliter persistit’ (LI De Int. 264, 507–12). ‘Sicut enim, si quis ante me ambulet, quem videam et sciam ambulare, visus meus et scientia non confert ei, ut ex necessitate ambulet, nec tamen ambulantem videre vel scire possum, nisi ipse ambulet, ita dei providentia me ita ambulaturum providit vel peccaturum, ut mihi necessitatem in altero non inferret; alioquin ipse me compelleret peccare, nec reus essem, qui coactus peccarem, sed ipse per quem peccare cogerer’ (LI De Int. 264, 501–7). Cf. (Marenbon 2013b, p. 18).

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Abelard offers an analysis of this argument both in the Dialectica (Dial. 217, 16–219, 24) and the Logica (LI De Int. 265, 520–267, 3), and we may reconstruct the argument’s structure in the following way: 1. If things happen otherwise than they happen, then things happen otherwise than God foreknows [locus a pari]. 2. If things happen otherwise than God foreknows, then God is fallible [definition of fallibility]. 3. If things happen otherwise than they happen, then God is fallible [transitivity of the conditional]. 4. Necessarily, if things happen otherwise than they happen, then God is fallible [Abelard’s definition of conditional]. 5. If it is possible for things to happen otherwise than they happen, then it is possible for God to be fallible [distribution of modal operator over the conditional]. 6. It is possible for things to happen otherwise than they happen [hypothesis of contingency]. 7. It is possible for God to be fallible [modus ponens].62 In the version of the argument presented in the Dialectica Abelard continues by saying that, since it is impossible that God is fallible (on the basis of the dogma of divine infallibility), it is impossible for things to happen otherwise, and therefore everything necessarily happens as it happens, which violates the hypothesis of contingency. A similar version of this argument is repeated in the Theologia Scholarium.63

62 Cf. LI De Int. 265, 524–266, 539: ‘Si possibile est rem aliter evenire, quam evenit, possibile est rem aliter evenire, quam deus eventuram esse providit. A pari. Et ita possibile est deum rem aliter providere, quam evenit, et ita possibile est deum falli. Si enim aliter evenit res, quam deus providit, vel aliter providit deus, quam evenit, deum fallitur. Unde si possibile est aliter evenire, quam deus providit, vel aliter providisse, quam evenit, possibile est deum falli. Cuiuscumque enim antecedens est possibile, possibile est et consequens. [...] Cum itaque haec consequentia vera sit: “Si res aliter evenit, quam deus providit, vel aliter providit, quam evenit, deus fallitur”, vera est et haec: “Si possibile est aliter providisse vel evenire, possibile est deum falli”. Itaque per medium probata est proposita consequentia, haec scilicet: “Si possibile est rem aliter evenire quam evenit, possibile est Deum falli”.’ 63 (Abaelard 1987a, p. 541, 1337–1355): ‘Quaerendum denique videtur utrum res possint aliter evenire quam deus providit? Quod quidem si ut verum est ponamus, videtur necessario consequi quod deus falli possit, iuxta illam regulam: Cuius possibile est antecedens, et consequens. Verum quippe est, inquiunt, quod si res evenit aliter quam deus providit, deus fallitur. Quare si possibile est rem aliter evenire quam deus providit, possibile est deum falli.’ For a comparative analysis of Abelard’s argument in his logical and theological works, see (Marenbon 2005, pp. 82–7).

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The argument takes its move from the conditionals stated in (1) and (2), which are both considered true by Abelard. The truth of the first, he explains, is guaranteed by a locus a pari, whereas the second simply follows from the definition of ‘fallible knowledge’. Abelard does not explicitly define what he means by saying that God is fallible or that he might be in error. Such a definition is instead provided by William of Champeaux in the Sententiae while considering a similar argument.64 If one accepts (1) and (2) as true, together with the hypothesis of contingency expressed in (6), the conclusion of the argument logically follows once granted: (i) a certain definition of the conditional according to which a conditional proposition is true only if it is necessarily true; and (ii) the validity of three principles of inference: modus ponens; transitivity of implication; and a rule for distributing possibility over the conditional, according to which whenever ‘if p, then q’ is true, then it is true that ‘if it is possible that p, it is possible that q’. As was shown in Chapter 6, Abelard accepts this last principle and mentions it in both the Dialectica (e.g. 217, 22–3) and the Logica (e.g. 265, 531–2), where he writes that, whenever the antecedent is possible, the consequent is also possible (‘Cuiuscumque antecedens est possibile, possibile est et consequens’). John Marenbon has proposed the following formulation for this principle: ‘((p → q) & ◊ p) → ◊ q’,

where ‘◊’ stands for possibility, ‘&’ for conjunction, and ‘→’ for implication.65 It is possible to give an informal justification for the validity of this principle based on Abelard’s definition of the conditional, as Marenbon remarks. As mentioned earlier, it is a necessary criterion for the truth of Abelard’s conditionals that they express a necessary consecution, so that ‘if p then q’ is true only if q follows necessarily from p, that is, if it is impossible that p is true and q false.66 Suppose that the conditional is true and that proposition p is possible, that is, there is some possible situation in which it is the case that p. In such a situation, q will also be the case; otherwise, the conditional ‘p → q’ would be 64 65 66

(Guillelmus Campellensis 1959, p. 195, 28–31): ‘Et nota quod Deum falli est credere tale quid eventurum quod numquam eveniet, vel aliquid latere providentiam illius. Posse autem falli est hoc posse credere, vel posse hoc ignorare, quod est eventurum.’ (Marenbon 2005, p. 68). According to Abelard, this is a necessary condition for the truth of a conditional but not a sufficient one. Abelard maintains, in fact, that the truth of a proposition such as ‘if p, then q’ requires two conditions: (i) that it is impossible for p to be true while q is false, and (ii) that the meaning of q is contained in that of p. On this see (Martin 2004b, pp. 176–86).

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false. We then have a possible situation in which q is true and therefore q is possible. Marenbon calls this principle of distribution the ‘transfer of possibility principle’67 and shows that the strategy proposed by Abelard to solve the deterministic argument is based precisely on a re-examination of this principle and on the restriction of its validity to certain modal propositions, as we will see. Before going into the details of Abelard’s solution, it might be useful to consider one version of the same argument advanced in the Sententiae of William of Champeaux, which has several elements in common with Abelard. William examines the two conditional propositions that are at the core of the infallibility argument – namely, (i) ‘Si possibile est rem aliter evenire quam evenit, possibile est Deum falli’ and its converted form (i*) ‘Si non possibile est Deum falli, non possibile est rem aliter evenire quam evenit’ – in some of his writings on theology, included in the Sententiae.68 Here, William tries to undermine the following deterministic argument: 1. 2. 3. 4.

If it is possible for something to happen otherwise than it actually happens, then it is possible for something that God has foreknown not to take place. If it is possible for something that God has foreknown not to take place, then it is possible that the opposite of what God has foreknown will happen. If it is possible that the opposite of what God has foreknown will happen, then God’s knowledge could be false. If God’s knowledge could be false, then this knowledge is not necessarily true.69

William initially reports the opinion of some who try to unravel the dilemma by stating that, although it does follow that God could be wrong, in fact, he never is wrong, and so the truth of his knowledge would be preserved.70 According to

67 68 69

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See (Marenbon 2005, p. 68) and (Marenbon 2013a, pp. 53–4). (Guillelmus Campellensis 1959, pp. 195–6). See (Guillelmus Campellensis 1959, p. 195, 1–9): ‘De providentia Dei sic quidam argumentantur: Si providentiam Dei necesse est esse veram, tunc res impossibile est aliter evenire quia ita omnia fiunt ex necessitate, quia si possibile est res aliter evenire, et providentiam Dei possibile est falli. Quod ita probatur: Si possibile est res aliter evenire, tunc potest non esse quod Deus providit. Si autem hoc est, tunc potest evenire contrarium divine providentie. Et si hoc est, tunc potest evenire esse falsa divina providentia. Et si potest esse falsa providentia divina, tunc potest non esse vera. Quod si est, tunc non necesse est eam esse veram.’ See p. 195, 33–4: ‘Quidam concedunt quod Deus possit falli sed numquam fallitur, quod dicere insanum est.’

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their opinion, God would then be fallible but at the same time, as Guilfoy put it, ‘very lucky epistemically’.71 William firmly rejects this opinion, insisting that it is false and blasphemous to hold both that God actually fails and that he is, in principle, fallible. His aim is then to show that the deterministic argument is invalid and that, although both conditionals (1) and (2) are true, proposition (3) does not follow from them, namely, that although the contrary of what God has foreknown could happen, this does not entail that God could be wrong or have false knowledge. William’s strategy to defend this claim is articulated in three passages. First, he affirms that God knows not only all events that will take place but also the mode of these events, that is, in which mode they will take place, whether necessarily or contingently.72 Specifically, God knows that certain events that are included in his providentia are such that they might also not happen. William particularly insists on the fact that God knows, before their occurrence, that certain events will take place as a result of human free choice, and he knows these events to be contingent. It is therefore true, William says, that certain events that will happen could not happen, and that the opposite of what God has foreknown could therefore happen. This, however, does not entail that he is fallible, for the contingency of these events was itself included in divine knowledge.73 William’s first strategy is in line with the traditional response to theological determinism offered by Augustine and Boethius, but in this context it appears quite unsatisfactory, as it fails to clarify where the invalidity of the aforementioned argument exactly lies. More promising is William’s second point against the argument, which, as we will see, will also be included by Abelard in his discussion of the same issue. In Sententia 237 William concedes that one could still insist that the contingency of events entails the fallibility of God.74 71 72

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See (Guilfoy 2012) on this. Cf. (Marenbon 1997, p. 226). See (Guillelmus Campellensis 1959, p. 197, 18–21): ‘Nota etiam quia Deus non solum providet actus hominum, sed etiam omnes modos. Cum enim modo sedeam, hoc providet Deus et modum etiam, scilicet posse non sedere, sedere enim et posse non sedere non sunt contraria.’ (Guillelmus Campellensis 1959, p. 195, 17–28): ‘Et nota, cum Deus providerit omnia eventura, ita providit quod nihil eum latere potuit. Nec tamen omnia providendo necessitatem rebus intulit. Cum enim omnia quae facturi sunt homines per liberum arbitrium ante providerit, sic tamen providit ut homines sua voluntate quedam facturos et aliter sua voluntate eos posse facere provideret. Vidit itaque Deus quid in hominum factis esset eventurum et vidit quod aliter possent facere homines quam esset eventurum. Itaque cum verum sit quod homines possent facere aliter quam Deus providit, et cum sic Deus providerit, quia aliter possent facere, et ita contrarium eius providentia possit evenire, non sequitur ex hoc vero quod Deus possit falli.’ (Guillelmus Campellensis 1959, p. 196, 35–46).

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S­ uppose, for instance, that God knows that Socrates will read tomorrow, which is a contingent fact. If we say that it is possible for Socrates not to read, then it must be possible for God to foreknow that Socrates will not read. This is because everything that has the possibility to happen also has the possibility of being included in God’s knowledge. But if it is possible for God to foreknow that Socrates will not read, this means that it is possible for him to foreknow the opposite of what will in fact take place, and so it is possible for God to be mistaken, as he would believe the occurrence of an event that in fact never occurs. William answers this by saying that we should distinguish the possibilities of things to be otherwise than they are from the possibilities of God to have a different knowledge. It is not granted that the two ranges of ‘possibilities’ are coincident. In particular, the fact that it is possible for a certain event to either happen or not does not entail that it is possible for God to either know or not know it. 75 The proposition (*) ‘Si possibile est res aliter evenire [quam eveniunt], possibile est Deum falli’ is then considered false by William, since it has a true antecedent and a false consequent. This point is only briefly mentioned by William but is developed in Abelard’s Logica and Dialectica and, in fact, constitutes the central point of Abelard’s solution. As we will see, Abelard asserts that the claim ‘It is possible for things to be otherwise’, when interpreted de rebus, does not entail the de re proposition ‘It is possible for God to be in error’. It is also interesting to notice that William seems to deny here that God could have a different providentia than the one he in fact has, while Abelard, on the contrary, embraces the idea that God’s providence could have been different from the actual one. I will return to this. As Abelard will also do, William then wonders whether the truth of (*) does not follow from the truth of the corresponding non-modal conditional (**) Si res aliter evenient, tunc Deus est vel fuit deceptus. One might suppose, in fact, that, from the truth of the conditional ‘if p, then q’, it follows that if ‘it is possible that p, it is possible that q’ (what we have called above, following Marenbon, the ‘transfer of possibility principle’).76 William’s answer to this is very 75

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(Guillelmus Campellensis 1959, p. 196, 47–54): ‘Huius oppositionis solutio est Deus non posse providere omnia que possunt contingere, hoc modo quod credat eventurum quicquid potest evenire. Cum enim Socrates, qui cras leget, posset cras non legere, Deus qui providit eum lecturum non potest providere eum non lecturum. Si enim aliter diceremus, videtur posse falli, quod omnino denegandum putamus, quia Deum posse falli merito inconveniens reputatur.’ (Guillelmus Campellensis 1959, p. 196, 58–66): ‘Et iterum hec alia [consequentia]: Si possibile est res aliter evenire, tunc possibile est Deum posse falli, falsa est. Cum ex vero antecedenti falsum consequens inferatur, quidam hanc per hanc regulam volunt probare. Cum vera sit ista consequentia: Si res aliter evenient, tunc Deus est vel fuit deceptus, tunc simi-

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c­ oncise, but we gather that he takes the aforementioned transferability principle only for certain conditionals, those that are not only true but necessarily so. Because he takes the conditional expressed in (**) to be true without being necessary, he concludes that, even though (**) is true, the truth of (*) does not follow from it.77 We may wonder what William intends when he says that some conditionals are true but not necessarily true, and which truth conditions he attributes to conditionals such as (**). Unfortunately, the Sententiae do not answer these questions. It is interesting, though, that Abelard also endorses a position very similar to the one advanced by William in the Dialectica (219, 19–24), but he abandons this view in the Logica Ingredientibus. In the following Sententia William proposes a third and last element of his strategy against theological determinism. He claims that, even though every event is determined and necessary according to God (quantum ad Deum; quantum ad providentiam), it might still be contingent with respect to human action (quantum ad actus hominum) and to the nature of things (ad naturas).78 William then repeats the idea that God knows not only what happens but also the modes of the happening of things, namely, whether they occur necessarily or contingently.79 Let us turn now to Abelard’s analysis of the deterministic argument. Like William, Abelard insists on rejecting the infallibility argument as invalid and sophistical. Despite a few differences, he proposes the same solution to the argument in both the Dialectica and the Logica, and he re-proposes a version of it in his Theologia Summi Boni and Theologia Scholarium.80

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liter debet esse vera haec: Si possibile est res aliter evenire, tunc possibile est Deum falli; quia si aliquid infert aliud sine modo, illud idem cum modo infert, aliud cum eodem modo, ut cum vera sit: Si Socrates legit, tunc agit.’ (Guillelmus Campellensis 1959, p. 196, 67–70): ‘Cum autem vera sit hec: “Si res aliter evenient, tunc Deus est aut fuit deceptus”, tamen non est necessaria. Nulla enim est necessaria qua ex possibili sequitur impossibile. Hoc autem est possible quod res aliter evenient, et impossibile Deum esse vel fuisse deceptum.’ He holds that, instead, every present and past event is determinate, even with respect to human experience (‘Omne enim praesens determinatum’), by virtue of the fact that it has happened in time (‘quantum ad presentiam sui’). This idea is rehearsed in (Guillelmus Campellensis 1959, p. 197, 25–39) and was also adopted by Abelard and many of his contemporaries (see, for example, Dial. 210, 35–211, 5; 212, 1–2; LI De Int. 250, 169–76). (Guillelmus Campellensis 1959, p. 197, 18–21): ‘Nota etiam quia Deus non solum providet actus hominum, sed etiam omnes modos. Cum enim modo sedeam, hoc providet Deus et modum etiam, scilicet posse non sedere; sedere enim et posse non sedere non sunt contraria’. See also p. 197, 39–42: ‘Cum providisset Deus futura que modo sunt et que facta sunt et que futura sunt, sic providit futura quod quedam fierent per rerum necessitatem […] quedam sine necessitatem rerum.’ A comparison between these versions is proposed in (Marenbon 2005, pp. 55–91).

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Abelard’s first solution consists in saying, similarly to William, that God’s omniscience does not impose necessity on events, for God knows not only the events that will happen but also the ‘modal status’ with which they will happen, either contingently or necessarily.81 Abelard, however, does not elaborate on this idea, and he quickly turns to another line of reasoning. He says that the fact that things could be otherwise than they are does not entail the fallibility of God, because if things were in fact different than they actually are God would have had a different knowledge of them. In a hypothetical situation in which events were not as they are, God would have a different providentia, but there would always be a perfect consistency between what happens and what God knows.82 This idea is also mentioned in the Logica Ingredientibus,83 although there Abelard is more concerned with what is meant by saying that things might ‘happen otherwise’ (evenire aliter), which for him should not be taken as implying that alternative courses of history different to the actual one exist. In both the Logica and the Dialectica Abelard then proposes another strategy against the deterministic dilemma, which will be repeated in his theological works. This consists in pointing out the semantic ambiguity of modal claims such as ‘It is possible for something to happen otherwise than it happens’ (Possibile est rem aliter evenire quam evenit), which can be interpreted either de rebus or de sensu. Interpreted de rebus, the proposition affirms that the nature of the thing referred to by the subject is not incompatible with being different to the way it actually is. Abelard considers this to be true, since the nature of many things is indeed compatible with a course of history alternative to the actual one. The same proposition taken de sensu, on the contrary, says that the following is possible (or can happen): ‘a certain thing is different than it is’ (Possibile est ita contingere: res evenit aliter quam evenit). This is obviously false, according to Abelard. The hypothesis of contingency that was included in the deterministic argument – passage (6) in the reconstruction presented at p. 298 – is then true only if we intend it de rebus. The same is the case for this 81 82

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This is said in both the Dialectica (Dial. 218, 3–16) and the Logica (LI De Int. 264, 491–512). ‘Res tamen aliter evenire quam eveniunt possibile est atque aliter evenire quam in provi­ dentia Dei fuit, quam iam habuit, nec tamen ideo Ipsum posse decipi. Si enim res aliter eventurae essent, alia fuisset Dei providentia quam ipse eventus sequeretur, nec istam quam modo habuit providentiam, umquam habuisset, immo aliam quae alii eventui congrueret, sicut ista isti’ (Dial. 218, 16–22). LI De Int. 266, 558–267, 564: ‘Posset enim aliter evenire quam deus habuit in providentia sua, quam habuit. Nec tamen falleretur deus, quia sicut res aliter posset evenire, ita et ipse aliter posset providisse, ut, sicut hoc modo tantum providit, ita et alio tantum providisset, qui similiter cum eventu alio rei concordasset sicut iste modus providentiae cum isto eventu. Et sic sana tunc esset providentia sicut et nunc.’ See also LI De Int. 267, 577–87; Cf. (Marenbon 2005, pp. 79–81).

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other modal proposition: ‘It is possible for a thing to happen otherwise than God knows it’ (Possibile est rem aliter evenire quam Deus providit).84 A very similar position is maintained by Abelard in the Dialectica. Although he does not employ the same terminology, it is clear from his discussion that the distinction between the de rebus and de sensu interpretations of modal claims was already fully grasped in the Dialectica, since Abelard says that the proposition ‘It is possible for a thing to happen otherwise than God foreknows it’ (Possibile est rem aliter evenire quam Deus providit) might be true or false, depending on the scope that we assign to the different syntactic components of the proposition. Instead of speaking of the modal operator being attributed to the thing itself (de rebus) or to the sense of a proposition (de sensu), Abelard explains the difference between the two interpretations in the following terms: although in both cases ‘possible’ is the predicate of the proposition and ‘to happen’ is the subject, in the first case we must interpret the expression ‘otherwise than God foreknows’ as a determination of the predicate, and in the second case we must interpret it as a determination of the subject, in this way:85 i. ii.

For things to happen (subj) [it is possible (pred) otherwise than God foreknows(det)]; [for things to happen (subj) otherwise than God foreknows(det)] it is possible(pred).

The proposition is true when interpreted in the first sense, and it signifies that things have the potency to happen differently from how they actually happen (‘[res] potentiam aliter proveniendi habet’), so that the term ‘possible’ is attributed to the things themselves and refers to their possibilities. It is false if we instead attribute the modal term to the whole sense of a categorical proposition, taking it as the subject of the modal term (totum subiectum est), as if we said that this whole sense is possible (‘istud totum est possibile’): ‘Things happen otherwise than God foreknows.’ The same could be said of the other modal

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See on this LI De Int. 266, 541–552: ‘Cum dicitur: “Possibile est rem aliter evenire quam evenit” duo sunt sensus, sicut duo, cum dicitur: “Possibile est stantem sedere”. Si enim ita dicimus quod rem illam quae stat, natura permittit sedere, verum est; si vero ita quod natura permittit ita esse ut dicit haec propositio: “Stans sedet” falsa est. Similiter si dicamus quod possibile est rem evenire aliter modo, quam evenit vel quam Deus adhuc in sua providentia habuerit, qui tantum eam evenire providit, verum est. Si vero ita dicamus quod possibile sit ita contingere, ut haec propositio dicit: “Res evenit aliter, quam evenit vel aliter, quam deus providit” falsum est.’ See (Marenbon 2005, p. 59).

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claim involved in the argument, ‘It is possible for things to happen otherwise than they happen’, which is again true de rebus and false de sensu.86 In both the Dialectica and the Logica, then, Abelard holds that the modal propositions included in the argument are true only de rebus. He goes on to attack this argument’s validity, by pointing out that the ‘transfer of possibility’ principle that is applied in it is only valid for de sensu modal claims, that is, only if the modal term is applied to an entire propositional content and not to things.87 Abelard is then able to offer a purely logical way out of a well-known and long-standing theological puzzle by resorting to the logical apparatus and the rules of inferences that he had developed within his reflection on modal propositions. At the same time, though, Abelard’s solution may leave the reader unsatisfied, for no substantial or philosophical answer is offered concerning the issues of contingency and determinism; nor does Abelard clarify the philosophical reasons for which the transfer of possibility principle is not valid when applied to propositions de re, that is, to the possibilities of things. In fact, in the Dialectica Abelard tries to justify his limitation of the principle, saying that the inference from (3) ‘If things happen otherwise than they happen, then God is fallible’ to (5) ‘If it is possible for things to happen otherwise than they happen, then it is possible for God to be fallible’ fails because the consecution expressed in (3) is true but not necessarily true, since antecedent and consequent are concomitant but not related by a proper necessary connection, which would require a semantic connection between the antecedent and consequent’s meanings.88 As we have seen, William of Champeaux’s analysis of 86

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See also Dial. 218, 26–219, 2: ‘Dicimus autem eam [si possibile est rem aliter evenire quam Deus providit, possibile est Deum falli], quodammodo intellectam, veram esse, cum scilicet antecedens quoque ipsius verum est, alio vero modo, falsam, cum videlicet ipsum antecedens falsum accipitur. Est autem verum hoc modo intellectum, cum illud aliter quam Deus providit determinatio est praedicati quod est possibile, hoc modo rem evenire est possibile aliter quam Deus providit, quippe potentiam aliter proveniendi habet. Si vero ad subiectum determinatio ponatur, quod est evenire, atque ita dicatur: rem evenire aliter quam Deus providit (istud totum) est possibile, falsum est nec probari potest. Omnino enim impossibile est quod haec propositio dicit: res aliter evenit quam Deus providit, quod scilicet totum subiectum est, possibile vero simpliciter praedicatum, sicut et istud: res aliter evenit quam evenit. Multum autem refert ad sententiam orationis determinationes praedicatis modis adiungi seu eorum subiectis, sicut in tractatu modalium supra monstravimus.’ LI De Int. 266, 552–5: ‘Tunc enim regula praedicta locum habet: Cuiuscumque antecedens possibile est, et consequens quia tunc possibile est ad totas propositiones, non ad res applicator.’ Dial. 219, 21–4: ‘Illa quoque fortasse consequentia necessitatem non tenet: si res aliter quam providit Deus evenire non possibile, nec aliter quam eveniunt evenire queunt, […] Insuper quamvis paria concedantur (et) sese comitantia rei eventus et Dei providentia quae de ipso est, non tamen necessariam inferentiam tenent, quorum neuter in enuntiatione alterius intelligitur.’

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the argument relied on a similar point, claiming that a conditional such as (3) was true but not necessarily true. Nonetheless, Abelard does not mention this solution in the Logica Ingredientibus, where he offers no justification for the inadmissibility of the transfer of possibility principle for de rebus modal claims. Abelard’s solution to this argument for theological determinism, then, relies not on some philosophically relevant discussion about the nature of necessity or contingency but on a purely theoretical application of syntactic and semantic tools that he had developed within his categorical and modal logic, such as the de re/de sensu distinction or the distinction between proper inferentia and mere ‘equipollence’ (comitatio) between propositions. Although perhaps not entirely philosophically satisfactory, however, Abelard’s use of modalities in this and other arguments for theological determinism is perfectly in line with the intents of his logical programme, a programme the consistency of which I hope to have highlighted throughout the book, and to which I will return once more in the Conclusion.

Conclusion Abelard’s theory of the nature of modalities and the logical system he created for modal propositions have long deserved to be examined and evaluated in their entirety. Several scholars have already brought to light, and brilliantly analysed, some crucial and innovative aspects of Abelard’s modal thought. However, an all-encompassing reflection on his works on modalities was still missing, as was a comparison between these works and the parallel reflections advanced by other masters and logicians in the early 12th century. With this book I hope that I have contributed to partially filling, or at least tackling, both these gaps. In particular, I hope I have shown that the significance of Abelard’s theory of modalities lies not only in the sophistication of some of its details but rather in his theory as a whole. His modal thought, which is certainly deeply connected to the context in which it was produced, is at the same time highly innovative and remarkably consistent – both internally and with other parts of Abelard’s philosophy. Although Abelard’s reflections stem from the interplay between different sources and traditions (grammatical, logical, theological), he offers a very original analysis of modal concepts, with respect to their use in both logic and metaphysics. From a logical point of view, Abelard is the first (known) medieval author to have offered a clear account of existential import in modal logic, as well as a systematic reflection on the syntactic structure of modal propositions and on the interaction of the scope of modal operators with respect to other logical connectives, quantifiers, and temporal indexes. He was probably also the first to construe, based on the very few elements available to him, an account of modal syllogistics and modal conversions. From a metaphysical point of view, Abelard’s reflections on the nature of modalities are built upon the definition of possibility as non-incompatibility with nature, a definition that was standard at the time and probably came from Boethius’s thought. However, Abelard goes well beyond the received and contemporary views, using this definition to design new linguistic and logical devices that allow him to deal with puzzling cases of possibilities, such as that of a standing man sitting or a human being dead. He also uses this nature-based characterization of possibility to justify a broad domain of the possible, the boundaries of which he stretched in order to account for unrealized, past, counterfactual, and even unactualizable possibilities. Whilst examining the theory of modalities that Abelard offers in the Dialectica and the Logica Ingredientibus, we are also struck by the level of consistency it displays, both internally and with other parts of Abelard’s philosophy and logic. This is worth pointing out, because past studies have often presented © koninklijke brill nv, leiden, 2022 | doi:10.1163/9789004470460_016

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Abelard’s modal thought as an encounter of different paradigms and insights, which Abelard eventually failed to intertwine into a coherent picture. As for internal coherence, I have remarked throughout the book how some distinctive elements of Abelard’s theory (such as his interest in the relation between the grammatical and semantic structure of modals, his preference for de re modalities, his use of the notion of natura to define all modal terms, and his reflections on the logical and semantic relation between possibility and necessity) insistently return, both in his logical works and in later writings. As for the consistency of Abelard’s modal views with other areas of his thought, we may recall here three aspects as exemplification. First, Abelard conceives of his modal logic as an extension of his logic for propositions de puro inesse, which means that all the rules and principles that he considers valid in the latter also remain valid in the former. There is, therefore, an attempt on his part to preserve a unitary logical system for all categorical propositions. Moreover, relevant features of Abelard’s discussion of modalities resound with the theory of conditionals that he offered in the Dialectica, which is correctly believed to be one of his most important logical results. Second, Abelard is interested in the ontological foundation of modalities, and he grounds modal concepts in the nature of substances. He holds that the truth-makers of modal predications – what renders possibility- and necessitypropositions true or false – are entities that belong to the actual world and the actual history, namely, the individuals themselves that currently exist. This is consistent with his irrealist ontological position, according to which nothing exists apart from particular substances and their particular forms. Abelard’s modal metaphysics, thus, does not commit him to the existence of any other res other than these, and, in particular, it does not commit him to the acceptance of dicta, eventus, or counterfactual states of affairs within his ontology. A third element is the consistency of Abelard’s modal theory with his theory of the intellect, at least as he presents it in De Intellectibus. As other scholars have recently remarked, the domain of what is ‘intelligible’ is defined by Abelard through an appeal to the concept of nature. In this sense we, as rational agents, are able to understand a res and reason about it only by focusing our attention on some of its properties and by discriminating between the features that constitute its nature(s) and those that do not. It is natures, then, that set the limits of our ways of conceiving, just as they set the metaphysical limits of what is possible, or not possible, for a substance. This means that, for Abelard, the broad domain of possibility coincides with that of intelligibility, so that to be possible is to be intelligible, and vice versa. Many other examples could be brought up to exemplify the coherence of Abelard’s modal theory with other elements of his philosophy. I have

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highlighted these connections throughout the book, so, rather than returning to them here, let me conclude by saying something on future research perspectives. As is known, important research is presently being conducted by different scholars on unpublished sources reporting early 12th-century debates on logic. Needless to say, the transcription, edition, and analysis of these sources will certainly contribute to reassessing parts of Abelard’s logic, and they will provide a better understanding of the context that stimulated his modal thought. In the first part of this book I included a preliminary account of unpublished sources on modalities from the first half of the century and connected their content to Abelard’s theories. Yet, I should stress here that what can currently be said about these texts is far from conclusive, and will be so until we have critical editions of texts and good evidence on these texts’ datation and interrelations. I have also suggested that Abelard’s reflections on modalities are closely linked to the grammatical tradition reported in the Notae Dunelmenses and the Glosulae-complex, a subject that deserves further study. Another important area that is still greatly unexplored is the influence that Abelard’s modal logic and theory of modalities had on later logicians and philosophers. Although it is true that the rediscovery of Aristotle’s Prior Analytics (and, later on, the modal theories that were conveyed by Aristotle’s physical and metaphysical texts) completely changed the logical and conceptual framework in which modalities were discussed, it would still be interesting to follow the remnants of some Abelardian elements in later modal logic, both in the 12th century and beyond. It would be interesting to retrace, for instance, the development of Abelard’s de re/de dicto distinction and of his reflection on existential import in modal logic, as well as his distinction between the grammatical and semantic structure of modals, his intuitions about synchronic and unrealizable possibilities, and, lastly, his views concerning the domain of things to which we refer when asserting a modal predication – and whether modal terms may be used to ‘ampliate’ this domain. Further studies on this topic will certainly contribute to putting Abelard’s theory in the place it deserves within the history of modal logic.

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Index ab esse ad posse 79–80, 169, 203 accidental attributes 95, 96, 206, 207, 212, 225, 239, 240, 242, 243, 266, 270 per se accidents 241 propria 207, 225, 227, 240, 242–246, 248 separable vs. inseparable 6, 96, 112, 207, 224–227, 230, 240, 241, 243, 244, 247 actualism 216–218, 229 Alberic of Paris 8, 9, 140 Albricani 8 alethic modalities 51, 54, 68, 202 Alexander of Aphrodisias 28, 35, 102, 241, 250 Ammonius 25, 35, 282, 284 ampliation 140, 310 Anselm of Canterbury 2, 17, 29, 41, 42, 44, 71, 85, 98 Aristotle 1, 15, 20–22, 24, 26–31, 36, 39, 42, 44, 66–68, 80, 81, 91, 97, 101, 103, 107, 108, 130, 133, 141, 146, 157, 160, 164, 169, 174, 202, 234, 236, 241, 257, 258, 280, 282, 287, 288, 310 attentio 229, 263–267 Augustine 2, 17, 18, 44, 105, 106, 296, 301 beings contingent beings 21, 22, 24, 25, 31, 35–39, 109, 114–116, 181, 182, 275, 276 future beings 76, 79, 81, 82, 143, 232 necessary beings 24, 35, 109, 276 sempiternal beings 39, 272, 275 bivalence. See principle of bivalence Boethius 2, 15, 17–19, 25, 56, 90, 100, 102, 104, 169, 178 on absolute vs. qualified modalities 36, 41 on contingency 277 on contingent beings 37 on conversions 147 on determinacy vs. indeterminacy 210, 222, 282 on diachronic vs. synchronic modalities 257 on inseparable accidents 241, 244 on modal syllogisms 68

on modes as qualifiers 54, 59 on nature 94, 204 on necessity 19, 20, 22, 23, 35, 104, 108, 205 on negation 145, 161 on possibility 23, 26–29, 31, 33 on principle ‘ab esse ad posse’ 79–80 on repugnantia 93 on temporally qualified modalities 33, 36, 37, 42, 178, 187 on the modal asymmetry of time 19, 43 on unrealized possibilities 91 chance. See Contingency change 21, 22, 41, 107, 111, 113, 237, 253, 279 chimaera. See non-things Cicero 281, 296 comitatio. See inferentia complexio 57, 120 compossibility 136, 180, 182, 185, 220 conceivability 241, 247 constructio 70, 72, 120 contingency 20, 26, 30, 33, 40, 43, 276–278, 280, 281, 285, 294, 295, 297, 301, 306, 307 chance 28, 109, 111, 276–278 contingency of the present and the past 42–44, 219, 222, 224, 261, 276, 278–280, 303 free will 109, 111, 276–278 future contingents 33, 278, 280–287, 289, 291, 294, 296 ontological correlate of contingent events 277 co-signification 51, 76, 83 creation 29, 30, 76, 85, 95, 206, 209 de re vs. de dicto 5, 11, 49, 58, 63, 64, 74, 84, 87–89, 118, 120–126, 128–133, 135–142, 148–150, 154, 157–159, 163, 169, 174, 175, 185, 194, 204, 219, 227–229, 234, 262, 264, 302, 304–307 de sensu. See de re vs. de dicto determinacy. See necessity

index determinism 15, 108, 201, 224, 271, 276, 280, 281, 285, 286, 289, 290, 294, 301, 303, 306, 307 dicta 84, 135, 220, 309 differentiae 95, 96, 112, 206–209, 212, 225, 240, 242, 243, 249, 266, 267, 270, 275 Diodorus 28, 32 domain of discourse 138–141, 169, 228, 233, 234, 310 empty terms 142–145, 147–156, 162, 168, 170, 204 epistemic logic 54, 294 epistemology of modality 92, 210, 212, 238, 239 essentia 208, 213, 268 essentialism 209, 216, 265, 267, 270, 275 eternity 109, 209, 297 eventus 277–280, 285, 286, 289, 291, 309 existential import 11, 79, 118, 138, 139, 141–143, 145, 147, 148, 154–156, 274, 308, 310 figurative predication 59, 60, 61, 63 foreknowledge. See God free will. See contingency Garland 8, 25, 30, 33, 37–39, 47, 48, 63, 65, 67, 72, 97, 98, 133, 147, 170, 179–182, 204, 236, 283 Gerbert of Aurillac 3, 24, 109 God foreknowledge 17, 33, 41, 42, 105, 169, 294–297, 302 omnipotence 2, 43 omniscience 2, 17, 304 predestination 294–296 providence 105, 294–297, 302 identity 112, 204, 209 essential sameness 268, 269, 296 numerical sameness 268 persistence 112 sameness in nature 92, 206–208, 237 sameness in property 208, 268 theory of 261, 270 imagination 245, 248 impersonal predications 11, 64, 89, 132–136, 141, 159, 228, 234

325 impossibility 23, 24, 26, 31, 32, 43, 44, 56, 77, 100, 102, 109, 152, 169, 203, 205, 225, 246, 247, 258, 260, 264, 267, 297 indeterminism 28, 32, 210, 276, 278, 279, 285–287, 291. See also contingency; determinism individuality 112, 209, 261, 270 inevitability. See necessity inferentia 153–155, 168, 187, 203, 204, 307 intelligibility 211, 309 John of Salisbury 247 Joscelin of Soissons 7, 9, 59, 60, 73, 74, 87 law of contradictory pairs 288 law of excluded middle 285, 286, 294 law of nature 26, 274, 279. See also nature logical form 57, 64, 70, 71, 120, 141 logica vetus 6, 16, 18, 104 Meludinenses 8, 62 modal conversions 128, 129, 134–136, 156, 163, 170, 172, 174, 233, 257, 258, 262, 308 modal matter 25 modal propositions adverbial vs. nominal modals 46, 50, 52, 53, 57, 61–67, 70, 72–74, 77, 89, 128, 130, 134, 135, 141, 157, 159, 171, 172, 175, 235 compound vs. divided 124, 129–131, 136–141, 149, 227, 228, 234, 256 de rebus and de sensu. See also de re and de dicto impersonal construction of. See impersonal predications negation 67, 160–162, 174, 177, 190, 191 principal and secondary subject 62, 68, 69, 89, 159 relation with simple propositions 158 syntactic structure 14, 52, 62, 67, 89, 120, 132, 158, 177, 308 temporally determined modals 33, 39, 41, 106–108, 110, 112, 114, 119, 162, 176, 177, 179, 181–189, 191–195, 210, 223, 276 what makes a proposition modal 47, 51, 52 modal syllogistics 15, 66, 133, 141, 156, 163, 175, 308

326 modes adverbial vs. nominal 46, 62–67, 70, 72, 73, 77, 87, 89, 128, 130, 134, 135, 141, 157, 159, 163, 171, 172, 175, 235 definition of 45–54 denotation of 14, 75, 76, 78, 80–82, 84, 85, 277 proper vs. improper 53, 54, 56–59, 186 Montani 8 natural kinds 23, 92, 94, 95, 206, 209, 210, 214, 237, 264, 265. See also nature nature 81, 82, 84, 90–97, 99–102, 116, 123, 163, 173, 205–213, 230, 235–240 necessity as determinacy 43, 106–108, 110–112, 114, 222, 261, 278, 279, 284, 293, 294 as immutability 18, 21, 22, 25, 41, 106, 107, 110, 113, 114 as inevitability 39–41, 43, 44, 83, 84, 103–110, 112, 113, 271, 272, 276 as omnitemporality 18–24, 31, 35, 37, 39, 106, 107, 113–116, 149, 178, 181, 271, 272 as what is required by nature 81, 82, 84, 89, 116, 205, 207, 214, 225–227, 244, 246, 247, 249, 271, 275, 278 Nokter 3 Nominales 8, 9 nominalism 207, 208 omniscience. See God oratio 67, 68, 83, 133, 163 Peter Damian 17, 41, 43, 44 Philo 102 Porphyry 6, 94, 103, 104, 207, 225, 240, 241, 243–248 Porretani 8 possibility as non-repugnancy with nature 93, 96, 97, 99, 100, 205, 235, 254, 255, 259

index as potentiality 21, 26, 32, 33, 38, 252, 254, 259 simple vs. determinate potencies 249– 254 synchronic vs. diachronic 219, 222–224, 233, 257, 258 unrealized possibilities 19, 23, 25, 28, 80, 91, 92, 97, 198, 204, 219, 221, 222, 224, 230, 231, 233, 236, 238–240, 249, 277, 308 possible worlds 214–219, 223, 224 predestination. See God principle of bivalence 280–286, 289, 291, 293, 294 Priscian 16, 18, 50–52, 55–57, 84, 132 qualified vs. unqualified inherence 45–53, 57, 58, 61, 62, 65, 73, 77, 125, 132, 158, 159, 186, 202, 223, 235 Robert of Melun 8 sameness and difference. See identity Simplicius 281 square of opposition 25, 146, 148, 150, 154, 156, 162, 164, 165, 168, 191 Stephanus 35 Stoics 50, 281 syllogismi incisi 8, 68, 133, 134, 172 Theophrastus 35 Trinity 208, 269 tropes 270 understanding 11, 52, 56, 83, 85, 87, 88, 210, 211, 265 universals 207, 208 William of Champeaux 2, 4, 7, 9, 17, 25, 72, 125, 128, 262, 299, 300–302, 304 William of Lucca 9, 46, 58, 205, 276 William of Sherwood 49, 71, 202