Metaphysics: Aristotelian, Scholastic, Analytic 9783110322446, 9783110322163

Table of contents :
CONTENTS
PREFACE
SECTION I: CATEGORIES AND BEYOND
What is an Ontological Category?
Scholastic Debates about Beings of Reason and Contemporary Analytical Metaphysics
SECTION II: METAPHYSICAL STRUCTURE
What Is Constituent Ontology?
Elemental Transformation in Aristotle: Three Dilemmas for the Traditional Account
Essential Dependence, Truthmaking, and Mereology: Then and Now
SECTION III: SUBSTANCE & ACCIDENT
Essence and Ontology
An Aristotelian Argument Against Bare Particulars
The Ontology of Number: Is Number an Accident?
SECTION IV: EXISTENCE
Existential Inertia
Aquinas vs. Buridan on Essence and Existence, and the Commensurability of Paradigms
SECTION V: MODALITIES
Potentiality in Scholasticism (potentiae) and the Contemporary Debate on “Powers”
Dispositional Necessity and Ontological Possibility
The Optimal and the Necessary in Leibniz’ Mathematical Framing of the Compossible
SECTION VI: PREDICATION
The Interpretation(s) of Predication
Towards a Thomistic Theory of Predication
Authors
General Index
Index of Persons

Citation preview

Lukáš Novák | Daniel D. Novotný | Prokop Sousedík | David Svoboda (Eds.) Metaphysics: Aristotelian, Scholastic, Analytic

CONTEMPORARY SCHOLASTICISM EDITED BY

Edward Feser • Edmund Runggaldier

ADVISORY BOARD Brain Davies, Fortham University, U.S.A. Christian Kanzian, University of Innsbruck, Austria Gyula Klima, Fordham University, U.S.A. David S. Oderberg, University of Reading, U.K. Eleonore Stump, Saint Louis University, U.S.A. Band 1 / Volume 1

Published in Cooperation with

Studia Neoaristotelica A Journal of Analytical Scholasticism

Lukáš Novák • Daniel D. Novotný Prokop Sousedík • David Svoboda (Eds.)

Metaphysics: Aristotelian, Scholastic, Analytic

Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de

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CONTENTS Preface ...............................................................................................................................5

Categories and Beyond Peter van Inwagen What is an Ontological Category? ............................................................................... 11 Daniel D. Novotný Scholastic Debates about Beings of Reason and Contemporary Analytical Metaphysics..............................................................25

Metaphysical Stucture Michael J. Loux What Is Constituent Ontology? ....................................................................................43 Anne Siebels Peterson Elemental Transformation in Aristotle: Three Dilemmas for the Traditional Account ........................................................... 59 Ross Inman Essential Dependence, Truthmaking, and Mereology: Then and Now .................73

Substance & Accident E. J. Lowe Essence and Ontology ...................................................................................................93 Lukáš Novák An Aristotelian Argument Against Bare Particulars ............................................ 113 Prokop Sousedík & David Svoboda The Ontology of Number: Is Number an Accident?................................................123

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CONTENTS

Existence Edward Feser Existential Inertia........................................................................................................ 143 Gyula Klima Aquinas vs. Buridan on Essence and Existence, and the Commensurability of Paradigms................................................................ 169

Modalities Edmund Runggaldier SJ Potentiality in Scholasticism (potentiae) and the Contemporary Debate on “Powers” ........................................................... 185 David Peroutka OCD Dispositional Necessity and Ontological Possibility .............................................. 195 Mark Faller The Optimal and the Necessary in Leibniz’ Mathematical Framing of the Compossible .......................................................................................................209

Predication Uwe Meixner The Interpretation(s) of Predication ........................................................................ 229 Stanislav Sousedík Towards a Thomistic Theory of Predication ........................................................... 247 Authors .......................................................................................................................... 257 General Index ...............................................................................................................263 Index of Persons ........................................................................................................... 281

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PREFACE Just like any other philosophical discipline, metaphysics has a history and a  present. It flourished in the classical and mediaeval period, gradually declined in the modern period and almost ceased to exist in the first half of the 20th century. Its present is characterised by a revival of some traditional speculative topics, which has been taking place within analytical philosophy since the 1960s. The fact that the current renewal of interest in metaphysics occurs in the context of analytical philosophy is somewhat surprising. Analytical philosophy has been deeply influenced by logical positivism with its strong anti-metaphysical orientation. Its proponents saw the task and future of philosophy in the  ontologically neutral analysis of scientific or natural language – not in metaphysical speculations. Many were convinced that the progress of mankind, which they wished to assist, requires various obstacles to be cleared out of the way. Metaphysics was considered to be one such intellectual obstacle. How are we to understand, then, that the philosophical discipline, which the older analytical philosophers stood so radically against, has reappeared within the intellectual context of this very anti-metaphysical current? This question does not seem to be satisfactorily answered yet, neither in socio-psychological terms nor in purely philosophical ones: answering it may require a time interval which has not elapsed yet. One of the causes is most probably to be sought in the analytical philosophy itself. With time, its development came to cast doubt on some of the anti-metaphysical points of departure. In this respect, for instance, Wittgenstein’s criticism of private languages, which problematised Cartesian subjectivism, or Kripke’s systematisation of modal logic, which facilitated a return to the previously rejected topic of modalities, ought to be mentioned.1 The renewed interest in these and similar topics advanced the revival of metaphysical investigations. Of course, there are as yet many authors who reject metaphysics, as well as some of its presuppositions, such as modal logic.2 They consider analytical metaphysics to be one of the many delusions of our time. Perhaps they think of contemporary metaphysicians as of the prodigal son who has left his home and   Ludwig Wittgenstein, Philosophical Investigations, transl. G. E. M. Anscombe (Oxford: Basil Blackwell, 1963); Saul Kripke, “Semantical Considerations on Modal Logic”, Acta Philosophica Fennica 16 (1963): 83–94. 2   In the 20th century modal concepts were subjected to criticism especially by Willard van Orman Quine, see his “Two Dogmas of Empiricism”, in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1954); or his Word and Object (Cambridge, MA: MIT Press, 1960). 1

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PREFACE

wilfully violates the morality impressed on him by his parents. The prodigal son should return home in order not to perish in a world full of delusion and hazard. The editors of this publication are teachers of philosophy at Czech theological faculties. In the controversy between contemporary analytical metaphysics and its opponents they side with the renewal of speculative thinking. We are interested not only in the current debate but also in earlier discussions taking place within the tradition of Christian Aristotelism (the so-called First and Second Scholasticism). Historical research has often led us to the remarkable observation that older scholastic discussions are in many respects similar to current debates. This naturally induced in us the effort to enhance contemporary metaphysical thinking by the treasures of the Aristotelian-scholastic past. Contemporary metaphysical speculation could thereby gain not only new stimuli and inspiration for solving challenging philosophical problems but also firm grounding in the intellectual history of the Western world. In this we are not entirely original but can follow up on the already existing tradition of Analytical Thomism. However, unlike the proponents of Analytical Thomism we are inspired not only by the legacy of Thomas Aquinas but also seek advice from the technically more elaborate Thomistic, Scotistic, and other traditions of Second Scholasticism, which have not been thoroughly researched yet. The endeavour of Renaissance and Baroque scholastic authors at technical refinement makes them intrinsically related to the analytical tradition. We are honoured that several outstanding proponents of contemporary analytical metaphysics as well as prominent specialists in the history of scholastic philosophy have appreciated our idea of relating the traditional and the new metaphysics and accepted the invitation to the conference Metaphysics: Aristotelian, Scholastic, Analytic (Prague, the Czech Republic, June 30 – July 3, 2010). This publication is the fruit of this conference. It contains both historical and systematic contributions. We have grouped them according to their topic to form six sections titled Categories and Beyond, Metaphysical Structure, Substance and Accident, Existence, Modalities, and Predication. The first section, dealing with categories (and what is beyond), is devoted to the problem of ontological classification in general. It opens with the article by Peter van Inwagen who explores the notion of ontological category such that it may be utilised in defining ontology. Inwagen proposes that “ontology proper” (as opposed to meta-ontology) is an attempt to set out a satisfactory list of ontological categories. In the second article, Daniel D. Novotný broadens the scope of enquiry by focusing on the problem of the ontological status of the so-called “beings of reason”: entities or pseudo-entities beyond the confines of reality proper. In his approach he fruitfully combines the contributions of scholastic and analytical thinkers, thus implicitly providing a positive answer to his concluding question whether contemporary analytical metaphysics can draw some inspiration from scholastic debates. 6

Preface

The section on metaphysical structure is closely connected to the previous one in dealing with the most general ontological problems. In the first article, Michael Loux contrasts two fundamentally distinct approaches to explaining the mould of “familiar particulars”: the “Aristotelian” or “constituent” strategy, and the “Platonic” or “relational” strategy. Loux seeks first to clarify the dichotomy by distinguishing it from the dispute over the nature of universals, and then proceeds to analyse the “constituent” approach and point out its various problems. In the following contribution Anne Siebels Peterson explores the Aristotelian notion of “prime matter” as the substratum of elemental transformation with no essence of its own; she exposes certain conflicts between the theory of prime matter and other doctrines commonly ascribed to Aristotle. The concluding contribution of this section is by Ross Inman. It focuses on the notion of “essential dependence” and tries to show how scholastic analyses of this notion (especially those undertaken by Duns Scotus) can help to remedy a certain void in contemporary analytical discussions regarding the topic of truthmaking. The third section comprises three contributions related in some way or other to the problems of substance and accident. E. J. Lowe opens the section with the article “Essence and ontology”, in which he tries to show how by combining a neoAristotelian account of essence with a neo-Aristotelian “four-category ontology” of individual substances, modes, substantial universals, and property universals, a thoroughgoing metaphysical foundation for modal truths can be provided. Lukáš Novák continues in a similar vein by presenting an “Aristotelian” argument against the theory of the so-called “bare particulars”, thus providing a defence of an essentialist account of substances and accidents. Prokop Sousedík and David Svoboda, who jointly authored the concluding contribution of this section, pose the question whether number is an accident. By way of an answer they develop a neo-Aristotelian theory of number which attempts to steer a middle way between “the Scylla of Aristotelian naturalism” and “the Charybdis of Platonic idealism”. The fourth section is devoted to existence. In his article Edward Feser criticises, from a broadly Aristotelian-Thomistic standpoint, the doctrine of existential inertia, contrasting it with the doctrine of divine conservation. In the other article of this section, Gyula Klima takes the comparison of two different accounts of the relation between essence and existence, namely those of Aquinas and Buridan, as a point of departure for some more general thoughts concerning the possibility of cross-paradigm argumentation. The subject of the penultimate section is the modality and its metaphysical grounding. In the first contribution, Edmund Runggaldier reconstructs the scholastic theory of potentiality which draws an important distinction between subjective and objective potencies. He shows how these two kinds of potencies allow for two complementary accounts of modalities, of which the first corresponds more to the “common sense” perception of modalities while the other approximates to modern possible-world semantics. In a further development of 7

PREFACE

the topic, David Peroutka combines the contemporary and Aristotelian analysis of “powers” or “potencies” to explain the necessity of causal nexus and the grounding of possibility in active and passive causal capabilities. The concluding contribution by Mark Faller focuses on Leibniz’s understanding of necessity and possibility. Working in quite a broad context, Faller tries to develop a unified reading of Leibniz and praises him for his realist view of the nature of truth and its corresponding reality. The topic of the final section is predication in a metaphysical perspective. Uwe Meixner provides an historical survey of various interpretations of predication and its metaphysical basis. He defends the view that Frege, despite some deficits in his conception, was the first to bring the philosophy of predication on the right track, and proposes his own Frege-inspired theory. On the contrary, Stanislav Sousedík in the closing contribution defends a pre-Fregean notion of predication and presents a theory of his own, conceived as a modern recasting of the Thomistic, metaphysically grounded identity theory of predication. We would like to thank all the participants of the Prague conference for their contributions, especially to the authors of the papers published in this book. It was an honour and pleasure to work with them. Special thanks belongs to our language editor and proofreader Světla Jarošová, who has spared us many errors and substantially contributed to the quality of the text. For any remaining mistakes and shortcomings we take, of course, full responsibility. We are also grateful to Rafael Hüntelmann of Ontos Verlag for his interest in this volume and his patience with our work on it. We are also obliged to express our gratitude to His Grace, Right Reverend Michael Josef Pojezdný, O.Praem., the Abbot of the Strahov Monastery, for generously providing the historical premises of the monastery for the conference. We are further indebted to the Dean of the Catholic Theological Faculty of the Charles University Prague, Spectabilis ThDr. Prokop Brož, and to the Director of the Institute of Philosophy of the Academy of Sciences of the Czech Republic, PhDr. Pavel Baran, CSc., for the sympathy with which they accepted patronage of the conference. The conference was organised by the Catholic Theological Faculty of the Charles University together with the Institute of Philosophy of the Academy of Sciences of the Czech Republic. The conference proceedings are being published with the financial support of the Grant Agency of the Academy of Sciences of the Czech Republic, Grant No. IAA908280801 “Metaphysics in contemporary analytical philosophy and its relations to the metaphysics of modern Aristotelianism”. Stanislav Sousedík David Svoboda, Prokop Sousedík Daniel D. Novotný, Lukáš Novák

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SECTION I

CATEGORIES AND BEYOND

WHAT IS AN ONTOLOGICAL CATEGORY? Peter van Inwagen ABSTRACT In the paper the author examines the concept of a natural class, and proposes a definition of “ontological category” in terms of that concept. Say that a class is “large” if its membership comprises a significant proportion of the things that there are. Say that a class is “high” if it is a proper subclass of no natural class. Then a natural class is a primary ontological category if and only if (a) there are large natural classes, and (b) it is a high class. (Secondary, tertiary, etc., ontological categories are defined by an extension of this definition.) The author defends the definition, considers various ways in which it might be modified, and applies it to the problem of constructing a taxonomy of ontologies.

As names of divisions of philosophy go, “ontology” is a rather new word. Although it is older than that terminological parvenu “epistemology”, it is much newer than “metaphysics” or “ethics” or “logic” – and, of course, it is much newer than “philosophy”. But the word is as hard to define as any of her elder sisters. Within analytical philosophy,1 one finds three understandings of the word “ontology” – or, if you like, three conceptions of ontology.2 One of them, the use of the word by Bergmann and his school, is that ontology is the study of the ontological structure of objects. I reject this conception of ontology. I reject it as provincial, as the identification of a kingdom with one of its provinces. (In my view – I defend this view in an unpublished companion piece to this paper entitled “Relational vs. Constituent Ontologies” – that province is uninhabited. But I do not reject the Bergmanian conception of ontology on that ground alone: I contend that it is a provincial conception even if objects do have ontological structures.) There is, secondly, what I will call the “bare Quinean” conception of ontology. Quine has famously called the question “What is there?” “the ontological   For a discussion of the existential-phenomenological conception of ontology, see my essay, “Being, Existence, and Ontological Commitment”, in Metametaphysics: New Essays on the Foundations of Ontology, ed. David J. Chalmers, David Manley, and Ryan Wasserman (Oxford: Oxford University Press, 2009), 472–506. 2   This count – three conceptions of ontology – is problematical, owing to the fact that many analytical philosophers who have made important contributions to ontology (on anyone’s conception of ontology) have not given an explicit statement of what they take ontology to be. Perhaps I should say: Within analytical philosophy, one finds three potential or implicit or tacit understandings of ontology (see note 3). 1

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Peter van Inwagen What is an Ontological Category?

question”, and one might incautiously infer from this label that he conceives of ontology as the attempt to answer the ontological question. But neither Quine nor anyone else would regard just any answer to the ontological question as the kind of answer a discipline called ontology might be expected to provide. Quine himself has observed that one correct answer to the ontological question is “Everything” – and we certainly do not need to turn to any science or discipline to satisfy ourselves that that answer is correct. Another sort of correct answer might well be of the following form: a very long – no doubt infinite – conjunction of existential quantifications on “low-level” predicates, a conjunction that would perhaps read in part “… and there are bananas and there are electron neutrinos and there are protein molecules and there are locomotives … and there are colours and there are political parties and there are nontrivial zeros of the Riemann zeta function…”. (Perhaps its final conjunct – if a sentence comprising infinitely many conjuncts can have a final conjunct – would be: “and there is nothing else”.) If the only answers (other than answers that involve the “everything trick”, answers like “Everything” and “Locomotives and everything else”) that can be given to the ontological question are those provided by the investigative techniques native to everyday life and the special sciences, then all answers to the ontological question may well be of that sort. But if there is a philosophical discipline called ontology, it will attempt to give an answer to the ontological question that is in some sense more general, more abstract, more systematic than a long conjunction of existential quantifications on low-level predicates. And the “bare Quinean” will agree with this statement: on the bare Quinean conception of ontology, ontology is the discipline whose business it is to provide an abstract or general or systematic answer to the ontological question – answers that are less abstract and more informative than “Everything” and less informative and more abstract than “long list” answers. The bare Quinean will, however, be happy to regard the ideas expressed by the words “general”, “abstract”, and “systematic” as entirely subjective. On the bare Quinean conception of ontology, it is the business of the practitioners of ontology to produce and defend answers to the ontological question that – as one might say – strike them and their peers as “general” and “abstract” and “systematic”, answers that it seems appropriate to them to apply those terms to. If, for example, I say that there are abstract objects or sets or temporal parts of persisting objects, the bare Quineans will almost certainly recognise this as an assertion of the kind that characterises ontology. But if I say that there are bananas or protein molecules or solutions to Einstein’s field equations that are without physical interest, these assertions will almost certainly seen by the bare Quineans as having a place in ontology only as examples that illustrate some much more general existential thesis or as premises of some argument for some much more general existential thesis. And they will offer no account of what it is for an existential thesis to be “much more general” than these theses. They 12 • CATEGORIES AND BEYOND

Peter van Inwagen What is an Ontological Category?

will indeed insist that it would be a mistake to try to provide such an account owing to the fact that those words are no more than expressions of the subjective reactions of various philosophers to the degree of generality exhibited by various existential theses.3 The third conception of ontology – it is the conception I favour – rests on the conviction that the notion of a “general” or “abstract” or “systematic” answer to the ontological question can be given an objective sense. The third conception rests on the conviction that there are ontological categories and that it is the business of ontology to provide answers to the ontological question in terms of a specification of the ontological categories. I will attempt to give an account of the concept on which this conception of ontology rests, the concept of an ontological category. * * * I begin with the idea of a natural class. One of the assumptions on which the third conception of ontology rests is that natural classes are real. By this I do not necessarily mean that there are objects called “natural classes”, for an ontologian (why is there no such word?) may well deny that there are classes of any description.4 Indeed, anyone who did deny the existence of classes would ipso facto be engaged in ontology. What I mean by saying that there are natural classes is a consequence of the thesis that there are natural – non-conventional – lines of division among things. This assumption was famously rejected by Hobbes, and, following him, by Locke and the other empiricists. As Locke says (in the concluding passage of Chapter 3 of Book III of the Essay), Recapitulation. – To conclude: This is that which in short I would say, viz., that all the great business of genera and species, and their essences, amounts to no more but this, that men making abstract ideas, and settling them in their minds, with names annexed to them, do thereby enable themselves to consider things, and discourse of them, as it were in bundles, for the easier and readier improvement 3   I have not said that Quine or anyone else is a bare Quinean. I suspect, however, that Quine would at the very least find bare Quineanism an attractive formulation of the nature of ontology (see note 2). 4   The “classes” that figure in this essay are – or are if they really exist – much more like biological taxa than they are like sets. Like taxa, and unlike sets, they can change their membership with the passage of time and the membership of a class in one possible world may not even overlap its membership in another. Like taxa, and unlike sets, moreover, they may have “borderline members” (if there is something that is neither determinately a cat nor determinately a non-cat, that does not prevent “cat” from being a natural class). But I am not seriously asserting that there really are things that have the properties I have ascribed to classes. I issue this promissory note: I could – the result would be rather awkward, I concede – eliminate the apparent reference to and quantification over classes in the sequel by paraphrase. In my view, the only substantive philosophical issue raised by my talk of “natural classes” is whether there are real lines of division among things.

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Peter van Inwagen What is an Ontological Category?

and communication of their knowledge, which would advance but slowly, were their words and thoughts confined only to particulars.

I am not wholly convinced that what Locke says in this “recapitulation” is consistent with everything he says in the Essay (or even with everything he says in Chapter 3 of Book III), but, whether it will do as an unqualified statement of Locke’s views or not, it is a good statement of the point of view whose rejection is one of the assumptions on which the third conception of ontology rests. (From this point on, when I ascribe features to “ontology”, I shall be speaking from the point of view of the third conception – my own conception.) According to this anti-Lockean philosophy of classification, some classes of things – a minuscule proportion of them, if classes are anything like as numerous as sets – correspond to real divisions among things: in each case, the real division between the things that are members of that set and those that are not.5 To say that there are real divisions among things implies the existence of natural classes,6 but this statement does not say enough to settle the question of what natural classes there are – not even to settle it in the rather abstract and uninformative way I want to settle it in this initial discussion of the natural classes. To show you what I mean by this statement, I’m going to ask you to consider two questions about the relation between the concepts “real division among things” and the concept “natural class”. I shall introduce the first of these two questions by the following example. Suppose that the line that marks the division between horses and non-horses is one of those real lines of division among things. Does it follow that “horse” is a natural class? Before you answer, consider this question: Does it follow that “non-horse” is a natural class? That “non-horse” is a natural class certainly does not seem to be a thesis that should be true by definition. But the boundary of that class marks a real division among things. At any rate, it does if the boundary of “horse” marks a real division among things, since the two classes have the same boundary. We therefore do not want to say that a class is a natural class given only that its boundary marks a real division among things. I think that the following statement is a more plausible candidate for what we want to say about the relation between “real division” and “natural class”: 5   Real divisions need not be sharp divisions. If one divides the world into things that are determinately cats, things that are determinately not cats and things that are neither determinately cats nor determinately non-cats, one may have thereby have marked a real division among things. 6   Or, to speak more carefully (see note 4), it implies that those who have no objection to affirming the existence of classes should regard some of those classes as natural classes. And even nominalists who believe in real divisions among things may find it useful to speak as if those divisions marked the boundaries of natural classes. (Such nominalists will presumably be able to eliminate, at least in principle, apparent reference to and apparent quantification over natural classes from their discourse.)

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Peter van Inwagen What is an Ontological Category?

For any class, if its boundary marks a real division among things, then either that class or its complement is a natural class – but not necessarily both.

If you ask me, “In such a case, how do we determine which of two given complementary classes are natural classes?”, I’m afraid I do not have any very informative answer. I could try this: The ones with “sufficient internal unity”. It does seem obvious to me that if the boundary between a class and its complement marks a real division among things, at least one of the two must exhibit sufficient internal unity for it to be called a natural class. If this thesis is granted, the existence of natural classes follows from the existence of real divisions among things. Nevertheless, the concept of “natural class” cannot be defined solely in terms the concept “real division.” We must also appeal to the concept of “sufficient internal unity” if we are to provide a full explanation of “natural class”. (Or, at any rate, we must appeal to some concept other than “real division”.) One might in fact contend that, if we really have the concept “sufficient internal unity”, we could use it to define the concept “real division among things”. (Suppose a class exhibits “sufficient internal unity”; suppose its union with no unit class other than its unit subclasses has this feature; then it is plausible to suppose that its boundary marks a real division among things.) Why, then, have I assigned such a fundamental role to “real division” in my exposition of the concept “natural class”? Because, first, it seems to me that “real division” is a far easier idea to grasp than the idea “exhibits sufficient internal unity”. And because, secondly, in most interesting cases in which the boundary between two complementary classes marks a real division among things, it will be simply evident that – whatever internal unity may be – either one of them exhibits vastly more internal unity than the other or they both exhibit an approximately equal (and very high) degree of internal unity. Now the second question about the relation between “real division” and “natural class”. Consider the universal class, the class of all things.7 Is it a natural class? I propose to leave this an open question – to provide an account of “natural class” that leaves it an open question.8 Does what I have said have any implications for this question? The only relevant implication of what we have said is this: if the boundary of the universal class marks a real division among things, then either the universal class or the empty class is a natural class. Well, what is the boundary of the universal class? In one sense, it has no boundary – not if boundaries divide 7   Even those who are realists about classes will be well advised to treat the universal class as a virtual class – that is to treat apparent reference to it as a mere – and dispensable – matter of speaking. 8   Suppose that Meinong was wrong and that one name for the universal class is “being”. Aristotle held that “being” was not a category. On the account of “ontological category” I shall propose – and given that Meinong was wrong –, “being” will be a category if it is a natural class. I do not want to give an account of “natural class” that will imply either the truth or the falsity of Aristotle’s thesis.

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Peter van Inwagen What is an Ontological Category?

things from other things. But we might not insist that a boundary must divide things. (Suppose the universe is finite in extent; adopt a relational theory of space. Isn’t it reasonable to say that in that case the universe has a boundary, a boundary that nothing is outside?) The simplest way to leave it an open question whether the universal class is a natural class is to stipulate that it has no boundary (in which case our principle says nothing about whether it is a natural class). We say, that is, that a class has a boundary if (and only if) both that class and its complement are non-empty. Those who want to say that the universal class is a natural class – or that it is not – must defend their thesis on some ground that does not involve the properties of its boundary (perhaps on the ground of its “internal unity” or lack thereof). It will be observed that, in virtue of this stipulation, we have left it an open question whether the empty class is a natural class. I hereby stipulate that the empty class is not a natural class – but for no profound reason; whether the empty class is a natural class seems to be one of those “don’t care” questions, one of those questions that can properly be settled by stipulation, and stipulating that it is not a natural class will simplify some of my definitions and the statements of some of my theses. Are there any natural classes? Well, it seems plausible to suppose so. The class of electrons is a plausible candidate for the office “natural class” – as plausible a candidate as there could be, in my view. (The boundary between electrons and non-electrons is certainly a plausible candidate for the office “boundary that marks a real division among things”, and it seems evident that the class of electrons exhibits vastly more internal unity than the class of non-electrons.) The class of horses (members of the species Equus caballus) would be a rather more controversial but still reasonably plausible example. Whether there are natural classes or not, it is one of the assumptions of ontology that there are. (If there are no natural classes, ontology is like astrology: a science that rests on a false assumption.) It is, moreover, one of the assumptions of ontology that, although some pairs of natural classes may have non-empty intersections otherwise than by one’s being a subclass of the other, there are nested sequences of natural classes – sequences ordered by the subclass relation. The class of electrons, the class of leptons, and the class of fermions provide a plausible example of such a sequence. The class of horses, the class of mammals, and the class of chordates would (again) be a rather more controversial but still reasonably plausible example. One could, however, affirm the existence of natural classes and of nested sequences of natural classes without involving oneself in ontology – or in any other part of philosophy. Suppose, for example, that Alice maintains that the largest natural classes are the class of bosons and the class of fermions and that every natural class is a subclass of one of these two non-overlapping classes. And suppose that she also maintains that (in some sense) only a very small 16 • CATEGORIES AND BEYOND

Peter van Inwagen What is an Ontological Category?

proportion of the things that there are are bosons or fermions. We might, for example, imagine that she supposes that, for any xs, the mereological sum of the xs exists, and that among these sums are to be found atoms and molecules and cats and locomotives and galaxies and most of the tangible or visible things that we unreflectively believe in. (And, of course, Alice believes that there are a vast number of convoluted gerrymanders most of which are not – considered individually – possible objects of human thought.) The class of cats, Alice contends, is not a natural class: the vague and imperfect boundary we have drawn around the cats is a mere product of convention and fails to reflect a real division among things, unlike the boundary we have drawn around the bosons. And the same goes for the locomotives and the galaxies. (Of course most classes of sums are cognitively inaccessible to us, but, says Alice, if, per impossibile, we were to draw boundaries around any of these classes, those boundaries would be merely conventional – and with a vengeance.) And, of course, she maintains that the class of things that are neither bosons nor fermions is, as one might say, radically deficient in internal unity and is not a natural class. If Alice is right, ontology is, again, like astrology: a science that rests on a false assumption. For one of the assumptions on which ontology rests is this: that membership in the natural classes is not restricted to any such minuscule proportion of the things that there are as Alice supposes it to be. It is an assumption of ontology that there indeed are natural classes whose membership comprises a really significant proportion of the things that there are. I am acutely aware that the idea of a class whose membership comprises a really significant proportion of the things that there are is an idea that it is hard to give any precise sense to. But it does not seem to me to be an obviously meaningless or entirely vacuous idea. Take our friend Alice. In her view there are certainly a lot more things – even a lot more concrete things – than there are things that are members of some natural class. If, for example, there are 10  exp  80 bosons and fermions, then there are 2 exp  (10  exp  80)  −  1 things (abstractions aside): there are 10 exp 80 things that belong to some natural class and ((2 exp (10 exp 80) − 1) − 10 exp 80 things that belong to no natural class, and the latter number is inconceivably larger than the former. (The ratio of the latter to the former can be described this way. Think of the number that is expressed by a “1” followed by eighty zeros. The ratio of the number of things that belong to no natural class to the number of things that belong to some natural class is a number that can be expressed by a “1” followed by – approximately – onethird that many zeros.) Or if the number of bosons and fermions is denumerably infinite, then the number of (concrete) things that belong to no natural class is indenumerably infinite. There are various ways in which there might be natural classes whose membership comprised “a really significant proportion of the things that there are”. CATEGORIES AND BEYOND • 17

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(Let us call such a class “large”.) One of them is this: the universal class is a natural class – for the membership of a class is certainly a “significant proportion” of itself. Here is another way. It may be that, although the class of all things, the universal class, is not a natural class, it is the union of a small number of natural classes. (A “small” number would be a number like 2 or 6 or 19. And what do I mean by “a number like”? You may well ask. But if you want a definition of “small number”, I offer the following. A number n is small in just this case: if a class is the union of n subclasses, the membership at least one of them must comprise a really significant proportion of the membership of that class.) And here is a third. Say that a natural class is “high” if is not a proper subclass of any natural class. At least one high natural class is large – although some things belong to no natural class. (Suppose, for example, that God exists and that a vast number of creatures exist and that everything is either God or a creature. Suppose that God belongs to no natural class – and hence that the universal class is not a natural class – and that the class of creatures is a natural class.) Note that the assumption we are considering, that there are large natural classes, leaves open the possibility that that there are high natural classes that are not large. Our assumption is, for example, consistent with the following threefold thesis: everything is either a substance or (exclusive) an attribute; “substance” and “attribute” are both natural classes and every natural class is a subclass of one or the other; there are finitely many substances and too many attributes to be numbered even by a transfinite number. In this case, “substance” is a high class, despite the fact that only an insignificant proportion of the things that there are are substances. We may now define “ontological category”. Let us say, first, that a natural class x is a primary ontological category just in the case that – there are large natural classes – x is a high natural class. Consider for example the case presented in the previous paragraph. In this case “substance” and “attribute” are high natural classes and are in fact the high natural classes. And there are large natural classes – the class of attributes if no other. “Substance” and “attribute are therefore primary ontological categories – and are the primary ontological categories.9 The primary ontological categories are the highest links in the great chains of classification – the great chains of non-arbitrary classification, of not-merely9   Note that the definition does not rule out overlapping primary ontological categories. Suppose, for example, that Phoebe maintains that “abstract” and “concrete” are the primary ontological categories. She may consistently go on to maintain that the proposition that Socrates was a philosopher is abstract (in virtue of being a proposition) and concrete (in virtue of having a certain concrete object, Socrates, as an ontological constituent).

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a-matter-of-convention classification. But remember that the highest links in the great chains of classification are primary ontological categories only if primary ontological categories exist – just as the highest buildings are skyscrapers only if skyscrapers exist. If our friend Alice is right about what natural classes there are, the highest natural classes are not primary ontological categories. (If she is right, the highest natural class, the class of elementary particles, is not an ontological category, since there are no large natural classes.) Her world corresponds, in the analogy, to a world in which the highest buildings are three stories high: highest buildings but no skyscrapers. Having defined “primary ontological category”, we may proceed to define “secondary ontological category”, “tertiary ontological category”, and so on, by repeated applications of essentially the same device. We say that x is a natural subclass of y if x is a subclass of y and x is a natural class. We say that x is a large subclass of y if x is a subclass of y and x comprises a significant proportion of the members of y. We say that x is a high subclass of y if x is a natural proper subclass of y and is a proper subclass of no natural proper subclass of y. Then, a natural class x is a secondary ontological category if There is a primary ontological category y such that – y has large natural proper subclasses – x is a high subclass of y. And so for tertiary ontological category, quaternary ontological category, … . And, finally, an ontological category (simpliciter)10 is a class that, for some n, is an n-ary ontological category.11   In formulating this definition of “ontological category”, I have assumed that every sequence of natural classes ordered by the proper-subclass relation has a first member. (If this were not so, there might be large natural classes but no high natural classes – and hence no primary ontological categories and hence no ontological categories of any order. But it is at least plausible to suppose that any large natural class is an ontological category, and even more plausible to suppose that if there are large natural classes, some of them are ontological categories.) This is a consequence of the stronger statement that every such sequence is finite. I see no reason to question either of these theses. 11   Note that this definition allows ontological categories to overlap. Suppose that everything is either an A or a B, that A and B are natural classes, and that neither is a proper subclass of any natural class. Then A and B are primary ontological categories. But nothing we have said implies that A and B do not overlap. (Cf. n. 9). Suppose further that they do overlap and that their intersection is a natural class that is not a proper subclass of any natural class. Then their intersection is also a primary ontological category. Or suppose that A and B do not overlap, and that A can be partitioned into two subclasses C and D, each of which is a natural class and that B can be partitioned into two subclasses E and F, each of which is a natural class. Suppose that the union of C and E is a natural class that is a proper subclass of no natural class. Then the union of C and E is a primary ontological category that overlaps both the primary categories A and B and the secondary categories C and E. 10

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Peter van Inwagen What is an Ontological Category?

One might wonder whether this account of “ontological category” has the consequence that this concept is “entirely subjective” – and thus wonder whether the account of ontology that I am proposing in the end reduces to the “bare Quinean” conception of ontology. It is certainly true that the account depends essentially on certain vague terms. (For example, “the membership of x comprises a significant proportion of the membership of y”.) I would contend, however, that the vague is not the same as the subjective. For example, “delicious” is a subjective term, in contrast to “edible” and “nutritious”, which are merely vague. I would also point out that there can be perfectly clear cases of objects that fall under vague terms, and that this account, when applied to a particular metaphysic may yield determinate answers to the question, “What, according to that metaphysic, are the ontological categories?” It may be obvious, for example, that according to Albert’s metaphysic, there are no secondary ontological categories, since all his primary categories have infinitely many members and all other natural classes have only finitely many members – which entails that none of Albert’s primary categories have large natural subsets. Assuming that the “subjectivity” worry has been adequately answered, is the above account of “ontological category” satisfactory? I am inclined to think that this account is incomplete. I am inclined to think that there should be a further condition on what an “ontological category” is, a modal condition. I think this because what I have so far said allows ontological categories to be rather fragile, modally speaking, much more fragile than I’m comfortable with their being. One kind of example that makes me uneasy is this: it is consistent with this account that the natural class “dog” (let’s assume that this is a natural class) turn out to be, oh, let’s say, a 23-ary ontological category. And this result seems wrong to me – and not because I have anything against either dogs or allowing the science of biology to have implications for ontology. It seems wrong to me because the fact that there is such a natural class as “dog” is – no doubt – radically contingent. Very small changes in the world of a hundred million years ago – changes local to the surface of the earth – would have resulted in there never having been any such class. And it seems evident to me that a satisfactory account of “ontological category” should not allow the list of ontological categories to be dependent on the contingencies of history to that extent. But to what extent might the list be a matter of contingency? I do not want to say that an ontological category must be, by definition, necessarily existent (that is, represented in every possible world). If some school of metaphysicians proposes “contingent thing” as an ontological category, I do not think that that proposal should commit them to the proposition that there are, of necessity, contingent things – although it should commit them to the proposition that, of necessity, if there are contingent things they form or constitute an ontological category. The example I have said makes me uneasy might be “handled” by some sort of restriction on the “n” in “n-ary ontological category” – say, by insisting that 20 • CATEGORIES AND BEYOND

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the lowest ontological categories are the quaternary categories. (Someone might be happy to suppose that “you’d have to get down into the twenties” before things you were calling ontological categories became objectionably dependent on the contingencies of history.) This idea is, obviously, attended by all manner of difficulties, but there is no point in trying to solve them, because there are imaginable cases of “modally fragile” primary and secondary categories. Consider, for example, Bertram, who, like Alice, believes that the highest natural classes are “boson” and “fermion”. But – unlike Alice – Bertram is a mereological nihilist (and a nominalist to boot): he believes that everything is either a boson or a fermion. By the above definition, then it follows from these beliefs of his that “boson” and “fermion” are primary ontological categories. So far forth, this might not be objectionable. But suppose Bertram also believes that the physical economy of most possible worlds is radically different from the physical economy of the actual world. Suppose he believes that there are non-arbitrary measures of the sizes many sets of possible worlds (the measure of the whole of logical space being 1), and that the measure of the set of worlds that contains bosons and fermions is [insert here a decimal point and a string of sixty zeros]13 – or believes that the measure is infinitesimal or even 0. In that case, I think it would be just wrong to say that it follows from his beliefs that “boson” and “fermion” are ontological categories. It seems to me to be wrong to call a natural class an ontological category if it exists in “hardly any” possible worlds. I am inclined to think, therefore, that the account of “ontological category” that I have given needs to be supplemented by a clause to the effect that an ontological category must in some sense be “modally robust” – but almost certainly not so robust that an ontological category must, by definition, exist in all possible worlds. I leave for another occasion the problem of spelling out what this means – and the question whether my modal scruples as regards ontological categories are justified. Let us now return to the concept of ontology. Ontology, as I see ontology, rests on the following assumption: there are ontological categories. We may, in fact, define ontology as the discipline whose business is to specify the ontological categories. Remember that the empty set or class is not to count as a natural class, and it is therefore true by definition that all ontological categories are non-empty. To specify the ontological categories is therefore to make an existential statement – even if one regards the categories themselves as virtual classes and thus as not really “there”. If for example, one says that “substance” is an ontological category, this statement implies that there are substances. The goal of ontology is to provide an answer to the ontological question in the form of a specification of the ontological categories. It is a commonplace that the word “ontology” is used both as a mass term and a count-noun. When it is used as a mass term, it denotes a certain discipline, a certain sub-field of philosophy or of metaphysics – just that discipline that CATEGORIES AND BEYOND • 21

Peter van Inwagen What is an Ontological Category?

I have been attempting to give an account of. When it is used as a count-noun, it is used to refer to certain philosophically interesting answers to the ontological question. If my account of ontology is right, an ontology is a specification of the ontological categories. I briefly show how this account of “ontology” fares when it is applied to two very different ontologies. My first example is the ontology I myself favour. According to this ontology, there are two primary categories, substance and relation. (Unless the universal class is a natural class, in which case it is the primary category, and substance and relation are the two secondary categories. I have no firm opinion about whether the universal class – I suppose the best name for it would be “being” if it is thought of as a category – is a natural class and therefore a category. The category “relation” subsumes propositions (0-adic relations) and attributes (monadic relations). The category “substance” goes by two other names, “concrete thing” and “individual (thing)”.12 Similarly, the category “relation” is also called “abstract thing” and “universal”. It is not my position that that, e.g., “substance” and “individual” are synonymous. Although I say that all substances are individual things and all individual things are substances, I regard this as a substantive thesis, one of the component propositions of my ontology that requires a philosophical defence. And the same goes for the pairs “substance” and “concrete thing”, “concrete thing” and “particular”, “relation” and “abstract thing”, “abstract thing” and “universal”, and “universal” and “relation”. I contend only that the extensions of each pair are the same.13 My second example is the Meinongian ontology.14 The universal class, the class of “objects” or the realm of Sosein divides into the two ontological categories the concrete and the abstract (I do not mean to imply that those two terms are actually used by Meinongians). The category “the concrete” divides into the   Or “particular (thing)”. As I use the words, “individual” and “particular” are synonyms. (Some writers give different senses to these two words.) I use “thing” as the most general count-noun: everything is a thing; “every thing” and “everything” are synonyms; a “thing” is anything that can be the referent of a pronoun. I use such words as “object”, “entity” and “item” in the same sense. 13   One possible “version” of the ontology called “austere nominalism” raises a problem for my account of ontology. This is the version I have in mind: there are only concrete particulars; there are no high natural classes: neither “concrete particular” nor any other large class is a natural class. This version of austere nominalism seems clearly to be “an ontology” but it implies that there are no ontological categories. 14   Meinongians will no doubt object to my use of the terms “the Meinongian ontology” and “ontological category” in my description of their position – since, of course “to on” means “being”. They will insist that providing an answer to the question, “What is there?” is only one small part of their project. Well, let them fi nd their own terminology. This is mine. 12

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two categories “the existent” and “the (concrete but) non-existent”, and the category “the abstract” divides into the two categories “the subsistent” and “the (abstract but) non-subsistent”. The union of the existent and the subsistent is itself an ontological category, the category of Sein, and the complement of that category is a category, the category Nichtsein.15 If Sosein is not a natural class, then the abstract, the concrete, Sein, and Nichtsein are primary categories and the categories that pertain to existence and subsistence are secondary categories. Let me now say something to connect the definition of ontology I have given with an ancient and important definition of ontology. The definition I am thinking of derives from one of Aristotle’s definitions of “first philosophy” in Metaphysics: Ontology is the science of being as such or being qua being. In my view, this Aristotelian definition of ontology is, if not entirely satisfactory, not wholly wrong either. I would defend this position as follows. The universal class, the class of all things, is either the class of all beings – the class whose membership is just exactly the things that there are –, or else it is the class that comprises both all beings and all non-beings. (Or, as a Meinongian might prefer to say, the universal class, the “realm” of Sosein, comprises two non-overlapping realms, the realm of being and the realm of non-being.) In the former case, being is what is common to the members of all ontological categories, and, if there is something common to all the ontological categories, it seems plausible to say that a science or discipline whose business is to specify the ontological categories should have as one of its first orders of business to say what this “something” is. In the latter case, being and non-being are the two of the highest ontological categories (perhaps Sosein is the highest category) and, if there is such a category as non-being, the task of explaining what being is and the task of explaining what non-being is can be divorced from each other only by an act of severe abstraction: if those tasks are in any sense “two”, they must nevertheless be seen as two sub-tasks of one task. If I reject the Aristotelian definition of ontology, it is not because I deny that the question “What is being?” is one of the questions that ontology must answer. I reject it because I deny that it is the primary ontological question, the question that defines the business of ontology. A word on terminology. In other discussions of ontology, I’ve said that ontology divides into meta-ontology and ontology proper. Ontology proper, I said, is the investigation of what there is, and meta-ontology addresses the two questions, What does “there is” mean? and What methods should be employed in the investigation of what there is? But here I have defined ontology as the discipline that attempts to specify the ontological categories. Does this definition not identify ontology (ontology simpliciter) with “ontology proper”? My earlier characteri15   Assuming that “the concrete”, “the abstract”, “the existent”, “the subsistent”, “the non-existent”, “the non-subsistent”, Sein, and Nichtsein are all natural classes.

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sation of ontology and the present characterisation can be reconciled if we adopt a sufficiently liberal understanding of “specify the ontological categories”: to specify the ontological categories is not merely to set out a list of categories; specifying the ontological categories also involves explaining the concept of an ontological category and describing the relations between the categories and attempting to answer any philosophical questions that may arise in the course of doing this. One of these philosophical questions will be the question of the nature of being – which is essentially the question, What is it for a category to be nonempty? (So, at any rate, we anti-Meinongians say. I leave it to the Meinongians to explain in terms they find satisfactory what it is for a category to be non-empty.) We may say then that “ontology proper” is the attempt to set out a satisfactory list of ontological categories; everything else in ontology belongs to meta-ontology.

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SCHOLASTIC DEBATES ABOUT BEINGS OF REASON AND CONTEMPORARY ANALYTICAL METAPHYSICS Daniel D. Novotný ABSTRACT Prima facie it would seem that the traditional scholastic debates about entia rationis (“beings of reason”) may be easily brought into dialogue with debates about nonexistent objects in contemporary analytical metaphysics. It turns out, however, that the scholastic debates about beings of reason are placed within a very different ontological framework or paradigm, so that bringing scholastic and analytical authors into common discussion about this topic is not trivial. In this paper I make the first step toward establishing such discussion by describing the ontological framework presupposed by the scholastic debates about beings of reason, and by identifying the roles that beings of reason were supposed to play in it.

1. INTRODUCTION One of the main tasks of metaphysics – as it was conceived by Aristotle – is to provide a list of categories of what exists.1 Late scholastic authors of the Renaissance and Baroque periods, however, were increasingly preoccupied not just with what exists but also with what does not exist.2 The most important and well-known label with which these late scholastic discussions are associated is ‘ens rationis’, literally “being of reason”.3 Prima facie it would seem that the traditional 1   This is, of course, an oversimplification and a bold claim, see e.g. Jorge J. E. Gracia, Metaphysics and Its Task: The Search for the Categorial Foundation of Knowledge (Albany, NY: SUNY Press, 1999); Robert A. Delfino, ed., What are We to Understand Gracia to Mean: Realist Challenges to Metaphysical Neutralism (Amsterdam and New York: Rodopi, 2006); and van Inwagen’s contribution in this volume. 2   For an introduction into these scholastic discussions see, e.g., John P. Doyle, “Suárez on Beings of Reason and Truth (First part)”, Vivarium 25 (1987): 47–75; “Suárez on Beings of Reason and Truth (Second part)”, Vivarium 26 (1988): 51–72; Daniel D. Novotný, “Prolegomena to a Study of Beings of Reason in Post-Suarezian Scholasticism, 1600–1650”, Studia Neoaristotelica 3, no. 2 (2006): 117–141. 3   Henceforth in this paper, for the sake of simplicity, whenever I shall speak about scholasticism I shall mean “scholasticism of the Renaissance and especially Baroque period”, to wit, scholasticism of the seventeenth century. Baroque scholastic culture and discussions differed in many ways from the scholasticism of the Middle Ages and the Renaissance. See Daniel D.  Novotný, “In Defense of Baroque Scholasticism”, Studia Neoaristotelica 6, no. 2 (2009): 209–233.

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Daniel D. Novotný Scholastic Debates about Beings of Reason

scholastic debates about beings of reason may be easily brought into dialogue with the current work on nonexistent objects in analytical metaphysics.4 It turns out, however, that the scholastic debates about beings of reason are placed within a very different ontological framework or paradigm, so that bringing scholastic and analytical authors into common discussion on this topic is not trivial. In this paper I make the first step toward establishing such discussion by (1) providing a description of the framework presupposed by the scholastic debates about beings of reason, and (2) identifying the roles that beings of reason were supposed to play in it. 2. THE ONTOLOGICAL FRAMEWORK OF SCHOLASTIC DEBATES Let me start with a scheme (see the opposite page) attempting to classify into “super-categories” whatever non-existing items one might encounter in scholastic works. At the very left of our scheme we see the term ‘item’. By this term I mean anything to which one can refer and of which one can say that “it is (in some sense) there” (datur) – regardless of such issues as to whether it exists or whether it is real. (The asterisk next to this and some other super-categories indicates that it is a term that scholastic authors themselves did not use but that is useful to have for our talk about their views). For comparison, in analytical philosophy Bertrand Russell tried to capture this broad meaning of ‘item’ by the term ‘term’:5 Whatever may be an object of thought, or may occur in any true or false proposition, or can be counted as one, I call a term. This, then, is the widest word in the philosophical vocabulary. I shall use as synonymous with it the words unit, individual, and entity. The first two emphasise the fact that every term has being, i.e. is in some sense. A man, a moment, a number, a class, a relation, a chimaera, or anything else that can be mentioned, is sure to be a term…

And Peter Strawson, to take another example, also acknowledged the possibility to have such a “widest word in philosophical vocabulary”:6 Anything whatever can be introduced into discussion by means of a singular, definitely identifying substantival expression… Since anything whatever can be identifyingly referred to, being a possible object of identifying reference does not distinguish any class or type of items or entities from any other. 4   For an overview of these debates see, e.g., Maria Reicher, “Nonexistent Objects”, The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), ed. Edward N. Zalta, http://plato.stanford. edu/archives/fall2010/entries/nonexistent-objects/. 5   Bertrand Russell, The Principles of Mathematics, http://fair-use.org/bertrand-russell/ the-principles-of-mathematics/ (1st ed. Cambridge: At the University Press, 1903; 2nd ed. 1938), §47. 6   Peter F. Strawson, Individuals: An Essay in Descriptive Metaphysics (New York: Routledge, 1959, repr. 2005), 137.

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Actual

Things in the strict sense

MerelyPossible

Possible things

Positive

Second intentions and other relations of reason

Negative

Negations, privations, selfincompatibles

Possible

Being

Impossible

Integral*

Non-Being

Object*

ParaBeing*

Extrinsic Being

Accidental

Item*

Objective*

Items are divided into objects and objectives by which I mean things and propositions/states-of-affairs, respectively.7 Let me expand a bit. Etymologically, the word ‘object’ means “thrown in the way”; a stone, for instance, could be an object. The stone is something that catches our attention and hence it becomes 7   The division and the terminology is inspired by Alexius Meinong. What I call ‘item’ Meinong calls ‘Gegenstand’. He then divides it into Objekt and Objektiv. See Alexius Meinong, Untersuchungen zur Gegenstandstheorie und Psychologie (Leipzig: J. A. Barth, 1904), 6; translated in Roderick M. Chisholm, Realism and the Background of Phenomenology (New York: The Free Press, 1960), 80. See also John N. Findlay, Meinong’s theory of objects and values, 2nd ed. (Aldershot: Ashgate Publishing (Gregg revivals), 1995), 60–69 (1st ed. 1933).

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an object of perception and thought. But the expression ‘object of thought’, as A. N. Prior points out, is ambiguous:8 The phrase ‘object of thought’ may be used in two very different ways. An object of thought may be (1) what we think, or (2) what we think about; e.g. if we think that grass is green, (1) what we think is that grass is green, and (2) what we think about is grass. ‘Objects of thought’ … are sometimes called ‘propositions’, not in the sense of sentences, but in the sense of what sentences mean. … What we think, may be false; and what we think about may be non-existent. These are quite different defects, though philosophers have sometimes slipped into treating them as if they were the same.

Some analytical philosophers consider Prior’s propositions to be primary truthmakers, corresponding or failing to correspond to facts or obtaining statesof-affairs as truthmakers. These distinctions within the “genus” of objectives, however, need not concern us at this point, because Baroque scholastics paid virtually no attention to them – at least in the context of beings of reason.9 For them, the world is the totality of things and not of facts (pace Wittgenstein).10 Next comes the division into accidental objects (per accidens, loosely united objects, aggregates) and integral objects (per se, “innerly integrated”, tightly/ naturally united objects). Accidental objects include artefacts, heaps, or any kind of arbitrary wholes. The following division, the division of integral objects, is of crucial importance, because many scholastic authors simply identify integral (per se) objects with beings (entia). There are, however, texts in which, for instance, Francisco Suárez acknowledges the categories of non-beings and extrinsic beings. These, for the lack of a better term, I call “para-beings”, a term I have made up but which captures the idea of a category of objects parasitic on beings in the strict sense.11   Arthur N. Prior, Objects of Thought, ed. Peter Geach and Anthony Kenny (Oxford: Clarendon Press, 1971), 3–4. 9   There were some exceptions, see Daniel D. Novotný, “The Historical Non-Significance of Suárez’s Theory of Beings of Reason: A Lesson From Hurtado”, in Metaphysics of Francisco Suárez (1548–1617): Disputationes metaphysicae in their systematic and historical context, ed. Daniel Heider, Lukáš Novák, and David Svoboda (Prague, forthcoming), ch. 9. There is an evidence that propositions and states-of-affairs (under the heading ‘complexe significabile’ – ‘something signifiable in a complex way’) were discussed in different contexts by Renaissance scholastics, see Gabriel Nuchelmans, Late-Scholastic and Humanist Theories of the Proposition (Oxford, New York: North Holland Publishing Company, 1980). I prefer Meinong’s term ‘objective’ to the medieval term ‘complexe significabile’ for two reasons. First, Meinong’s term highlights the correlation between objectives and objects, and second, it is neutral with respect to the question whether objectives are mental constructs or not. The term ‘complexe significabile’ or ‘complexly signifiable’ may seem to imply that it is something mental. 10   Cf. Ludwig Wittgenstein, Tractatus Logico-Philosophicus (New York: Cosimo, Inc., 1922, repr. 2009), 29, prop. 1.1. 11   The term is mine but it is inspired by Caramuel’s ‘πάϱοντα’, see Ioannes Caramuel, 8

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Then we get to the division of beings into possible in the broad sense and impossible (impossibilia). Broadly possible beings are divided into actual (entia actu, vera entia) and merely possible (possibilia). Actual beings, i.e. beings in the narrowest sense of the word, make up the world/reality of the scholastics.12 They are ontologically prior to everything else. Beings divide into substances, such as people, animals, plants, or stones, and their various accidents, and are typically classified into nine structured groups, called ‘categories’. Merely possible beings were enormously controversial among the scholastics.13 Finally, we get to the impossible beings, i.e. beings that cannot exist in actual reality. These, according to the common default scholastic assumption, are minddependent and hence they are called ‘entia rationis’. As I have already said, this expression means literally “beings of reason” although there are at least three other translations of this term in use: ‘mental being’ (Gracia), ‘rationate being’ (Schmidt), and ‘intentional being’ (Sousedík). I use ‘being of reason’ not only because it is the most common (Doyle, Canteñs), but also because its oddity highlights the fact that we speak about a kind of item taken from within a specifically scholastic context.14

Leptotatos (Vigevani: Typis Episcopalibus, apud Camillum Conradam, 1681), diss. 2, pars 2, a. 1, concl. 5, 96a; cf. Daniel D. Novotný, “Ens rationis in Caramuel’s Leptotatos (1681)”, in Juan Caramuel Lobkowitz, the Last Scholastic Polymath, ed. Petr Dvořák and Jacob Schmutz (Praha: Filosofia, 2008), 71–84. 12   This world/reality has material and non-material “regions”. Angels, for instance, belong to the non-material region and human beings are peculiar hybrids of the two worlds (they have a non-material “part”). God has a sui generis ontological status: Everything, whether material or non-material, depends on God both for the beginning and for the continuation of its existence (cf. E. Feser’s contribution to this volume). 13   There are several studies of the late scholastic views on merely possibles, e.g.: Jeffrey Coombs, “The Possibility of Created Entities in Seventeenth-Century Scotism”, The Philosophical Quarterly 43 (1993): 447–459; Stanislav Sousedík, “Der Streit um den wahren Sinn der Scotischen Possibilienlehre”, in John Duns Scotus: Metaphysics and Ethics, ed. Ludger Honnefelder, Rega Wood, Mechtild Dreyer (Leiden: Brill, 1996), 191–204; Tobias Hoffmann, Creatura intellecta: Die Ideen und Possibilien bei Duns Scotus mit Ausblick auf Franz von Mayronis, Poncius und Mastrius (Münster: Aschendorff, 2002). 14   Jorge J. E. Gracia, “Suárez’s Conception of Metaphysics: A Step in the Direction of Mentalism?”, American Catholic Philosophical Quarterly 65 (1991): 287–309; Robert W. Schmidt, “The translation of terms like Ens rationis”, The Modern Schoolman 41 (1963): 73–75; Stanislav Sousedík, “Pomyslná jsoucna (entia rationis) v aristotelské tradici 17. století”, Filozofický časopis 52 (2004): 533–544; John P. Doyle, “Suárez on Beings of Reason and Truth (First part)”; Bernardo Canteñs , “Suárez on Beings of Reason: What Kind of Being (entia) are Beings of Reason, and What Kind of Being (esse) Do they Have?”, American Catholic Philosophical Quarterly 77 (2003): 171–187.

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Now the surprising fact: Suárez and most other Baroque scholastics considered merely possible beings to be real and hence they were not classified as beings of reason. This fact is often overlooked. Nicholas Rescher, for instance, writes:15 With regard to non-existents, the medieval mainstream thus sought to effect a compromise. On the one hand, their lack of reality, of actual existence, deprived nonentities of a self-sustaining ontological footing and made them into mind-artifacts, entia rationis. On the other hand, their footing in the mind of God endowed them with a certain objectivity and quasi-reality that precluded them from being mere flatus vocis fictions, mere verbalisms that represent creatures of human fancy16

Hence, using non-scholastic terminology, beings of reason might be best described as intentional or mind-dependent impossible objects. This mind-dependency of beings of reason, however, is more precisely characterised by the scholastics as merely objective mind-dependency. This sort of mind-dependency is contrasted by them with subjective mind-dependency, which is a real relation of dependency of the mental accidents, such as sensations, emotions, thoughts, and volitions, on the mind. There are two sorts of objective mind-dependency. (1) Suppose there is a person p who apprehends a real being x. In this case x is not merely objectively in the intellect of p, for x also has its own real being in itself. (2) Suppose there is a person p who apprehends x and x has no other being besides the being it has in the intellect of p. In this case x is merely objectively in the intellect of p. It is only in this last sense of ‘mind-dependency’ that the word ‘ens rationis’ is appropriately used.17 Impossible beings (beings of reason, necessarily mind-dependent beings) divide into negative beings (entia negativa) and positive beings (entia positiva). The former are further divided into negations (negationes) and privations (privationes), and the latter are identified with relations of reason (relationes rationis). Impossible beings should be understood as objects for which it is impossible to exist in actual reality and hence they need to be distinguished from what I call “selfcontradictory beings”, which are objects, such as square-circles or goat-stags, that   Rescher, Imagining Irreality, 362.   Antonio Millán-Puelles (see The Theory of the Pure Object, trans. and ed. by Jorge García-Gómez, Heidelberg: Universitätsverlag C. Winter, 1996) does not make the same historical mistake, although for systematic reasons he agrees with Rescher’s view that mere possibles are non-real. Even some contemporary Thomists argue that for systematic reasons the traditional thesis about the reality of the possibles is inconsistent with other tenets of scholastic ontology, see, e.g., Norris W. Clarke: “What is Really Real?”, in Progress in Philosophy. Philosophical Studies in Honor of Rev. Doctor Charles A. Hart, ed. by J. A. McWilliams (Milwaukee, 1955). 17   Note that in contemporary usage the words objective/subjective are used in exactly the reversed sense. The term ‘objective’ means real and mind-independent, whereas ‘subjective’ means apparent and mind-dependent. How this reversal of meaning happened is still an untold story of the history of philosophy. 15 16

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contain explicit contradictions.18 Although many later Baroque authors reduced impossible beings to self-contradictory objects, this is not a trivial move. For Suárez and other scholastics there seem to be objects that cannot exist in actual reality but still, they are not self-contradictory (for instance, the universal human being or blindness). So far for the explanation of the above given schematic classification of scholastic super-categories. Before we go on to the second part of my paper, let me make three clarificatory notes about this classification. Note 1: Classifications and natural classes The classification of super-categories (if I am right) provides an overview of various strange ontological items one can encounter in scholastic texts. But why did the scholastics themselves not formulate such a classification? I can only speculate. First of all, many elements of the classification I give were controversial among them. Not all scholastics agreed, for instance, that extrinsic beings or non-beings were in some sense real and hence a special “genus” of items. Hence, since there was no agreement on these issues, they did not feel the need to provide an explicit classification of the items they talked about. Secondly, the hesitancy to formulate such a classification might be due to their assumption that “good” concepts must delimit natural classes (members of which are at least analogically related). And since there is no natural class, for instance, of existing and nonexisting beings, the two should not be lumped under one label. Today, however, we feel free to draw such classifications, provided that we keep in mind that some of the “fields” of our classification may represent just arbitrarily united classes. The fact that x and y belong to a class C does not imply that x and y share some common (intrinsic) feature. Later Baroque scholastics seem to go in this direction in that they started to acknowledge “extrinsic thinkability”, i.e. the possibility of subsuming x and y under a common concept, without implying that they share anything intrinsically in common – except for the extrinsic feature of belonging to the same class. The notion of extrinsic thinkability gave rise to the idea that there are supertranscendental terms, such as ‘thinkable’ or ‘something’, which are applicable both to real and non-real objects.19

18   Millán-Puelles calls these “paradoxical quiddities” or “openly paradoxical beings” (Millán-Puelles, The Theory of the Pure Object). 19   It is also noteworthy that Baroque scholastic authors in Catholic lands, with some exceptions, did not use graphs in their philosophical and theological works. One of the reasons might be that they wished to avoid associations with the infamous ex-Catholic Petrus Ramus (1515–1572) and his movement (Ramism) that was using them extensively.

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Note 2: Existence and being One of the presuppositions of any classification of non-existing items is the distinction between the meanings of ‘there is’ and ‘exists’. Many analytical philosophers, notably those in the Frege-Quine tradition, like to treat the expression ‘there is’ with metaphysical seriousness. In their view ‘there is’ and ‘exists’ are synonymous – they both have “ontological import”. The scholastics would disagree.20 According to them one needs to make a distinction between ‘there is’ (datur, “is given”), which is meant to be as neutral and broad as possible, and narrower predicates, such as ‘exists’, which express a fi rst-order non-trivial feature of individuals.21 Note 3: Categories and transcendentals There is another group of terms one may encounter in scholastic texts, the so-called transcendentals (one, true, good, etc.) that apply to every being. Beside these there are also other terms, such as actual/potential, real/nonreal, perhaps whole/part, one/many, etc. that apply to beings from various categories but not to everything. Although one could perhaps subsume these trans-categorial terms (and whatever they express) under item, it is more convenient and closer to scholastic usage of the words to keep the super-categories and the supertranscendentals separately, not to include them in the same classification. To put the difference between the two in a rather simplistic way one could say that the aim of the categories and super-categories is a general division of what there is and is not, whereas the aim of the transcendentals and super-transcendentals is a general characterisation of what there is and is not.22 20   Cf. Klima’s distinction between soft and hard ontological commitments in pre-Ockhamist philosophy. For Aquinas beings of reason are “objects of thought and signification that are required by a certain kind of semantics but undesirable as objects simpliciter in ontology”. Gyula Klima “The Changing Role of Entia rationis in Mediaeval Semantics and Ontology: A Comparative Study with a Reconstruction”, Synthese 96 (1993): 25. 21   In the latter part of the twentieth century some analytical philosophers came to defend the distinction as well. For instance, Terence Parsons (Nonexistent Objects, New Haven: Yale University Press, 1980) constructed a logic distinguishing the existence predicate (‘E!’) from the quantifier (‘∃’). Another way of dealing with the distinction was developed by Graham Priest (Towards Non-Being: The Logic and Metaphysics of Intentionality, Oxford University Press, 2005), who treats ‘there is’ and ‘exists’ synonymously but interprets them as ontologically neutral. Still, to acknowledge that existence is a property of individuals as such does not imply that it is a non-trivial property. For instance, Peter van Inwagen in Metaphysics, Third Edition (Philadelphia, PA: Westview, 2009, 277–292) argues that existence is a trivial property of individuals (amounting to self-identity). For more on existence “as one of the deep topics in philosophy, if not the deepest”, see William F. Vallicella, A Paradigm Theory of Existence (Dordrecht: Kluwer Academic Publishers, 2002). 22   The traditional idea of transcendentals is one that does not seem to have emerged so far as a topic in analytical metaphysics. With some exceptions: cf. Uwe Meixner, Einführung

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3. THE ROLES OF BEINGS OF REASON IN SCHOLASTIC DEBATES Having classified non-existing items discussed by the scholastics into supercategories and identified the position of beings of reason within the classification, let us take a look now at the roles they were supposed to play in scholastic ontology. Why did the scholastic authors feel the need to talk about them? They used them to address various philosophical puzzles, most conspicuously the problem of nonbeing/intentionality. Hence we start with the latter issue (3.1) and then discuss several other problems related to beings of reason (3.2). 3.1 The problem of non-being/intentionality Thought and language direct our attention to various sorts of objects that either clearly do not exist or whose existence is questionable. This fact is the main source of the problem (or the family of problems) addressed first by Parmenides and discussed by philosophers ever since. From one point of view, the problem concerns non-being including questions such as, What is the status of non-being? Is it in some sense real and mind-independent? What belongs to its domain: past, future, potential, merely possible, impossible, fictitious, and so on? From another point of view, the problem concerns intentionality and intentional being. The pertinent questions in this case include: What is an intentional object, if any? Does a category of intentional objects help to explain our thinking of and about non-being? Several basic strategies have been used to deal with the problem of non-being. First, however, we need to note that the problem of non-being divides into the problem of non-existing objects and the problem of negative facts (also referred to as negative truths). The question whether there are negative facts is more fundamental than the question whether there are non-existing objects. Indeed, negative facts are sometimes taken as evidence that there are non-existing objects but not vice versa. And it is possible to hold that there are negative facts and no non-existing objects, but not vice versa.23 in die Ontologie (Darmstadt: WBG, 2004), 22–29. For an introduction into transcendentals in Baroque scholasticism, see, e.g., Jorge J. E. Gracia and Daniel D. Novotný, “Fundamentals in Suárez’s Metaphysics: Transcendentals and Categories”, in Interpreting Suárez: A Collection of Critical Essays, ed. Daniel Schwartz (Cambridge, MA: Cambridge University Press, 2012), 19–38. 23   At this point one might wonder whether there is a distinction between negative objects and non-existent objects. This question is posed by Meinong, Über Annahmen (Leipzig: J. A. Barth, 1902), 7ff. Examples of putative negative objects that Meinong gives include nothing, immortal, infinite, A without B, not-A. In the end Meinong rejects negative objects as distinct from non-existing objects which I agree with because I do not see any difference between the two: non-redness of an apple is just non-existent redness of it, immortality of the soul is just the non-existent capacity-to-die of the soul, etc. For Meinong’s arguments, see Findlay, Meinong’s theory of objects and values, 81–89.

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With respect to non-being one may adopt views of various sorts. The most radical one holds that there are no negative facts, and consequently no nonexisting objects. A less radical view acknowledges negative facts, but rejects non-existing objects. The least radical position acknowledges both. These views might be further subdivided according to the account they give of negative facts and of non-existing objects. With respect to non-existing objects, drawing on Meinong and Findlay, I would distinguish three accounts: Intentional, Quasi-Being, and Ausser-Being Views.24 The Intentional View explains non-existing objects in terms of mind-made, intentional being. Quine ascribes a version of the Intentional View to (the fictional philosopher) McX and dismisses it as a deception “by the crudest and most flagrant counterfeit”. Quine asks, what can be more dissimilar and unlike than, for instance, Pegasus, an alleged non-existing object, and the Pegasus-idea, the intentional object? If it comes to real objects, Quine contends, such as Parthenon and the Parthenon-idea, we would never be deceived, but when it comes to Pegasus, somehow, confusion sets in.25 Meinong also rejects the Intentional View for “with regard to an innumerable multitude of non-existent objects it may be the case that no one thinks of them or needs to think of them”.26 The Quasi-Being View explains non-existing objects in terms of some peculiar sort of being that pertains to everything. Every object, whether existing or not, whether non-existing contingently or necessarily, has it. As early Russell puts it “being is a general attribute of everything, and to mention anything is to show that it is”.27 Meinong suggests calling this sort of being ‘quasi-being’ for it has no contrary and thus it is a very unusual sort of being. Quine ascribes a version of the Quasi-Being View to Wyman and dismisses it for it offends his “aesthetic … taste for desert landscapes”, and is to him “a breeding ground of disorderly elements” in the case of unactualised possibles and even of contradictions in the case of unactualisable impossibles.28 In the end, Meinong also rejects the Quasi-Being View, although for some time he was, as he says, tempted by it.29 The Ausser-Being View is Meinong’s own child, although in a different context an analogy to it might be seen in Aquinas’s notion of natura absoluta (something which is neither one nor many, neither individual nor universal). Findlay summarises the Ausser-Being View as follows:   See Findlay, Meinong’s theory of objects and values, 42–58.   Willard Van Orman Quine, “On what there is”, Review of Metaphysics 2, no. 5 (1948); reprinted in From a Logical Point of View: Nine Logico-Philosophical Essays, (Cambridge, MA; London, England: Harvard University Press, 1980), 2. 26   Findlay, Meinong’s theory of objects and values, 45. 27   Russell, The Principles of Mathematics, 449. 28   Quine, “On what there is”, 2–5. 29   Findlay, Meinong’s theory of objects and values, 48. 24

25

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[T]he pure object stands beyond being and non-being; both alike are external to it. Whether an object is or not, makes no difference to what the object is. The pure object is said to be außerseiend or to have Außersein: it lies ‘outside’. What the object is … consists in a number of determinations of so-being. … [S]uch determinations are genuinely possessed by an object whether it exists or not … [T]his does not mean that any objects are exempt from being or non-being; the law of excluded middle lays it down that every object necessarily stands in a fact of being or a fact of non-being. … [but] being and non-being have nothing to do with the object as object. 30

This view and its distinctive thesis was dubbed by Ernst Mally ‘The Principle of the Independence of So-being from Being’. It has been the main source of the attraction to Meinong in contemporary philosophy.31 The scholastics usually accepted the Intentional View: non-existent objects are immanent to (=staying within) our mental/intentional activity and they “exist” only as long as somebody actually thinks about them. 32 For the most part, however, this was the view that was simply assumed and not argued for because no alternative was seriously entertained by them.33 3.2 Other problems Although beings of reason have to do primarily with non-being and intentional being, the scholastics used the theory of beings of reason for various other purposes, two of which stand out. First, to account for higher-order predicates (“second intentions”).34 Second, to account for self-contradictory objects, such as square-circles or chimeras.35 (The standard view was that the latter are reducible to negative beings of reason.)   Findlay, Meinong’s theory of objects and values, 49.   Richard Routley (Exploring Meinong’s Jungle and Beyond, Canberra: Australian National University, 1980), for instance, takes up Meinong’s ideas to develop so-called noneism that posits (1) there are non-existent objects, (2) these objects have no existence, being, or whathave-you. The main principle of noneism, which amounts to Mally’s Independence Principle, is the so-called Characterisation Principle: An object has (only those?) properties that it is characterised as having. 32   We can think of it this way: Let us take, for instance, the proposition “The apple is not red”. This proposition is true in virtue of the real/mind-independent fact that the apple is not red. This fact involves a non-existent object, namely the apple’s non-redness, which is, however, not real but purely intentional: the apple’s non-existent redness “exists” only as long as somebody actually thinks about it. 33   There were exceptions: some scholastics seem to come close to a version of Quasi-Being View according to which beings of reason have a peculiar type of (essential) being, which is in some sense mind-independent. 34   For an excellent study of second intentions in late scholasticism, see Larry Hickman, Modern Theories of Higher Level Predicates: Second Intentions in the Neuzeit (München: Philosophia Verlag, 1980). 35   Jennifer Ashworth distinguishes between literary and logical definition of ‘chimera’ in the late fifteenth and early sixteenth century scholastics: “References [in the literary definition] 30 31

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Several kinds of questions were addressed with respect to beings of reason in standard philosophical works in seventeenth-century scholasticism. The issues can be divided into three areas: Nature: What is a being of reason? Do beings of reason exist? Are they to be identified with extrinsic denominations? Why do we construct beings of reason? In what sense do beings of reason exist? Is there a sense of ‘being’ which is common to real beings and beings of reason? Is there a science that studies beings of reason? Causes: What mental powers are involved in conceiving beings of reason? Intellect, will, sense, imagination? Division: What is the division of beings of reason? (negation, privation, relation, ...) What is a negation? What is a privation? What is a relation of reason? Various “additional” issues, which perhaps could be subsumed under the heading ‘nature’, were also treated. For instance: motivation (Why do we need beings of reason?) and methodology (Does the study of beings of reason belong to the domain of logic or metaphysics?). Scholastic authors of the seventeenth century did not care much for semantic problems (the meaning of being-of-reason terms, the truth-value of sentences with such terms, etc.). For a comparison, contemporary philosophers seem to discuss the following issues related to beings of reason: (1) (2) (3) (4) (5) (6) (7) (8)

Non-being (in thought): non-existent objects, negative facts Non-being (in perception): vacuum, holes Intentionality: mental objects, objects of thoughts, semantic content Modality I: possible (i.e. contingently non-existing) objects Modality II: impossible (i.e. necessarily non-existing) objects Temporality: past or future (i.e. now non-existing) objects Fictitiousness: texts, objects of literary fictions Fallibility: objects of errors, mis-representations, illusions

were made to such diverse sources as Ovid, Virgil, Lucian, and the Koran, and the consensus of opinion was that a chimera is a monster formed out of parts of other animals having, on one account, the head of a lion, the torso of a girl, and the tail of a dragon. This was said to be impossible. … [For] chimera was thought of not as a mere hybrid, but as something which had the essences of all the creatures which entered into it, and it was for that reason that it was thought to be an impossible object. … One of the important features of this definition of “chimera” is … [that it] is not thought of as a mere aggregate, a random assemblage of different parts. If the term “chimera” is to refer, it must refer to some one thing. … The logician’s definition of “chimera”, which stems from Buridan, was considerably less picturesque … for it said merely that a chimera is a being composed of parts which cannot be put together, or which it is impossible to put together.” – Jennifer E. Ashworth, “Chimeras and Imaginary Objects: A Study in the Post-Medieval Theory of Signification”, Vivarium 15 (1977): 63.

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(9) Ontologically Suspicious Items I: abstract entities (universals, sets, numbers, etc.) (10) Ontologically Suspicious Items II: extrinsic properties, logical, semantic, social relations, etc. (11) Methodology: fictionalism, ontological commitments, paraphrases The scholastics have much to say about all of these matters, with the exception of (7), which is astonishing, given the extent and detail of Baroque scholastic works.36 In the treatises on beings of reason the scholastics were concerned mainly with (1), (3), (5), (10), and (11), although some authors discussed (8). The remaining issues, i.e. (2), (4), (6), and (9) were extensively treated elsewhere, but not under the heading ‘beings of reason’.37 4. CONCLUSION Thus I have finished a brief description of the ontological framework presupposed by the scholastic debates about beings of reason. First I provided a list of super-categories of various non-existing items one might encounter in scholastics works of the Baroque era. Then I identified the roles that the most important of these items, namely beings of reason, were supposed to play in scholastic ontology. In this paper I have not tried to say whether the scholastic approach to perennial issues of non-being, intentionality and other related issues makes sense for us today or not. My aim was more modest: to take the first step toward making scholastic discussions and concerns somewhat more intelligible to contemporary analytical metaphysicians. Whether contemporary analytical metaphysics can be inspired or challenged by these scholastic debates or whether these debates have merely historical value remains at this point an open question.38

  An explanation for this strange neglect might be the assumption that literary fiction describes possible entities and possible worlds and hence there are no special questions about literary fiction that would not be dealt with in the discussion of possibility. 37   Some of these topics in scholasticism have already been treated in secondary literature; for possibility, see note 13; for vacuum, see Edward Grant, Much Ado About Nothing: Theories of space and vacuum from the Middle Ages to the Scientific Revolution (Cambridge: Cambridge University Press, 1981); for temporality, see Jacob Schmutz, “Juan Caramuel on the Year 2000: Time and Possible Worlds in Early-Modern Scholasticism”, in The Medieval Concept of Time. Studies on the Scholastic Debate and Its Reception in Early Modern Philosophy, ed. Pasquale Porro (Leiden, New York, Köln: Brill 2001), 399–434. 38   The work on this paper received support from the Czech Science Foundation (grant no. P401/11/P020). 36

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BIBLIOGRAPHY Ashworth, Jennifer E. “Chimeras and Imaginary Objects: A Study in the Post-Medieval Theory of Signification”. Vivarium 15, 1977. Canteñs, Bernardo: “Suárez on Beings of Reason: What Kind of Being (entia) are Beings of Reason, and What Kind of Being (esse) Do they Have?” American Catholic Philosophical Quarterly 77 (2003): 171–187. Caramuel y Lobkowicz, Ioannes. Leptotatos. Vigevani: Typis Episcopalibus, apud Camillum Conradam, 1681. Chisholm, Roderick M., ed. Realism and the Background of Phenomenology. New York: The Free Press, 1960. Clarke, Norris W.: “What is Really Real?” In Progress in Philosophy. Philosophical Studies in Honor of Rev. Doctor Charles A. Hart, edited by J. A. McWilliams, 61–90. Milwaukee: Bruce, 1955. Coombs, Jeffrey. “The Possibility of Created Entities in Seventeenth-Century Scotism”. The Philosophical Quarterly 43 (1993): 447–459. Delfino, Robert A., ed. What are We to Understand Gracia to Mean: Realist Challenges to Metaphysical Neutralism. Amsterdam, New York: Rodopi, 2006. Doyle, John P. “Suárez on Beings of Reason and Truth (First part)”. Vivarium 25 (1987): 47–75. ― “Suárez on Beings of Reason and Truth (Second part)”. Vivarium 26 (1988): 51–72. Feser, Edward. “Existential Inertia”. In Metaphysics: Aristotelian, Scholastic, Analytic, edited by L. Novák, D. D. Novotný, P. Sousedík, D. Svoboda, 143–168. Ontos Verlag, 2012. Findlay, John N. Meinong’s theory of objects and values. Second edition. Aldershot: Ashgate Publishing (Gregg Revivals) 1995. Gracia, Jorge J. E. Metaphysics and Its Task: The Search for the Categorial Foundation of Knowledge. Albany, NY: SUNY Press, 1999. ― “Suárez’s Conception of Metaphysics: A Step in the Direction of Mentalism?” American Catholic Philosophical Quarterly 65, no. 3 (1991): 287–309. Gracia, Jorge J. E. and Novotný, Daniel D. “Fundamentals in Suárez’s Metaphysics: Transcendentals and Categories”. In Interpreting Suárez: A Collection of Critical Essays, edited by Daniel Schwartz, 19–38. Cambridge, MA: Cambridge University Press, 2012. Grant, Edward. Much Ado About Nothing: Theories of space and vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press, 1981. Hickman, Larry: Modern Theories of Higher Level Predicates: Second Intentions in the Neuzeit. München: Philosophia Verlag, 1980. Hoffmann, Tobias. Creatura intellecta: Die Ideen und Possibilien bei Duns Scotus mit Ausblick auf Franz von Mayronis, Poncius und Mastrius. Münster: Aschendorff, 2002. Inwagen, Peter van. Metaphysics. Third edition. Philadelphia, PA: Westview, 2009. ― “What is Ontological Category?” In Metaphysics: Aristotelian, Scholastic, Analytic, edited by L. Novák, D. D. Novotný, P. Sousedík, D. Svoboda, 11–24. Ontos Verlag, 2012.

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Klima, Gyula. “The Changing Role of Entia rationis in Mediaeval Semantics and Ontology: A Comparative Study with a Reconstruction”. Synthese 96 (1993): 25–58. Meinong, Alexius. Untersuchungen zur Gegenstandstheorie und Psychologie. Leipzig: J. A. Barth, 1904. ― Über Annahmen. Leipzig: J. A. Barth, 1902. Meixner, Uwe. Einführung in die Ontologie. Darmstadt: WBG, 2004. Millán-Puelles, Antonio. The Theory of the Pure Object. Translated and edited by Jorge García-Gómez. Heidelberg: Universitätsverlag C. Winter, 1996. Novotný, Daniel D. “The Historical Non-Significance of Suárez’s Theory of Beings of Reason: A Lesson From Hurtado”. In Metaphysics of Francisco Suárez (1548–1617): Disputationes metaphysicae in their systematic and historical context, edited by Daniel Heider, Lukáš Novák, David Svoboda (forthcoming). ― “In Defense of Baroque Scholasticism”. Studia Neoaristotelica 6, no. 2 (2009): 209–233. ― “Ens rationis in Caramuel’s Leptotatos (1681)”. In Juan Caramuel Lobkowitz, the Last Scholastic Polymath, edited by Petr Dvořák and Jacob Schmutz, 71–84. Praha: Filosofia, 2008. ― “Prolegomena to a Study of Beings of Reason in Post-Suarezian Scholasticism, 1600– 1650”. Studia Neoaristotelica 3, no. 2 (2006): 117–141. Nuchelmans, Gabriel. Late-Scholastic and Humanist Theories of the Proposition. Oxford, New York: North Holland Publishing Company, 1980. Parsons, Terence. Nonexistent Objects. New Haven: Yale University Press, 1980. Priest, Graham. Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford: Oxford University Press, 2005. Prior, Arthur N. Objects of Thought. Edited by Peter Geach and Anthony Kenny. Oxford: Clarendon Press, 1971. Quine, Willard Van Orman. “On what there is”. Review of Metaphysics 2, no. 5 (1948): 21–38. Reprinted in From a Logical Point of View: Nine Logico-Philosophical Essays. Cambridge, MA; London, England: Harvard University Press, 1980), 1–19. Reicher, Maria. “Nonexistent Objects”, in The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), edited by Edward N. Zalta, http://plato.stanford.edu/archives/fall2010/ entries/nonexistent-objects/. Rescher, Nicholas. Imagining Irreality: A Study of Unreal Possibilities. Chicago, IL: Open Court, 2003. Routley, Richard. Exploring Meinong’s Jungle and Beyond. Canberra: Australian National University, 1980. Russell, Bertrand. The Principles of Mathematics, http://fair-use.org/bertrand-russell/ the-principles-of-mathematics/. First edition Cambridge: At the University Press, 1903. Second edition 1938. Schmidt, Robert W. “The translation of terms like Ens rationis”. The Modern Schoolman 41 (1963): 73–75.

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Schmutz, Jacob. “Juan Caramuel on the Year 2000: Time and Possible Worlds in EarlyModern Scholasticism”. In The Medieval Concept of Time. Studies on the Scholastic Debate and Its Reception in Early Modern Philosophy, edited by Pasquale Porro, 399–434. Leiden, New York, Köln: Brill, 2001. Strawson, Peter F. Individuals. An Essay in Descriptive Metaphysics. New York: Routledge, 1959, repr. 2005. Sousedík, Stanislav. “Pomyslná jsoucna (entia rationis) v aristotelské tradici 17. století”. Filozofický časopis 52 (2004): 533–544. ― “Der Streit um den wahren Sinn der Scotischen Possibilienlehre”, in John Duns Scotus: Metaphysics and Ethics, ed. Ludger Honnefelder, Rega Wood, Mechtild Dreyer (Leiden: Brill, 1996), 191–204. Vallicella, William F. A Paradigm Theory of Existence. Dordrecht: Kluwer Academic Publishers, 2002. Wittgenstein, Ludwig. Tractatus Logico-Philosophicus (New York: Cosimo, Inc., 1922, repr. 2009).

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SECTION II

METAPHYSICAL STRUCTURE

WHAT IS CONSTITUENT ONTOLOGY? Michael J. Loux ABSTRACT This article focuses on one style of ontological explanation – what the author calls the constituent strategy. Very roughly, a proponent of the constituent approach attempts to explain the character of a familiar particular by way of underived sources of character that function as something like parts, components or constituents of the particular. Then, the author examines some contemporary versions of the constituent approach and considers objections frequently raised against them. The claim is that these accounts are unable to accommodate certain facts: (1) that familiar particulars persist through change; (2) that familiar particulars have some of their properties essentially and others merely contingently; (3) that familiar particulars are concrete individuals; and (4) that numerically diverse particulars can have all and only the same properties.

PART I A central focus of metaphysical concern is what Russell calls the character of familiar particulars,1 that is, the fact that individual material objects, plants, animals, and human beings possess properties, fall under kinds, and enter into relations. This talk of possessing properties, falling under kinds, and entering into relations is supposed to be prephilosophical discourse; it is supposed to be the sort of talk we engage in outside the philosophy seminar room. But there is a metaphysical project to which this sort of talk is supposed to give rise – that of providing a theoretical account of the individual facts making up what Russell calls the character of ordinary objects. The project is, of course, a very old one. By the time of Plato and Aristotle, the general structure of the project is pretty well worked out. Its underlying assumption is that familiar particulars have this or that form of character derivatively. As Aristotle puts it, an ordinary object has a given form of character kat’ allo (in virtue of something else).2 So ordinary objects derive their character from other things, and the objects from which they derive their character are or include things that have their own distinctive forms of character nonderivatively

1 2

  B. Russell, Problems of philosophy (Oxford: Oxford University Press, 1912), 92.   Aristotle, Metaphysics VII, 6, 1031 b 13.

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or, as Aristotle again puts it, kath’ hauto (in their own right).3 The metaphysical project is just that of telling the proper story about how this character derivation works itself out. Aristotle tells us that there two different and opposed stories we can tell here.4 According to the first, the underived sources of character are things that exist, as he puts it, “apart from” or “in separation from” the sensible particulars whose character they underwrite; and a sensible particular has a given form of character by entering into some sort of tie or connexion to the appropriate bearer of underived character. On the second story, the privileged bearers of character are immanent in familiar sensible particulars, immanent in the sense of being something like parts, components, or ingredients of familiar particulars, and a familiar particular has the various forms of character it does because it has the appropriate underived bearers of character as parts, components, or ingredients. So there are supposed to be two different strategies for explaining the facts making up the phenomenon of character. Those strategies differ in their accounts of familiar particulars. Defenders of Aristotle’s second strategy attribute to ordinary objects something like a mereological structure, a mereological structure over and above their commonsense mereological structure. As they see it, ordinary objects are composites or wholes made up of parts or components other than their familiar parts or components, and the claim is that it is in virtue of what we can call its metaphysical parts that a familiar object has the character it does. Defenders of Aristotle’s first strategy, by contrast, deny that familiar particulars have this sort of metaphysical structure. They restrict the parts of ordinary object to their commonsense parts. Nonetheless, they insist that ordinary objects stand in a variety of significant nonmereological connexions or ties to things that have character kath hauto or nonderivatively; and they tell us that in virtue of doing so those objects have whatever character they do. In discussing the metaphysical project of character explanation, Nicholas Wolterstorff identifies the two strategies we meet in Aristotle. He dubs them the ‘relational’ and ‘constituent’ approaches.5 I will stick with Wolterstorff ’s labels, but a couple of cautionary notes are in order. First, proponents of Aristotle’s first strategy are, by and large, uncomfortable talking of relations here. As they see it, talk of the relations into which an object enters is talk about its character; but, then, they worry that the appeal to relations in the account of character will be regressive. Accordingly, they speak of the nonrelational ties, connexions, or nexus between ordinary objects and the transcendent sources of character. The suggestion that there is a metaphysically significant contrast between relational   Ibid.   See Met. III, 1, 996 a 15; ibid. 3, 998 a 21–23; ibid. XII, 6, 1080 a 37–b2. 5   See N. Wolterstorff, “Bergmann’s Constituent Ontology”, Nous 4 (1970): 109–134; and “Divine Simplicity”, Philosophical Perspectives 5 (1991): 531–552. 3 4

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and nonrelational hookups is likely to arouse suspicions. At least, it arouses Wolterstorff ’s suspicions; and while himself a defender of the nonimmanentist strategy, he insists that any regress to which the strategy might give rise is nonvicious.6Second, it is not as though what Wolterstorff calls the constituent strategy does without relations in its account of familiar particulars. On that strategy, the various items that count as constituents of a familiar particular are related (or, if one prefers, tied) to one another in ways that help explain the structure and nature of the whole they make up; and obviously defenders of that strategy must concede that a whole or composite stands in something like mereological relations to the underived sources of character that count as its constituents. Neither sort of relation or tie is the kind of relation or tie at work in what Wolterstorff calls his relational strategy, but they are relations or ties nonetheless. It is easy to give examples of the two strategies to which Aristotle and Wolterstorff call our attention. Although the later Russell (the Russell of Inquiry into Meaning and Truth and Human Knowledge: Its Scope and Limits) endorses an immanentist or constituent approach, the Russell of The Problems of Philosophy seems inclined to a relational account of character. He tells us that where familiar particulars agree in character, “they all participate in a common nature or essence”, and he insists that the nature in question “cannot itself exist in the world of sense”. Indeed, it exists “nowhere and nowhen”.7 Russell, of course, is not alone. Among recent ontologists, P. F. Strawson, Roderick Chisholm, and Alvin Plantinga all seem to favour a relational account;8 and, as I have already mentioned, Wolterstorff himself does as well. On the other hand, it is difficult to understand the metaphysical discussions of Locke, Berkeley, or Hume without construing them as exercises in constituent ontology; and more recent proponents of the constituent approach include, besides the later Russell, Gustav Bergmann, David Armstrong, Hector Castañeda, and, most recently, Laurie Paul.9 But, of course, these examples of relational and constituents ontologists aren’t the ones that initially come to mind.   N. Wolterstorff, On Universals (Chicago: University of Chicago Press, 1973), 101–104.   Russell, Problems of Philosophy, 92. 8   See P. F. Strawson, Individuals (London: Methuen, 1959), chapters 5 and 6; R. Chisholm, “Properties and States of Affairs Intentionally Considered”, in Person and Object (La Salle, IL: Open Court, 1976); and A. Plantinga, The Nature of Necessity (Oxford: Oxford University Press, 1974). 9   See B. Russell, An Inquiry into Meaning and Truth (London: Allen and Unwin, 1940); B. Russell, Human Knowledge: Its Scope and Limits (London: Allen and Unwin, 1948); G. Bergmann, Realism. A critique of Brentano and Meinong (Madison: University of Wisconsin Press, 1967); H. Castañeda, “Thinking and the Structure of the World”, Philosophia 4 (1974): 3–40; D. Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997); L. Paul, “Logical Parts”, Nous 36 (2002): 578–596; and L. Paul, “Logical Parts”, Nous 36 (2002): 578–596. 6 7

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The paradigms of the two approaches are found in the work of their two great sources – Plato and Aristotle. While appropriate, the mention, in this context, of Aristotle and Plato can lead us to misunderstand the opposition between our two strategies. We tend to associate the labels ‘Platonism’ and ‘Aristotelianism’ with two opposed views in the debate over universals, the contrast being that between metaphysical theories that reject and those that endorse what is called the Principle of Instantiation, the claim that necessarily every universal is instantiated. But our opposition is not restricted to views about universals. One can deny the existence of universals altogether and still count as a relational or constituent ontologist. Certainly, contemporary trope theorists want to construe themselves as constituent theorists, but they typically deny that there are such things as universals; at least, they typically deny that among the ontologically fundamental items there are such things as universals. If we understand tropes in the standard way, then we will agree that trope theorists endorse the reality of properties or attributes; but note: one can endorse either of our two ontological strategies while denying that there are properties or attributes, even when understood trope-theoretically as particulars. Aristotle gives examples here. He characterises Plato’s successor, Speusippus, as a relationist who construes numbers as separated substances responsible for the character of familiar sensibles,10 and Aristotle takes the theories of his materialist predecessors, both those who endorse a gunk ontology and those who believe in physical simples, as exercises in constituent ontology.11 Presumably, we are to understand these early materialists as construing the relevant material constituents as prior to any properties they might induce. But even when we restrict ourselves to philosophers who accept the existence of universals, it is not as though the Principle of Instantiation is what divides relational and constituent theorists. It is true that constituent ontologists regularly deny the possibility of uninstantiated universals. Think of Aristotle, Bergmann, and Armstrong.12 It is likewise true that relational ontologists typically insist on the existence of uninstantiated or possibly uninstantiated universals. But neither pairing is mandatory. If one thinks that constituent ontologists must accept the Principle of Instantiation, then one is likely confusing the existence and instantiation of a universal. Constituent ontologists are committed to holding that for a first order universal to be instantiated is for it to be a constituent in some familiar particular; but that commitment does not preclude uninstantiated   See Met. XIII, 6, 1080 b 15–16, for what is almost certainly a reference to Speusippus.   See, for example, Met. III, 3, 998 a 30–31, where Empedocles functions as a stand-in for all the materialists. 12   See Aristotle, Categoriae, 11, 14 b 7–14; G. Bergmann, Realism. A critique of Brentano and Meinong (Madison: University of Wisconsin Press, 1967), 43 and 88; D. Armstrong, Universals (Boulder, CO: Westview, 1989) 75–82. 10

11

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universals. Nor is it the case that accepting the existence of uninstantiated universals makes one a relationist. It is rather supposing that for a thing to instantiate a universal is for it to enter into some sui generis nonmerelogical tie or connexion (participation, say, or exemplification) to an underived source of character. One can concede the existence of uninstantiated universals without entertaining that supposition. But not only can a constituent ontologist reject the Principle of Instantiation; it is also possible for a relational metaphysician to endorse the Principle of Instantiation and deny the possibility of uninstantiated universals. Consider a metaphysician who couples a relational account where universals are transcendent sources of character with a general doctrine of selfpredication for universals. We are often told that the middle Plato, at least, was a philosopher who held precisely that combination of views. In any case, it is a mistake to identify our opposition with an opposition over the nature of universals. Another mistake here is to suppose that the two strategies Aristotle and Wolterstorff point to are mutually exclusive and collectively exhaustive. In fact, they are neither. There are treatments of character that are neither relational nor constituent. I am thinking of the views of what I have elsewhere called austere nominalists. They reject the assumption underlying our target project, insisting that we take the facts expressed by our prephilosophical character ascriptions to be metaphysically primitive. The Quine of “On What There Is” is one obvious example.13 Furthermore, a genuinely substantive account of those same facts can instantiate both of our strategies. Consider a theory that construes tropes as constituents of familiar objects responsible for their character, but takes those tropes themselves to be instantiations of what we might call trope types, where those types are, as Aristotle puts it, “separate from” familiar sensible particulars. But notice: such a theory manages to exemplify both strategies only because it is a two step theory. At each stage of explanation, the ontologist must choose between the two explanatory strategies. PART II So there is a genuine opposition here. The philosopher seeking a substantive explanation of the character of familiar particulars seems forced to choose between some version of the immanentist or constituent strategy and some version of the relational strategy. When he points to the two strategies, Wolterstorff tells us that the latter is currently the dominant approach. He is, I think, correct in this. Over the whole history of metaphysics, the constituent approach is arguably the more popular; but in recent years, the relational approach has occupied centre stage. Its influence is felt in virtually every compartment of contemporary philosophy, where talk of exemplifying properties contingently or necessarily, 13   See W. V. O. Quine, “On What There Is”, in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1954), 10ff.

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possibly or actually provides the accepted framework for the formulation of just about any philosophical issue. As we have seen, there are constituent theorists actively at work on the current metaphysical scene, but not only are they in the minority; their efforts are typically viewed with puzzlement or suspicion, if not downright distain. One seldom meets with an explicit statement of the grounds of the prejudice here. But if probed, contemporary metaphysicians will suggest that the constituent approach is, at bottom, incoherent. Its central claim, they will say, embodies something like a category mistake. The claim is that the items that have character nonderivatively are components or parts of familiar particulars. Those items, however, are abstract entities. Familiar particulars, by contract, are concrete objects; and, we are told, no concrete object can be composed of or made out of abstract entities. More than anything else, I think, this line of thinking explains why contemporary metaphysicians have been so ready to endorse the relational approach. To endorse the opposing immanentist or constituent approach, the thinking goes, is to make the category mistake just set out: it is to endorse the incoherent idea that abstract entities can be parts, ingredients, or components of concrete particulars. But as influential as this line of argument may be, it is not altogether convincing. It is just not clear that the distinction between abstract and concrete will bear the weight the line of argument assigns it. For the objection at work here to succeed, we need some principled way of drawing the distinction so that the things philosophers want to call abstract turn out abstract and those they want to call concrete turn out concrete. We need, that is, criteria that give the right results; but, further, those criteria must be such that by reflecting on them we can see why a concrete entity cannot have abstract entities as components or constituents. But what are the criteria here? We might suppose that an entity is concrete iff it has a spatial location and that it is abstract iff it is not concrete.14 One difficulty is that this way of drawing the distinction either gives the wrong results or presupposes controversial philosophical claims that are independent of the issues at hand. Traditional dualists tell us that minds are nonspatial beings; but, then, our criteria force us to hold either that individual minds are abstract entities or that materialism is true. One might try to repair things by saying that an object is concrete iff it either has a spatial location or is made up of temporal parts and abstract iff not concrete.15 Minds have temporal parts, don’t they? But do they all? Orthodox theists will certainly deny this; but, then, the revised criterion either 14   See P. Simons, “Particulars in Particular Clothing”, Philosophy and Phenomenological Research 54 (1994): 553–575 for this sort of criterion. 15   See E. J. Lowe, “The Metaphysics of Abstract Objects”, Journal of Philosophy 92 (1995): 509–524; and chapter 10 of E. J. Lowe, The Possibility of Metaphysics (Oxford: Oxford University Press, 1998) for an account along these lines.

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gives the wrong result by holding that at least one person is an abstract entity, or it forces us to hold an independently controversial claim – atheism. And atheism isn’t the only controversial claim associated with the revised criterion. The account works for finite mental substances only if they really do have temporal parts; but presentists, philosophers who insist that only what exists now or in the present is real, will deny that there are such things as temporal parts. So the account works only if some form of four dimensionalism is true. But there is a further difficulty, one that arises for both ways of drawing the distinction. Properties, we may assume, are abstract entities. Unfortunately, many constituent ontologists will insist that the properties constitutive of a familiar particular have a spatial location: they are where the particular is.16 And these same constituent ontologists will typically go on and say that a single property can wholly and completely occupy more than one spatial location at a time – indeed, as many locations as the familiar particulars it goes to constitute. Of course, the relationists who want to accuse constituent theorists of a category mistake will deny that properties have spatial location; but if the issue of spatial location is one that, in general, divides constituent and relational ontologists, the assumption that properties have no spatial location can hardly play a role in an argument designed to adjudicate between the two approaches. In any case, the contrast between abstract and concrete is problematic. Some philosophers respond to the problems by resorting to lists or inventories. As Peter van Inwagen suggests, the motivating theme is much like that Strawson and Grice expressed with regard to the analytic/synthetic distinction.17 Even if we cannot identify criteria for drawing it, the distinction gets vindicated by the fact that we tend to agree about which items fall under the respective headings. Properties, propositions, and relations are all abstract; whereas, persons, plants, animals, and atoms are all concrete. I have sympathy with this move. Nonetheless, I cannot resist pointing out that there is less agreement about the classification than sanguine philosophers might have us believe. Trope theorists, for example, disagree about whether tropes are abstract or concrete; but most trope theorists want to deny that, in the final analysis, there is anything besides tropes.18 Likewise, metaphysicians disagree about the status of events: some think they are concrete; others, abstract.19 Still, there are ontologists who insist that events exhaust the 16   See, for example, A. Donagon, “Universals and Metaphysical Realism”, Monist 47 (1963): 211–247. 17   See P. van Inwagen, “A Theory of Properties”, Oxford Studies in Metaphysics 1 (2005): 107–138. 18   D. C. Williams, “Elements of Being”. Part One. Review of Metaphysics 7 (1953): 3–18; and P. Simons, “Particulars in Particular Clothing”, Philosophy and Phenomenological Research 54 (1994): 553–575 take opposing sides on the status of tropes. 19   See, for example, D. Davidson, “Events as Particulars”. Nous 4 (1970): 25–31; and R. M. Chisholm, Person and Object (La Salle, IL: Open Court, 1976) for this opposition.

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inventory of what there is. Again, we are all familiar with the claim that states of affairs or facts are the ultimate realities; nonetheless, there is disagreement about whether such things are abstract or concrete.20 Let us assume, however, that such disagreements can be resolved and that there is a genuine distinction here, one given by the traditional inventories. A difficulty remains. Once we acquiesce in the Strawson/Grice strategy, we are left without any account of just what makes a thing abstract or concrete; and in the absence of that sort of account, we lack the resources for showing why it should be problematic to think that concrete entities are composed of or constituted by abstract entities. At this point, the objector will likely retrench and make one kind of concrete entity – material particulars – the focus of the objection. The parts of a material particular, the revised objection will go, are one and all material; but only at the risk of a category mistake can we suppose that things like properties are material objects. Constituent ontologists, however, want to claim that the properties of a material particular count as its components or constituents, so we once again get the conclusion that constituent ontologists are guilty of some sort of category mistake. As we have noted, it is not quite accurate to say that all constituent ontologists want to make the properties of a material particular its constituents;21 nonetheless, many do. But none of those who do will find the revised objection any better than the original. The difficulty, they will claim, is that the revised objection mistakenly identifies the constituents of a material particular with its commonsense parts. Constituent ontologists, however, are anxious to distinguish the two; and while conceding that the latter must be material, they will deny that this is true of the former. As early as Aristotle, we meet with this distinction. He distinguishes between “the parts that measure a thing according to quantity” and “the parts of which its substance is composed” (1034 b 33–35). The former are the commonsense parts of a thing; the latter, its constituents or what we might call its metaphysical parts. Now, parts of both sorts are less than, fall short of the wholes they compose; but Aristotle is telling us that the two sorts of parts fall short in different ways. Each of the commonsense parts of a thing is spatially less than the thing: the primary place each occupies is a proper part of the primary place occupied by the whole. Accordingly, the part can be used to provide a spatial measure of the whole, so that we can speak of the whole as being so many feet long, so many cubits wide, or so many hands high. Aristotle’s talk about the substance of a thing, by contrast, is talk about its being what it is, its being the kind of thing 20   Chisholm, Person and Object, and Armstrong, A World of States of Affairs, hold opposed views on the status of states of affairs. 21   Another exception is Aristotle who denies that the accidents predicated of a substance are among its constituents. They are constituents of the associated coincidentals, but they are not predicated of them. See M. J. Loux, Metaphysics, 3rd ed. (London: Routledge, 2006).

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it is. Hence, the idea at work in talk about the substantial or metaphysical parts of a thing is that each such part involves or induces a form of being that is less than or a component of the overall form of being displayed by the whole thing. While Aristotle would concede that the commonsense parts of a thing are one and all material, he would insist that its substantial or metaphysical parts can include an item that is not properly material at all. Unlike Aristotle (who is a presentist), David Lewis uses a temporal parts framework as the backdrop for his characterisation of what I am calling the constituent approach and speaks of nonspatiotemporal parts; and while he thinks that the spatiotemporal parts of a material object are every bit as material as the object itself, he takes it to be a defining feature of the constituent approach that nonmaterial things like properties can count as the nonspatiotemporal or metaphysical parts of a material object.22 Lewis, of course, does not himself favour a constituent approach to character. Indeed, he denies that we need to give a substantive account (whether of the relational or constituent variety) of the phenomenon; but he recognises that constituent ontology does not, from the very start of the project, harbor a category mistake. And the idea that there is a contrast between the commonsense material parts of a thing and its metaphysical parts or constituents is shared by every practitioner of the constituent strategy;23 nor is it any accident that this is so. Recall that the proponent of this strategy makes the constituents of a thing responsible for its overall character; but its commonsense mereological structure is just one aspect of that character. And not just the arrangement of a thing’s commonsense parts is due to a thing’s constituents. Constituent ontologists will say that the intrinsic nature of the parts themselves is due to the constituents of the whole, or they will say that those parts have constituents of their own that account for their nature. In either case, we have the result that, in the story the constituent ontologist tells, constituents or metaphysical parts turn out to be prior to commonsense material parts. We may concede that the distinction serves to answer the revised objection, but if we are to take the constituent approach seriously, we will want to know more about constitution. As a start, we can identify its formal properties. If we restrict ourselves to what might be called the proper constituents of a thing, we can agree that the relation of constituent to whole is irreflexive, asymmetrical, and transitive. Functionally, it is a relation of composition, so it might be tempting to identify it with other more familiar composition relations, but the temptation should be resisted. It is not the relation tying the members of a set to the set: 22   See D. Lewis, “New Work for a Theory of Universals”, Australasian Journal of Philosophy 61 (1983): 343–377. 23   See, for example, L. A. Paul, “Logical Parts”, Nous 36 (2002): 578–596, where we fi nd talk of “qualitative” or “logical parts”.

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familiar particulars aren’t sets. Nor is it the relation tying properties to the conjunctive property whose conjuncts they are. Many constituent ontologists refuse to restrict the constituents of familiar particulars to their properties; and even those that do accept the restriction will typically deny that familiar particulars are themselves properties, whether molecular or atomic. More plausible is the suggestion that the constituent/whole relation is a case of the relation of composition at work in what is properly called mereology, the logic of parts and wholes; but even this suggestion has its problems. The relation in question (called summing or fusion) is just too generous; and in this respect it agrees with both set-theoretical composition and the composition involved in property conjunction. In all three cases, if it is possible for a given plurality of objects to compose the relevant whole, then the plurality does compose it. Not so in the case of the objects constituting a familiar particular. It is possible for those objects to exist without constituting the particular: they play their constitutional role only contingently, and constituent ontologists routinely take this fact to underlie the contingency of the constituted particular. Now, some constituent ontologists will claim that we can supplement the concept of fusion with restrictions which ensure that the only composites are those we meet in the case of actually existing ordinary objects.24 But whether they endorse a thoroughly mereological interpretation of the constituent/whole relation, constituent ontologists will agree that if a plurality of objects, a … n, constitutes a particular, x, then it does so only contingently. Nonetheless, they will also agree that the resulting whole, x, has necessarily the property of having all and only a … n as constituents. Call this claim Constituent Essentialism. It needs to be distinguished from what is called Mereological Essentialism, the claim that a thing has each of its commonsense parts necessarily. It is plausible to think that constituent ontologists are free to disagree about the latter claim; but what I have called Constituent Essentialism is something like a framework principle for constituent ontologists. They hold that familiar particulars are nothing but composites of their constituents; but, then, it is difficult to understand how a constituent ontologist could hold that it is possible for a particular to have constituents other than those it does. Given a different group of constituents, we would have the existence of a different composite and, therefore, a different familiar particular. So it is a structural fact about constituent ontologies, first, that the items constituting a given particular do so only contingently and, second, that the particular has the constituents it does necessarily. Constituents ontologists will typically add that it has those constituents uniquely; or, at least, they will add that it has uniquely the property of having just those constituents in just the order in which they are found there; and they will claim that this, like the claim 24

  See again Paul, “Logical parts”.

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I have dubbed Constituent Essentialism, is a framework principle for this style of metaphysical explanation. On this view, all there is to a familiar particular is its constituents; but, then, it should be impossible for numerically diverse objects to be made up of identical constituents identically arranged. I will call this claim the Principle of Constituent Identity and will formulate it as the claim that necessarily, for any objects, x and y, if x and y have all and only the same constituents in precisely the same order, x and y are identical. PART III Towards characterising the concept of constitution at work in immanentist theories, I have said that the relation of constituent to whole is a compositional relation that is irreflexive, asymmetrical, and transitive. Furthermore, I have said that while the constituents of a thing only contingently constitute it, the thing has its constituents in the appropriate order both necessarily and uniquely. This characterisation is very general. The concept of constitution I have delineated is one ontologists of quite different stripes will be comfortable making the centrepiece of their disparate theoretical frameworks. But that is how it should be. Theories as different as Berkeley’s phenomenalism and Aristotle’s hylomorphism count as constituent ontologies. In our own day, the constituent strategy has taken three main forms. There are (1) theories that construe a familiar par ticular as a bundle of compresent, but repeatable properties, the properties we prephilosophically associate with the particular;25 (2) theories that posit, in addition to the repeatable properties making up a thing, a categorically different kind of constituent, a constituent that serves as subject, possessor, or bearer of those properties;26 and (3) theories that restrict the constituents of a familiar object to nonrepeatable properties or what have become known as tropes.27 Now, I have argued that attempts by relationists to show the enterprise of constituent ontology incoherent fail. But even those who would deny that the enterprise is fatally flawed from the start find problems in the various theories that make up the recent history of constituent ontology. To set the stage for the discussions that will follow, let me close by reminding you of some of these problems. Persistence through change has been thought to present problems for constituent theorists. Where a thing changes, the argument goes, there is a variation in the properties associated with the thing. Constituent theorists, however, construe the properties associated with a thing as its constituents; but, then 25   See Castañeda, “Thinking and the Structure of the World”; L. A. Paul, “The Context of Essence”, Australasian Journal of Philosophy 82 (2004): 170–184; and Paul, “Logical Parts”. 26   See Bergmann, Realism, and Armstrong, A World of States of Affairs. 27   See Willliams, “Elements of Being”, Simons, “Particulars in Particular Clothing”, and K. Campbell, Abstract Particulars (Oxford: Blackwell, 1990).

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they are committed to denying that the composite emerging from a change is numerically identical with the composite that entered the change. Persistence, however, requires identity, so we get the conclusion that constituent ontologists cannot accommodate our prephilosophical belief that ordinary objects persist through change. What underlies the problem here is, of course, constituent ontologists’ commitment to what I have called Constituent Essentialism. It is because they take a composite to have its constituents necessarily that they must deny identity through change. But not only does that doctrine preclude identity through change; it seems as well to make it impossible for constituent ontologists to do justice to the distinction between the properties essential to a familiar particular and those that are merely contingent. All the properties of a thing appear to turn out essential on the constituent approach. Two comments here. First, although closely related, the two problems are different. The first bears on variation and persistence through time; the second, on variation and persistence through what we might call the modal dimension. The second problem concerns the various ways a particular could have been otherwise; for the formulation of that problem it is not required that the particular realise the relevant possibilities by actually undergoing a change. In any case, the actual practice of constituent ontologists implies that the two problems are different. Where they deal with both, constituent ontologists deal with them in different ways.28 Second, while conceding that our second problem may arise for both bundle theorists and trope theorists, one might deny that the same holds for substratum theorists. After all, do they not tell us that the ultimate bearers of properties are particulars that are bare or thin? Yes, but our second problem bears not on the relationship between a substratum and the properties compresent with it, but on the relationship between the whole familiar particular and the properties that constitute it. For the substratum theorist, no less than the bundle or trope theorist, that relationship is governed by Constituent Essentialism. So our first two problems would seem to create difficulties for all three forms of constituent ontology. But each of the different patterns faces problems of its own. Trope theorists, for example, face problems about the individuation of items from their favoured category.29 Although they speak freely and almost casually about this or that trope, the fact is that it is not altogether clear just what a trope is. Take the colour of the desk top on which I am now writing. Presumably, it is a single discrete trope. But what happens when I cut the desk top in two? Do I thereby bring two colour tropes into existence? If I do, then what was beforehand not a trope now is one; but how can what was not a trope become one? Well,   See, for example, Paul, “Logical Parts”, and “The context of Essence”.   These problems are clearly presented in Campbell, Abstract Particulars, chapter 6.

28 29

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perhaps, we should say that the two colour tropes were there beforehand. The difficulty, of course, is that I could go on and cut each of the two new sections of the original desk top in two. So were there really four rather than just two colour tropes there before the first division? It is not clear that any answer we might give here is satisfactory. Defenders of theories of the first sort I mentioned tell us that familiar particulars are bundles of repeatable properties. On their theory, the “materials” out of which a familiar particular is composed are one and all properties, but what they compose is an individual that has those properties, what we might call a propertied individual. But they owe us an explanation of just how we are supposed to get the propertied individual from “materials” that are restricted to properties. How is it that we get a φ-er, a thing that is φ, from the property φ-ness? The response, doubtless, will be that individuals arise out of the agglomeration of properties. We begin, so to speak, with one property, add another, add still another, and what ultimately emerges is an individual having all those properties. But why should we suppose that agglomeration yields the multi-propertied individual? Why not suppose instead that what results from the agglomeration is, say, just the conjunctive property whose conjuncts are all the various properties that have been agglomerated?30 And there is a more familiar problem that dogs traditional bundle theorists. They tell us that a thing’s character hinges on its repeatable properties. Those properties are its constituents. They further tell us that different familiar particulars can share a given form of character and that where this happens a single property is a constituent of the numerically different particulars. As constituent ontologists, however, they are committed to what I have called the Principle of Constituent Identity. But, then, they are committed to some strong version of the Identity of Indiscernibles, the principle that necessarily if an object, a, and an object, b, have all and only the same properties, a is numerically identical with b. The difficulty, of course, is that there appear to be counterexamples to the appropriate version of that principle.31 Substratum theorists appeal to the apparent counterexamples in defence of their own version of the constituent approach. 32 They argue that what the possibility of diverse, but qualitatively indiscernible objects shows is that each ordinary object has a constituent that is idiosyncratic to a single composite and that functions as the literal possessor of the properties that enter into the composite. But, they insist that only constituents that have no properties essentially are suited to play the diversifying role here. So we get the doctrine of 30   To my knowledge, the only bundle theorist who explicitly responds to this problem is Castañeda, “Thinking and the Structure of the World”. 31   See, for example, M. Black, “The Identity of Indiscernibles”, Mind 61 (1952): 153–164. 32   See, for example, E. B. Allaire, “Bare Particulars”, Philosophical Studies 14 (1963): 1–8.

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the bare or thin particular; and most philosophers think that there are serious problems attaching to that doctrine.33 So even if there is no single a priori objection that shows the constituent project to be doomed from the start, there are problems aplenty for constituent ontologists. If they are to convince us of the viability of their project, they need to address there problems. Let’s see how they fare.

BIBLIOGRAPHY Allaire, Edwin B. “Bare Particulars”. Philosophical Studies 14 (1963): 1–8. Aristotle. The Complete Works of Aristotle: The Revised Oxford Translation. Edited by J. Barnes. 2 vols. Bollingen Series. Princeton, NJ: Princeton University Press, 1984. Armstrong, David. A World of States of Affairs. Cambridge: Cambridge University Press, 1997. ― Universals. Boulder, CO: Westview, 1989. Bergmann, Gustav. Realism. A critique of Brentano and Meinong. Madison: University of Wisconsin Press, 1967. Black, Max. “The Identity of Indiscernibles”. Mind 61 (1952): 153–164. Campbell, Keith. Abstract Particulars. Oxford: Blackwell, 1990. Castañeda, Héctor-Neri. “Thinking and the Structure of the World”. Philosophia 4 (1974): 3–40. Chisholm, Roderick M. Person and Object. La Salle, IL: Open Court, 1976. ― On Metaphysics. Minneapolis: University of Minnesota Press, 1989. Davidson, Donald. “Events as Particulars”. Nous 4 (1970): 25–31. Donagon, Alan. “Universals and Metaphysical Realism”. Monist 47 (1963): 211–247. Inwagen, Peter van. “A Theory of Properties”. Oxford Studies in Metaphysics 1 (2005): 107–138. Lewis, David. “New Work for a Theory of Universals”. Australasian Journal of Philosophy 61 (1983): 343–377. Loux, Michael J. Metaphysics. Third edition. London: Routledge, 2006. ― “Aristotle’s Constituent Ontology”. Oxford Studies in Metaphysics 2 (2007): 207–250. Lowe, E. J. “The Metaphysics of Abstract Objects”. Journal of Philosophy 92 (1995): 509–524. ― The Possibility of Metaphysics. Oxford: Oxford University Press, 1998. Paul, Laurie A. “Logical Parts”. Nous 36 (2002): 578–596. ― “The Context of Essence”. Australasian Journal of Philosophy 82 (2004): 170–184. 33   I discuss this issue in my Metaphysics, chapter 3. For a reply, see T. Sider, “Bare Particulars”, Philosophical Perspectives 20 (2006): 387–397.

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Plantinga, Alvin. The Nature of Necessity. Oxford: Oxford University Press, 1974. Quine, Willard Van Orman. From a Logical Point of View. Cambridge, MA: Harvard University Press, 1954. Russell, Bertrand. An Inquiry into Meaning and Truth. London: Allen and Unwin, 1940. ― Human Knowledge: Its Scope and Limits. London: Allen and Unwin, 1948. ― Problems of Philosophy. Oxford: Oxford University Press, 1912. Sider, Theodore. “Bare Particulars”. Philosophical Perspectives 20 (2006): 387–397. Simons, Peter. “Particulars in Particular Clothing”. Philosophy and Phenomenological Research 54 (1994): 553–575. Strawson, Peter Frederick. Individuals. London: Methuen, 1959. Williams, Donald C. “Elements of Being”. Part One. Review of Metaphysics 7 (1953): 3–18. Wolterstorff, Nicholas. “Bergmann’s Constituent Ontology”. Nous 4 (1970): 109–134. ― On Universals. Chicago: University of Chicago Press, 1973. ― “Divine Simplicity”. Philosophical Perspectives 5 (1991): 531–552.

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ELEMENTAL TRANSFORMATION IN ARISTOTLE: THREE DILEMMAS FOR THE TRADITIONAL ACCOUNT Anne Siebels Peterson ABSTRACT According to the traditionally held interpretation of many texts in Aristotle, that which plays the role of substratum for elemental transformation is a matter with no essence of its own, prime matter. I argue that the traditional account of elemental transformation, in its appeal to prime matter, conflicts with three doctrines which many commentators would take Aristotle himself to endorse. First, it conflicts with that variety of essentialism according to which everything that exists has an essence which marks it out as what it is. Second, it conflicts with actualism. And third, it conflicts with the view that Aristotle’s four elements are to be understood in accordance with that version of the constituent ontological strategy according to which one constituent of a whole serves as subject and the other as predicate. I argue that these three conflicts are such that satisfactory resolutions of them would involve controversial metaphysical commitments not usually associated with the traditional account. My aim is not to undermine the traditional account, but rather to show that it should not be regarded as a general framework that can be shared by many widely variant accounts of elemental transformation and of the place of prime matter in Aristotle’s ontology. The traditional account is far more theory-laden than it is often taken to be.

1. INTRODUCTION According to the traditional account of elemental transformation in Aristotle, prime matter is that substratum common to the four elements (fire, air, earth, and water) and paired, in each case, with a different pair of the elemental contraries. Furthermore, in any case of transformation between two elements, prime matter serves as a pre-existent and persistent substratum. As C. J. F. Williams puts it: It is not heat or cold – the abstract qualities – which change into each other, but the single underlying nature which takes on now one, now the other, of the pair of contraries. Again we have something which remains when one element changes into another, i.e. prime matter.1

Thus, in the transformation of water into fire, the contraries that characterise water (the cold and the wet) are replaced by the contraries that characterise 1   C. J. F. Williams, Aristotle’s De Generatione et Corruptione (New York: Oxford University Press, 1982), 213.

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fire (the hot and the dry); but the same prime matter persists throughout as the substratum of both the pre-existent and the generated element in turn. The traditional account’s insistence on a persistent substratum in any case of transformation derives from its adherence to the claim that a persistent substratum is necessary in order to free any case of coming to be from the Parmenidean argument, given at Physics I, 8, 191 a 25–34,2 for the incoherence of coming to be.3 The argument I want to make is that the traditional account’s notion of prime matter as a persistent substratum for elemental transformation conflicts with the following three metaphysical doctrines also often associated with Aristotle: a certain variety of essentialism, actualism, and the view that the four elements are to be understood according to a certain variety of the constituent ontological strategy. 2. PRIME MATTER: A PROBLEMATIC DOCTRINE Since the same aspect of the traditional account’s notion of prime matter is the source of its conflict with each of these doctrines, it will be important to have a grasp on what this problematic aspect is. Prime matter is posited by the traditional account as the substratum for the elements, which are endowed with the lowest-level essences there are (after all, if there were any lower-level essences, the things endowed with those essences would be the true elements). As Friedrich Solmsen puts it, “There are no bodies or substances in Aristotle’s physical system that could be regarded as more primitive and simple than the elements; if there is anything at all of this description, it can only have ‘potential’ reality.”4 Prime matter, on the traditional account, is, in virtue of itself, pure potentiality. We can say what prime matter happens to be (hot and wet, cold and dry, etc.), as the man happens to be musical; or we can say what prime matter is potentially (fire, earth, air, or water), as flesh is potentially some kind of animal; but, since it is the substratum for the things with the lowest-level essences there are, we cannot say   All references to Aristotle’s work are taken from the Complete Works of Aristotle, ed. J. Barnes. (Princeton, NJ: Princeton University Press, 1984). 3   The point, according to proponents of the traditional account, is that if nothing of the terminus a quo (that which pre-exists the case of coming-to-be), a, persists in the terminus ad quem (the thing that comes to be), b, then we have a case of a’s being annihilated and replaced by b rather than a case of a’s genuinely coming-to-be (or in the case of elemental transformation, being transformed into) b. Just as, in the case of the man’s coming to be musical, described at Physics I, 7, 189 b 34–190 a 21, we must have the very man who was unmusical persisting as the subject for the predication of the accident musicality, so in the case of substantial change we must have something of the terminus a quo persisting as the substratum of the terminus ad quem. See, e.g., Michael Loux, “Aristotle and Parmenides: An Interpretation of Physics A.8”, Proceedings of the Boston Area Colloquium in Ancient Philosophy 8 (1992): 302–308. 4   Friedrich Solmsen, “Aristotle and Prime Matter: A Reply to Hugh R. King”, Journal of the History of Ideas 19 (1958): 245. 2

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what prime matter is in virtue of itself.5 Prime matter is essenceless.6 As David Bostock writes, prime matter is for Aristotle “all things potentially, which is just another way of saying that there is nothing which it has to be.”7 H. M. Robinson describes prime matter as: … a bare ‘stuff ’, lacking all positive determinations, which is the matter of the elements and which makes elemental change possible. This prime matter is nothing but a potentiality which can exist only as actualised in some determinate matter – i.e. in one of the elements – and which is what persists when one contrariety is replaced by another and the identity of an element changes.8

It is this thesis that the persistent substratum for elemental transformation is, in virtue of itself, pure potentiality – that it is essenceless – that spells trouble for the traditional account with respect to the three doctrines just mentioned.9

5   On the other hand, we can say what it is to be for each of the four elements. To be fire is to be prime matter that is hot and dry; to be air is to be prime matter that is hot and wet; etc., employing the model of Metaphysics VIII, 2, 1043 a 1–28. Here I am sensitive to the fact that the elements are probably not supposed to be full-fledged substances, as Metaphysics VII, 16, 1040 b 8–9 affirms: “for none of them is one, but they are like a heap before it is fused by heat and some one thing is made out of the bits.” Still, we can say what something is, according to the model of VIII, 2, even if that thing is not a full-fledged substance; Aristotle tells us this at Metaphysics VIII, 2, 1043 a 3–7. We do this by giving a form-matter predication: “E.g. if we had to define a threshold, we should say ‘wood or stone in such and such a position’, and a house we should define as ‘bricks and timbers in such and such a position’.” 6   Indeed, it seems that Aristotle would not accept a view according to which the substratum for the elements is some kind of stuff that does have an essence, rather than essenceless prime matter – for then there would no longer be four elements, but only one. The four elements would not be genuine elements, because they would not be at the lowest level of the hierarchy of being – they would be composites made up of the one true element, their substratum. And Aristotle finds strict monism of this variety utterly objectionable, though he also finds strict pluralism objectionable – his view is supposed to balance somehow between these extremes (see On Generation and Corruption II, 7, 334 a 22–334 b 8); but the argument to this effect lies beyond the scope of this paper. For Aristotle’s arguments against strict monism, see, for example, On Generation and Corruption I, 1, 314 b 1–5 and II, 7, 334 b 2–8. 7   David Bostock, Space, Time, Matter, and Form: Essays on Aristotle’s Physics (Oxford University Press, 2006), 34. 8   H. M. Robinson, “Prime Matter in Aristotle”, Phronesis 19 (1974): 168. 9   There have been many proposed emendations to the traditional account, which may or may not harbor a satisfactory response to the difficulties I will lay out. I will consider a few of these views throughout the paper, although to focus on them would take me too far afield from my main aim here, which is to explore some difficulties that arise for the traditional account as it stands.

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3. PRIME MATTER AND ARISTOTELIAN ESSENTIALISM Consider first that variety of essentialism according to which every genuine being is such that, among those properties which belong to it necessarily, one property marks it out as what it is, endowing it with an essence.10 In other words, for any x, if x lacks an essence, then x is not a genuine being. I will refer to this view as Aristotelian essentialism.11 At first glance, it might seem that there is no trouble here for the proponent of the traditional account of elemental transformation who wants to retain Aristotelian essentialism, as long as the proponent of that account does not hold that prime matter is a genuine being. But it is not clear that the proponent of the traditional account can make this move. The trouble arises from the traditional account’s thesis that in any case of elemental transformation, the prime matter of the pre-existent element must persist as the substratum of the newly generated element. In order for the prime matter of the pre-existent air to count as genuinely persistent, it would seem, it must be identical to the prime matter of the generated fire in the strictest sense, that of numerical identity (sameness in any more generic sense, i.e. in species or genus, would not guarantee that anything has persisted).12 However – and here is where the conflict with Aristotelian essentialism arises – only genuine beings are subject to claims about   See Categories 5, 2 b 31–35: “For if one is to say of the individual man what he is, it will be in place to give the species or the genus (though more informative to give man than animal); but to give any of the other things would be out of place – for example, to say white or runs or anything like that.” 11   This variety of essentialism contrasts, for example, with that defended in Alvin Plantinga, “Actualism and Possible Worlds”, in Essays in the Metaphysics of Modality, ed. M. Davidson (New York: Oxford University Press, 2003), 111–114. 12   See Frank Lewis, “What’s the Matter with Prime Matter?” in Oxford Studies in Ancient Philosophy 34, ed. Sedley (New York: Oxford University Press, 2008), 137: He argues that the substrata of a pre-existent element and of a generated element count as the same persistent matter because they share the property of “being prime matter”. I find this view unsatisfactory, because the persistence of a property does not guarantee the persistence of what has that property; we have no guarantee, on this view, that the same prime matter has persisted. The prime matter of the pre-existent element might share the property of being prime matter with the prime matter of the generated element even if the prime matter of the pre-existent element is destroyed in the course of the transformation. For an argument that the persistence of generic physical properties of prime matter is sufficient to guarantee its persistence, see Theodore Scaltsas, Substances and Universals in Aristotle’s Metaphysics (New York: Cornell University Press, 1994), 25: “If there is no kind of matter that survives radical transformation, how can one claim that it is matter that is surviving at all? The answer to this question is that, although the particular physical properties do not remain the same, there are generic physical properties that do.” On this view, because the pre-existent matter in a case of elemental transformation is (say) hot, while the matter of the generated element is cold, we do not have the same kind of matter (since these do not share the same specific properties); but we do have the same matter, because both will always have the same generic properties of being thermal, hydral, spatial, and causal (26–27). But this view faces the same problem that undermines Lewis’s view: the persistence of a property does not guarantee the persistence of what has that property. 10

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numerical identity. Hence, to say that prime matter, which lacks any essence, is subject to claims about numerical identity is to say that there is a genuine being with no essence at all. But that contradicts Aristotelian essentialism. I am sympathetic with the hope that a proponent of the traditional account might circumvent this conflict with Aristotelian essentialism by focusing on the fact that prime matter is not supposed to be a full-fledged being, and maintaining that it is therefore not subject to being parcelled out into numerically identical or distinct parcels, and therefore is not subject to claims about numerical identity or distinctness. But this move alone would not free the traditional account from difficulty. For the question would become, what is the criterion for the persistence of prime matter throughout a case of elemental transformation, if not that of numerical identity throughout the transformation? If we give up on the idea that prime matter is subject to claims about numerical identity, do we not thereby give up on the idea that it can genuinely persist? Alternatively, we might see the problem in terms of numerical distinctness, since giving up numerical identity as a concept that applies to prime matter requires giving up numerical distinctness as a concept that applies to it as well. And without the idea that the prime matter of numerically distinct elements is itself numerically distinct, it would come out trivially true that the prime matter involved in any given transformation persists; for that prime matter would not be distinct from any other prime matter, and so it could only fail to persist if all the prime matter there is failed to persist. But surely the traditional account’s thesis that there must be a persistent substratum for any case of elemental transformation is not supposed to be a triviality. So we have a dilemma: given the usual way of understanding persistence, in terms of numerical identity, the traditional account conflicts with Aristotelian essentialism. Perhaps a view could be devised which provides a criterion for persistence of prime matter without appealing to numerical identity and of distinctness of prime matter without appealing to numerical distinctness. Such a view would obviate this dilemma. Or perhaps we might, as Bostock argues, be able to do without a universally applicable criterion for the persistence of matter.13 However, if I am right that the traditional account 13   See Bostock, Space, Time, Matter, and Form: Essays in Aristotle’s Physics, 44: According to Aristotle’s theory, Bostock argues, “the appropriate criterion of identity for matter is left open. It is constrained…but not in a way which tells us how to apply it in all cases.” It is constrained, he thinks, by Aristotle’s thesis that “The same matter is always conserved, which is to say: If we take any boundary which is not crossed by matter over a certain period, then the matter inside that boundary will be the same matter all through the period. Thus, within such a boundary, new matter is never created, or old matter destroyed, either ‘out of or into nothing’ or by ‘increasing or decreasing’ the quantity of matter already there.” But this constraint could not allow us to determine whether we have the same matter; to say that it could would be circular, as Bostock points out on the same page. For we could only establish that a certain boundary is not crossed by matter over a period of time if we already know that the matter inside the boundary is the same matter throughout the period.

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must adhere to some such view in order to cohere with Aristotelian essentialism, then it is far more theory-laden than many appeals to it would like to recognise, and because of this it will not be able to serve in the way in which it is often used: as a general framework employed by many widely variant accounts of the specifics of elemental transformation with different understandings of precisely where prime matter fits into Aristotle’s ontology. Rather, to accept the traditional account of elemental transformation will require one either to reject Aristotelian essentialism or to accept an understanding of elemental transformation with significant theoretical commitments – one that can explain the persistence of prime matter without appealing to its numerical identity. 4. PRIME MATTER AND ACTUALISM A second doctrine with which the traditional account conflicts is actualism, the view that something must actually be to be at all.14 Although, according to the traditional account, prime matter will always have some actuality – it will always be either actually hot and dry, actually hot and wet, actually cold and dry, or actually cold and wet – it can only have these properties accidentally. Taken by itself, apart from any merely accidental properties, prime matter will lack any actuality whatsoever – it will be pure potentiality. But then given actualism, prime matter, taken by itself, does not exist. But prime matter, taken by itself, is just what the traditional account appeals to as the substratum of each of the elements. If, taken by itself, it does not exist, then neither the pre-existent nor the generated element in a case of elemental transformation even has a substratum. And if these do not even have a substratum, then it follows, trivially, that they do not share a substratum – that is, it follows, contrary to the traditional account, that there is no persistent substratum for elemental transformation.15 Thus, in its With regard to the aim of this paper, the point to note here is this: If a view like Bostock’s, according to which there is no determinate criterion of persistence for prime matter, is the best that can be done as far as understanding prime matter’s persistence goes, then this would be a significant theoretical commitment; but given my argument, the traditional account could not maintain Aristotelian essentialism without making it. 14   There is support for thinking that this too is a doctrine endorsed by Aristotle. For example, Aristotle writes at Metaphysics IX, 3, 1047 b 1–2: “For of non-existent things some exist potentially; but they do not exist, because they do not exist in fulfilment”. See also Metaphysics XIV, 2, 1089 a 28–29: “the false is said not to be and so is the potential”. 15   Aristotle himself brings up what looks to be precisely this difficulty in a passage which, like the two passages just given, takes actualism as a premise, in On Generation and Corruption I, 3, 317 b 23–29: “For if a substantial thing comes-to-be, it is clear that there will be (not actually, but potentially) a substance, out of which its coming-to-be will proceed and into which the thing that is passing-away will necessarily change. Then will any predicate belonging to the remaining categories attach actually to this? In other words, will that which is only potentially a ‘this’ (which only potentially is), while without qualification it is not a ‘this’ (i.e. is not), possess, e.g., any determinate size or quality or position? For if it possesses none, but all of them potentially, the result is that a being, which is not

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affirmation that prime matter serves as the substratum of each of the elements and persists throughout each case of elemental transformation, despite the fact that it is, in itself, pure potentiality, the traditional account conflicts with actualism. It is not clear to me that there is any way for the traditional account to avoid this conflict without significant modification. To summarise my argument: If the traditional account holds that prime matter, taken by itself, is pure potentiality, and that prime matter, taken by itself, is the substratum for the elements, it follows that pure potentiality is the substratum for the elements. But then given actualism, it follows that the substratum for the elements does not exist. In order to avoid this conflict, the proponent of the traditional account would have to argue that prime matter can be an existent substratum for an element despite the fact that, taken by itself (that is, taken in abstraction from the element for which it serves as substratum), it does not exist. It is not, on the face of it, clear how such an argument would go – if the traditional account is committed to such a view, it would be at the very least a controversial addition to that account, rendering it more theory-laden than it is often taken to be and not nearly as susceptible for use as a general framework as it is often taken to be. But without such an addition, the traditional account is at odds with actualism. There is a second way in which we can show that the traditional account conflicts with actualism. According to the traditional account, prime matter derives its only actual features from the very predication of a pair of contraries for which it is supposed to serve as subject: hot and dry, hot and wet, cold and dry, or cold and wet. But then given actualism, which implies that existence comes only with actuality, it follows that prime matter derives its very existence from the predication for which it serves as subject. In other words, it follows that the subject for this predication is an entity yielded by this predication; the subject of the predication is ontologically dependent upon the predication, not vice versa. There are, of course, predications for which this result would not be objectionable – specifically, predications which are such that if they were to cease to hold, their subjects would thereby cease to exist. Consider, for instance, the predication holding between a substance-kind and one of its members: if a certain horse were to cease to have the corresponding substance-kind predicated of it, that horse would cease to exist. In this case it seems correct to say that the horse is ontologically dependent upon the predication of its substance-kind for which it serves as subject. In the case of prime matter, however, we have something that is supposed to persist when the predication for which it serves as subject ceases to obtain and a new pair of contraries comes to be predicated of it. (Otherwise it a determinate being, is capable of separate existence; and in addition that coming-to-be proceeds out of nothing pre-existing.” Without actualism as a premise, Aristotle could not make this inference that if the pre-existent entity possesses no actual characteristics but only potentialities, then coming to be proceeds ex nihilo.

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could not serve as the persistent substratum for elemental transformation.) This implies that prime matter must, in every case, be able to exist independently of the predication for which it serves as subject. And this result conflicts with the previous result that prime matter is ontologically dependent upon the predication of contraries for which it serves as subject. So although the counterintuitive result that the subject for a predication is ontologically dependent upon that predication may not be a difficulty for the predication that holds between a substance-kind and one of its members, it does seem to be a difficulty for the predication that holds between prime matter and a pair of contraries, since prime matter is supposed to be able to exist independently of those contraries. Since it is the premise of actualism that leads the proponent of the traditional account to this result, we have another manifestation of the conflict between the traditional account and actualism. Given actualism, prime matter is ontologically dependent upon the contraries for which it serves as subject, but given certain modal properties ascribed to it by the traditional account (e.g., being able to survive apart from those contraries), it does not seem that it can be ontologically dependent upon them. One might respond that this conflict can be solved by adopting a weaker notion of ontological dependency as the sense in which prime matter depends on those contraries for which it serves as subject – a notion of ontological dependency as a contingent relation.16 Then we could hold that prime matter only happens to be ontologically dependent on that pair of contraries for which it serves as subject – it could become ontologically dependent on a different pair of contraries, which is precisely what happens when elemental transformation occurs. With a notion of ontological dependency as a contingent relation, we could then say, without conflict, that prime matter is ontologically dependent upon whatever pair of contraries for which it serves as subject; nonetheless, it could exist independently of that pair of contraries (as long as it is the subject for some other pair of contraries). Of course, if such a move were made, it would face the same difficulties we have already seen: it would render the traditional account far more theory-laden and not susceptible for use as a general framework. And there is another factor to consider. Adopting this weaker sense of ontological dependency in this case would blur the line between subject and predicate in Aristotle in a way that may be undesirable. It is a special feature of Aristotelian universals, which occupy the predicate position, that they obey the principle of instantiation – they cannot exist unless some particular thing instantiates them, but they could have been instantiated by different things than they in fact are instantiated by. Here we have ontological dependency understood as a contingent relation running from predicate to subject. If we allow it to run in the other 16   If we want to save the term “ontological dependency” for relations that hold necessarily, we can substitute some other name for the relation I am about to describe.

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direction as well, by holding that prime matter is contingently ontologically dependent on a certain pair of contraries, we lose this as a feature distinctive of universals in Aristotle. 5. PRIME MATTER AND ARISTOTELIAN CONSTITUENT ONTOLOGY Thirdly, the traditional account conflicts with that variety of the constituent ontological strategy according to which a whole that comes to be and passes away is a predicative entity, of which one constituent serves as subject and the other as predicate.17 I will refer to this view as Aristotelian constituent ontology.18 This conflict is perhaps the most troubling of the three; for the thesis that the elements, which come to be and pass away by being transformed into each other, are predicative entities in which prime matter serves as the subject for the predication of a pair of contraries is often included as a part of the traditional account. The conflict between the traditional account and Aristotelian constituent ontology arises with respect to the question of how a new pair of contraries could come to be predicated of some prime matter which is already the subject for a different pair of contraries, as in elemental transformation. We can bring this conflict into focus by considering the following reductio which a sceptic might bring against the thesis that a form or accident F could come to be predicated of a substratum s: Assume that F did genuinely come to be predicated of s. Then before this predication came to hold, s must have been non-F. But then we are committed to the conclusion that the non-F served as the subject for the predication of F, and this is absurd. For F could never come to be predicated of the non-F.19 In certain cases – for example, the coming to be of the musical man as described in Physics I, 7 – Aristotle has a ready way out of this argument. Although the subject for the coming to be of the musical man, s, was indeed unmusical before it came to be musical, s was also a man. And indeed, according to Aristotelian essentialism, “man” provides the most proper characterisation of what s is, since it is the substance-kind under which s falls.20 “Unmusical,” since it picks   This relationship between subject and predicate is supposed to be metaphysical, not merely linguistic. 18   In contrast, contemporary bundle theories, though versions of constituent ontology, do not involve the claim that a predicative tie holds between the constituents of a whole. According to these theories (at least for the most part), the constituents of a whole are all of the same categorical form, all universals, so they are united not by way of predication but in some other way. 19   As Aristotle tells us at Physics I, 7, 190 b 32–33: “it is impossible for the contraries to be acted on by each other.” 20   Aristotle continues at Physics I, 7, 190 b 33–38: “But this difficulty also is solved by the fact that what underlies is different from the contraries; for it is itself not a contrary. The principles therefore are, 17

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out a merely accidental property of s, is a characterisation subordinate to and entirely trumped by “man.” We are thus wholly justified in holding that the proper description of this predication’s coming to hold refers not to musicality coming to be predicated of “the unmusical” or “the unmusical man,” but to musicality coming to be predicated of “the man.”21 And this predication can coherently come to hold. So in describing this case of coming to be, we have justification for excising the problematic reference to unmusicality altogether. The analogous way out of the sceptic’s reductio is unavailable, however, for the case of elemental transformation as understood by the traditional account. Consider as an example the coming to be of fire, the element characterised by the hot and dry. If fire comes to be from air (the element characterised by the hot and wet), then the prime matter which serves as the subject for this transformation will start out as the substratum of air, and hence as hot and wet. Here the sceptic’s reductio will conclude that hot and wet prime matter cannot coherently come to serve as the subject for the predication of the hot and dry; for the wet and the dry are opposed contraries, as are musical and unmusical. Hot and wet prime matter, on account of its being wet, could never come to have the dry predicated of it, just as the unmusical man, on account of his being unmusical, could never come to have musicality predicated of him. In this case, Aristotle cannot respond, as he could for the case of the musical man, that there is an unproblematic characterisation of the prime matter of air that trumps the problematic characterisation of it as hot and wet. There is no justification for simply excising “wet” from the characterisation of the air’s prime matter and characterising this transformation as a case in which hot prime matter comes to have the hot and dry predicated of it, because “hot” is no more privileged in the characterisation of the prime matter than “wet” is (while “man” was a more privileged characterisation of the man than “unmusical”). Both “hot” and “wet” are accidental features of the substratum for this change, and hence equally privileged in its characterisation. And of course, since prime matter is essenceless, there is no feature of it which trumps both “hot” and “wet” – we cannot excise the reference to both. Another way of putting the problem is as follows: how can essenceless prime matter play the role assigned to the subject in Physics I, 7, given that in any case it will always have some contrary predicated of it that opposes one it is supposed to take on? Analogous reasoning will hold for fire’s coming to be from earth, since the prime matter of earth is cold and dry, the former of which conflicts with the hotness of fire. And things are even simpler in the case of fire’s coming to be in a way, not more in number than the contraries, but as it were two; nor yet precisely two, since there is a difference of being, but three. For to be man is different from to be unmusical, and to be unformed from to be bronze.” 21   For further discussion of the proper characterisation of the coming to be of Aristotle’s musical man, see Loux, “Aristotle and Parmenides”, 303–306.

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from water, since both features of water (cold and wet) conflict with those of fire. In none of the three possible scenarios for the coming to be of fire, then, can we find a feature of the pre-existent prime matter which provides us with a reply to the sceptic’s reductio by trumping any problematic features of that prime matter, in the way that “man” trumps “musical” in the description of the subject for the predication that yields the musical man.22 The best description of prime matter (whether as the substratum of air, earth, or water) that we can give is one which includes a feature (cold, wet, or both) that disallows that prime matter from becoming hot and dry. It looks, then, like the case of prime matter’s coming to have the hot and dry predicated of it must, in the end, be characterised as a case in which the non-F comes to be F, where F is one of the contraries and non-F the opposed contrary. For prime matter has no features which can trump those features that belong to it accidentally; the best characterisation of it must retain both accidental features.23 But this is incoherent. And analogous reasoning will hold for the coming to be of any of the three elements other than fire. We thus have a conflict between the traditional account and the thesis that prime matter can come to serve as the subject for the predication of a pair of contraries that yields an element, since the best characterisation of prime matter will always involve at least one contrary opposed to one of the contraries it is supposed to take on in any given case of coming to be. This conflict threatens the traditional account’s ability to hold that we can give an Aristotelian constituent analysis of the elements, according to which they have a predicative structure. How could one who wishes to adhere to both the traditional account and to an Aristotelian constituent analysis of the elements respond to this dilemma? One could not, it seems, respond by arguing that the whole problematic does not apply in the case of elemental transformation; for Aristotle himself seems to consider it at On Generation and Corruption I, 6, 322 b 15–22: The hot thing, e.g., would not be cooled and the cold thing in turn be warmed; for heat and cold do not change reciprocally into one another, but what changes (it is clear) is the substratum. Hence, whenever there is action and passion between things, that which underlies them must be a single something.

Indeed, he seems to think that he has it resolved for the case of elemental transformation. But if this substratum is prime matter as traditionally understood, it is far from clear how it is supposed to solve the dilemma at hand, given 22   Indeed, things do not look hopeful; for what we need to fi nd is a characterisation of this prime matter that trumps any accidental features, given that its problematic features in every case belong to it accidentally. But prime matter has no essence, according to the traditional account. 23   In the case of the man becoming musical, on the other hand, one of the substratum’s actual features (namely, being a man) was both unproblematic with respect to his becoming musical and was privileged over his problematic features.

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that it is best characterised only by the very contraries which are the source of the problem.24 In order to reply one who wants to retain the traditional account’s thesis that prime matter is indeed essenceless would have to lay out some view according to which prime matter can serve as a subject despite the fact that it is best characterised only by the very contraries which are the source of the problem. Once again, this shows the traditional account to require more theoretical commitments than it is usually taken to require. Until any such commitments have been laid out and shown to yield a coherent view, it is not clear that the traditional account can maintain Aristotelian constituent ontology. 6. CONCLUSION In summary, I have argued that the traditional account of elemental transformation in Aristotle conflicts with three doctrines. First, it conflicts with that variety of essentialism according to which everything that exists has an essence which marks it out as what it is. This conflict arises from the traditional account’s thesis that the same essenceless prime matter must persist throughout any case of elemental transformation. Second, it conflicts with actualism. This conflict can be brought out in two ways. According to one way of bringing out the conflict, if actualism is true then prime matter, taken in abstraction from the element for which it serves as substratum, does not exist; but then it seems that none 24   For a view which departs from the traditional account in that it sees the matter shared by the four elements as having certain essential properties, see Sheldon Cohen, “Aristotle’s Doctrine of the Material Substrate”, The Philosophical Review 93 (1984): 172–178. Cohen argues that “Aristotle does posit a common matter for the four elements, but this does not commit him to prime matter. The common matter of the four elements is not prime – that is, it is not bare or characterless…. It is per se neither hot nor cold, fluid nor solid, light nor heavy…. But if it does not possess any of these characteristics per se, it does not follow that it possesses no characteristics per se. In fact, that it is potentially light and heavy, and that at any given time it will be either light or heavy, can themselves be taken to specify a per se characteristic.” Cohen’s view is an interesting modification of the traditional account. His view may avoid the third difficulty I have articulated – however, it would have to be shown that one of the essential properties that he attributes to prime matter counts as privileged above all the others in the requisite way. Perhaps his view could, in addition, be argued to avoid the difficulties regarding essentialism and actualism. (I am, however, sceptical of whether it could. For not just any predicate we can truly ascribe to something corresponds to a metaphysical essence or accident on Aristotle’s view; moreover, if Cohen’s view does succeed in endowing prime matter with an essence and an actuality, then it entails that the notions of essence and actuality for something in the sublunary realm can be cut asunder from the notion of form – for prime matter is, in virtue of itself, formless.) I do not here have the space for an adequate consideration of whether his view could avoid these difficulties. Still, if it could do so that would not undercut the aim of this paper, which is to show that the traditional account of prime matter faces these three difficulties, and that the available pathways away from them which do not involve modification of the traditional account (as Cohen’s does) involve significant theoretical commitments not usually associated with the traditional account.

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of the elements even has a substratum, and so a fortiori that substratum cannot persist throughout a case of elemental transformation as the traditional account requires. According to another way of bringing out the conflict, if actualism is true then prime matter is ontologically dependent upon the predication of contraries for which it serves as subject; but this seems problematic, given that, according to the traditional account, it is supposed to be able to persist through the loss of one or both of those contraries. And third, it conflicts with the view that Aristotle’s four elements are to be understood according to that version of the constituent ontological strategy according to which one constituent of a whole serves as subject and the other as predicate. It is not clear how prime matter is supposed to be able to come to have a new pair of contraries predicated of it, when, according to the traditional account, the best characterisation of it will always involve some contrary opposed to at least one of the contraries it is supposed to take on. Some might conclude that we should give up on one or more of Aristotelian essentialism, actualism, and Aristotelian constituent ontology rather than go down the pathways required to find a solution to these dilemmas. But perhaps responses can be found which are less problematic than the rejection of any of these three doctrines would be. In some cases more than others, one can see, however vaguely, what direction a response on the part of the traditional account might take. For example, one might respond to the conflict with Aristotelian essentialism by relaxing the constraint on what it would be for prime matter to persist. In the case of the dilemma that given actualism, it seems that the elements do not even have a substratum, or the dilemma that given Aristotelian constituent ontology, prime matter must in any case of elemental transformation come to have predicated of it at least one contrary at odds with one of the contraries that serves in the best characterisation of it, it is not so clear what direction a response might take. But suppose that the traditional account can be made to cohere with these three doctrines – suppose satisfactory responses to be devisable. Since they will no doubt involve controversial metaphysical theses, we are still left with the result that the traditional account is far more theory-laden than it is often taken to be. Hence, it cannot be so easily employed as a general framework that can be shared by variant accounts of elemental transformation and of the place of prime matter in Aristotle’s sublunary realm. Moreover, we are left with the result that more work needs to be done before the traditional account can be appealed to as a coherent and justified framework for understanding elemental transformation – at least if Aristotelian essentialism, actualism, and Aristotelian constituent ontology are to be maintained. Thus, even if it can somehow be made to cohere with these three doctrines, the traditional account commits one to far more than one might think from the way in which it is often laid out.

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BIBLIOGRAPHY Aristotle. Complete Works of Aristotle. Ed. J. Barnes. Princeton, NJ: Princeton University Press, 1984. Bostock, David. “Aristotle’s Theory of Matter”. In Space, Time, Matter, and Form: Essays in Aristotle’s Physics, 30–46. Oxford University Press, 2006. Cohen, Sheldon. “Aristotle’s Doctrine of the Material Substrate”. The Philosophical Review 93 (1984): 171–194. Lewis, Frank. “What’s the Matter with Prime Matter?” In Oxford Studies in Ancient Philosophy 34, ed. Sedley, 123–146. New York: Oxford University Press, 2008. Loux, Michael J. “Aristotle and Parmenides: An Interpretation of Physics A.8”. Proceedings of the Boston Area Colloquium in Ancient Philosophy 8 (1992): 302–308. Plantinga, Alvin. “Actualism and Possible Worlds”. In Essays in the Metaphysics of Modality, ed. M. Davidson, 102–121. New York: Oxford University Press, 2003. Robinson, H. M. “Prime Matter in Aristotle”. Phronesis 19 (1974): 168–188. Scaltsas, Theodore. Substances and Universals in Aristotle’s Metaphysics. New York: Cornell University Press, 1994. Solmsen, Friedrich. “Aristotle and Prime Matter: A Reply to Hugh R. King”. Journal of the History of Ideas 19 (1958): 243–252. Williams, C. J. F. Aristotle’s De Generatione et Corruptione. New York: Oxford University Press, 1982.

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ESSENTIAL DEPENDENCE, TRUTHMAKING, AND MEREOLOGY: THEN AND NOW Ross Inman ABSTRACT One notable area in analytic metaphysics that has seen a revival of Aristotelian and scholastic inspired metaphysics is the return to a more robust construal of the notion of essence, what some have labelled “real” or “serious” essentialism. It is only recently, however, that this more robust notion of essence has been implemented into the debate on truthmaking, mainly by the work of E. J. Lowe. The first part of the paper sets out to explore the scholastic roots of essential dependence as well as an account of truthmaking for accidental predications in terms of accidents. Along the way, the author examines the dialectical role the possibility of separated accidents in the Eucharist play with respect to developing a scholastic account of truthmaking as essential dependence. In conclusion the author utilises Aquinas’s hylomorphic ontology to suggest a new way forward for an essentialist account of truthmaking.

1. INTRODUCTION One notable area in analytic metaphysics that has seen a revival of Aristotelian and scholastic inspired metaphysics is the return to a more robust construal of the notion essence, what some have labelled “real” or “serious” essentialism.1 However, it is only recently that this more robust notion of essence has been implemented into the debate on truthmaking, mainly by the work of E. J. Lowe. The first part of the paper sets out to explore the scholastic roots of essential dependence as well as an account of truthmaking for accidental predications in terms of accidents. Along the way, I examine the dialectical role the possibility of separated accidents in the Eucharist play with respect to developing a scholastic account of truthmaking as essential dependence. I conclude by utilising Aquinas’s hylomorphic ontology to suggest a new way forward for an essentialist account of truthmaking.

1   See D. Oderberg, Real Essentialism (London: Routledge, 2007) and E. J. Lowe, “Two Notions of Being: Entity and Essence”, in Royal Institute of Philosophy Supplement, 62 (2008): 23–24.

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2. CONTEMPORARY TRUTHMAKING AND ESSENTIAL DEPENDENCE Let us, then, begin by explicating the current discussion surrounding the notion of truthmaking, with an emphasis on the notion of essential dependence.2 The fundamental insight driving the commitment to truthmakers is that truth is determined by reality. To say that something determines some particular truth is to say that it is the ontological ground of that truth; its existence explains why that truth is true. Consider the singular existential proposition that e exists, e exists, and suppose that e exists is true. Now, intuitively, it is e itself that is the truthmaker for e exists that is, e determines the truth of e exists. We can call this relationship between e and e exists the relation of truthmaking, TM henceforth, and represent “e is the truthmaker for e exists” as TM(e, e exists).3 With this in mind, let us formulate what I will call the truthmaker principle (TMP) as follows:4 (TMP) Truthmaker Principle: pT ≡ E!x TM(x, p)5 That is, p is true (pT henceforth) if and only if there exists something, x, that stands in the truthmaking relation to p. While there are many important questions regarding the notion of truthmaking operative in TMP (like the status of truthmaker maximalism, i.e. whether every truth has a truthmaker), I limit my discussion here to the status of truthmaker necessitarianism; whether the relation of truthmaking (TM) carries modal import such that the existence of the truthmaker necessitates pT. The proponent of truthmaker necessitarianism claims that if x is the truthmaker for p in some world W, then x is the truthmaker for p not only in W but in every possible world in which x exists. Most truthmaker theorists agree that truthmakers necessitate the propositions they make true.6 We can formulate truthmaker necessitarianism as follows: (TNec) Truthmaker Necessitarianism: TM(x,p) → □(E!x → pT) 2   For an excellent introduction to the contemporary debate on truthmaking see Gonzalo Rodriguez-Pereyra, “Truthmakers”, Philosophy Compass 1, no. 2 (2006): 186–200. 3   I take it for granted that TM is a relation. For a denial of this assumption, see Joseph Melia, “Truthmaking without Truthmakers” in Truthmakers: The Contemporary Debate, ed. H. Beebee and Julian Dodd, Oxford: Oxford University Press, 2005, 67–84. What’s more, for our purposes in this paper I will generally assume that truthmaking is a cross-categorial relation that obtains between propositions (truthbearers) and entities in the world. 4   I use the existence predicate ‘E!x’ (‘x exists’) as shorthand for ‘∃y(x = y)’. 5   My quantifiers are to be taken as universal unless otherwise noted. 6   Though Josh Parsons is a notable exception, see his “There is No ‘Truthmaker’ Argument Against Nominalism”, Australasian Journal of Philosophy 77, no. 3: 325–334.

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That is, if x is the truthmaker for p, then, necessarily, if x exists then pT. In this way, the existence of x is said to necessitate pT. For our purposes here, let us assume the truth of TNec, together with the rather contentious thesis that TNec, in some form or other, is both necessary and sufficient for truthmaking.7 If so, we then get the following explication of the notion of the truthmaking relation: (TM) Truthmaker: TM(x,p) ≡ E!x  □(E!x →pT) In words: x is a truthmaker for p if and only if x exists and it is necessary that if x exists, then p is true. Many truthmaker advocates are of the opinion that the modality operative in the above formulation of TM is to be construed as metaphysical necessity (as opposed to logical or physical necessity) such that, at the very least, pT metaphysically depends on the existence of x. Several truthmaker theorists, however, have expressed doubts as to whether or not standard conceptions of metaphysical necessitation – where the existence of the truthmaking entity is necessary for the truth in question – is fine-grained enough to capture the sort of dependence that obtains between a true proposition and its truthmaker(s).8 One such contemporary truthmaker theorist is E. J. Lowe.9 Following closely the influential work of Kit Fine regarding the shortcomings of modal construals of essence, Lowe questions the adequacy of standard accounts of metaphysical necessitation in its ability to capture the dependence operative in TM.10 Lowe critiques modal construals of TM that rely on what he calls “rigid-existential dependence”, which can be formulated as follows: (RD) x depends rigidly on y =def □(E!x → E!y)11 As a construal of metaphysical dependence in terms of modality and existence, RD states that x depends on y just in case it is necessary that y exists if x exists. As an example of RD, Lowe cites the dependence of a boundary or a hole on its host or that of a heap of stones upon the individual stones that it contains. A boundary, thus, rigidly necessitates the existence of its host in that it exists only if its host   Thanks to Jeff rey Brower for conversation on this point.   The plural here denotes the fact that TM can be a many-one relation. 9   See E. J. Lowe, “An Essentialist Approach to Truthmaking”, in Truth and Truthmaking (Acumen Press, 2008), 201–217; and The Four Category Ontology (Oxford: Oxford University Press, 2006), 192–210. 10   Kit Fine, “Essence and Modality”, in Philosophical Perspectives 8: Logic and Language, ed. James E. Tomberlin (Atascadero, CA: Ridgeview, 1994), 1–16. 11   Alternatively, ¬◊(E!x  ¬E!y), i.e. x cannot exist unless y exists. RD also goes by the name ‘weak foundation’ in Peter Simons, Parts: A Study in Ontology (Oxford: Oxford University Press, 1987), 295. 7 8

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exists. According to an understanding of TM along the lines of RD, pT rigidly depends on the existence of x such that it is necessarily the case that pT only if x exists. It is in this sense that x is said to rigidly necessitate pT. Lowe contends that a modal construal of TM in terms of RD leads to some rather untoward consequences, what we might generally dub the objection from irrelevance. Fundamentally, an RD reading of TM suggests that every true proposition rigidly depends on necessary beings. Again, recall that x is a truthmaker for some proposition p, say Socrates is pale, if and only if x exists and it is necessarily the case that if x exists, then Socrates is pale is true. But suppose that x is a necessary being, say the number 7, and thus exists in every possible world. If the number 7 exists in every possible world, then it, ipso facto, exists in the world in which Socrates is pale is true. It follows from this that Socrates is pale rigidly depends for its truth on the number 7 and, consequently, the latter is what makes the former true.12 But this seems implausible as the existence of the number 7 is wholly irrelevant regarding whether or not Socrates is pale is true. Though Socrates is pale may well necessarily imply the existence of the number 7, one is hesitant to make the further claim that therefore the number 7 is the truthmaker for Socrates is pale. In light of this, Lowe contends that to say that x metaphysically necessitates pT is not merely to espouse the view that x exists in every world in which pT, i.e. that x is necessary for pT. Rather, metaphysical necessitation is better expressed by the fact that the non-existence of x is necessary for the falsehood of p.13 Alternatively, for x to be the ontological ground for pT is for x’s non-existence to be necessary for the falsehood of p. Consequently, Lowe claims that RD fails to adequately construe the modal dependence operative in TM. Lowe maintains that the failure of RD to capture the relevant notion of metaphysical necessitation in TM does not entail that all species of metaphysical dependence are therefore inadequate to do so. In the place of RD, Lowe puts forward a relation – essential dependence – that he takes to entail rigid existential dependence, but is not entailed by it. That is, every case of essential dependence is a case of rigid-existential dependence, but not the converse.14 As such, essential dependence is more fine-grained than rigid-existential dependence and thus is better suited to capture the notion that pT metaphysically depends on x. Lowe states the notion of essential dependence as follows:   For an early statement of this sort of worry, see Simons, Parts, 295.   Lowe, The Four-Category Ontology, 202. 14   It should be noted that Lowe in “Two Notions of Being” takes the notion of essence to be primitive and does not reify essences. Rather, Lowe takes the locution “the essence of x” to denote “what x is, or what it is to be x”. Further, Lowe states the fact that essential (identity) dependence entails rigid existential dependence as follows: “that if one entity depends for its identity upon another, then the former could not have existed without the latter” – Lowe, The FourCategory Ontology, 35. 12 13

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(ED) x essentially depends on y =def There is a function f such that it is part of the essence of x that x is f(y).15 One particular example of ED would be the relationship between Socrates and his singleton {Socrates}, the set whose sole member is Socrates. Now, according to ED, {Socrates} essentially depends on Socrates precisely because it is of the essence – the very identity – of {Socrates} that it be the singleton set of Socrates, that is, to be the value of the singleton-set-of function, where Socrates serves as the argument. Let us consider how ED might serve to elucidate the species of metaphysical dependence operative in TM. It is precisely in virtue of the fact that ED is more fine-grained than RD that the former is able to sidestep the objection from irrelevance. Recall that an RD reading of TM stated that x is the truthmaker for Socrates is pale if and only if x exists and rigidly necessitates the truth of Socrates is pale, thereby allowing the unintuitive notion that every true proposition is rigidly necessitated, and thus made true, by some necessary being (the number 7). On a more fine-grained ED reading of TM, however, such an inference is unwarranted on the grounds that it is not part of the essence of Socrates is pale that it be true only if the number 7 exists. While Socrates is pale might be rigidly necessitated by the number 7, it is not essentially necessitated by it in the sense that Socrates is pale does not depend for what it is – its very identity – on the existence of the number 7.16 Consequently, as one cannot infer from the existence of a necessary being (number 7) that everything is essentially dependent upon it, the objection from irrelevance is avoided, thereby making essential dependence a welcome candidate for the species of metaphysical necessity operative in TM. In the case of accidental predications, an ED reading of TM proves to be fruitful. Take, for instance, an accidental predication of the form x is F, where the mode F-ness is predicated of a substance x. On Lowe’s four-category ontology, F-ness essentially depends on x as well as the universal F (F-ness being a particularised instance of F). That is, it is part of the essence of F-ness that it (i) characterise or inhere in x and (ii) be an instance of F. Since F-ness is essentially dependent on these two entities, it follows, according to Lowe, that the existence of F-ness essentially necessitates x’s being F and thus the truth of the proposition x is F. In other words, the existence of F-ness suffices to secure the existence of x, F, x’s 15   More generally, R(□XRxy): for some relation R, x is essentially related by that relation to y. I should note that Lowe takes identity dependence to be a species of essential dependence, though I do not think this affects what I say here. For an extensive treatment of different conceptions of ontological dependence see Fabrice Correia, Existential Dependence and Cognate Notions (Philosophia Verlag, 2005). 16   Although, as David Oderberg suggests in Real Essentialism, the number 7 is a virtual part of the essence of Socrates is pale in so far as the latter, an existing entity, is essentially selfidentical and thus has as a (virtual) part of its essence being distinct from the number 7.

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being F, and therefore the truth of the proposition x is F. As a result, F-ness is said to metaphysically necessitate the truth of x is F in the right sort of way, thereby satisfying TM. 3. SCHOLASTIC ESSENTIAL DEPENDENCE In spite of this recent turn to essence in the contemporary literature on truthmaking, there has been little exploration of the historical roots of the formal concept of essential dependence as it pertains to the notion of truthmaking broadly conceived. My aim in this section is to explore the scholastic roots of the notion of essential dependence as developed in the work of Duns Scotus. In section 4, I proceed to examine the relationship between Scotus’s understanding of essential order with his account of truthmaking for accidental predications in terms of accidents. I then show how his account fails to satisfy the modal constraints on TM in light of his commitment to the possibility of separated accidents in the Eucharist as well as the objection from irrelevance outlined above. I conclude with a brief examination of a scholastic account of truthmaking for accidental predications that does satisfy the modal constraints of TM and thus presents itself as a viable option for contemporary truthmaker theorists. 3.1. Scotus on essential order The notion of one entity depending on another for its existence and/or essence has a formidable history in the Aristotelian tradition. Let us begin, then, with an examination of Scotus’s understanding of dependence, as displayed in his philosophical theology and substance-accident ontology. In the context of the metaphysics of the Incarnation, Scotus contends that the union that takes place between the Word, the second person of the Trinity, and the human nature of Christ (i.e. the hypostatic union) is a “union of order.”17 After considering and rejecting two other kinds of unity that might obtain between the Word and the human nature of Christ, Scotus states, All that remains therefore is the third type, namely, a union of order. The order, however, is that of the posterior to the prior. The Word obviously is not posterior to [human] nature; hence it is the other way around. The nature is posterior with respect to the Word and thus dependent on him.18

For Scotus, then, the Word is ordered with respect to the human nature of Christ in such a way that the latter is posterior to, and thus dependent on, the former. Scotus’s most developed treatment of the notion of dependence is found in his De Primo Principio. There, he elucidates the notion of posteriority and priority, 17

  John Duns Scotus, Quaestiones Quodlibetales [Quodl.], q. 19, n. 2.   Ibid., n. 5.

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labelling it “essential order” and proceeds to explicate two distinct varieties of essential order: the order of eminence and the order of dependence.19 The order of eminence pertains to the notion of perfection; x is eminently ordered with respect to y if x’s perfection (of essence) exceeds the perfection of y, and is thereby said to be prior to y in the order of eminence. The order of dependence, on the other hand, involves the notion of priority and posteriority with respect to the essence or nature of the two relata involved; “the dependent is said to be posterior whereas that on which it depends is prior”.20 Here it is crucial to note that Scotus maintains that the relata of essential ordering relations are essences (i.e. forms). Again, in the context of the hypostatic union, Scotus explicitly endorses the notion that the relata of essential ordering relations are essences, “As for the case at hand, the personal or hypostatic entity has no essential priority in respect to creatures, for an essential order obtains per se only between essences (in contrast to hypostatic entities), since it is forms (i.e. essences) that are like numbers”.21 In short, the order is one of essential dependence in so far as the priority or posteriority stems from the nature or essence of the entity in question. Scotus further suggests that essential ordering relations imply a sort of existential dependence of the posterior on that which is prior, “the prior according to nature and essence can exist without the posterior but the reverse is not true”.22 He continues, And this I understand as follows. Even though the prior should produce the posterior necessarily and consequently could not exist without it, it would not be because the prior requires the posterior for its own existence, but it is rather the other way about. For even assuming that posterior did not exist, the existence of the prior would not entail a contradiction. But the converse is not true, for the posterior needs the prior. This need we can call dependence, so that we can say that anything which is essentially posterior [in this way] depends necessarily upon what is prior but not vice versa, even should the posterior at times proceed from it necessarily.23

Following Aristotle, Scotus maintains that if x is essentially posterior to y, then x depends on y for its existence. He states that if x is essentially ordered to y, then x’s existence “needs” or “requires” y’s existence, i.e. it is impossible that x exist without y’s existing.   John Duns Scotus, De Primo Principio [DPP] 1.6.   DPP 1.8. 21   Quodl. q. 19, n. 19. However, it should be noted that Scotus does, at times, allow for a wider variety of relata in essential ordering relations. See Quodl. 19., a. 2, n. 30 where he distinguishes different conceptions of essential dependence by their different relata. 22   DPP 1.8. 23   DPP 1.8. 19

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Here, however, we must proceed with caution. The claim that x is existentially dependent on y admits of two readings, each differing in its respective scope. We have already encountered the strong variety of existential dependence in Lowe’s explication of rigid-existential dependence (RD) above. Recall that this stronger notion stated that necessarily, x exists only if y exists, □(E!x → E!y), where ‘y’ denotes some particular entity such that necessarily, x exists only if that particular y exists. While rigid-existential dependence captures the notion of an entity’s existence requiring the existence of a particular entity, the weaker reading captures the notion of an entity’s existence requiring the existence of an object of a particular sort. As such, the weaker reading states that necessarily, x exists only if F exists, where ‘F’ is a general term denoting some instance of the class of Fs. Thus, on this weak reading, x cannot exist unless something is an F, i.e. □(E!x → E!y  Fy). Let us follow Lowe once more and label this weak variety of existential dependence “non-rigid existential dependence”. In the passage above it is not clear as to which notion of existential dependence Scotus takes essential order to entail. For now, let us just say that if an entity is essentially ordered to another entity, then the former is existentially dependent on the latter in some sense or other (understood in a wide enough sense to capture both rigid and non-rigid existential dependence). Let us, then, formulate Scotus’s conception of essential order using our sentential operator ‘□X’ to stand for ‘it is part of the essence of x’: (EO): x is essentially ordered to y ≡ □X (E!x → E!y)24 That is, x is essentially ordered to y if and only if x is essentially such that it exists only if y exists. Michael Gorman has pointed out that Scotus puts forward several formal features that govern EO in De Primo Principio 2: irreflexivity, asymmetry, and transitivity.25 Using “□O” to stand for “essentially ordered”, Scotus maintains that EO is governed by the following axioms: Irreflexivity: “Nothing whatever is essentially ordered to itself.”26 ¬(□O(x,x))

24   Scotus defines “of the essence of x” (what I am referring to in EO above as “part of the essence of x such that”) as “that which is included per se in the quidditative concept of x and therefore, is posited in the essential notion of its quiddity, and not as something added.” See John Duns Scotus, Quaestiones super libros Metaphysicorum Aristotelis [In Met.] VII, q. 1. 25   Michael Gorman, “Ontological Priority and John Duns Scotus”, in The Philosophical Quarterly 43 (173) (1993): 460–471. 26   DPP 2.2.

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Asymmetry: “In any essential order a circle is impossible.”27 □O(x,y) → ¬□O(y,x) Transitivity: “What is not subsequent to the prior is not subsequent to the posterior”28 (□O(x,y)  □O(y,z)) → (□O(x,z)) Consequently, what emerges from our above discussion of Scotus’s conception of dependence is a partial ordering relation that obtains between essences that is governed by the axioms of irreflexivity, asymmetry, and transitivity. Though essential order is commonly understood within the context of distinguishing per se and per accidens causal series, Scotus takes essential ordering relations to be commonplace, especially as it pertains to his substance-accident ontology.29 In attempting to distinguish essential order from any sort of causal dependence, he suggests that essential order “can be shown somehow in [the relation of] subject and accident.”30 What’s more, referring again to the essential order that obtains in the hypostatic union, Scotus notes that the human nature of Christ is dependent on the Word such that the latter sustains the former in existence and, further, that this sustenance is “maximally similar to that of an accident by its subject”.31 But how exactly does Scotus conceive of the relation between a substance and its accidents? The issue, as we will see shortly, is complicated given his commitment to the Eucharistic doctrine that upon consecration the accidents of the bread and the wine remain in existence, even though their underlying substance ceases to exist.32 Let us turn, then, to examine Scotus’s notion of EO as applied to his understanding of the relation between a substance and its accidents with an eye on the prospects of its application to the notion of truthmaking below. Scotus operates out of an Aristotelian ontology where substances are the fundamental units of being and accidents are taken to inhere in substances. By an accident “inhering” in a substance, Scotus means to convey either: (i) the actual union of an existing accident with its existing subject as a kind of act with the potential or (ii) the dependence of the accident upon the substance, where the   DPP 2.4.   DPP 2.6. 29   DPP 1. 30   Ord. III, dist. 1, q. 1, n. 3, as cited in Richard Cross, The Metaphysics of the Incarnation: Thomas Aquinas to Duns Scotus (New York: Oxford University Press, 2002), 123. 31   Ord. III, dist. 1, q. 4, n. 2, as cited in Cross, ibid. 32   For an excellent treatment of the Eucharist and its role in scholastic metaphysics, see Marilyn McCord Adams “Aristotle and the Sacrament of the Altar: A Crisis in Medieval Theology”, Canadian Journal of Philosophy, Supplementary Volume 17 (1991): 195–249. 27

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substance is essentially prior and the accident is naturally posterior.33 Regarding (i), we can say that if x inheres in y then x actualises some potency in y, call this ‘inherenceA’ as it underscores the fact that x informs y in such a way that y’s passive potency (to be x) is actualised by x. Concerning (ii), if x inheres in y, then x is dependent on y for its continued existence, call this ‘inherenceD’ (to be read in the broadest terms to include rigid and non-rigid existential dependence). By claiming that accidents are “naturally posterior” to substances, Scotus means that “the natural entity of these [accidents] is through substance”. 34 That is, it is the natural order of things that accidents depend on substances as external, efficient causes of their continued existence. Furthermore, Scotus is clear that inherenceD is more fundamental than inherenceA in so far as an accident’s (natural) dependence on substance serves as the ground for its capacity to actualise some potency in its substance. If an accident, F-ness, is to actualise some potency in Socrates (inherenceA), to be pale for instance, then there must be a sense in which F-ness depends on Socrates (i.e. inherenceD) as opposed to Crito, say. Scotus further distinguishes two ways an accident may inhere simpliciter (i.e. inhereA or inhereD) in a substance: actual inherence and aptitudinal inherence.35 Heavily influenced by the Eucharistic doctrine concerning separated accidents (i.e. accidents that no longer depend on their host substance for their sustained existence), Scotus argues that while it is not of the essence of an accident to actually inhere simpliciter in a substance (as is the case with separated accidents present in the Eucharist), it is of the essence of an accident that it aptitutidinally inhere simpliciter in a substance (the separated accidents are such that they naturally tend to inhere in a substance, though it is not part of their essence that they actually do so).36 Hence, the aptitude or disposition to inhereA and inhereD in a substance is part of the essence (what Scotus calls the “quidditative concept”) of an accident, irrespective of whether or not it actually does so. Consequently, we have the following classification of accidental inherence: INHERENCE ACTUAL INHERENCEA

INHERENCED

APTITUDINAL INHERENCEA

INHERENCED

33   Quodl. q. 19, n. 13; In Met. VII, q. 1, n. 9. However Scotus intends the modal import of ‘natural’ here, I understand it to be (at the very least) weaker than metaphysical necessity (broad logical necessity) as construed by contemporary philosophers. See Cross, The Metaphysics of the Incarnation, 104 for more on Scotus’s view of accidents being naturally posterior to substances. 34   In Met. VII, q. 4, n. 2. 35   See In Met. VII, q. 1, n. 10; and Quodl. q. 19, n. 24. 36   In Met. VII, q. 1, n. 12.

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One apparent implication of Scotus’s metaphysics of the Eucharist for his substance-accident ontology (and for his view of truthmaking as we will see shortly) is that while an accident may be naturally ordered to substance, it is not essentially ordered (posterior) to it.37 The reasoning here is straightforward. In so far as it is metaphysically possible for an accident to exist without actually inheringD in a substance38 it follows that it is not part of its essence to actually inhereD in a substance and, ipso facto, is not essentially ordered to it. This reasoning relies on Scotus’s earlier contention that that which is essentially ordered is existentially dependent (in either the rigid or non-rigid sense) on that which is prior.39 Here I interpret Scotus as espousing the view that that which is essentially ordered to another must actually depend for its existence on that which is prior, i.e. it must actually inhereD in either its particular host substance or some substance or other.40 Consequently, Scotus’s adherence to the metaphysical possibility of an accident existing without actually inheringD in either the strong or weak sense implies that accidents are not, strictly speaking, essentially ordered to substance. At the same time, however, Scotus does speak as though accidents, in the normal order of things, actually inheredD in a substance. In fact, he is of the opinion that accidents are (naturally) sustained in existence by their host substances in such a way that the latter is “the end term of the dependence of the actual existence of an assumed nature”.41 Elsewhere, he refers to this dependence relation as the substance communicating its existence to the accident.42 In adhering to the possibility of separated accidents together with the fact that accidents do at times actually inhereD in their host substances, Scotus appears to be affirming the seemingly implausible thesis that being existentially dependent is a contingent affair. In fact, Scotus says just this when he states: 37   See Quodl. q. 19, n. 13. Also, as Richard Cross has shown, Scotus does provide independent philosophical argumentation in support of the thesis that accidents are not essentially ordered to their host substances. See his The Physics of Duns Scotus (Oxford: Oxford University Press, 1998), 100. 38   Something Scotus explicitly affirms, “the natural entity of these [accidents] is through substance; they can [however] exist without substance with an aptitude for a subject” – In Met. VII, q. 4, n. 2). The implication here is that an accident may exist without actually inhering (simpliciter) in a substance, though it cannot exist without having the aptitude to inhere in a substance. 39   DPP 1.8. 40   Further evidence for this reading is found in his using the notions of actual inherenceD and essential order interchangeably (In Met. VII, q. 1, n. 9) and then, shortly after, stating explicitly that it is not of the essence of an accident that it actually inhereD (ibid., n. 12) in a substance. 41   Ord. III, dist. 1, q. 5, n. 8, as cited in Cross, The Metaphysics of the Incar nation. 42   Ord. III, dist. 1, q. 5, n. 8, as cited in Cross, The Metaphysics of the Incar nation; Quodl. q. 19, n. 23.

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We show this thirdly as follows: An accident can have the mode of substance [i.e. it can exist without inhering in a substance], although not perfectly in the sense that it would be repugnant for it to depend on a subject, but in some analogous way, viz., insofar as it does not actually depend; this is seen in the case of a separated accident.43

The way in which an accident has the mode of substance in the Eucharist is that it enjoys independent existence. Be that as it may, separated accidents remain as accidents in so far as they retain their aptitude to actually inhereD in a substance (substances do not have this feature). Nonetheless, it remains that the view has the rather untoward consequence that being existentially dependent is a contingent matter.44 I must, at this point, leave these interpretive niceties to those with a  more detailed knowledge of the issues surrounding Scotus’s ontology of accidents. As a result, we have seen that Scotus relies on a conception of essential dependence (i.e. essential order) that is governed by (i) the notion of priority and posteriority between essences (ii) the existential dependence of the posterior on the prior (in some sense or other) and (iii) the axioms of irreflexivity, asymmetry, and transitivity. Let us turn, then, to discuss several scholastic conceptions of truthmaking for accidental predications and their relation to the notion of essential dependence (order). 4. SCHOLASTIC TRUTHMAKING AND ESSENTIAL DEPENDENCE Though the scholastics did not express the notion of truthmaking in precisely the same terms as we do today, the idea is not without witness in the Aristotelian tradition.45 In fact, both Scotus and Aquinas, with Aristotle, adopt the fundamental intuition behind the notion of truthmaking: the dependence of truth on being.46 As John Fox has noted,   Quodl. q. 19, n. 84.   One rather contentious way out of this would be to suggest that while it appears that being rigidly existentially dependent is non-contingent, being non-rigidly existentially dependent might be a contingent feature of an entity (as it is a weaker dependence relation). That is, a non-rigidly dependent entity can fail to be dependent as such and yet exist nonetheless. For an excellent historical treatment of the scholastic debate concerning the view that accidents have various modes of existence (modus essendi), see Robert Pasnau, Metaphysical Themes 1274–1689 (Oxford: Oxford University Press, 2011). 45   For Aristotle, see especially Categories 14 b 16–23. For a defence of the thesis that the scholastics utilised a truthmaking theory of predication see John Fox, “Truthmaker”, Australasian Journal of Philosophy 65 (1987): 188–207; Jeffery Brower, “Simplicity and Aseity”, The Oxford Handbook to Philosophical Theology (Oxford: Oxford University Press, 2009); Tim Pawl, A Thomistic Account of Truthmakers for Modal Truths (doctoral dissertation, St. Louis University, 2008); and Cross, The Metaphysics of the Incarnation. 46   For Aquinas see his Quaestiones Disputatae de Veritate [QDV], q. 1, a. 2, ad 3; ibid. ad l. For Scotus see Ord III, dist. 6., q. 1, n. 6; Reportata Parisiensia III, dist. 1, q. 2, n. 5, as cited in Cross, The Metaphysics of the Incarnation. 43

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Medieval philosophers customarily defined something’s whiteness, heaviness, existence, manhood, or colour, as that by which it was white, was heavy, existed, was a man, or was coloured… this ‘by which’ is to be elucidated in terms of truthmaking.47

For both Scotus and Aquinas, substances are “made to be” by their accidents in a qualified sense; accidents are said to actualise some potency in their substances, thereby causing substances to be in some particular manner. In particular, Aquinas speaks of an accident being related to a substance as act to potency and that “a subject, in virtue of an accident, is in certain ways” and that “whiteness makes a potentially white human being actually white … non-essential forms make it [substance] actually exist in various non-essential modes”.48 What’s more, he states that, “Snow is ‘white’ by reason of its whiteness”.49 Consequently, Aquinas emphasises the role of accidents in a substance’s coming to be modified in a particular manner (although we will see shortly that his account does not appeal to accidents alone). As for Scotus, the actualisation of passive potency in a substance by an accident is, as we have already seen, embodied in his notion of inherenceA. Scotus, like Aquinas before him, argued that Socrates is white “by the existence of a white thing”.50 Following Richard Cross (2002), I take this feature of accidents to be what Scotus elsewhere calls their ability to confer existence denominatively on their respective substances.51 Consequently, both Scotus and Aquinas were of the opinion that Socrates’ potency for being white is actualised by the inhering of the accident whiteness. However, both of these thinkers differed as to the details concerning the truthmaking role for accidents. To get clear on this, let us represent their views regarding the multifaceted relationship between an accident and its substance as follows: (A) For any accident F-ness and any substance x in which F-ness inheres, (1) F-ness existentially depends on x, either actually or aptitudinally. (2) F-ness actualises x’s potency to be F.52 (3) F-ness is a truthmaker, such that x is F is true.53   Fox, “Truthmaker”, 190.   Summa theologiae [STh] I, q. 3. a. 6 and De principiis naturae 1, respectively. 49   STh III, q. 77, a. 1, ad 4. 50   Ord III, dist. 6, q. 1, n. 6, as cited by Cross ibid. 51   Cross, ibid., 125, n. 21. See also Ord. III, q. 6, a. 1, n. 6, as cited by Cross ibid., and In Met. VII, q. 1, n. 10. 52   As with (1), F-ness may either actually or aptitudinally actualise x’s potency to be F. Since both Scotus and Aquinas appear to ignore an accident’s having the aptitude to actualise x’s potency to be F, I focus here on an accidents actually doing so. 53   Ord. I, dist. 8, pars 1, q. 4, n. 213–214, adapted from Cross, ibid., 34. 47

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Both Scotus and Aquinas were committed to (1) and (2) regarding the relationship between an accident and its host substance. 54 However, they differ as to how (1) and (2) bear on (3), that is, the truthmaking role of accidents. Here, I consider Scotus’s account of truthmaking for accidental predications and proceed to Aquinas’s more detailed account in the final section. 4.1 Scotus’s account of truthmaking In general, Scotus construes (3) in terms of (1). In fact, Scotus is quite adamant that (3) can be understood without reference to (2). He states: You will object: how is something formally wise by wisdom unless [wisdom] is its form? I reply: a body is animate denominatively (as it were), because the soul is its form. A human being is said to be animate essentially, and not (as it were) denominatively, because the soul belongs to him or her as a part. So being of a certain sort because of something does not require that the thing [paleness] is a form informing something [Socrates], because a form [paleness] is not a form informing the whole, even though [the whole] is said to be of a certain sort because of it.55

Thus, paleness need not actualise some passive potency in Socrates in order to serve as the truthmaker for Socrates is pale. Rather, Scotus was of the opinion that the truthmaking role for accidents is best construed in terms of (1); it is in virtue of a substance x’s possessing an accidental form F-ness via actual inherenceD that it is true that x is F, i.e. F-ness is the truthmaker for the accidental predication x is F. As Marilyn McCord Adams notes, Scotus declares that ontological dependence of a broad sense property thing on a subject is sufficient for characterization. Even if whiteness did not actualise a potency in Socrates, Socrates would be the subject on which the whiteness ontologically depended and that would be enough to make it true that Socrates is white.56

Scotus’s explication of truthmaking in terms of (1) instead of (2) is ultimately tied to his view that inherenceD is more fundamental than inherenceA in so far as an accident’s actualising some passive potency in a substance requires that the accident depend on that very substance for its existence. Given the earlier line of reasoning in section 2 above, however, it appears that this proposal is inadequate to secure the requisite modal strength contemporary philosophers commonly ascribe to the relation of truthmaking. Recall our earlier attempt to construe existential dependence (and hence inherenceD) in the broadest possible terms in order to allow for either a strong or weak reading (i.e. rigid or non-rigid respectively) in light of the ambiguity latent in Scotus’s   For Aquinas, see STh III, q. 77, a. 1, ad. 2.   Ord. I, dist. 8, pars 1, q. 4, n. 213–214, adapted from Cross, ibid. 56   Marylyn McCord Adams, Christ and Horrors (Cambridge: Cambridge University Press, 2006), 126. 54 55

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claim that essential order entails existential dependence in some sense or other. Unfortunately, we can no longer remain neutral on this matter as the tenability of Scotus’s proposal of truthmaking in terms of (1) heavily depends on whether or not he understands an accident to be rigidly or non-rigidly existentially dependent on a substance. To see this, suppose we construe (1) in terms of non-rigid existential dependence and thus explicate (3) as F-ness non-rigidly depending on x. On this account, the existence of F-ness does not, strictly speaking, necessitate the truth of x is F, say, Socrates’ being F. Rather, at most, the existence of F-ness necessitates that some x is F, not that this particular, viz. Socrates, is F. On this reading, the existence of F-ness could just as easily necessitate the truth of Glaucon is F. Consequently, interpreting (1) in terms of non-rigid existential dependence is not strong enough to capture the modal force operative in TM. The same fate awaits an interpretation of (1) in terms of rigid-existential dependence. As was previously demonstrated, this species of metaphysical dependence does not appear to be fine-grained enough to capture the notion of truthmaking, hence the objection from irrelevance we met in section II. As Lowe (2006) has pointed out, “a truthmaker is not, or not merely, something whose existence is necessary for the truth of a proposition but something whose nonexistence is necessary for its falsehood.”57 Lastly, we might underscore here the implications of Scotus’s metaphysics of the Eucharist for his account of truthmaking in terms of (1). If separated accidents are metaphysically possible, then there could be instances where the F-ness (the whiteness of the bread) of x exists and yet the accidental predication x is F (the bread is white) is false given that x ceases to exist altogether. Yet this undermines the fact that truthmakers are said to metaphysically necessitate their truths. Consequently, in so far as we place any stock in the objection from irrelevance and thereby require the modal force of truthmaking to be stronger than that of rigid-existential dependence, it appears that we must bid farewell to a scholastic account of truthmaking for accidental predications in terms of accidents alone. 4.2 Hylomorphic truthmakers I want to conclude by briefly unpacking an alternative essential dependence account of truthmaking for accidental predications, one that finds its roots in the hylomorphic ontology of Thomas Aquinas. Aquinas’s hylomorphic account, I believe, has much to offer the contemporary truthmaker theorist as it provides a novel alternative to tropes and states of affairs as truthmakers for accidental predications. Though at times Aquinas speaks as though accidents alone serve as truthmakers for accidental predications in virtue of satisfying (2) above, he clearly 57

  Lowe, The Four-Category Ontology, 202.

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states that it is the combining of an accident and its host substance that serves as the truthmaker for accidental predications. Aquinas is clear that, “when I say, “Man is white,” the cause of the truth of this enunciation is the combining of whiteness with the subject”.58 Elsewhere, he makes the same point, albeit more subtly, “But the reasoning by which the affirmative enunciation, ‘Man is worthy,’ is true, i.e., by some worthy man existing, is the same as the reasoning by which ‘Man is shameful’ is true, i.e., by a shameful man existing”.59 For Aquinas, the result of the combining of seatedness and Socrates is a numerically distinct hylomorphic compound, seated-Socrates (what he calls an “accidental being” generally), whose matter is Socrates and accidental form is seatedness. And, it is the existence of this numerically distinct accidental being, seated-Socrates, which is said to ground the truth of the accidental predication Socrates is seated. As a result, Aquinas is of the opinion that what enters into the truthmaking relation for accidental predications are not accidents alone (pace Scotus), but rather a distinct mereologically complex entity that is composed of an accident and a substance. How does Aquinas’s hylomorphic proposal fair as an explication of the truthmakers for accidental predications? For one, accidental beings have the requisite modal features such that their existence essentially (as opposed to rigidly) necessitates the existence of each of their proper parts (in our example of seatedSocrates, the substance Socrates and the accidental form seatedness), thereby avoiding the objection from irrelevance. To help bring out the modal features of accidental beings qua hylomorphic compounds, we can represent the essential and ontological priority of the parts of these compounds as being governed by the following mereological principle: necessarily, if any object x is part of an accidental being, y, then, it is part of the essence of y that if y exists then x is a part of y. As an accidental being, seatedSocrates exists and is what it is in virtue of the existence and essence of its proper parts, Socrates and seatedness. It is precisely because accidental beings exhibit these modal features that the existence of seated-Socrates is said to essentially necessitate Socrates’ being seated and not merely the co-existence of two, unrelated entities: Socrates and seatedness. In so far as the essence of seated-Socrates – its very identity – involves reference to Socrates as modified by his inhering mode of seatedness, it follows that the existence of seated-Socrates essentially necessitates Socrates’ being seated and, ipso facto, the accidental truth of Socrates is seated. Aquinas’s hylomorphic account of truthmaking for accidental predications will most likely find favour with those who are already favourably disposed 58   Thomas Aquinas, Commentary on the Metaphysics of Aristotle IX, lect. 11, n. 1898. I owe this and the following reference to Pawl, Thomistic Account of Truthmakers. 59   Thomas Aquinas, Sententia super Peri hermenias I, lect. 11, n. 10.

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toward a hylomorphic ontology and whose aesthetic sensibilities are not offended by including what Gareth Matthews has famously dubbed ‘kooky objects’ in their ontology.60 Nevertheless, I take Aquinas’s hylomorphic account of truthmaking to be yet another example of how a hylomorphic ontology is remarkably fecund in its application to contemporary issues in metaphysics and thus deserves to be taken seriously as a viable metaphysic of material objects.

BIBLIOGRAPHY Adams, Marilyn McCord. “Aristotle and the Sacrament of the Altar: A Crisis in Medieval Theology”. Canadian Journal of Philosophy, Supplementary Volume (1991): 195–249. ― Christ and Horrors. Cambridge: Cambridge University Press, 2006. Aquinas, Thomas. Translated by Fathers of the English Dominican Province. London: Burns, Oates, and Washbourne 1912–36. Reprint, New York: Benziger Brothers 1947–48. Reprint, New York: Christian Classics, 1981. ― Questiones Disputatae de Veritate: The Disputed Questions on Truth. Translated by Robert W. Mulligan, S.J. Chicago: Henry Regnery Co., 1952. ― Sententia super Metaphysicam: Commentary on the Metaphysics of Aristotle. Translated by J. P. Rowan. Chicago: Regnery, 1964. ― Sententia super Peri hermenias: Aristotle on Interpretation: Commentary by St. Thomas and Cajetan. Translated by J. T. Oesterle. Milwaukee: Marquette University Press, 1962. ― De Principiis Naturae: On the Principles of Nature. Translated by Timothy McDermott. In Aquinas: Selected Philosophical Writings. Oxford: Oxford University Press, 2008. Aristotle. The Complete Works of Aristotle: The Revised Oxford Translation. Edited by J. Barnes. 2 vols. Bollingen Series. Princeton, NJ: Princeton University Press, 1984. Brower, Jeffrey. “Simplicity and Aseity”. The Oxford Handbook to Philosophical Theology. Oxford: Oxford University Press, 2009. Correia, Fabrice. Existential Dependence and Cognate Notions. Philosophia Verlag, 2005. Cross, Richard. The Metaphysics of the Incarnation: Thomas Aquinas to Duns Scotus. New York: Oxford University Press, 2002. ― The Physics of Duns Scotus. Oxford: Oxford University Press, 1998. Fine, Kit. “Essence and Modality”. In Philosophical Perspectives 8: Logic and Language, edited by James E. Tomberlin, 1–16. Atascadero, CA: Ridgeview, 1994. Fox, John. “Truthmaker”. Australasian Journal of Philosophy 65 (1987): 188–207. Gorman, Michael. “Ontological Priority and John Duns Scotus”. The Philosophical Quarterly 43 [173] (1993): 460–471. 60   Gareth Mathews, “Accidental Unities”, in Language and Logos, ed. M. Schofield and M. Nussbaum (Cambridge: Cambridge University Press, 1982).

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Lowe, E. J. The Four-Category Ontology. Oxford: Oxford University Press, 2006. ― “Two Notions of Being: Entity and Essence”. Royal Institute of Philosophy Supplement, 62 (2008): 23–48. DOI:10.1017/S1358246108000568. Lowe, E. J. and Rami, A. Truth and Truthmaking. Acumen Press, 2008. Matthews, Gareth. “Accidental Unities”. In Language and Logos, edited by M. Schofield and M. Nussbaum, 223–240. Cambridge: Cambridge University Press, 1982. Melia, Joseph. “Truthmaking Without Truthmakers”. In Truthmakers: The Contemporary Debate, edited by H. Beebee & J. Dodd, 67–84. Oxford: Oxford University Press, 2005. Oderberg, David. Real Essentialism. London: Routledge, 2007. Parsons, Josh. “There is No “Truthmaker” Argument Against Nominalism”. Australasian Journal of Philosophy 77, no. 3 (1999): 325–334. Pasnau, Robert. Metaphysical Themes 1274–1689. Oxford: Oxford University Press, 2011. Pawl, Tim. A Thomistic Account of Truthmakers for Modal Truths. Doctoral dissertation, St. Louis University, 2008. Scotus, John Duns. Quaestiones Quodlibetales: God and Creatures: The Quodlibetal Questions. Translated with an introduction, notes and glossary by Felix Alluntis and Allan B. Wolter. Washington, D. C.: The Catholic University of America Press, 1975. ― Quaestiones super libros Metaphysicorum Aristotelis: Questions on the Metaphysics of Aristotle by John Duns Scotus. Edited by Girard J. Etzkorn and Allan B. Wolter OFM. St. Bonaventure, NY: The Franciscan Institute, 1997–1998. ― De Primo Principio: John Duns Scotus, A Treatise on God as First Principle. Edited by Allan B. Wolter. 2nd edition, revised with a commentary. Chicago: Franciscan Herald Press, 1983. Simons, Peter. Parts: A Study in Ontology. Oxford: Oxford University Press, 1987.

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SECTION III

SUBSTANCE & ACCIDENT

ESSENCE AND ONTOLOGY E. J. Lowe ABSTRACT The aim of this paper is to show how, by combining a neo-Aristotelian account of essence with a neo-Aristotelian four-category ontology (of individual substances, modes, substantial universals, and property universals), a thoroughgoing metaphysical foundation for modal truths can be provided – one which avoids any appeal to ‘possible worlds’ and which renders modal truths objective, mind-independent, and yet also knowable.

1. ONTOLOGY In Aristotle’s mature ontological system, as presented in the Metaphysics, individual substances are taken to be combinations of matter and form, with each such substance being constituted by a particular parcel of matter embodying, or organised by, a certain form. For example, an individual house has as its immediate matter some bricks, mortar and timber, which are organised in a certain distinctive way fit to serve the functions of a human dwelling. Similarly, an individual horse has as its immediate matter some flesh, blood and bones, which are organised in a certain distinctive way fit to sustain a certain kind of life, that of a herbivorous quadruped. In each case, the ‘matter’ in question is not, or not purely, ‘prime’ matter, but is already ‘informed’ in certain distinctive ways which makes it suitable to receive the form of a house or a horse. Thus, bricks, mortar and timber would not be matter suitable to receive the form of a horse, but at best that of something like a statue of a horse. According to this view, the matter and form of an individual substance are each ‘incomplete’ entities, completed by each other in their union in that substance. But its form is essential to the substance, unlike its matter, in the following sense: an individual house, say, cannot lose the form of house without thereby ceasing to be, whereas – while it must always have matter of an appropriate kind so long as it continues to be – it need not always have the same matter of that kind. Individual bricks and timbers in a house may be replaced without destroying the house – indeed, this may be the only way to preserve a certain house – but once its bricks and timbers cease to be organised in the form of a house, the house necessarily ceases to be. Clearly, according to this hylomorphic Aristotelian picture, an individual substance is a ‘combination’ of matter and form in a sense which rules out our SUBSTANCE & ACCIDENT • 93

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thinking of its matter and form as being parts of the substance, at least in the normal sense of ‘part’. Here it might be objected that, for example, a brick in a house is a part of it in this familiar sense, and yet belongs to the ‘matter’ of the house: so can’t we at least say that the matter of a house is a ‘part’ of it in this sense? Not easily: for even if we were to concede that a brick is literally a part of the house, all the matter of the house, considered collectively, can hardly be so regarded. For the house coincides with its matter as a whole and hence, it appears, that matter could not qualify as a proper part of house, as the brick might. Nor, however, can the matter qualify as an improper part of the house, in the standard sense, since that would make it identical with the house: and yet the house is clearly not identical with its matter, not least because its matter can change while it persists. Equally, on the hylomorphist view, the house’s form cannot be regarded as a part, either proper or improper, of the house, in the standard sense of ‘part’. Nothing forbids the hylomorphist from saying that, in some other sense of the term, the matter and form of an individual substance are ‘parts’ of it, but saying this would at least not be very helpful, since it would invite confusion. It is better just to say that the matter and form are constituents, but not parts, of the substance. The key point is that, on this view, individual substances exhibit ‘internal’ ontological complexity, being combinations of ‘incomplete’ entities that are completed by each other in the substance. So far, I have spoken a lot about forms, but not much about features, and how they might be accommodated by the approach now under discussion. Very roughly, I think that the answer should run somewhat as follows. The form of a substance constitutes its essence – what it is, its ‘quiddity’ – whereas its features, or ‘qualities’, are how it is. A horse is what Dobbin is, for example. If Dobbin is white, however, that is partly how he is – a way that he is. I say ‘partly’ only to acknowledge that there are many other ways Dobbin is besides being white – such as being heavy – and by no means intend to imply that Dobbin’s whiteness is a part of Dobbin. However, Dobbin’s whiteness might nonetheless be thought to be a constituent of Dobbin, on this view, distinct from his form, which is equinity. And this might be maintained whether one thought of Dobbin’s whiteness as being a particular whiteness peculiar to him, or just the universal whiteness that he shares with other white substances. But how, then, are a substance’s features related to its form? Some of its features, it seems, are necessitated by its form – such as warmbloodedness in the case of Dobbin – and these may be called, in the strictest sense of the term, the substance’s properties. Other of its features, however, are ‘accidental’, such as Dobbin’s whiteness, which may therefore be denominated one of his accidents. Even so, although Dobbin’s whiteness is accidental, that Dobbin has some colour is necessitated by his form and is thus essential to him. So we arrive at the following picture: an individual substance possesses a certain form, which constitutes its essence, from which ‘flow’ by necessity certain features of the substance, which are its properties in the strictest sense of the term. Some of 94 • SUBSTANCE & ACCIDENT

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these properties are ‘determinables’ rather than ‘determinates’, such as colour in the case of Dobbin, and then it is necessary that the substance should possess some determinate feature falling under the relevant determinable, but contingent which feature this is. Such contingent determinate features are the substance’s accidents, which can obviously change over time compatibly with the continued existence of the substance. The overall picture, even in this relatively simplified version of it, is quite complex, with an individual substance portrayed as having a rich and in some respects temporally inconstant constituent structure of form, matter, properties, and accidents, with form and properties remaining constant while matter and accidents are subject to change. Hylomorphism certainly has many attractive aspects. But its core difficulty lies in its central doctrine – that every concrete object, or more precisely every concrete individual substance, is a ‘combination’ of matter and form. For what, really, are we to understand by ‘combination’ in this sense? Clearly, we are not supposed to think that combination in this sense just is, or is the result of, a ‘putting together’ of two mutually independent things, since matter and form are supposed to be ‘incomplete’ items which complete each other in the substance that combines them. Now, certainly, when some concrete things – such as some bricks, timbers and quantities of mortar – are put together to make a new concrete object, such as a house, those things have to put together in the right sort of way, not just haphazardly. But does this entitle us to suppose that the completed house is some sort of ‘combination’ of the things that have been put together and the way in which they have been put together? The challenge that the hylomorphist presents us with is to explain why, if we do not say something like this, we are entitled to suppose that a new individual substance is brought into being. One presumption behind that challenge would seem to be that a substance can’t simply be a socalled mereological sum of other substances – and with this I can agree, at least if by a ‘mereological sum’ we mean an entity whose identity is determined solely by the identities of its ‘summands’, rather as the identity of a set is determined solely by the identities of its members. I agree that only when other substances have been put together in the right sort of way does a new substance of a certain kind come into being, the way in question depending on the kind in question. Moreover, I have no objection to the ‘reification’ of ‘ways’, understood as features or forms, provided that we do not treat ways as substances – so here too I am in agreement with the hylomorphist. Reification is not the same as hypostatisation, but is merely the acknowledgement of some putative entity’s real existence. What I do not understand is what it means to say that the completed house’s form – the way in which its ‘matter’ is organised – is an ‘incomplete’ constituent of the house which ‘combines’ together with that equally ‘incomplete’ matter to constitute the house, a complete substance. The words that particularly mystify me in this sort of account are ‘incomplete’, ‘combine’ and ‘constitute’. It’s not that I do not understand these words perfectly well as they are commonly used in other SUBSTANCE & ACCIDENT • 95

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contexts, just that I do not understand their technical use in the hylomorphic theory and, equally importantly, why a need should be felt for this use of such terms. If I could understand the supposed need to say something like this, then I would make every possible effort to grasp the technical terminology. So let us remind ourselves why, allegedly, there is indeed such a need. As was just mentioned, the need supposedly arises in order to meet the challenge of explaining how a new substance is brought into existence. The suggestion seems to be that, unless we can see the new substance as being a combination of items neither of which can exist independently of the other in just such a combination, rather than as merely being composed of other independently existing things each possessing their own features, we shall be unable to justify the judgement that a new concrete object – an ‘addition of being’ – really has been brought into existence, rather than some previously existing things merely being rearranged. Put in this way, the supposed problem is one that is familiar from recent debates in metaphysics. Here, though, I would urge that some types of ‘rearrangement’ are ontologically more weighty than others. When a free proton and a free electron are ‘rearranged’ by increasing the distance between them from one mile to two miles, there is no reason at all to suppose that a new concrete object is brought into existence. But when they are ‘rearranged’ so that the electron is captured by the proton and occupies an orbital around it, then indeed we have a new concrete object of a very different kind: a hydrogen atom. This object has certain features, notably certain powers, which are quite different from those of protons and electrons and quite different, too, from those of a mereological sum of a free proton and a free electron. In the newly created hydrogen atom, the proton remains exactly what it was before, just a proton, and the electron remains just an electron. A new form is instantiated – one that is possessed neither by the proton nor by the electron – namely, the form of a hydrogen atom. This form is the form of the newly created object, the atom, not that of the proton or the electron, nor even of the pair of them. The form does not, in any sense that I can understand, ‘combine’ with the proton and the electron so as to constitute, together with them, the atom. The only things that do any ‘combining’ are the proton and the electron, when the former captures the latter and the latter occupies an orbital around the former. And the only things that constitute the atom are, again, the proton and the electron, which are its parts, in the perfectly familiar sense of ‘part’. So, as can be seen, I am perfectly happy to describe the case of the newly created hydrogen atom in terms of ‘combination’ and ‘constitution’, and indeed in terms of ‘form’. It’s just that I do not need, and do not understand, the ‘logical grammar’ of the hylomorphist who uses these terms in his own distinctively technical fashion. Furthermore, I have no serious need for the hylomorphist’s category of matter. I might be prepared to say that the ‘matter’ of the hydrogen atom is or consists of its proton and electron, but just in the sense that these are its parts and serve to compose it. But the atom’s 96 • SUBSTANCE & ACCIDENT

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‘matter’ in this sense is not, as the hylomorphist takes it to be, some ‘incomplete’ constituent of the atom that is completed by the atom’s ‘form’. In fact, I would prefer to abandon the term ‘matter’ altogether, as modern physics has done, at least as a fundamental theoretical term. Thus, although modern scientists talk, for instance, of ‘condensed matter physics’, fundamental particle physicists do not nowadays speak of protons and electrons as having, or being composed of, matter – although they might happily speak of them as being ‘packets of energy’ and certainly as possessing mass. The hylomorphist ontology described above is inspired by Aristotle, as modified perhaps by later thinkers such as Aquinas. But the basis of another kind of ontology can also be traced to Aristotle, this time to the Aristotle of his presumed early work, the Categories.1 The kind of ontology that I now have in mind is one whose key notions are briefly sketched in the opening passages of that work, before the classificatory divisions commonly known as the Aristotelian ‘categories’ are set out later in the treatise. In those opening passages, Aristotle articulates a fourfold ontological scheme in terms of the two technical notions of ‘being said of a subject’ and ‘being in a subject’. Primary substances – what we have hitherto been calling ‘individual’ substances – are described as being neither said of a subject nor in a subject. Secondary substances – the species and genera to which primary substances belong – are described as being said of a subject but not in a subject. That leaves two other classes of items: those that are both said of a subject and in a subject, and those that are not said of a subject but are in a subject. Since these two classes receive no official names and have been variously denominated over the centuries, I propose to call them, respectively, attributes and modes. It seems that secondary substances and attributes are conceived to be different types of universal, while primary substances and modes are conceived to be different types of particular. Since the Aristotelian terminology of ‘being said of’ and ‘being in’ is perhaps less than fully perspicuous, with the former suggesting a linguistic relation and the latter seemingly having only a metaphorical sense, I prefer to use a different terminology: that of instantiation and characterisation. Thus, I say that attributes and modes are characterising entities, whereas primary and secondary substances are characterisable entities. And I say that secondary substances and attributes are instantiable entities, whereas primary substances and modes are instantiating entities. These terminological niceties, which though necessary are apt to prove confusing, are most conveniently laid out in diagrammatic form, using the familiar device known as the Ontological Square. I present it below.2 1   See Aristotle, Categories and De Interpretatione, trans. J. L. Ackrill (Oxford: Oxford University Press, 1963). 2   For a much fuller account, see my The Four-Category Ontology: A Metaphysical Foundation for Natural Science (Oxford: Oxford University Press, 2006).

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In my own version of the Ontological Square, I prefer to use the terms ‘object’ and ‘kind’ in place of the more cumbersome ‘primary substance’ and ‘secondary substance’. I also include a ‘diagonal’ relationship between objects and attributes, which is distinct from both instantiation and characterisation, calling this, as seems appropriate, exemplification. Here is my version:

KINDS

characterised by

ATTRIBUTES

instantiated by

exemplified by

instantiated by

OBJECTS

characterised by

MODES

I call the four classes of entities depicted here ontological categories, albeit with a cautionary note that these are not to be confused with, even though they are not unrelated to, Aristotle’s own list of ‘categories’ later in his treatise. More precisely, I regard these four as the fundamental ontological categories, allowing that within each there may be various sub-categories, sub-sub-categories, and so on. How exactly are the two ‘Aristotelian’ systems of ontology related to one another? Unsurprisingly, they overlap in many respects, but one key respect in which they obviously differ is that the four-category ontology, as I call it, unlike the hylomorphic ontology, does not include the category of matter. It might be thought that it also lacks the category of form, but that is not in fact so. For I believe that form, conceived as a type of universal, and more perspicuously termed substantial form, is really nothing other than secondary substance or substantial kind. We may refer to such universal forms either by using certain abstract nouns, such as ‘humanity’ and ‘equinity’, or else by using certain substantival nouns – what Locke called ‘sortal’ terms – such as ‘man’ and ‘horse’. I believe that this is a grammatical distinction which fails to reflect any real ontological difference. However, if that is so, then there is a very important ontological consequence. This is that primary substances, or individual concrete objects, ‘have’ forms only and precisely in the sense that they are particular instances of forms. Thus Dobbin is a particular instance of the substantial kind or form horse, whereas Dobbin’s whiteness is a particular instance of the colour universal or attribute whiteness. By this account, it makes no sense at all to say that Dobbin is a ‘combination’ of the form horse and some ‘matter’. He is, to repeat, just a particular instance of that form, other such instances being the various other particular horses that exist or have existed. Being an instance of this form, Dobbin must certainly have material parts, such 98 • SUBSTANCE & ACCIDENT

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as a head and limbs, but in no sense is he a ‘combination’ of anything material and the universal form in question. What I am saying, then, is that individual objects or primary substances are nothing other than particular forms, or formparticulars – particular instances of universal forms, in precisely the same sense in which modes (or ‘tropes’, as they are now often called) are particular instances of attributes. A crucial question that now arises is whether the four-category ontology is, like the hylomorphic ontology, a constituent ontology or whether, rather, it is a relational ontology.3 The answer that I want to defend is that it is neither – and that this is very much to its credit. At first sight, it might seem that the fourcategory ontology must be a relational ontology, since the Ontological Square apparently depicts three relations supposedly holding between entities in different categories of the system: the instantiation relation between objects and kinds and between modes and attributes, the characterisation relation between attributes and kinds and between modes and objects, and the exemplification relation between objects and attributes. However, if the system includes such relations amongst the entities whose existence it acknowledges, those entities must find a place in one or other of the system’s four fundamental categories. There seem to be only two that could possibly house them: the category of attributes and the category of modes. That is to say, the relations in question would have to be categorised as being either relational attributes or relational modes. In fact, they would have to be classified in both of these ways, in the following sense: since the theory maintains that every attribute is instantiated by modes and that every mode instantiates an attribute – because to this extent, at least, the theory is ‘immanentist’ where universals are concerned – it would have to maintain that there are relational instantiation, characterisation and exemplification modes which instantiate corresponding relational attributes. But this really makes no sense on the system’s own terms. Consider, for instance, the case of the characterisation of an object by a mode: for example, Dobbin’s particular whiteness’s being a characteristic of Dobbin. As this example illustrates, characterisation is supposed to ‘obtain’ between entities in the category of modes and entities in the category of objects. This is so even if there are relational modes, such as, perhaps, a loving mode that characterises John and Mary. What there cannot be is a relational mode that characterises an object and a mode. Moreover, if we supposed that there could be, we would immediately be faced with the threat of an infinite regress, of the sort that F. H. Bradley famously described. For if it were the case that, in order for mode M to characterise object O, a relational characterisation mode, M’, had to characterise M and O, then by the same token another relational characterisation mode, M’’, would have to characterise M’, M and O – and so on ad infinitum. Here it may be responded that this is just so much the worse for the four-category 3   For more on this distinction between ‘constituent’ and ‘relational’ ontologies, see Nicholas Wolterstorff, “Bergmann’s Constituent Ontology”, Noûs 4, no. 2 (1970): 109–134.

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ontology and simply demonstrates its inadequacy or even its incoherence. But that would be far too rash a conclusion, for the system certainly has the resources with which to dissolve the apparent difficulty, as we shall now see. An important distinction is commonly made between internal and external relations, the idea being that an internal relation holds of necessity between its terms or relata, in virtue of their intrinsic features or natures, whereas an external relation may hold or fail to hold between its relata irrespective of their intrinsic features or natures. For instance, spatial relations between objects are commonly supposed to be external, because it seems that the distance between two objects could be altered without affecting in any way the intrinsic features or natures of those objects. By contrast, resemblance seems intelligible only when conceived as being an internal relation. For example, that red resembles orange, and indeed that it resembles orange more closely than it resembles yellow, seem to be necessary truths that depend solely on the intrinsic natures of the colours in question. But to talk of there being – that is, of there existing – internal relations in cases like these is to indulge in unnecessary reification. We can put the point in this way: while there may be relational truths to be recognised in such cases (truths whose logical form is relational) – such as the truth that red resembles orange – there need not be relational truthmakers of those truths. Understanding a truthmaker of a given proposition to be, at the very least, an entity (or plurality of entities) whose existence necessitates the truth of that proposition, we can see that the truthmaker of the proposition that red resembles orange is quite simply the colours red and orange themselves. For, in the language of possible worlds, in every world in which those colours exist, the proposition that red resembles orange is true. We do not need to invoke, as a putative truthmaker of this proposition, or even as part of any such truthmaker, a relation of partial or imperfect resemblance between red and orange, conceived as an entity additional to red and orange themselves.4 The lesson is that, while it might be convenient to talk of ‘internal relations’, we should not suppose that in so talking we are talking of really existing entities of a relational nature, such as relational attributes or modes. Consequently, if the four-category ontology can fairly represent instantiation, characterisation and exemplification being internal relations, it can avoid serious ontological commitment to them as entities to be included in one or other of its ontological categories and thereby avoid the threatened Bradleian regress, while at the same time escaping classification as a relational ontology. Now, the three ‘relations’ in question most plausibly are internal, or at least explicable in internalist terms. I make this latter qualification to accommodate the ‘relation’ of exemplification. That instantiation and characterisation are internal relations is relatively easy to argue for. In the case of instantiation, all 4   For more on truthmaking, see E. J. Lowe and Adolf Rami, eds., Truth and Truth-Making (Stocksfield: Acumen, 2009).

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that we need to maintain is that an object necessarily instantiates its kind and that a mode necessarily instantiates its attribute, both of which claims are prima facie highly plausible. It is surely part of the essence of a whiteness mode, for instance, that it is an instance of the universal whiteness. Similarly, it is very plausibly part of the essence of a particular horse, Dobbin, that he is an instance of the kind horse. Analogous points can be made regarding characterisation. It is surely part of the essence of Dobbin’s whiteness mode that it characterises Dobbin: for that mode depends for its very identity on its being Dobbin’s, and could not possibly ‘migrate’ to another object, much less continue to exist in Dobbin’s absence (any more than the Cheshire Cat’s grin could continue to exist without the cat). This leaves us only with characterisation as a ‘relation’ between attributes and kinds. But what I have in mind in speaking in these terms are precisely certain essential connexions between attributes and kinds, which are normally expressed in the language of natural law. We say, for instance, that electrons are negatively charged particles, thus expressing an essential connexion between the kind electron and the attribute negative charge. Electrons, as a natural kind, have certain essential characteristics, of which negative charge – or, more exactly, unit negative charge – is one. To put it another way, in no possible world are there electrons which lack negative charge. A world which contained particles exactly similar to electrons in every respect save that they were neutral, say, would not be a world containing neutral electrons. Kinds depend for their very identity on their essential characteristics, just as modes depend for their very identity on their objects or ‘bearers’. Consequently, the characterisation ‘relation’ between attributes and kinds is an internal one and so ‘no addition of being’. I concede that in saying all this I am glossing over certain complications which would need to be accommodated by a more detailed account, but I think that these complications raise no real difficulties for the sort of approach that I am now recommending. For instance, one difficulty might be thought to be that the exact numerical value of the negative charge on the electron is arguably not a necessary feature of the electron, even if it necessarily possesses unit negative charge: for the ‘size’ of this unit might conceivably differ in different possible worlds. But then the proper response to this might just be to say that that value is not an essential characteristic of electrons and universally characterises all particular electrons in the actual world for some reason that is extrinsic to their nature as electrons – a reason to do, say, with some global property of space in this world. I now pass on to the slightly more complicated case of exemplification. It seems clear that we can’t simply say that exemplification, like instantiation and characterisation, is an ‘internal’ relation, because which attributes an object exemplifies can be a contingent matter. Dobbin, for example, is white, but could perhaps instead have been brown. This is unlike the truth that Dobbin is warmblooded, which is plausibly necessary, at least in a qualified sense that will be explained below. However, what we can say is the following. Dobbin is white in SUBSTANCE & ACCIDENT • 101

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virtue of being characterised by a certain whiteness mode, call it W. Now, it is part of the essence of W that it characterises Dobbin, since W depends for its identity on Dobbin. Equally, it is part of the essence of W that it instantiates the attribute whiteness. Hence, in any possible world in which W exists, W instantiates whiteness and characterises Dobbin, whence it follows that in any such world it is true that Dobbin is white, since he is characterised by a whiteness mode in that world. Thus W is a truthmaker of the proposition that Dobbin is white, as indeed would be any whiteness mode of Dobbin. But the proposition that Dobbin is white simply affirms that Dobbin exemplifies whiteness. Hence, we can explain truths of exemplification like this without invoking the existence of an exemplification relation. As for the contingency of the truth that Dobbin is white, this simply arises from two facts: first, that any whiteness mode of Dobbin’s, such as W, is itself a contingent being, and second that the ontological dependence between any such mode and Dobbin is asymmetrical. Such a mode does not exist in every possible world, and there are possible worlds in which Dobbin exists but no such mode exists. By contrast, the reason why Dobbin is necessarily warm-blooded is that Dobbin instantiates the kind horse, and warm-bloodedness is an essential characteristic of that kind. Here the truthmaker for the truth that Dobbin is warm-blooded is just Dobbin himself: for in any possible world in which Dobbin exists, he instantiates the kind horse and that kind is characterised by the attribute warm-bloodedness. This truth of exemplification is, then, a necessary truth: not in the unqualified sense that it obtains in every possible world whatsoever, but in the qualified sense that it obtains in every possible world in which Dobbin exists. It is an essential truth about Dobbin, whereas the truth that Dobbin is white is not. In short, we can explain all truths of exemplification, and explain too their modal status, whether they be contingent or necessary, without invoking the existence of any relation of exemplification, but simply by appealing to the ‘internal’ relations of instantiation and characterisation, together with the truthmaking roles of objects and modes. For this reason, I maintain that the four-category ontology cannot fairly be classified as being a relational ontology. I turn now, more briefly, to the question of whether the four-category ontology can instead fairly be classified as a constituent ontology. I take it to be a necessary feature of any such ontology that objects are regarded by it as possessing significant ontological structure, where this does not involve their mere composition by other objects in at least some cases. That is to say, the mere fact that an ontology takes at least some objects not to be simple, in the sense of allowing that they possess other objects as parts, is not sufficient for it to be classified as being a constituent ontology – not even if the ontology allows that one object may be constituted by another, distinct object (for instance, a bronze statue by a lump of bronze), both of which are composed of the same parts at the time of constitution. Rather, what is crucial for an ontology to qualify as ‘constituent’ is that it should maintain that objects have an ontological structure involving ‘constituents’ 102 • SUBSTANCE & ACCIDENT

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which belong to ontological categories other than the category of object itself. The hylomorphic ontology is clearly a constituent ontology in this sense, since it maintains that objects, or individual substances, are ‘combinations’ of matter and form, where neither matter nor form is conceived to be an entity belonging to the category of individual substance. Now, if the four-category ontology were fairly to be classified as a constituent ontology, what could it be taken to regard as being the ‘constituents’ of objects, in the sense now relevant? Clearly, there are only three candidates, since there are only three other ontological categories for these putative constituents to be drawn from – kinds, attributes, and modes. However, even without examining the case of each in detail, it seems clear from what has already been said about instantiation, exemplification, and characterisation – the three key ‘relations’ that ‘relate’ objects to entities of each of these other categories respectively – that they are not ‘constitutive’ or ‘combinative’ in nature. If any of them were, the consequence would be that the four-category ontology is committed to some version of the bundle theory of objects – and yet it is most emphatically not. Take the case of modes, for instance. The proper thing for a four-category ontologist to say about modes, I believe, is that they are ‘abstractions’ from objects, not constituents of them, for this explains their identity-dependence on their objects. Identity-dependence is not only an asymmetric relation of ontological dependence: it also implies ontological priority on the part of the entity depended upon, with respect to the dependent entity. And this is precisely in accordance with the Aristotelian spirit of the four-category ontology, according to which individual substances – objects, as we are calling them – have ultimate ontological priority over entities in any of the other three categories. I suggest, then, that within the four-category ontology we need to regard modes as being ‘aspects’ of objects, to which we can attend selectively in thought or perception, by means of what Locke called a ‘partial consideration’. These aspects explain the differential behaviour of different objects: for instance, why some objects roll down an inclined plane while others do not – the former being spherical or cylindrical, the latter not. But it is, after all, the whole object that rolls, not its sphericity or cylindricality. Nor does it make much sense to suppose that its sphericity or cylindricality ‘drags along’ the object’s other modes with it, and thereby makes the object as whole move. To think in such terms is illicitly to hypostatise modes, treating them as simple substances within an object, rather than just as particular ‘ways’ an object is. I conclude that the four-category ontology, properly understood, has to be excluded both from the class of relational ontologies and from that of constituent ontologies. Attempts to force it into either of these camps simply turn it into some other kind of ontology altogether. It cannot have escaped notice that, in setting out and defending the fourcategory ontology, I have frequently used modal notions, such as those of necessity and possibility, and also the notion of essence. In the remainder of this paper, SUBSTANCE & ACCIDENT • 103

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therefore, I shall try to explain and defend my usage, which is once more inspired by the work of Aristotle. 2. ESSENCE Currently dominant accounts of the traditional metaphysical distinction between essence and accident attempt to explain it in modal terms, and more specifically in terms of the notions of metaphysical necessity and possibility. These in turn are commonly explicated in terms of the language of ‘possible worlds’. Thus, a property F is said to be an essential property of an object a just in case, in every possible world in which a exists, a is F. And a’s essence is then said to consist in the set or sum of a’s essential properties. One difficulty of this approach, brought to our notice by the work of Kit Fine, is that it seems grossly to overgenerate essential properties.5 For instance, by this account, one of Socrates’s essential properties is his property of being either a man or a mouse and another is his property of being such that 2 + 2 = 4. It might be objected that these are not genuine properties anyway and so a fortiori not essential properties of Socrates. But there are other examples which cannot be objected to on these grounds, such as Socrates’s property of being the sole member of the set singleton Socrates, that is, the set {Socrates} whose sole member is Socrates. Fine urges, plausibly, that it is not part of Socrates’s essence that he belongs to this set, although it is plausibly the case that it is part of the essence of singleton Socrates that Socrates is its sole member. The modal account of essence cannot, it seems, accommodate this asymmetry. These points are too well-known for it to be necessary for me to dwell on them further. Suffice it to say that I am persuaded by Fine’s objections to the modal account of essence and accept the lesson that he draws: 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. This may also enable us to dispense with the language of possible worlds as a means of explicating modal statements. That would be a good thing, in my view, since I regard this language as being fraught with ontological difficulties, even if it can sometimes have a heuristic value. However, if we are to take this alternative line of approach, we need, of course, to provide a perspicuous account of the notion of essence which does not seek to explicate it in modal terms. Fortunately, we do have at our disposal some resources wherewith to accomplish this, drawing on the Aristotelian and Scholastic traditions in metaphysics. A key notion here, pointed out and exploited by Fine himself, is that of a real definition, understood as being a definition of a thing (a res, or entity), in contradistinction to a verbal definition, which is a definition of a word or phrase. A real definition of an entity, E, is to be understood 5   See Kit Fine, “Essence and Modality”, in Philosophical Perspectives 8: Logic and Language, ed. James E. Tomberlin (Atascadero, CA: Ridgeview, 1994).

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as a proposition which tells us, in the most perspicuous fashion, what E is – or, more broadly, since we do not want to restrict ourselves solely to the essences of actually existing things, what E is or would be. This is perfectly in line with the original Aristotelian understanding of the notion of essence, for the Latin-based word ‘essence’ is just the standard translation of a phrase of Aristotle’s which is more literally translated into English as ‘the what it is to be’ or ‘the what it would be to be’. We find a similar turn of phrase in Locke’s Essay, where he tells us that the word ‘essence’, in what he calls its ‘proper original signification’ just means ‘the very being of any thing, whereby it is, what it is’.6 It will be helpful at this point to proceed by way of examples, the first of which I borrow from Spinoza.7 Consider a familiar geometrical figure, such as a circle. And suppose that someone asks us what a circle is. This can be understood as a request for a real definition of this kind of geometrical figure – not a request for the meaning of the English word ‘circle’, for which we would do well to resort simply to a good English dictionary. And here, plausibly, is the real definition that is required – one that will typically be found in textbooks of elementary geometry: (C1) A circle is the locus of a point moving continuously in a plane at a fixed distance from a given point. The ‘given point’ here is, of course, the circle’s centre. This formula or recipe tells us what a circle is, and it does so by revealing its generating principle – what it takes for there to be or, more exactly, for there to come into being, a circle. Here is another geometrical example: (E1) An ellipse is the locus of a point moving continuously in a plane in such a fashion that the sum of the distances between it and two other fixed points remains constant. These ‘fixed points’ are the ellipse’s foci. By contrast, consider this alternative description of an ellipse (as a type of conic section), which is equally true of all ellipses: (E2) An ellipse is the closed curve of intersection between a cone and a plane cutting it at an oblique angle to its axis greater than that of the cone’s side. 6   See John Locke, An Essay Concerning Human Understanding, ed. P. H. Nidditch (Oxford: Oxford University Press, 1975), III, III, 15. 7   See Benedict de Spinoza, On the Improvement of the Understanding, Ethics, Correspondence, trans. R. H. M. Elwes (New York: Dover, 1955), 35.

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This, I suggest, tells us a necessary property of all ellipses, but not the essence of an ellipse – what an ellipse is. For it does not capture an ellipse’s generating principle. It characterises an ellipse in terms that are extrinsic to its nature as the particular kind of geometrical figure that it is. Certainly, one can make an elliptically shaped surface by cutting a cone in the prescribed fashion, but this procedure does not really explain why it is that what is so produced is an ellipse. On the other hand, once we understand what an ellipse is, by learning its real definition, we can go on to understand why it is that the cutting procedure in question generates an ellipse, as opposed to any other kind of geometrical figure. The reverse does not seem to hold: taking an ellipse to be the shape we get when we cut a cone in the prescribed fashion does not help us to understand why an ellipse is the locus of a point moving continuously in a plane in such a fashion that the sum of the distances between it and two other fi xed points remains constant. So, at least, I suggest. The necessary property of all ellipses that I have just identified – that of being a closed curve of intersection between a cone and a plane cutting it at an oblique angle to its axis greater than that of the cone’s side – holds of all ellipses not purely in virtue of their essence, but at least partly in virtue of the essence of a quite different kind of geometrical object, a cone. That is what I mean by saying that to characterise an ellipse in terms of this property is to characterise it in terms that are extrinsic to its nature as the particular kind of geometrical figure that it is. Here is another way of making this point: an ellipse can exist even in a purely two-dimensional space, but a cone can exist only in a space of at least three dimensions – hence it can’t be right to define an ellipse in terms of its relationship to a cone, since ellipses can exist perfectly well without cones. Yet another way of making the same point is the following: an ellipse evidently does not depend for its identity on any cone of which it may happen to be a section, but it does depend for its identity on the distances between its foci and the sum of the distances between them and any point on the ellipse. As I intimated earlier, the view of essence and real defi nition that I have just been articulating is one with a lengthy philosophical pedigree. We find it, for instance, in Spinoza’s On the Improvement of the Understanding, where indeed he uses the example of a circle with which I began. Now, any essential truth is ipso facto a metaphysically necessary truth, although not vice versa: there can be metaphysically necessary truths that aren’t essential truths – understanding an essential truth to be a truth concerning the essence of some entity. If we can truly affirm that it is part of the essence of some entity, E, that p is the case, then p is an essential truth and so a metaphysically necessary truth. Thus, for example, it is part of the essence of a certain ellipse, E, that its foci are a certain distance apart, whence it follows that it is metaphysically necessary that E’s foci are that distance apart. By something’s being a ‘part of the essence’ of a certain entity, I just mean that it either is the whole essence of that entity or else is properly 106 • SUBSTANCE & ACCIDENT

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included in its essence. Thus, for instance, since the essence of an ellipse is that it is the locus of a point moving continuously in a plane in such a fashion that the sum of the distances between it and two other fixed points remains constant, and having foci a certain distance apart is properly included in this essence, it is part of the essence of an ellipse that it has foci a certain distance apart – but this is obviously not the whole essence of an ellipse, since it is also a part of the essence of an ellipse that the sum of the distances between its foci and any point on the ellipse is constant. Consider now a metaphysically necessary truth such as the fact that an ellipse is the closed curve of intersection between a cone and a plane cutting it at an oblique angle to its axis greater than that of the cone’s side. It is not part of the essence of any ellipse that this condition holds, nor is part of the essence of any cone that it does. What it is very plausible to contend, however, is that this metaphysically necessary truth holds in virtue of the essences of an ellipse and a cone, respectively. It is because of what an ellipse is, and what a cone is, that this relationship necessarily holds between ellipses and cones. But it is not part of anything’s essence that it holds. For ellipses and cones, which are the only things whose essences have a role to play in explaining why this necessary truth holds, are quite different things. Nor is there any such thing as a ‘cone-ellipse’, part of whose essence it could be that this truth obtains. Our proposal concerning metaphysically necessary truths is, then, this: a metaphysically necessary truth is a truth which is either an essential truth or else a truth that obtains in virtue of the essences of two or more distinct things. On this account, all metaphysical necessity (and by the same token all metaphysical possibility) is grounded in essence. A concern that might be raised here is that our example of ellipses and cones concerns geometrical objects, rather than material ones – for it might be suspected that our account cannot easily be extended to cover the latter. I think this concern is unfounded. Consider instead, for instance, material objects of the following two kinds: a bronze statue and a lump of bronze. I would urge that it is a metaphysically necessary truth, obtaining in virtue of the essences of such objects – obtaining, that is to say, in virtue of what a bronze statue is and what a lump of bronze is – that at any time at which it exists a bronze statue coincides with a lump of bronze, which is numerically distinct from that statue. Likewise, it is a metaphysical possibility, again obtaining in virtue of the essences of such objects, that the same bronze statue should coincide with different lumps of bronze at different times. And I say this despite the protestations of some metaphysicians that they do not understand how such things can be the case – how, for instance, two numerically distinct things, one of them a bronze statue and the other a lump of bronze, can be composed of exactly the same bronze particles at one and the same time. If they genuinely do not understand this, then I say that they have not properly grasped what a bronze statue is or what a lump of bronze is. For in grasping those essences they would grasp what the identity and persistence conditions of such objects are, and thereby know that these are different and that in virtue of SUBSTANCE & ACCIDENT • 107

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these different identity and persistence conditions the truths that they purport not to understand are indeed truths. It will be recalled that, according to the currently prevailing modal account of essence, an entity’s essence consists in the set or sum of its essential properties, these being the properties that it possesses in every possible world in which it exists. Hence, according to this view, an entity’s essence is a further entity, namely, a set or sum of certain properties. According to my version of the neo-Aristotelian account of essence, however, an entity’s essence is not some further entity.8 Rather, an entity’s essence is just what that entity is, as revealed by its real definition. But what E is is not some entity distinct from E. It is either identical with E (and some scholars think that this was Aristotle’s view) or else it is no entity at all: and the latter is my own view. On my view, we can quite properly say that it is part of the essence of a certain entity, E, that it possesses a certain property, P. But this does not entitle us to say that P is a part of the essence of E. The latter would imply that E’s essence is a further entity, with P as a part, which accords with the orthodox view that E’s essence is a set or sum of certain properties. But I have rejected that view. We should not, in my opinion, reify essences. And although I speak of essences as having ‘parts’, I have already explained what I mean by this, in a way that does not require us to reify essences. Note that there is a particularly objectionable feature of the view that an entity’s essence is some further entity. This is that, since it seems proper to say that every entity has an essence, the view generates an infinite regress of essences. Neither the view that an entity is identical with its own essence, nor my preferred view that an entity’s essence is not an entity at all, has this defect. And my view, as we shall shortly see, has an additional advantage when we come to consider the epistemology of essence, that is, the proper account of our knowledge of essence. Given that all metaphysical modality is grounded in essence, we can have knowledge of metaphysical modality if we can have knowledge of essence. Can we? Most assuredly we can. We have already seen this in the case of geometrical figures, such as an ellipse. Knowing an entity’s essence is simply knowing what that entity is. And at least in the case of some entities, we must be able to know what they are, because otherwise it would be hard to see how we could know anything at all about them. How, for example, could I know that a certain ellipse had a certain eccentricity, if I did not know what an ellipse is? In order to think comprehendingly about something, I surely need to know what it is that I am thinking about. And sometimes, at least, we surely succeed in thinking comprehendingly about something – for if we do not, then we surely never succeed in thinking at all, which is absurd. Here it may be objected that currently prevailing causal or ‘direct’ theories of reference precisely deny that a thinker must know what it is that s/ 8   See further my “Two Notions of Being: Entity and Essence”, in Being: Developments in Contemporary Metaphysics, ed. Robin Le Poidevin (Cambridge: Cambridge University Press, 2008).

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he is thinking about in order to be able to think about it. For, on this account, a thinker need not grasp the ‘sense’ of some referring expression in order to be able to refer successfully by means of such an expression to its referent: rather, reference is supposedly secured by a causal connexion between the expression and the thing referred to. This is not the place for me to enter into a full-scale debate about theories of reference. I would only urge that, even if the causal approach accommodates some of our referential practices, it does not make sense to suppose that, for successful reference to occur, no one need ever know what it is that they are thinking about. It suffices for my purposes that at least sometimes a thinker must be able to know this. Here another objection may be raised, as follows. Sometimes, it may be conceded, we have a concept of what it is that we are thinking about: but that is all, and we cannot be entitled ever to suppose that anything actually falls under that concept. For instance, we might have the concept of a table, and believe that we are thinking about such a thing: but for all that, it might well be that in reality there are no tables, and hence no table for us to be thinking about. But let us reflect for a moment on what concepts are. And note that in thus reflecting we are considering the essence of a concept: what a concept is. I propose that a concept is a way of thinking of some thing or kind of things. But ways of thinking of things can be more or less adequate to the nature of the things in question – that is, more or less adequate reflections of their essence. A child’s way of thinking of a triangle is less adequate than that of an experienced geometer. A concept of an entity E is fully adequate only if it captures the whole essence of E. Now, I concede that a thinker may be able to think of some entity without fully grasping its whole essence, and this is no doubt the case with the child’s thought about triangles. But I see no reason to suppose that we may never fully grasp the whole essence of a certain kind of entity. Bear in mind, too, that we want to allow that we can grasp the essences not only of actually existing things, but also, at least sometimes, of nonexistent things – things such as unicorns and mermaids, perhaps. So I can happily allow that sometimes, in thinking about something, we succeed in grasping its essence and hence in thinking about it, even though no such thing actually exists. I know, for instance, what a table is or would be, and hence grasp the essence of such a thing and can thereby think about tables: but this does not commit me to acknowledging the actual existence of tables. I might be open to persuasion, by a suitably ingenious philosopher, that tables do not really exist. But if I am even to be able to understand what such a philosopher is contending, I must know what a table is or would be – what its essence is. Otherwise, I do not really know what it is whose actual existence the philosopher is denying, when s/he denies that tables actually exist. However, only a global sceptic is going to affirm that nothing that we can think about actually exists, including even ourselves and our thoughts. And such an all-embracing scepticism is self-undermining and incoherent. So I find nothing in the present line of attack to suggest that I am wrong in supposing that SUBSTANCE & ACCIDENT • 109

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we can, at least sometimes, grasp the essences of at least some things – including some actually existing things – and thereby come to know some modal truths. I mentioned earlier that, according to my account of essence, essences are not entities. This means that grasping an essence – knowing what something is – is not, by my account, a kind of knowledge by acquaintance of a special kind of entity, the thing in question’s essence. All that grasping an essence amounts to, on my view, is understanding a real definition, that is, understanding a special kind of proposition. To know what a circle is, for instance, I need to understand that a circle is the locus of a point moving in a plane at a fixed distance from a given point. Provided that I understand what a point and a plane are, and what motion and distance are, I can understand what a circle is, by grasping this real definition. And bear in mind that I do not insist that we need fully grasp the whole essence of a thing in order to be able to think about it to some degree adequately, so that even if I do not fully grasp what motion, say, is, I can still achieve at least a partial grasp of what a circle is by means of the foregoing real definition. If, by contrast, knowledge of essence were knowledge by acquaintance of a special kind of entity, then indeed we would have cause to be doubtful about our ability ever to grasp the essences of things. For what mental faculty of ours could possibly be involved in this special kind of acquaintance? Surely not our faculty of sense perception. Sense perception may provide us with knowledge by acquaintance of concrete, physical things, existing in space and time, but hardly with knowledge of their essences, conceived as further entities somehow grounding modal truths about those concrete things. If appeal is instead made to some special intellectual faculty of ‘insight’ or ‘intuition’, with essences as its special objects, then one is open to the charge of anti-naturalistic obscurantism. My own account of what it is to grasp an essence appeals only to an intellectual ability that, by any account, we must already be acknowledged to possess: the ability to understand at least some propositions, including those that express real definitions. We now have in place the basic ingredients for a thoroughgoing epistemology of metaphysical modality. Put simply, the theory is this. Metaphysical modalities are grounded in essence. That is, all truths about what is metaphysically necessary or possible are either straightforwardly essential truths or else obtain in virtue of the essences of things. An essence is what is expressed by a real definition. And it is part of our essence as rational, thinking beings that we can at least sometimes understand a real definition – which is just a special kind of proposition – and thereby grasp the essences of at least some things. Hence, we can know at least sometimes that something is metaphysically necessary or possible: we can have some knowledge of metaphysical modality. This itself is a modal truth, of course, and one that obtains in virtue of our essence as rational, thinking beings. And since we can, it seems clear, grasp our own essence – at least sufficiently well to know the foregoing modal truth about ourselves – we know that we can have some knowledge of metaphysical modality. 110 • SUBSTANCE & ACCIDENT

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BIBLIOGRAPHY Aristotle. Categories and De Interpretatione, trans. J. L. Ackrill. Oxford: Oxford University Press, 1963. Fine, Kit, “Essence and Modality”. In Philosophical Perspectives 8: Logic and Language, edited by James E. Tomberlin, 1–16. Atascadero, CA: Ridgeview, 1994. Locke, John. An Essay Concerning Human Understanding, edited by P. H. Nidditch. Oxford: Oxford University Press, 1975. Lowe, E. J. The Four-Category Ontology: A Metaphysical Foundation for Natural Science. Oxford: Oxford University Press, 2006. ― “Two Notions of Being: Entity and Essence”. In Being: Developments in Contemporary Metaphysics, edited by Robin Le Poidevin. Cambridge: Cambridge University Press, 2008. Lowe, E. J. and Rami, Adolf, eds. Truth and Truth-Making. Stocksfield: Acumen, 2009. Spinoza, Benedict de. On the Improvement of the Understanding, Ethics, Correspondence, translated by R. H. M. Elwes. New York: Dover, 1955. Wolterstorff, Nicholas. “Bergmann’s Constituent Ontology”. Noûs 4 (1970): 109–134.

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AN ARISTOTELIAN ARGUMENT AGAINST BARE PARTICULARS Lukáš Novák ABSTRACT The aim of the article is to provide an Aristotelian-inspired argument against the thesis that particulars do not have any (non-trivial) de re necessary properties. This anti-essentialist claim is addressed in the form it takes within the implicit ontology of the Transparent Intensional Logic (TIL) of Pavel Tichý, the most developed logical formalism based on Fregean fundaments up to date. The author sets out to show that given the reality of “accidental change” (or any contingent variation across time or possible worlds), there must be tropes or particular accidental forms – quite irrespectively of any assumptions concerning the nature of universals. Since the tropes must ultimately differ essentially, it follows that there are many essentially distinct natural kinds of particulars, so that insistence on essential sameness of substances turns out as unwarranted. The article concludes with some general thoughts concerning the relationship between ontology and logic. The author defends the view that our ontology should not be tailored to fit the expressive and demonstrative powers of a pragmatically chosen logical formalism, but precisely the other way around.

1. PRELIMINARIES The distinction between de dicto and de re application of modal operators is one well established in philosophy and logic since mediaeval times. Nevertheless, whereas de dicto modality is usually regarded as quite unproblematic (I am leaving Quine and his likes aside now) and the existence of de dicto necessary truths is seldom taken into question, de re modality and especially de re necessity involves a whole bunch of puzzles, of which the most fundamental one consists simply in the question, whether there is anything as de re necessity at all. De re necessity is the necessity of a property’s belonging to a subject. If we define the essence of an individual as the sum of its necessary properties, we can say that belief in de re necessity amounts to essentialism, whereas denial of de re necessity entails anti-essentialism. Nevertheless, the stipulative defi nition of essence that just has been given, however common it is among the analytics, will probably be regarded as quite imperfect by an Aristotelian. The elementary difference (among other, more subtle ones) between the “Aristotelian” and the “analytical” essence consists in the fact that the Aristotelian essence does not comprise all of the de re necessary properties of a subject, but merely those that are constitutive for it. SUBSTANCE & ACCIDENT • 113

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This is the classical difference between properties predicable per se primo modo, or the true essential properties, and the properties predicable per se but only secundo modo, a bit improperly called propria or properties in the strict sense, which do not constitute that which the thing is, but merely flow, of necessity, from its essence. contingent properties essence non-essential necessary properties Analytic essentialism

Aristotelian essentialism

Taking into account this difference, we may be tempted to distinguish between weak essentialism and strong essentialism: Weak essentialism would amount to the claim that there are de re necessary properties, strong essentialism would in addition posit properties that are not only necessary, but also constitutive for their subject. On the other hand, it seems that weak essentialism entails the strong one: if there are properties that are necessary for a subject, they either are constitutive for that subject (and thus we have strong essentialism), or there must be something in the subject that makes it require precisely these properties – and this “something” will then ultimately be some constitutive, i.e. strictly essential property. If this argument is correct, it follows that the strong, or classical Aristotelian essentialism is implied in the very acceptance of de re necessity; and since the fact that the implication holds the other way around is evident, we can say that Aristotelian essentialism is equivalent to the belief in de re necessity. One of the greatest challenges both to Aristotelian essentialism and to the belief in de re necessity is the ontological conception of “bare particulars”, which amounts to saying that all properties (except trivial ones like self-identity, and some others1) belong contingently to their subjects, or in other words, that individuals have no (non-trivial) essences. I will tackle this view more or less in the form it takes in the implicit ontology of the so-called Transparent Intensional Logic (or TIL) of Pavel Tichý, arguably the most comprehensive and elaborate formal hyper-intensional language existing (or, as its proponents like to put it, a system for the logical analysis of natural language).2 The choice of TIL is not   Like “having the same size as x” for x etc.   Tichý simply identifies individuals with bare particulars in his “On Describing”, Organon F 14, no. 4 (2007): 424–425 (draft online, http://til.phil. muni.cz/text/Tichy-OnDescribing.pdf : 1 2

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systematically unmotivated: its philosophical background is in general quite “metaphysics-friendly” – it eschews nominalism, reductionism of all sorts, and above all, it is radically objectivist. Besides, the highly-developed devices of TIL devised to capture the logical semantics of natural language constitute a very straightforward development (and correction) of the Fregean semantic insights; therefore, we can regard TIL as one of the best developed incarnations of the contemporary Fregean conception of the nature of logic.3 On the other hand, in the proposed argumentation I need not invoke anything of the special technical apparatus of TIL and I believe that my reasoning applies equally to any version of the theory of bare particulars. I will not review here the various arguments for the conception of bare particulars.4 I would just like to point to the fact that the intuitions behind the theory seem to be rooted, in some way or other, in the Fregean approach to semantics – especially, in the strict distinction between “object” and “concept” (“individual” and “office” or “role” in TIL). Once this distinction has been made, it is very hard to see how there might be a genuine case of logical de re necessity. 5 For logical necessity is the necessity that is distinguished against contradiction – but how can there ever be any contradiction between a particular and a negation of a property? It seems that contradiction requires by definition two properties. It is never the case that a property (whether a positive or a negative one) contradicts a subject. When we say, for example, that being an octopus contradicts Socrates, “Consider a specific type of thing: individuals. I would like the planet Venus to be a paradigm individual. But what I mean is the massive body of rock rushing through space utterly indifferent to whether we take an interest in it, refer to it, describe it, or even affi x the name ‘Venus’ to it. The Venus I have in mind is, I think, roughly what Gustav Bergmann aptly calls a ‘pure individuator’ and what Miss Anscombe scornfully refers to as a ‘bare individual’ (implying there are no such things). Venus is, of course, bare not in the sense of lacking properties: indeed, for any relevant property X, Venus instantiates either X or non-X. The planet is bare underneath this attire; it is the entity which enters the relation of instantiation with the properties it happens to have while remaining itself, distinct from each property and from any collection of them. Venus is bare because for any non-trivial property X it happens to instantiate, Venus might conceivably have lacked X without thereby ceasing to be the same thing. There are, of course, sundry trivial properties (e.g. the property of being X or non-X) which are necessarily instantiated by Venus – and by everything else. Exactly one (trivial) property is both necessarily instantiated by Venus and necessarily not instantiated by any other individual: the property of being identical with Venus.” 3   For a comprehensive list of resources concerning the TIL see the TIL website: http:// til.phil.muni.cz/. 4   For an argumentation by Tichý see his “Einzeldinge als Amtsinhaber”, Zeitschrift für Semiotik 9, Heft 1–2 (1987): 13–50, translated as: “Individuals and their Roles”, in Pavel Tichý’s Collected Papers in Logic and Philosophy, edited by Vladimír Svoboda, Bjørn Jespersen, and Colin Cheyne (Otago: Otago UP, Praha: Filosofia, 2005), 711–748; but especially his “On Describing”. 5   An attempt to maintain essentialism in terms of any weaker kind of necessity (say, “metaphysical necessity”) would of course amount to implicit surrender to the anti-essentialist’s case.

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what we actually mean is that being an octopus contradicts being a man, and since Socrates is a man, he cannot be, as such, an octopus. But this is merely a de dicto impossibility, and we cannot derive any de re conclusion from that, unless we first assume that being a man is de re necessary for Socrates. And again: where is our justification for such a claim?6 Notice that this failure to justify essentialism is not merely accidental, but it appears to be systematic: it seems to be impossible in principle to transcend the sphere of properties in our modal reasoning, all necessities and impossibilities seem to be inherent in properties, not their subjects. From this point of view the thesis that all particulars are “bare”, that is, have no logically necessary properties (except the trivial ones) seems almost analytic; or at the very best, essentialism must remain a for ever unsubstantiated object of faith alone. In what follows, I would like to propose a very simple argument in Aristotelian vein to the effect that anti-essentialism is, despite appearances, unsustainable. I will also try to hint at the direction where one should, in my opinion, look for the solution to the anti-essentialist argument just sketched. I say “hint”, for I feel that a thorough refutation of the anti-essentialist line of reasoning would require much more labour and much better understanding of the nature of the problem than I have at the moment. 2. THE ARGUMENT Let us take for granted that in the world of particulars there exists what Aristotle would call “accidental change” – that is, a change in which the subject that undergoes it retains its identity and merely loses or gains a certain property. This is an assumption the anti-essentialist has no reason to deny: to claim the opposite, namely that all change is essential, amounts to the position directly opposite to anti-essentialism, namely to hyper-essentialism. For example, let us assume that Peter’s acquiring the knowledge of Pythagoras’ theorem is an instance of such a change. 6   I am a bit overstating the case of the anti-essentialist here. As I have already mentioned, even the anti-essentialist has to concede that there are some “trivial” properties which are essential even to bare particulars. As it turns out, the class of this properties is not as negligible as e.g. the proponents of TIL originally wished to think – specifically, it turns out that properties can be construed that are “trivial” for one individual and “non-trivial” for another. (This was shown by Pavel Cmorej in several articles in Slovak language; an English translation of the most important one is available online: P. Cmorej, “Empirical Essential Properties and Their Constructions”, Masaryk University Brno, the homepage of Transparent Intensional Logic, http://til.phil.muni.cz/text/cmorej_empirical_essential_properties.pdf . Nevertheless, it seems that the existence of this kind of de re necessity is not regarded by the proponents of the theory of bare particulars as a true counterexample. At any rate, my argument does not depend at all on assumptions of any kind concerning the status of the “trivial” essential properties.

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Now let us analyse the situation. We have two states here: the terminus a quo, characterised by Peter’s still being ignorant of Pythagoras’ theorem, and the terminus ad quem, the state of Peter’s having already acquired the relevant knowledge. Let us call these states “S-1” and “S-2” respectively. We also have two (apparently complex) items here: Peter-as-ignorant-of-PT in S-1 – let us call that item “P-1” –, and Peter-as-knowing-the-PT in S-2 – let us call this entity “P-2”. What can we say about P-1 and P-2? In the first place, they clearly are not entirely and in all respects identical: for we are assuming that a change has taken place. On the other hand, we assume that Peter taken as such, the subject, remains one and the same individual during the change. From that it clearly follows that at least one of the items P-1 and P-2 contains something that (i) is not identical to Peter, and that (ii) accounts for the absence of perfect identity of P-1 and P-2. Now what is the nature of this “something”, the distinguishing item? Clearly, what distinguishes P-2 from P-1 is the item of knowledge that Peter acquired – let us call that item K. But what is K? What I am going to claim is that the item must be particular, i.e. not universal. For we have assumed that a change has taken place in the world of particulars: both P-1 and P-2 are thoroughly particular items. In our example, the distinguishing item can be identified as the knowledge that Peter has acquired; but this knowledge is something particular, it is an entity that exists in a certain time and place (namely the place where Peter finds himself) and can easily cease to exist again. In no way can this entity be regarded as a universal, then. I would like to be perfectly clear that I am not making here any anti-Platonist argument against the independent existence of universals. For the sake of the argument I readily concede that there well may be some universal Knowledge, which, due to the change having taken place, Peter exemplifies now but did not exemplify before.7 What I want to argue is that positing such a universal can never be a sufficient explanation of what has happened. It is not enough to say that first Peter exemplified ignorance and subsequently knowledge of the PT. It may well be so, but unless the exemplification made some real difference in the world of particulars, there would not be any real change in the world of particulars, the world we all live in. So in addition to a (putative) universal, there must be something particular that had not been there before, some particular item distinct from Peter that starts its presence in Peter as a result of the change. Let me make the argument a bit more clear. Suppose that what happens during the change P-1 → P-2 is that Peter starts to exemplify Knowledge-of-PT. So, presumably, what we have there at S-1 is Peter and Knowledge, but no relation of exemplification between them, whereas at S-2 there is Peter, Knowledge-of-PT, and the relation of exemplification of Knowledge-of-PT by Peter – let us call it 7   I will avail myself of the terminological distinction between instantiation and exemplification as maintained e.g. by E. J. Lowe in his contribution to this volume (see p. 98).

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“EpK”. Now what kind of entity is EpK, ontologically? It is clear in the first place that it cannot be ontologically reduced to the (ordered) pair of Peter and Knowledge-of-PT alone – for all that belongs to the make-up of that pair had been there already at S-1, and we suppose that some change took place between S-1 and S-2. Likewise, EpK cannot be explained away as a mere linguistic or conceptual product of indirect talk about Peter and Knowledge-of-PT – for there must at any rate be some grounding in reality that makes the talk about Peter exemplifying Knowledge-of-PT false in S-1 and true in S-2. And this grounding, whatever it might be, is what we have called “EpK”. So EpK must be some real entity in its own right; the entity that distinguishes the “ontological furniture” of S-2 from that of S-1. But now we may ask again: is this relation of exemplification a universal or a particular? If it is a particular, then we have shown that (irrespectively of whether some universal Knowledge-of-PT exists) in order that there be a real change of P-1 into P-2, there must be some individual entity in reality that distinguishes P-2 from P-18 – no matter whether we call it an individual instance of knowledge, or an individual relation of exemplification that “formally” (in the scholastic jargon) makes Peter exemplify knowledge-of-PT. But can EpK be a universal at all? It seems that it cannot, for several reasons. For example, universals are not generated and corrupted, but we have assumed that EpK has been generated in Peter at S-2, because it could not have been there at S-1.9 Besides, universals seem not to be located in space and time; but EpK seems to be located in time (the time from S-2 onwards), and probably, at least in a certain sense, also in space (for it is something that ontologically modifies Peter, and Peter is a spatial entity10). So it seems that EpK cannot be regarded as a universal. Even if we assumed that there is some universal relation of exemplification EU (let us leave aside the question whether it be the relation of Exemplification, the relation of Exemplification-of-(Knowledge-of-PT)-by-Peter, or something else), that universal would not be the item that distinguishes P-2 from P-1, because, as long as it were a universal, we could always construe the situation so that it is “already there” at 8   We are assuming that knowledge is something positive; if it were something negative, a mere privation, then, analogically, there would have to be some particular entity within P-1 in addition to what P-1 has in common with P-2 that Peter would lose in the change. 9   Even if universals are conceived in a non-Platonic way, so that the Principle of Instantiation holds (“every universal is instantiated”), and therefore it is assumed as generally possible that universals be occasionally generated or corrupted, the example can be construed in such a way that in this case Knowledge-of-PT is neither generated nor corrupted (by assuming that there is another instance of it enduring throughout the respective interval of time). 10   It is quite common to speak of some particular item of knowledge as located somewhere – in ancient times people used to travel far abroad in order to get into contact with the knowledge of famous teachers or university masters. Of course this fact can be explained away – but what cannot?

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S-1, even if we conceived of universals as necessarily instantiated or exemplified in order to exist. Furthermore, we would have to posit another relation of exemplification that would obtain between Peter and IU at S-2 but not at S-1. No matter how far we would be willing to allow the regress to go, there would ultimately have to be some particular instance of exemplification to stop it. To sum up this line of reasoning: it seems that instantiation must have a certain particular “formal effect”, to speak scholastically, otherwise it would be a merely extrinsic relation that could not be used to explain real and particular change at all. And in order that this effect may “come and go”, that the subject may acquire and lose it, it must be really distinct from the changing subject. It must be a particular entity in its own right, then. In short, what I am trying to show is that any non-essential change presupposes the existence of particular “accidental forms”, or “tropes”, or “modes”, irrespectively of whether we do or do not posit really existing universals as well. My argument appealed to temporal variation or change in time. But it could as well have appealed to modal variation, that is to say, to mere synchronous possibility for a subject to have different properties than it in fact has. If there exist real possibilities “to be otherwise” in the world of particulars (for example, I could have decided not to type this parenthesised sentence at all), then the real difference of these alternatives requires really distinct particular accidental forms or tropes that constitute the differing particular patterns of situations. If this line of argumentation is correct, it means that we have to concede that there exist at least two sorts of particulars: ontological subjects or substances, and tropes or Aristotelian accidents. Now: can the distinction between a substance and an accident be a merely accidental one? Clearly not: for if it were, it would require another really distinct accidental form that would contingently make this particular item an accident and that particular item a substance. Since this new entity would clearly be an accident as well, and since we have assumed that accidentality is itself accidental, it would require another entity to explain its accidentality, and so on, in infinitum. In other words: once we concede that accidental differences are based on really distinct particular entities that “inform” the given subjects, we must also concede that ultimately, some entities must differ by themselves, that is, essentially. Notice furthermore that what is being proved here is not merely the existence of two essentially distinct natural kinds, namely, substances and accidents. The same argument can be used to show that all differences between accidents must ultimately be essential – for if they were but accidental on a certain level, they could only be so due to different higher-level accidents, so if there were to be any differences at all, there ultimately would have to be some accidents whose essential difference could account for the accidental difference of their bearers. Or put even more generally: all differences in reality are ultimately essential differences, either of substances, or at least of accidents. If there were SUBSTANCE & ACCIDENT • 119

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no essentially different particulars, there would be no differences in the realm of particulars at all. Someone might object, though, that I have only proved the existence of essentially different tropes, but it still remains to show that substances are anything more than almost-bare substantial particulars. But this objection does not take into account the fact that as long as there is proof that there are at least some essential differences among particulars, it is not the essentialist but the antiessentialist who bears the burden of proof. It has been shown that – broadly speaking – essentialism is true. It is the anti-essentialist’s task to show why substances should be such an exception among all the particulars as to lack all the lower-generic and specific essential determination; or, in other words, why there is just one natural kind of substances, despite the vast variety of accidental kinds. 3. SOME CONCLUDING REMARKS By way of conclusion, let me say a few words concerning the anti-essentialist argument sketched above and the light which the present refutation can shed on it. The Aristotelian analysis of reality distinguishes between two very different kinds of distinctions: the distinction between a substance/subject and an accident, and the distinction between a universal and a particular. The presented refutation of bare particulars was nothing but a defence of the view that in the realm of particulars there must be both substances and accidents (and therefore the two distinctions do not coincide). Fregean semantics, on the other hand, identifies these two distinctions, to the effect that for Frege a subject is always a particular, whereas its “properties” are always universals.11 It seems to me that it is this unhappy confusion that prevents those confined to the Fregean optics to see the justification for de re modalities. In Fregean semantics, essential properties have been isolated from their subjects as it were a priori, as an outcome of the Fregean strict semantic distinction between object and concept. For an Aristotelian, universals do not form a distinct ontological category – they are just abstractions from particulars. All predicable properties are therefore originally located in the things themselves, they form the essences of particular substances and particular accidents. In terms of Wolterstorff and Loux, Aristotelian ontology is “constituent”, not “relational”.12 The particulars are, so to speak, self-sufficient, as regards the explanation of their variety. It appears therefore not only as unmotivated, but as ultimately absurd, to deny them essential determination. What remains is the question, how and whether at all Fregean logic and semantics might possibly be amended in order to be able to capture formally the de re necessity. I will not go into that question here. But one thing seems to be clear 11

  Speaking about first-order predication only, of course.   Cf. M. Loux’s contribution to this volume (p. 43).

12

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at least: the problem whether there are de re necessities seems to be a genuine, non-trivial metaphysical question which deserves to be solved by means of an enquiry into the nature of reality itself. If it seems that it is trivially solved as it were a priori, merely by way of an implication of the formal make-up of our formal system of logic, then we should not assume that what looks like a genuine problem is in fact a pseudo-problem, but rather that our formal system of logic has some metaphysical presumptions, whose validity cannot be properly evaluated within or by means of that system. In other words: just like a physicist cannot disprove the existence of immaterial entities, because due to the limits of his methodology he simply is not capable, as a physicist, to “see” anything immaterial, so a Fregean cannot disprove the existence of de re necessity, because his system of logic simply would not allow him to see it, even if it existed. The argumentation of those who would like to discard de re necessity on the basis of the fact that it cannot be captured by means of Fregean logical systems make the error of equating logic as such with a particular and limited notational system. But whereas there are many different logical systems of different expressivity, capable of capturing different aspects of “logical forms” of statements, logic, or the logic, is just one. The correct step in case some system proves ill-fit to capture those features of reality (or of our statements about reality) which we have chosen to enquire about seems to be to try to amend the system, or devise a better one, – and not give up the envisaged enquiry instead.13

BIBLIOGRAPHY Cmorej, Pavel. “Empirical Essential Properties and Their Constructions”, Masaryk University Brno, the homepage of Transparent Intensional Logic, http://til.phil.muni. cz/text/cmorej_empirical_essential_properties.pdf . Loux, Michael J. “What is constituent ontology”. In Metaphysics: Aristotelian, Scholastic, Analytic, edited by L. Novák, D. D. Novotný, P. Sousedík, D. Svoboda, 43–57. Ontos Verlag, 2012. Lowe, E. J. “Essence and ontology”. In Metaphysics: Aristotelian, Scholastic, Analytic, edited by L. Novák, D. D. Novotný, P. Sousedík, D. Svoboda, 93–111. Ontos Verlag, 2012. Tichý, Pavel. “Einzeldinge als Amtsinhaber”. Zeitschrift für Semiotik 9: 12–50. Translated as: “Individuals and their Roles”. In Pavel Tichý’s Collected Papers in Logic and Philosophy, edited by Vladimír Svoboda, Bjørn Jespersen and Colin Cheyne, 711–748. Otago: Otago UP and Praha: Filosofia, 2005. ― “On Describing”. Organon F 14, no. 4 (2007): 423–469. Draft online, http://til.phil.muni. cz/text/Tichy-OnDescribing.pdf . 13   The work on this paper has been supported by the grant no. P401/11/0906 “Možnosti realistické epistemologie tváří v tvář novověké kritice” of the Czech Science Foundation (GAČR).

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THE ONTOLOGY OF NUMBER: IS NUMBER AN ACCIDENT? Prokop Sousedík, David Svoboda ABSTRACT The paper deals with the ontological status of number. The authors of the paper are convinced that it is useful to discuss the concept of number within the framework of the Aristotelian basic division of being into substance (ens in se) and accident (ens in alio). Number can thus be taken as ens in se or ens in alio. Aristotle and his followers believed that number is an accident and this concept is explained in the fi rst part of the paper. In the second part it is shown that the Aristotelian concept is not correct. However, if number is not an accident then it seems that it must be identified with a Platonic entity (ens in se). In the third part the authors reject this Platonic conclusion that G. Frege seems to have defended. In the fourth and fifth part the authors show that from the logical point of view number is an object but from the ontological point of view it is an entity that depends on linguistic structure (ens in alio).

1. INTRODUCTION The issue of number has attracted attention since the origin of philosophy. Many conceptions have arisen since then. An appropriate instrument by which these conceptions can be classified is the fundamental idea of the Aristotelianscholastic ontology according to which being (ens) can be divided into two different groups. In the first group there are substances, i.e. entities that exist independently (entia in se); in the other group there are accidents (entia in alio), i.e. entities that are dependent upon substances. As the entities are divided into two groups, the various conceptions of number can be similarly divided into two groups. In the first group there are conceptions whose supporters (e.g. Pythagoras and Plato) held number to be an entity existing independently outside of time and space (i.e. ens in se). In the other, there are conceptions whose followers (Aristotle, Thomas Aquinas) considered number to be an entity dependent on other beings (i.e. ens in alio). It is obvious at first sight that the well known dispute between Plato and Aristotle (even in this sort of modification) penetrates into this discussion on the nature of number. If we take Plato’s side, we assume the existence of independently existing entities including numbers that are separated from our empirical world; if we hold Aristotle’s view we must deal with the empirical world and numbers should be entities that are somehow in our empirical world and depend on it.

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In this dilemma, we prefer Aristotle’s view. Plato’s conception seems to be problematic for various ontological and epistemological reasons. We not only reject the Platonist metaphysics of number but we also disagree with the seemingly more sober contemporary conceptions. We reject Frege’s solution – however inspiring it may be in many respects – which in our opinion also leads to the conclusion that numbers are independently existing objects which bear the nature of classes. On the other hand, Aristotle’s approach seems metaphysically more acceptable to us. This approach leads to the conclusion that number is ontologically dependent on its bearer: hence it is not ens in se but ens in alio, in concrete terms an accident of quantity.1 The Peripatetic solution to the problem leads us to the question to what extent this conception is acceptable. Is number an accident in the same way as e.g. wisdom? These questions determine the first two parts of our contribution. In the first part we put forth Aquinas’s conception of number according to which number is an accident of quantity. In the second part this conception is critically considered and rejected. However, this makes our position questionable, for if number is not an accident of quantity (i.e. ens in alio), then it seems that it is a substance (ens in se). This conclusion, however, implies (as mentioned above) the Platonic conception of number, which we do not accept. That is why in the rest of the paper we try to set out a reinterpretation of the Peripatetic concept of ens in alio so that number can be conceived as a special kind of “accident”. 2. NUMBER AS A SPECIES OF QUANTITY As mentioned above, Aristotle and Thomas considered quantity to be an accident. The characteristic feature of this accident is that it belongs only to material and not to spiritual substance,2 since only a material substance can be more or less extended, i.e. quantitative. On the contrary, it can’t be said that any spiritual substance is extended. However, what does quantity as a real accident cause in a material substance? This question can be answered if we realise what is the difference and similarity between material and spiritual substance. Both kinds of substance are similar as far as they represent a certain whole, i.e. a spiritual whole and a material whole. What is the difference? The material whole consists of parts which are ordered in such a way that one part has its being next to the other part; on the contrary, the spiritual whole has no parts ordered in such a way (since it is simple). Thus quantity adds to the material whole a certain order of (integral) parts.   Cf. Aristotle, Categoriae, c. 6.   Quantity is the first accident of a material substance, every other accident inheres in the composite substance through quantity. Cf. Thomas Aquinas, Summa theologiae [STh] I, q. 77, a. 7, ad 2. 1 2

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Therefore quantity is traditionally defined as “the order of parts in the whole” (ordo partium in toto).3 There are various species of quantity, since there are different kinds of ordering parts in the whole. The way of ordering the parts in the whole is determined by the kind of relationship which is among the parts. This relationship can be twofold: either the parts of the whole are connected to each other or there is no such connexion between them. If the parts are connected to each other we call quantity continuous; if the parts are not connected to each other quantity is named discrete. Discrete quantity is also called categorical multitude. The specific difference between continuous and discrete quantity is thus the existence or non-existence of the connexion between the appropriate parts. By connexion we mean this: the parts of a quantitative whole are connected to each other if the end of one part is identical to the beginning of the other; the parts are not connected to each other if the end of one part is not identical to the beginning of the other. If the endpoint of one part is not identical to that of the other, these parts are materially divided. Since this kind of division concerns only continuous quantity which determines only material substances, we call it a material division.4 Hence, it is obvious that parts of continuous quantity are connected to each other while parts of discrete quantity are not connected to each other. Discrete quantity originates by a material division of continuous quantity, thus materially divided units are given.5 On the contrary, the negation of a material division defines the quantitative one or the one as the principle of number.6 It does not follow explicitly from St. Thomas’s texts whether he holds the discrete quantity for a genus of particular numbers (two, three, four etc.) or not; i.e. whether or not he identifies discrete quantity with number as such. On the one hand there are statements in his works that make us hold that discrete quantity is an intermediate genus of particular numbers, i.e. statements that identify discrete quantity with number as such; on the other hand, when Thomas explicitly defines number, it seems that number as such cannot be identified with discrete quantity and that number is subordinated to discrete quantity.7   STh I, q.14, a. 12, ad 1: “De ratione quantitatis est ordo partium.”; Summa contra gentiles [SCG] 4, c. 65: “… positio, quae est ordo partium in toto, in eius [quantitatis] ratione includitur: est enim quantitas positionem habens.” 4   STh I, q. 30, a. 3, co.: “Est autem duplex divisio. Una materialis, quae fit secundum divisionem continui, et hanc consequitur numerus qui est species quantitatis.” 5   STh I, q. 30, a. 3, co.: “… divisionem continui … consequitur numerus qui est species quantitatis.” 6   Thomas Aquinas, In II Sent., dist. 3, q. 1, a. 3, ad 1: “… unum quod est principium numeri, qui est discreta quantitas, causatus ex divisione materiae vel continui…” 7   The problem presented dealing with the mutual relation between number and quantitative multitude (discrete quantity) is of minor importance for our further observations. We will thus further incline toward the opinion that the number itself is – according to Thomas – a species of discrete quantity. 3

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Let us consider the two definitions of number which can be encountered in Thomas‘s texts. According to the first, number is “an aggregate of (materially divided) units”8 while according to the other, number is “[categorical] multitude measured by the one” (numerus est multitudo mensurata per unum).9 It is clear that in both of these definitions the genus is multitude (respectively materially divided units), whereas in the first definition the specific difference is to be aggregated; in the other to be measured by the one. Number as such is divided into particular numbers (two, three, four etc.) and is thus a genus and particular numbers are species. Particular numbers differ by specific differences. This is – in accordance with Thomas – the last unit of number, which defines its species. It is the last unit which makes number three different from number two, number four different from number three etc. From the above presented definition of number, it follows that the quantitative one is not number but it is the principle of number.10 Since the numbers two, three, etc. are gained by the abstractive act of our intellect from concrete numbers of things, the former numbers exist only as an object of our intellect. Numbers which originated by the abstractive act of our intellect are called absolute numbers and under these numbers the so-called concrete numbers of things are situated, e.g. two particular people, two particular rams etc.11 A concrete number exists, unlike an absolute number, in the real world. What we have done so far in accordance with Thomas and Aristotle is the reconstruction of Porphyrian Tree for the category of quantity. It can be seen, hence, that number as a species of quantity does not differ essentially from other accidents. A number exists either as an absolute number (number 2, 3, 4 etc.) or as a concrete number of some particulars (two people, three rams, four dogs etc.). It follows that (from the logical point of view) the statement in which an absolute number is predicated (let us call it in accordance with Frege a number statement) has the same subject-predicate structure as any common singular statement. In any number statement there must be a singular term in place of the subject which refers to the logical particular of a certain kind (in this case to an aggregate) and a common term in place of the predicate to which the given par ticular is subordinated. The only difference between “common” accidents and numbers lies in the fact that the subject of a number statement is not one   Thomas Aquinas, In VII Physic, lect. 8: “numerus… est… aggregatio unitatum”.   In I Sent, dist. 24, a. 2, obiec. 4: “numerus est multitudo mensurata per unum”; In I Sent, dist. 24, a. 3, ad 3; STh I, q. 7, a. 4. 10   Thomas Aquinas, De instantibus, c. 3: “… unitatem numeri, quam constat non esse numerum…”; this statement is, however, specified in De potentia, q. 7, a. 3, ad 7: “… per reductionem [est] … unitas in genere numeri…” 11   STh I, q. 30, a. 1, ad 4: “… numerus est duplex, scilicet numerus simplex vel absolutus, ut duo et tria et quatuor; et numerus qui est in rebus numeratis, ut duo homines et duo equi. Si accipiatur numerus absolute sive abstracte… sic non.” 8 9

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substance but an aggregate of more substances.12 The subject of the statement the Evangelists are four is not only one concrete substance (let us say John), but the whole set of Evangelists – Matthew, Mark, Luke and John. Thus the logical subject of number statements is a singular term referring to an aggregate and not to a first substance.13 The epistemological scheme of this Aristotelian account corresponds to the ontological scheme, for our knowledge starts from sensual perception. In our case, we begin with the observation of some aggregates (concrete numbers). In abstraction, which was later on called “psychological”, we will leave aside the fact that these are aggregates of apples, sheep or people. Thus an aggregate of further unspecified units is gained, i.e. the concept of particular number. This aptly corresponds to the definition according to which number is an aggregate of materially divided units. However, the definition according to which number is a multitude measured by one seems to be less plausible from this perspective, since it is unclear how some multitude measured by one could result from a psychological abstraction. Hence in the following observations we will use the first mentioned definition (number is an aggregate of materially divided units).14 3. PROBLEMS WITH THE CATEGORY OF QUANTITY The Peripatetic approach seems, at first sight, to be ontologically and epistemologically very sober and well in accordance with the “healthy spirit” of Aristotle’s philosophy. In spite of this there are many problems connected with this conception which can hardly be overcome. There are many arguments against this conception. Although these arguments seem to be somewhat heterogeneous, they can be arranged. If number is subsumed under the category of quantity, then number statements must have a subject – predicate structure. In place of the subject there is a singular term which refers to a concrete aggregate; in place of the predicate there is a universal term which is in our case a number. Hence the arguments against the subsumption of number under the category of quantity can be divided into two groups. In the first group there are arguments that question the claim that the subject of a number statement is a singular term   Thomas Aquinas, Quaestiones de quolibet XI, q. 1, ad 1: “… numerus non est in rebus numeratis sicut in loco, sed sicut accidens in subiecto.” 13   Ibid.: “Praeterea, unus numerus, licet sit in omnibus numeratis sicut unica essentia, non tamen est in qualibet parte; quia non quaelibet pars numeratur eodem numero.” 14   It should be said that a very similar conception was later on defended by J. S. Mill, A System of Logic (London: Parker, 1843), book III, chap. 24, §5. A resembling approach is defended nowadays e.g. by E. J. Lowe, who claims that a number is a universal and its instances are particular groups or aggregates. This corresponds almost literally to Aquinas’s conception according to which it is necessary to distinguish between an absolute number and a concrete number. Cf. E. J. Lowe, The Possibility of Metaphysics – Substance, Identity, and Time (Oxford: Clarendon Press, 1998), 210–227. 12

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which refers to a concrete aggregate. In the second group there are arguments that question the claim that the predicate of a number statement is a number. For historical reasons we start with the second group of arguments. The scholasticists themselves noticed that there is a very disagreeable consequence of the subsumption of number under the category of quantity. For if we say that some aggregate is n-numbered, we predicate of it the whole content of the predicate. Now it is clear that the content of a predicate includes every concept which is superior to it. So if a number is predicated, the predicate includes the concept of discrete quantity. However, discrete quantity, as we know, can be predicated only of a set of materially divided units. In the number statement the Evangelists are four it is therefore claimed that Matthew, Mark, Luke and John are materially divided units. Numbers, however, can be predicated not only of aggregates, whose parts are materially divided, but also of aggregates whose parts are not materially divided. We commonly speak about the number of prime numbers, the number of Aristotelian categories, the number of ideas etc. However, categories or ideas are certainly not materially divided.15 Aquinas was well aware of this problem. A property abstracted from external things surely cannot be predicated of non-material entities without a change in the sense. So far there is agreement between Aquinas and Frege. Further on, however, the views of the two philosophers differ. While Thomas holds that number statements predicated of non-materially divided entities have a different sense than number statements concerning materially divided entities (they are analogical or metaphoric), Frege regards it as a reductio ad absurdum of the categorical conception of number. It seems absurd to claim that number ten is predicated of the Aristotelian categories in a different sense than of the fingers of my hands.16 Another problem is linked with the manner in which a number is formed, i.e. with the process of abstraction. If the definition according to which number is an aggregate of units is accepted, it must also be admitted that number, in the absolute sense, originates through an abstraction from concrete numbers (concrete n-tuples). In this abstraction we leave aside all dissimilarities due to which the concrete units differ from each other. Hence, the result of this abstraction is an absolute number, i.e. a set of units which do not mutually differ. However, the problematic consequence of this abstraction is the fact that the set of units abstracted in such a way becomes an undistinguishable unity. While among 15   Frege says to this problem: “It would be really remarkable if we could transfer the property abstracted from external things to events, ideas, concepts without any change of the sense. The result would be the same as if we wanted to speak about fusible event, blue idea, salty concept or solid judgement.” – G. Frege, Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl (Breslau: Koebner, 1884) [GA], 31. 16   Cf. GA, 31.

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concrete units there are many dissimilarities, among abstract units there cannot be any differences and thus one can hardly speak about their aggregation.17 Let us proceed to the second group of arguments now. As stated above, these arguments are concerned with the subject of a number statement. What is then the subject of the statement The Evangelists are four? At first sight it is obvious that the subject Evangelists cannot be applied distributively. (It cannot refer in the same way as it refers in the statement The Evangelists are saints, in which saintliness is predicated of each of the Evangelists separately.) Evangelists are surely not four separately but only collectively. Hence, the subject of the number statement must be (according to Aquinas) a group of individuals who participated in the origin of the New Testament and thus they create a unity of a special kind. This unity, to which we refer through a singular term in the place of the subject, has been called an aggregate and it is characterised by the number four. So it is clear that there is the same subject in the following two statements: The Evangelists are four and The Evangelists are the authors of the first part of the New Testament. However, if we admit that in number statements there is in place of the subject a singular term which refers to the appropriate aggregate, serious difficulties arise. The first problem is closely connected with the ontological character of number. It should be recalled that a concrete number is a special kind of accident, since its subject is not one singular substance but an aggregate of substances. So if a number is predicated it is clear that the subject of the number statement is not a concrete individual substance but it is an aggregate of individuals and the number is thus predicated not of a concrete substance but of a group of substances. The scholasticists were well aware of this problem and it aroused many discussions. Let us leave these discussions aside and assume that a good solution to this problem was found. However, even under this presupposition (which is of ontological character) other problems arise which can hardly be overcome. If a number is predicated of an aggregate, then the aggregate must have a certain kind of unity. This unity can be either a fusion of individuals, or a set of individuals. If the aggregate does really have a certain kind of unity, then in place of the subject there must be a singular term and in place of the predicate there has to be a universal term. The predicate (number) must determine the unity of the aggregate as a whole and not distributively parts of this whole, since e.g. the Evangelists are four altogether and not separately. From the logical point of view it should be a singular statement. However, from the ontological point of view the particular which the subject term refers to must be an instantiation of the universal to which it is referred by the predicate. Just as a group is characterised by non-distributive predicates, e.g. a class can be called disciplined, so a group is determined by number predicates. 17

  Cf. GA, 40–41.

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However, if a statement with a number predicate is a singular statement, then the rules of logic must be applicable to it. One logical rule says that in extensional contexts expressions with the same reference can be replaced salva veritate. Let us apply this rule to a singular term which stands in place of the subject and which refers to a concrete aggregate. For the sake of our argument it will be useful to examine primarily the statements which have in place of the predicate a common (not quantitative) property. E.g. a teacher says: The pupils of the class in which I taught maths today were undisciplined. The subject (in our case a definite description) refers to a definite unity (aggregate) and the predicate to the property which the unity instantiates. “To be undisciplined” is naturally the property of the class as a whole and not of its parts taken separately. The teacher does not naturally want to say that each and every student was undisciplined and thus that some of his favourite pupils were undisciplined as well. Now, it is clear that in statements like these the subject term can be replaced by another term which has the same reference. In our case the term the pupils of the class in which I taught maths today can be replaced by the proper name of this class. We can thus say VIII. C was undisciplined. A similar conclusion should be reached in the case of a number statement. It can be said The pupils of the classroom in which I taught maths today were thirty. However, if the subject term of this statement is replaced by the proper name of the class, then we come to the senseless statement VIII.C were thirty. It is clear that the logic of our speech does agree with the solution according to which number is a predicate which is predicated of a singular subject. However, it does not follow that the Peripatetic conception of number is necessarily unacceptable. Our considerations so far stayed only at the linguistic or logical level. An ontologist or metaphysician could object that language only disguises our ideas and that is why the inadequacy of the metaphysical conception cannot be proved in the merely linguistic domain. Although our approach to metaphysics is descriptive and the argument presented above could thus be sufficient, the same argument can be introduced at the ontological level as well. In other words: as the identification of number with a predicate can be shown as unacceptable, so the identification of number with a universal can be shown to be unacceptable too. It should be recalled that if a singular term is used in place of a subject it is presupposed that there is a certain unity to which the subject term refers. This unity is represented not only by a concrete individual substance (St. John the Evangelist), but also by an aggregate (the Four Evangelists). In any case, the unity is always an instance of various universals. St. John the Evangelist is an instance of saintliness, a concrete pupil is an instance of naughtiness, the Four Evangelists are the instance of authors of the first part of the New Testament, the class of students is an instance of undiscipline. The relation between an individual and a universal should be applicable to number as well. A concrete aggregate (or concrete number) should be a particular which is an instance of a universal number (absolute number). Thus, the 130 • SUBSTANCE & ACCIDENT

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Evangelists should be an instance of the universal number four. However, it seems to us very problematic. If some particular is an instance of a universal number, then this particular should possess everything subsumed under the concept of number. Since number is a species of discrete quantity, it must include multitude. However, multitude negates unity. So if number includes multitude, it seems that its instances cannot be real unities. Frege says in a similar way: “... number is only another name for dissimilarity. Exact identity is unity, multitude originates with dissimilarities.”18 Further, a similar argument can be encountered in the The Foundations of Arithmetic where Frege criticises the conception according to which number is a property of external things. In fact, Frege refuses the view that the subject of a number statement is a singular term which refers to a concrete aggregate. Frege’s argument can be reconstructed as a reductio ad absurdum. Let’s presuppose that number is a property of external things and this fact is expressed through a singular statement in which we refer to the appropriate aggregate by a singular term. From the logical point of view it is thus clear that a number statement does not differ from a statement, e.g. This stone weighs 2 kg.19 However, the identification of number statements with usual singular statements leads, according to Frege, to contradictory consequences. Frege says: If I put a stone in someone’s hand asking how much it weighs, I gave him the whole object for his consideration. If I give him a pack of cards and ask him about number, the person does not know if I want to know the number of cards, the number of the complete pack or the number of trumps in skat.20

Hence, it is clear that various numbers can be ascribed to the pack of cards. It is obvious that one thing cannot be in the same way a bearer of contrary predicates (various numbers). The assumption that in a number statement we characterise external things (aggregate) leads to a contradictory conclusion and thus it must be rejected. Our two kinds of arguments against the identification of numbers with the accident of quantity have something in common. Both hint at the fact that direct reference to an aggregate whose elements are counted, leads to an absurd or contradictory conclusion. In other words, they hint at the fact that, in the case of number statements, the traditional division of statements into the subject (aggregate) and the predicate (number) fails.

  GA, 42.   There is a certain difference only at the ontological level. While in the statement This stone weighs 2 kg the subject term refers to a concrete individual, in a number statement the singular term refers to a group or an aggregate of individuals. 20   GA, 29. 18

19

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4. FROM THINGS TO CONCEPTS – FROM BEING TO LANGUAGE We have shown in the previous paragraph that the identification of number statements with singular subject-predicate statements has absurd or even contradictory consequences. This implies that the whole Peripatetic conception according to which number is subsumed under the category of quantity is unacceptable. If number is not a species of quantity, it does not exist in external things. However, where else could number exist if not in external things? In solving this question we are inspired by Frege’s example of the pack of cards. The main problem lies in the fact that contrary predicates (different numbers) are ascribed to one and the same pack of cards. According to Frege we come to this unacceptable conclusion because we incorrectly conjoin number with an object (aggregate). However, what else besides an aggregate should number be conjoined with? Trying to answer to this question we shall notice that the same pack of cards can be referred to in many different ways, e.g. the cards in my hand, piles of cards in my hand, suits in my hand etc. If we refer to the pack in these various ways, what is changed is not the object of reference but the concept determining “the way of givenness” (Art des Gegebenseins) of the appropriate object (aggregate). Herewith the answer to our question can already be given. Number cannot be conjoined with the constant object, i.e. with the same pack of cards, but rather with the concept through which we refer to the object (pack of cards). One and the same pack of cards can be referred to by various concepts and different numbers can be further conjoined with these concepts. What kind of concepts, however, are we dealing with? These concepts must provide the criterion of identity through which we are able to identify an appropriate aggregate. In other words, these concepts have to be descriptions. Nevertheless, this is only a necessary but not a sufficient condition. Besides, these concepts must also have so-called unifying power. This power causes that mutually divided entities (i.e. some multitude) form a certain type of unity to which it is further referred. E.g., it is the concept a card in my hand through which the real cards in my hand have a special type of unity. This unity is possible only if the concept expresses a property shared by the units of some multitude and thanks to this property we are able to determine the united objects as opposed to other objects. These concepts are nowadays called sortal concepts.21 It should be said that sortal concepts not only help us to define the united objects but they are also used as a unit of counting.22 So it is clear that the united objects include 21   Cf. GA, 55; P. F. Strawson, Individuals, An Essay in Descriptive Metaphysics (London: Routledge, 1964), 168; D. Heider, “Sortální termíny a problém identity. Neoaristotelismus v současné analytické metafyzice”, Filosofický časopis 53, no. 2 (2005): 167–194. 22   Since if we count individuals that form a certain kind of unity thanks to this concept, a unit of the counted multitude must be available beforehand. Thanks to this unit we can

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only those individuals of which the given sortal concept can be truly predicated. Hence, number is not conjoined with an aggregate of external things but rather with a sortal concept. If we agree with Frege on this point together with him we have turned from objects to concepts or (in other words) we have made a shift from being to language. Following this linguistic turn other problems mentioned above can easily be solved. E.g. let us reconsider the argument according to which the replacement of a singular term (in the place of the subject of a number statement) with another singular term with the same reference leads to a meaningless statement. In our case the description the pupils of the class where I taught maths today was replaced by the proper name VIII. C. It can easily be explained why we came to the meaningless statement if Frege’s conception is accepted. The replacement of the description by the proper name leads to nonsense because there is no concept conjoined with the proper name VIII. C.23 However, we come to a nonsensical statement even if the description is replaced by another description. This happens if the concept cannot be held as a unit of multitude, i.e., as a sortal concept. An example of the concept which is chosen inappropriately (i.e. of a non-sortal concept) could be the class where I taught maths today. It is clear that in the number statement Pupils of the class where I taught maths today were thirty it is inadequate to replace the subject of this statement with the expression the class where I taught maths today. It would also lead to a nonsensical statement. It should not be overlooked that thanks to “the turn to concepts” we can also solve the above mentioned problem with the application of number to a non-material multitude, since sortal concepts make up the unity of both materially divided unities and materially not divided entities. The concepts under which materially undivided unities are subsumed do not ontologically differ from the concepts through which materially divided units are united. Number can be conjoined with these concepts every time and in the same sense. Therefore the absurd idea – according to which we predicate number of material objects in another sense than of non-material objects – can be rejected. There is no ontological difference between the concepts the fingers of my hand and the Aristotelian categories, the ontological difference is rather between my material fingers and non-material categories. Frege’s concept of number differs from that of Aristotle’s or Aquinas’s primarily in the fact that Frege conjoins number to concept and not to object. It is, however, interesting to point out that the essential difference cannot be found in the definitions themselves. Frege would probably not object to Aquinas’s definition identify the counted elements. Something is thus held as a part of the counted amount, something is not. The only sensible candidate in this respect is a sortal concept. The unit of counting can be e.g. a card in my hand or a suit of cards. 23   This can be seen as another argument in favour of Mill-Kripke theory of proper names.

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according to which number is a multitude measured by the one.24 Nevertheless he would certainly add that the one is an arbitrarily chosen unit, i.e. a sortal concept. Frege would not probably object to the other definition according to which number in an aggregate of units, but he might also add that this aggregation or unification is achieved again by the sortal concept.25 However, these additions are very important from our point of view. They show that number must be conjoined to a concept and not to an aggregate. These thoughts could lead us to the incorrect conclusion that in place of the subject of number statements there stands not an aggregate but rather a concept and in place of the predicate there is a number. It would follow that from the logical point of view a number statement is a subject-predicate statement. However, according to Frege number cannot be conjoined to a concept in such a way! Number is not attributed to a concept in the same manner as properties are ascribed to individuals, e.g. as the discoverer of America is ascribed to Columbus. According to Frege it is precisely on the contrary: number is conjoined to a concept in the same manner as a concrete object is conjoined to its description. Similarly, as the descriptive concept the discoverer of America is conjoined with the concrete object, Columbus, so the abstract object – number four – is conjoined with the concept Jupiter’s moons.26 The expressions discoverer of America and Jupiter’s moons play the same logical role – they refer to the appropriate object that is said to be conjoined with the appropriate concept. This logical function of expression is also often expressed at the level of natural language: we put the definite article in front of descriptions in some languages; we often put the expression the number of in front of a concept referring to an abstract number. The expression (the number of) Jupiter’s moons thus does not refer to some aggregate of astronomic objects but rather to the abstract object which is number four. Now it is clear that our perspective so far must be changed. The number statement (the number of) Jupiter’s moons is four is (from the logical point of view) of the same kind as the statement the discoverer of America is Columbus. Both sentences express identity, i.e. the expressions on both sides of the copula are singular terms referring to the same object. Frege puts it in this way: Hence, we have an equation that claims that the expression “the number of Jupiter’s moons” denotes the same object as the expression “four”.27 However, this object is not a concrete (as it holds for the discoverer of America) but rather an abstract object.

24   Thomas Aquinas, In I Sent. dist. 24, a. 2, obiec. 4: “numerus est multitudo mensurata per unum”. 25   Thomas Aquinas, In Phys., lect. 8: “numerus… est… aggregatio unitatum” 26   Cf. GA, 57. 27   Cf. GA, 57.

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5. BACK TO PLATONISM? If a number statement really expresses identity and is not a subject-predicate statement, then we have definitively left Aquinas’s concept of number. Number is not an aggregate or the property of materially divided units. Now, what conception of number should further be considered? Above we have come to the conclusion that the statement The number of Jupiter’s moons is four has the same logical structure as the statement The discoverer of America is Columbus (both statements express identity). The number (four) is related to the concept (Jupiter’s moons) in the same way as the empirical object (Columbus) to the concept (discoverer of America). However, it leads us to a very problematic conclusion. Columbus is apparently a self-standing entity (ens in se) and it seems that numbers should have the same ontological status as well. The expression Columbus should thus denote an entity of the same ontological category as the numeral four. Both Columbus and number four should thus be a self-standing entity, i.e. ens in se. Intuitively, however, it is obvious that there is an essential difference between Columbus and number four. Columbus is a self-standing and empirical object while number four is certainly not an empirical object. However, if number four is not an empirical object, it seems that it should exist outside of our time and space. It seems that non-empirical objects have a similar ontological status as Plato’s ideas. Hence one should not be surprised that Frege admits the existence of ideal objects which exist in the so-called Third Realm.28 As it is known, Frege’s Platonism is closely connected with a very important logical-technical issue. Frege is convinced that the conditions of the identity of any abstract object make up the constitutive features of this object. If numbers are conjoined with concepts, then a criterion must be put forth through which it can be determined whether any two concepts are identical. Frege sets out that the two concepts are identical if there is a one-to-one relationship among the elements which are subsumed under these concepts (so-called Hume’s principle). Consequently, number is a class of such concepts among which there is such a relation. Thus, numbers are reduced to set-theoretical objects (classes of equivalent classes). This reduction causes serious technical problems. The first problem is of a logical-mathematical nature and is the well known paradox articulated by Bertrand Russell at the beginning of the 20th century. 28   Cf. G. Frege, “Der Gedanke. Eine logische Untersuchung”, Beiträge zur Philosophie des deutschen Idealismus 1, Heft 2 (1918–1919): 58–77: “So scheint das Ergebnis zu sein: Die Gedanken sind weder Dinge der Außenwelt noch Vorstellungen. Ein drittes Reich muß anerkannt werden. Was zu diesem gehört, stimmt mit den Vorstellungen darin überein, daß es nicht mit den Sinnen wahrgenommen werden kann, mit den Dingen aber darin, daß es keines Trägers bedarf, zu dessen Bewußtseinsinhalte es gehört. So ist z. B. der Gedanke, den wir im pythagoreischen Lehrsatz aussprachen, zeitlos wahr, unabhängig davon wahr, ob irgendjemand ihn für wahr hält. Er bedarf keines Trägers. Er ist wahr nicht erst, seitdem er entdeckt worden ist, wie ein Planet, schon bevor jemand ihn gesehen hat, mit andern Planeten in Wechselwirkung gewesen ist.”

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Russell shows in a short letter to Frege that classes or extensions cannot be held ipso facto for objects. Frege’s definition, according to which number is an extension of extensions (a class of equivalent classes), is thus unacceptable. This fact, however, did not lead Russell to the complete rejection of Frege’s conception but rather to a modification of it.29 From our perspective, the critique of Paul Benacerraf seems to be more interesting.30 It is useful to recall that Frege aimed at the solid foundation of arithmetic. In his project he followed – to a certain extent – Descartes’s idea according to which it is necessary to search for an indubitable foundation of our knowledge. Frege thought that the indubitable foundation of arithmetic is a set or a class. Benacerraf, however, pointed out that within a set theory there can be different definitions of number. E.g., number two can be identified, according to von Neumann, as a set-theoretical object {Ø,{Ø}} or, according to Zermelo arithmetic, {{Ø}}.31 If Benacerraf’s observation is accepted, it follows that sets or classes can hardly be held as the foundation on which the whole of arithmetic can be founded. Neither Russell’s, nor Benacerraf’s arguments are decisive from our point of view. What seems questionable to us is the fact that Frege’s reflections reintroduce the possibility of identifying numbers with independently existing entities and herewith the Platonic concept of numbers. The Platonic conception of number, however, is unacceptable for us. 6. NUMBER AS ENS IN ALIO The situation in which we find ourselves is anything but enviable. The more ontologically sober solution according to which number is an accident (and it is subsumed under the category of quantity) leads to unacceptable, sometimes even contradictory consequences. If we, together with Frege, reject this solution, there seems to be only one way out – it should be admitted that number is an object. However, this conception leads to Platonism which is unacceptable for us. We are facing two mutually incompatible conceptions (“Aristotelian naturalism versus Platonic idealism”). Now, the question is whether there is a middle way out which could avoid the Scylla of “Aristotelian naturalism” and the Charybdis of “Platonic idealism”. Let us return first to Frege’s solution and accept the conclusion according to which number is an object which is conjoined with a concept. Number four is thus conjoined with Jupiter’s moons in the same way as Columbus is conjoined with the concept discoverer of America. There is an agreement between Columbus   V. Kolman, Logika G. Frega (Praha: Filosofia, 2002).   P. Benacerraf, “What Numbers Could Not Be”, Philosophical Review 74 (1965): 47–73. 31   J. von Neumann, “Eine Axiomatisierung der Mengenlehre”, Journal für die reine und angewandte Mathematik 154 (1925): 219–240; E. Zermelo, “Untersuchen über die Grundlagen der Mengenlehre I”, Mathematische Annalen 65 (1908): 261–281. 29

30

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and number four, since both are objects. However, while Columbus is an empirical object, number four is an abstract object. The distinction between a concrete and an abstract object is apparently well in agreement with Platonism: empirical objects are perceived by our senses while abstract objects by our reason. Nevertheless, it seems to us that the expression “abstract” conceals an important clue, thanks to which this Platonist conclusion can be reasonably modified. The verb “to abstract” means literally to tow away. An abstract concept of wisdom can be gained if we “tow away” the form of wisdom from its subject, e.g. from a concrete man. It seems that in the case of wisdom the abstraction is clear. However, there are some problems as far as the abstraction of numbers is concerned. In our previous observation we have shown that the foundation of abstraction cannot be a concrete aggregate; we do not acquire number four from Jupiter’s moons; number four thus cannot inhere in Jupiter’s moons in the same manner as wisdom inheres in Socrates. What else then should be taken into account? The answer is ready at hand. Since we know that numbers must be conjoined with concepts let us try to focus on the concepts instead of objects! At first sight it seems that this will not be of much help. It is clear that a concept can be analysed into its elements, e.g. in the concept of moon of Jupiter there are concepts like an astronomic object, a satellite etc. Nevertheless, it is obvious that if we analyse this concept as far as we can, no concept of number can be found. No concept as such is therefore conjoined with any number, hence no abstraction from any concept taken on its own could lead us to number. To find the way out of this problem it is useful to compare the consideration of a concept taken on its own with the examination of a concrete man.32 A concrete man can be considered in two ways. Firstly, he can be examined as an independently existing object, i.e. his absolute properties (weight, height, health condition etc.) can be taken into account; secondly, his relationships to other objects can be investigated, i.e. his relational properties (to be subordinate to someone or to be superior to someone else, etc.) can be explored. Let us focus on the relational properties of a concrete individual, e.g. someone who is the dean of the Catholic Theological Faculty in Prague. It means that there are strictly defined relationships between him and the other employees of the university. Nobody is a dean taken on its own, but only in relation to other people. The function of a dean is defined purely by different industrial relations. In other words: if we want to understand who is a dean, then the functions of other representatives of the faculty must be comprehended as well. So if we say that someone is a dean, we connect with him a “position” in a relational system. Dean is thus an object, which is produced by the industrial relations of a given university. From the logical point of view this object can be 32   We are inspired here by S. Shapiro, Philosophy of Mathematics – Structure and Ontology (Oxford: Oxford University Press, 1997).

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characterised in the same way as any common empirical object. As we say Socrates is wise, it can be said The dean is an employee of the university. Both Socrates and dean refers to an object which is subsequently determined by a predicate. From the logical point of view there is no difference between these two sentences. However, from the ontological point of view one should be cautious. While Socrates refers to an object, which has an independent existence on its own, dean refers, as follows from our observations, to an object that has a completely different ontological status. The dean does not exist independently on his own, but the existence of this object depends on the industrial relations of a given university, it depends on the system of a university. Hence, it can be put forth that a dean, unlike Socrates, is not an object which has an independent existence on its own, but rather it is an object, like Socrates’s wisdom, whose existence depends on another subject. This subject is not a concrete individual but the system of a university: as Socrates’s wisdom cannot exist without Socrates, so the dean cannot exist without the system of a university; as Socrates’s wisdom depends on its subject, so the function of a dean depends on its subject. In this sense it can be said that a dean is, like Socrates’s wisdom, ens in alio and the system of a university is, like Socrates, ens in se. However, it is clear that in comparison with the original Peripatetic tradition the terms ens in alio, ens in se are used (to a certain degree) in a different sense. Of course it is questionable to maintain that the system of a university has an independent existence on its own. Even if there is a difference between a system and a concrete individual it is clear that both can be considered in the same way. Firstly, both can be considered in their “concreteness”. If we consider the system of a faculty in this way, it can be taken into account who is employed at this faculty, how old this faculty is etc. Secondly, both can be considered in their “abstractness”. Socrates instantiates the abstract property “human being” and the concrete system of the Catholic Theological Faculty in Prague instantiates some properties as well. If we consider the faculty in this way, we have in mind those relationships which produce certain positions (dean, vice dean etc.) and take into account only its structure. This structure can certainly be carried out by various systems of different faculties that differ as far as their staff constitution is concerned. The faculties of one university can be considered as various concrete systems that share the same abstract structure or (to put it in a slightly different way) they can be seen as instantiations of the same abstract structure. The faculty which has been just under consideration is one of many kinds of systems in which concrete individuals are ordered. Besides such systems there are also systems in which concepts or classes are ordered. If we accept the fact that concepts can be truly predicated of certain multitudes of individuals, then it is possible to order these concepts according to relations of more or fewer. It can thus be said that the individuals subsumed under the concept people in the square are more numerous than the individuals subsumed under the concept people in 138 • SUBSTANCE & ACCIDENT

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this room. Such information, however, usually needs specification, i.e., we want to know the number of the people in the square or, respectively, the number of the people in this room. If we want to know the number, we thereby want to know which object is conjoined with the appropriate concept. This object is naturally the appropriate number. Through assigning a number we have defined the “place” which a concept has in a relational system. A system whose relations produce numbers is, in many respects, similar to other systems. As the industrial relations of a faculty order concrete people, so the relations of more or fewer order concepts or classes. As a concrete man is conjoined with an abstract object produced by industrial relations (e.g. dean), so the concept is conjoined with an appropriate object which is not a working position but rather a certain number. It is clear that in the systems of concepts which are ordered by the relation more or fewer we can abstract from the given concepts and thereby to acquire an abstract structure. This abstract structure can be called arithmetic. We can surely consider arithmetic in a similar manner as we consider the abstract structure of faculty. We do it when we leave aside the concept which we order through counting and it happens when we are not counting things (e.g. people in the square) but rather when we are just counting (e.g. 7 + 5 = 12). It is perhaps not necessary to add here that mathematicians want to describe general properties of the structure which they examine.33 An examination of this structure is not, however, the goal of our paper for it belongs rather to mathematics than to philosophy. The important thing for us is the fact that if we turn our attention to the system or structure, the aforementioned problems with number can be solved. This shift will enable us to speak about the position in a system or a structure – from the logical point of view –in the same way as we speak about ordinary empirical objects. This shift also makes clear that the ontological status of these objects is somewhat different than the ontological status of some empirical objects (substances). While common empirical objects exist on their own, i.e., they are entia in se, numbers are produced by the relations of the system. From the ontological point of view it must be said that numbers depend on the appropriate system. This leads us to the conclusion: If we modify the meaning of the Peripatetic concept substance (ens in se) and accident (ens in alio), we could say that a system that is ordered by the relation of more and fewer is a “substance”, and objects which are produced by these relations are its “accidents”.

33   Mathematicians tend to describe the properties of a structure with the help of axioms. From the axioms of arithmetic it follows that it is a structure with the successor relation, the initial object 0 and a second order induction principle.

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BIBLIOGRAPHY Aquinas, Thomas. Summa theologiae. Vol. 4–12 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1888–1906. ― Summa contra Gentiles. Vol. 13–15 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1918–1930. ― Quaestiones de quolibet I–XII. Edited by R. M. Spiazzi. Turin, 1956. ― De instantibus. Edited by P. Mandonet. Vol. 4 of Opuscula omnia. Paris: Lethielleux, 1927. ― Scriptum super libros Sententiarum. Edited by P. Mandonnet and M.  F.  Moos. Paris, 1929–1947. ― De potentia. Vol. 2 of Quaestiones disputatae. Cura et studio R. P. Pauli M. Passion. Taurini: Marietti 1965. ― Sententia super Physicam. Vol. 2 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1884. Aristotle. Categoriae et liber De interpretatione, Ed. L. Minio-Paluello. Oxford: Oxford University Press, 1894. Benacerraf, Paul. “What Numbers Could Not Be”. Philosophical Review 74 (1965): 47–73. Frege, Gottlob. “Der Gedanke. Eine logische Untersuchung.” In Beiträge zur Philosophie des deutschen Idealismus 1, Heft 2 (1918–1919): 58–77. ― Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl. Breslau: Koebner, 1884. Heider, Daniel. “Sortální termíny a problém identity. Neoaristotelismus v současné analytické metafyzice”. Filosofický časopis 2 (2005): 167–194. Kolman, Vojtěch. Logika G. Frega. Praha: Filosofia, 2002. Lowe, E. J. The Posibility of Metaphysics – Substance, Identity, and Time. Oxford: Oxford Clarendon Press, 1998. Mill, John Stuart. A System of Logic. London: Parker, 1843. Neumann, John von, “Eine Axiomatisierung der Mengenlehre”. Journal für die reine und angewandte Mathematik 154, (1925): 219–240. Shapiro, Stewart. Philosophy of Mathematics – Structure and Ontology. Oxford: Oxford University Press, 1997. Strawson, Peter Frederick. Individuals. An Essay in Descriptive Metaphysics. London: Routledge, 1964. Zermelo, Ernst. “Untersuchen über die Grundlagen der Mengenlehre”. Mathematische Annalen 65 (1908): 261–281.

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SECTION IV

EXISTENCE

EXISTENTIAL INERTIA Edward Feser ABSTRACT The “existential inertia” thesis holds that, once in existence, the natural world tends to remain in existence without need of a divine conserving cause. Critics of the doctrine of divine conservation often allege that its defenders have not provided arguments in favour of it and against the rival doctrine of existential inertia. But in fact, when properly understood, the traditional theistic arguments summed up in Aquinas’s Five Ways can themselves be seen to be (or at least to imply) arguments against existential inertia and in favour of divine conservation. Moreover, they are challenging arguments, to which defenders of the existential inertia thesis have yet seriously to respond. The paper presents these arguments and reaffirms the traditional Thomistic doctrine of divine conservation.

1. INTRODUCTION The Doctrine of Divine Conservation (DDC) holds that the things that God has created could not continue in existence for an instant if He were not actively preserving them in being. DDC is a standard component of classical philosophical theology. It is implied in scripture,1 affirmed by St. Augustine2 and St. Thomas Aquinas, 3 and taught by the Catholic Church.4 That suffices to establish the theological importance of DDC, and thus the significance of any challenge to the doctrine, such as that posed by what Mortimer Adler called the “principle of inertia in being”5 and what, following John Beaudoin’s more elegant formulation, we will call the Doctrine of Existential Inertia (DEI).6 According to DEI, the world   Wisdom 11, 25; Hebrews 1, 3; Colossians 1, 17.   De Genesi ad litteram IV, 12 and V, 20. 3   Summa contra gentiles III, c. 65 and Summa theologiae [STh] I, q. 104, a. 1. 4   It is taught explicitly in the Catechism of the Council of Trent (or Roman Catechism), Part I, Article I. Theologians regard it as implicit in the teaching of the first Vatican Council that “God protects and governs by His providence all things which He created” (H. Denzinger, Sources of Catholic Dogma (St. Louis: Herder, 1957), § 1784 [DS 3001]). It is classified as de fide in Ludwig Ott’s Fundamentals of Catholic Dogma (Cork: Mercier Press, 1955), 87. 5   Mortimer Adler, How to Think About God: A Guide for the 20th-Century Pagan (New York: Collier/Macmillan, 1980), 125, 132. 6   John Beaudoin, “The world’s continuance: divine conservation or existential inertia?”, International Journal for Philosophy of Religion 61 (2007): 83–98. The expression “existential inertia” 1 2

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of contingent things, once it exists, will tend to continue in existence on its own at least until something positively acts to destroy it. It thus has no need to be conserved in being by God. Beaudoin asserts that “despite its centrality to the orthodox view about God’s relationship to his creation … attempts to prove that the world could not endure but for God’s conserving activity are scarce.”7 Similarly, Robert Pasnau and Christopher Shields claim that Aquinas, when defending DDC, “does not offer anything like a decisive refutation” of DEI.8 If accurate, such claims would be surprising given the centrality of DDC to the tradition. But such claims are not accurate. For the main arguments for God’s existence within classical philosophical theology are, when properly understood, themselves arguments for DDC and against DEI. In particular, this is precisely how Aquinas’s famous Five Ways (which are really just summaries of traditional arguments Aquinas did not claim to have invented himself) should be understood, or so I will argue. DDC is not regarded by Aquinas and other defenders of the arguments in question as some additional thesis that must be established separately, after God’s existence has first been demonstrated via the theistic proofs. Rather, the proofs are intended to establish God’s existence precisely by showing that the world could not exist even for an instant, or at least could not exist in the specific ways it actually does exist, were it not for the continual conserving action of God. And if the proofs succeed, then DEI would by implication be thereby “decisively refuted” (as Pasnau and Shields put it). In the next section, I will develop and defend the suggestion that the traditional proofs represented by the Five Ways are best read as defences of DDC and, consequently, as implicit critiques of DEI. That they are challenging critiques, deserving the attention of contemporary philosophers, is something I hope will be evident from the discussion, as well as from the third section, where I will explore how the traditional proofs so interpreted might form the basis of a response to recent defences of DEI. While the paper does not pretend to resolve the dispute between DDC and DEI, I hope it will contribute to a proper understanding of that dispute. is used by other writers too. See e.g. Norman Kretzmann, The Metaphysics of Theism (Oxford: Clarendon Press, 1997), 98. Cf. Robert Pasnau and Christopher Shields, The Philosophy of Aquinas (Boulder, CO: Westview Press, 2004), 144–145, which speaks of “the principle of inertia for existence”. Jonathan Kvanvig and Hugh McCann characterise the rival to DDC as the doctrine of the world’s “self-sustenance”, and regard talk of existential inertia as one possible construal of self-sustenance. See their article “Divine Conservation and the Persistence of the World”, in Divine and Human Action: Essays in the Metaphysics of Theism, ed. Thomas V. Morris (Ithaca: Cornell University Press, 1988), 13–49. 7   Beaudoin, “The world’s continuance: divine conservation or existential inertia?”, 84. 8   Pasnau and Shields, Philosophy of Aquinas, 144.

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2. DDC, DEI, AND THE FIVE WAYS How to interpret the Five Ways, and whether and how they might be defended against the standard objections, are, of course, large questions that I cannot address in any detail here. I have done so elsewhere.9 Here I will ignore exegetical questions, borrowing freely from the history of Thomistic interpretation of the proofs rather than sticking closely to Aquinas’s texts.10 I will focus on what I take to be the nerve of each of the arguments, treating them (somewhat anachronistically) as representative of the five main traditional Thomistic approaches to arguing from the world to the existence of a divine conserver of the world (some of the details of which are not explicit in Aquinas but suggested in the work of later Thomists). These approaches can be summarised as follows: The first argues that the existence, even for an instant, of composites of act and potency presupposes the simultaneous existence of that which is pure act; the second argues that the existence, even for an instant, of composites of essence and existence presupposes the simultaneous existence of that which is being or existence itself; the third argues that the existence, even for an instant, of composites of form and matter presupposes the simultaneous existence of an absolutely necessary being; the fourth argues that the existence, even for an instant, of things which are many and come in degrees of perfection presupposes the simultaneous existence of something one and absolutely perfect; and the fifth argues that the existence, even for an instant, of finality or directedness toward an end presupposes the simultaneous existence of a supreme ordering intellect. Let us examine each of these in turn. 2.1 The First Way The First Way is otherwise known as the argument from motion to an Unmoved Mover, where by “motion” Aquinas means change of any sort and where by “change” he means the reduction of potency to act (or potentiality to actuality). Given the details of Aquinas’s presentation of the argument in the Summa theologiae and elsewhere, contemporary discussions of it tend, understandably, to focus on a myriad of questions about whether its treatment of local motion is vitiated by Newton’s law of inertia, whether the cause of something’s actually having some feature F must itself actually be F, and so forth. But I would suggest that the heart of the argument is actually much more straightforward than it might at first appear, or at least that the argument suggests a more straightforward argument that can be expressed exclusively in the language of act and potency, leaving to one side questions about local motion and the like. Moreover, while it   See Edward Feser, Aquinas (Oxford: Oneworld, 2009), especially chapter 3.   Aquinas’s own presentation of the Five Ways is to be found in STh I, q. 2, a. 3. All quotes from the Summa theologiae are taken from St. Thomas Aquinas, Summa Theologica, trans. Fathers of the English Dominican Province (New York: Benziger Brothers, 1948). 9

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is natural and useful to introduce the notion of the reduction of potency to act using events as examples – like Aquinas’s example of wood being heated by fire – I would suggest also that the thrust of the argument is best understood in terms of substances rather than events. For the occurrence of an event ultimately presupposes (for an Aristotelian like Aquinas, certainly) the existence of a substance or substances;11 and the existence of a natural substance involves, no less than the events it enters into do, the reduction of potency to act. Accordingly, we might present a “streamlined” reconstruction of the argument as follows: 1. That the actualisation of potency is a real feature of the world follows from the occurrence of the events we know of via sensory experience. 2. The occurrence of any event E presupposes the operation of a substance. 3. The existence of any natural substance S at any given moment presupposes the concurrent actualisation of a potency. 4. No mere potency can actualise a potency; only something actual can do so. 5. So any actualiser A of S’s current existence must itself be actual. 6. A’s own existence at the moment it actualises S itself presupposes either (a) the concurrent actualisation of a further potency or (b) A’s being purely actual. 7. If A’s existence at the moment it actualises S presupposes the concurrent actualisation of a further potency, then there exists a regress of concurrent actualisers that is either infinite or terminates in a purely actual actualiser. 8. But such a regress of concurrent actualisers would constitute a causal series ordered per se, and such a series cannot regress infinitely. 9. So either A itself is purely actual or there is a purely actual actualiser which terminates the regress of concurrent actualisers. 10. So the occurrence of E and thus the existence of S at any given moment presupposes the existence of a purely actual actualiser. The argument is, admittedly, highly abstract compared to Aquinas’s own presentation. Again, I am not putting forward textual exegesis here, but something more like “rational reconstruction” (if such positivist jargon can be forgiven in this context) in light of the history of Thomistic interpretation of the argument. But the reduction of potency to act – the explanation of which, as I have indicated, 11   “It is evident that anything whatever operates so far as it is a being” (Quaestiones disputatae de anima, a. 19, co., as translated by John Patrick Rowan in St. Thomas Aquinas, The Soul (St. Louis: B. Herder, 1949)). See Feser, Aquinas, 74–76 for discussion and defence of the suggestion that the argument from motion is ultimately concerned to explain the existence of the things which move no less than the fact of their motion.

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is Aquinas’s ultimate concern in the argument – is itself a highly abstract notion in any event. And the point of focusing on it is to make as evident as possible the relevance of the argument from motion to the dispute between DDC and DEI. All the same, the reader might reasonably ask what sort of potency it is the actualisation of which premise (3) tells us is presupposed by the existence at any moment of a natural substance S. The answer is that there are several possible answers. In an Aristotelian vein, one might hold that any natural substance S must be a composite of prime matter and substantial form, and that since prime matter is of itself purely potential, S cannot exist unless some actualiser A conjoins (and keeps conjoined) to its prime matter the substantial form of S. Or, in a more distinctively Thomistic vein, one might hold that any natural substance S must be a composite of an essence and an act of existence, and that since an essence is of itself purely potential, S cannot exist unless some actualiser A conjoins (and keeps conjoined) to its essence S’s act of existence. Or, in a more Neo-Platonic vein, one might hold that any natural substance S will be in some respect or other composite so that its parts only potentially constitute the whole unless conjoined (and kept conjoined) by some actualiser A which is incomposite or One. Indeed, among the rest of the Five Ways are arguments which deploy precisely these sorts of analyses of natural substances. The argument from motion to an Unmoved Mover – or what we might more fittingly (if less elegantly) call the argument from the actualisation of potency to that which is Actus Purus – can be understood, then, as holding that whatever the metaphysical details turn out to be vis-à-vis the structure of events and substances, they will involve the actualisation of potency, and that this presupposes the operation of that which is pure act. The rest of the argument will be familiar to those acquainted with the literature on the Five Ways. For example, the notion of a causal series ordered per se, to which (8) appeals, is the notion of a series all but one of whose members have no independent causal power, but derive their efficacy from an uncaused cause to whom they are related as instruments. (Recall Aquinas’s example of the stick which can move the stone only insofar as it is being used by the hand to move it.) That Aquinas has this sort of series in mind (rather than a series ordered per accidens, of the sort which might trace back infinitely into the past) is well known to serious students of the argument, even if not to some of its popular critics and defenders. And the idea (at least as some commentators would interpret or extend Aquinas’s argument) is that if A’s existence depends on the concurrent existence and actualising activity of some further actualiser B, and B’s existence depends on the concurrent existence and actualising activity of some further actualiser C, then we clearly have a series ordered per se which can terminate only in that which can actualise without itself requiring actualisation – something that just is, already, purely actual. As I have said, a more detailed discussion and defence of the argument is not something I can get into here, and I have in any event done so elsewhere. The point for now is to note that the argument clearly EXISTENCE • 147

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constitutes a defence of DDC and a critique of DEI. For if successful, it would show that no natural substance could exist at any given moment without a purely actual actualiser either directly or indirectly maintaining it in existence. And the notion of Actus Purus or pure act is the philosophical core of at least the Aristotelian-Thomistic conception of God. 2.2 The Second Way The Second Way is also known as the argument from efficient causality to an Uncaused Cause. As is often noted, the argument can seem at first glance to differ from the First Way only verbally. But several commentators have suggested (correctly, in my view) that there is a substantive difference between them insofar as the Second Way takes as its explanandum the existence or being of things, whereas the First Way seeks to explain their motion or change (even if it, too, as I have suggested, must account for their existence in the course of explaining their motion). In this respect, the Second Way is reminiscent of what is sometimes called the “existential proof” of Aquinas’s De ente et essentia, and since the point of the Five Ways is to survey what Aquinas takes to be the main arguments for God’s existence, it is natural to wonder whether the former argument was intended as a summary of the latter. The suggestion is controversial but, I think, correct, and I will take it for granted in my discussion here.12 Now, the existential proof presupposes Aquinas’s famous doctrine (alluded to above) of the real distinction between essence and existence in everything other than God. The proof seeks to show that nothing in which essence and existence are distinct could exist even for an instant unless there is something in which essence and existence are identical – something which just is ipsum esse subsistens, Subsistent Being Itself – conjoining its essence to an act of existence and thereby maintaining it in being. Reading the Second Way in light of this approach suggests the following reconstruction: 1. That efficient causation is a real feature of the world is evident from sensory experience. 2. Nothing can be the efficient cause of itself. 3. The existence of any natural substance S at any given moment presupposes that its essence is concurrently being conjoined to an act of existence. 4. If S itself were somehow conjoining its own essence to an act of existence, it would be the efficient cause of itself.   William Lane Craig, who agrees that the Second Way is concerned to explain the existence or being of things, nevertheless resists any assimilation of it to the argument of De ente et essentia. See his The Cosmological Argument from Plato to Leibniz (New York: Harper and Row, 1980), 177. I defend the assimilation and reply to Craig in my Aquinas, 84–87. 12

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5. So there must be some concurrent efficient cause C distinct from S which is conjoining S’s essence to an act of existence. 6. C’s own existence at the moment it conjoins S’s essence to an act of existence presupposes either (a) that C’s essence is concurrently being conjoined to an act of existence, or (b) that in C essence and existence are identical. 7. If C’s existence at the moment it conjoins S’s essence to an act of existence presupposes that C’s own essence is concurrently being conjoined to an act of existence, then there exists a regress of concurrent conjoiners of essences and acts of existence that is either infinite or terminates in something whose essence and existence are identical. 8. But such a regress of concurrent conjoiners of essence and existence would constitute a causal series ordered per se, and such a series cannot regress infinitely. 9. So either C’s own essence and existence are identical, or there is something else whose essence and existence are identical which terminates the regress of concurrent conjoiners of essences with acts of existence. 10. So the existence of S at any given moment presupposes the existence of something in which essence and existence are identical. There are obvious parallels between this argument and the argument for a  purely actual actualiser. The notion of a causal series ordered per se plays a similar role in both, and that which initiates the potential regress is similar too. In the first argument, the idea was that the existence of any natural substance S at any given moment presupposes the actualisation at that moment of a potency, and that whatever does the actualising must itself already be actual. We saw that this actualising might be conceived of more concretely in terms of S’s prime matter having conjoined to it the substantial form of S, or in terms of S’s essence being conjoined to an act of existence. The argument for an Uncaused Cause, as I have interpreted it, essentially makes a separate argument of this second more concrete conceptualisation of the actualising of S. It holds that S’s essence, and thus S itself, is merely potential until that essence is conjoined with an act of existence. But if S or S’s essence did this conjoining, then S would be the cause of itself, which is impossible. Hence the conjoining must be done by some cause C distinct from S. But the distinction between S’s essence and existence that this presupposes is as real after S first comes into existence as it was before; and for S or S’s essence to conjoin S’s essence to an act of existence even after S first comes into existence would be for S to cause itself, which is no less impossible after S already exists than before. Hence the conjoining of S’s essence and existence by a cause distinct from S must be maintained at any moment S exists. EXISTENCE • 149

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As with the argument for a purely actual actualiser, there is much more to be said about the argument, and as with the former argument, a completely general treatment is beyond the scope of this paper. The point to emphasise for our purposes is that here too we have an argument for DDC and against DEI. For if S cannot cause its own continuance in existence any more than its coming into being, then DEI is false. And if what does cause its continuance in existence must ultimately be something in which essence and existence are identical, then since this just is the core of the Thomistic conception of God, DDC is true. 3.3 The Third Way The Third Way is otherwise known as the argument from the contingency of the world to the existence of an absolutely necessary being. It would be a serious mistake to read into the argument themes of the sort familiar from contemporary discussions of contingency and necessity, such as appeals to the “conceivability” of this or that, or to possible worlds, or the assimilation of metaphysical necessity to logical necessity. For Aquinas, as for Aristotelians generally, possibility and necessity are grounded in what is actual. We do not determine the essence of a thing by first considering what it would be like in various possible worlds; rather, we determine what it would be like in various possible worlds only after first determining its essence, which means determining what it is like in the actual world. Hence, when in the Third Way Aquinas says that the things our senses reveal to us are “possible not to be”, he does not mean that we can “conceive” of them going out of existence or that there is at least one possible world in which they do so. He means that there is something in their nature that makes them inherently incapable of persisting indefinitely. And when he goes on to say that “that which is possible not to be at some time is not”, he is not fallaciously arguing that if some event is possible in some completely abstract way – in the sense that we can conceive of it without contradiction, say, or that there is a possible world where it occurs – then it will happen in the actual world. He is saying rather that if a thing has an inherent tendency to go out of existence, then eventually that tendency will be manifested in its actually going out of existence. The basis of this tendency in the things of our experience is their form/matter composition, for “a possibility of non-being is in the nature of those things… whose matter is subject to contrariety of forms”.13 But even if one concedes that material things have and will realise such a tendency, and even if one concedes too Aquinas’s further claim that if everything is “possible not to be” then at one time there would have been nothing, might one not argue that the underlying matter out of which the things of our experience are made is itself not “possible not to be”, that it is a kind of necessary being? Indeed, some critics of the Third 13   De potentia q. 5, a. 3, co., as translated by Lawrence Shapcote in Thomas Aquinas, On the Power of God (Westminster, MD: The Newman Press, 1932).

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Way make precisely this suggestion.14 Where they go wrong is in assuming that Aquinas would disagree with them. For in fact, Aquinas himself holds that while individual material things are generated and corrupted, matter and form themselves are (apart from special divine creation, to which he would not appeal for the purposes of the argument at hand lest he argue in a circle) not susceptible of generation and corruption.15 So, Aquinas is happy to concede, at least for the sake of argument, that matter might be a kind of necessary being. Moreover, he recognises the existence of other non-divine necessary beings as well, such as angels and even heavenly bodies (which, given the astronomical knowledge then available, the mediaevals mistakenly regarded as not undergoing corruption). This should not be surprising when we keep in mind that getting to the existence of a necessary being is only the first half of the Third Way. The second half is devoted to showing that any necessary being that does not have its necessity of itself must ultimately derive it from a necessary being which does have its necessity of itself. In particular, it is Aquinas’s view that even if matter and form, angels and heavenly bodies count as necessary beings of a sort, they do not have their necessity of themselves but must derive it from an absolutely necessary being, namely God.16 That the matter which persists throughout the generations and corruptions of particular material objects cannot have its necessity of itself should be obvious when we consider that for Aquinas such matter is just prime matter or pure potentiality, which by itself and apart from the forms it takes on has no actuality nor indeed any reality at all, necessary or otherwise. And for Aquinas the forms in question have (apart from the postmortem souls of human beings) no existence apart from matter, so that they cannot be said to have their necessity of themselves either. Nor will it do to suggest that any particular form/matter composite might have its necessity of itself, even apart from the fact that such composites have an inherent tendency to go out of existence. For since in purely material substances matter depends on form and form depends on matter, we would have a vicious explanatory circle unless there was something outside the form/matter composite which accounts for its existence.17 Then there is the fact that material objects are composites of essence and existence as well, as are disembodied 14   See e.g. J. L. Mackie, The Miracle of Theism (Oxford: Clarendon Press, 1982), 91; and Bede Rundle, Why there is Something rather than Nothing (Oxford: Clarendon Press, 2004), 96–97. 15   De principiis naturae, c. 2. 16   That angels and the like are “necessary” in this derivative sense does not entail for Aquinas that they cannot go out of existence, only that they cannot do so in the way material things do, i.e. via corruption. Such a derivatively necessary being could go out of existence via annihilation, if God ceased conjoining its essence to an act of existence. 17   Cf. Christopher F. J. Martin, Thomas Aquinas: God and Explanations (Edinburgh: Edinburgh University Press, 1997), 166–67.

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human souls and angels; and for reasons already stated, such composites must be sustained in being by something in which essence and existence are identical. In this way, then, necessary beings other than God must derive their necessity from God.18 With this interpretive background in place, we can propose the following reconstruction of the basic thrust of the argument from contingency: 1. That the particular substances revealed to us in sensory experience are contingent is evident from the fact that they are generated and corrupted. 2. Their generation and corruption presuppose matter and form, which are neither generated nor corrupted and are thus necessary. 3. But matter of itself is pure potency and material forms of themselves are mere abstractions, so that neither can exist apart from the other; and even when existing together they cannot depend on each other alone on pain of vicious circularity. 4. So matter and form do not have their necessity of themselves but must derive it from something else. 5. Material substances are also composites of essence and existence, as are non-divine necessary beings like angels, and any such composite must have its essence and existence conjoined by something distinct from it. 6. So these other necessary beings too must derive their necessity from something else. 7. But a regress of necessary beings deriving their necessity from another would constitute a causal series ordered per se, which of its nature cannot regress infinitely. 8. So there must be something which is necessary in an absolute way, not deriving its necessity from another and (therefore) not a composite of form and matter or essence and existence. Note that prime matter cannot at any moment exist without form and a material form cannot at any moment exist without prime matter; they depend on each other at every moment in which they are conjoined together in a material substance. Hence the circularity inherent in explaining the existence of a material substance’s form in terms of its matter and the existence of its matter in terms of its form holds at any moment at which the substance exists, so that they require an external cause of their conjunction at any moment it exists. Something similar holds of any composite of essence and existence, for reasons already explained. So, we have in the present argument too an argument against DEI and, since the 18

  For a detailed defence of this reading of the Third Way, see Feser, Aquinas, 90–99.

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ultimate explanation arrived at is an absolutely necessary being which is not a compound of essence and existence but that in which essence and existence are identical, an argument for DDC as well. 2.4 The Fourth Way The Fourth Way is sometimes described as an argument from grades of perfection to a divine Exemplar, and sometimes as a henological argument from the multiplicity of things to a divine Unity. Like the Five Ways in general, it is very widely misunderstood, perhaps even more so than the other arguments. For example, it is often assumed that Aquinas is arguing that every attribute that comes in degrees must have its fullest exemplar in God; and it is then objected that this entails such absurdities as that God must be the supreme exemplar of smelliness. But in fact Aquinas is concerned only with what the Scholastics called the transcendentals – being, one, good, true, and the like – which, unlike smelliness, sweetness, heat, cold, red, green, etc., are predicable of everything without exception. And it is because the transcendentals are (as the Scholastics held) “convertible” with one another that Aquinas takes what is most true, most good, and so forth to be one and the same thing, and to be identical in turn with what is “uttermost being”. The argument is also often read in Platonic terms, and while this is not an egregious misunderstanding, it is also not quite right. Aquinas is indeed committed to a doctrine of “participation”, but he does not understand participation in terms of purely formal causation, and he does not regard the being, goodness, unity, and truth in which things participate as abstract objects à la Plato’s Forms. Rather, he takes the transcendentals participated in to be also the efficient causes of things’ being good, true, one, etc. to the extent that they are, where what this ultimately entails is that the Subsistent Being Itself with which all the transcendentals are identical is the one efficient cause of their being, goodness, truth, unity, etc. at any given moment. In short, we can think of the Fourth Way as a kind of extension, via the doctrine of the transcendentals, of the basic thrust of the earlier argument for an Uncaused Cause whose essence and existence are identical. That in which essence and existence are distinct, and which is thus limited in being, depends upon that which just is pure existence or being. But being is convertible with goodness, unity, truth, etc. Hence that which is good only in some limited way must depend on that which is pure goodness, that which has unity only in some limited way must depend on that which is absolutely one, and so forth.19 This suggests the following reconstruction of the argument from grades of perfection: 19   Once again, see my Aquinas for a detailed defence of my proposed reading of the Fourth Way, especially 99–109.

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1. The things of our experience exhibit goodness, unity, and the other transcendentals only to some limited degree. 2. But they can do so only insofar as they participate in that which is good, one, etc. without limitation. 3. Moreover, the transcendentals are convertible with one another, and ultimately with Being Itself. 4. So there is some one thing which is being itself, goodness itself, unity itself, and so forth, in which the things of our experience participate to the degrees they do. 5. But that in which things participate is their efficient cause. 6. So the one thing which is being itself, goodness itself, unity itself, etc. is the efficient cause of the things of our experience. Keep in mind that for Platonism, things participate in the Forms at every moment in which they exist at all, and otherwise would not exist at all. For instance, a dog is a dog only insofar as it participates in the Form of Dog, and if it were to cease participating in that Form even for an instant, it would cease to exist qua dog. And though Aquinas’s notion of participation is not identical to Plato’s, it has that much in common with it. Just as that in which essence and existence are distinct – that is to say, that which has being only in a limited way – could not in Aquinas’s view exist for an instant if it were not sustained in being by that which just is Being Itself, so too he thinks that that which has goodness, unity, etc. only in a limited way could not exist (or at least not exist qua good, one, and so forth) even for an instant if it were not sustained by that which just is supreme goodness, unity, etc. So, once again we have an implicit argument against DEI and (given that that which is being itself, goodness itself, unity itself, etc. is God) an implicit argument for DDC. 2.5 The Fifth Way The Fifth Way is also known as the argument from finality to a supreme ordering intelligence. It might also be described as a teleological argument, but it has nothing to do with the “design argument” of William Paley. Paley and other defenders of the latter sort of argument take for granted a mechanistic conception of the natural order on which it is devoid of anything like Aristotelian substantial forms or final causes. While they argue that certain natural phenomena are teleological, the teleology in question is understood to be extrinsic or imposed from outside rather than immanent or “built in”, as Aristotelian natures and final causes are. The basis for a Paleyan inference to design is a judgement to the effect that certain natural phenomena are too complex plausibly to have arisen through natural processes and are thus probably the artefacts of a superior intelligence. 154 • EXISTENCE

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Aquinas’s argument is nothing like this. He regards teleology as immanent to the natural order, as manifest in even the simplest causal processes rather than only in complex phenomena, and as something that leads us conclusively to the existence of a supreme intellect rather than merely as a matter of probability. Take a simple causal regularity, such as a match’s tendency to generate flame and heat when struck, or ice’s tendency to cool the air or liquid surrounding it, or some even more basic causal regularity at the micro level.20 Why is it that it is flame and heat specifically that a match will tend to generate when struck? It will not always actually generate it, of course, for it might be impeded in some way from doing so – oxygen might be absent, or it might have been water damaged, or it might have simply gotten so old that the chemicals in the match head have lost their potency. But unless impeded in such ways, it will produce its characteristic effects, and only those effects, rather than generating frost and cold, say, or the smell of lilacs, or a thunderclap. Again, why? Aquinas’s answer is that “every agent acts for an end: otherwise one thing would not follow more than another from the action of the agent, unless it were by chance.”21 By “agent” he means an efficient cause, and by “acting for an end” he means that such a cause is as it were “directed toward” the production of its characteristic effect or effects as to an end or goal. In this way, efficient causality presupposes final causality: If we do not suppose that some cause A of its nature “points to” or is “directed at” the generation of some effect or range of effects B, specifically – rather than to C, D, or no effect at all – then we have no way of making intelligible why it does in fact regularly generate B rather than these other effects. Notice that this does not involve attributing anything like a biological function to such causes – biological functions are, contrary to a common misconception, only one, relatively rare kind of finality in nature, and do not exhaust final causality – and that it has nothing to do with complexity. Furthermore, the end-directedness in question is inherent to causes, something they have by virtue of their natures or essences. At least in the case of natural causes (such as ice’s tendency to cool surrounding water or air) we can determine from the regularity of their behaviour alone what their causal tendencies and thus “final causes” are, and do not need to advert to the intentions of a designer. (Indeed, Aristotle, who believed both in final causes and in God, did not think that the former needed to be explained in terms of the latter.) This essentially Aristotelian, anti-mechanistic conception of the world as immanently teleological is what Aquinas means to affirm in the first half of the Fifth Way, when he writes: 20   Nothing hinges on the specific examples. If a reductionist insists that the causal properties of matches, or ice, or any macro level object can be reduced without remainder to the causal properties of some micro level entities, the defender of the Fifth Way can simply re-state the point in terms of those more basic regularities. 21   STh I, q. 44, a. 44, co.

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We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end.22

By “designedly” (ex intentione), he does not mean “because of a designer”, à la Paley. Rather, he means, as Aristotle would, “because of the teleology or enddirectedness inherent in things, rather than by chance”.23 Whether this teleology must itself be explained in terms of intelligence is a further question, one Aquinas gets to only in the next sentence, when he writes that “whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence.” The claim is peremptory; there is no question here of “weighing probabilities” or the like. Why? The basic idea is this. A cause cannot be efficacious unless it exists in some way. But in the case of the final cause of some unintelligent causal process, the cause in question does not exist in the natural order. For instance, the oak is the end or final cause of the acorn, and yet until the acorn develops into the oak, the oak does not actually exist in the natural world. Now with artefacts, the final cause can be efficacious because it exists (or rather its form exists) in the mind of the artificer. For example, a building is the final cause of the actions of a builder, and it serves as a genuine cause despite its not yet existing in the natural order by existing at least as an idea in the builder’s intellect. Now unless there is some third alternative, this is how the final causes operative in the order of unintelligent natural things must exist, for they have to exist somehow in order to be efficacious. But there is no third alternative, given Aquinas’s rejection of Platonism. If the oak does not exist in a Platonic third realm and it does not yet exist either in the natural world, the only place left for it to exist, as it must if it is to have any efficacy vis-à-vis the acorn, is as a form or idea in an intellect. And the same thing is true of all   STh I, q. 2, a. 3, co.   Christopher F. J. Martin translates ex intentione as “in virtue of some tendency” (Thomas Aquinas: God and Explanations, 179), which is, I think, to be preferred both to the widely used Fathers of the English Dominican Province translation quoted above and to the common alternative translation “by intention”. “Designedly” and “by intention”, while not incorrect, can be misleading given the way “design” and “intention” are typically used in contemporary philosophical discussion of these issues, which differs from the way they are used in Scholastic philosophy. As Bernard Wuellner explains in his Dictionary of Scholastic Philosophy (Milwaukee: Bruce Publishing Company, 1956), 63, in Scholastic metaphysics “intention” can mean “the direction or application of causal power to an effect; the influence of the primary cause on the instrument”. (For the first “of”, Wuellner’s text actually reads “or”, but this is evidently a typo.) Wuellner adds: “This may be the primary meaning of intention as it best shows the notion of directing or tending on the part of a being or power.” Again, what is in view is the Aristotelian notion of immanent teleology, rather than the extrinsic teleology in terms of which Paley and his contemporary successors frame their “design argument”. 22

23

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the other final causes operative in the order of unintelligent natural processes, which means it is true of the entire order of efficient causes making up the natural world, since all efficient causality presupposes final causality. So, there must be an intellect outside the natural order directing things to their ends, where these ends pre-exist as ideas in said intellect. And notice that this must be the case at any moment at which natural substances exist at all, for they retain their inherent causal powers and thus their immanent finality or end-directedness at every moment at which they exist. Notice too that precisely since this finality or end-directedness is immanent, “built into” things given their natures or essences, that which directs natural things to their ends must be what gives them their natures or essences, and thus what conjoins their essences to an act of existence. Since for reasons already stated this must ultimately be something in which essence and existence are identical, we are led by yet another route to the existence of God, and not merely to a finite designer (which Paleystyle arguments cannot rule out).24 We are led, then, to the following reconstruction of the overall thrust of the argument from finality: 1. That unintelligent natural causes regularly generate certain specific effects or ranges of effects is evident from sensory experience. 2. Such regularities are intelligible only on the assumption that these efficient causes inherently “point to” or are “directed at” their effects as to an end or final cause. 3. So there are final causes or ends immanent to the natural order. 4. But unintelligent natural causes can “point to” or be “directed at” such ends only if guided by an intelligence. 5. So there is such an intelligence. 6. But since the ends or final causes in question are inherent in things by virtue of their natures or essence, the intelligence in question must be the cause also of natural things having the natures or essences they do. 7. This entails its being that which conjoins their essences to an act of existence, and only that in which essence and existence are identical can ultimately accomplish this. 8. So the intelligence in question is something in which essence and existence are identical. 24   For a more detailed defence of the reading of the Fifth Way proposed in the text, see Feser, Aquinas, 110–20. For further discussion of the differences between a Paleyan conception of teleology and an Aristotelian one, see Edward Feser, “Teleology: A Shopper’s Guide”, Philosophia Christi 12, no. 1 (2010): 142–159.

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Once again we have an implicit argument against DEI, since the claim is that a natural substance could not have the final cause or end it has even for an instant without some intelligence distinct from it ordering it to that end, which (it is argued) entails in turn that this intelligence must be keeping its essence conjoined to an act of existence at every such instant. And since that intelligence would have to be something in which essence and existence are identical, we also have an implicit argument for DDC. The reference, yet again, to the essence/existence distinction is likely to raise in many readers’ minds a thought that has no doubt occurred to them already, viz. that the Five Ways as I (and other Thomists historically) have interpreted them overlap significantly. That impression is not entirely misleading. The AristotelianThomistic metaphysical framework upon which the arguments rest – comprising the act/potency, form/matter, and essence/existence distinctions, the notions of the transcendentals, of causal powers, finality, causal series ordered per se, and so on and so forth – constitutes a tightly integrated structure which offers several avenues of approach to what is ultimately one and the same summit. Still, the avenues are different, at least at their beginning points. And even where they overlap, there is value in considering the proofs individually. If we might borrow Wittgenstein’s description of his own (admittedly very different!) method, in order fully to grasp the theological implications of the Aristotelian-Thomistic system, “the very nature of the investigation … compels us to travel over a wide field of thought criss-cross in every direction”, making “a number of sketches of landscapes … in the course of these long and involved journeyings”, and with “the same or almost the same points … always being approached afresh from different directions, and new sketches made.”25 3. RECENT DEBATE OVER DDC AND DEI If I am right, then, each of the traditional theistic arguments represented by the Five Ways embodies, or at least suggests, an argument for DDC and against DEI. Let us turn now to some recent defences of DEI and critiques of DDC and consider how a defender of the Five Ways as I have interpreted them might respond. 3.1 Radical versus superficial contingency One of the more noteworthy defences of DEI comes, somewhat surprisingly, from Mortimer Adler, who was himself something of a Thomist.26 Adler presents two arguments, a negative argument intended to undermine what he takes to be the main grounds for rejecting DEI, and a positive argument from Ockham’s razor for preferring DEI to its rejection. I will address the positive argument in 25   As translated by G. E. M. Anscombe in Ludwig Wittgenstein, Philosophical Investigations, 3rd ed. (New York: Macmillan, 1968), v. 26   Adler, How to Think About God, especially chapter 13.

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a later subsection. Let’s consider for the moment the negative argument, which appeals to a distinction between radical and superficial contingency. The reason the opponent of DEI maintains that a natural substance will go out of existence without a divine sustaining cause, Adler says, is because such substances are contingent in the sense of being generated and corrupted, and thus have no tendency of their own to continue in existence. But the contingency in question, objects Adler, is only superficial. When natural substances go out of existence, they are merely broken down into their material components, which persist in another form. They are not radically contingent in the sense of being utterly annihilated. If they were, we would have grounds for saying that they have no inherent tendency to remain in existence, but since their contingency is only superficial – they do not really go out of existence, but merely change form – such an inference is blocked. And with the inference to the falsity of DEI blocked, so too is the inference to DDC. Adler attributes to Étienne Gilson an acknowledgement that generation and corruption are not the same thing as exnihilation (coming into being out of nothing) and annihilation, but says that he cannot find an explicit acknowledgement of this distinction in Aquinas.27 This is odd, given that (as I noted above when discussing the Third Way) Aquinas explicitly affirms in De principiis naturae that it is only particular individual material substances that are generated and corrupted, while matter and form themselves are not. It is also odd that Adler does not take account of the fact that Aquinas explicitly acknowledges in the Third Way that there can be non-divine beings which are necessary – that is to say, beings which have no inherent tendency to go out of existence – while maintaining that such beings nevertheless require a divine sustaining cause insofar as they do not have their necessity of themselves. Had he taken account of it, he might have seen that the fact that something has no tendency to go out of existence by itself does nothing to show that it possesses existential inertia. For everything depends on why it lacks such a tendency. If there is something in a thing’s own nature that explains why it lacks that tendency, then DEI would indeed be vindicated. But if there is nothing in its nature that could account for the lack of such a tendency, then DEI is false and we have to appeal to something external to the thing to account for it. Unfortunately, Adler never addresses the question of what there might be in a thing’s nature that could either give it, or prevent it from possessing, existential inertia. But that question is at the heart of the dispute between Aquinas and the defender of DEI. Adler mistakenly assumes that Aquinas’s position has to do fundamentally with contingency as such, that Aquinas is saying something like: If S is contingent, then S lacks existential inertia. 27

  Ibid., 127.

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and Adler’s objection is that at least in the case where the contingency in question is superficial rather than radical, the conditional is false. But Aquinas is not saying that, or rather not merely saying that. He is saying instead something like: If S has feature F, then S lacks existential inertia whether S is contingent or necessary. And what F is, specifically, is being metaphysically composite – being, that is to say, a compound of form and matter, or of essence and existence, or, more generally, of act and potency. This is explicitly what is at issue in the first three Ways as I have proposed interpreting them, and it is implicit in the Fourth and Fifth Ways as well insofar as they too ultimately infer to something which maintains its effect in existence by conjoining an essence to an act of existence.28 Adler’s failure to see that it is compositeness rather than contingency that lies at the heart of Aquinas’s objection to DEI is related to a muddle in his distinction between radical and superficial contingency. Adler holds that a cat, say, is only superficially rather than radically contingent because its parts remain after the cat dies; and this is meant to support the claim that the cat possesses existential inertia. This at least gives the impression that the cat is no more than the sum of its parts – that something of the cat in fact remains after its death insofar as its parts persist, which is at least a natural way to read the claim that its contingency is only “superficial”. Alternatively, D. Q. McInerny sug gests that Adler thinks of a radically contingent being as one which depends on something else for its very existence, but of a superficially contingent being as one which depends on something else only for a “mode of being”.29 And if so, then (now to go beyond what McInerny himself says) it would seem to follow that for Adler, being a cat – or being a tree, or a stone, or a car, or any other of the ordinary objects of our experience – is really only a mode of the material world itself, which persists as a substance throughout the acquisition and loss of these modes. Whichever of these readings we adopt, from the point of view of the Aristotelian hylomorphism informing Aquinas’s position, Adler simply misunderstands the nature of material substances, or at least begs the question against Aquinas. For the hylomorphist, a cat is neither an aggregate of material parts nor a mode   That it is being composite that ultimately makes a thing dependent for its continued existence upon a sustaining cause is emphasised in David Braine, The Reality of Time and the Existence of God: The Project of Proving God’s Existence (Oxford: Clarendon Press, 1988). See especially pp. 177–196 and 342–345. That whatever is composite must ultimately be explained in terms of that which just is existence itself is also more or less the thrust of the arguments of Barry Miller, From Existence to God (London: Routledge, 1992) and William F. Vallicella, A Paradigm Theory of Existence: Onto-Theology Vindicated (Dordrecht: Kluwer Academic Publishers, 2002). 29   D. Q. McInerny, Natural Theology (Elmhurst, PA: Priestly Fraternity of St. Peter, 2005), 137. 28

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of some material substance, but rather is itself a substance composed of prime matter and substantial form. Its going out of existence consists in its prime matter losing the substantial form of a cat and taking on some other substantial form or forms, such as the forms of the chemical elements that existed in the cat virtually while it was still alive. And because the substantial form of the cat is lost, there is absolutely nothing of the cat left after its death. The “parts” which carry on are not really cat parts in the strict sense – they cannot be, since there is no substantial form of a cat left to inform them – but rather new substances which came into being when the prime matter acquired new substantial forms. (A dead cat is not a kind of cat, but rather, as Monty Python might put it, an “ex-cat”.)30 Even if Adler insisted that a cat or any other natural object was really just an aggregate of material parts or a mode of a substance constituted by the material world as a whole, the hylomorphist could respond that the fundamental material parts themselves – basic particles, or whatever – or the world considered as one gigantic substance, would still be composed of prime matter and substantial form. And if the material world is susceptible of a hylomorphic analysis at some level of description, we have an argument from the nature of material substances against DEI. That argument is already implicit in what was said in the previous section about the Third Way, but it will be worthwhile to make it explicit at this point, adding as a first premise a familiar principle of Scholastic metaphysics: 1. A cause cannot give what it does not have to give. 2. A material substance is a composite of prime matter and substantial form. 3. Something has existential inertia if and only if it has of itself a tendency to persist in existence once it exists. 4. But prime matter by itself and apart from substantial form is pure potency, and thus has of itself no tendency to persist in existence. 5. And substantial form by itself and apart from prime matter is a mere abstraction, and thus of itself also has no tendency to persist in existence.31 6. So neither prime matter as the material cause of a material substance, nor substantial form as its formal cause, can impart to the material substance they compose a tendency to persist in existence.   Accordingly, McInerny says that in the relevant sense, and contrary to what Adler claims, a material substance qua substance is “annihilated” when it goes out of existence; for the substance really is completely gone even if its prime matter persists under another substantial form. (Ibid., 138) But it seems to me less misleading to reserve the description “annihilation” for the case where neither the substance nor its prime matter persist in any way. 31   I ignore for present purposes the special case of the rational soul. 30

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7. But there are no other internal principles from which such a substance might derive such a tendency.32 8. So no material substance has a tendency of itself to persist in existence once it exists. 9. So no material substance has existential inertia. 3.2 Nothing to explain? This argument, as well as the readings of the Five Ways I’ve proposed, also constitute an obvious response to an objection sometimes raised against DDC to the effect that it is an answer to a question that we shouldn’t bother asking in the first place. For instance, Bede Rundle holds that “no form of causation, divine or otherwise, is in general required to ensure persistence in being … [M]any things in the universe, as indeed the universe itself, do not have to fight for their survival, but, in the absence of forces which would bring them to an end, their continuation from moment to moment is in no need of explanation.”33 But if the composite act/ potency or form/matter or essence/existence structure of natural substances entails that they cannot persist in existence on their own, then the fact of their persistence does require explanation, and the arguments in question purport to show that DDC is that explanation. Other critics of DDC do not deny that the persistence of natural substances requires explanation, but claim that DEI suffices to explain it. Adler takes this approach himself, as does Beaudoin. The trouble is that for this strategy to work, the defender of DEI has to provide some account of natural substances that is both consistent with what we know about them and does not entail rejecting DEI, and no such account has been offered. For instance, as Beaudoin acknowledges, a plausible version of DEI will have to acknowledge that natural substances are contingent. But why are they contingent? As we saw when discussing Adler, Aquinas’s answer is that they are composite in various ways, and it is this compositeness that entails that they cannot enjoy existential inertia. Only something non-composite, and thus something necessary (indeed something divine) can in his view have that. So, to defend his proposal Beaudoin would have to provide some account of natural substances on which their contingency does not derive from their being 32   This premise reflects the Aristotelian thesis that among the four causes of a thing, its formal and material causes are intrinsic to it while its final and efficient causes are extrinsic. See Aquinas, De principiis naturae, c. 3. To be sure, that a natural substance has such-and-such a final cause is something intrinsic to it, but that is true by virtue of its formal cause. To take an example from earlier, the tendency of ice to cool what surrounds it is intrinsic to it, something determined by the substantial form of the water that it is composed of. It is part of its nature to have the generation of this outcome as an “end”. But the end itself – coolness in the surrounding environment – is obviously something extrinsic to the ice. 33   Rundle, Why there is Something rather than Nothing, 93.

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composite, or on which it does but where this compositeness somehow does not entail a rejection of DEI. Yet he gives no such account. What he does tell us is merely that DEI is committed to the minimal claim that there exist some fundamental constituents of the natural world – whether they are conceived of as particles, or superstrings, or some continuous evermorphing kind of stuff is irrelevant, he says – which are contingent but which nevertheless given their nature have no inherent tendency to go out of existence. 34 He acknowledges that it will not do to suggest that it is simply a “brute fact” that things have existential inertia, and that it would be a “metaphysical muddle” to think of existential inertia as an active power a thing exerts on itself.35 At the same time, he never explains how it is that the basic constituents he speaks of would have existential inertia despite being contingent. He merely puts forward the suggestion that they could have it as a claim that is not obviously incoherent, and suggests also that “it is far from clear that the proponent of DDC will fare better” in explaining why God’s existence is not a brute fact.36 But it is obvious from the foregoing that the DDC proponent does fare better, for he can say that the reason God’s existence is necessary is that He is Pure Act, Subsistent Being Itself, something absolutely One. The DDC proponent has – in the Aristotelian-Thomistic theories of act and potency, form and matter, essence and existence, final causality, the transcendentals, and so forth – a worked-out general metaphysics that both explains why natural substances lack existential inertia and provides an account of the divine nature. This general metaphysics is independently motivated, put forward as a way of accounting for basic features of the natural world and of our scientific knowledge of it that are acknowledged by the theist and the atheist alike. By contrast, Beaudoin offers little more than the bare assertion that at least at some, fundamental level, the natural world of contingent things enjoys existential inertia, where the assertion seems to have no theoretical motivation other than as a means of blocking an inference to DDC. It would be tempting to accuse Beaudoin of putting forward a “dormitive power” explanation of why things have existential inertia, except that this would be unfair to “dormitive power” explanations. For to say that opium puts people to sleep because of its dormitive power is (contrary to the stock dismissal of such   Beaudoin, “The world’s continuance: divine conservation or existential inertia?”, 86–87. Beaudoin says that a stronger version of DEI would assert that the everyday objects comprised of arrangements of these fundamental constituents also enjoy existential inertia, but that this is not essential to countering DDC and that such a stronger thesis is in any event implausible in light of “radioactive decay and some other quantum-level events”. 35   Ibid., 88 and 93. Beaudoin agrees with Kvanvig and McCann that it would be incoherent to suggest that the continued existence of a thing can be explained in terms of an “active power” of self-sustenance, since the operation of such a power would itself presuppose the thing’s continued existence. 36   Ibid., 89. 34

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explanations as tautologous) at least minimally informative: It tells us that the fact that opium puts people to sleep is no accident, but is rooted in some active power opium has by nature. But Beaudoin explicitly eschews the suggestion that existential inertia involves the operation of an active power, and offers no other explanation of why a thing might have it. For this reason, it will not do to suggest, as both Adler and Beaudoin appear to, that an appeal to Ockham’s razor or the principle of parsimony favours DEI over DDC. For this would be so only if both views offered equally good explanations of the relevant facts – such as the contingency of the natural world – where DEI did so without postulating as many entities as DDC. But DEI does not offer any explanation at all. It simply amounts to the denial of the DDC explanation. DEI proponents do not say: “Yes, given an Aristotelian-Thomistic analysis of natural substances in terms of act and potency, form and matter, essence and existence, and so forth, no such substances can have existential inertia; but here is an alternative analysis of the nature of such substances on which they do have it.” Rather, they offer no analysis at all. True, they do not affirm the Aristotelian-Thomistic conceptual apparatus, but neither do they put anything in its place. And merely to refrain from describing a phenomenon in some particular way is not to provide an alternative description of it. 3.3 The mythology of inertia To reason from the premise that material substances are governed by Newton’s law of inertia with respect to motion to the conclusion that they therefore enjoy existential inertia as well would be a gross non sequitur, and Beaudoin explicitly rejects any such argument.37 He also follows Jonathan Kvanvig and Hugh McCann in rejecting the suggestion that the principle of the conservation of mass-energy entails DEI.38 Still, both principles hover like specters over the debate about DEI and DDC, and defenders of DEI clearly believe that these findings of modern science at least lend plausibility to DEI and to that extent pose a difficulty for DDC. The idea seems to be that since the principles in question “explain” the phenomena of motion, mass, and energy, so too might a further inertial principle plausibly “explain” the continuance of the world. David Braine characterises this sort of thinking as beholden to what he aptly labels “the mythology of inertia”, and he quotes the following lines from Wittgenstein to indicate what is wrong with it: The whole modern conception of the world is founded on the illusion that the socalled laws of nature are the explanations of natural phenomena. Thus people today stop at the laws of nature, treating them as something inviolable, just as God and Fate were treated in past ages.   Ibid.   Ibid., 90–91; and Kvanvig and McCann, “Divine Conservation and the Persistence of the World”, 31–34. 37

38

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And in fact both are right and both wrong: though the view of the ancients is clearer in so far as they have a clear and acknowledged terminus, while the modern system tries to make it look as if everything were explained.39

Of course, Wittgenstein was not endorsing the Thomistic arguments for God’s existence, or any other such arguments. But those arguments are indeed “clearer” than is the scientism Wittgenstein is criticising, not only about what their proposed terminus is but also (and contrary to what Wittgenstein implies) about how that proposed terminus really does “explain everything”. For if there really is something that just is Pure Act, Subsistent Being Itself, absolute simplicity, and so forth, then there is no mystery about why this something requires no further explanation. But the same cannot be said for “laws of nature”, inertial or otherwise. As Kvanvig and McCann emphasise, “laws, after all, are descriptive in import. They do not operate at all, despite our figures of speech, and they do not do anything in or to the world. If they are true, it is because things themselves have features the laws describe.”40 But neither will it do to appeal to these “things themselves”, to some basic material entities which by their nature operate in accordance with the laws, as if they constituted a plausible explanatory terminus. For we need to know why these entities exist – not merely how they got here in the first place, but why they persist in existence. And as Braine emphasises, it would be incoherent to suggest that their natures explain their persistence in being, since their having natures in the first place presupposes that they persist in being.41 It is worth reemphasising that the DEI proponent has no tu quoque escape available here, no way of stalemating the defender of DDC by accusing him of a similar failure of explanation. For, to repeat, the difficulty arises from the composite nature of any explanans posited by DEI, and the whole point of DDC, at least as understood by thinkers like Aquinas, is to end the explanatory regress by concluding to something non-composite.42

39   Braine, The Reality of Time and the Existence of God, 14–15. The Wittgenstein passage is from the D. F. Pears and B. F. McGuinness translation of Tractatus Logico-Philosophicus (London: Routledge and Kegan Paul, 1961), at 6.371 and 6.372. 40   Kvanvig and McCann, “Divine Conservation and the Persistence of the World”, 34. 41   Braine, The Reality of Time and the Existence of God, 10. 42   Though Beaudoin eschews an active power construal of DEI, he does regard existential inertia as part of the essence or nature of whatever fundamental material elements turn out to have it (p. 94). But here as elsewhere, he never considers, much less answers, the question of how something composed of act and potency, or form and matter, or essence and existence could possibly have existential inertia, despite the Thomist’s claim to have shown that it cannot have it.

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4. CONCLUSION Obviously, whether the Aristotelian-Thomistic critique of DEI and defence of DDC that I have been developing here succeeds is a question that cannot be settled apart from a more detailed evaluation of the family of theistic arguments represented by the Five Ways. (As I have said, I have presented such an evaluation elsewhere, in my Aquinas.) Equally obviously, there are more fundamental metaphysical considerations to be evaluated as well. In particular, as my discussion has made clear, the dispute between the proponent of DEI on the one hand and at least Thomistic defenders of DDC on the other crucially hinges on whether something like a general Aristotelian-Thomistic metaphysics and philosophy of nature are correct. These issues too are beyond the scope of this paper (though I have also defended the relevant metaphysics and philosophy of nature elsewhere43). Enough has been said here, though, to show that the Thomistic critique of DEI and associated defence of DDC constitute serious arguments, and have yet to be seriously answered by defenders of the existential inertia thesis.44

BIBLIOGRAPHY Adler, Mortimer. How to Think About God: A Guide for the 20th-Century Pagan. New York: Collier/Macmillan, 1980. Augustinus, Aurelius. De Genesi ad litteram. Patrologia Latina 43: 391–446. Aquinas, Thomas. Summa contra gentiles. Vol. 13–15 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1918–1930. ― On the Power of God. Translated by Lawrence Shapcote. Westminster, MD: The Newman Press, 1932. ― Summa theologiae. Vol. 4–12 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1888–1906. ― Summa Theologica. Translated by Fathers of the English Dominican Province. London: Burns, Oates, and Washbourne 1912–36. Reprint, New York: Benziger Brothers 1947–48. Reprint, New York: Christian Classics, 1981. ― The Soul. A translation of St. Thomas Aquinas’ De anima. Translated by John Patrick Rowan. St. Louis: B. Herder, 1949.   See Feser, Aquinas, and, for a semi-popular and more polemical treatment, Edward Feser, The Last Superstition: A Refutation of the New Atheism (South Bend, IN: St. Augustine’s Press, 2008). Cf. David S. Oderberg, Real Essentialism (London: Routledge, 2007), and James Ross, Thought and World: The Hidden Necessities (Notre Dame: University of Notre Dame Press, 2008). 44   A longer version of this paper was published under the title “Existential Inertia and the Five Ways”, in American Catholic Philosophical Quarterly 85, no. 2 (2011): 237–267. For comments on earlier versions of the paper, I thank Mark Anderson, David Clemenson, David Oderberg, Bill Vallicella, an anonymous referee, and audience members at a conference on Metaphysics: Aristotelian, Scholastic, Analytic in Prague in July 2010. 43

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Beaudoin, John. “The world’s continuance: divine conservation or existential inertia?”. International Journal for Philosophy of Religion 61 (2007): 83–98. Braine, David. The Reality of Time and the Existence of God: The Project of Proving God’s Existence. Oxford: Clarendon Press, 1988. Catechism of the Council of Trent. For Parish Priests Issued by Order of Pope Pius V. Translated by John A. McHugh OP and Chas J. Callan, OP. Tan Books & Pub, 2008. Craig, William Lane. The Cosmological Argument from Plato to Leibniz. New York: Harper and Row, 1980. Denzinger, Heinrich. Sources of Catholic Dogma. St. Louis: Herder, 1957. Feser, Edward. Aquinas. Oxford: Oneworld, 2009. ― “Existential Inertia and the Five Ways” in American Catholic Philosophical Quarterly 85, no. 2 (Spring 2011): 237–267. ― “Teleology: A Shopper’s Guide”. Philosophia Christi 12, no. 1 (2010): 142–159. ― The Last Superstition: A Refutation of the New Atheism. South Bend, IN: St. Augustine’s Press, 2008. Kretzmann, Norman. The Metaphysics of Theism. Oxford: Clarendon Press, 1997. Kvanvig, Jonathan and McCann, Hugh. “Divine Conservation and the Persistence of the World”. In Divine and Human Action: Essays in the Metaphysics of Theism, edited by Thomas V. Morris, 13–49. Ithaca: Cornell University Press, 1988. Mackie, J. L., The Miracle of Theism (Oxford: Clarendon Press, 1982. Martin, Christopher F. J. Thomas Aquinas: God and Explanations. Edinburgh: Edinburgh University Press, 1997. McInerny, D. Q. Natural Theology. Elmhurst, PA: Priestly Fraternity of St. Peter, 2005. Miller, Barry. From Existence to God. London: Routledge, 1992. Oderberg, David S. Real Essentialism. London: Routledge, 2007. Ott, Ludwig. Fundamentals of Catholic Dogma. Cork: Mercier Press, 1955. Pasnau, Robert and Shields, Christopher, The Philosophy of Aquinas. Boulder, CO: Westview Press, 2004. Ross, James. Thought and World: The Hidden Necessities. Notre Dame: University of Notre Dame Press, 2008. Rundle, Bede, Why there is Something rather than Nothing. Oxford: Clarendon Press, 2004. Vallicella, William F. A Paradigm Theory of Existence: Onto-Theology Vindicated. Dordrecht: Kluwer Academic Publishers, 2002. Wittgenstein, Ludwig. Philosophical Investigations. Translated by G. E. M. Anscombe. 3rd edition. New York: Macmillan, 1968. ― Tractatus Logico-Philosophicus. Translated by D. F. Pears and B. F. McGuinness. London: Routledge and Kegan Paul, 1961. Wuellner, Bernard. Dictionary of Scholastic Philosophy. Milwaukee: Bruce Publishing Company, 1956.

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AQUINAS VS. BURIDAN ON ESSENCE AND EXISTENCE, AND THE COMMENSURABILITY OF PARADIGMS Gyula Klima ABSTRACT This paper argues that although Anthony Kenny’s objections to Aquinas’s “intellectus essentiae” argument for the real distinction of essence and existence in creatures are quite easily answerable in terms of a proper reconstruction of the argument, the argument thus reconstructed is still open to an objection offered by John Buridan in his Questions on Aristotle’s Metaphysics. The discussion of how Aquinas could handle Buridan’s objection will show that the conflict between their judgements concerning the validity of the argument rests on a fundamental difference between Aquinas’s and Buridan’s conceptions of how our concepts latch onto things in the world. These considerations lead at the end of the paper to some general reflections on the possibility of arguing “across” paradigmatically different conceptual frameworks.

1. INTRODUCTION In this paper I will argue that although Anthony Kenny’s objections to Aquinas’s “intellectus essentiae” argument for the real distinction of essence and existence in creatures are quite easily answerable in terms of a proper reconstruction of the argument, the argument thus reconstructed is still open to an objection offered by John Buridan in his Questions on Aristotle’s Metaphysics. The discussion of how Aquinas could handle Buridan’s objection will show that the conflict between their judgements concerning the validity of the argument rests on a fundamental difference between Aquinas’s and Buridan’s conceptions of how our concepts latch onto things in the world. These considerations will lead at the end of the paper to some general and rather sketchy reflections on the possibility of arguing “across” paradigmatically different conceptual frameworks. 2. KENNY ON THE “INTELLECTUS ESSENTIAE” ARGUMENT Aquinas’s famous intellectus essentiae argument in his De Ente et Essentia is taken by many commentators to be one of his most serious attempts to prove his metaphysical thesis of the real distinction of essence and existence in creatures. Others would claim that this argument is only a part of a larger argument, which as a whole intends to prove the real distinction of essence and existence EXISTENCE • 169

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in creatures and the identity thereof in God. In any case, that interpretational issue aside, the intellectus essentiae argument in itself can quite justifiably be taken to be an intriguing attempt to prove the real distinction between essence and existence at least in some cases, which then can be regarded as the starting point of the larger argument for the entire thesis. The larger argument would then seek to establish that if essence and existence are identical in some case, then they can be identical only in a unique case, namely, in the case of God, from which it follows that essence and existence must be distinct in all other cases, namely, in all creatures. In this paper, however, leaving the rest of the argument aside, I will confine my discussion to the piece of reasoning embodied in the following lines in Aquinas’s text: Whatever is not included in the understanding of an essence or quiddity is coming to it from outside, entering into composition with the essence; for no essence can be understood without its parts. But every essence can be understood without knowing about its existence, for I can understand what a man or a phoenix is, and not know whether it actually exists in the nature of things. Therefore, it is clear that existence is distinct from essence, unless, perhaps, there is a thing whose quiddity is its own existence.1

In his controversial book, Aquinas on Being,2 Anthony Kenny launched a twopronged attack against Aquinas’s argument. On the first prong, he tried to establish that if Aquinas in this argument was talking about existence in the sense of “specific existence”, expressed by the Fregean existential quantifier, then he was either talking nonsense or essence and existence are distinct both in God and in creatures. Kenny’s reasoning is based on the idea that Aquinas’s argument can plausibly be understood as claiming in its premises that while we know, for instance, what is meant by the word ‘phoenix’, namely, a mythical bird that sometimes bursts out in flames and is later reborn from its ashes, we just do not know if there is such a thing, i.e., we do not know if the word is true of something. Indeed, we actually know that the word ‘phoenix’ is not true of anything, for nothing is a phoenix, which is precisely the Fregean quantificational interpretation of the notion of existence. However, as Kenny correctly concludes, on this interpretation Aquinas’s argument would either amount to nonsense or it would prove too much. For on this understanding of the notion of existence, the thesis of the real identity of God’s essence and existence would amount to something like the ungrammatical gibberish: “God’s essence is ”. On the other hand, if we assume that the argument is not nonsensical and works, then it must work in the same way for the term ‘God’ as it does for the 1   Thomas Aquinas, “On Being and Essence”, c. 5, in Medieval Philosophy: Essential Readings with Commentary, ed. G. Klima (Blackwell Publishers, 2007), 240. 2   Anthony Kenny, Aquinas on Being (Oxford: Oxford University Press, 2002).

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term ‘phoenix’. But then the argument proves too much, for then, in the same way, we know what the term ‘God’ means, but we do not know whether it is true of anything, for we do not know whether there is a God. Thus, if this is what the distinction of essence and existence means, then they are distinct in God just as well as they are in creatures. On the other prong of his attack Kenny argues that if Aquinas was talking about existence in the sense of “individual being”, meaning actuality, corresponding to the Fregean notion of Wirklichkeit, then essence and existence are identical both in God and in creatures. For then we have to say that just as for God to be actual is for Him to be God, so for a dog, say, Fido, to be actual is for Fido to be a dog. Therefore, if this is what the identity of essence and existence means, then Fido’s essence is just as identical with his existence as God’s essence is with His existence. Thus, Kenny concludes, either way, the intellectus essentiae argu ment fails to establish Aquinas’s desired conclusion. However, as I have argued in detail elsewhere,3 Kenny’s argument fails on several counts. In the first place, Aquinas simply does not have a notion equivalent to the Fregean notion of an existential quantifier. In fact, a notion that would come closest to this notion in Aquinas’s conceptual arsenal would be regarded by him not as a concept of existence, but as a signum quantitatis, namely, a signum particulare, the syncategorematic concept expressed by the Latin terms ‘quidam’, ‘aliquid’ or their equivalents, which render a proposition to which they are prefixed a particular, as opposed to a universal, singular or indefinite proposition (as in, ‘Quidam homo est animal’ = ‘Some man is an animal’, as opposed to ‘Every man is an animal’, ‘Socrates is an animal’ or ‘A man is an animal’, respectively). In any case, Kenny’s reason for holding that Aquinas would have to use in his argument the notion of specific existence, and, correspondingly, the notion of nominal as opposed to real essence,4 is his unjustified assumption that Aquinas would take a phoenix by definition to be a fictitious bird as we do. However, from his argument, as well as from the parallel text of his Commentary on the Sentences (In II. Sent., d. 3, q. 1, a. 1, co.), it is quite clear that Aquinas uses this example as 3   G. Klima, “On Kenny on Aquinas on Being: A critical review of Aquinas on Being by Anthony Kenny”, feature review in International Philosophical Quarterly 44 (2004): 567–580. 4   A nominal essence is what is described by a nominal definition, which merely provides the meaning of a name, regardless of whether there is or even just can be anything that fits that description, while a real essence is what is signified by a real or quidditative definition, which identifies the essential features of the thing that is referred to by name according to the meaning specified by the corresponding nominal definition. Therefore, we can have nominal essences expressed/described by nominal definitions even of non-entities or mere impossibilia, whereas real essences can only be had by really existing genuine entities. For a good description of the contrast between nominal and quidditative defi nitions in the Thomistic tradition, see Thomas de Vio Cardinalis Cajetanus, “Super Librum De Ente et Essentia Sancti Thomae”, in idem, Opuscula Omnia (Bergomi: Typis Comini Venturae, 1590), 299.

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the illustration of a real, but ephemeral natural phenomenon, like a lunar eclipse or a rainbow, the essence of which we could know perfectly well in terms of a scientific definition without knowing whether this kind of thing actually exists at the present time. So, Kenny’s objection definitely fails on the first prong, on account of simply missing Aquinas’s point in the argument, taking it to deal with nominal, rather than real essences, and operating with a notion of existence that is alien to Aquinas’s thought. But Kenny’s objection fails on its second prong as well, even if the interpretation it involves is somewhat closer to Aquinas’s original intention. For Kenny bases his objection on the false assumption that the distinctness of essence and existence would have to mean that it is possible to have one without the other. And so, he argues, since it is impossible to have a dog’s existence without its essence – for a dog cannot be without being a dog – essence and existence would have to be the same also in the case of this creature. However, this assumption is obviously false: for it is clearly possible to have distinct, yet necessarily co-occurring items in reality. For example, it is clear that the triangularity of any particular triangle (its having three angles) is not the same as its trilaterality (its having three sides), unless sides and angles are the same items. But it is also clear that one cannot have a particular triangu larity without a particular trilaterality. So, we have two really distinct items here, which are nevertheless inseparable in reality. Again, this particular material form, say, the substantial form of this particular block of wood, cannot exist without the matter it informs, and the matter it informs cannot exist (at least on Aquinas’s conception), without this form actually informing it (since for both of them to be is nothing but for this particular block of wood to be). Still, Aquinas would take this form and this matter to be really distinct items in reality, since they are precisely those mutually exclusive, nonoverlapping, essential parts of the substance of this block of wood into which it has to be analysed in Aristotle’s hylomorphist metaphysics. Therefore, pace Kenny, real distinction does not have to mean real separability, which finishes off the other prong of his attack. 3. RECONSTRUCTING THE ARGUMENT Accordingly, to avoid the misunderstandings involved in Kenny’s criticism, we have to understand the argument as dealing with real, individualised essences, and arguing for their real, mind-independent distinction from real, individual acts of existence at least in those cases in which we have knowledge of the essence without knowing whether it is actually present in any actually existing individual. Therefore, taking c to be any arbitrarily chosen thing whose nature is known but whose existence is not known, the gist of the argument may be reconstructed as follows:

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1. The nature of c is known. 2. The existence of c is not known. 3. Therefore, the nature of c is not the existence of c. In fact, if we name the individualised nature of c by the proper name ‘n’, and its individualised act of existence by the proper name ‘e’, then this argument may be regarded as an instance of the following valid argument form of predicate logic: 1. Kn 2. ~Ke 3. e ≠ n Accordingly, in this reconstruction, the argument is certainly immune to Kenny’s criticism; indeed, it may appear to be absolutely uncontroversial. However, John Buridan attacked the argument precisely in this reconstruction, on account of the logical peculiarities of the intentional verb it involves. 4. BURIDAN’S CRITICISM Buridan takes on Aquinas’s argument in his Questions on Aristotle’s Metaphysics. In the first place, in the following passage he reconstructs the argument precisely in the way I presented it above, as an objection to his own position, which he is going to answer after his own determination of the issue: … I can have scientific knowledge of roses or thunder, and yet I may not know whether there is a rose or whether there is thunder. Therefore, if one of these is known and the other is unknown to me, then it follows that the one is not the same as the other.5

It is noteworthy in this reconstruction that Buridan is absolutely clear on the point of the argument Kenny missed, namely, that it is to prove the thesis of real distinction concerning the real essences of scientifically known but ephemeral natural phenomena, whose actual existence may not be known at any given time despite our scientific knowledge of their nature. Buridan’s criticism is based on the well-known phenomenon of the breakdown of the principle of the substitutivity of identicals in intentional contexts. It is easy to see this point, if we consider that the validity of Aquinas’s argument as reconstructed above requires that its premises together with the negation of the conclusion should form an inconsistent set of propositions. Indeed, if the principle of the substitutivity of identicals is valid, then from the negation of the conclusion, which would claim the identity of existence and essence, we could promptly derive a contradiction, proving the requisite inconsistency. However, if this principle is not valid, then the 5   Johannis Buridani Quaestiones in Aristotelis Metaphysicam: Kommentar zur Aristotelischen Metaphysik (Paris, 1518; reprint, Frankfurt am Main: Minerva, 1964), selections from lb. 8, q. 4, emended ad sensum and translated by G. Klima, in Medieval Philosophy: Essential Readings with Commentary, ed. G. Klima (Blackwell Publishers, 2007), 250.

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contradiction is not derivable, which invalidates the original argument. Accordingly, Buridan starts his response to Aquinas’s argument as he reconstructed it by making two important claims: first, that essence and existence differ in their concepts; second, that for this reason the argument as stated is a non sequitur:… for the sake of answering the objections it seems that we should say in this question that essence and existence differ in their concepts. For the name “rose” and this name or expression “that a rose exists” are imposed from different concepts. Therefore, when it is said that I think of a rose, while I do not think that it exists, this I concede. But from this it does not follow that, therefore, the existence of a rose6 differs from the rose; what follows is only that it is according to different concepts or on different accounts that the rose is thought of in terms of the name “rose” and the expression “that a rose exists.”7

However, besides simply claiming the invalidity of the argument, Buridan also provides an explanation why it has to be invalid with an intentional verb: Here you need to know that we recognise, know, or understand things according to determinate and distinct concepts, and we can understand a thing according to one concept and ignore it according to another; therefore, the terms following such verbs as “understand” or “know” appellate [i.e., obliquely refer to] the concepts according to which they were imposed [to signify], but they do not so appellate their concepts when they precede these verbs. It is for this reason that you have it from Aristotle that this consequence is not valid: “I know Coriscus, and Coriscus is the one approaching; therefore, I know the one approaching.” And this is because to know the one approaching is to know the thing according to the concept according to which it is called the one approaching. Now, although I know Coriscus, it does not follow, even if he is the one approaching, that I recognise him under the concept according to which I know him to be approaching. But this would be a valid expository syllogism: “Coriscus I know; and Coriscus is the one approaching; therefore, the one approaching I know.” Therefore, the situation is similar in the case under consideration: I understand a rose, but I do not understand a rose to exist, although a rose to exist I understand. The same applies to the other case: I concede that I have scientific knowledge about roses and thunder in terms of several conclusions, yet I do not have scientific knowledge about roses or thunder in terms of the conclusion that a rose or thunder exists. 8

Buridan’s criticism, as can be seen, is based on his celebrated theory of appellatio rationis, the theory according to which intentional verbs and their participles make their grammatical direct objects following them appellate, that is, obliquely refer to, their concepts. Indeed, if we make this oblique reference explicit, then the proposed argument will obviously be invalid. For then, using Buridan’s ex-

6   Buridan uses these sentential nominalisations equivalently with the abstract nouns formed from their verbs. This issue need not detain us here. 7   Ibid. 8   Ibid.

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ample, the premises and the conclusion would have to be reformulated in the following way: 1’. I know the essence of a rose qua the essence of that rose. 2’. I do not know the existence of that rose qua the existence of that rose. 3’. Therefore, the existence of that rose is not the same as the essence of that rose. That this argument is not valid is clear from the fact that from its premises and the negation of its conclusion we cannot derive a contradiction. For if we assume that the existence of that rose is the same as the essence of that rose, then from the two premises we can only conclude either that I know the existence of that rose qua the essence of that rose, or that I do not know the essence of that rose qua the existence of that rose, but either of these is clearly compatible with the other premise, namely, that I do not know the existence of that rose qua the existence of that rose or that I know the essence of that rose qua the essence of that rose. After all, I can clearly know something qua F and not know it qua G, even if it is both F and G, for I simply do not know that this F is also a G. To see that it is quite possible that I know the existence of that rose (which is the same as the essence of that rose) qua the essence of that rose while I do not know the existence of that rose qua the existence of that rose, we should just consider the perfectly analogous example from Aristotle, according to which it is quite possible that I know the one approaching (who is Coriscus) qua Coriscus, but I do not know the one approaching qua the one approaching (for I see him from afar and I do not recognise that he is Coriscus, which is the relevant sense of ‘knowing’ in this context). Thus, it seems that as long as we can know the same item qua some essence, but not qua some act of existence, it is quite possible for us to know the essence of a certain thing without knowing whether it exists or not, despite the fact that its essence and existence are the same. Therefore, Aquinas’s argument fails to establish its desired conclusion, the real distinction of the essence and existence of a thing on the basis of the fact that we may know its essence without knowing its existence. 5. A THOMISTIC RESPONSE TO BURIDAN’S CRITICISM, AND ITS IMPLICATIONS But this does not have to be the end of the story for Aquinas. In fact, if we take a closer look at Aquinas’s actual formulation of the argument, we have to notice something that is entirely neglected in the version of it criticised by Buridan; namely, Aquinas’s talking about “parts of the essence” without which it cannot be understood. What can he possibly mean by this? And what is the relevance of this to the validity of his argument?

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Since according to Aquinas the essence or quiddity of a thing is what is signified in it by its quidditative definition9 and the essence of a thing in and of itself is not a conglomerate of several distinct items, by “the parts of its essence”, he means whatever is signified precisely by the parts of the quidditative definition of the thing.10 In fact, since on his interpretation the definition is not primarily a linguistic expression, but an intention, that is, a concept of the mind expressed by the corresponding linguistic expression rendering this expression meaningful, we can say that on Aquinas’s conception having scientific, quidditative knowledge about a thing is having in mind its quidditative concept, expressible by a scientific, quidditative definition. In this context, therefore, we need to distinguish between merely having some (no matter how vague and confused) concept of a thing, resulting from the mind’s fi rst, spontaneous abstractive act, and having its quidditative concept, which is a clear and distinct, articulate concept, resulting from scientific enquiry into the nature of the thing.11 Having this sort of quidditative concept, therefore, means clearly knowing its implications: for instance, if I have the clear and distinct quidditative knowledge of diamonds as being tetrahedrally crystallised pieces of carbon, then on account of having that concept, as well as the concept of electric conductivity, I know just as well that diamonds are poor conductors (as opposed, say, to graphite). Now what does all this mean concerning the validity of Aquinas’s argument and its Buridanian criticism? Concerning Buridan’s criticism we should note that the breakdown of the substitutivity of identicals on account of the appellation of concepts in intentional contexts is conditioned on the logical independence of the appellated concepts in terms of which one and the same thing is conceived, known or understood. This is why it is possible for me to know, e.g., my father, and not to know the man approaching, even if the man approaching is actually my father. For I may certainly have the recognition of him in terms of the concept whereby I conceive of him as my father, while lacking the recognition of him insofar as I merely cognise him as the man approaching (insofar as ‘having the recognition’ of this person would mean being able to give an adequate answer to a question asking about the identity of this person). But this is so because the two acts of cognition in question are logically independent, whence I may perfectly well have the one without the other. However, if the appellated concepts or acts of cognition are not logically independent, whence I cannot have the one without the other, then the situation is   See the end of c. 1 of De Ente et Essentia. The quidditative definition of the thing Aquinas has there in mind is the definition of its most specific species consisting of its proximate genus and its specific difference. 10   For this point see for instance the entire discussion of c. 4 of his De Ente et Essentia. 11   For a painstaking and extremely illuminating discussion of distinct versus confused concepts or acts of cognition, see q. 1 of Cajetan’s commentary on Aquinas’s De Ente et Essentia. 9

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radically different. For instance, suppose I have perfect quidditative knowledge of all things moving toward me as such. Therefore, anything that moves toward me I know precisely insofar as it moves toward me. But I also know that anything that moves toward me approaches and anything that approaches moves toward me. Thus, it cannot be the case that I know the thing moving toward me insofar as it is moving toward me and I do not know the same thing insofar as it is approaching. And this is because the concepts appellated by the phrases ‘the thing moving toward me’ and ‘the thing approaching’ are logically equivalent; indeed, they are the same. Or consider another, perhaps more intuitive example. If I have the scientific concept of a rainbow, say, as being the refraction of light on water suspended in air, then I cannot know a rainbow qua rainbow, without knowing it at the same time qua the refraction of light on water suspended in air. To be sure, before forming the scientific concept, I can certainly have some vague and confused knowledge of it as some colourful arch in the sky, without knowing it qua the refraction of light on water suspended in air. However, once I have formed its quidditative concept, I cannot have knowledge of the same thing without knowing the implications of its quidditative concept. But then the situation would have to be similar with the notions of essence and existence, provided we are talking about the clear and distinct scientific understanding of a thing’s essence, which involves having the articulate, quidditative concept of the thing, and knowing its logical implications. For in this situation, if the existence of the thing were the same as the essence of the thing, or, using Aquinas’s phrase, it were “a part of” the essence of the thing, then this would mean that having the quidditative cognition of the thing would entail also having its cognition in terms of its existence: that is to say, we could not have its quidditative knowledge without knowing that it exists. Indeed, this is precisely what Aquinas hypothetically concedes in the conclusion of his argument: Therefore, it is clear that existence is distinct from essence, unless, perhaps, there is a thing whose quiddity is its own existence.

That is to say, if there is a thing whose essence and existence are the same, then having a clear and distinct cognition of the thing’s essence would immediately give us the knowledge that the thing exists, which is the exact reason why Aquinas would say that although God’s existence is self-evident in itself, that is, it would be knowable a priori by anyone with a clear and distinct cognition of divine essence, still, it is not self-evident to us, namely, human beings in our natural state, for in this state we just cannot have the clear and distinct cognition of divine essence that would allow us to realise the self-evident character of His existence.12 12

  Thomas Aquinas, Summa theologiae I, q. 2, a. 2.

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But then, how come Buridan didn’t realise this point when he formulated his objection? Didn’t he notice the possibility of the logical dependency of the appellated concepts that would again render Aquinas’s argument valid? Without going into much detail, I would suggest that the answer to these questions is that on Buridan’s conception of how our essential concepts latch onto things in the world, our concept of the quiddity of a contingently existing thing always has to be distinct and logically independent from our concept of the existence of that thing even if the thing in reality is both its own essence and its own existence. For on Buridan’s conception the quidditative definition of a certain specific kind of things signifies these things absolutely, whether they are past, present, future or merely possible, while in the context of a present tense proposition it supposits only for the presently existing ones, if there are any. The term ‘exists’ on the other hand, supposits only for presently existing things. Therefore, if the kind of thing in question merely contingently exists, then there is no way for us to know on the basis of simply comprehending the definition of this kind of thing whether even a single thing of this kind falls under term ‘exist’ right now, i.e., whether it actually exists. The picture, however, is radically different with Aquinas’s conception. For Aquinas, our specific quidditative concept of a thing grasps precisely that formal content in the thing that essentially “shapes” the thing into the kind of thing it is. (A good illustration of what this formal content is would be the genetic code of a biological species determining the essential features of the kind of organism pertaining to that species, or the configuration of the nuclei of elemental atoms describable in terms of their atomic number, determining their electron-configuration and thereby their essential chemical features.) Therefore, if this formal content involves the existence of the thing, then it is impossible to form this quidditative concept of any single thing of this kind without at the same time forming the concept of its existence and conceiving of it as existent and thereby knowing that it exists. For Buridan, on the other hand, concept formation does not consist in this sort of mental grasping of a formal content. It is merely the formation of an indifferent mental representation of a certain kind of things, the content of which is nothing but those things themselves, regardless of whether they actually exist or not. But it is quite obvious that one could form a concept of this sort without forming the concept of the existence of any single thing of this kind. Thus, it appears that in view of Buridan’s objection formulated on the basis of his conception of the mental representation of essence and existence, the issue of the validity of Aquinas’s argument in the last analysis turns on Aquinas’s own conception of mental representation. For the ultimate question is, whether Aquinas’s conception can support the claim that if essence and existence were in general the same, then their concepts could not be logically independently formed in our minds, and thus we could not have the scientific knowledge of essences of things without 178 • EXISTENCE

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knowing, on that account, the existence of these things, that is to say, knowing their essence, we would have to know that they exist. 6. A FINAL OBJECTION AND REPLY Perhaps, the best way to explicate this last claim is to answer on Aquinas’s behalf one final objection.13 For on this understanding of Aquinas’s position, one may still raise the following objection: can I plausibly assume that I can have scientific knowledge of a certain kind of thing without knowing whether any singular thing of that kind exists at the moment, without also assuming that the essence and existence of any singular thing of that kind are really distinct items in reality? If not, then the argument, implicitly assuming its own conclusion is clearly question-begging. In response, it would seem we might just ask back: do we acquire scientific knowledge of the essence of ununoctium by learning that it is an element of atomic number 118? One can certainly raise this question and answer it affirmatively without even thinking about the issue of whether there are any presently existing samples of this very unstable element in any lab on earth (let alone in any uncharted parts of the physical universe). However, based on this affirmation, and then reflecting on the issue that we have no idea whether any atoms of this element are in existence right now, one can, without further ado, accept the generalised premise that one can know the essence of a certain kind of thing without knowing its existence. However, relying on Buridan’s objection, one might retort at once that I could claim to have scientific knowledge of the essence of ununoctium only if I knew its actual existence, provided its essence and existence were in fact the same. I may simply (mistakenly) think that I know its essence on the basis of this definition, but in fact this is a very imperfect form of knowledge of that essence, not explicating everything it involves, whence I claim to have knowledge of essence without knowing existence simply on the basis of having a rather lax criterion for scientific knowledge, which, however, by stricter criteria, would have to contain the knowledge of the existence of the thing, if the essence and existence of the thing are in fact the same. So, I can assume that I know the essence of the thing without its existence only by presuming the conclusion, which still leaves the argument begging the question. In answering this retort, we must not forget that the charge of questionbegging (petitio principii) is the charge of an informal, epistemic fallacy (i.e., the argument is not claimed to be invalid or unsound): according to this charge, one cannot plausibly assume the premises without assuming the conclusion, i.e., the knowledge of the premises cannot be obtained without a previous knowledge of the conclusion (or something equivalent to it). So, a defender of an argument 13   I owe the original objection and the retort to my initial response to it to my student Timothy Kieras SJ.

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so accused should be able to point out independent, plausible grounds for the acceptability of the premises. That is precisely what I attempted in the fi rst paragraph of this section, with reference to ununoctium. But the retort, as I summarised it in the second paragraph of this section above, seems to undermine this attempt by claiming that as long as I do not know whether essence and existence are not the same, I cannot claim to have scientific knowledge of the essence of something without knowing its existence, which may just not be explicated in the rather incomplete knowledge of the essence I have in terms of the formulaic quidditative definition of the thing in question. However, this objection is based on a very, indeed, as I will argue, unreasonably strong interpretation of what is required for the scientific knowledge of the essence of something. For let us not forget that for Aquinas the essence of something is whatever it is that its specific quidditative definition signifies in it. So, if I have the specific quidditative definition of the thing, I do have scientific knowledge of this essence (as opposed to the confused, pre-scientific knowledge I may have on the basis of knowing some generic and typical accidental attributes of that kind of thing), and this may still not involve the existence of the thing. Nevertheless, the objector might still claim that I do not have a sufficiently clear and distinct knowledge of this essence until I know everything its essence involves, i.e., all the essential attributes the thing has by virtue of having this essence, whereas a quidditative definition merely provides us explicitly with two specifying attributes (genus and specific difference, plus the more generic attributes implied by these higher up on the Porphyrian Tree); and so, it may well be possible that existence is also among these essential attributes, just like any other essential attribute not explicated by the simple, formulaic definition. Do we really understand, for instance, everything that is essentially involved in having a rational nature? If not, then it may well be the case that existence is one of those things, but we claim to ignore it, simply because it is not explicated by the definition. But it is at this point that the unreasonably strong requirement for the scientific knowledge of essence becomes explicit. The retort in this form assumes that we can have scientific knowledge of essence only if we are able to explicate a priori all the essential attributes a thing has by virtue of having that essence. But this is an unreasonably strong requirement, for scientific knowledge of specific essences certainly does not require a priori, logical omniscience (i.e., the claim that if x’s having F implies its having G, then if I know that x is an F, then I know that x is a G; for then by knowing the axioms I would have to know all conclusions of any axiomatic deductive science, which is simply not the case). Thus, I certainly can have scientific knowledge of some essence without knowing all attributes a thing must have by virtue of having that essence. Furthermore, and more importantly, I do not have to know all essential attributes of a thing (i.e., attributes the thing 180 • EXISTENCE

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has by virtue of having its essence) in order to know of some attribute that it is not one of its essential attributes in this strict sense (just like I do not have to know every place on earth in order to know that something is nowhere on this earth, simply because I know that it is, say, on the moon). But then, I can certainly know the essence of the thing in terms of its scientific, quidditative definition, by virtue of which I know a priori that every singular thing that had, has, will have, or can have that essence had, has, will have, or can have the attributes explicitly or implicitly involved in that definition (even if I may not explicitly know all the attributes involved in that definition in this way). However, at the same time, I know that by virtue of knowing the essence of all these singulars in terms of their quidditative definition I do not know of any of them a priori whether they actually exist; I can only learn about their actual existence a posteriori. Therefore, even if I may not explicitly know all essential attributes of the thing a priori (while I do know some, namely, at least those explicated in the definition and those implications of this definition that I am aware of), I know that their existence is not one of them; that is to say, I do have scientific knowledge of the essence of this kind of thing, but I do not have this knowledge of the existence of any single thing of that kind by virtue of having this knowledge. However, on the basis of this understanding of what is and what is not involved in the scientific understanding of the essence of a thing one can plausibly concede to know scientifically what a certain kind of thing is and not to know whether any instance of that kind of thing actually exists without presuming, or even thinking about, the issue of the real distinction of essence and existence. Therefore, Aquinas’s argument proves this claim, without begging the question. But even if this defence answers the charge of its begging the question, one really big question still remains concerning the demonstrative force of Aquinas’s argument. If it can be “saved” from Buridan’s criticism only with appealing to Aquinas’s own interpretation of the notion of essence as it is described in his own conceptual framework, whereas Buridan’s criticism seems to be justified in his conceptual framework, does this mean that there is no absolute answer to the question whether the essence and existence of at least some creatures are really distinct? In other words, do we have to make our answer relative to the conceptual framework of each author, thereby somehow trivialising both their disagreement and the metaphysical point of the thesis itself? I would briefly reply that we do have to make our answer concerning the validity of Aquinas’s argument relative to the conceptual framework in which it is evaluated, but this still will not trivialise the issue. For even if we have to say that Aquinas’s argument is demonstrative in his own conceptual framework, but not in Buridan’s, this does not mean that their disagreement is something as trivial as a mere verbal disagreement. For in the case of mere verbal disagreement, the parties can easily resolve their apparent disagreement by simply “re-labelling” the concepts they both share, but simply express by different terms. However, with EXISTENCE • 181

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the disagreement between Aquinas and Buridan the case is just the reverse: they share the same words in the same language to express their own, rather different concepts of essence and existence, fitting into radically different conceptual frameworks, based on their very different conceptions of how our concepts latch onto things in reality. Therefore, if we want to deliver judgement on the demonstrative force of the argument without talking past Aquinas, but also taking into account the historically accumulated different conceptual frameworks in which it can still be competently evaluated, then we should evaluate not only the argument itself, and not only relative to this or that conceptual framework, but we should also evaluate those frameworks themselves. However, that is a whole new ball game, requiring the consideration of overall consistency, explanatory force and comprehensiveness of entire systems of thought in a conceptual framework that accommodates them all, in the sense of making all their claims and arguments at least logically commensurable with each other. This is certainly a difficult task; nevertheless, once we are aware of what it involves, it should not be impossible. After all, the very existence of this paper should demonstrate that such a conceptual framework is at least possible; we just need to work it out to make it actual.

BIBLIOGRAPHY Aquinas, Thomas. “On Being and Essence”. In Medieval Philosophy: Essential Readings with Commentary, edited by G. Klima, 227–249. Blackwell Publishers, 2007. ― Summa theologiae. Corpus Thomisticum. Textum Leoninum Romae 1888 editum ac automato translatum a Roberto Busa SJ in taenias magneticas denuo recognovit Enrique Alarcón atque instruxit. http://www.corpusthomisticum.org/sth0000.html Buridan, Johannes. Quaestiones in Aristotelis Metaphysicam: Kommentar zur Aristotelischen Metaphysik. Paris, 1518. Reprint, Frankfurt am Main: Minerva, 1964. ― Quaestiones in Aristotelis Metaphysicam. Selections from lb. 8, q. 4. Emended ad sensum and translated by Gyula Klima. In Medieval Philosophy: Essential Readings with Commentary, edited by Gyula Klima, 250–253. Blackwell Publishers, 2007. Cajetanus, Thomas de Vio, cardinalis. “Super Librum De Ente et Essentia Sancti Thomae”. In Opuscula Omnia, 299. Bergomi: Typis Comini Venturae, 1590. Kenny, Anthony. Aquinas on Being. Oxford: Oxford University Press, 2002. Klima, Gyula. “On Kenny on Aquinas on Being: A critical review of Aquinas on Being by Anthony Kenny”. Feature review in International Philosophical Quarterly 44 (2004): 567–580.

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POTENTIALITY IN SCHOLASTICISM (POTENTIAE) AND THE CONTEMPORARY DEBATE ON “POWERS” Edmund Runggaldier ABSTRACT Scholastic philosophers distinguished between potentiae in a logical sense (potentiae obiectivae) on the one hand and potentiae in the sense of capacities or active dispositions of living beings or real things (potentiae subiectivae) on the other. They were familiar with two different accounts of modality. One corresponds in a certain sense to the modern possible-worldsapproach; the other has its basis in everyday life, i.e., in our experience of having certain capacities and acting accordingly: We bring about certain states of affairs. Nowadays we have a similar duality of approaches to the problem of powers and active dispositions, and a new debate on agent causation.

1. INTRODUCTION Empiricist and conventionalist philosophers reduced disposition-ascriptions to conditional statements: an object or individual has a disposition D towards some manifestation M in certain conditions C iff that object would display M if exposed to C. On this reductive account, there is no explanatory work left for dispositions to do. Disposition-ascriptions do not explain why an event happens; they do only state, in an abbreviated manner, that one event follows another in certain circumstances. The reductionist approach has been subject to criticism in recent years. Stephen Mumford,1 George Molnar,2 Brian Ellis,3 Alexander Bird4 – to name just a few – have argued against a mere conditional analysis of dispositions, and pleaded for a realist understanding instead: dispositions are irreducible properties whose reality is not exhausted by their manifestations. They thus figure among the basic furniture of the world, existing independently of whether they are manifested. Being disposed to shatter or to dissolve are real properties that distinguish 1   S. Mumford, Dispositions (Oxford: Oxford University Press, 1998); Laws in Nature, (London: Routledge, 2004). 2   G. Molnar, Powers: A Study in Metaphysics (Oxford: Oxford University Press, 2003). 3   B. Ellis, Scientific Essentialism (Cambridge: Cambridge University Press, 2001); The Philosophy of Nature (Chesham: Acumen, 2002). 4   A. Bird, Nature’s Metaphysics (Oxford: Oxford University Press, 2007).

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their bearers from objects that lack them, even if these bearers never shatter or dissolve. Thoroughgoing argumentation for claims such as these has rehabilitated dispositions and powers in metaphysical debates. The reasons for the claim that dispositions and powers are real, irreducible properties, stem mainly from two fields: recent realist accounts in the philosophy of science, especially the philosophy of chemistry and biology on the one hand and the presuppositions we harbour when interacting with macroscopic objects in our everyday life, including living beings on the other. According to some philosophers of science (see, e.g., Cartwright5), dispositions play an essential part in the scientific picture of reality. Therefore, if we want to stick to this picture, they cannot be eliminated. Chemical substances and elements, for instance, are typically characterised in terms of the dispositions they have. Their identity does not depend on subjective factors such as conventions, decisions, or opinions, but on their objective valences. In fact, chemists do not explain chemical reactions mechanistically, using exclusively categorical terms, but by reference both to external triggering causes and to internal dispositions. A look at scientific practice thus suggests that we must not let go of dispositions and powers if we want to account for the various processes that take place in nature. The assumption that dispositions are real properties is central to our everyday life as well. We quite naturally ascribe dispositions to other persons and to animals, as well as to materials, and even to machines. In order to understand the behaviour of other persons, we want to know their convictions, character traits and habits, all of which are dispositional in nature. Dispositional realism is thus deeply rooted in our conception of the world: the assumption that the macroscopic objects we interact with – be they persons, animals, plants, etc. – have various tendencies, capacities, powers, etc., is fundamental for our orientation in everyday life. Hence, not only do the microscopic worlds of chemistry and the biological sciences support the dispositionalist view, so does our daily acquaintance with the macroscopic world of everyday life. The scholastic approach in the Aristotelian tradition to the problem of dispositions and powers is centred on everyday life, i.e., our Lebenswelt, in particular on our personal experience of being agents. This experience of being able to act and react is the key notion for understanding what power ascriptions consist in. We experience ourselves as having the power to change our environment and thus to change ourselves too. The scholastic assumption that dispositions and powers are real properties is grounded in the firm belief that we are able to do certain things and that it is the disposition which makes all the difference between being able and not being able to do these things. This does not exclude that there are other 5   N. Cartwright, Nature’s Capacities and their Measurement (Oxford: Oxford University Press, 1989).

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senses or accounts of dispositions and powers, but on this Aristotelian approach they are ontologically primary. There are similarities between the contemporary and the scholastic reasons for maintaining dispositions and powers in one’s ontology. The greater ontological contexts of agency and causality which provide a backdrop for these reasons are, however, different between the contemporary and scholastic accounts. To appreciate the scholastic account as an alternative worthy of consideration, it is helpful to see in more detail the diverging ontological frameworks. The scholastic ontology of dispositions is, first of all, grounded in the ontology of their bearers. The reality of dispositions depends on the reality of agents having them. This presupposes a multi-categorical ontology with substances and properties. The account of their causal role, then, is different too. For explanatory purposes contemporary realists assume that dispositions and powers have causal roles, but in the Aristotelian scholastic ontology their causal role is derivative. It is their bearers that are causally efficacious. Dispositional explanations of events thus ultimately refer to things being – in a wide sense – agents. This presupposes that it is not only conscious beings endowed with intentionality which are agents, but so are other living beings and even inorganic macroscopic objects. To talk of things acting and reacting does not imply that one attributes intentional attitudes to inanimate things, but it does imply a more complex theory of causality. The Aristotelian conception of causality is, as we will see, wider than mere event causality or causality in the Humean sense. 2. MAIN SCHOLASTIC DISTINCTIONS Scholastics distinguished between potentiae subjectivae and potentiae objectivae: “subjective potencies” are dispositions and powers inherent to a subject or bearer. “Subjective” in this context means predicable of a real subject or individual. Typical examples of subjective potencies are our own capacities and powers: We are, due to certain dispositions and powers, capable of acting and doing certain things. Potentiae subjectivae are not only instantiated in persons, but in other living beings as well and, as mentioned, even in everyday things. They are real properties, belonging to real things, and are thus called “potentiae reales” as well: they are not conceived of as mere possibilities existing in another possible world accessible from our own world. Potentiae subjectivae are integral parts of the world we inhabit. That they are real properties means that objects having them in this world are able to do or to receive certain things (potentia rei existentis ad aliquid faciendum vel recipiendum).6

6

  J. Donat, Ontologia (Oeniponte: Felicianus Rauch, 1953), 32.

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The scholastics contrasted the potentiae subjectivae with the potentiae objectivae: “objective potencies” are potentialities as mere possibilities. Potentia in this sense of objectiva simply means that something can exist or be real (aptitudo ad existendum…, ad modum rei recipientis existentiam). As a merely possible entity it does not exist in the actual world (reapse non existit…, non est quidquam reale existens), it is thus called “potentia logica” as well, something conceived in the mind or captured as mental content (non existit nisi tamquam objectum in mentis repraesentatione).7 Potentia objectiva and logica, not being a real property, does not need a bearer. Potentia in both its senses is always seen in relation to its manifestation or realisation, called its “actus”. It is the actus which is primary or fundamental, both on the epistemic and ontological levels. It would not be possible to acquire knowledge of potencies without knowledge of their manifestations or actualisations and there would not be any potency without the actus. The actus, on the other hand, is twofold. In the most general sense the actus is simply the realisation of something possible, i.e., of a potentia objectiva, whereas in the strict or fundamental sense it is the realisation or manifestation of a real capacity or a power, i.e., of a potentia subjectiva. Scholastics distinguished accordingly between first act (actus primus) and second act (actus secundus). In the case of a realisation in the first sense some object or living being begins to exist, whereas in the second case some existing object begins to act or some living being starts to operate. In the Aristotelian tradition events are changes understood as realisations of potencies. They are shifts from potentiae to actus. According to the abovementioned distinction, these changes are twofold: they can be realisations of potentiae objectivae, possibilities in a wide sense or possible entities, i.e., actus primi, or realisations of potentiae subjectivae, dispositions or powers, i.e., actus secundi. The key for understanding actus as the realisation or actualisation of a potentia is our experience as acting agents: we act and operate in virtue of our capacities as potentiae subjectivae. Aquinas summarises the point at the beginning of his quaestio de potentia: “…we must observe that we speak of power in relation to act. […] the word ‘act’ was first universally employed in the sense of operation...” 8 Scholastics distinguished further between potentia activa as the capacity to act actively, for example deciding, speaking or doing something, and potentia passiva as the capacity to be affected or to receive something, i.e., between the power of acting and that of being acted upon. If something has the capacity to change another thing, this other thing has the capacity to be changed. If it is impossible to alter it, it lacks the necessary potentia passiva. The scholastic account of the modalities of “possible” and “impossible” is grounded in the distinction between active and passive potencies and their con7 8

  Ibid.   Thomas Aquinas, De potentia, q. I, a. 1, co.

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traries, i.e., active and passive incapacities. Potency, capacity, power, and their contraries are the basic notions for the account of possibilities and impossibilities.9 Incapacity or impossibility is the privation (privatio) of potency. For something to be a privation, however, two conditions are required: (1) the absence of the opposite state; (2) the privation must belong to a bearer or definite subject at a definite time. To be blind, i.e., to be incapable of seeing, is a typical privatio. But only that is said to be blind which is naturally fitted to have sight and at the time when it is naturally fitted to have it.10 On the other hand, some modalities are accounted for in an objective or logical sense, i.e. in the sense of the modern possible-worlds approach. For example, it is impossible that the diagonal of a square should be commensurable with a side. “Impossible” in this context means that the statement that it is commensurable is necessarily false.11 The most basic of the various senses of the modalities “possibility” and “impossibility”, however, is that of being capable or incapable: an event or action is possible when its bearer or subject can change, otherwise it is impossible. All the other senses of “capable” or “potent” refer to this kind of potency.12 To sum up: For Aquinas and the scholastics the proper notion of possibility, in the primary sense of potency, refers to the capacity to change.13 3. THE ARISTOTELIAN BACKGROUND Aristotelian ontologies are multi-categorical: beside the fundamental distinction between the first category of individual things and living beings, i.e. substances on the one hand and the categories of properties and other accidental determinations on the other, there is the distinction between that which is real or actualised (ἐντελεχείᾳ, in actu) and that which is merely possible (δυνάμει, in potentia). We read in Aristotle: And since ‘being’ is in one way divided into individual thing, quality, and quantity, and is in another way distinguished in respect of potency (κατὰ δύναμιν) and complete reality (ἐντελέχειαν), and of function (κατὰ τὸ ἔϱγον), let us now add a discussion of potency and complete reality.14

Change or movement is accordingly the passage from a potential or possible state to a real one and vice versa. Aristotelian ontologies are thus characterised by a kind of tension between potency (potentia) and actuality (actus).   Thomas Aquinas, In Duodecim Libros Metaphysicorum Aristotelis [In Met.] V, lect. 14.   Ibid., n. 967. 11   Ibid., n. 971. 12   Ibid., n. 975. 13   Ibid., n. 976. 14   Aristotle, Metaphysics IX, 1, 1045 b 33 ff (ed. and transl. W. D. Ross). 9

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The topic of book IX is potency (δύναμις) and actuality (ἐνέϱγεια, ἐντελέχεια), i.e., the tension between that which is possible and that which is real or actual. The background of the Aristotelian approach to this division is, however, not the distinction between merely possible worlds and our actual world, but rather the experience of planning for the future, deliberating, and deciding: we take into consideration the real possibilities we have in our everyday-life world, which we live in. Aristotle distinguishes in book IX in detail between the different kinds or modes of potency hinted at in book V and relates them to a primary kind, easily accessible or experienceable in everyday life, which is, ultimately, the capacity to change. When things change, living beings included, they actualise certain possibilities and thereby lose others. Change is – as we have seen – passing from a possible state to an actual one. In book V Aristotle defines “potency” (δύναμις) in the most general sense as the “principle of change” in things, and in the narrower sense as the power of producing change or of being changed. He thus refers explicitly to that which has potency (τὸ δυνατόν).15 In book IX Aristotle also characterises potency as the power to produce change or motion, in both an active and a passive sense. Potency presupposes the reality of a bearer’s having this power. The causal efficacy of powers is due to some more basic kind of reality, i.e., to the reality of individual substances or things. These do the acting, as we shall see. Aristotle, in fact, explicitly refers to his treatment of primary or basic reality, to substance, the category to which all other categories imply a reference.16 Aquinas comments that Aristotle accordingly points out, first, that he has already discussed the primary, most basic kind of reality (de ente primo) to which all the other categories are referred, namely, substance. All other entities – quantity, quality, and the like – involve and presuppose substance. One can speak about them only by speaking about the individuals which have them (dicuntur secundum rationem substantiae). Predicating quantity, for example, is predicating the measure of substance, and predicating quality is predicating a certain disposition of substance. Qualities are real as some or other disposition of a substance (quaedam dispositiones substantiae). The definition too of any property includes a proper bearer or subject; in order to define, for example, “snub” it is necessary to refer to the nose which has a certain form.17As we can see, this Aristotelian multicategorical substance ontology clearly differs from the modern mono-categorical ontologies.

  Met. V, 12, 1019 a 32 ff.   Met. IX, 1, 1045 b 27. 17   Thomas Aquinas, In Met. IX, lect. 1, n. 1768. 15 16

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Besides, Aristotle and the scholastics were not sensitive to the modern notion of consciousness. Nonetheless, they distinguished between rational or mental capacities and natural ones. Rational capacities are those potentiae subjectivae which are not directed toward one single type of manifestation, but towards contraries. For example, men who have learnt an art possess capacities to do contrary things. A doctor who possesses the art of healing is capable of healing as well as making sick. Natural or physical potencies on the other hand are directed toward only one manifestation. We read in Aristotle: And all those potencies which are rational are open to contrary determinations, and those which are irrational are each determined to one thing; for example, what is hot is capable of heating, whereas the medical art is concerned with both sickness and health.18

Since potencies are real only if instantiated in a bearer or substance, one has to analyse them in relation to the things in which they are found. Potencies differ from each other on the basis of a difference in their subjects. 4. EFFICIENT CAUSATION In scholastic philosophy potencies and powers, potentiae subjectivae, have a causal role, but this role is derivative. The proper causae are their bearers. The presupposition for this understanding is a plurality of senses of ‘cause’, one of them being the so-called efficient cause. Efficient causes are not to be confused with necessary and sufficient conditions as explanans of an explanandum in the modern sense. The scholastic notion of efficient cause corresponds in a broad way to what we nowadays call “agent causation”. The natural way of characterising this type of causation is to refer to our experience of making something or bringing it about that something be the case: I am the source of my own activity. Of course, the defence of agent causation by reference to this experience is controversial. Those defending agent causation contend, however, that the commonsense view of ourselves as fundamental causal agents is theoretically understandable, internally consistent, and consistent with what we have come to know about the nature and workings of the natural world. They understand agent causation as a species of the more primitive “causal production”, underlying realist or non-Humean conceptions of causation. The idea of causal production corresponds to the wider notion of efficient causation in the Aristotelian tradition as is apparent from the Aristotelian definition: Aristotle defines efficient cause as “that from which the first beginning of change or of rest comes […]; for example, an adviser is a cause, and a father is 18

  Met. IX, 2, 1046 b 4–7.

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the cause of a child, and in general a maker is a cause of the thing made, and a changer a cause of the thing changed.”19 Agent causation in the Aristotelian tradition is not limited to conscious intentional beings: it is predicable of inanimate things as well. Actio is synonymous with doing, making, or producing, and is thus intimately linked to the notion of power or potentia subjectiva. In order to avoid misunderstandings it should be said that the relation of causing in the sense of efficient causation holds not between the agent and her action or her doing, but between the agent and the effect of the doing: The actio is not the efficient cause’s effect; instead, it is the very nature of the causing: “... actionem autem non esse effectum causae efficientis, sed rationem causandi...”20 At the beginning of modernity the Aristotelian causes came under attack, and so scholastics like Suárez tried to clarify them. Suárez even concedes a certain obscurity of the notion of efficient causation but defends it by referring to its role in everyday life. We know by experience, by the experience of acting and bringing it about that something is the case, that we are agents and thus efficient causes. Suárez refers to the first example of an advisor given by Aristotle: it is a personal cause, a human person acting on another person. “An advising cause of an effect E is, roughly, a rational agent who, by means of counsel, inducement, provocation, request, persuasion, threat, command, prohibition, etc., influences another agent to contribute freely to E.”21 To characterise agency and agent causality by the activity of acting or producing seems circular. Suárez sees the danger of a certain circularity of the Aristotelian account of agent causation. He is not bothered, however, since many philosophical notions have circular explications. Nowadays we would say that some philosophical notions are primitive or basic. Efficient causality does not exclude event causality. The two corresponding kinds of explanation can complement each other. Suárez himself declares that in the realm of nature an efficient cause always acts via changes or events and points out that according to Aristotle a natural cause always acts through motion or change: “… si Aristotelis mentem inspiciamus, videtur quidem solum definivisse causam efficientem naturalem, quae semper agit per motum vel mutationem.”22 Since the term “cause” is used in many senses, it is possible that one and the same state of affairs or phenomenon has several causes. The maker of a statue is a proper cause and not an accidental cause of the statue, and so also is the bronze,   Met. V, 2, 1013 a 29–32.   F. Suárez, Disputationes Metaphysicae, d. 17, s. 1, n. 5. 21   A. F. Freddoso, Note 4 in F. Suárez, On Efficient Causality. Metaphysical Disputations, transl. by A. J. Freddoso (New Haven: Yale University Press, 1994), 8. 22   Suárez Disputationes Metaphysicae, d. 17, s. 1, n. 4. 19

20

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but not in the same way. For it is impossible that there should be many proper causes of the same thing within the same genus and in the same order.23 5. CONCLUSION We have seen that scholastic philosophers distinguished between potentiae subjectivae, as capacities or active dispositions of living beings and real things on the one hand and potentiae objectivae in a logical sense, as mere possibilities on the other. They were correspondingly familiar with two different accounts of modalities, one rooted in everyday life, i.e. in our experience of having certain capacities and acting accordingly, the other corresponding in a certain sense to the modern possible-worlds approach. The more basic account is for them the first one. It presupposes agent causation in a wide sense, however, understood as the causa efficiens. Scholastic philosophers defended the reality and the causal role of powers by appeal to their bearers: The reality of dispositions depends on the reality of agents having them. This presupposes a multi-categorical ontology with substances and properties. For explanatory purposes contemporary realists assume that dispositions and powers have causal roles, but in the Aristotelian scholastic ontology their causal role is derivative. What is causally efficacious are the living beings and the things having causal powers.

23

  Thomas Aquinas, In Met. V, lect. 2, n. 773.

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BIBLIOGRAPHY Aquinas, Thomas. In Duodecim Libros Metaphysicorum Aristotelis. Cura et studio P. Fr. M.-R. Cathala et P. Fr. R. M. Spiazzi. Taurini: Marietti, 1964. ― De potentia. Vol. 2 of Quaestiones disputatae. Cura et studio R. P. Pauli M. Passion. Taurini: Marietti, 1965. Aristotle, Aristotle’s Metaphysic. A Revised Text with Introduction and Commentary by W. D. Ross. 2 vols. Oxford: Oxford University Press, 1924. Reprint, Oxford: Oxford University Press, 1997. Bird, Alexander., Nature’s Metaphysics. Oxford: Oxford University Press, 2007. Cartwright, Nancy. Nature’s Capacities and their Measurement. Oxford: Oxford University Press, 1989. Donat, Joseph. Ontologia. Oeniponte: Felicianus Rauch, 1953. Ellis, Brian. Scientific Essentialism. Cambridge: Cambridge University Press, 2001. ― The Philosophy of Nature. Chesham: Acumen, 2002. Molnar, George. Powers: A Study in Metaphysics. Oxford: Oxford University Press, 2003. Mumford, Stephen. Dispositions. Oxford: Oxford University Press, 1998. ― Laws in Nature. London: Routledge, 2004). Suárez, Franciscus. Disputationes Metaphysicae. Vol. 25–26 of Opera Omnia. Parisiis: apud Ludovicum Vivès, 1861. ― On Efficient Causality. Metaphysical Disputations. Translated by A. J. Freddoso. New Haven: Yale University Press, 1994.

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DISPOSITIONAL NECESSITY AND ONTOLOGICAL POSSIBILITY David Peroutka ABSTRACT Potency (disposition, power) is a property leading necessarily to an effect, whenever its bearer is suitably tested. A power belongs to the essence of the corresponding quality, it belongs to it as its relation to some (possible) effect. If powers belong to the essence of qualities, a qua lified thing, qua qualified, necessarily has the corresponding power. As a power ascription can be substituted with a conditional sentence, we may formulate the following proposition: Necessarily (in all possible worlds): a qualified thing is tested in relation to some power corresponding to its quality → it manifests this power. Having defined the notion of causal potency I offer then an account of ontological possibility, i.e. possibility founded not only on logical non-contradiction, but also on causal powers, dispositions or potencies. Causal accessibility of two different worlds means that the two worlds differ from one another by some causal process or processes (“distinguishing” causal processes), and that the two worlds share each bearer of potency, which in one of them manifests its potency by initiating some distinguishing causal process. The ontologically possible can then be defined as something that exists in some causally accessible world.

1. INTORDUCTION The first aim of this paper is to show the necessity of causal connexions by means of an ontological analysis of what is called “potency” in the Aristotelian tradition and “power” or “disposition” in contemporary philosophy. I will argue that the modality of necessity is needed for feasible conditional analysis or definition of potency. The second aim is to give an account of possibility founded not only on logical non-contradiction, but also on the notion of causal powers or potencies. In the last section I will argue that something is ontologically possible if there are active and passive causal capabilities enabling its production (which happens either immediately or as a result of a causal chain). 2. CONDITIONAL ANALYSIS OF DISPOSITIONAL PREDICATES In order to introduce the topic of dispositions, I first have to describe the problem of the conditional analysis of dispositional predicates.

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The conditional analysis of dispositions tells us that a disposition ascription such as “x has disposition to an effect Φ” can be adequately paraphrased by a conditional sentence of the following type: “if x is/were suitably tested, x manifests/ would manifest Φ”. For example the disposition ascription “wood is combustible” can be analysed by the conditional sentence “if wood is/were left in fire, it burns/ would burn”. This analysis is correct, if the disposition ascription and the corresponding conditional sentence are equivalent: (x has disposition to Φ) ↔ (if x is suitably tested, x manifests Φ) It cannot be denied that if the conditional sentence is true, then the disposition ascription must also be true: (if x is suitably tested, x manifests Φ) → (x has disposition to Φ) But various philosophers have denied the inverse direction: (x has disposition to Φ) → (if x is suitably tested, x manifests Φ) Charles B. Martin offered the following counter-example. It could be the case that a live wire is connected to an electro-fink, which is a device that detects when the wire is about to be touched, and instantaneously renders the wire dead. But according to the conditional analysis “the wire is live” means “if the wire is touched by a conductor then electric current flows from the wire to the conductor”. Therefore the conditional analysis fails…1 I do not think that this objection is fatal. Each description of a test implicitly includes suitable conditions for the test. By “suitable test” I mean a test (1) corresponding to the given disposition, (2) carried out under favourable conditions and without hindrances. Saying that a match lights up when suitably struck, we implicitly suppose the presence of oxygen and the absence of water at the moment of the described test. Such an implicit assumption can always be made explicit. In the case of the live wire we may protect our conditional analysis against Martin’s objection by extending the description of the test: exclude explicitly the influence of an electro-fink for the moment of testing. Martin’s objection would merit a more elaborate answer; however this is not the main concern of this paper. I do not want to prove the accuracy of the conditional analysis; my goal is to prove the causal necessity. The conditional analysis is only one of many prerequisites. Nevertheless, since this assumption can be called into question more than other assumptions, I will add the following argument in favour of it. 1

  Charles B. Martin, “Dispositions and Conditionals”, Philosophical Quaterly 44 (1994): 2.

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Let us suppose that the conditional analysis does not hold, because it is possible that the object having the disposition in question is suitably tested without showing its disposition, i.e. without producing the effect. Let us suppose that the following formula sometimes may be true: ¬((x has disposition to Φ) → (if x is suitably tested, x manifests Φ)) Let us consider two objects both having dispositions and both being suitably tested. Given our suppositions, it is possible that one of the two objects manifests its disposition, while the other does not. Since we suppose that both objects do have their dispositions and both tests are suitable, there is not a sufficient reason for such a divergence. Therefore if anyone wants to refute the conditional analysis and (consequently) allow this kind of divergence, he also has to drop the principle of sufficient reason. If we are determined to retain the principle of sufficient reason, we have to retain the conditional analysis as well. In this way my assumption of the accuracy of the conditional analysis is reduced to another more basic assumption, that of the validity of the principle of sufficient reason. By this principle I mean the claim that no state of affairs can obtain, and no statement can be true unless there is sufficient reason why it should not be otherwise. Without trustworthy general validity of this principle, the world would not be very intelligible. Whenever we look for an explanation, a truthmaker, a cause, a justification of some statement, we implicitly presuppose and confirm the validity of the principle of sufficient reason. In this paper the recourse to the principle shall be a “refrain” of my argumentation. Even if my reader is not convinced of the necessary validity of the principle of sufficient reason, I hope he regards its violation (i.e. the absolute non-availability of a required explanation) as a strange situation. I hope he agrees that every good theory refuses to suppose such situations as long as it is not necessary to allow them. Violation of the principle of sufficient reason might be declared possible only if there were a case in which it would be necessary to allow it. But why should it ever be necessary? Now let us begin our research of the necessity involved in the application of a disposition. Rudolf Carnap drew attention to the question of how to formalise the conditional analysis. Certainly we cannot do it by means of a material implication (test → manifestation). Since the falsity of such a material implication requires (in all cases) the truth of the antecedent describing the test, then the whole sentence is true of every untested object, and therefore it would ascribe the disposition to every untested object.2 Therefore we need to use a modally 2   Rudolf Carnap, “Testability and Meaning”, in Readings in the Philosophy of Science, ed. H. Feigl et M. Brodbeck (New York: Appleton-Century-Crofts, 1953), 52–53. Reprinted from Philosophy of Science 3 (1936); 4 (1937). In this paper Carnap tries to resolve the problem by means of a “reductive sentence”, but his analysis is applicable only in the case of tested

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reinforced implication3 □(test → manifestation). In this paper I will try to show that the ontological reasons for the application of necessitation consist in saying that power or disposition belongs essentially to the qualitative constitution on which it is based. If the needed necessity is found, the Carnap problem will be resolved, the Humean account of causality will be refuted, and the concept of natural law will be clarified. 3. HOW DISPOSITION IS ESSENTIALLY IDENTIFIED WITH QUALITY Sidney Shoemaker argued that a disposition essentially belongs to its qualitative basis. His argument goes as follows. We come to know (qualitative) properties only thanks to their causal potentialities, to dispositions or powers based in them (for example their dispositions to influence our senses). If dispositions didn’t belong to the corresponding (qualitative) properties essentially, “a thing might undergo radical change with respect to its properties without undergoing any change in its causal powers…” Such a situation implies “that it is impossible for us to know various things which we take ourselves to know”, because on these suppositions “there would be no way in which a particular property could be picked up so as to have a name attached to it…”4 To Shoemaker’s argument I will add another one. If dispositions do not belong to qualities essentially, the following situation would be possible: two objects differ in dispositions without differing in qualities. Since each disposition ascription can be translated into a conditional sentence, it follows that the conditional if the object were tested, it would manifest the effect would be false about one of our objects, but true about the other. Where is the sufficient reason for such a divergence? There is no truthmaker, which could justify this divergence in the truth-value of the sentence about qualitatively equal objects. If we want to avoid these consequences which violate the principle of sufficient reason, we have to accept the thesis that a disposition is essential to the qualitative constitution in which it is grounded. dispositions. We may object that we need to defi ne the term “disposition” ascribable also to non-tested objects. Sometimes we do ascribe disposition to non-tested objects: “…a certain nuclear fuel may have a disposition to explode, which justifies the taking of special precautions in its use, even if (thanks to those precautions) no fuel of that kind ever does explode.” – J. L. Mackie, Truth, Probability and Paradox (Oxford: Clarendon Press, 1973), 127. 3   Willard V. O. Quine intended to avoid the application of modality. According to Quine, the dispositional ascription “x is soluble” should be paraphrased thus: “there is y such that x and y are alike in molecular structure and y dissolves” (the employed verbs are understood as tenseless). Willard V. O. Quine, Word and Object (Cambridge: Massachusetts Institute of Technology, 1960), 224. The insufficiency of Quine’s resolution is obvious: it may happen that x and y are alike in molecular structure without sharing a disposition; for example in the case when a given disposition of y is grounded in certain macrostructure that differs from the macrostructure of x. 4   Sydney Shoemaker, “Causality and Properties”, in Metaphysics. An Anthology, ed. J. Kim et E. Sosa (Oxford: Blackwell Publishers, 1999), 257–258.

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With Stephen Mumford we may argue for the numerical identity of a disposition with its qualitative basis (with quality or qualities). We sufficiently explain the behaviour of physical things by their qualities. The “causal role” is occupied by qualities. A disposition conceived as something additional, non-identical with the corresponding qualitative constitution would be quite superfluous; it would not serve an explanation. If there are (causally relevant) dispositions at all, they are identical with their qualitative grounds.5 Mumford says that the difference between a quality and the corresponding disposition is similar to the Fregean difference between the morning star and the evening star in the case of Venus.6 This comparison is not exact since it is not essential for the morning star to be the evening star. However, I agree with Mumford that the difference between quality and corresponding disposition is a conceptual one: we can conceive the same accident in two different manners – according to its two essential aspects: (1) according to its basic qualitative aspect and (2) according to its dispositional aspect. For example we may describe the same accidental property of a stone as “round shape” or as “disposition to roll”. 4. THE QUESTION OF “PROPERTY MONISM” Against the thesis of identity (property monism) it may be objected that in a micro-world there are dispositions without any basis describable in a nondispositional manner. The nuclear physicist and philosopher Ian J. Thompson wrote: “For suppose that the exact shape and size of an object were known, the shapes and sizes of all its constituents, along with a list of these facts at every time. We would still know nothing about how or why the object would change with time or on interactions.”7 S. Mumford cannot give a sufficient answer, since he conceives the “categorical basis” of disposition only as “shape and structure“8 or “shape, macrostructure and microstructure”.9 George Molnar challenged Mumford’s monism at this point: “In the case of essential properties of the funda mental subatomic particles we have, on the very best of experimental and theoretical evidence, no reason for supposing that they have a non-dispositional or qualitative nature (certainly not a nature exemplified by size and shape).”10 In order to respond to such an objection we may ask: why does a certain object on similar occasions manifest similar behaviour? Why do we expect similar   Stephen Mumford, Dispositions (Oxford: Oxford University Press, 2003, first published 1998), 114–117; 146–150. 6   Ibid., 147. 7   Ian J. Thompson, “Real Dispositions in the Physical World”, British Journal for the Philosophy of Science, 39 (1988): 67–79. 8   S. Mumford, Dispositions, 111–112. 9   Ibid., 148. 10   George Molnar, Powers, ed. S. Mumford (Oxford: Oxford University Press, 2003), 156–157. 5

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behaviour on future occasions of similar type? If the explanation does not recourse to the qualitative constitution of the given object, the only reason for expecting the usual behaviour would be the persistent numerical identity of the object. But is that enough? David M. Armstrong rightly asks: “What is the magic in numerical identity?”11 Furthermore, let us consider that if there were “ungrounded dispositions”, the following situation would then be possible: two objects differing in dispositions without differing in qualities. Consequently the dispositional conditional if the object were tested, it would manifest the effect would be false for one of our objects, but true for the other. The problem is that there is no sufficient reason for such divergence in the truth-value of the same sentence when it is said about qualitatively equal objects. Therefore there are no ungrounded dispositions. Molnar’s abovementioned objections play up the fact that sometimes a disposition is not grounded in a shaped microstructure. But this fact does not give rise to any problem for property monism. With Max Kistler we may suppose “la base categorique” without always requiring micro-reductive basis describable in terms of shapes and spatial structures.12 We may recall the scholastic philosophy supposing that each quality is a form, but not necessarily a shape. Each quality is a form, but not each quality is a geometrical (stereo-metrical) figure or a configuration. According to Thomas Aquinas a form is (generally speaking) an inner determination or modification of a subject.13 But the form is not necessarily a geometrically describable determination. Even if some dispositions are not based on “shaped” microstructures, they are based on qualitative forms and are essentially identical with them. 5. DISPOSITION AS A RELATION So far we know that a disposition belongs essentially to the corresponding quality. This means that by a dispositional term we conceive an aspect of the essence of the corresponding quality. The disposition is merely an essential aspect of the quality, i.e. a special aspect of the essence of the quality. The disposition is namely the relational aspect of the essence of the quality. Let us now try to explain the pertinent “relationality”.

  David M. Armstrong, A Materialist Theory of the Mind (London and New York: Routledge, 1993–2002, first published 1968), 87. 12   Max Kistler, “L’efficacité causale des propriétés dispositionnelles macroscopiques”, in Cause, pouvoirs, dispositions en philosophie – Le retour des vertus dormitives, ed. Bruno Gnassounou and Max Kistler (Paris: Presses Universitaires de France, 2005), 144. 13   Thomas Aquinas, Summa theologiae Ia-IIae, q. 49, a. 2, co. 11

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• A certain determination of an object can be conceived insomuch as it determines the object itself; then we have the concept of quality. (Aristotle says: “By ‘quality’ I mean that in virtue of which things are said to be such and such”.14) • But the same determination can by conceived according to its relation to some possible effect, and thus we have the concept of power or disposition. A disposition is a relation to some possible effect, “directedness” to an effect (as Charles B. Martin called it).15 But, as George Molnar observed, it is a relation in a very special sense, because the existence of such a relation does not require the existence of the correlative, namely of the corresponding effect (as the object can have a disposition also at a time when the corresponding effect does not obtain).16 Scholastic philosophers knew of such a relation; they called it relatio transcendentalis.17 Such a relation does not belong to the predicament of relation (to the category of relation).18 Thomism supposed that potency, as “transcendental” relation (or relation secundum dici), is included in the essence of a related thing (in the essence of a quality) without constituting a further accident or accidental essence.19 In the case of potency, there is no connexion of two accidents, quality plus relation; there is only the accident of quality, which is related “by itself”, by its proper essence. Apart from potencies that are identical with accidents (namely with qualities), there are also ontologically more basic receptive potencies, which belong to the category of substance. Substance can be conceived as a transcendental relation   Aristotle, Categoriae, cap. 8, 8 b 25.   Charles B. Martin, “Final replies to Place and Armstrong”, in D. M. Armstrong, C. B. Martin and U. T. Place, Dispositions – A debate, ed. Tim Crane (London and New York: Routledge, 1996), 187–188. 16   G. Molnar, Powers, 62. 17   “Sed relatio transcendentalis, etiam non existente termino ad quem, intelligitur manere, quia manet essentia subiecti, quod ad aliud dicit ordinem.” – Vincen tius Remer, Summa praelectionum philosophiae scholasticae, editio tertia (Prati: Universitas Gregoriana – Giachetti, filii et soc., 1912), vol. 1: 332. 18   “…differt relatio pertinens ad praedicamentum relationis ab aliis respectibus caeterorum generum, qui a quibusdam transcendentes vocantur…” – Thomas de Vio Cajetanus, Commentarium super Opusculum De Ente et Essentia Thomae Aquinatis (Romae ex Pontificia officina typographica, 1907), cap. 7, q. 16, p. 218. 19   “Similiter scientia, sensus et similia dicuntur relativa secundum dici, quia significant res quas consequuntur quaedam habitudines, sive reales, sive rationis; et ideo propter relationes adductas videntur relativa et dicuntur talia. Apellantur vero relativa transcendentalia, quia propria eorum essentia, ad quam sequuntur tales relationes, licet sit quid absolutum, sumitur tamen in ordine ad aliquid extrinsecum, et sic habent aliqualem modum relationis. […] siquidem habitus, potentiae et plures aliae qualitates sunt relationes transcendentales, ut patet.” – Collegium Complutense S. Cyrilli OCD, Artium cursus sive Disputationes in Aristotelis dialecticam et philosiphiam naturalem (Compluti: apud Ioannem de Orduña, 1624), disp. 13, q. 2, p. 560–561; disp. 15, q. 2, p. 628. 14

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to accidents. Substance is potency towards an accidental form, because substance can receive further accidental determination. Similarly, prime matter is transcendental relation or potency towards substantial form. Nevertheless, the receptive potentiality of a substance demonstrates itself in the physical world always through accidental potencies, namely through qualities. Certain qualities allow the substance to receive other qualities or accidents. 6. PROOF OF CAUSAL NECESSITY Now finally let us return to our research of the necessitation needed in the definition of potency. Shoemaker asserted that potencies are essential to qualitative properties; he meant that potencies belong to the identity of a qualitative property.20 From this thesis he quickly and quite intuitively passed to the further assertion of “causal necessity”. He said that “the introduction into certain circumstances of a thing having certain properties causally necessitates the occurrence of certain effect” and that it is “logically necessary” that such an introduction has such an effect.21 I agree with Shoemaker’s opinion, nevertheless it has to be proved. Let us continue our considerations in the following way. If powers belong to the essence of qualities, a qualified thing, qua qualified, necessarily has the corresponding power. If powers belong to the essence of qualities, there is no possible world in which the bearer of a quality (or qualities) lacks the corresponding disposition. (Essential affiliation is per definitionem an across-all-worlds connexion). • In every possible world it is true, that the bearer of a quality also has the disposition belonging to the essence of the given quality. As a disposition-ascription can be adequately expressed by a conditional sentence, we may simply reformulate the last sentence in this way: • In every possible world it is true that if the bearer of a quality is properly (under suitable conditions) tested, then the bearer of the quality manifests the effect (which is proper to the disposition belonging to the essence of the given quality). If we assume that the range of the variable x is not the realm of bare substances, but of things considered insomuch as they are determined by their qualities, we may define disposition-ascription as follows: D(x) ↔df □(T(x) → M(x)) D means to have a disposition, T means to be (properly) tested, and M means to manifest it by the effect.   S. Shoemaker, “Causality and Properties”, 259.   Ibid., 261.

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According to Aristotle, the same necessity holds also for rational potencies,22 but in this case the description of the test must also comprise a (free) decision of the agent. For rational potencies, the Aristotelian analysis could be expressed thus: x has the disposition if and only if it is necessary that if x is suitably tested and (freely) decides to manifest the effect, then x manifests it. (In the case of God’s omnipotence the application of the Aristotelian analysis would be quite special, as the description of the test includes only a free decision: God has the power to cause a certain effect iff it is necessary that if He decides to cause the effect, He causes it.) Somebody would perhaps object that there may exist a world, in which the bearer of a given quality does not manifest the corresponding disposition, when suitably tested, because that world differs from the actual world in laws of nature. I answer that there is no reason to suppose the existence of laws as powerful entities directing the behaviour of things and influencing upon causal processes. With regard to ontological parsimony and Ockham’s razor I claim that laws are rather mere abstractions which generally describe the necessary behaviour of things. Laws are nothing but generalised descriptions of the behaviour of things, behaviour that is directed by causal necessity, which is based on dispositions of things. Laws depend on dispositions and not vice versa.23 There may possibly be a world with different laws of nature, but as Shoemaker said, “if the laws are different, then the properties will have to be different as well.”24 If my reasoning is right so far, it seems that the validity and necessity of natural laws consists in the here-described causal necessity based on the dispositional character of qualities. And since the said necessity (the necessity contained in our analysis of dispositions) works in the cases of causal connexions,25 Hume’s account of causal necessity as a psychological necessity26 is wrong. In our analysis of dispositions the test is nothing but the application of causal potencies; and the manifestation is the manifestation of the effect. We have found that the causal

22   Aristotle, Metaphysics IX, 5, 1048 a 10–14. Cf. Ursula Wolf, Möglichkeit und Notwendigkeit bei Aristoteles und heute (München: Wilhelm Fink Verlag, 1979), 29. 23   Stephen Mumford, Laws in Nature (London and New York: Routledge, 2004), 17; 181; 199–200; Alexander Bird, “The Dispositionalist Conception of Laws”, Foundations of Science 10 (2005): 353–370. 24   S. Shoemaker, “Causality and Properties”, 263. 25   Cf. Ullin T. Place, “Structural properties: Categorical, dispositional or both?”, in D. M. Armstrong, C. B. Martin and U. T. Place, Dispositions – A debate, ed. Tim Crane (London and New York: Routledge, 1996), 111. 26   “Either we have no idea of necessity, or necessity is nothing but that determination of the thought to pass from causes to effects and from effects to causes, according to their experienc’d union.” – David Hume, A Treatise of Human Nature, ed. G. Mossner (London: Penguin Books, 1969, 1984), book I, part IV, sect. 5, p. 216.

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connexion between them is necessary, as Aristotle supposed.27 With Thomas Aquinas we note, that causal necessity works whenever (universaliter) a cause is “sufficient and not prevented”,28 i.e. whenever a cause bears the pertinent causal potency and is tested without hindrances (suitably tested). 7. DISPOSITIONAL FOUNDATION OF POSSIBILITY Now, having defined the notion of causal potency or disposition, I may define the possibility, which is grounded in potency: something is possible if and only if there are active and passive causal capabilities enabling its production. Thomas Aquinas knows the “absolute” possibility, given only by the non-contradictory character of the possible, and the possibility guaranteed by an existing causal potentiality.29 The second case obtains when the possible exists “in the potency of some cause” (in potentia alicuius causae).30 In this sense Petr Dvořák rightly claimed: “The key is that the ontological status of the possible can, at least partly, be reduced to actual things possessing causal powers….”31 I start the reasoning by marking the insufficiency of the concept of possibility based purely on non-contradiction. Let us consider a maximal class of sentences, i.e. class containing the negation of every sentence not contained in it. Such a class of sentences, according to Carnap, represents or describes a possible world.32 This class of sentences must be above all non-contradictory: it contains either 27   Aristotle, Metaphysics IX, 5. See also Physics VIII, 4, 255 a 34–35, where Aristotle says: “It is always the case that when we have something capable of acting and something capable of being correspondingly acted on, in the event of any such pair being in contact what is potential becomes at times actual…” U. Wolf interprets this sentence as a description of causal necessity (Möglichkeit und Notwendigkeit, 24). Indeed, Aristotle’s expression “always” (aei) means “necessarily”. In De generatione et corruptione II, 11, 337 b 35 – 338 a 4 Aristotle says: “what is of necessity (ex anankes) coincides with what is always (aei)”. Cf. Michael J. White, “Aristotle and Temporally Relative Modalities”, Analysis 39, no. 2 (1979): 88; Jeroen van Rijen, Aspects of Aristotle’s Logic of Modalities (Dordrecht: Kluwer Academic Publishers, 1989), 5. 28   Summa theologiae Ia-IIae, q. 75, a. 1, arg. 2; ibid. ad 2: “Praeterea, causa est ad quam de necessitate sequitur aliud. … si illa definitio causae universaliter debeat verificari, oportet ut intelligatur de causa sufficienti et non impedita.” Scriptum super Sententiis II, d. 36, q. 1, a. 1, ad 2: “… et quod dicitur, quod ad causam de necessitate sequitur effectus, intelligitur de causa completa non impedita.” 29   Summa theologiae I, q. 25, a. 3, ad 4: „Ad quartum dicendum quod possibile absolutum non dicitur neque secundum causas superiores, neque secundum causas inferiores sed secundum seipsum. Possibile vero quod dicitur secundum aliquam potentiam, nominatur possibile secundum proximam causam.“ De potentia, q. 3, a. 1, ad 2: “Dicitur enim V Metaph., aliquid aliquando dici possibile, non secundum aliquam potentiam, sed quia in terminis ipsius enuntiabilis non est aliqua repugnantia… Vel potest dici, quod erat possibile propter potentiam activam agentis…” 30   Scriptum super Sententiis I, d. 38, q. 1, a. 4, co. 31   Petr Dvořák, “The Ontological Foundation of Possibility: An Aristotelian Approach”, Organon F 14, no. 1 (2007): 75. 32   Rudolf Carnap, Meaning and Necessity (Chicago: University of Chicago Press, 1947), 9.

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a sentence or its negation, but not both. The possibility of a world-description is identified with its logical consistency. But, as it seems to us, there are some logically consistent world-descriptions which include sentences describing some in facto impossible things. For example, things not admitted by the laws of nature. In addition to the non-contradiction of possible worlds some philosophers urge also the nomological accessibility of possible worlds. In this view something is possible, if it is part of a consistently describable world that does not differ from the actual world in the laws of nature. But (even if we leave aside many questions about the laws of nature) the nomological accessibility does not seem satisfactory. For example a world in which God exists, a “theistic” world, seems not to be accessible from any “atheistic” world, despite the supposed natural nomological parity of a “theistic” world with some “atheistic” world. It is because nothing in the history of an atheistic world has the real causal power to introduce the existence of God (as God cannot be conceived otherwise than as non-creatable). In order to define ontological possibility, first let us introduce the notion of causal accessibility of a possible world. If we speak about possible worlds, what are the conditions for y being causally accessible from x? • The first condition is that x and y differ from one another just (only) by some causal process or processes. Causal process is a chain – or ramified chain – of causes and effects (including at least one cause and one effect). To be a distinguishing causal process means to exist in one of the two worlds, but not in both. • The second condition of causal accessibility between x and y is that each entity playing the role of the causal initiator of a distinguishing process exists in both worlds, though it plays this singular causal role only in one of them. Causal initiator is the bearer of causal potency that manifests its potency in that one of the two worlds, in which it initiates a distinguishing causal process or processes. These conditions define causal accessibility between two different possible worlds. Let us also stipulate that each possible world is accessible from itself. Finally I may define the ontologically possible and also the ontologically necessary. If the range of the variable x includes individuals: • x is possible in the world w iff there is some possible world causally accessible from w in which x exists; • x is necessary in w iff x exists in each possible world that is causally accessible from w. In the end of my speculation the following question may arise. It may seem that the causal necessity, which works in the application of potencies, implies that every ontological possibility must necessarily be effectuated. But it would be MODALITIES • 205

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a mistake. In reality, the causal necessity is not absolute, but only hypothetical. Such a necessity may be described by a hypothetical or conditional sentence (“necessarily: if…, then…”). And the antecedent of the conditional may sometimes include a description of a free (not necessary) decision, as we have seen above. 8. CONCLUSION Let us now recapitulate the reasoning offered in this paper. I explained that a disposition belongs to the essence of that quality in which it is based. Since essential appurtenance is defined as an across-all-worlds connexion, we may assert that in every possible world the bearer of a quality bears also the disposition belonging to the essence of the given quality. If we suppose the accuracy of the conditional analysis, then the last sentence can be reformulated thus: In every possible world it is true that if the qualified thing (insomuch as qualified) is properly (under suitable conditions) tested, then the qualified thing manifests the effect. In this way I have described potency as a property leading necessarily to an effect, whenever suitably tested. This means that the Aristotelian account of causality as a necessary connexion is confirmed, and the concept of natural law is explained by means of ontological analysis of dispositional properties. Having defined the notion of causal potency, I based on this notion the concept of ontological possibility. At first I introduced the notion of causal accessibility. The reciprocal causal accessibility of two different worlds means that the two worlds differ from one another only by some causal process or processes (distinguishing causal processes), and that the two worlds share each bearer of potency, which in one of them manifests its potency by initiating some distinguishing causal process. This notion of causal accessibility permitted me to define the ontologically possible as something that exists in some causally accessible world: x is possible iff there are active and passive causal capabilities enabling the production of x, so that the bearers of such potencies are either immediate causes of x, or causal initiators of a causal process leading to the production of x. 33

33   The research was supported by the Grant Agency of the Academy of Sciences of the Czech Republic, project no. IAA 908280801.

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BIBLIOGRAPHY Aquinas, Thomas. Corpus Thomisticum. Sancti Thomae de Aquino Opera Omnia. Recognovit ac instruxit Enrique Alarcón. Automato electronico Pampilonae ad Universitatis Studiorum Navarrensis aedes a MM A. D. http://www.corpusthomisticum.org/ iopera.html. Aristotle. Complete Works of Aristotle. Ed. J. Barnes. Princeton, NJ: Princeton University Press, 1984. Armstrong, David M. A Materialist Theory of the Mind. London and New York: Routledge, 1993–2002, first published 1968. Bird, Alexander. “The Dispositionalist Conception of Laws”. Foundations of Science 10 (2005): 353–370. Cajetanus, Thomas de Vio, cardinalis. Commentarium super Opusculum De Ente et Essentia Thomae Aquinatis. Romae: ex Pontificia officina typographica, 1907. Carnap, Rudolf. Meaning and Necessity. Chicago: University of Chicago Press, 1947. ― “Testability and Meaning”. In Readings in the Philosophy of Science, edited by H. Feigl et M. Brodbeck, 47–92. New York: Appleton-Century-Crofts, 1953. Reprinted from Philosophy of Science 3 (1936): 420–468; 4 (1937): 1–40. Collegium Complutense S. Cyrilli OCD. Artium cursus sive Disputationes in Aristotelis dialecticam et philosiphiam naturalem. Compluti: apud Ioannem de Orduña, 1624. Dvořák, Petr. “The Ontological Foundation of Possibility: An Aristotelian Approach”. Organon F 14, no. 1 (2007): 72–83. Hume, David. A Treatise of Human Nature. Edited by G. Mossner. London: Penguin Books, 1969, 1984. Kistler, Max. “L’efficacité causale des propriétés dispositionnelles macroscopiques”, in Cause, pouvoirs, dispositions en philosophie – Le retour des vertus dormitives, ed. Bruno Gnassounou and Max Kistler, 115–154. Paris: Presses Universitaires de France, 2005. Mackie, J. L. Truth, Probability and Paradox. Oxford: Clarendon Press, 1973. Martin, Charles B. “Dispositions and Conditionals”. Philosophical Quaterly 44 (1994): 1–8. ― “Final replies to Place and Armstrong”. In D. M. Armstrong, C. B. Martin and U. T. Place, Dispositions – A debate, edited by Tim Crane, 163–192. London and New York: Routledge, 1996. Molnar, George. Powers. Edited by S. Mumford. Oxford: Oxford University Press, 2003. Mumford, Stephen. Dispositions. Oxford: Oxford University Press, 2003, fi rst published 1998. ― Laws in Nature. London and New York: Routledge, 2004. Place, Ullin T. “Structural properties: Categorical, dispositional or both?” In D. M. Armstrong, C. B. Martin and U. T. Place, Dispositions – A debate, edited by Tim Crane. London and New York: Routledge, 1996. Quine, Willard Van Orman. Word and Object. Cambridge: Massachusetts Institute of Technology, 1960.

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Remer, Vincentius. Summa praelectionum philosophiae scholasticae. Editio tertia. Prati: Universitas Gregoriana – Giachetti, filii et soc., 1912. Rijen, Jeroen van. Aspects of Aristotle’s Logic of Modalities. Dordrecht: Kluwer Academic Publishers, 1989. Shoemaker, Sydney. “Causality and Properties”. In Metaphysics. An Anthology, ed. J. Kim et E. Sosa, 253–268. Oxford: Blackwell Publishers, 1999. Originally published in: Time and Cause, edited by Peter van Inwagen, 109–135. Dordecht: Reidel, 1980. Thompson, Ian J. “Real Dispositions in the Physical World”. British Journal for the Philosophy of Science, 39 (1988): 67–79. White, Michael J. “Aristotle and Temporally Relative Modalities”. Analysis 39, no. 2 (1979): 88–93. Wolf, Ursula. Möglichkeit und Notwendigkeit bei Aristoteles und heute. München: Wilhelm Fink Verlag, 1979.

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THE OPTIMAL AND THE NECESSARY IN LEIBNIZ’ MATHEMATICAL FRAMING OF THE COMPOSSIBLE Mark Faller ABSTRACT This paper tries to show that Leibniz had a metaphysics of possibility and necessity that attempted to clarify and develop the usages of the two concepts. It further establishes that this system bridged the reciprocal weaknesses of both relativism and scepticism in order to nurture an organically realist model for the nature of truth and its corresponding reality. Working out the details of his full system is complicated by two factors. Leibniz never lays out the full details of this system in any extended work. And he often overstates the conditions of one or another of these categories in response to contentious debates he is involved with at the time. My paper will show that we can develop a unified reading of his position by comparing a number of his works on freedom, determinism and causality into a seamless and consistent view on the nature of possibility and necessity. More precisely, this paper will demonstrate how Leibniz’ works on mathematical analysis and mathematical optimality contribute to the framing of his radically novel concept of “compossibility”. It is this conceptual model that allows him to reconcile the dialectical poles of telos and necessity in a rich and complex synthesis that anticipates many of the problems that will haunt his heretical intellectual descendent, Kant.

1. INTRODUCTION The meaning of the concepts “necessity” and “possibility” have become vitiated and equivocal as the dual ideologies of relativism and empirical scepticism have undermined their metaphysical moorings. Empirical scepticism from its foundations with Heraclitus and Gorgias up to its heyday with Hume has cast a “duality” spell on our vision of the world. They preach an “evening” knowledge that idealises the past and the dead as the model for the living. Knowledge of the world is like, and therefore reducible to, the stable and inert facts that have already passed. Anything that is not translatable to this paradigm is dismissed as ethereal or merely of the mind. Empirical sceptics are “twoness” thinkers where necessity can either be from reason or from the world. Under this spell, necessity is either empty (from reason) or a mythical narrative we tell ourselves, but not fully applicable to the world.

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The only type of necessity that is relevant to reality is one based on habit and empirical probabilities (Hume). Relativism on the other hand, attempts to transfi x our vision toward the “morning” knowledge of an ever unformed future, where all things are equally possible. Berkeley’s “threeness” perspective rejects any robust distinctiveness between truth and fiction and instead holds that the justified beliefs of any community or individual are equally “true”. Within this Protagorean vision, necessity is in the eye of the beholder, with rhetoric the only tool of negotiating whether one view is more useful than another. We need to return to a time before the great transfi xing webs of Hume and Berkeley to appreciate the possibility of a more balanced idea of truth. It is in the subtle and complex metaphysical nuances of Leibniz that we may begin to purge our souls of these dual contaminants of modernity. I will make the case that Leibniz had a metaphysics of possibility and necessity that attempted to clarify and develop the usages of the two concepts. I will further show that this system attempted to bridge the reciprocal weaknesses of both relativism and scepticism in order to nurture an organically realist model for the nature of truth and its corresponding reality. Working out the details of his full system is complicated by two factors. He never lays out the full details of this system in any extended work. And he often overstates the conditions of one or another of these categories in response to contentious debates he is involved with at the time. I will try to show that we can develop a unified reading of his position by comparing a number of his works on freedom, determinism and causality into a seamless and consistent view on the nature of possibility and necessity. More precisely, I will try to demonstrate how Leibniz’ works on mathematical analysis and mathematical optimality contribute to the framing of his radically novel concept of “compossibility”. It is this conceptual model that allows him to reconcile the dialectical poles of telos and necessity in a rich and complex synthesis that anticipates many of the problems that will haunt his heretical, intellectual descendent, Kant. 2. LEIBNIZ’ DIVIDED LINE One concrete way in which to envision Leibniz’ full spectrum for the grounds of necessity and possibility is to project his kinds of judgements onto a model of a Divided Line (se the opposite page). A Divided Line can help us to recognise how two distinct kinds of relationships may be brought under a consistent relational rubric. On one side we have the ontological relationships between the levels of being. There is a spectrum of necessity and possibility that holds with respect to their position on this continuum. There is also the lateral relationships between the ontic levels and their 210 • MODALITIES

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Truths of Reason God’s Reason

Truths of Fact God’s ‹ŽŽ Ϋ o’oss‹„Že

Original identities

Derived identities

›’otŠeti…al ne…essities

Moral ne…essities

ogi…

MatŠ

…ien…e

—an aơairs

epistemic counterparts. In a realist line the conditions of knowability flow from the conditions of being and the epistemic gradations are analogical to the ontic. A Divided Line can for Leibniz, as it did for Plato, mediate the passage between scepticism and relativism. As a continuum with objective “cuts”, a Divided Line represents a kind of “fourness” thinking that is able to reconcile the apparently conflicting logics of relativism and scepticism, through a dimensional embellishment of our ontological model. There are some interesting differences and similarities we can immediately mine from Leibniz’ Line when compared with Plato’s. For one, there are unworkable inconsistencies in Plato’s model. The knowability of ontological kinds is laid out on a continuum with the faculties of knowing. Yet Plato has clearly specified that within man, it is usually the lower faculties that predominate, and that we have little and tenuous direct access to the divine nous. The two sides of the line should rightly be in inverse proportion, with knowledge itself some monstrous hybrid ratio. In the Leibniz Line there is no demand for such a tension. It is judgements of truth, not faculties, which he lines up with the types of possible being. Since judgements just are the identity between knowledge and being no inconsistencies need arise. The grounds of knowing and those of being just are the same: The nature of truth consists in the connection of the predicate with the subject, or the predicate is in the subject either in a way that is manifest, as in identities, or hidden. In identities this connection and the inclusion of the predicate in the subject are explicit; in all other prepositions they re implied and must be revealed through the analysis of the notions, which constitutes a demonstration a priori.1

But there are also strong similarities. The truths of logic and mathematics are together as two distinct categories on one side of a major division, with those of the phenomenal world on the other. The truths of logic and mathematics are truths of reasoning. They are necessary truths and their opposites are contradictions. Truths of the phenomenal realm are truths of fact; they are contingent, and their opposites are possible: 1   A quote of G. W. Leibniz, in Martin Heidegger, The Metaphysical Foundations of Logic, transl. Michael Heim (Bloomington: Indiana University Press, 1984), 39.

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There are in turn two genera of derivative truths: for some can be reduced to primary truths; others can be reduced in an infinite progression. The former are necessary, the latter are contingent.2

We should be careful not to interpret this seemingly complete disjunction as any kind of absolute dualism in either ontology or judgement. Leibniz’ Line, like Plato’s, is in fact a line, a continuum. The truths of fact can be construed as tautologies – implicit identities between the subject and predicate. The continuum of relationships between the subject and predicate cannot, however, be made explicit in a finite number of steps. The physical facts of which these truths refer can also be classified as “contingent” only in a qualified sense. They have a hypothetical necessity for which they are grounded by a sufficient reason for their being as they are: There is thus the tendency in his theory to assimilate as far as possible the veritates facti to truths of reasoning – though this is not stated with complete accuracy, since truths of fact are supposed to retain their own quality and nonetheless have the character of Identities.3

Hypothetical necessity is conditioned by the double constraints of mechanical determinism and economic compossibility. The compossible, Leibniz’ novel contribution to causal thinking, framed to reconcile the traditional polemic between mechanism and teleology, is the set of interactions between discretely determined events that mediates their “compatibility”: “My principle, namely is that whatever can exist and is compatible with other things, does exist, because the reason for existing in preference to other possible cannot be limited by any other considerations than that not all things are compatible.”4 Leibniz’ recognition that the compossible could be tamed by his mathematics of the optimum, informs the implicit identity between the contingent and reason. Equally as significant as the disjunction between the truths of reason and fact, is that distinction drawn within the truths of reason. Truths of definition are logically transparent and immediately identical. They are original truths. Those of mathematics are preponderantly derived. They are implicit or virtual identities that can be fully analysed into their explicit identities in a finite number of steps, and are deducible from them.   G. W. Leibniz, “On Freedom”, in L. A. Foucher de Caleil, ed., Nouvelles lettres et opuscules inédits de Leibniz (Paris, 1857) [henceforward F. de C.], 179; English translation L. E. Loemker, ed. and transl., G. W. Leibniz: Philosophical Papers and Letters, 2nd edition (Dordrecht: Reidel, 1969) [henceforward Loemker], 264. 3   Heidegger, The Metaphysical Foundations of Logic, 43. 4   G. W. Leibniz, “Two Notations for Discussion with Spinoza”, in C. I. Gerhardt, Hrsg., Die philosophischen Schriften von Gottfried Wilhelm Leibniz, 7 vols. (Berlin: Weidmannsche Buchhandlung, 1875–1890) [henceforward G], vol. 7: 262 (Loemker, 169). 2

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3. MATHEMATICAL ANALYSIS IN LEIBNIZ There are important implications for the development of modern philosophy in general, and Kant in particular, in how we frame Leibniz’ understanding of this process of conceptual/mathematical analysis. Wolff ’s interpretation of Leibniz, and that of most contemporary logical positivists, is that mathematical truths just are reducible to logical truths with no residue. This simplistic reading of Leibniz would seem to ignore many of his most penetrating works on the nature of mathematical thinking and knowledge. In particular his work on in situ geometry and the attempt to frame a geometrical semantics for his Universal Characteristic, indicate that Leibniz believed that mathematical knowledge was far richer and more semantically determinate than the syntactical relationships accessible solely from the law of identity. There are two ways to flesh out the nuances of Leibniz’ analytic framework. The first is to demarcate the substantial differences between mathematical and logical truths. The other is to illustrate how they remain fully reconcilable. Logical propositions are inherently tautologies, in and of themselves completely empty of semantic content. In order for logic to have any utility beyond playing with definitional identities, semantic content must be imported from the more determinate segments of our divided line. It is the precise nature of the limits and possibilities that this spectrum of ontological kinds introduces which makes Leibniz’ continuum of grounds so provocative. The Principle of Contradiction holds throughout all the subsequent realms of necessity and possibility, but it has an extremely thin realm of its own. Analysis is just the working out of the specific spatial or phenomenal conditions within which the Principle of Contradiction may gain footing. For Leibniz analysis went beyond what Hume or Kant meant by the taking apart of a concept. Leibniz explored a new kind of analysis, an analysis situs: The true analysis of situation is therefore still to be supplied. This can be shown from the fact that all analysts, whether they use algebra in the new manner or deal with the given and the unknown after the ancient pattern, have to assume many things from elementary geometry which are not derived from the consideration of magnitude but from that of figure, and which have not yet been explained in any determinate way. Euclid himself was forced to assume certain obscure axioms, without proof, in order to proceed with the rest. And the demonstration of theorems and the solution of problems in his Elements sometimes seem to be achieved through hard labor rather than method and skill, even though he also seems sometimes to conceal the ingenuity of his method.5

Leibniz held that this science was known to the ancients and involved the specific interpretation of geometrical loci, or the continuum of qualitative relationships. While algebraic analysis could only deal with quantity or magnitude, this   G. W. Leibniz, “On Analysis Situs”, in C. I. Gerhardt, Hrsg., Leibnizens mathematische Schriften, 7 vols., Berlin and Halle, 1849–1863 [henceforward GM], vol. 5: 178 (Loemker, 254). 5

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other analysis could capture the inherent nature of quality itself. Key to this distinction was identifying the essential quality of the similarity of figures: “Thus a true geometric analysis ought not only consider equalities and proportions which are truly reducible to equalities but also similarities and, arising from the combination of equality and similarity, congruences.”6 Similarity for Leibniz was the measure of quality and its significance reached beyond geometry: Besides quantity, figure in general includes also quality or form. And as those figures are equal whose magnitude is the same, so those are similar whose form is the same. The theory of similarities or of forms lies beyond mathematics and must be sought in metaphysics.7

Where algebra and logic were forced to reduce all relationships to mere identity, geometry could work with the more complex and subtle nature of forms that were both alike but different. Leibniz developed an invariant definition for the concept of similarity which he believed would finally free the property of quality or form from its subservience to quantity: “In undertaking an explanation of quality or form, I have learned that the matter reduces to this: things are similar which cannot be distinguished when observed in isolation from each other.”8 He believed, like Lull and Bruno before him, that he was on the threshold of discovering the Adamic language of the imagination, which could finally open the soul to the free gaze of the intellect: “All other matters which the power of imagination cannot penetrate will also follow from it. Therefore this calculus of situation which I propose will contain a supplement to sensory imagination and perfect it, as it were.”9 While defining the Truths of Reason as those that can be analysed in a finite number of propositions achieves precise conceptual clarity, there remain significant problems. There are many mathematical relationships that represent potentially infinite processes. The relationships between incommensurables or those elaborated in the squaring of a circle can only be approximated within a finite set of calculations. Although there are mathematical operations that can fully comprehend infinite processes within a finite procedure, like differentiation and integration, there remain kinds of operative definitions that defy such handling – the calculation of pi. But Leibniz also realises that there is in mathematics the possibility of “capturing” such potentially infinite processes. This is the very nature of the calculus   Ibid. (GM 5: 179; Loemker, 255).   Ibid. (GM 5: 178; Loemker, 254). 8   Ibid. (GM 5: 179; Loemker, 255). 9   Ibid. (GM 5: 181; Loemker, 257). 6 7

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he helped to develop and it is clear that we can have necessary knowledge of such “contained” infinite processes in his example of an asymptote: Ordinarily, for example, we find that two lines which approach each other continuously finally meet, and many people would be quick to swear that this could never happen otherwise. Yet geometry does furnish exceptional lines, called asymptotes for this reason, that when extended to infinity they approach each other continuously and yet never meet.10

Mathematics in general, and geometry in particular, has a unique capacity to represent the unlimited. And it is through the mining of the geometrical facility within the soul that we can begin to grasp the deeper mysteries of the world and mind: A new and unexpected light arose at last, however, from where I least expected it, namely, from mathematical considerations of the nature of the infinite. For there are two labyrinths in which the human mind is caught. One concerns the composition of the continuum, the other concerns the nature of freedom. And both arise from the same source, the infinite.11

Once I have determined a mathematical truth, its statement and derivation can be fully translated into a logical proof. It is less clear whether that truth could have been reasonably derived using only logical rules, in less than an infinite number of steps. And if the truth were derivable with logic, the question remains whether logic would have the capacity to finally identify that truth as a significant mathematical truth. In this sense the comparison is similar to the problem of computer searches and their relationship to the Meno paradox: How can I find something if I do not already know what it is I am looking for. There is a rich mathematical content, with its own complex order of necessity and possibility that is “lost” in a reduction to merely logical principles. In this sense, geometrical thinking is like the strategic logic (vs. the syntactic rules of play) for winning an infinite game (or the Slave Boy Problem). No logic can develop an algorithm for final victory. But once an “optimum” strategy is discovered through geometrical insight, it can subsequently be translated into a logical proof. 4. A MISPLACED DISJUNCTION IN KANT If my interpretation is substantially correct, we can discover two relevant insights into its significance for Kant. First, following Leibniz, Plato and the Empiricists, Kant realised that there were significant differences between the kinds of 10   G. W. Leibniz, “On What is Independent of Sense and Matter” (Letter to Queen Sophia of Prussia, 1702) (G 4: 504; Loemker, 551). 11   F. de C., 179; Loemker, 264.

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knowledge represented by experience and reason. The first was particular and fleeting, the latter universal and invariant. Second, with Plato and Leibniz, Kant recognised a differential hypotheticality for mathematical judgement in his interpreting mathematical judging as a priori synthetic. Mathematical thinking is not strictly logical. It is a liminal middle kind of “figuring” that shares aspects of both pure reason and imaginative experience. It is a priori in that it can be fully translatable to logical identities in a finite set of propositions. It is synthetic in the sense that it takes a synthetical construction to bridge the intuitional gap and discover the explicit analytical steps. We must be very careful here in parsing our terms. It is exactly in the period between Leibniz and Kant that the meaning of the terms analysis and synthesis get completely inverted by the empiricists. For Leibniz, analysis is that art of the ancient geometers that took apart problems before inverting them into synthetic proofs. So when he refers to analysis in mathematics he is referring to the same taking apart of figures and relationships that Kant would later refer to as synthetic, due to its origins in the intuition. For both thinkers this was an “art” deeply buried in the soul. But Kant goes perhaps too far in establishing the uniqueness of mathematical concept formation. He wants to absolutely disjoin this process from that which frames concepts of the understanding. In this effort he comes up with the enchanting, but misleading maxim: “Philosophical cognition is rational cognition from concepts. Mathematical cognition is rational cognition from the construction of concepts.”12 This neat divide produces two one sided caricatures of conceptual formation and leaves both frameworks open to sceptical attack: Hence philosophical cognition contemplates the particular only in the universal. Mathematical cognition, on the other hand, contemplates the universal in the particular, and indeed even in the individual, yet does so nonetheless a priori and by means of reason.13

First we must recognise how important it is for Kant to establish the principle of mathematical cognition on an absolutely firm and autonomous grounding. Mathematical knowledge holds the key to defeating the Humean sceptical fork, i.e. that synthetic a priori judgements were possible. The vicious dichotomy of nominalism maintains that there are two absolutely incommensurable types of knowledge, the a priori analytic and a posteriori synthetic, each deriving from two radically distinct sources, reason and experience. This divide makes the product of reason, logic, empty and relegates knowledge of nature as merely particular and therefore blind. Kant’s insight was to recognise that mathematical 12   Immanuel Kant, The Critique of Pure Reason, transl. W. Pluhar (Indianapolis: Hackett, 1996) [CPR], 668 (B 741 | A 713). 13   CPR 669 (B 742 | A 714).

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knowledge seems to bridge this dichotomy in a way that defeats the sceptical claim. Mathematical thinking is both a priori in the universality and necessity of its results and synthetic in the expansively ampliative promise of its enquiry. To understand why he got mathematical thinking so wrong we will have to understand how an inherent disposition interacted with this driving motivation. Kant is not a dialectical thinker. His priority as a critical philosopher is clarity over coherence, and he most often dismisses dialectical oppositions as “antinomies” and “paralogisms”. Even though he needs mathematics to hold as an absolute “middle” to bridge the Humean fork, he is little able to illustrate the essentially liminal nature of mathematical thinking. Kant creates an absolute duality between the mathematical and the philosophical uses of reason. One is “quantitative” while the other is “qualitative”; One is constitutive of its object, the other merely regulative; One is rational cognition from concepts while the other is rational cognition from the construction of concepts: “Mathematical definitions can never err. For since the concept is first given through the definition, it contains exactly just what the definition wants us to think through the concept.”14 This clean dichotomy between the mathematical and dynamical uses of reason does allow Kant to set an autonomous ground for mathematics against the reductive thesis of the empiricists. It also allows him to build a critical bulwark against the claims of dogmatism that haunts the historical rationalists like Leibniz and Plato who apparently just assume that mathematical ideas apply to the world. But there is a serious cost to this clarity. Concepts that I construct can have constitutive clarity, but how do I objectively compare and contrast them to the empirical concepts I have formed through abstraction? How do I know that the circle I have constructed in my intuition has at all the same sense as the circle I “see” in the plate?15   CPR 682 (B 759 | A 731).   This issue has a very old pedigree. The ancient academy was divided over the issue of whether universals were abstracted or projected. The mathematical followers of Plato leaned toward the projection thesis, while those of the linguistic-orientated Aristotle leaned towards an abstraction thesis. A similar debate would rage after Kant within the philosophy of mathematics. Dedekind and Cassirer followed Kant in holding that mathematics was a  projective process, typified by the ordinal generation of the number line. Russell and Cantor, on the other hand, seeing mathematical concepts as the cardinal abstractions from set theory. But if mathematical thinking can truly bridge the conceptual divide of concepts and experience it must be inherently liminal. Numbers must somehow be both ordinal and cardinal – constructed and discovered. There is an implicit proof of the invariance of mathematical liminality in the Theaetetus. The only way to uniquely understand the number six is to see it as a scaled relationship between its cardinal and ordinal properties: six is the uniquely smallest perfect number, where its multiplicative or formal factors add up to its material sum. This hybrid formulation of the nature of number would match well Leibniz’ idea of an invariant, universal characteristic. 14

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It is at this point, when we transition from the Truths of Reason to those of Fact, where the consequences of Kant’s first mathematical error get compounded. The rigid distinction between the construction of concepts in math and the use of concepts in the understanding, leads Kant to develop an equally rigid distinctive ground for their determination of phenomena. The physics of Newton, based on the constructive patterns of geometry just are constitutive of the phenomena of nature, while the dynamic purposiveness of biology can only be “regulative” of our understanding of nature: “It has just been shown that since this principle of purposiveness is only a subjective principle of the division and specification of nature, it does not determine anything with regard to the forms of the products of nature.”16 These two sets of disjunctions are merely aspects of the same error. This insight can be illustrated with a look at the inherent ambiguity within the emerging controversies surrounding the biological definition of species. Taxonomists and cladists argue for two radically distinct ways by which to group organisms. Functional or dynamical causal frameworks will determine a substantially different kind of biological classification than one presuming a morphological or genetic basis for the generation of species. The choice one makes is presumed by and further determines ones causal narrative. With Leibniz, the form of mathematical thinking cannot be so easily simplified. In different writings Leibniz appears as both a logicist and a functionalist with regard to the formation of mathematical concepts. We have shown earlier that he develops the idea that there is a unique and implicit qualitative knowledge within geometry that can never be merely captured by quantity or reduced to logic. And mathematics has a double directionality. There is an “upward” and a “downward” path in the differential and integral calculus. Some critics have judged this dualist-like approach within Leibniz as a type of weakness or equivocation, but as we move towards an examination of the “lower” half of our Divided Line, that which deals with the compossible relationships between phenomena, we find that this pluralism is the source of much of the enduring richness in his metaphysics. Leibniz in his work with the calculus would be aware that it is the dynamical and functional aspects of geometrical representations that empower mathematical models to completely capture and determine the hypothetical necessity of the phenomenal world. The dynamical relationships of the regulative laws of nature are every bit as determinate of the phenomenal world as the mathematical relationships of the mechanical causes. In fact for Leibniz they are sufficiently more so. For Leibniz this mutuality already infects his model of the grounding of phenomenal truth. We can understand causes of the physical from both a mechanical 16   Immanuel Kant, The Critique of the Power of Judgment, transl. P. Guyer and E. Matthews (Cambridge: Cambridge University Press, 2000), 22.

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and a purposive perspective, and each is equally as “mathematical”. It is precisely the mathematically dynamic aspects of the phenomenal world that contribute directionality to the causal interplay of the compossible. 5. THE MATHEMATICAL GROUNDING OF LEIBNIZ’ OPTIMISM The full success or failure of Leibniz’ project of reconciling teleology with necessity lies in the possibility of bringing his conceptual model of compossibility onto a rigorous foundation of mathematical formulation, something ironically akin to Newton’s rehabilitation of his mysterious “gravity” through the equations of mass and distance. The vision and vehicle for this formulation is his mathematically dynamic model of pulchritude and plenitude. In the fall of 1697, Leibniz wrote “On the Radical Origination of Things”, in which he attempted to illustrate the complex orders of necessity that ruled the compossible world of nature. His major focus in this essay was to “explain how temporal, contingent, or physical truths arise out of truths that are eternal and essential, or if you like, metaphysical…”17 Leibniz proceeds by attempting to demonstrate how those forms which are most likely to emerge into reality are those which have some sort of priority of metaphysical perfection in possibility. So he states that in the undertaking of the drawing of an unspecified triangle, that figure which will be most easily constructed with a compass will be also the “best” one – the equilateral triangle, “Hence it is very clearly understood that our of the infinite combinations and series of possible things, one exists through which the greatest amount of essence or possibility is brought into existence.”18 He goes on to complete this formulation with his statement that the actual world is the best of all possibilities in that “a maximum effect should be achieved with a minimum outlay”19 This definition of optimality or elegance by the specification of the identity of sides is completely consonant with contemporary information theory. The accepted standard of measuring the complexity of a phenomenon is by the amount of information it takes to specify it. The recursiveness of the equilateral triangle makes it the ultimately “simplest” triangle from this aspect of informational describeability. Paul Schrecker has noted that this effort by Leibniz is in fact an explanation of how order arises out of chaos in Plato’s Timaean receptacle.20 Plato implies that his elemental triangles are the result of the interplay between likelihood (symmetry)

  G. W. Leibniz, “On the Radical Origination of Things” (G 6: 303; Loemker, 487).   Ibid. 19   Ibid. 20   Paul Schrecker, “Leibniz and the Timaeus”, Review of Metaphysics 4 (1951): 495–505. 17

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and necessity (dynamic stability). There is a thermodynamic rational for why the triangular, mechanical vectors rule the micro-dynamics of atomism. This reading of the consonance between the Leibnizean and Platonic cosmos perhaps does not go far enough. According to Leibniz the order that rules the diverse levels of the phenomenal hierarchy is determined not by God’s reason, or the laws of Newtonian mechanics (although it can be translated to them), but rather the goodness of God’s will. It is not enough, however, to merely show that the mechanical laws are an exemplification of the most probable. For both Leibniz and Plato mechanics represents the bare necessary conditions of causal interaction, that set of constraints within which possibility can be framed. It cannot be Socrates’ “ligaments and bones” that finally keeps him in his imprisonment. In the Timaeus it is reason, in the form of the harmonic movements of the heavens that finally persuades necessity to do its bidding. This formulation of persuasion is also central to Leibniz’ concept of God’s will determining towards what is best. Heidegger notes that Leibniz’ framing of the Principle of Sufficient Reason, with the phrase “rather than” is a direct implication of ground as “preference”: We can only have the ground as preference where freedom and ground go mutually together as a “decision about value.”21 For both Plato and Leibniz the value that is designed into the cosmos is the stochastic good of mathematical order. In this sense there can be no conflict between God’s will and His knowledge, the Good is just the perfection of the whole and to know the good is to do it. Since the time of Voltaire’s Dr. Pangloss, defending Leibniz’ dual doctrines of pulchritude and plenitude- that God has chosen the most perfect world, “the simplest in its hypotheses and the richest in phenomena”,22 – has become a double burden. First, one must show that such a belief can be based on scientific principle, not simply optimism or dogmatic faith. And one must further demonstrate that such a principle is not in substantial conflict with established scientific practices. If such a task should seem daunting, hopeful challengers can take heart in the quality of the company. Leibniz is joined by no less that Fermat, Maupertuis, and Euler in his belief that the universe was guided by some principle of beauty or efficiency. And all four of these great minds thought they had found the fount of that elegance in some form of “least action” principle. While modernity has mostly accommodated some form of such a principle, it has unilaterally rejected the metaphysical implications drawn by these four great mathematical philosophers. The enduring stature of these brilliant and sober intellects demands that we carefully re-examine such an easy dismissal. Leibniz based his principle of an efficiently ordered universe, like Fermat before him, largely on evidence such as Snellius’ Law for the propagation of 21

  Heidegger, The Metaphysical Foundations of Logic, 116.   G. W. Leibniz, Discourse on Metaphysics (G 4: 431; Loemker 306).

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light23. The fact that light seemed to seek the path of shortest time, eliminated the possibility of mechanical or efficient explanations. Only an end-driven or teleological hypothesis could explain such activity, and that end was to an efficient order. Leibniz’ own development of the methods of differential calculus aided him in envisioning the economic elegance of such an optimisation principle. Even though Leibniz’ work predates the theoretical work on thermodynamics by more than a generation, it is clear that his vision of nature is equally as “stochastic”. Compossibility is the unitary outcome of the totality of mechanical micro-states of a system. Compossibility is Leibniz’ anticipation of thermodynamic theory. Both the principle of least action and his work in the Origination show a sophisticated dynamic view about how such systems are mathematically disposed toward self-organisation. I will therefore, try to make the case that his vision about the way the phenomenal world is ordered to following God’s will towards what is the most perfect, is inherently a rigorous elaboration of what will be thermodynamic theory. The Second Law is indisputably a teleological principle. The Second Law just does determine the final state of any closed system, regardless of any unique initial configuration of the elements. This condition establishes that the Second Law is “end driven” or “pulled” rather than “pushed”. The establishment of the Second Law as teleological would seem to be little consolation to the grand optimism and romance of our Metaphysical Mathematicians. Their vision was of a universe designed by God to be the best and most beautiful, not a chaotic soup of heat death. In this sense Maxwell’s finalism seems untranslatable to Aristotle’s. What Aristotle implies by his “telos” is not disorder, but quite the opposite. Purpose is some ordering entelechy that, except for its autonomy from initial conditions, seems the very antithesis of the end predicted by the Second Law. Here we must account for the fact that Aristotle affirmed that the final cause was most closely associated with the formal cause. It is this relationship, between the formal principles of how transitions must take place, and the teleological or final conditions, of where the transitions are headed, that must be understood if we are to make sense of either order or disorder. 5.1 The thermodynamic origins of harmony It has been widely recognised since the time of Helmholtz that the overtone series and its relationship to musical harmonics, through the occurrence of beats, is an objective phenomenon of the physical world and not merely a cultural or subjective preference. The motion of a plucked string successively breaks downs into harmonic patterns, the overtone series, expressing the progressively increasing ratios of small integers: 23

  Ibid. (G 4: 449; Loemker 318).

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Ratio to Fundamental

Ratio to Preceding

1:1

Harmonic

Relationship to Preceding

Fundamental

Note   C

1:2

1:2

2nd Harmonic

Octave

  C’

1:3

2:3

3rd Harmonic

Fifth

  G’

1:4

3:4

4th Harmonic

Fourth

  C’’

1:5

4:5

5th Harmonic

Major Third

  E’’

1:6

5:6

6th Harmonic

Minor Third

  G’’

This harmonic pattern holds great physical significance for a variety of diverse, continuously dissipative sources that to some degree conform to these same orderly patterns. From the indefatigable motion of the electron, to the massive symphonic stroll of the heavenly bodies, the mathematics of harmonic consonances order much of the world around us. Fourier found that heat dissipates from a solid object in such an harmonic pattern. What has been less clear is why this pattern of simple whole number ratios is a physical determiner of the harmonic order. The overtone series of harmonics is the pattern of sinusoidal waves into which a plucked string progressively declines as its energy dissipates. The pattern is that of simple whole number ratios and corresponds closely to the traditional harmonic consonances: 1:1, 2:1, 3:1, 4:1, 5:1 etc.:

1:1 fundamental octave (1:2) 1:2 1st overtone Ƥfth (2:3) nd

1:3 2 overtone fourth (3:4) rd

1:4 3 overtone major third (4:5) 1:5 4th overtone 1:6 5th overtone 222 • MODALITIES

minor third (5:6)

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This overtone series is the basis of all the diverse, traditional systems of scaling – diatonic, just and equal temperament – and therefore cannot in any absolute way determine which “musical” system is “better”. All the varieties of scale “cutting” share certain absolute and objective characteristics. The octave (2:1) and the higher harmonies, the fifth (3:2) and the fourth (4:3) appear to be essential to both the “sweetness” and the ordering capacity of the overtone series. The lesser harmonies and the sizes of the whole and half notes appear to have only a “normative” or cultural hold on diverse tastes. Once we are given the overtone series, the arithmetic pattern itself determines all the relationships of harmony. The mystery remains: Why do continuously dissipating systems conform to such a pattern? The Second Law of thermodynamics states that any closed system whose initial state is out of equilibrium, will eventually work its way to a final state of equilibrium. In a two chamber system with a set number of particles (eight) in one half and a vacuum in the other, will eventually settle into the equilibral state of maximum probability distribution when the chambers are opened to each other. The final and most probable state of the system is given by the equal distribution of particles in the two chambers. With all eight molecules in one chamber the maximum number of unique distributions is eight. However, with four molecules in each chamber the number of possible distribution states maximises at 70: N=8

1 arrangement

8! / 4! 4! = 70 arrangements

When a constrained string is plucked, energy dissipates in a lawfully ordered progression. Since the disturbance is to a continuous medium, the string, the number of possible intermediary states approaches the indefinite. Not all intermediary states, however, are equally probable. Those states that attain an equal distribution of the system’s parts will attract the motion of the string as being the states of maximum possible distribution. Since equality can only attain where there are an integer number of divisions: 2, 3, 4, etc., the successive intermediary states of the string returning to its rest state will be through the series of integer divisions – the harmonic series. This theoretical hypothesis of how continuity directs the way in which gradients within a system must “dissipate” has been empirically well verified within MODALITIES • 223

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many different kinds of phenomena. It has been identified variously as a “spite” principle by Joseph Kestin or a “moderation” principle by Prigogine.24 This principle also stands as an explanatory ground that illuminates the multiple faces of the enigmatic Least Action Principle. What can be understood from the thermodynamic origins of harmonics is the underlying ordering power of the law of disorder. The final state parameters of the Second Law are that any system will continually move towards a minimisation of gradient differentials. There are, however, continuity parameters that govern the way in which such systems transition to those final states. These transition parameters, that continuously dissipative systems will be attracted to the most probable intermediary states, determine that the retreat of stochastic dissipative systems from gradient extremes will necessarily be maximally ordered. 6. CONCLUSION It should perhaps not surprise us that our Divided Line turns out to be a “cut ting of a cannon”, a harmonic division. Our avowed purpose in transposing Leibniz’ spectrum of norms onto a line was to make sense of the dimensions of conditionality within his complex ontology. Harmonic theory offers us just such a spectrum of necessities. Science, since the enlightenment, has pushed for the absolute disjoining of nature from value in explaining the world. Neuro-philosophers have attempted to go even further in eliminating the place of the non-mechanical in human affairs. An accurate study of the great Leibniz should serve as a healthy prophylactic to these incursions. For Leibniz there are two principles of necessity, one negative, the Principle of Contradiction, and one positive, the Principle of Sufficient Reason. While the negative principle is stronger, it can never be violated under any circumstances, the Principle of Sufficient Reason is the determinant cause of all of nature and all of reason. God’s good will does not overrule his reason, so much as it frames the continuing and progressive context within which it has authority to legislate. The good is the final, absolute necessity within which reason manages the possibilities of expression. The good determines the providence and forces of historical development. Physics marshals the movements of the particulate conditions. The interplay of compossible, mathematical forces will determine the development of that world which evolves towards perfection: It is the awakening of the sleeping god, in its progressively conscious choice of its self-determination. Plato and Leibniz have looked upon that face, and it is us. 24   Eric Schneider and Dorion Sagan, Into the Cool: Energy Flow, Thermodynamics, and Life (Chicago: University of Chicago Press, 2005), 76.

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BIBLIOGRAPHY Foucher de Caleil, L. A., ed. Nouvelles lettres et opuscules inédits de Leibniz. Paris, 1857. Gerhardt, C. I., Hrsg. Die philosophischen Schriften von Gottfried Wilhelm Leibniz. 7 vols. Berlin: Weidmannsche Buchhandlung, 1875–1890. ― Leibnizens mathematische Schriften. 7 vols. Berlin (vol. 1–2) and Halle (vol. 3–4), 1849–1863. Heidegger, Martin. The Metaphysical Foundations of Logic. Translated by Michael Heim. Bloomington: Indiana University Press, 1984. Kant, Immanuel. The Critique of Pure Reason. Translated by Werner Pluhar. Indianapolis: Hackett 1996. ― The Critique of the Power of Judgment. Translated by Paul Guyer and Eric Matthews. Cambridge: Cambridge University Press, 2000. Loemker, Leroy. E., ed. and transl. G. W. Leibniz: Philosophical Papers and Letters. 2nd edition. Dordrecht: Reidel, 1969. Schneider, Eric and Sagan, Dorion. Into the Cool: Energy Flow, Thermodynamics, and Life. Chicago: University of Chicago Press, 2005. Schrecker, Paul. “Leibniz and the Timaeus”. Review of Metaphysics 4 (1951): 495–505.

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SECTION VI

PREDICATION

THE INTERPRETATION(S) OF PREDICATION Uwe Meixner ABSTRACT In the course of the history of Western philosophy, various philosophers have given various answers to the question of the ontological basis of predication. This essay presents the main, the crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. The essay follows (to some extent) the most influential – the Aristotelian or quasi-mereological – paradigm of predication in its continuity and modification through the many centuries of its reign. But this essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, a philosophically satisfactory theory of predication was not even in the offing, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication-theory it considers. Frege, in the 19th century, brought the philosophy of predication on the right track. But his own theory of predication has its own deficits (which it shares with still other predication-theories). The essay ends with the presentation of a theory of predication that the author himself considers adequate.

In the economy of science, and of knowledge in general, simple predicative statements have a fundamental and indispensable role to play. Such statements, simple as they are: containing no logical functors, have various forms in natural language. Here is a far-from-complete list of such forms, each item in the list combined with an illustrative example: Forms

Examples

α Φs [covering also: α is] α is Φ α is a Φ α Ψs β [covering also: α is β] α is+pr β α is Φ+pr β α is a Φ+pr β α is+pr β and γ

Kate laughs Kate is beautiful Kate is an actress Kate loves George Kate is in Boston Kate is married to George William is a descendant of Albert The tree is between the house and the street

[pr: some preposition]

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Notwithstanding these many forms, the general form of simple predicative statements, which is familiar from first-order predicate logic, is just this: Φ(α1, …, αN) Here the sequence “α1, …, αN” represents the occurrences of the singular terms in a simple predicative statement, all of them without syntactical structure, in the order in which they follow each other in the statement (noting that a singular term may occur more than once in it); and the letter “Φ” represents the rest of the statement: the predicative basis, devoid of all logical functors, in which all of the occurrences of singular terms in the statement are embedded; finally, the unifying function of the predicative basis is indicated by the embracing brackets, “(” and “)”. In order to make matters as simple as possible – that is: in order to focus on the basic problem of predication – I stipulate, in addition to the description of simple predicative statements just given, that the singular terms in simple predicative statements are not to refer to linguistic items or abstract entities, and that the predicates in simple predicative statements are to be chosen accordingly. Some simple predicative statements are true. But from the earliest times of philosophy to this day the nature of the truth of true simple predicative statements has been controversial among the philosophers. Does the truth of such statements have ontological import? And if it has ontological import, what exactly is that import? These questions are philosophical evergreens, and not accidentally so: their importance can hardly be overestimated. For what is at stake in these questions is nothing less than the basic determination on what it truly amounts to when we claim to have knowledge of the world and to speak the truth about the world. In this essay, I shall look at some of the milestones of a discussion that spans almost 25 centuries: among other predication-theories, at the theories of Plato, Aristotle, and the Aristotelian-minded non-nominalists, at the theories of Leibniz and of Frege. At the end of the essay, I shall briefly present my own approach. The positions on predication of the just-mentioned philosophers – different as they are – have at least one thing in common: all of them are opposed to the view that simple predicative statements have no ontological import at all. According to the no-ontological-import view, if a simple predicative statement is true, then its truth is a product merely of social convention, and hence a product merely of the allocation of power in the relevant group of speakers, since social convention follows social power. This view – the conviction that social convention, social power are the basic truthmakers, that basic truth itself is a social construction – was present at the beginning of philosophy in the teachings of the Sophists, it unmistakably shines through the voluntarism of mediaeval nominalists, and it reappears recognizably in the philosophy of the later Wittgenstein.1 1   Significantly, Wittgenstein says the following in the Philosophical Investigations (§ 381): “How do I know that this colour is red? – It would be an answer to say: ‘I have learnt English’.”

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Put formally, that is: in the most general way, the described view is this: Social conventionalism in predication-theory: “Φ(α1, …, αN)” is true – this amounts, “ontologically”, to the following: α1, …, αN is purely on the basis of social convention designated by the general term “Φ”. Hence, for the special case of non-relational predications: “Φ(α)” is true – this amounts, “ontologically”, to the following: α is purely on the basis of social convention designated by the general term “Φ”. If this were true, then the following instantiation of this general schema would have to be true, too: “Kate is a woman” is true – this amounts, “ontologically”, to the following: Kate is purely on the basis of social convention designated by the general term “woman”. Now, this does not seem to be true; for, while it is true that Kate is a woman, it is hard to believe that Kate is purely on the basis of social convention designated by the general term “woman”. On the other hand, I can to some extent understand it – psychologically – if social conventionalism in predication-theory is adopted as a weapon against classifications that are, one feels, merely socio-conventionally based but masquerade as hard and objective, ontologically based truths. One may be prompted by the – hardly rational – implicit belief that the charge “Mere convention!”, if advanced against such classifications, can only be truly effective in one’s mouth if one has managed to convince oneself of its being true for all classifications that are generally thought to be true. A fundamental attitude of protest against established social power – mere power, but manifesting itself, the protester believes, in disguise: in simple predicative statements that rather persuasively pretend to express incontrovertible objective facts – may be something that modern feminist philosophers2 have in common with the ancient Sophists. The prime target of the Sophists, however, were not simple predicative statements expressing what is generally regarded to be natural facts, but simple predicative statements expressing what is generally regarded to be axiological facts, statements like “This decision is just”, or “That deed is courageous”, where everyone in the community, on being informed of the relevant circumstances, feels compelled to say, “Yes, that’s true”. Nevertheless, it is total, unrestricted social conventionalism in predication-theory which, very plausibly, underlies the famous homo-mensura-dictum of the Sophist Protagoras, according to which “man is the measure of all things, of the things that are, that they are, and of the things that are not, that they are not”. Applying the homo-mensuradictum to axiological statements, one can very well declare that “This decision is just” and “This deed is courageous” are true (in the relevant circumstances) – “as 2

  For example (and paradigmatically), Judith Butler.

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everybody says they are”; but one will add that all that is implied by these truths is this: the mentioned decision is purely on the basis of social convention designated by the term “just”, and the mentioned deed is purely on the basis of social convention designated by the term “courageous”; for man – in another word: society, in other words: the social group which is in power – is the measure of all things. It was this utterly subversive attitude that Plato, following Socrates, was reacting against. His philosophically most significant move in this was to offer a predication-theory which is not conventionalistic. Showing full awareness of the problem of predication, Plato came up with the fi rst explicitly formulated predication-theory ever. Now, Plato, in the course of his career as a philosopher, underwent substantial development in his thinking about predication, and in fact, in later phases, became critical of earlier positions of his. But this did not hinder that the predication-theory that is imposingly present in the dialogues from the middle of Plato’s career – in the Symposium, the Phaedo, the Republic – had a massive effect on the history of ideas. Very soberly – quite without the poetic splendour of philosophical mythology – that predication-theory can be formulated in the following way (and Plato himself formulates it that way in Parm., 132 d 1–5): Plato’s (classical) predication-theory: “Φ(α)” is true – this amounts, ontologically, to this: α is sufficiently similar to the Φ itself. Applying this theory, we get for example: “This deed is just” is true – this amounts, ontologically, to the following: this deed is sufficiently similar to the just itself. “Kate is beautiful” is true – this amounts, ontologically, to the following: Kate is sufficiently similar to the beautiful itself. “Kate is a woman” is true – this amounts, ontologically, to the following: Kate is sufficiently similar to the woman itself. Even when divested of its poetic splendour (involving an eternal, unchangeable transcendent realm of being itself, which one is likely to imagine awash with “the white light of truth”), Plato’s predication-theory has fascinating features. One of them is, of course, the introduction of an entirely new order of objects: the eidē, as Plato called them, the separate forms, serving as paradeigmata: the just itself, the beautiful itself, the woman itself, and so on. And note, since the Φ itself is certainly sufficiently similar to the Φ itself (no matter which general term Φ we are looking at), Plato’s predication-theory has the following logical consequence: Platonic self-predication: Φ(the Φ itself).

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Thus, the beautiful itself is beautiful, the just itself is just, the human being itself is a human being. Indeed, since the Φ itself is not only sufficiently similar to the Φ itself, but is the only object that is maximally similar to it, in other words: the only object that is identical to it, the logic of Plato’s predication-theory requires that the Φ itself is the unique object that is maximally Φ. Thus, the beautiful itself is the unique object that is maximally beautiful, the just itself is the unique object that is maximally just – and all the other beautiful or just items are beautiful or just only by being more or less remote likenesses of those two eidē. – And, note, according to Plato’s predication-theory, the woman itself is the unique object that is maximally a woman. Unfortunately, this last consequence, if nothing else, constitutes a reductio ad absurdum of Plato’s predication-theory. If there is such a thing as the woman itself, it is certainly not maximally a woman, nor even a woman. Plato himself noted (through the mouth of one of his dramatis personae: Parmenides) that it seems ridiculous to postulate that there are such things as the hair itself, or the dirt itself (cf. Parm., 130 c 7–8). Even if the existence of such eidē were not ridiculous, it would still be incontrovertibly absurd to suppose, as Plato’s predication-theory forces one to suppose, that no other dirt is dirt in the degree that the dirt itself is dirt. This is a much more serious problem for Plato’s predication-theory than the much canvassed so-called Third-Man-Argument, which, in essence, can already be found in Plato’s dialogue Parmenides and might also be called “the Third-LargeObject-Argument” (see Parm. 132 a 1 – b 2). It can be put in the following way: The visible large objects are large in virtue of participating in a first largeness. But this first largeness is another large object. Hence the first-mentioned large objects and this other large object are large in virtue of participating in a second largeness. But, again, this second largeness is another large object. Hence the first-mentioned large objects, the second-mentioned one and this now apparent third large object are large because they participate in a third largeness. But, again, this third largeness is another large object – and so on ad infinitum. This argument tries to settle Plato’s predication-theory – not only for the term “large”, which is merely an example, but for each and every general term that can be truthfully applied in the empirical world – with an infinite number of different eidē without a real difference to them. But the argument fails. According to Plato’s predication-theory, the visible large objects and the first largeness are indeed large, but not in virtue of participating in a second largeness: the visible (or empirical) large objects are large because they are sufficiently similar to the first largeness, and the first largeness is large – for the same reason: it is sufficiently similar to (since it is identical with) the first largeness: the large itself. Thus, there is no need whatsoever to postulate any other largeness than the first largeness.

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Plato’s predication-theory has, however, a very limited scope of plausible applicability. There are some cases where the theory is not obviously inadequate: statements like “Kate is beautiful” and “Kate is just”. But the theory is certainly not adequate for the statement “Kate is a woman”, or even the statement “Kate is a human being” – or, for that matter, for the statements “Kate is hungry” and “Kate is pregnant”, although these latter two statements have adjectives standing in predicative position just as the statements “Kate is beautiful” and “Kate is just” have. Moreover, Plato’s predication-theory is meant for non-relational predications only – and, in fact, I have formulated it only for non-relational predications. If one tries to extend it to relational predications, inadequacy looms large: Suppose the statement “George loves Kate” is true; but does this mean – in the spirit of Plato – that the ordered pair consisting of George in the first place, and of Kate in the second, is sufficiently similar to love itself? Presumably not. However, the mystical implications of this Platonising ontological interpretation of the statement “George loves Kate” will surely not fail to fascinate minds that are receptive to such implications. The same can be said of the mystical implications of the Platonic ontological readings of simple predicative statements that are straightforwardly true and involve the term “good” as predicate, or merely the word “is”. Given acceptance of the classical Platonic predication-theory, it is possible to elevate oneself – as it were – in one leap from rather earthly matters right up to the transcendent Godhead Itself (though only in ontological theory). Especially in Late Antiquity and the Early Middle Ages there were many minds that very much appreciated this asset of the Platonic predication-theory. Inadequate treatment of relational predications is a deficiency that is shared by all predication-theories prior to Frege’s. It is a deficiency not only Plato can be criticised for. Nor is the long persistence of it due to Plato’s influence. As a matter of fact, its persistence is due to the influence of Aristotle. In Plato’s predication-theory, the partners of predication – the ontological subject and the ontological predicate – are external to each other, just as a likeness is external to what it is a likeness of. Moreover, in Plato’s predication-theory, the ontological predicate is the dominant partner in predication. Aristotle, however, adheres to a paradigm of predication that is fundamentally different from Plato’s, a paradigm that is also rather more down to earth than Plato’s. According to Aristotle’s paradigm, the ontological subject is the dominant part ner in predication, and the ontological predicate is, in predication, in some sense encompassed by the ontological subject, comparable to the way in which a part is encompassed by what it is a part of. There are significant indications that Plato himself was moving towards some form of the mereological or, better, quasi-mereological paradigm of predication in the latter part of his philosophical career.3 But, in 3   See Franz von Kutschera,“Parts of Forms. An Essay concerning Plato’s Parmenides”. Logical Analysis and History of Philosophy 1 (1998): 57–74.

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the main, the origin of this paradigm must be associated with Aristotle. Mainly on the basis of the wide-spread reception of Aristotle’s writings since the beginning of the 13th century, the quasi-mereological paradigm of predication became rather influential in Western philosophy. It stayed the standard approach for just about six centuries. Aristotle’s predication-theory – which means: the predicationtheory which, given the data from Aristotle’s writings, is the best summative reconstruction of his opinions on predication – is a particular version of the quasi-mereological paradigm (which, indeed, has many versions); it can be put in the following way: Aristotle’s predication-theory / The quasi-mereological predication-theory with particular forms: “Φ(α)” is true – this amounts, ontologically, to the following: the α-particular form of being Φ is in α. Thus we have for example: “Socrates is wise” is true – this amounts, ontologically, to the following: the Socrates-particular form of being wise is in Socrates. “Kate is beautiful” is true – this amounts, ontologically, to the following: the Kate-particular form of being beautiful is in Kate. “Kate is a woman” is true – this amounts, ontologically, to the following: the Kate-particular form of being a woman is in Kate. It should be noted that a special case of the situation that the α-particular form of being Φ is in α is this: the α-particular form of being Φ is identical to α; this is the traditional Aristotelian ontological analysis of, so-called, substantial predication (as in “George is a man”); whereas if the α-particular form of being Φ is in α, but is not identical to α, we have before us the traditional Aristotelian ontological analysis of, so-called, non-substantial predication (as in “George is sitting”). There are two plausible equivalents for the phrase “the α-particular form of being Φ is in α”, each of which, if substituted for that phrase in Aristotle’s predication-theory, yields a predication-theory that is plausibly equivalent to Aristotle’s predication-theory: (1) Plausibly, “the α-particular form of being Φ exists” is true if, and only if, the α-particular form of being Φ is in α. (2) Plausibly, “the form of being Φ is in α” is true if, and only if, the α-particular form of being Φ is in α. But in fact Aristotle denies that The quasi-mereological predication-theory with universal forms: “Φ(α)” is true – this amounts, ontologically, to the following: the form of being Φ is in α, PREDICATION • 235

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is true. In the Categories (Cat. 1 a 20–23; see also Cat. 3 a 11–13), he declares that Man – in other words: the form of being a human being – is, on the one hand, (truthfully) said of a subject, namely, of a particular human being, but that it is, on the other hand, not in any subject. This can only be taken to imply that, according to Aristotle, the statement “George is a human being” is true, although the form of being a human being is not in George, and that therefore the quasimereological predication-theory with universal forms is not true (because it is counter-instantiated). Indeed, the quasi-mereological predication-theory with universal forms can seem to be rather non-equivalent to the quasi-mereological predication-theory with particular forms, that is: to Aristotle’s predication-theory. After all, the former theory involves universal forms, the latter only particular ones. But scepticism regarding universal forms – or briefly, universals – was certainly not Aristotle’s problem with the former theory: he accepted universal forms at least as secondary entities, whereas he did not accept Plato’s eidē, that is, Plato’s separate forms.4 His problem was that some universal forms are said of some subjects, but are not in any subject because they can exist apart from any subject they may tentatively be supposed to be in5 – because, as Aristotle believed at one point, they are substances: universal – or second – substances (in contrast to particular – or first – substances).6 However, in several places of the Metaphysics, we also find Aristotle denying that universals – any universals – are substances.7 Now, if no universal were a substance for Aristotle after all, then it would seem most plausible to assume that, for Aristotle, any universal is said (truthfully) of a subject8 after all on the 4   For an explicit statement of Aristotle’s acceptance of universals in contrast to Plato’s separate forms, see An. Post. 77 a 5–9; that passage also contains Aristotle’s defi nition of universal, which is this: one which can be truthfully said of many. 5   See Cat. 1 a 24–25, where Aristotle defines – or rather: gives a partial explication of – being in a subject: “In a subject I call that which exists in something, but not as a [literal] part, and cannot be separate from that in which it is.” [Translation U. M.] Note that the “cannot be separate from” is not meant by Aristotle to express a symmetrical relationship: “x cannot be separate from y” does not entail, for Aristotle, “y cannot be separate from x”. For he understands “x cannot be separate from y” in the sense of “x cannot exist apart from y”, and “y cannot be separate from x” in the sense of “y cannot exist apart from x”, and of course it can be – and sometimes is – the case that x cannot exist apart from y, while y can very well exist apart from x. 6   That this is the correct diagnosis is strongly suggested by Cat. 3 a 7–15. Regarding Aristotle’s asserting separability – the ability to exist apart from any supposed subject – of substances, see Met. VII, 1029 a 27–28. But note that in the same short passage Aristotle also asserts particularity of substances. 7   See Met. III, 1003 a 8–10; Met. VII, 1038 b 8–12, 34–37, 1041 a 3; Met. X 1053 b 16–20; Met. XIII 1087 a 2. 8   Note that for Aristotle any universal is said truthfully of some subject (because it is by definition truthfully said of many subjects; cf. note 4).

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necessary and sufficient basis of its being in that subject (though in it only in a derivative, analogical sense) – Man and Animal being no exceptions to this rule. In any case, vacillations in Aristotle’s writings are bound to have contributed, in the centuries after Aristotle and especially in the Middle Ages, to the waning of his distinction between universals that are not substances and are in some subject, and universals that are substances and are not in any subject. This distinction – a significant residue of Platonism in Aristotle – became less and less important. The distinction finally dissolved – in favour of all universals being just as much in some subject as all universals are said of some subject, and in favour of all universals being precisely in the subjects of which they are said. A striking documentation of the endpoint of this development can be found in the commentary of Thomas Aquinas on the Posterior Analytics of Aristotle. There, Thomas simply connects a universal’s being (truthfully) predicated of a subject, being said of a subject, with its being in the subject of which it is predicated; no distinction is made in his characterisation of predication between substantial and non-substantial universals. Interpreting Aristotle, Thomas says (In Posteriorum Analyticorum I, lect. 11, n. 6): Primo, dicit [Philosophus: Aristotle] quod tunc est universale praedicatum, cum [cum iterativum] non solum in quolibet est de quo praedicatur, sed et primo demonstratur inesse ei, de quo praedicatur. Firstly, he [the Philosopher] says that a universal is a predicate [of something: α] whenever it is not only in everything of which it is predicated, but is first demonstrated to be in that [i.e., the something: α] of which it is predicated.

From this quotation, it is apparent that Thomas accepted – under the presumed authority of Aristotle – the quasi-mereological predication-theory with universal forms, because the quotation can, without much effort, be made to support the following reasoning that yields just that predication-theory: 1. The (universal) form of being Φ is (demonstrated to be) in α. 2. Hence according to Thomas [“tunc est universale praedicatum, cum … demonstratur inesse ei, de quo praedicatur”]: the form of being Φ is (truthfully) predicated (said) of α. 3. And hence: “Φ(α)” is true. 1'. “Φ(α)” is true. 2'. Hence: the form of being Φ is (truthfully) predicated (said) of α. 3'. Hence according to Thomas [“universale… in quolibet est de quo praedicatur”]: the form of being Φ is in α. Now, as long as one assumes what Aristotle himself at some time – for some cases – did not assume, namely, PREDICATION • 237

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that “the form of being Φ is in α” is true if, and only if, the α-particular form of being Φ is in α [cf. the plausible assumption (2) above], the quasi-mereological predication-theory with universal forms will be found to be equivalent to the quasi-mereological predication-theory with particular forms. This equivalence and, in the first place, the assumption on which it is based seem plausible without argument. One can also rather plausibly argue for them in the following way: Asserting of a universal form that it is in a subject is merely a non-literal, analogical way of speaking. Such an assertion cannot be literally true, because the universal form is not a particular, whereas the subject is one. Only a particular can be literally in a particular. What is literally true in those cases where a universal form is truthfully but analogically said to be in a subject can only be this: the particularisation relative to the subject of the universal form is – literally – in the subject. Thomas and his Aristotelian-minded non-nominalist contemporaries and successors – and, for that matter, Husserl, who much later in the history of ideas once again followed Aristotelian lines in formal ontology – would have found this argument entirely convincing.9 However, the history of ideas after the Middle Ages took a course that was not in keeping with the argument’s Aristotelian spirit. After the Middle Ages one rather tended to forget the analogical equivalence – Aristotelian in spirit – of the quasi-mereological predication-theory with universal forms to the quasi-mereological predication-theory with particular forms, an equivalence based on the assumption that the phrase “the form of being Φ is in α” is merely an analogical façon de parler (though no denial of universal forms is involved in that assumption) and that the phrase’s ultimate truth-relevant import – what it really says – just amounts to what is expressed by the phrase “the α-particular form of 9   Regarding Husserl, the following passage from his lecture Phenomenological Psychology [Phänomenologische Psychologie] of 1925 rather strongly suggests his being ready to uphold the two classical quasi-mereological predication-theories simultaneously, the universalistic one standing, as it were, on top of the particularistic one: “One must not believe that the identity of the eidos [which for Husserl merely amounts to the universal] is just an exaggerating way of speaking. … [It is not merely the case that] every object has its in-being moment, for example, of redness, and [that] each of the many objects, all of which are red, has its individually own moment, but in sameness. Rather, one must see that the sameness is only a correlate of the identity of something that is general and in common [eines Allgemeinen], that can, in truth, be intuited as one and the same out of – and as a ‘counterpart’ of – what is individual. This identical something ‘particularises’ itself in many ways and can be thought, in an open infinity, arbitrarily particularised. All of these particularisations are, in virtue of their relationship to what is identical, related to each other, and are accordingly called ‘each the same as the other’. In an extended, non-literal way of speaking, the concrete objects themselves are, in virtue of having eidetic particularisations in them, each called the same as the other ‘with respect to the red’, and are themselves, in a non-literal sense, particularisations of the something that is general and in common [des Allgemeinen].” – Phän. Psych., 80; translation and italics U. M.

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being Φ is in α”, or by the equivalent phrase “a particularisation of the form of being Φ is in α” – these phrases being taken to express the original Aristotelian ontological basis for predication.10 After the Middle Ages, the quasi-mereological predication theory with universal forms started a life of its own. During the Renaissance, due to the influx of ancient Platonic texts to Italy af ter the fall of Constantinople in 1453, there was a significant resurgence of Platonism, broadly conceived. This led to a very strong reaction against the Aristotelianism of the Schools and – combining with forces that emphasised the importance of the individual human being, of the individual human mind – brought about the philosophical (so-called) Enlightenment of the 17th century. In the field of ontology, a significant consequence of these revolutions was the following: universals turned into absolute concepts for those thinkers who, on the one hand, did not deny universals, like the nominalists had always done, and who on the other hand, Platonically and humanistically inspired, did not want to continue along the old mediaeval Aristotelian lines. For those thinkers, universals took on an absoluteness that traditional Aristotelians had not conceded to universals; it faded into the background that universals were supposed to be anthropogenic abstractions from particulars. At the same time, those thinkers emphasised the conceptualness of universals more strongly than it had ever been: the affinity of universals to mind – which, given the absoluteness newly accorded to universals, could of course only be their affinity to a transcendent supermind. Mind-affinity had to some extent already been a characteristic of Plato’s eidē. But it was Plotinus who had, in late Antiquity, explicitly conceptualised the eidē by 10   See R. E. Allen, “Substance and Predication in Aristotle’s Categories”, in Exegesis and Argument. Studies in Greek Philosophy Presented to Gregory Vlastos, ed. E. N. Lee et al. (Assen, Netherlands: van Gorcum, 1973), 367: “If Socrates is just, there is, according to the Categories, an instance of justice in him, an instance which is individual, numerically one, and inseparable from Socrates in the sense that it cannot exist apart from him.” In other words: If Socrates is just, there is a particularisation of the form of being just (“an individual instance of justice”) in him – and, clearly, that particularisation is the Socrates-particular form of being just. In general we have: (a) If a particularisation of the form of being Φ is in α, then the α-particular form of being Φ is in α (because every particularisation of the form of being Φ that is in α is identical with the α-particular form of being Φ). And we also have the converse: (b) If the α-particular form of being Φ is in α, then a particularisation of the form of being Φ is in α (because the α-particular form of being Φ is, if in α, a particularisation of the form of being Φ). One can derive both (a) and (b) on the basis of the following definition: the α-particular form of being Φ =Def the particularisation of the form of being Φ that is in α – presupposing, for all cases of α and Φ, that there is no more than one particularisation of the form of being Φ that is in α and that there is a particularisation of the form of being Φ that is in α if the particularisation of the form of being Φ that is in α is in α. One might object that there can easily be more than one particularisation of the form of being red (for example) in a subject: if a table has a red area here and a red area there. But one can stipulate that the phrase “[there is] a particularisation of the form of being Φ [that] is in α” is understood to refer, if true, to the (relatively to α) entire particularisation of the form of being Φ in α.

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making them denizens of the nous, while maintaining their absoluteness, their ontological independence from particulars. It is not unlikely that the influence of Plotinus (via Marsilio Ficino and Pico della Mirandola) helped bring about the described post-mediaeval developments.11 Remarkably, these developments did not necessarily endanger the acceptance of the quasi-mereological paradigm, that is, of precisely that paradigm of predication that Aristotle, setting himself off from Plato, had inaugurated with his particular version of a quasi-mereological predication-theory. The predicationtheory of Leibniz can serve as a striking example of a syncretistic result of the post-mediaeval developments I just sketched. Leibniz was an Enlightened follower of the quasi-mereological paradigm and, in fact, had more sympathies with traditional Aristotelianism than most of the new intellectuals of his time. He did subscribe to the Scholastic slogan of praedicatum inest subjecto, but he did so in a new manner, reflecting the revolution of ideas which had come about. In Section 8 of the Discours de Métaphysique he very clearly formulates Leibniz’s predication-theory: “Φ(α)” is true – this amounts, ontologically, to the following: the Φ-concept is in the α-concept. Obviously, the predication-making relation of in-being (inesse) in Leibniz’s predication-theory is neither of the two relations of in-being that are invoked in the two previously canvassed quasi-mereological predication-theories. In fact, it is not a relation of in-being between the predicate and the subject at all: it is a relation between the predicate-concept and the subject-concept. This latter relation of inbeing, between concepts, was already at the time of Leibniz not a newly discovered one; it had already been familiar for a long time, and, as a matter of fact, it had not been clearly distinguished from the other two relations of in-being I have already considered.12 The common form of the statements “homo est animal” and “Socrates est homo” suggests that they both are simple predicative statements, and that therefore the relation of in-being invoked under a quasi-mereological theory of predication for analysing “Socrates est homo” must be the same as the relation of in-being invoked for analysing “homo est animal”. But in fact “homo est animal” is not a simple predicative statement – it is a statement of essential subsumption. It is true that “homo est animal” is true in virtue of the animalconcept being in the homo-concept (or in other words: in virtue of the extension 11   From the 17th to the 19 th century, the idea of the mind-affi nity, the conceptualness of universals remained present, but, progressively, it took on decidedly human proportions; for the initially co-present Platonic/Plotinic idea of the absoluteness of universals progressively disappeared – until it triumphantly re-appeared in the work of Frege. 12   For the history of in-being between concepts and its relationship to predicative in-being, see Uwe Meixner, “Negative Theology, Coincidentia Oppositorum, and Boolean Algebra”, Logical Analysis and History of Philosophy 1 (1998): 75–89.

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of the homo-concept being essentially subsumed under the extension of the animalconcept). But it does not follow from this that the simple predicative statement “Socrates est homo” is, analogously, true in virtue of the homo-concept being in the Socrates-concept – because “homo est animal” cannot serve as a paradigm for “Socrates est homo”, since “homo est animal” is, contrary to appearances, not a simple predicative statement, but a statement that is different in meaning from “Socrates est homo” even in the very category of meaning. Thus, Leibniz’s predication-theory would seem to rest on a simple confusion: the confusion of the in-being of a universal in a particular with the in-being of one concept in another – if one weren’t reluctant to settle the great man with such a big blunder. And, indeed, there is a more favourable perspective on Leibniz’s predication-theory than that: Given that the quasi-mereological predication-theory with universal forms emancipated itself in post-mediaeval times along the lines I have described (which emphasise both the absoluteness and the conceptualness of universals) from the quasi-mereological predication-theory with particular forms, the problem of how a universal predicate could be in a particular subject needed a new solution. In this situation, making use of the relation of inbeing between concepts must have seemed the only way to go. It was, therefore, not unreasonable – relatively speaking – of Leibniz to interpret “praedicatum inest subjecto” as “the predicate-concept is in the subject-concept”. What else could it mean? Leibniz dauntlessly accepted the strange consequences of his predicationtheory: that Alexander once defeats Darius (cf. Discours de Métaphysique 8) – this is so because the concept of once defeating Darius is in the concept of Alexander; that Caesar once crosses the Rubicon – this is so because the concept of once crossing the Rubicon is in the concept of Caesar (cf. Discours de Métaphysique 13). But if this is true, then these historical truths about Caesar and Alexander, which we regard as contingent, are not contingent at all, but necessary truths in the strictest sense. We human beings learn only a posteriori and never completely – and hence with an almost irresistible appearance of contingency – what is, for example, the content of the concept of Caesar (a consistent concept maximally rich in content, a notio completa). But, according to Leibniz, that concept cannot be otherwise for Caesar than it is (would it be otherwise, then it wouldn’t be the concept of Caesar), and God, according to Leibniz, knows it a priori and completely. Because Caesar once crosses the Rubicon, the concept of once crossing the Rubicon is contained in that concept of Caesar according to Leibniz’s predication-theory – we just saw –, hence contained in it with strict necessity, since the relation of in-being between concepts is a relation that holds with strict necessity whenever it holds at all.13 And hence it follows, again according to Leibniz’s predication-theory, that 13   For concluding that the concept of once crossing the Rubicon is necessarily contained in the concept of Caesar, the reason given is, in fact, not in itself sufficient: “the concept

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it is necessary in the strictest sense that Caesar once crosses the Rubicon. Leibniz might have noticed that we can learn to know the concept of Caesar a posteriori (which is the only way for us) only by coming to believe in the truth of simple predicative statements about Caesar – and that for our coming to believe in the truth of these statements the concept of Caesar is, in fact, entirely irrelevant. This might have given pause to Leibniz. Like all predication-theories prior to Frege’s, Leibniz’s predication-theory is not adequate for relational predications, although, because it deals in concepts, it is not as inadequate as other theories under the quasi-mereological paradigm. Notice that relational predications are implicit in the very examples Leibniz chooses: Alexander once defeating Darius, Caesar once crossing the Rubicon. It is possible to assimilate relational predications to non-relational ones, along the lines of “Caesar once crosses the Rubicon” being read as “Caesar is a Rubicon-crosser”. And while it is surely absurd that an original-Aristotelian universal form of being a Rubicon-crosser is in Caesar – because it is absurd that an original-Aristotelian Caesar-particular form of being a Rubicon-crosser is in Caesar (Caesar carrying that thing around with him, and with it the Rubicon, it would seem) –, it is not absurd that the concept of being a Rubicon-crosser is in the concept of Caesar. But we have seen that, still, there are reasons for not accepting this as the basis that is appropriate for predicating being a Rubicon-crosser of Caesar. A time came – by and large with the 19th century – when the anti-relationalist, substantialist conception of the world began to loosen its grip on the human mind, and concatenations of non-privileged, non-dominant beings (such concatenations may be called “states of affairs”) instead of privileged, dominant gravitational centres of being (such centres may be called “substances”) began to capture the ontological imagination. But it took a philosopher-mathematician who had less respect – and probably less knowledge – of the philosophical tradition than Leibniz for progress to be made with regard to relational predications. Frege finally abandoned the quasi-mereological paradigm, and came up with something entirely new. There is no precedent or analogue in the antecedent history of ideas for Frege’s predication-theory: “Φ(α1, …, αN)” is true – this amounts, ontologically, to the following: the functional value of the Φ-concept for α1, …, αN is the true. of Caesar” and “the concept of once crossing the Rubicon” must also each refer to one and the same (respective) concept in every possible world (compare the situation regarding the necessity or contingency of true identity statements). Leibniz certainly assumed the rigidity of the mentioned designators; but in the case of “the concept of Caesar” rigidity is, as a matter of fact, doubtful (the reason being this: if the concept of Caesar is the sum of all concepts that apply to Caesar, then that sum seems to be different in different possible worlds, since, apparently, in different possible worlds different concepts apply to Caesar).

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The intuitive oddness of this predication-theory decreases considerably if one takes into account that Frege conceived, in extension of the mathematical concept of a function, of concepts as functions whose functional values are the true or the false, and of functions, employing a chemical metaphor, as entities that are in themselves unsaturated, but that are saturated by their functional arguments, thus producing their functional values (see Frege’s 1891 paper “Funktion und Begriff ”). Therefore, instead of saying that the functional value of the Φ-concept for α1, …, αN is the true, one can, following Frege, just as well say: the saturation of the Φ-concept by α1, …, αN is the true. This is still somewhat odd, the main reason for this impression being Frege’s assumption of a truth-object, the true, corresponding to which he has an even odder falsity-object, the false. But notice the flexibility and ease Frege’s predicationtheory displays in the treatment of relational predications. What is the ontological basis for the fact that the statement “George loves Kate” is true whereas “Kate loves George” is not true? Why, the saturation of the concept of love by the ordered pair that has George first and Kate second is the true, whereas the saturation of that same concept by the inversely ordered pair is the false. There is nothing wrong with this – except, of course, that it does not make contact with what it actually is that we base our judgements on when we assert that George loves Kate, and that Kate does not love George. Frege’s predicationtheory is a mere logical rationalisation of predication, not an account of predication that tries to honour the actual ontological foundation of our actual human practice of making simple predicative statements intended to be true – something which Aristotle’s predication-theory, and, indeed, Plato’s, did try to do, though not with entire success. As far as a mere logical rationalisation of predication goes, Frege’s theory is true and adequate, just as true and adequate as its nearest equivalent not employing the notion of function is, which became a standardly used technical tool in 20th-century model-theoretic logical semantics: The set-theoretical theory of predication: “Φ(α1, …, αN)” is true – this amounts, ontologically, to the following: α1, …, αN is an element of the Φ-set.14 14   Frege’s concepts (Begriffe) are extensional concepts (that is: they are identical if, and only if, they have the same extension); they are, therefore, one-to-one correlates of sets. Extensionality is not the only feature of Fregean concepts that fits ill with the normal concept of a concept: another is lack of mind-affinity (which is in part a consequence of their extensionality). Thus: Frege’s use of the word “concept” (“Begriff ”) – for the items that are really intended by him – still bears witness to the (above-described) emphasis on the conceptualness of universals, after the Middle Ages, but it does so only on the linguistic surface.

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But one certainly does not – not explicitly, and not implicitly – apply the set-theoretical theory of predication, or Frege’s theory, when determining, for example, the truth of the statement “George loves Kate”, nor would it be a good idea to apply these theories in the effort to explicate the ontological basis for the truth of “George loves Kate”. The same can be said of an account that – restricted to non-relational predications – was in use as a purely logical tool throughout the entire Aristotelian tradition, which I therefore call The minimal Aristotelian theory of predication: “Φ(α1, …, αN)” is true – this amounts, “ontologically”, to the following: the (monadic or relational) Φ-universal is said (truthfully) of α1, …, αN. The three last-mentioned theories (beginning with Frege’s), though true, have no belief-foundational and no truth-explanatory value. Though they do introduce onto-theoretical entities in order to account for predication – concepts, the truthobject, sets, universals – they, in essence, just reformulate the normal expression of predication in technical logico-ontological terms; though they have some ontological content, they, in essence, just logically rationalise predication.15 They do so in keeping with the truth (though those who do not believe in universals or concepts or sets would deny this). But truth is not enough – as can easily be seen by a glance at what may be dubbed The “redundancy theory” of predication: “Φ(α1, …, αN)” is true – this amounts, “ontologically”, to this: Φ(α1, …, αN). Or by a glance at the so-called (historically not unimportant and, like the immediately preceding theory, nominalism-compatible) “Identity theory” of predication: “Φ(α)” is true – this amounts, “ontologically”, to this: “Φ” refers (as general term) to the same object that “α” refers to (as singular term). These theories are obviously true (true for simple predicative statements as specified at the beginning of this essay, the “identity theory” being additionally restricted in its range to the non-relational ones among those statements); but just as obviously they are not helpful at all for belief-foundation or truth-explanation. But here, finally, follows a theory of predication which, like Frege’s, falls under the functional paradigm of predication. It is recognizably a modification of Frege’s theory and preserves the great advantage of that theory: the capturing of   If one leaves out Leibniz’s assumption of the rigidity of the designator “the concept of α” (for example, “the concept of Caesar”; see footnote 13), then Leibniz’s predication-theory turns out to be adequate also with respect to our normal modal expectations. But what it then offers is merely a true logical rationalisation of non-relational predication; it has no belief-foundational or truth-explanatory value. 15

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relational predications; but it is, in contrast to Frege’s predication-theory, helpful for belief-foundation and truth-explanation. It is the theory I myself favour, The fact-referring functional predication-theory: “Φ(α1, …, αN)” is true – this amounts, ontologically, to the following: the completion of the Φ-universal by α1, …, αN is a fact, that is: an obtaining state of affairs. Universals that need at least in some cases two entities for completion are called “relations”, universals that always need only one entity for completion are called “properties”. Thus, we have: “Kate is a woman” is true – this amounts, ontologically, to the following: the completion of the woman-property (i.e., the property of being a woman) by Kate is a fact, or in other words: Kate has the property of being a woman. “George loves Kate” is true – this amounts, ontologically, to the following: the completion of the love-relation (i.e., the relation of love) by George, Kate is a fact, or in other words: George stands in the relation of love to Kate. Facts – the states of affairs that obtain, or are actualised – are sometimes, in their factuality, a product purely of social conventions; but normally they are not. In any case, facts that are merely made up of universals and particulars – in a manner that I have here merely hinted at, using the metaphor of completion16 – are the primary objects of human objective cognition, not particulars as such and not universals as such. To particulars and universals we come in cognition only via states of affairs that involve them, and foremost via facts that involve them. Because facts that are merely made up of universals and particulars are the primary objects of human objective cognition, the fact-referring functional predication-theory is helpful for founding belief in the truth, and for ontologically explaining the truth, of simple predicative statements. We apply this theory implicitly when we judge that a simple predicative statement is true, and we do well to apply this theory explicitly when we seek to explain, from the ontological point of view, why – that is, on what ontological basis – a simple predicative statement is true.

16   The full theory is presented non-metaphorically in Uwe Meixner, The Theory of Ontic Modalities (Heusenstamm bei Frankfurt a. M.: Ontos, 2006).

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BIBLIOGRAPHY Allen, R. E. “Substance and Predication in Aristotle’s Categories”. In Exegesis and Argument. Studies in Greek Philosophy Presented to Gregory Vlastos, edited by. E. N. Lee et al., 362–373. Assen, Netherlands: van Gorcum, 1973. Aristotle. Kategorien. Hermeneutik. Vol. 2 of Organon. Edited by H.-G. Zekl. Darmstadt: Wissenschaftliche Buchgesellschaft, 1998. ― Erste Analytik. Zweite Analytik. Vol. 3–4 of Organon. Edited by H.-G. Zekl. Darmstadt: Wissenschaftliche Buchgesellschaft, 1998). ― Aristoteles’ Metaphysik. Bücher I(A) – VI(E). Edited by H. Seidl. Hamburg: Meiner, 1989. ― Aristoteles’ Metaphysik. Bücher VII(Z) – XIV(N). Edited by H. Seidl. Hamburg: Meiner, 1991. Butler, Judith. Gender Trouble. Feminism and the Subversion of Identity. New York: Routledge, 1990. Frege, Gottlob. “Funktion und Begriff ”. In Funktion, Begriff, Bedeutung, edited by G. Patzig, 17–39. Göttingen: Vandenhoeck & Ruprecht, 1975. Husserl, Edmund. Phänomenologische Psychologie. Edited by D. Lohmar. Hamburg: Meiner, 2003. Kutschera, Franz von. “Parts of Forms. An Essay concerning Plato’s Parmenides”. Logical Analysis and History of Philosophy 1 (1998): 57–74. Leibniz, Gottfried Wilhelm. “Discours de Métaphysique”. In Gottfried Wilhelm Leibniz, Opuscules Métaphysiques / Kleine Schriften zur Metaphysik, edited by H. H. Holz, 49–165. Darmstadt: Wissenschaftliche Buchgesellschaft, 1985. Meixner, Uwe. “Negative Theology, Coincidentia Oppositorum, and Boolean Algebra”. Logical Analysis and History of Philosophy 1 (1998): 75–89. ― The Theory of Ontic Modalities. Heusenstamm bei Frankfurt a. M.: Ontos, 2006. Plato. Phaidros. Parmenides. Epistolai. Vol. 5 of Werke in 8 Bänden. Edited by G.  Eigler. Wissenschaftliche Buchgesellschaft: Darmstadt, 1990. Thomas Aquinas. In Aristotelis Libros Peri Hermeneias et Posteriorum Analyticorum Expositio. Cum textu ex recensione Leonina. Augusta Taurinorum: Marietti, 1964. Wittgenstein, Ludwig. Philosophical Investigations. New York: Macmillan, 1953.

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TOWARDS A THOMISTIC THEORY OF PREDICATION Stanislav Sousedík ABSTRACT Thomas Aquinas formulates a theory of predication, according to which a predicative statement expresses identity of some sort of the subject and the predicate. Such a theory can be dubbed an “identity theory of predication”. The author of the present paper aims to to work out a modernised version of this theory, on the basis of the interpretation of Aquinas’s legacy provided by some important 17th century Thomists. In his paper he demonstrates his approach on the case of singular essential statement. The paper is divided in two parts. In the first part the author examines, how we actually predicate essential properties to empirical individuals in natural language. In the other part he propounds a theory aiming to explain the facts observed in the first part by means of the assumption of a peculiar intelligible structure in empirical individuals.

1. INTRODUCTION The principal idea of the Thomistic theory of predication was formulated by Thomas Aquinas in his Summa theologiae. There he claims that a positive predicative sentence is signum identitatis eorum, quae componuntur.1 A simple predicative sentence is compounded of a subject and a predicate. The composition of a sentence is according to Aquinas the composition of the intellect. Composition of the intellect differs from the composition of things; for in the latter the things are diverse, whereas the composition of the intellect is a sign of the identity of the components. So it seems that Thomas intended to say that what we mean by the subject and the predicate of such a sentence refers to one and the same thing. His theory can be thus called the identity theory of predication. The identity theory proposed by Thomas certainly gives very incomplete semantics of propositions, since Thomas and his followers were concerned mostly with predicative (atomic) propositions only, leaving the problems of so called molecular propositions aside. This fact may be one of the reasons why this identity theory is nowadays not presented besides other contemporary predication theories. Yet the importance of the identity theory for the revival of metaphysics seems to be principal.

1

  Summa theologiae I, q. 85, a. 5, ad 3.

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The aim of my paper is to clarify the meaning of the identity theory by means of a quite simple but important example, viz. the case of a positive, singular, predicative proposition with a proper name as the subject and a common term as its predicate. In that type of propositions it is possible to distinguish two ways of how a predicate can be attributed to a subject: The first may be called essential predication (e.g. Socrates is a man), the other one accidental predication (e.g. Peter is ill). For the sake of brevity I will consider here the essential predication only, viz. sentences of the type Socrates is a man.2 In the first part of my paper I will give some observations on the meaning of such kind of propositions in natural language. These observations will raise some questions that cannot be answered by observation of natural language itself. They can be only answered by means of a theory. In the second part I shall argue that the identity theory of predication proposed by some later pupils of Aquinas – representatives of the so called Second Scholasticism such as Thomas de Vio (Cajetanus, †1534),3 Ioannes a Sancto Thoma (= João Poinsot, †1644),4 Ludovicus Babenstuber (†1726)5 (and last but not least their late follower Josephus Gredt, †1940)6 – provides an acceptable starting point for such a theory. My present aim nevertheless is not to offer a historical reconstruction of the teaching of these authors, but rather to contribute to some future version of an acceptable Thomistic theory of predication on the basis of their doctrines. 2. OBSERVATIONS 2.1 First observation Let us begin by considering propositions of the type Socrates is a man! It seems to be clear that if such singular predicative proposition concerning an empirical individual is true, there must exist something in the world that is a necessary condition for its being true. Thus, e.g., if it is true that Peter is a man, then (1) Peter must exist, and (2) there must be something observable in Peter’s body (e.g. he laughs, he has a certain DNA pattern etc.), that qualifies him (i.e. his substance) 2   The problems connected with the Thomistic conception of accidental predication are discussed more widely in my book: Identitní teorie predikace [= The Identity Theory of Predication] (Praha: OIKOYMENH, 2006). 3   Cajetanus, Commentarius in opusculum S. Thomae Aquinatis De ente et essentia, cap. 4. (there are many old and modern editions of this work). 4   Ioannes a Sancto Thoma, Cursus Philosophicus Thomisticus, vol. 1, Logica, pars 2, q. 1–5 (first edition Romae, 1636; modern critical edition by B. Reiser, Turin: Marietti, 1948 [this edition is cited here, henceforward Reiser]), 251–369. 5   Ludovicus Babenstuber, Philosophia Thomistica Salisburgensis (Augustae Vindelicorum, 1706), tomus 1: 139–185. 6   Josephus Gredt, Elementa Philosophiae Aristotelico-Thomisticae, § 114–139, 13th ed. (Barcinonae, Friburgi Brisgoviae, Romae, Neo-Eboraci, 1961), vol. 1: 108–133.

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as human. So we have to distinguish: the empirical feature of Peter (the laughter, the DNA pattern etc.) and a trait of his substance hinted at by that feature (in our example: Peter’s humanity).7 It generally holds that if A is a necessary condition of B, then B can be considered as a sign of A. Consequently we can take a proposition as a whole for a compound sign for something that is a condition of its being true, i.e. for the „truthmaker“. The truthmaker (= the “verificativum” of the scholastics) consists – in the case of essential predication – of what was mentioned in points (1) and (2), i.e. of an individual substance with a trait hinted at by a certain feature of it. 2.2 Second observation If a singular proposition is a compound sign, the question arises, how its parts (viz. subject and predicate) contribute to what is signified by it as a whole. The answer seems to be clear in the case of the subject term, Peter in our example. Such a term picks out a certain individual we want to speak about. I hold that a proper name refers directly to the bearer of the name without a mediation of some “sense”. I have two reasons for my opinion: Firstly, I find the causal theory of S. Kripke convincing. The second reason is that a very similar theory was also held by many old Thomists (scholars such as Ioannes a S. Thoma8). That follows from the fact that in the case of proper names they didn’t admit any so called “suppositio simplex”. So I suppose together with them that we refer directly to an individual (person or thing) by a proper name. Let us consider the predicate, is a man in our case, now. The task of the predicate is to “characterise” the individual referred to by the subject term in some way. To characterise an individual means in general to direct the attention of the hearer to some trait which the thing characterised has. If this is true, an important question arises: What does it mean, when we say that an individual has some trait?9 In other words: what is the relation between an individual substance and its trait? 2.3 Third observation It is well known, that we use proper names not only in affirmative, but also in vocative sentences. We say not only e.g. 7   So by “feature” I mean what the scholastic tradition calls “proprium”. According to Thomists, we do not have direct knowledge of substance, we are able to get only an indirect one, by means of “propria”. Proprium is not a concrete accident, but the fourth “praedicabile”, that means a concept of a certain concrete accident. 8   Cursus Philosophicus Thomisticus, vol. 1, Logica, pars 1, q. 6, a. 3 (Reiser, 176). 9   A different question would be: What does it mean, when we say that an individual has some feature? But this question does not pertain to the essenial, but to the accidental way of predication, so I leave it aside here.

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(1) Peter is a man, but also (2) Peter, come here! Now it seems clear, that a proper name used in an affirmative sentence refers to an individual who is identical with what is addressed by using the same proper names in vocative sentence. Let us notice now that instead of proper names, we can also use common terms in addressing individuals. A teacher can say e.g.: (3) Peter, don’t speak without permission! but he can express the same thought by saying (4) Man, don’t speak without permission! Now, if the proper name Peter used in (3) refers to a certain individual (viz. Peter), the common term man used in (4) seems to refer (in the right situation) to the same individual. So we can see that not only proper, but also common names refer to individuals in natural language. So if common terms, used as predicates, direct our attention to some traits of the individual referred to by the subject term, it means consequently that these traits must be identical with that individual in some sense.10 2.4 Fourth observation The traits of an individual we refer to by the predicate cannot be identical with the individual in the usual way of speaking. It is clear that by Peter is a man we provide some information, but no information is offered by Peter is Peter. So the “is” in the first sentence must express some other type of identity than in the other. Nevertheless, it seems that both cases of “is” have something in common.11 If this is correct we have to abandon (what is after Frege generally accepted) that there is a principal difference between “is” as a sign of identity and “is” as a sign of predication. In both cases “is” seems to express some identity relation: in one case (Peter is Peter) we shall speak about “strong” identity, in the other (Peter is man) about “weak” one.   An interesting fact follows from the third observation: The grammatical predicate e.g. “is a man” does not seem to be an unanalysable whole, but a composite sign consisting of what is traditionally called “copula” and the predicate in the strict sense of the word, “man” in our example. 11   It is generally accepted that “Peter is Peter” expresses identity. But from 2.3 it follows that “Peter is a man” expresses some kind of identity, too. So it seems there cannot be a principal difference between the “is” occuring in the first and “is” in the second sentence. 10

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2.5 Fifth observation (a) We can predicate more than one common term of an individual, we say e.g. not only Peter is a man but also Peter is an animal, Peter is a living being, Peter is a substance etc. (b) We can often predicate one and the same common term of more than one individual. 2.6 Sixth observation Every empirical individual and every part or trait of it is particular. The individual is “all through” particular. 2.7 Seventh observation No real part of an individual, which is actually distinguished from the whole, can be predicated of it. So every proposition like “Peter is his left foot” is logically false. 2.8 The problem The task is now to answer the question, what the “weak identity” means and by means of it to show, how the six observations mentioned above build a coherent whole. To solve this problem, it doesn’t suffice what we have done so far, viz. to observe the way we understand and use natural language. It is necessary to explain all that by a certain theory. 3. THE THEORY 3.1 The distinctions According to the fifth observation it is possible to assert more than one essential predicate about one and the same individual subject. If – according to the second observation – these predicates refer to some trait of the individual, the question arises, what the difference between these traits in one and the same individual is. In the identity theory of predication it is presupposed that between these traits there is the so called “virtual distinction”. What kind of relation is it? (Def. 1)  Between x, y there is virtual distinction, iff (i) x, y are really identical; (ii) x can become an object of some cognitive act Φ, without y being the object of the same act Φ (the range of variability of x, y are entities, viz. individuals and any kind of components these individuals may have). Now what does the term “real identity” used in the above definition mean? (Def. 2) Between x, y there is real identity, iff x, y have all properties F in common (the range of variability of F being every property with the exception of “to be an object of a cognitive act Φ”). PREDICATION • 251

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Let us now make a stipulation, that we shall use the word “metaphysical part” (abbreviated: “MP”) instead of the word “trait”. By the word “part” we usually mean a piece of a body, so e.g. we can call Peter’s left leg a part of his body. So it may seem strange to call a trait of a substance its “metaphysical part”. However, it is a traditional scholastic way of speaking,12 and – if we respect the stipulation above – an absolutely innocent one. By means of this new term one may say that between metaphysical parts there is virtual distinction. 3.2 The essence Our consideration 2.5b seems to suggest that really distinct individuals can have a numerically identical metaphysical part. But this is with respect to observation 2.6 unacceptable. To prevent what seems to follow from 2.5b, we must suppose that among the proper metaphysical parts of an individual, there must be one improper part, which (in contrast to the proper parts) can be from any point of view only in the individual, whose part it actually is. Let us call this special part “individuality”.13 Let us suppose that between the individuality of an individual x and every other MP of x there is virtual distinction. Since the individuality is really identical with the other MPs, it makes them individual. Thus observation 2.6 is satisfied. (Def. 3) The specific essence of an individual is the sum of all proper metaphysical parts of that individual. (Def. 4) The individual essence of an individual is the sum of all proper and improper metaphysical parts of that individual.14 (Consequently the individual essence is thus really identical with the substance of the individual).

12   See e.g. Ioannes a S. Thoma, Cursus philosophicus Thomisticus, vol. 1, Logica, pars prima, Summulae, lib. 2, cap. 3 (Reiser 20 b 11). 13   Individuality differs from Scotistic haecceitas by having its source (= principium) in a certain physical part of the (empirical) substance, viz. in prime matter. We are able to refer to the individualities of different individuals by the common term “individuality” in consequence of the fact, that the relations of singular individualities to “their” substances are similar. So the concept “individuality” is an analogous one. 14   Thomas Aquinas does not speak about “individual”, but about “particular” essence: „Sed quia individuationis principium est materia, ex hoc forte videtur sequi, quod essentia, quae materiam complectitur in se simul et formam, sit tantum particularis et non universalis…“ – Thomas Aquinas, De ente et essentia, cap. 2.

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3.3 Metaphysical parts in concrete and abstract states So far we have considered the metaphysical parts only in as much as they are in the concrete state (“in an individual”). We have seen that according to the identity theory they are really identical, but virtually distinct in that state. Now, as proper MPs are virtually distinct, they may be grasped separately from one another by our understanding. If so (i.e. separately or “abstractly”) grasped they get into another state than they originally were in. Let us call their original state the concrete state (abbreviated: “C”), that new state the abstract state (abbreviated: “A”). It seems clear that a metaphysical part in the abstract state is partly different from what it has been in the concrete state. What are the properties that differentiate a metaphysical part in one state from the same metaphysical part considered in the other? First difference: Each in C occurring metaphysical part of an individual is only potentially distinguished from every other MP contained in the same individual, the same part considered in A is distinguished actually from every other. Note: Between MPs in A there is an “intentional distinction” (traditionally: distinctio rationis ratiocinatae): We can define it as follows: (Def. 5) There is an intentional distinction between F, G, iff (i) F, G are actually distinguished, and (ii) there is an individual essence in which (the absolute subjects15 of) F, G are really identical. Second difference: The metaphysical parts in the state C exist really, the metaphysical parts in the state A exist intentionally. Note: In the identity theory existence is considered to be a first level predicate. Two kinds of first level existence are distinguished within this theory: real existence belongs to entities which exist independently of the fact whether they are object of our understanding or not. Intentional existence belongs to entities which exist only in dependence upon the fact that they are objects of our understanding. The proper metaphysical parts in the C state are particular in consequence of their real identity with individuality, the same metaphysical parts in the A state are universal in consequence of their intentional distinction from individuality. 3.4 Weak identity We have stated in our fourth observation that the meaning of a predicate is “somehow” identical with the individual of which it is predicated. Our task will now be to explain, what that “somehow” exactly means. A proper metaphysical part in A state is called by the late scholastic tradition “conceptus obiectivus”. Within the identity theory of predication these objective 15

  The meaning of the term “absolute subject” will be explained later in 3.4.

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concepts are held for the meaning of a certain kind of predicates, let us call them elementary predicates. The most conspicuous feature of elementary predicates is that they are built up without any formal signs (as conjunctions, quantifiers etc.). Now, one could be tempted to say that a metaphysical part F in the abstract state is weakly identical with an individual, if this individual has F among its MPs. However, this cannot be correct, because a MP in A is universal, has an intentional existence etc. and as such it cannot be one of the MP in C(oncrete state) of an individual. It is necessary to define weak identity with more caution: (Def. 6)  The metaphysical part F in A is weakly identical with an individual x, if the individual x has among its metaphysical parts in C such a metaphysical part Φ that Φ and F have a common constituent. Stipulation: Let us call this common constituent “absolute subject”. By the term “absolute subject” I mean what remains, if we abstract from both the properties that are possessed by F only in A, and the properties possessed by Φ only in C. The tradition (following Avicenna) speaks about “natura secundum se”. But I prefer to call it “the absolute subject” here. We shall call the converse relation of weak identity the relation of participation. The notion of universality is linked with weak identity. Universality is a property of a MP in A consisting in the fact that it may be weakly identical with more than one individual. Between “weak” and “strong” identity there is obviously a great difference. Strong identity is reflexive, symmetric and transitive, weak identity has none of these formal properties. Despite that there is an interesting connexion between both these identities. Weak identity may have degrees (e.g. the weak identity between the notion “body” and Socrates is weaker, than the weak identity between “man” and Socrates). It seems clear that one can conceive strong identity as a final state, a certain “maximum”, of weak identity. Within the identity theory the principal difference between “is” as a copula and “is” as a sign of identity (as stated by Frege) is not admitted. 4. TRUTH 4.1 Truth conditions The notion of weak identity offers a tool for formulating the main idea of the Thomistic adequacy theory of truth a little clearer (with respect to the tradition). The truth conditions of a singular predicative proposition are as follows: (Def. 7) A singular positive predicative proposition is true, if (i) the individual denoted by the subject term exists in the time indicated by the verb, and (ii) the meaning of the predicate is weakly identical with that individual. 254 • PREDICATION

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According to the adequacy theory, truth is a kind of relation (“adaequatio”) between the meaning of a proposition with the piece of the world we speak about.16 At the end of my paper I would like to say something about the terms of that relation, i.e. about (a) the meaning of a proposition, and then (b) about its denotatum. 4.2 The meaning of a proposition Let us remind the reader once more that by a true singular predicative proposition we characterise an individual x by means of a universal concept F. In a positive proposition the universal concept F is – as we have seen – a MP in A of the individual x. So it seems to be clear that a positive proposition about an empirical individual expresses weak identity of F (= a MP in A) with x (an individual). As the converse of weak identity is what we have called participation,17 we can express the same idea by saying that a true singular predicative proposition expresses that an individual participates on a MP in A (= on a universal concept). On the other hand, a negative true singular proposition (e.g. Peter is not a horse) expresses the lack of participation of an individual on a MP in A.18 Consequently, it seems that the meaning of a singular proposition (irrespective of its truth-value) is a compound entity, in which a really existing individual is placed into a relation with an intentionally existing object, i.e. with an objective concept. The most important (but also the most scandalous for many people) feature of the identity theory is the thesis that two profoundly different objects are connected within the meaning of a singular proposition, namely a real existing individual on the one hand and an intentionally existing concept on the other. However, this is a sign of the Aristotelian origin of the theory. 4.3 Denotation True singular propositions not only have a meaning, but they also denote some piece of the world by means of that meaning. It seems possible to conceive the relevant piece of the world that a true positive proposition denotes as its denotatum. In the case of a true positive proposition of the type Peter is a man the denotatum is an individual considered as having the same M(etaphysical)P(art) in the concrete state which in the abstract state is the meaning of the predicate. By “the same” I mean “having a common absolute subject” here. In the case of a true negative proposition (Peter is not a horse) the denotatum is an individual considered as lacking the relevant MP. A false proposition like Peter is a horse applies to Peter, but lacks a denotatum: There is no such a thing as Peter having the MP horse. 16   It is not necessary to stress, I presume, that the relation of adequacy is quite different from the relation of correspondence. 17   See above, section 3.4. 18   Hence negative facts are admitted in the identity theory.

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BIBLIOGRAPHY Aquinas, Thomas. Summa theologiae. Vol. 4–12 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1888–1906. ― De ente et essentia. Vol. 43 of Opera omnia iussu Leonis XIII P. M. edita. Romae, 1976. Babenstuber, Ludovicus. Philosophia Thomistica Salisburgensis. Augustae Vindelicorum, 1706. Cajetanus, Thomas de Vio, cardinalis. In De ente et essentia divi Thomae Aquinatis commentarius. Edited by M.-H. Laurent. Turin: Marietti, 1934. Gredt Josephus. Elementa Philosophiae Aristotelico-Thomisticae, 13th ed. Barcinonae, Friburgi Brisgoviae, Romae, Neo-Eboraci, 1961. Ioannes a Sancto Thoma. Cursus Philosophicus Thomisticus. Edited by B. Reiser. Augusta Taurinorum: Marietti, 1948. Sousedík, Stanislav. Identitní teorie predikace. Praha: OIKOYMENH, 2006.

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AUTHORS Mark Faller is Professor of Philosophy and former Chairperson at the Liberal Studies Department of the Alaska Pacific University. As an undergraduate Physics and Philosophy major at Harvard University he worked under Hilary Putnam and David Layzer on an Honors Thesis challenging the PreChaos Theory assumptions of an easy reconciliation between Evolutionary Theory and the Second Law. As a Doctoral student under Edward Halper at the University of Georgia, Dr. Faller worked on interpreting the mathematical puzzles in Plato’s dialogues as a heuristic system for determining how geometrical analysis can guide logical argument. His writing continues to follow both vectors. Along the way he has taught rock climbing, coached college and Olympic wrestlers, and sailed around the world in the merchant marine. He is an addict of used book stores and chocolate, and now teaches philosophy because he is convinced that ideas are the living tools by which we transform the world. E-mail: [email protected] Edward Feser is Associate Professor of Philosophy at Pasadena City College in Pasadena, California. He holds a Ph.D. in philosophy from the University of California at Santa Barbara, an M.A. in religion from the Claremont Graduate School, and a B.A. in philosophy and religious studies from the California State University at Fullerton. He is the author of On Nozick, Philosophy of Mind, Locke, The Last Superstition: A Refutation of the New Atheism, and Aquinas, and editor of The Cambridge Companion to Hayek, and of many academic articles. His primary academic research interests are in the philosophy of mind, moral and political philosophy, and the philosophy of religion. Feser also writes on politics and culture, from a conservative point of view; and on religion, from a traditional Roman Catholic perspective. He lives in Los Angeles with his wife and six children. E-mail: [email protected]

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Ross Inman is a Ph.D. candidate in philosophy at Trinity College, Dublin. His general interests include metaphysics, mediaeval philosophy, value epistemology, and philosophy of religion. He has a particular interest in bringing ancient and mediaeval metaphysics to bear on current debates in material objects. His current research focuses on the intersection of metaphysical grounding and mereology. E-mail: [email protected]

Peter van Inwagen is the John Cardinal O’Hara Professor of Philosophy at the University of Notre Dame, Indiana. His work in the fields of ontology (nature of material objects), philosophical theology (problem of evil, bodily resurrection) and philosophy of action (he introduced the “compatibilism vs. incompatibilism” distiction into the free will debate) make him one of the leading figures in contemporary analytical metaphysics broadly construed. E-MAIL: [email protected]

Gyula Klima is Professor of Philosophy at the Fordham University, New York. His scholarly interests comprise mediaeval philosophy, semantics, metaphysics, philosophy of mind and language, and, significantly, comparative studies of mediaeval and modern theories. He has published almost a hundred articles and several books on these topics. In his research he pays special attention to Aquinas and Buridan. E-MAIL: [email protected]

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Michael J. Loux is Emeritus Professor of Philosophy, past George Shuster Professor of Philosophy, and past dean of the College of Arts and Letters at the University of Notre Dame. His interests include Greek philosophy (especially Aristotle) and metaphysics. He has authored numerous influential works in metaphysics and Greek philosophy, including Substance and Attribute (1978), Primary Ousia: An Essay on Aristotle’s Metaphysics Ζ and Η (1991), Metaphysics: a Contemporary Introduction, 3rd ed. (2006), and “Aristotle’s Constituent Ontology” (2006). He has edited Universals and Particulars (1970), The Possible and the Actual (1990), and The Oxford Handbook of Metaphysics (with Dean Zimmerman, 2003). E-MAIL: [email protected] E. J. Lowe is Professor of Philosophy at the Durham University, UK. He has published over 150 articles on metaphysics, the philosophy of mind and action, the philosophy of logic, the philosophy of language, and early modern philosophy. Some of his books include: Kinds of Being (1989), Locke on Human Understanding (1995), Subjects of Experience (1996), The Possibility of Metaphysics (1998), An Introduction to the Philosophy of Mind (2000), A Survey of Metaphysics (2002), Locke (2005), The Four-Category Ontology (2006), and Personal Agency (2008). He is a General Editor of the Cambridge Studies in Philosophy monograph series. E-MAIL: [email protected] Uwe Meixner teaches philosophy at the University of Augsburg, Germany. His main philosophical interests are metaphysics (general and special, including the philosophy of mind and the philosophy of causation), the history of philosophy, and logic. He is currently working on a comparative study of the philosophies of psychology of Husserl and Wittgenstein. His main publications in English are: Axiomatic Formal Ontology (1997), The Two Sides of Being. A Reassessment of Psycho-Physical Dualism (2004), The Theory of Ontic Modalities (2006), Modelling Metaphysics. The Metaphysics of a Model (2010). E-mail: [email protected]

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Daniel D. Novotný is Assistant Professor of Philosophy at the Faculty of Theology, University of South Bohemia in České Budějovice, Czech Republic. His interests include history of philosophy, metaphysics, philosophical anthropology, comparative philosophy, and teaching philosophy. His current research focuses on the history of the controversies about entia rationis in post-mediaeval scholasticism. He is the Editor-in-Chief of Studia Neoaristotelica, A Journal of Analytical Scholasticism. E-MAIL: [email protected]

Lukáš Novák is Assistant Professor of Philosophy at the Faculty of Arts and Philosophy, Charles University, Prague, and Faculty of Theology, University of South Bohemia in České Budějovice, Czech Republic. Historically, he is interested in the philosophical legacy of Duns Scotus and its later development especially in the 17th century. In his systematic work he attempts to combine traditional scholastic and contemporary analytic approach in areas such as metaphysics, philosophy of logic and epistemology. He has been editor of the journal Studia Neoaristotelica since its foundation in 2004. E-MAIL: [email protected] David Peroutka OCD studied theology and philosophy at the Charles University, Prague. He teaches philosophy at the Faculty of Philosophy, Jan Evangelista Purkyně University, Ústí nad Labem, Czech republic. Up to now his research has focused mainly on the dialogue between Aristotelian and analytic philosophy. E-MAIL: [email protected]

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Anne Siebels Peterson is a philosophy Ph.D. candidate at the University of Notre Dame. She focuses on metaphysical issues in Aristotle, in particular on topics surrounding Aristotle’s hylomorphism. She is writing her dissertation on the issue of numerical diversification in Aristotle’s Metaphysics, with an eye toward exploring the implications which Aristotle’s metaontology has for this issue. She is also especially interested in Aristotle’s account of change, including his reply to the Parmenidean argument for the impossibility of generation and destruction, as well as the understanding of matter presupposed by this reply. Having also studied contemporary metaphysical issues, she concentrates on ontology and metaontology in the contemporary scene, and on exploring ways in which Aristotle’s views might provide a promising perspective different from those currently on offer in contemporary metaphysics. She is also interested in the philosophy of biology, wherein she has focused on the problem of articulating the metaphysical basis for the homology of biological traits. E-MAIL: [email protected] Edmund Runggaldier SJ was born in 1946, studied theology (Mag. Theol.) and philosophy – he received his Ph.D. from Oxford University in 1977, his thesis having been supervised by A. J. Ayer. He has been Professor for Philosophy at the Theological Faculty of Innsbruck University since 1990 and from 2003 to 2007 he was “Professore titolare” for analytic ontology at the Università Cattolica di Milano. From 2007 to 2009 he held the Romano Guardini Chair at the Protestant Theological Faculty, Humboldt University, Berlin. From 2000 to 2006 he was President of the Austrian Ludwig Wittgenstein Society. His interests comprise ontology, classical metaphysics and scholasticism. Currently he is working on a research project “Powers and the Identity of Agents” funded by the Austrian Science Fund (FWF Austria). E-MAIL: [email protected]

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Prokop Sousedík works at the Department of Logic, Institute of Philosophy of the Academy of Sciences of the Czech Republic. He teaches logic, epistemology and analytic philosophy at the Catholic Theological Faculty of the Charles University and at the Faculty of Arts of the Jan Evangelista Purkyně University. He is interested in philosophy of mathematics. E-MAIL: [email protected]

Stanislav Sousedík, born 1931, is Professor Emeritus of the History of Philosophy at the Faculty of Arts and Philosophy and the Catholic Theological Faculty, Charles University, Prague. Among the main areas of his scholarly interest belong history of early modern scholasticism, and analytical philosophy. His aim is to find inspiration there for the renewal and development of Catholic-orientated philosophy (in the spirit of the encyclical Fides et ratio) in the Czech republic. E-MAIL: [email protected]

David Svoboda is Assistant Professor of Philosophy at the Department of Philosophy, Catholic Theological Faculty, Charles University, Prague. His scholarly interests include history of mediaeval and early modern academical philosophy, metaphysics, and philosophy of mathematics; he is specially interested in the thought of Thomas Aquinas and his followers. His current research focuses on the problem of the ontological status of number and the ontology of relations in post-mediaeval scholasticism. E-MAIL: [email protected]

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GENERAL INDEX The index does not comprise the abstracts and the descriptions of individual articles in the Preface. References to occurences in footnotes are in parentheses, bold numbers imply substantial discussion in the text. In crossreferences, semicolons separate distinct entries, commas parts of the same entry. a priori vs. a posteriori 177, 180–181, 211, 216–217, 241–242 abstract – answer 12–13 – concept 137 – idea 13 – nouns 98, (174) – number 134–137 – object, thing, entity 12, 18, 22–23, 37, 48–50, 134–139, 153, 230 – quality 59 – state: see state concrete vs. abstract – structure 138–139 – units 129 – vs. concrete 17–18, 22–23, 48–50, 138;  cf. state concrete vs. abstract abstraction 17, 23, 103, 120, 137, 139, 152, 161, 176, 203, 217, 239 – mere 103, 120, 152, 161, 203, 239 – of numbers 126–128, 137 – of prime matter 65, 70 accessibility – of possible worlds 187 – – causal 205–206 accident – a modified meaning of 139 – and predication (50), 67, 73 – and truthmaking 86–89 – concrete (249) – conditioned 202 – contingent, vs. property 94–95 – dispositional 199; cf. disposition; power; potency

– in relation to substance 29, 81–86, 119–120, 123; cf. inherence – mental 30 – separated 73, 78, 81, 83, 87 – vs. essence 104 accidental – being: see being accidental – form 86, 88, 119, 202 – property: see property1 essential vs. non-essential or accidental act1 (vs. potency) 85, 145–146, 160;  cf. actuality – first vs. second 188 – of existence: see existence act of – pure 145–150, 163, 165 act2: see action – abstractive: see abstraction – mental 35, 176, 251 action: cf. operation – and causality 191–192 – and reaction 186–187 – as second act 188 – belongs to the substance 190 – for an end 155–156, 221 – indicative of active potency 187–188, 193 active vs. passive potency, power, capability 163–165, 188–190, 193, 195, 204, 206; cf. power; capability causal; disposition actual – actualiser 146–149 – dependence: see dependence actual vs. aptitudinal

263

GENERAL INDEX

– distinction 251, 253 – existence 30, 52, 64, 83, 85, 105, 109–110, 156, 170–173, 178–181 – foundation of predication 243 – generation of effect 155 – object, thing, entity 27, 29, 52, 105, 109–110, 172, 204 – reality 29–31 – thinking 33 – union of substance and accident; inherence: see inherence actual vs. potential – world : see world actual, this, real actualism 60, 64–66, 70–71, 150, 204 actuality: cf. act1; actual – amounts to keeping one’s essence 171 – condition of being at all 64 – given by accidents 85 – of prime matter 64–65, 70, 151 – pure: see act1 pure – vs. potentiality 32, 82, 85, 145–146, 150, 189–190 aggregate 28, (36), 126–137, 160–161 analysis – algebraic 213 – Aristotelian of the elements 69 – conceptual 137, 211, 213 – mathematical 210, 213–216 – of dispositions cf. disposition; power; potency – – Aristotelian 186, 190, 195, 203, 206 – – conditional 185, 195–197, 206 – of free action 203 – of language (logical) 5, 114, 129–131 – of natural substances 164 – of predication Aristotelian 235, 239, 244, 255; cf. predication – situs, geometric 213–214, 216 analytic vs. synthetic 49, 116, 216–217 analytical metaphysics 5–6, 26, 32, 37, 73 analytical philosophy 5–8, 11, 26, 28, 32, 113–114 Analytical Thomism 6 angel (26), 151–152

264

anti-essentialism: see essentialism vs. anti-essentialism Antiquity 234, 239 appellatio 174–178 Aristotelian – account of dispositions: see analysis of dispositions Aristotelian – account of events 188 – account of number 127 – account of predication: see analysis of predication Aristotelian – analysis of the elements 69 – categories: see category Aristotelian – causes: see cause Aristotelian – constituent ontology 67–71; cf. ontology constituent vs. relational – definition of efficient cause 191–192 – definition of ontology 23 – essentialism: see essentialism Aristotelian – form: see form Aristotelian – hylomorphism: see hylomorphism Aristotelian – metaphysics: see metaphysics Aristotelian – ontology: see ontology Aristotelian – teleology: see teleology Aristotelian – tradition: see Aristotelianism – universals 66, 242; cf. universal Aristotelianism 78, 84, 150, 186–193, 195, 244 – vs. Platonism 46, 136, 239–240 Aristotelian-scholastic (doctrines) 6, 187, 193 Aristotelian-Thomistic (doctrines) 148, 158, 163–164, 165 arithmetic 131, 136, 139, 223 astrology 16–17 atheism 49, 163, 205 ausser-being 34 axiology 231 Baroque scholasticism 6, 25, 28, 30–33, 37

General Index

being (15), 22–24, 27, 32–36, 123, 153–154, 157, 210–211; cf. existence; object; entity – accidental 28, 88, 123 – actual: see actual object, thing, entity – contingent: see contingency of things, beings, objects – extrinsic 27–28, 31, 36 – genuine 62–63 – impossible 29–31 – intentional: see intentional object, being, entity – necessary: see necessary being – negative vs. positive 27, 30, 35 – of reason 25–37; cf. non-being; non-existence; intentional being, object, entity – possible: see possible being, entity – rationate, intentional, mental: see intentional being, object, entity – real 30, 36 boson 16–17, 21 calculus – differential and integral 214–215, 218, 221 – of situation 214 capability, capacity causal 82, 187–191, 195, 204, 206, 215; cf. causal power, potency, disposition; disposition; power; potency; active vs. passive potency, power, capability categorical basis 198–200 category 25, 28–29, 32–33, 128;  cf. super-category – Aristotelian 97–98, 128, 133, 189–190, 201 – non-material 128, 133 – of quantity: see quantity – ontological 13, (15), 18–24, 98–100, 103, 120, 135 category mistake 48–51 causal – accessibility 205–206 – capability: see capability causal – connexion, interaction 109, 195, 203–205 – dependence: see dependence causal

– necessity: see necessity causal – power, potency, disposition 147, (156), 158, 193, 195, 198, 204; cf.  capability, capacity causal – of God 203 – process 205–206 – – and laws of nature 203 – – unintelligent 156 – production 191 – regularity 155 – role and efficacy 187, 190–193, 199 – series, chain 195, 205; cf. causal connexion – – per se vs. per accidens ordered – 81, 146–147, 149, 152, 158 – tendency 155 – theory of reference 108–109, (133), 249 causality 187, 191, 195, 198 – divine 162, 203 – efficient 148, 155, 157, 191–192, 155, 191–192; cf. cause efficient – event vs. agent causation 187, 191–193 – final, finality 145, 154–158, 163, 218–219;  cf. cause final, teleology – formal 85, 153 – – of quantity 124 – in Leibniz 210, 212, 220 cause – and the principle of sufficient reason 197 – Aristotelian (162), 191–192 – determinant 224 – efficient 82, 148–149, 153–154, 191–192 – final 154–158, (162), 221; cf. end – formal 161–(162), 221; cf. form – has many meanings 191–192 – immediate 206 – intrinsic vs. extrinsic (162) – material 161–(162) – mechanical 218 – natural 155, 157, 192 – not power but bearer thereof 191 – of beings of reasons 36 – of oneself 149 – of return of metaphysics 5 – of the matter-form conjunction 152

265

GENERAL INDEX

– of truth: see truthmaking – personal 192 – proper vs. accidental 192–193 – sufficient 204 – sustaining 159–(160) – uncaused 147, 148–149, 153 class 26, 31, 97–98, 124, 135–136 – complementary 15–16 – empty 15–16, 21 – large 17–18, (22) – natural 13–23, 31 – high 18 – highest 19, 21 – of sentences maximal 204 – universal 15–18, 22–23 – virtual 21 coincidence (local) 94, 107 combination: cf. composition – of matter and form 93–99, 103 – of substance and accident 88 commitment ontological, metaphysical  (32), 37, 54, 100 composition: cf. combination; relation of composition – metaphysical 160, 162–163, 165; cf. part metaphysical – of essence and existence 145, 147, 151–152, 162, 170 – of matter and form 145, 147, 150–152, 161–162 – of (ordinary) objects 44–45, 51–55, 102 – of potency and act 145, 160, 162 – of the intellect 247 compossibility 210, 212, 218–221, 224 conceivability, thinkability 31, 150 concept 109, 132–139, 176 – absolute – abstract 137 – and number 132–139 – and opaque context 174, 176 – and predication 240–243, 255 – common 31 – complete 241–242 – determinate, clear, distinct 174, 176 – empirical 217

266

– extensional (243) – objective 255 – of an accident (249) – primitive: see primitive notion – quidditative (80), 82, 176–178 – scientific 176–177 – sortal vs. non-sortal 133–134 – superior 128 – universal 255 – vague, confused 176 – vs. object  115, 120, 132–133, 217 concept formation 178, 216 concrete – accident (249) – individual 137–138 – number, unit, aggregate 126–131, 137 – object, thing, entity 17–18, 22–23, 48–50, 95–98, 110, 134, 137–139, (238) – state:  see state abstract vs. concrete – substance 95, 127–130 – system 138 – vs. abstract: see abstract vs. concrete condition necessary 248–249 conditional analysis of dispositions: see analysis of dispositions conditional connexion causal: see causal connexion consistency 182, 192, 205, 241 constituent: cf. part constituent ontology, strategy: see ontology constituent vs. relational contingency – of constitutional role 52 – of dependence 66–67, 83–84 – of exemplification 47, 101–102 – of existence 178 – of history 20 – of non-existence 34, 36 – of properties, features 54, 95, 114 – of substantiality 119 – of the world 150, 164 – of things, beings, objects 20, 52–53, 102, 144, 152, 158–163, 178 – of truths 102, 211–212, 219, 241 – radical vs. superficial 158–160

General Index

continuum 211–215 contradiction 31, 34–35, 115–116, 173–175, 211; cf. incoherence contraries 34, 131–132, 191 – elemental 59, 65–71 convention 13, 17–18, 186 – social 230–232, 245 conventionalism social 231 copula 134, (250), 254 correspondence 210, (255) corruption: see generation and corruption creation 143–144, 151 creature 18, 79, 169–172, 181 de re vs. de dicto 113–116, 120–121 definition – as original truth 212–213 – biological 218 – mathematical 217 – of number 126–128, 133–134, 136 – of ontological category 19–21 – of ontology, first philosophy 23; see Aristotelian definition of ontology – of potency 202 – of small number 18 – real, quidditative vs. verbal, nominal  104–106, 108, 110, (171) – scientific, quidditative (171)–172, 176, 178–181 denomination, denominativeness 36, 85–86 denotatum of a proposition 255 dependence – actual vs. aptitudinal 83–85 – causal 81, 147 – contingent 66–67, 83–84 – essential 73–79, 84, 87; cf. order essential – existential 78–87, 147, 151–153, 160; cf. d. rigid vs. non-rigid – identity (77), 101–103, 106 – logical 178; cf. logical independence – metaphysical 75–77, 87 – of dispositions 187, 193, 203

– of matter and form 151–152 – of number 124, 139 – of truth 84, 100 – on mind: see mind-dependence – on substance or subject 81–84, 86, 123, 138 – ontological 65–67, (77), 86, 102–103 – rigid vs. non-rigid 75–76, 87 – the order of 79, 81; cf. order essential – upon predication 65–66, 71 description 130, 132–134 description of a world 205 disposition 185–190, 193, 195–206;  cf. potency; power; capability; active vs. passive potency, power, capability – causal: see causal power, potency, disposition – to inhere 82 – ungrounded 200 dissipation 222–224 distinction – essential vs. accidental 119 – grammatical 98 – intentional 253 – numerical 63, 88, 107 – real  119, 172, 252 – between essence and existence 148–149, 152–154, 158, 169–175, 177, 181 – virtual 251–253 divided line 210–213, 218, 224 divine conservation 143–145 division – material 125–128, 133 – real among things 13–17 dormitive power 163 dualism 48, 212, 218 dynamical vs. mathematical (model, relationship, explanation…) 217–221 eidē 232–233, 236, 239; cf. idea electron 12, 16, 96–97, 101, 178, 222 element1 – Aristotelian 59–71 – chemical 161, 179, 186

267

GENERAL INDEX

element2 (member) 131, 133, 135, 137, 221, 243 elemental transformation 59–71 ellipse 105–108 eminence 79 empirical – concept 217 – feature 249 – object, individual 135–139, 233, 247–249, 255 – world 123, 233 empiricism 13, 209–210, 185, 216–217 end1 (goal) 145, 155–158, (162), 221;  cf. cause final end2 (extremity) 125 Enlightenment 224, 239, 240 ens in se vs. ens in alio 123–124, 136–139 ens rationis 25, 29–30 see being of reason entelechy 221, 189–190 entity – abstract: see abstract object, thing, entity – and essence 108–110 – broadest meaning of 26 – complete vs. incomplete 93–94 – concrete: see concrete object, thing, entity – hypostatic 79 – characterising vs. characterisable; instantiated vs. instantiating 97–98 – predicative 65 – saturated vs. unsaturated 243 epistemology 11, 108, 110, 127 error 36 essence 60–64, 73–88, 94, 104–110, 252 – and essential order 79; cf. order essential – and universals 120 – divine 177; cf. act pure – includes transcendental relations 201 – individual vs. specific 172–173, 180, 252–253 – its built-in finality 155, 157

268

– knowledge thereof: see knowledge of essence – lack thereof 63–64 – low-level 60 – modal construal of 75, 104, 113–114, 150 – of a quality 200–202, 206 – part thereof: see part of essence – real (vs. nominal) 171–173 – robust construal of 73, 104–110, 114, 150 – vs. existence 145–165, 169–182, 219 – – real distinction thereof: see distinction real of essence and existence essential – dependence: see dependence essential – order: see order essential essentialism – analytic 114 – Aristotelian 60, 62–64, 67, 71, 105, 108, 113–114 – constituent 52–54 – mereological 52 – real or serious 73 – strong vs. weak 114 – vs. anti-essentialism 113–116, 120 Eucharist 73, 78, 81–84, 87 event 49, (128), 146–147, 150, 185, 187–189, 192, 212 – quantum level 163 event causality: see causality event vs. agent exemplification 47, 98–103, 117–119;  cf. instantiation existence: cf. being – act of 147–149, (151), 157–158, 160, 172–175; cf. essence vs. existence – actual: see actual existence – and dependence: see dependence existential – and its presuppositions 145–149 – and truthmaking 74–77 – as a predicate (32), (74), 253 – continued, persistent 81–82, 143–144, 150, 159, 161–163, 165 – gained or lost 54, 96, 148–151, 159, 161;  cf. change; generation and corruption

General Index

– individual 171–173 – intentional 253–255; cf. e. objective – knowledge thereof: see knowledge of existence – objective (in the intellect) 30; cf. e. intentional; intentional object, being, entity – of God 144, 163, 165, 170–171, 177, 205 – of natural classes 13–16 – of prime matter 65 – of universals 46–47 – real 95, 100, 119, (171), 188, 253, 255 – specific vs. individual 170–171 existential inertia 143–145, 159–165 existential quantifier: see quantification, quantifier experience 146, 148, 150, 152, 154, 157, 160, 216 – our as agents, deliberators 186, 188, 190–193 explanation – and the principle of sufficient reason 197 – end-driven 221 – of events, behaviour 187, 192, 199–200 – of change and variety 117 – of persistence 162–164 – of truth 244–245 – ontological, of character 44, 47, 53 – ultimate 153, 165 extension 22, 130, 136, 153, 240–241, 243 extrinsic – being: see being extrinsic – property, feature, relation 31, 37, 101, 106, 119; cf. extrinsic denomination – teleology 154, (156) – thinkability 31 fact 28, (35), 50, 245; cf. state of affair – axiological vs. natural 231 – brute 163 – negative 33–36, (255) – objective 231 – physical 212 – prephilosophical 47

feature – extrinsic vs. intrinsic 31 – necessary 101; cf. trait; property2 – of prime matter 68–69 – real of the world 146, 148 – vs. trait 249 fermion 16–17, 21 fiction 30, 36–37, 210 figure (geometrical) 105–106, 108, 200, 213–214 finality: see causality final form – abstracted 137 – accidental: see accidental form – in the mind 156 – inherent, Aristotelian 43–44, 55, 67, 79, 85–86, 93–98, 242, 200 – logical: see logical form – material 152, 172 – particular 99, 172, 235–236, 238–239, 241–242 – Platonic 153–154, 232, 236; cf. eidē – qualitative 200, 214 – separate 236, 232, 236 – substantial 98, 147, 149, 154, 161, 172, 202 – universal 55, 98–99, 235–239, 241–242 – vs. feature 94 – vs. matter 88, 93–95, 98, 103, 145, 150–152, 158–160, 162–165, 172, 202;  cf. hylomorphism formal content 178 freedom 210, 215, 220, 203, 206 function biological 155 function1 (mathematical etc.) 77, 242–245 function2 (role, office) 137–138 future 33, 36, 178, 190, 210 generating principle 105–106 generation – and corruption 151–152, 159;  cf. existence gained or lost – of universals 118 – of elements 60–64 generic (properties etc.) 62, 120, 180

269

GENERAL INDEX

genus 13, 97, 62, 180, 193 – of particular numbers 125–126 God 18, (29), 143–157, 163–164, 170–171, 203, 205, 220–221, 224. good 32, 153–154, 220, 220, 224, 234 harmony 220–224 Humanism 239 hylomorphism 53, 73, 87–89, 93–97, 99, 103, 160–161; cf. form; matter; combination of matter and form – Aristotelian 93, 147, 160 hyper-essentialism 116 hypostatisation 95, 103 change 53–54, 116–119, 145, 148, 159, 188–192, 198–199; cf. existence gained or lost; generation and corruption – accidental 95, 116–119 – elemental 59, 61, 68–69 – of matter 94–95 – substantial (60) character of familiar particulars  43–48, 51, 55 characterisation 32, 67–69, 71, 77, 97–103, 106, 129, 249, 255 Characterisation Principle 35 Cheshire Cat’s grin 101 chimera 35; cf. being impossible Christ 78, 81 idea1 (Platonic, exemplar) 135, 156–157;  cf. form Platonic, eidē idea2 (in mind) 128, 156–157 idealism 136 identity – i.e. whatness 77, 88, 95, 101–103, 106, 116, 186, 202 – is unity 131 – numerical 62–64, 199–200 – of essence and existence 170–171, 173 – of indiscernibles: see principle of the identity of indiscernibles – of knowledge and being 211 – real 251, 253 – statement 134–135, 250

270

– theory of predication 244, 247–248, 251, 253–255 – through change 54, 61, 107–108, 117, 200;  cf. persistence – vs. similarity 214 – weak vs. strong 250–251, 253–255 identity dependence: see dependence identity implication material 197 import – modal 74, (82) – ontological 32, 230 impossibility 29–31, 33, 36, 116, 188–189, 205 in-being, being in 97, (236)–237, 240–241;  cf. inherence incapability Incarnation 78 incoherence 48, 53, 60, 69, 100, 109, 163, 165; cf. self-contradiction individual – bare (115); cf. particualr bare – essence: see essence individual vs. specific – existence: see existence individual – office, role 115 – propertied 55 – substance: see substance primary, individual, particular – thing, object, entity 22, 26, 43, 55, 98–99, 114–118, 137–138, 248–255; cf. particular – vs. universal: see universal vs. individual, particular individuality 252–253 inertia 145, 164–165; cf. existential inertia inherence 50, 81–85, (124), 137; cf. in-being; characterisation – actual vs. aptitudinal 81–86 instantiation 46–47, 66, 96–103, (115), (118)–119, 129–130, 138, 191;  cf. exemplification – Principle of: see principle of instantiation

General Index

intellectus essentiae 169–171 intention1 (purpose, directedness)  155–156; cf. intentionality2 intention2 (notion) 176 – second 27, 35 intentional – act 35 – distinction: see distinction intentional – existence 253–255 – linguistic context 173–174, 176 – object, being, entity 29–30, 33–35;  cf. being of reason intentionality1 (mind-dependence) 30, 33–37, 253 intentionality2 (mental directedness)  187, 192; cf. intention1 ipsum esse subsistens, pure existence  148, 153 see act pure; God item (22), 26–27, 31–33, 37 kat’ allo vs. kath’ hauto 43–44 kind 43, 95, 98–99, 101–109, 211, 213 – natural 101, 119–120 – substantial 65–67, 98, 120–121;  cf. substance secondary knowledge: cf. cognition – a priori vs. a posteriori: see a priori vs. a posteriori – by acquaintance 110 – clear and distinct 176–177, 180 – divine 220 – empirical vs. rational 215–216 – evening vs. morning 209–210 – in general 211, 229 – mathematical 213–218 – of essence, quidditative 108, 110, 172–181, 211 – of existence 172–175, 177–181 – of metaphysical modality 108, 110 – of potencíes or dispositions 188, 198–199 – of the world, of nature 209, 216, 230 – scientific 163, 173–181, 211 language – formal 114 – natural 5, 114–115, 130, 134, 229, 248–251

– private 5 law – natural, of nature 101, 164–165, 198, 203, 205–206, 218, 220 – of (Newtonian) mechanics 145, 164, 220 – of excluded middle 35 – of identity 213 – of inertia 145, 164 – of thermodynamics 221, 223–224 – Snellius’ 220 linguistic – expression 176 – level etc. mere 130, 133 – product, item 118, 230 – relation 97 location in space (and time) 48–50, 118 logic 11, 36, 113, 121, 129–130, 211–218 – (first-order) predicate 173, 230 – formal 121 – Fregean 115, 120–121 – modal 5 – Transparent Intensional: see Transparent Intensional Logic logical – analysis: see analysis of language – commensurability 182 – form 100, 121, 230, 240 – functor 229–230 – grammar 96 – independence 176, 178 – modality: see modality logical – necessity: see necessity logical – omniscience 180 – positivism 5, 213 – possibility: see possibility logical – rationalisation  243–244 manifestation of a tendency or disposition 150, 155, 185, 188, 191, 196–200, 202–203, 205–206. material1 (stuff) 55, 186 material2 – cause: see cause material – division 125–128, 133, 135 – form 152

271

GENERAL INDEX

– implication 197 – object, thing 43, 50–51, 89, 107, 133, 150–151, 165; cf. substance material – part, constituent 46, 50–51, 98, 159–161 – substance: see substance material – vs. non-material (29), 124, 133 – whole 124; cf. division material materialism 46, 48 mathematics 139, 211–222, 243 matter 96–99 – prime 59–71, 93, 147, 149, 152, 161, 202, (252) – vs. form: see form vs. matter, hylomorphism mediaeval period, doctrines: see Middle Ages mechanics; mechanism 212, 218–221 mental representation 178 mereological – sum 95–96 – theory of predication 234–242 mereology 21, 44–45, 51–52 meta-ontology 24 metaphysics 5–6, 11, 21, 36, 47, 89, 104, 115, 214, 218 – analytical 5–6, 26, 32, 37, 73 – Aristotelian 25, 73, 104, 172 – descriptive 130 – scholastic 25, 37, 73, 104, 161 – Thomistic 163–166 Middle Ages 5, (25), 113, 230, 234, 237–239, (243) mind 215, 239–240, 242 mind-affinity 239–240, 243 mind-dependence: see intentionality1 modality 5, 21, 54, 75–76, 78, 86–88, 102– 104, 116, 119 ; cf. truth2 modal; necessity, contingency, possibility, potentiality – de re vs. de dicto: see de re vs. de dicto – logical 189 – metaphysical 108, 110 mode 77, 88, 99–102 – of being 160

272

– of substance 84 modus dicendi (per se) 114;  cf. predication essential multitude 125–127, 131–134 natural kind: see kind natural nature1 (essence) 45, 51, 79, 101, 106, 109, 150, 159, 163, 172–173, 176; cf. essence – common 34, 45, 254 – human in Christ 78, 81, 83 nature2 (non-artificial reality) 186, 192, 216–219, 221, 224; cf. law natural, of nature necessary – being 76–77, 145, 150–151, 153 – condition: see condition necessary – property: see property2 – feature 101; cf. trait; property2 necessity – absolute 145, 150–153 – causal 195–196, 202–206 – de re vs. de dicto: see de re vs. de dicto – dispositional 195, 197–198, 203;  cf. necessity causal – from reason vs. from the world 209–210 – Humean account 203, 209–210 – hypothetical 206 , 211, 212, 218 – Leibniz’s account 210–220, 224, 241–(242) – logical 75, (82), 115–116, 150, 202 – mathematical 217 – metaphysical 75, (82), 101–107, 110, 150;  see de re vs. de dicto – moral 211 – of itself vs. from another thing 151–152, 159 – physical 75 – psychological 203 – vs. possibility or contingency 103–104, 110, 150, 209–210, 213, 215; cf. modality negation1 (non-entity) 36, 115 negation2 (logical constant) 173, 175, 204–205 negation of material division 125

General Index

nominalism (14), 21, 115, 216, 230, 239, 244 – austere (22), 47 non-being 23, 27–31, 33–37; cf. being of reason; non-existence non-contradiction 204–205 non-existence 22–23, 33, (35), 28–37, 76, 150; cf. non-being number 17–18, 26, 76–77, 123–139, 222–223 – absolute vs. concrete 126–130;  cf. multitude – particular 125–127 – small 18 object – abstract: see abstract object – actual: see actual object – geometrical 106 – intentional: cf. existence objective in the intellect – kooky 89 – material: see material2 object, particular – mental : see object intentional – of thought: see object intentional – ordinary : see particular familiar – set theoretical – vs. concept: see concept vs. object objective1 (vs. object) 27–28 objective2 (vs. subjective) 30; cf. intentional object, being, entity; concept objective Ockham’s Razor 158, 164, 203 ontological – commitment (32), 37, 54, 100 – strategy: see ontology constituent vs. relational Ontological Square 97–99 ontology 11–24; cf. metaphysics – Aristotelian 23, 64, 81, 93, 97–98, 103, 120, 123, 187–193, 238–239 – constituent vs. relational 11, 43–54, 67, 70–71, 99–103, 120 – four-category 97–103 – Meinongian 22–24, 34–35 – Quinean 11–13, 19 – scholastic (30), 33, 37, 123, 187, 193

optimality 210, 219, 221 order – essential 78–84, 87 – of dependence vs. of eminence 79; cf. dependence essential – of parts in the whole 125 overtone 221–223 para-being 27–28 part: cf. constituent; component – commonsense 44, 50–52 – integral 124, 187 – material: see material2 part, constituent – metaphysical 44, 50–51, 252–255 – of essence 77, 80, 82, 88, 101–108, (165), 175–177, 252; cf. part metaphysical – proper vs. improper1 50, 88, 94 – proper vs. improper2 252 – substantial 51 – temporal 12, 48–51 – vs. whole: see whole vs. part, constituent participation 45, 47, 153–154, 233, 254–255 particular 13, (22), 94, 97–98, 115–120, 126, 129–131, 172, 216, 238–241, 245, 251, 253;  cf. individual – bare or thin 54, 56, 114–116, 120 – concrete (22), 48 – familiar 43–49, 52–55 – form: see form particular – material 50, 151 – number: see number particular – sensible 44, 47 – substance: see substance primary, individual, particular – vs. universal: see universal vs. individual, particular passive vs. active potency, power, capability: see active vs. passive potency, power, capability past 33, 47, 178, 209 per se vs. per accidens – causal series 81, 146–147, 149, 152, 158 – unity 28 perception 28, 36, 103, 110, 127, 137

273

GENERAL INDEX

persistence 53–54, 94, 150–151, 159–162, 165 – conditions 107–108 – of prime matter 59–66, 70–71, 151 person 49, 79, 186–187, 192 petitio principii 179 phenomenalism 53 phenomenon 164, 172, 192; cf. world phenomenal phoenix 170–171 physics (modern) 97, 218 place: see location in space (and time) Platonism 46, 124, 135–137, 147, 153–156, 220, 232, 234, 237, 239–240 Porphyrian Tree 126, 180 positivism 5, 146, 213 possibility 27, 29, 36, 54, 187–193, 195, 204–206, 209–215, 219–220; cf. potency; potentiality; power; disposition; contingency; modality – logical 150, 193, 195, 188, 195 – mere 29–30, 33, 146, 149, 178, 187–190, 193 – metaphysical 83, 87, 104, 107, 110, 150 – of non-existence 150 – ontological 195, 205 – real: see real capability, disposition, possibility, power – synchronous 119 – vs. impossibility 29, 33–34, 188–189 – vs. necessity: see necessity vs. possibility, contingency possible – being, entity 27, 29–30, 33–(37), 188, 211, 219 – world 7, 20–21, 74, 76, 101–104, 108, 150, 187, 189–190, 193, 202–206, (242) potency – active 188 – causal: see causal power, potency, disposition; potency active, passive – identical with accident 201–202 – knowledge thereof 188, 198–199 – logical 188 – objective 188

274

– passive 82, 85–86, 188; cf. active vs. passive potency, power, capability – pure 60–61, 65, 147, 151–152, 161;  cf. matter prime – rational vs. natural or physical 191, 203 – receptive 201–202 – subjective 187, 191 – vs. act: see actuality vs. potentiality potency, potentiality 33, 60–61, 64–65, 145–147, 149, 185–193, 195, 198, 201–205; cf. potency; possibility; power; disposition; capability – vs. act, actuality: see actuality vs. potentiality power1 (potency) 36, 163, 186–193, 195, 198–205; cf. disposition; potency; capability causal – active 163–(165); cf. active vs. passive potency, power, capability; capability causal; disposition – causal: see causal power – dormitive 163 – mental 36 power2 social 230–232 predicate – elementary 254 – essential 251 – existential (32), (74), 253 – grammatical (250) – higher-order 35 – low-level 12 – ontological 234 – universal 237; cf. universal – vs. subject: see subject vs. predicate predication 251 – accidental 77, 86–88, 248–(249) – and prime matter 65–71 – essential 114, 248–249 – identity theory thereof: see identity theory of predication – relational vs. non-relational 231, 234, 242–245 – various analyses thereof 229–245, 247–255 primitive notion (76), 192

General Index

principle – “spite”/“moderation” 224 – of conservation of mass-energy 164 – of constituent identity 53, 55 – of contradiction 213, 224 – of identity of indiscernibles 55 – of independence of so-being from being 35 – of instantiation 46–47, 66, (118) – of least action 221 – of sufficient reason 197–198, 200, 212, 220, 224 private language 5 privation 27, 30, 36, (118), 189 probability 154–156, 210, 220, 223–224 proper name 130, 133, 173, 248–250 property monism 199–200 property1 (wide sense) 43, 46–55, 86, 115–116, 119–120, 131–139, 187–190, 193, 203, 245, 251, 253–254; cf. feature – causal (155) see disposition; power; capability causal; active vs. passive potency, power, capability – contingent vs. necessary 47, 54, 62, 113–115; see property2 – essential vs. non-essential, accidental 54, 62, 64, 68, (70), 104, 106, 108, 114–115, 199 – extrinsic: see extrinsic property, feature, relation – generic: see generic (properties etc.) – material vs. non-material 128 – qualitative 198–199, 202, 214 – real, irreducible 185–188 – relational: see relational properties, attributes, modes – repeatable vs. nonrepeatable 53, 55 – trivial vs. non-trivial 32, 114–116 property2 (flowing from essence) 94–95, 106, 114–115; cf. trait proposition 110, 249, 255; cf. statement; sentence; truthbearer – atomic vs. molecular 247 – false 255 – logical 213, 216 – negative 255 – particular 171

– positive singular 248–249, 254–255 – predicative 247–249, 254–255 proton 96–97 pure act: see act pure; God quality 59, 94, 189–190, 198–203, 206, 214 quantification, quantifier 12, (13)–(14), (32), 170–171 quantity 50, 124–128, 131–132, 136, 189–190, 213–214, 218 – continuous 125 – discrete 125, 128, 131 quasi-being 34, (35) real – being, thing, object 30–36, 100, 118, (171), 187, 255 – capability, disposition, possibility, power  187–188, 119, 190–193, 205 – definition: see definition real, quidditative vs. verbal, nominal – difference, change 98, 117–119, 233 – distinction: see distinction real – division among things 13–17 – essence: see essence real (vs. nominal) – existence: see existence real – identity: see identity real – property: see property1 real, irreducible – world: see world actual, this, real realism (15), 185–187, 191, 193, 210–211 reason1 (ground) – ontological 198 – sufficient 197–200, 212, 220, 224 reason2 (faculty), reasoning 209, 211–218, 224 reductionism 115, (155), 185, 215 reference – identifying 26 – oblique vs. explicit 174 – same 160 – theory thereof 108–109 – to accidents or modes vs. to their bearer 68, 88, 190 – to aggregates 130–133 – to classes (13)–(15)

275

GENERAL INDEX

regress (infinite) – causal etc. 146, 149, 152, 165 – in explanations of characterisation or exemplification 44–45, 99–100, 119 – of essences 108 relation, relationship 22, 26, 43–45, 49, 137, 200–201, 214, 245 – across the categories 99–103; cf. r. transcendental – dynamical 218; cf. dynamical vs. mathematical – harmonic 222-223 – industrial 137–139 – internal vs. external 100–102 – linguistic, syntactical 97, 213 – mathematical 214, 218 – of accessibility: see accessibility of possible worlds – of composition 51–53; cf. composition – of dependency: see dependence – of exemplification: see exemplification – of identity: see identity – of more and fewer 138–139 – of parts in a whole 125 – of reason 27, 30, 36 – of subject and predicate 66, 212, 240;  cf. predication; subject vs. predicate – of substance and accident 81, 83, 85–86;  cf. inherence; in-being – of truthmaking: see truthmaking – ordering 79, 81; cf. order essential – secundum dici 201 – social 37 – spatial, geometrical 100, 213 – subclass 16, (19) – to act or effect 188, 192, 201;  cf. causality; act vs. potency; power; capability, capacity causal; disposition – transcendental 201–202 relational – ontology, strategy: see ontology constituent vs. relational – predication: see predication relational vs. non relational

276

– properties, attributes, modes 99–100, 137, 200 – system 137, 139 – theory of space 15 – truth 100 relativism 209–211, 229 Renaissance 6, 25, (28), 239 representation mental: see mental representation Russell’s paradox 136 scepticism 67–(70), 109, 209–211, 216–217, 236 Scotism 6, (252) second intention: see intention2 second Sein: cf. being; existence self-contradiction 31, 35; cf. contradiction; incoherence self-evidence 177 self-identity (32), 114 self-predication 232 semantics 36–37, 115, 213, 243, 247 – Fregean 115, 120 sense1 (meaning) 28, 109, 128, 133, 249 sense2 (cognitive faculty) 36, 110, 137, 150, 187, 198 sentence 28, 204–205 – conditional 196–202, 206 – positive predicative 247, 250 – vocative vs. affirmative 249–250 series causal: see causal series set 12–14, 21, 37, 51–52, 77, 95, 104, 108, 127–129, 136, 243–244 – of possible worlds 21 – of properties 104, 108 set theory 136, (217) set-theoretical – composition 52 – object 135–136 – theory of predication 243–244 shape 106, 199–200

General Index

scholasticism 6, 73, 78, 81, 84, 104, 161, 186–188, 191, 193, 200–201, 253 – second (Renaissance or Baroque) 6, 25–37, 248 signum – identitatis 247 – quantitatis, particulare 171 singleton 77, 104 social conventionalism 231 something 31 sophists 230–231 Sosein 22–23 soul (33), 86, 151–152, (161), 214–216 species – biological 16, 178, 218 – of metaphysical dependence or necessity  76–77, 87 – of quantity 124–126 – vs. genus 13, 62, 97, 126, 131–132, (176) state concrete vs. abstract 138, 253–255 state of affairs 27–(28), 50, 87, 192, 197, 242, 245; cf. fact statement: cf. proposition; sentence – axiological 231 – conditional 185; cf. sentence conditional – existential 21 – justification thereof 197 – modal 104 – number 126–135 – senseless 130, 133 – simple predicative 229–231, 234, 240–245 – singular 129–132 – subject-predicate 132, 134 strategy ontological (constitutive or relational): see ontology constitutive vs. relational subclass 15–16, 18–19 subject – absolute (253)–255 – of change, transformation 67–68, 116–119

– of predication 65–71, 97 – of properties, accidents 53, 65–67, 81, 84–88, 97, 113–116, 119–120 – ontological 119, 234 – vs. predicate 66–67, 71, 126–135, 211–212, 240–241, 247–254; cf. relation of subject and predicate; predication subjectivism 5 subjectivity 12–13, 19–20 substance – its constitution 50, 93–96, 103, 252 – its generation and corruption (64), 81, 96 – material 124–125, 151–152, 159–162, 164;  cf. material2 object – natural 146–149 – of a thing 50, 172, 248, 252 – primary, individual, particular 22, 83, 93–95, 97–99, 103, 120, 129–130, 152, 159, 189–190, 236, 249 – secondary, universal 97–98, 236–237;  cf. kind substantial – separated 46 – spiritual 124 – vs. accident 29, 78, 81–88, 94–95, 119–120, 123–124, 139, 190, 202 – vs. aggregate of substances 127–130 – vs. attribute 18, 21, 97 – vs. event or state of affairs 146–147, 242 – vs. feature and trait 248–249 – vs. mode 97 – vs. potency 191, 201–202 – vs. property 94–95, 193 – vs. relation 22 substance-kind: see kind substantial substratum 54, 59–71 substratum theory 54–55 subsumption 240–241 super-category 26–28, 31, 37 super-transcendentals 31–32 supposition 178 synthesis 216 tautology 164, 212–213

277

GENERAL INDEX

teleology 212, 219, 221; cf. causality final – Aristotelian 154–157 temporality 36, 48, 119, 219 tendency 155, (162), 186; cf. finality; teleology; disposition – to cease or continue to exist 150–151, 159, 161–163; cf. existential inertia test of a disposition 196–198, 200, 202–204, 206 theism 48, 163, 205 theory of predication (84), 229–245, 247–255 – Aristotle’s 235–236, 240, 243 – fact-referring 245 – Frege’s 242–243, 245 – identity 244, 247–248, 251, 253–255 – Leibniz’s 240–242, (244) – minimal Aristotelian 244 – Plato’s 232–234 – pre-Fregean 234, 241 – quasi-mereological 235–238, 240–241 – redundancy 244 – set-theoretical 243–244 – socially-conventionalist 231 – Thomistic 247–248 – truthmaking (84) thermodynamics 220–224 thinkability, conceivability 31, 150 Third Realm 135, 156 Third-Man-Argument 233 Thomism 6, (30), 201, 145–148, 150, 158, 163–166, (171), 175, 247–249, 254 – analytical 6 thought 33, 36, 103, 109 time (13), 54, 95, 107, 110, 117, 118–119, 123, 135; cf. temporality; past; future trait 249, 251–252; cf. property2 transcendentals 32, 153–154 Transparent Intensional Logic (TIL)  114–116 trope 46–47, 49, 53–55, 87, 99, 119–120;  cf. accident

278

truth1 (trueness) – adequacy theory thereof 254-255 – its grounding 74–78, 84, 87–88, 100, 210, 230–231; cf. truthmaking – its nature 210–211, 230–243, 254–255 – transcendental 153 – vs. fiction 210 truth2 (something true) 74–75 – contingent vs. necessary 100–102, 106–107, 113, 212, 219, 241 – essential 102, 106–107, 110, 219 – historical 241 – Leibniz’s classification thereof 211 – logical vs. mathematical 211–216 – modal 110 – negative 33 – of coincidence 107–108 – of exemplification 102 – of fact vs. of reason 211–212, 214, 218 – original vs. derived 212 – phenomenal 218 – physical, temporal vs. eternal, metaphysical 219 – relational 100 truth conditions 254 truth-explanation 244–245 truth-value 36, 198, 200, 255 truthbearer 28 truthmaker, truthmaking 28, 73–78, 81, 83, 84–88, 100, 102, 197–198, 230, 249 truthmaker necessiatrianism 74 unit1 – class 15 – charge 101 unit2 (of a multitude or number) 125–129, 132–135 – synonymous to individual etc. 26 unity – divine 153 – hypostatic 78 – internal of things 15–17, 28 – per se vs. per accidens 28 – transcendental 153–154 – vs. number 128–133

General Index

universal 22, 31, 34, 37, 46–47, 66–67, 77, 97–99, 101, 117–120, 129–131, 216, 236–245, 253–255 – class: see class universal – form: see form universal – substance: see substance secondary, universal – term 127, 129 – vs. individual, particular 34, 94, 97, 117–120, 130, 216, 253 Universal Characteristic 213, (217) universality 254 ununoctium 179–180 way of givenness 132 whole – arbitrary 28 – composite vs. its part, constituent 32, 44–45, 50–54, 67, 71, 125, 129–130, 147 – essence 106–107 – material vs. spiritual 124 – quantitative 125

Word (divine person) 78, 81 world – actual, this, real 21, (29), 101, 126, 150, 187–188, 190, 203, 205, 219 – empirical 123, 233 – its continuance 143–146, 148, 155–156, 164–165 – its furniture 185 – knowledge thereof 209, 215, 217 – material 160–161 – microscopic vs. macroscopic 186, 199 – most perfect 220 – natural 156–157, 163–164, 191 – of particulars 116–119 – of things 28–29, 169, 178 – phenomenal 211, 218–221 – physical 202, 221 – possible: see possible world – theistic vs. atheistic 205

279

INDEX OF PERSONS The index does not comprise the abstracts and the descriptions of individual articles in the Preface. Persons not discussed but merely cited in footnotes and bibliography are usually omitted, as well as the authors of the articles themselves (unless significantly mentioned by someone else) and persons mentioned merely in titles of written works. References to occurences in footnotes are in parentheses, bold numbers imply substantial discussion in the text. “GI:” refers to the General Index. Adams, Marilyn McCord (81), 86 Adler, Mortimer 143, 158–164 Aquinas, Thomas  – his “Five Ways” 143–158 – his legacy 6, 248; see also GI: Thomism – criticised by Buridan 173–176, 178, 181–182 – on absolute nature 34 – on beings of reason 32 – on change 145–147, 159 – on divine conservation 143–166 – on essence 150, 169, 171, 175–182 – on existence 148,159–162, 169–173, 177–179, 182 – on inherence 85–86 – on matter and form 73, 87–88, 97, 151, 159–160, 172, 200 – on mental representation 178 – on metaphysical composition 160–162, 165 – on modalities 150–153, 159, 188–189, 204 – on number 123–129, 133–134 – on participation 153–154 – on potency and act 146–147 – on predication 128, 237–238, 247 – on substance and accident 85–86, 146, 190 – on teleology 155–156 – on transcendentals 153 – on truthmaking 84–88 Aristotle  – on abstraction (217) – on act and potency 189–191, 207

– on being 15 – on causality 191–192, 207 – on change 116, 192 – on essence 105, 108 – on essential order 79 – on kat’ allo vs. kath’ hauto 43–44 – on kinds of composition 50–51 – on knowledge 174–175 – on matter and form 43, 53, 93, 97, 172 – on number 123–124, 126–127, 133 – on ontology and metaphysics 23, 25, 60, 97–98, 104 – – relational vs. constituent 43–47 – on predication 67–68, 97, 230, 234–237, 240, 243 – on prime matter 59–71 – on quality 201 – on rational potencies 191, 203 – on substance and accident (50), 97, 116, 123, 190 – on teleology 155–156, 221 – on truthmaking 84 – on universals 46, 67, 97, 236–237 Armstrong, David M. 45–46, 200 Augustine 143 Babenstuber, Ludwig 248 Beaudoin, John 143–144, 162–165 Benacerraf, Paul Joseph Salomon  136 Bergmann, Gustav 11, 45–46, (115) Berkeley, George 45, 53, 210 Bird, Alexander 185 Bradley, Francis Herbert 99

281

INDEX OF PERSONS

Braine, David 164–165 Bruno, Giordano 214 Buridan, John (36), 169, 173–182 Butler, Judith (231) Cajetanus, Thomas de Vio (171), 248 Cantor, Georg (217) Carnap, Rudolf 197–198, 204 Cartwright, Nancy 186 Cassirer, Ernst (217) Castañeda, Hector 45, (55) Chisholm, Roderick 45 Cmorej, Pavel (116) Cohen, Sheldon (70) Cross, Richard (83), 85, Dedekind, Julius Wilhelm Richard (217) Dvořák, Petr 204 Einstein, Albert 12 Ellis, Brian 185 Euler, Leonhard 220 Fermat, Pierre de 220 Ficino, Marsilio 240 Findlay, John N. 34 Fine, Kit 75, 104 Fox, John 84 Frege, Gottlob 32, 115, 120–121, 124, 126, 128, 131–136 Gilson, Étienne 159 Gorgias 109 Gorman Michael 80 Gredt, Josephus 248 Grice, Paul 49–50 Heidegger, Martin 220 Helmholtz, Hermann von 221 Heraclitus 209 Hobbes, Thomas 13 Hume, David 135, 187, 191, 198, 203, 209–210, 213, 216–217 Husserl, Edmund 238 Inwagen, Peter van 49

282

Kant, Immanuel 210, 213, 215–218 Kenny, Anthony 169–173 Kestin, Joseph 224 Kistler, Max 200 Kripke, Saul 5, (133), 249 Kvanvig, Jonathan (144), (163)–165 Leibniz, Gottfried Wilhelm 209–224, 230, 240–242, (244) Lewis, David Kellogg 51 Lewis, Frank (62) Locke, John 13–14, 45, 98, 103, 105 Loux, Michael 60, 68, 120 Lowe, E. J. (48), 73, 75–77, 80, 87, (117), (127) Lullus, Raymundus 214 Mally, Ernst 35 Martin, Charles B. 196, 201 Matthews, Gareth 89 Maupertuis, Pierre–Louis Moreau de 220 Maxwell, James Clerk 221 McCann, Hugh (144), (163)–165 McInerny, D. Q. 160, (161) Meinong, Alexius (15), 22–24, (27)–(28), (33)–35 Mirandola, Pico della 240 Molnar, George 185, 199–201 Monty Python 161 Mumford, Stephen 185, 199 Neumann, John von 136 Newton, Isaac 145, 164, 218–220 Ockham, William see GI: Ockham‘s Razor Paley, William 154, 156–157 Parmenides 33, 233 Pasnau, Robert 144 Paul, Laurie 45 Plantinga, Alvin 45, (62) Plato see also GI: Platonism – compared to Leibniz 211–220, 224 – his Divided Line 211–212 – on ideas 135, 153–154, 236, 239

Index of Persons

– on mathematics and numbers 123–124, 215–217 – on participation 154 – on predication 230, 232–234, 240, 243 – paradigm of relational ontology 43, 46 Plotinus 239–240 Poinsot, João (Ioannes a Sancto Thoma) 248 Porphyry see GI: Porphyrian Tree Prigogine, Ilya 224 Prior, Arthur Norman 28 Protagoras 210, 231 Pythagoras 116–117, 123 Quine, Willard Van Orman 5, 11–13, 32, 34, 47, 113, (198) Robinson, H. M. 61 Rundle, Bede 162 Russell, Bertrand 26, 34, 43, 45, 135–136, 217 Scaltsas, Theodore (62) Schrecker, Paul 219

Scotus, John Duns 78–88 Shields, Christopher 144 Shoemaker, Sidney 198, 202–203 Snellius, Willebrord 220 Socrates 232 – in examples 18, 76–77, 82, 85–88, 104, 115–116, 137–138, 171, 220, 235, 239–241, 248, 254 Speusippus 46 Spinoza, Baruch 105–106 Strawson, Peter Frederick 26, 45, 49–50 Suárez, Francisco 28, 30–31, 192 Thompson, Ian J. 199 Tichý, Pavel 114 Voltaire 220 Williams, C. J. F. 59 Wittgenstein, Ludwig 28, 158, 164–165, 230 Wolff, Christian 213 Wolterstorff, Nicholas 44–45, 47, (99), 120 Zermelo, Ernst 136

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