The Kalam Cosmological Argument for God [Hardcover ed.] 1591024730, 9781591024736

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THE CATHOLIC UNIVERSITY OF AMERICA The Kalam Cosmological Argument in Contemporary Analytic Philosophy

A DISSERTATION Submitted to the Faculty o f the School o f Philosophy o f The Catholic University of America In Partial Fulfillment o f the Requirements For the Degree Doctor o f Philosophy

© Copyright All Rights Reserved

Marie R. Nowacki Washington, D.C. 2002

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UMI Number 3067497

Copyright 2003 by Nowacki, Mark R. All rights reserved.

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This dissertation by Mark R. Nowacki fulfills the dissertation requirement for the doctoral degree in philosophy approved by Riccardo Pozzo, Ph.D., as Director, and by Michael Gorman, Ph.D., and Timothy Noone, Ph.D., as Readers.

Riccardo PozJo,'Ph.D., Director

th c K jtjc

—

Michael Gorman, ( Ph.D., Reader

u imothy Noone, Ph.D., Reader

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Abstract Approximately 1,500 years ago John Philoponus proposed a simple argument for the existence o f God. The argument runs thus: (1)

Whatever comes to be has a cause of its coming to be.

(2)

The universe came to be.

(3)

Therefore, the universe has a cause o f its coming to be.

Due to the influence of William Lane Craig, this argument and the family of arguments that support it have come to be known as the “kalam” cosmological argument (henceforth KCA). Craig’s account o f the KCA incorporates features that serve to distinguish his version as a significant advance. First, conceptual advances in mathematics now permit a clearer presentation of the argument than was previously possible. Second, contemporary Big Bang cosmology confirms the central contention o f the KCA, namely, that the past existence o f the universe is finite. Reflection upon the implications o f using Cantorian transfinite mathematics to model physical processes allowed Craig to develop a distinctively philosophical version o f the KCA which is relatively independent of changes in contemporary scientific cosmology. This dissertation is intended as a critical investigation and development o f this philosophical strand o f the KCA. The literature relating to the KCA has grown however to a significant bulk, and there is now danger o f duplication and misassessment due to the plurality o f interpretations that the argument has received. Part I o f the dissertation addresses this need by laying bare the underlying logical structure o f the KCA (chapter 1) and by providing a comprehensive “state o f the question”

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(chapter 2). Part II o f the dissertation, comprising chapters 3 through 6, focuses upon an important species o f objection made to the KCA. This species o f objection relies upon thought-experiments designed to show that an actual infinity is possible. I reply: this objection is effectively answered by introducing a metaphysics o f substances. In the course o f presenting a systematic response I develop an interpretation o f the notion o f substance that is useful for analytic philosophy, present a general account o f the logical requirements o f KCA thought-experiments, and outline a theory o f logical modality suited to the metaphysical requirements o f the KCA.

Director Riccardo Pozzo, Ph.D.

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Acknowledgements

My deepest thanks to— Professor Ricardo Pozzo, for his great kindness and most generous guidance as director of this dissertation; Professors Michael Gorman and Timothy Noone, for adding so much to the dissertation by being its readers; Professors Jean DeGroot and Therese-Anne Druart, for their insight and guidance during the early stages o f this work; Dean Kurt Pritzl, for providing the underlying presence o f the School o f Philosophy; Professors Ronald Calinger and Douglas Gropp, for their generous contributions during the dissertation defense; Ingrid Genzel and Gretchen Gusich, for being the kind o f neighbors and friends one can only hope for; Erik Tozzi, for his timely assistance and for furnishing a useful example; Loy Hui Chieh and Mitch Jones, for their philosophical contributions to this work; My parents, for their constant support; and My wife, Chuen, and children, Diogenes and Xanthippi, for being there and staying there.

AM .D.G.

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Contents INTRODUCTION________________________________________________________ 1 1. What is the KCA?....................................................................................................1 2. Why this dissertation was written........................................................................... 4 3. Order o f treatment.................................................................................................. 6 P A R T I_________________________________________________________________ XI Chapter 1....................................................................................................................... I I 4. Craig’s version o f the KCA as presented in TKCA.............................................11 4.1 Craig on premise I: Whatever comes to be has a cause o f its coming to be 11 4.2 Craig on premise 2: The universe came to b e ...............................................15 4.2.1 Preliminary remarks and terminology........................................................ 16 4 J2J2 Exposition of Cantorian transfinite number theory................................... 20 4.2.2.1 Brief history o f mathematical speculation on infinite............................ 21 4.2.2.2 Cantor and the development o f set theory.............................................. 24 4.2.3 Reflections on and reactions to Cantor...................................................... 37 4.2.3.1 Taxonomy o f positions within the philosophy of mathematics..............39 4.2.3.2 Paradoxes in paradise.............................................................................. 45 4.2.3.3 Reactions to the paradoxes......................................................................49 4.2.4 Craig’s argumentative strategy for premise 2............................................ 54 4.2.5 Argument (A )............................................................................................. 57 4.2.5.1 Premise (ii) o f argument (A )...................................................................61 4.2.5.2 Premise (i) of argument (A).....................................................................67 4.2.6 Argument (B).............................................................................................. 72 4.2.7 Argument ( Q .............................................................................................. 78 4.3 Craig on the conclusion: The universe has a cause o f its coming to b e 81 Chapter 2 ....................................................................................................................... 85 5. Purpose, method, and notation............................................................................ 85 6. Division I - Objections propadeutic to the KCA.................................................89 7. Division II - Objections to premise (1) o f the KCA........................................... 94 8. Division III - Objections to premise (2) o f the KCA.........................................100 8.1 Division Hl.a - Objections to argument (A) o f the KCA.............................101 8.1.1 Objections to premise (i) o f argument (A )...............................................101 8.1.2 Objections to premise (ii) o f argument (A )..............................................104 8.2 Division m .b Objections to argument (B) o f the KCA...................... 112 8.2.1 Objections to premise (a) o f argument (B)...............................................113 8.2.2 Objections to premise (b) o f argument (B)...............................................118 8.3 Division m .c - Objections to argument (C) o f the KCA............................129 8.3.1 Objections to premise (a) o f argument (C)...............................................129 8.3.2 Objections to premise (p) o f argument (C)_______________________ 131 9. Division IV - Objections to conclusion (3) o f the KCA....................................132

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PART I I _______________________________________________________________ 136 Chapter 3 ......................................................................................................................136 10. Appeals to logical possibility in objections to the K CA .................................136 11. Outline o f the argument of this chapter........................................................... 141 12. Establishing that the KCA requires more than logical possibility................. 143 13. Modal distinctions according to Braine........................................................... 149 14. Thought experiments and the KCA..................................................................157 Chapter 4 ......................................................................................................................168 15. Elements o f a theory o f substantial possibility................................................ 168 16. A metaphysics o f substances............................................................................170 16.1 Which theory o f substance?........................................................................171 16.2 Why an ontology o f substances?............................................................... 175 16.3 Reply to common objections......................................................................182 17. Substantial nature and the manifestation o f causal power...............................187 17.1 Connecting substance and active power.................................................... 188 17.2 Active power and natural necessity........................................................... 191 18. Substantial possibility.......................................................................................199 Chapter 5 ..................................................................................................................... 202 19. Applications o f substantial possibility and a substance-based metaphysics ..202 20. Why evaluation o f the KCA requires substantial possibility......................... 202 21. Events and temporal marks.............................................................................. 206 21.1 Clarification o f the notion o f “event” ........................................................206 21.2 Clarification and defense o f “temporal mark” .......................................... 209 22. A new KCA thought experiment..................................................................... 217 22.1 The “hyperlump” thought experiment.......................................................217 22.2 Consistent mathematical description insufficient for factual possibility..219 22.3 No determinate shape consistent with the hyperlump.............................. 226 22.4 Hyperiumps and time past......................................................................... 230 Chapter 6..................................................................................................................... 234 23. Summary...........................................................................................................234 24. Prospects and diagnosis................................................................................... 237 APPENDIX____________________________________________________________ 240 25. Cantor’s theory o f the actual infinite............................................................... 240 26. Operations with transfinite numbers................................................................ 251 BIBLIOGRAPHY.______________________________________________________ 257

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Introduction

1. What is the KCA? Approximately 1,500 years ago John Philoponus, a Christian Neoplatonist, proposed a simple argument for the existence o f God. Stated in modus ponens form, the argument runs thus: (1) (2) (3)

Whatever comes to be has a cause o f its coming to be. The universe came to be. Therefore, the universe has a cause o f its coming to be.

Due to the influence o f William Lane Craig, a contemporary analytic philosopher who defends a version o f Philoponus’ argument, this argument and the family o f arguments that support it have come to be known as the “kalam” cosmological argument (henceforth KCA).1 If proved to be sound, the KCA has profound implications for the philosophy of nature and the philosophy of religion. First, it shows that the universe did not exist forever but instead came to be. When properly understood, this coming-to-be o f the universe is recognized as a coming-to-be simpliciter, that is, as a coming into being ex nihilo. Second, the argument entails that the coming-to-be o f the universe was caused by something that transcends the universe itself. As the transcendent cause brought the universe into existence ex nihilo, it is appropriate to describe this transcendent cause as a creator. Third, as there are good reasons for holding that only a being that possesses all of the pure perfections could

1 In this introduction I will use “KCA" as shorthand for the entire family o f arguments that attempt to prove the existence o f God from the finitude o f the past. For the remainder o f the dissertation I will focus exclusively on contemporary variants o f the argument that either arise from or make reference to Craig's work. Unless specifically noted, the terms “KCA’*and “kalam" should not be read as historical allusions to an important branch o f medieval Muslim religious and philosophical speculation but instead as denoting the argument in its specifically contemporary setting.

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have the power to create, and only a deity could possess all o f the pure perfections, it follows that the transcendent creator o f the universe is none other than God.2 Though the KCA is o f ancient provenance and the cluster o f issues raised by the argument have been discussed at a high level o f sophistication from the argument’s very inception, the KCA fell out o f favor during the nineteenth century; serious interest in the KCA such as is found in the contemporary literature is o f comparatively recent origin. As late as 1979 a view like the following was customarily relegated to the extreme fringes o f the philosophy o f religion: “In my opinion the cosmological argument which is most likely to be a sound and persuasive proof for the existence o f God is the kalam cosmological argument based on the impossibility o f an infinite temporal regress o f events.”3 The prescience o f Craig’s remark is evidenced by the remarkable resurgence of and the continued philosophical interest in the KCA in the last decade. Three factors may be singled out as especially important in explaining this renewed interest: publication of extensive historical studies have revealed the rich and varied history o f the argument,4

2 While I believe that the God whose existence is proven through the KCA can ultimately be identified with the God who is worshiped in the three great monotheistic faiths, I also accept a division o f labor between philosophy and theology sim ilar to that espoused by Aquinas. The philosopher is not in a position to demonstrate certain revealed truths, e.g., the doctrine o f the Trinity, because such revealed truths exceed the capacity o f natural reason to demonstrate. Truths o f this sort are not properly said to be irrational but rather suprarationaL See Summa contra gentiles 1.3. 3 William Lane Craig, The Kalam Cosm ological Argument (London and Basingstoke: The Macmillan Press Ltd, 1979), 6 3 .1 will abbreviate this title to TKCA. 4 Pride o f place must be given to the extensive translation efforts o f the Aristotelian commentators o f late antiquity initiated under the leadership o f Richard SorabjL See for instance the translations o f John Philoponus, A gainst A ristotle, on the E ternity o f the World, trans. Christian Wildberg (London: Gerald Duckworth & Co., 1987) and his great opponent Simplicius in John Philoponus and Simplicius, Place. Void, and Etem ity-Philoponus: Corollaries on Place and Void; Sim plicius: A gainst Philoponus on the Eternity o f the W orld, trans. David Furley and Christian Wildberg (Ithaca: Cornell University Press, 1991). In the medieval Islamic, Jewish, and Christian periods key studies include Herbert A. Davidson, Proofsfo r Eternity. Creation and the Existence o f C od in M edieval Islam ic and Jew ish Philosophy (New York and Oxford: Oxford University Press, 1987), R.C. Dales, M edieval D iscussions o f the E ternity o f the W orld (Leiden: Brill,

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advances in mathematical approaches to the infinite in the late nineteenth and twentieth centuries have allowed clearer presentation o f the more abstract philosophical forms o f the argument,5 and the timely development o f Big Bang cosmology has promised surprising empirical confirmation o f the central contention o f the KCA, namely, that the past existence of the universe is finite. All three approaches, the historical, the mathematical, and the scientific, are woven into Craig’s 1979 work The Kalam Cosmological Argument. It is difficult to overstate the importance Craig’s work has had in contemporary discussions o f the KCA.6 While Craig would be the first to acknowledge his philosophical debt to previous thinkers, the shape and trajectory of the last two decades o f analytic speculation bear the unmistakable stamp o f Craig’s influence. The formal shape o f the argument, the variety o f issues considered to be significant to discussions o f the KCA, and the very name of the argument under discussion all find their origin in Craig. In addition to the early presentation of the KCA found in TKCA, Craig has authored an impressive number o f articles and book contributions that elaborate and defend his position. He has

1990), Ernst Behler, D ie Ewigkeit der W elt (Munchen: F. Schoningh, 1965). Under-appreciated discussions o f the argument appear in early modem philosophy, for example in the writings o f the Cambridge Platonist Ralph Cudworth. A noteworthy though somewhat truncated version o f the KCA appears as the thesis o f Kant’s First Antinomy: see CPR A426/B454. Afler Kant’s critique, however, discussion o f the argument abated and the distinctive KCA approach to proving the existence o f God fell into neglect for approximately 150 years. Philosophical discussions o f the KCA appeared sporadically in the early and mid-twentieth century, any list o f which should include the treatments o f the Thomist Fernand Van Steenberghen and of philosophers influenced by Kant such as G J . Whitrow and Pamela Huby. It was not until the publication o f Craig’s work, however, that discussions o f the KCA blossomed. Consideration o f various issues surrounding the KCA now accounts for a steady stream o f articles published in the analytic philosophy o f religion and the philosophy o f science. 5 Georg Cantor’s development o f transfinite mathematics is crucial here. More will be said about Cantor and the implications o f his work in the presentation o f Craig’s 1979 version o f the argument in chapter 1. 6 It is to be noted that interest in Craig’s contemporary restatement o f the KCA is almost exclusively an Anglophone phenomenon. Judging from a survey o f the literature, it can be said that Continental Europe has essentially ignored Craig’s work for the past two decades.

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also written (with Quentin Smith) a second book dedicated to the KCA, entitled Theism, Atheism, and Big Bang Cosmology.7 Besides Quentin Smith, who is the foremost critic o f the KCA, significant contributions to the contemporary understanding o f the KCA have been made by (among others) Adolf Grunbaum, Norman Kretzmann, J.P. Moreland, David Oderberg, Graham Oppy, and Robin Small. Their investigations, which are subsequent to Georg Cantor’s mathematical researches into the nature o f the infinite, have advanced the KCA far beyond its previous formulations: issues surrounding the argument that were once major sources of philosophical puzzlement—such as how an actually in fin ite set can be given a consistent description, and how the actual infinite and the potential infinite are related—can now be handled with clarity and precision. What is more, the current situation is unusually promising in that there is general agreement about what tools need to be brought to bear on the problem (e.g., transfinite mathematics, thought experiments), even if there is still little consensus on how those tools should be applied. Though it would be imprudent to expect a definitive resolution o f how the KCA should be assessed any time soon, the current state of research is ripe for a consolidation and clarification o f the key points at issue in the KCA. 2. Why this dissertation was written Much good work has been done on the KCA, and several key themes in the argument have been identified and pursued in depth. However, it has been over twenty

7 W illiam Lane Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (New York: Oxford

University Press, 1993). Henceforth, TA&BBC

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years since any systematic presentation o f the argument as a whole has been attempted.8 The body o f literature relating to the KCA has grown to a significant bulk, and there is now a real danger o f fragmentation, duplication, and misassessment due to the plurality of interpretations that the argument has received. So, the purpose o f this dissertation is to perform the scholarly service of laying bare the logical structure o f the KCA as a whole. Besides, it is time-consuming to track down all o f the relevant articles needed to build up a complete picture o f the KCA. This difficulty arises from two sources. First, many important articles are located in lesser-known journals. Second, the journals and monographs wherein topics touching on the KCA are discussed cut across several disciplines: philosophy of science, philosophy o f religion, philosophy o f logic, metaphysics, philosophy of mathematics, history o f philosophy, philosophy o f time, and theology—a list that is by no means exhaustive, for the KCA appears in works o f Christian apologetics, popularizations o f contemporary science, and in specialized scientific journals. Thus, another reason for writing this dissertation is to provide a guide to the significant literature on the KCA by providing a report on the “state o f the question” in contemporary analytic philosophy. Even so, I have been obliged to focus my attention on but one important strand o f the KCA literature—a concession to practical limits o f space and time that I elaborate more precisely in the next subsection.

8 The brief summary o f the KCA given in Chapter 1 o f TA&BBC is simply an excerpt o f TKCA. This is appropriate given the arm s and audience o f TA&BBC, b at much important augmentative detail is omitted. The omissions o f TA&BBC are unfortunate in that some participants in the debate appear to have taken TA&BBC for their starting point without going back to TKCA for important clarifications. This situation may be rectified somewhat in the near future with the recent (2000) softcover reprint o f TKCA.

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In addition to the above-mentioned ambitions regarding the KCA, I aspire to help move the discussion o f the argument beyond its current boundaries. I wish both to shore up some o f the weaker points o f the KCA in its current form, and to demarcate a path of future philosophical and investigative development. The key to shoring up the deficiencies of the KCA lies in situating the argument within an appropriate metaphysics. By situating the KCA within a substance-based metaphysics, it is possible to come to a more precise understanding o f both how and why the argument reaches the theistic conclusion its defender claims it does. It is hoped that the foundations laid here will form the basis of future work on the argument, tying into eventual articulations o f revised theories of causality and free agency. 3. Order of treatment Support for the KCA is drawn from two sources: philosophical arguments, which draw upon the traditional disciplines o f metaphysics, the philosophy o f nature, and the philosophy o f mathematics; and empirical confirmations, which draw upon current scientific speculation concerning Big Bang cosmology. This dissertation is intended as a critical investigation and development o f the contemporary philosophical strand o f the KCA. While occasional mention will be made o f the history o f the argument, this will always be done within the context o f a contemporary assessment o f the KCA. One frequently encounters philosophers who advance historically-derived responses to the KCA on their own merits.9 In all such cases I will simply accept the historical interpretation given

9 A good example o f this may be found in J J . M acintosh, "St. Thomas and the Traversal o f the Infinite," Am erican Catholic Philosophical Q uarterly 68, no. 2 (1994): 157-77.

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and assess the resultant arguments on their own merits. While it is true that getting the historical story straight is both desirable and interesting in its own right, the state of the question concerning the contemporary KCA is largely unaffected by the correctness o f the various historical interpretations encountered.10 My treatment of explicitly scientific versions o f the KCA will be conducted along the same lines: whenever possible I will avoid entering the current debate over how particular results o f current scientific cosmology are to be interpreted. This approach is motivated not only by the tendency o f the latest scientific scholarship to change only slightly less rapidly than the fashions of Parisian designers, but is also motivated by the consideration that the arguments embedded within the philosophical strand o f the KCA are largely detachable from the specific commitments o f contemporary science.11 It may also be noted that the philosophical strand o f the KCA itself affords considerable room for clarification and development. This dissertation falls into two main parts. Part I, comprising chapters 1 and 2, will set forth the logical structure o f the KCA as it is found in the literature (chapter 1) and will present an organized taxonomy o f the objections to the KCA that have been made in the literature (chapter 2). Part II, comprising chapters 3 through 6, focuses on the most

10 It is preferable to approach Craig’s own work this way: scholarly reception o f the historical part o f TKCA has been less enthusiastic than is the case for the rest o f the book. 11 Which is not to suggest that it is possible to detach the philosophical strand o f the KCA from all forms o f empirical confirmation altogether. The KCA defender relies upon certain basic facts about the world (and even certain interpretations o f those facts) that are commonly appealed to within contemporary science. For instance, any plausible scientific physics will have to give some account o f change, and the KCA will appeal to facts about change. Nor, in setting aside consideration o f the scientific strand o f the KCA, do I mean to suggest that there are no interesting and important arguments to be found in that strand o f the KCA. Craig has developed and refined a number o f arguments in support o f the KCA by drawing upon the resources o f contemporary scientific cosmology. The issue, rather, is one o f emphasis. Instead o f working out a defense o f the KCA from within the philosophy o f science, I propose to investigate the strand o f the KCA that is situated within the philosophy o f nature.

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important species o f objection to the KCA and attempts to reformulate the KCA in a way that allows the objection to be met. In this part I argue that the introduction o f a metaphysics o f substances allows the KCA defender to effectively answer certain challenges concerning the logical possibility o f instantiating an actual infinite in nature. In chapter 1 the KCA is presented in the form in which it is found in the current literature. In particular, I will focus on the 1979 version o f the KCA as Craig presents it in TKCA. Later developments in Craig’s approach will be taken up in chapter 2, as will certain detailed responses he develops in the appendices of TKCA.12 It is to be noted that Craig’s version o f the KCA is developed without any explicit allegiance to a metaphysics of substances.13 Chapter 2 lays out a taxonomy o f the various objections that have been made to the KCA, distinguishing (for example) among objections that call premise (1) into doubt,14 objections that call premise (2) into doubt, and objections that argue that what the conclusion (3) arrives at is not really God. Various sub-species o f each o f these kinds of objections can also be distinguished.

12 In the first appendix o f TKCA Craig relates the KCA to Zeno’s paradoxes and the analytic literature on “supertasks.” In the second appendix Craig discusses the thesis o f Kant’s First Antinomy. The germs o f Craig’s more detailed responses to critics is often to be found in these appendices and so reserving detailed consideration o f their contents until chapter 2 w ill help avoid needless repetition. 13 Based solely on texts available in TKCA it may reasonably be suspected that Craig rejects a metaphysics o f substances conceived along Aristotelian lines. For instance, Craig rejects Aquinas’ position that God enjoys an eternal mode o f existence after creation because Aquinas’ arguments for God not being really related to creatures turn upon Aristotelian understandings o f substance, relation, and accident: Although Aquinas argues that God rem a in s timeless after creation because He sustain s no real relation to the world, Aquinas’s solution is singularly unconvincing. For his solution is system-dependent upon a peculiar understanding o f relation as an accident inhering in a substance. Abandon these Aristotelian categories and it seems foolish to say God is not really related to the world as Creator to creature. If God is related to the world, then it seems most reasonable to maintain that God is timeless prior to creation and in time subsequent to creation. (TKCA, 152; I have omitted Craig’s footnote reference.)

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Chapter 3 focuses on one particular kind o f objection to the KCA, clear examples of which may be found in the work o f Graham Oppy. These are objections to premise (2), and they rely on certain thought-experiments designed to show that an actual infinity is possible. I will grant that these thought-experiments show that an actual infinity is possible in the sense o f being consistently conceivable. But I will also point out that if there is another kind o f possibility, one stronger than mere consistent conceivability, and moreover that this other kind is the one that is relevant for the KCA, then the defender o f the KCA could refute these objections by showing that they are making use of the wrong kind of possibility. Adopting a suggestion made by David Braine, I name the stronger sort of possibility required for the KCA “factual possibility.” Chapter 4 lays the metaphysical groundwork needed to justify and clarify this stronger kind o f possibility. The idea advanced is that not only should possibility be conceived in terms o f factual possibility, but also that the specific subdomain o f factual possibility that applies to the KCA is a type o f possibility that is grounded in the causal powers o f substances. This subdomain o f factual possibility I name “substantial possibility.” The notion of “substance” required for a proper understanding o f substantial possibility is worked out by drawing upon resources available within analytic philosophy. The specific analytic theory o f substance I defend is developed on the basis o f the work of G.E.M. Anscombe, David Braine, and Sarah Broadie. Anscombe reintroduces analytic philosophy to the notion o f substance as it is found in Aristotle’s Categories; namely, substance is that which functions as a subject o f predication but is not predicated of other

14 For these premises see the argument given in section I above.

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things. Braine elaborates Anscombe’s position, both noting the connections this idea of substance has with linguistic philosophy and bringing into view the idea o f substance as the locus o f active causal power. Broadie furnishes additional arguments for the metaphysical primacy o f substance and also helps fill in some details regarding how the active powers of substances are expressed in causation. The point about causality is further developed on the basis o f Rom Harre and E.H. Madden’s work on causal powers. My position is that the notions o f substance and causality already available within analytic philosophy are sufficient for the purposes of the KCA. Chapter 5 applies the results o f chapters 3 and 4 to the KCA. Three points will be made. First, it is explained why factual possibility, not mere logical possibility, is the right notion o f possibility to use in discussions of the KCA. Second, the notion o f substantial possibility developed in chapter 4 will be used to show that the anti-KCA thoughtexperiments discussed in chapter 3 do not yield the correct conclusion, i.e., they do not demonstrate that an actual infinite is substantially possible. Third, I will again use the notions o f factual and substantial possibility to show that the pro-KCA thought-experiments discussed in chapters 1 and 2 do use the correct notion o f possibility. Chapter 6 contains a summary o f the results obtained. Investigations such as the present one test the adequacy o f the resources of analytic metaphysics in one branch o f natural theology. This dissertation makes an original contribution to the field because Craig’s version o f the KCA is reworked and clarified (chapters I and 2), and because currently-outstanding objections to the KCA that have not yet been adequately met within the literature are resolved (chapters 3 through 5).

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P arti The Kalam Cosmological Argument in Contemporary Analytic Philosophy: The State of the Question

Chapter 1 4. Craig’s version o f the KCA as presented in TKCA Although Craig discusses each o f (1) through (3) o f the KCA, he perceives the main argumentative burden to lie on premise (2) and hence immediately turns to an examination o f that proposition. In this dissertation I will diverge from Craig’s actual order of presentation in TKCA and treat each step o f the argument in the order in which it appears. 4.1 Craig on premise 1: Whatever comes to be has a cause o f its coming to be Craig’s defense of premise I in TKCA is extremely sketchy. He begins with the following comments: We may now return to a consideration o f our first premiss, that everything that begins to exist has a cause o f its existence. The phrase ‘cause of its existence’ needs clarification. Here I do not mean sustaining or conserving cause, but creating cause.... Applied to the universe, we are asking, was the beginning o f the universe caused or uncaused? In this book I do not propose to construct and elaborate defence o f this first premiss. Not only do considerations of time and space (in their practical, not philosophical, sense') preclude such, but I think it to be somewhat unnecessary as well. For the first premiss is so intuitively obvious, especially when applied to the universe, that probably no one in his right mind really believes it to be false. Even Hume himself confessed that his academic denial o f the principle’s demonstrability could not eradicate his belief that it was nonetheless true. Indeed the idea that anything, especially the whole universe, could pop into existence uncaused is so repugnant that most thinkers intuitively recognize

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that the universe’s beginning to exist entirely uncaused out of nothing is incapable o f sincere affirmation.1 As may be expected, this approach provoked immediate reaction. In a series of journal exchanges, most notably with Quentin Smith, Craig has been most appropriately pressed to define and defend his views on causation.2 Craig’s exchanges with Smith and others will be surveyed in chapter 2. In fact, the curious lack o f suasive power demonstrated by Craig on this point was one of the factors that motivated the development o f the theory o f factual possibility presented in part H o f this dissertation. To anticipate somewhat, Craig’s underdetermined views on causation evidenced in his desultory defense of premise 1 make it difficult for him to respond to critics who base their objections to the KCA on the logical possibility o f instantiating the actual infinite in various forms. Although Craig is himself aware o f the important difference between logical possibility and various stronger notions o f possibility, and he firmly asserts that the KCA must be situated within a modal context richer than that o f mere logical possibility, what Craig intends by his references to a stronger notion o f possibility is unacceptably vague.3

1 TKCA 141.1 have removed Craig’s footnote citing the relevant passages in Hume. 2 The fullest treatm ent Craig presents in favor o f premise 1 is to be found in essays 5 and 10 o f TA&BBC. 3 It should be mentioned that Craig uses several different terms for the restricted domain o f possibility he has in mind, hi TKCA he typically employs variants o f “real possibility.” In his articles he sometimes speaks of ‘’metaphysical possibility” and at other tunes he speaks o f "broadly logical possibility.” Detailed exposition o f what he means and how these differently-named sorts o f possibility m ight (or might not) differ from one another are not forthcoming in Craig’s work. Would Craig unreservedly endorse the accounts o f factual possibility and substantial possibility I present in chapters 3 and 4? Probably not—but where he would distance him self from my position is an open question. To simplify matters, I will consistently refer to "factual possibility” in my presentation o f the KCA. This is not what Craig literally says. It is, however, what I think he should say. (M y apologies to W illiam Craig for adopting this device.) A representative example o f Craig’s use o f the distinction between logical and factual possibility is apposite here. In a brief survey o f analytic authors who have dismissed the KCA Craig offers the following critique o f W J. Matsom M atson sim ilarly asserts that since there is no logical inconsistency in an infinite series o f numbers, there is no logical inconsistency in an infinite series o f events, and therefore the first cause argument is incurably fallacious Matson foils to understand that the kalam argument holds that the existence o f an actual infinite is really, not logically, impossible.

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Continuing with Craig’s defense of premise 1, we find that he begins with an appeal to authority. A diverse wrangle o f philosophers is canvassed, including Sir Anthony Kenny, CJD. Broad, and P J . Zwart, who all comment on the intuitive plausibility o f the principle ex nihilo nihilJit.4 The purpose o f this assemblage is to create a presumption against David Hume’s famous challenge to that principle, which is the next subject introduced. In his response to Hume, Craig draws on the work o f G.E.M. Anscombe and F.C. Copleston. In a well-known article, Anscombe argues that Hume’s criticism o f the principle “whatever comes to be has a cause o f its coming to be” involves an illegitimate inference from something’s being imaginable to its being factually possible.5 As Craig then remarks. All Hume has really shown is that the principle ‘everything that begins to exist has a cause o f its existence’ is not analytic and that its denial, therefore, does not involve a contradiction or a logical absurdity. But just because we can imagine something’s beginning to exist without a cause it does not mean that this could ever occur in reality. There are other absurdities than logical ones. And for the universe to spring into being uncaused out o f nothing seems intuitively to be really, if not logically, absurd.6 Having concluded his response to Hume, Craig proceeds to sketch two lines of argument in favor o f the causal principle enshrined in premise 1.7 The first line o f argument he calls “the argument from empirical facts,” the second “the argument from the a priori

That there is a difference can be seen in the fact that God’s non-existence, if He exists, is logically, but not really, possible; if He does not exist, His existence is then logically, but not really, possible. Analogously, the existence o f an actual infinite is really impossible, even if it may not involve logical contradiction. {TKCA, 155 n. 17) 4 See TKCA, 141-44. 5 See G.E.M. Anscombe, "Whatever Has a Beginning o f Existence Must Have a Cause: Hume's Argument Exposed," in The C ollected Philosophical Papers o f G.E.M. Anscombe (Minneapolis: University o f Minnesota Press, 1981), 93-99. 6 TKCA, 145. 7 It should be noted that Craig’s argument is overly compressed here, for he shifts without warning from discussing die factual impossibility o f Hume’s imagined cases to a defense o f the reality o f causation broadly construed. The jum p is not much softened by the fact that Craig explicitly rejects certain causal theories, specifically the occasionalism o f al-Ghazali and Malebranche, later in the book. See TKCA, 181.

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category o f causality.” According to the first line o f argument, denying the reality of causality is arbitrary because there is no better-confirmed empirical proposition. “The empirical evidence in support o f the proposition is absolutely overwhelming, so much so that Humean empiricists could demand no stronger evidence in support of any synthetic statement.”8 The second line o f argument Craig develops from the work o f Stuart Hackett.9 Briefly, Hackett defends a neo-Kantian epistemology within which “the categories have application beyond the realm o f sense data”10 and do, in fact, “furnish knowledge o f things in themselves.”11 In sum, the position that Craig adopts from Hackett is one where "‘the categories are both forms o f thought and forms o f things—thought and reality are structured homogeneously.”12 Craig then argues that since causality is a validly-derived category and since validly-derived categories reveal the real structure o f both thought and world, it follows that the causal principle “whatever comes to be has a cause o f its coming to be” must be a synthetic a priori proposition. Since the principle is both universal and a necessary condition of thought it is a priori, and since the principle is not analytic (as Hume showed), it must be synthetic. And, with the remark that Hackett has provided an attractive defense o f the reality o f causation that merits further research, Craig brings his discussion of premise I to a close.13

8 TKCA, 145. 9 Craig’s references are to Stuart Hackett, The Resurrection o f Theism (Chicago: Moody Press, 1957). 10 TKCA, 146. 11 Ibid. 12 IbicL, 147. 13 IbicL, 147-48.

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4.2 Craig on premise 2: The universe came to be Developing a case for premise 2 requires the introduction of several technical specifications. Most o f the KCA defender’s work occurs in this preliminary stage, for the actual arguments for premise 2 are relatively straightforward once the proper interpretive framework is in place. Thus, in the subsequent subsections the following topics will be addressed. First, a technical vocabulary for various distinctions that must be made in discussions of the infinite is presented. Second, the portions o f set theory and Cantorian transfinite number theory that are required for discussion o f the KCA are expounded.14 Third, Craig’s philosophical summary of the various camps o f philosophical thought regarding the ontological status o f mathematics is presented. Fourth, taking the articulations made in response to the three prior points as given, Craig’s justifications for premise 2 are set forth. To keep the argumentative moves Craig makes in their proper perspective, it is important to introduce a few brief remarks here concerning the overall strategy of the KCA. The first point to keep in view is that Craig will actually offer two strands o f argument in support o f premise 2.IS The first such strand o f reasoning consists in arguments that aim to show that it is impossible for an actual infinite to obtain in nature.16 The second strand of argument in support of premise 2 turns upon Craig’s showing the impossibility o f forming an actual infinite through a process of successive addition. In both cases it is crucial that the mathematical notion o f the actual infinite be precisely understood. To clarify this crucial

14 Additional details concerning Cantor’s system are presented in an appendix to this dissertation. 15 See e.g. TKCA, 65, 69, & 102-103. 16 The precise understanding o f the term “actual infinite” will be given in the next section.

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concept Craig turns to the work o f Georg Cantor and the development o f axiomatic set theory that followed Cantor’s foundational efforts. Once the notion o f the actual infinite is properly understood, Craig argues that, while it may well be the case that the notion of the actual infinite is conceptually consistent and mathematically fruitful, it is intuitively obvious that the actual infinite cannot have extra-mental existence. The inapplicability of Cantor’s actual infinite to the real world is brought out by presenting several thought experiments wherein a literal application o f Cantor’s work to the realm o f nature yields absurd results. Since Cantor’s mathematical description o f the actual infinite is the clearest and most plausible understanding o f actual infinity we currently have or indeed are likely ever to possess, the absurd results generated by Craig’s thought experiments together yield a conclusive reductio ad abswrdum in favor o f premise 2.17 4.2.1 Preliminary remarks and terminology Craig identifies the main argumentative burden o f the KCA to fall on premise 2 and it is to the defense o f this premise that he dedicates the bulk o f his book. It should be noted that the account o f Craig’s position I give below departs from the order o f presentation adopted in TKCA. This is done with a view toward clarifying and improving the taxonomic efforts o f chapter 2. It is hoped that what is lost in such a departure from Craig’s order of presentation will be made up for in terms o f the greater logical clarity gained.

17 Craig details this strategy in TKCA, 69—72. O f course, more work needs to be done by the defender o f the KCA than merely showing the inherent absurdity o f finding the actual infinite in rerum natura. I would argue, however, that in securing this key point the defender o f the KCA is well along the path to proving the existence o f the Deity. The position o f the KCA defender is analogous to that St. Thomas found him self in after having presenting the Five Ways: if the arguments o f 5.7! L2.3 are sound, then extracting all o f the pure perfections from what has gone before is a relatively straightforward task.

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As a number o f authors have commented on the KCA and not all o f those commentators have restricted themselves to Craig’s idiom, a few preliminary remarks on terminology are apposite. Unless otherwise noted, in what follows whenever the term “infinite” is used I mean to be understood as referring to the “mathematical infinite” and not to the “metaphysical infinite.”18 By “metaphysical infinite” I denote an ontologically positive qualitative lack of limit. Metaphysical infinity thus marks off a family of concepts that find their proper home within philosophical theology: omnipotence, omniscience, and omnibenevolence are examples. Within philosophical theology talk o f the metaphysical infinite is associated with notions o f perfection, unity, wholeness, and completeness. Another term for the metaphysical infinite (commonly found in discussions either by or of Cantor) is “absolute infinite.”19 The “mathematical infinite,” on the other hand, denotes a quantitative lack of limit. This is the kind of infinity associated with the process o f counting, appealed to in explanations o f the continuum and open geometric curves, and talked about in discussions o f limits in algebra and the calculus. The mathematical infinite is further distinguished into the “potential infinite” and the “actual infinite.” The “potential infinite” denotes a limitless quantitative process. Potential infinity is therefore a dynamic concept: endless addition.

18 I borrow this terminology from A.W. Moore. 1 do not, however, accept Moore’s definitions o f these terms. 19 In this dissertation the term “metaphysical infin ite” will be preferred. This for two reasons. First, it is easy to confuse the terms “absolute infinite” and “actual infinite,” the latter o f which plays a key role in Craig’s version o f the KCA. Second, although “absolute infinite” is the preferred language o f Cantor, Cantor himself often fails to distinguish between metaphysical and mathematical senses o f infinity. The confusion in Cantor’s thought seems to arise through neglect o f the analogies embedded in the particular formula that guides his thinking on the absolute infinite, viz. that the absolute infinite is “that than which nothing greater can be thought.” Thus, Cantor moves easily from discussions o f God’s absolute infin ity to discussions o f a (supposed) quantity greater than any other possible quantity. Thu latter notion, as Cantor him se l f notes, is absurd: there can be no greatest transfinite quantity. For more com m en ts on this subject see Robin Small. “Cantor and the Scholastics,” American Catholic Philosophical Quarterly 66, no. 4 (1992): 407-28.

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endless division, endless succession: when one element is given another always follows. The potential infinite, o f its very nature, is never complete. The potential infinite is also known as the “improper infinite” and, more suggestively, as the “variable finite.”20 The “actual infinite,” on the other hand, denotes an unlimited simultaneous quantitative whole. The concept o f an actual infinity is therefore static: the whole in question is taken as a complete quantitative unity given all at once. An example o f the actual infinite drawn from the science o f continuous quantity (i.e., geometry) would be a line that lacks endpoints. From the science o f discrete quantity we have the example o f Cantor, who stood outside (so to speak) the set o f natural numbers and grasped them as a completed totality. The actual infinite is also known as the “proper infinite.”21 To add further precision to the notion of the actual infinite, Cantor introduces the idea o f quantities that are greater than any finite quantity. Such quantities he calls “transfinite,” and the numbers that stand for such

20 Although in some contexts Craig employs the Cartesian term ‘indefinite” as a synonym for the potential infinite {vide e.g. TKCA, 69) I will avoid using “indefinite” in this way in formal contexts. 21 Similar distinctions are to be found in Cantor. Jourdain summarizes Cantor’s position as follows: The Grundlagen begins by drawing a distinction between two meanings which the word “infinity” may have in mathematics. The mathematical infinite, says Cantor, appears in two forms: Firstly, as an im proper infinite (Uneigentlich-Unendliches), a magnitude which either increases above all limits or decreases to an arbitrary sm alln ess, but always re m ains finite; so that it may be called a variablefin ite . Secondly, as a definite, a proper infinite {Eigentlich-U nendliches), represented by certain conceptions in geometry, and, in the theory o f functions, by the point infinity o f the complex plane. In the last case we have a single, definite point, and the behaviour o f (analytic) functions about this point is e x am in ed in exactly the same way as it is about any other point Cantor’s infinite real integers are also properly infinite, and, to emphasize this, the old symbol “ao,” which was and is used also for the improper infinite, was here replaced by ‘m.* (Georg Cantor, Contributions to the Founding o f the Theory o f Transfinite Numbers, trans. Philip E. B. Jourdain (New York: Dover, 1955), 55-56.) For references to Cantor, see Georg Cantor, Gesammelte Abkandlungen m athem atiscken und philosophischen Inhalts, ed. Em st Zermelo (Hildeschcim: Georg Ohns, 1962). The distinction between the improper and the proper infinite may be found m Gesammelte Abhandlungen, 165-66. Cantor’s novel use o f the “co” symbol is discussed in ibid., 195.

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quantities he calls “transfinite numbers.” (Cantor’s theory o f transfinite numbers is treated in section 4.2.2 and in the appendix.) The actual and potential infinite can also be mapped onto what amounts to a grammatical distinction. Consider the different structural parsings of: “This body can move infinitely fast.” Understood in its “categorematic” sense, this means that the body in question is capable o f achieving a speed that surpasses any finite measure; that is, the body can move at an actually infinite speed. On the other hand, if “This body can move infinitely fast,” is understood in its “syncategorematic” sense, what one is saying is that there is no limit to the finite speeds that this body is capable o f obtaining; that is, the speed of the body is potentially in fin ite . Finally, in deference to an important body of related literature, I will employ the term “supertask.” “Supertask” denotes a completed in fin ite task. Since the in fin ite task realized through the performance o f a supertask is conceptualized as a completed whole, the term “infinite” in “completed infinite task” must be construed in a categorematic sense. As will become apparent later on, it is important to note that the realization of a categorematically infinite supertask is supposed to be brought about through a dynamic, syncategorematically infinite process.22 In the literature on supertasks it is common to find an additional element in the definition o f “supertask,” viz., that the in fin ite task is to be completed in a finite amount o f time. I will not include the note o f temporal finitude as a necessary condition in my use o f the term supertask but instead will use the term to cover cases o f infinite tasks that are supposed to be completed in either finite or infinite quantities

22 This immediately raises the problem o f how a supertask is supposed to be completed. Craig addresses this problem several times; see section 4.2.6 below for further details.

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o f time. Typical examples o f supertasks include Zeno’s paradoxes o f motion, Thomson’s lamp,23 and Bertrand Russell’s fable about a man who counts through all o f the natural numbers in two minutes flat.24 4.2.2 Exposition o f Cantorian transfinite number theory The purpose o f this section is to give a summary of Cantorian transfinite number theory as it applies to the KCA.25 Given the pragmatic focus, I will be glossing over a number o f mathematically significant details. For instance, I will not be concerned here with the continuum problem,26 and I will give a brief treatment o f only one o f the betterknown paradoxes o f the infinite, namely Russell’s paradox.27 Although Craig gives an accessible and remarkably clear exposition o f transfinite number theory in TKCA, he omits or states too briefly some technical points that were to become relevant to the KCA debate in its subsequent development. Instead o f reserving discussion o f those issues to chapter 2 ,1

23 J.F. Thomson, “Tasks and Super-Tasks,” Analysis 15 (1954): 1-13. 24 Bertrand Russell, M ysticism and Logic, 2d ed. (Garden City, NJ: Doubleday and Company Inc., 1957). 25 It might be mentioned here that in drawing upon the work o f Cantor for his proof o f the finitude o f the past Craig is on good historical ground: Cantor him self “suggested that his theory o f transfinite numbers could also be used to demonstrate the absolute impossibility o f the eternity o f time, space, and matter.” (Joseph Warren Dauben, Georg Cantor: His M athematics and Philosophy o f the Infinite (Cambridge, MA and London, England: Harvard University Press, 1979).) 26 That is, that 2Ka = X ,. Succinctly stated. Cantor's continuum hypothesis is that the cardinality associated with the real numbers (Le., the set o f numbers denoting a continuum) constitutes the next largest infinite cardinal after X0. Assuming only the standard nine axioms o f a Zermelo-Fraenkel set theory it is impossible to prove either that the continuum hypothesis is true or that it is false. Introduction o f a tenth axiom would allow derivation o f 2S° = N „ but none o f the tenth axioms proposed thus far have the same intuitive appeal as the first nine. W ithout such intuitive appeal the situation appears to be much like that encountered by Russell, who found him self obliged to introduce an axiom o f infinity and thereby vitiated his project o f reducing all o f mathematics to self-evident rules o f logic. A convenient exposition o f the continuum problem may be found in A. W. Moore, The Infinite (London and New York: Routledge, 1995), 154-55. For more details see Raymond M. Smullyan, “The Continuum Problem,” in Encyclopedia o f Philosophy, voL 2, ed. Paul Edwards (New York and London: Macmillan Publishing, The Free Press and Collier Macmillan Publishers, 1967), 207-12. There is also a generalized form o f the continuum hypothesis which asserts that for every ordinal n it is the case that = 2K*. For a compact discussion o f some technical aspects o f the continuum hypothesis see Alexander Abian, The Theory o f Sets and Transfinite Arithm etic (Philadelphia and London: W.B. Saunders Company, 1965), 392-94.

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will include them here for ease o f reference. Additional details regarding transfinite number theory are to be found in the appendix. 4.2.2.1 Brief history o f mathematical speculation on infinite The majority view concerning the nature o f the infinite that prevailed from the time o f Aristotle until the middle o f the nineteenth century was that of the potential infinite.28 The predominant view was that the actual infinite was impossible to realize in nature and was dispensable in mathematical practice.29 According to Aristotle, the infinite exhibits itself in different ways—in time, in the generation o f man, and in the division o f magnitudes. For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different.30 For over two thousand years the standard model for the mathematical infinite—a model well established by the time Aristotle mentions it in the quotation above—was that of a magnitude possessing a potency for being indefinitely divided or extended. A magnitude

27 Craig himself focuses on Russell’s paradox although he also mentions the antinomies o f Burali-Forh and Cantor. See TKCA, 90. 28 There were, o f course, some notable exceptions. The actual infinite was championed by such thmlcerc as Giordano Bruno, Spinoza, and Leibniz. Aristotle is careful to note that the use o f “potential’’ in “potential infinite” does not perfectly parallel the usage o f “potential" in other contacts. He writes: “But we must not construe potential existence in the way we do when we say that it is possible for this to be a statue—this will be a statue, but something infinite will not be in actuality. Being is spoken o f in many ways, and we say that the infinite is in the sense in which we say it is day or it is the games, because one thing after another is always coming into existence.” {Physics H I.6,206al9-23.) Unless otherwise noted, all citations o f Aristotle refer to Aristotle, The Complete Works o f A ristotle: The Revised Oxford Translation, ed. Jonathan Barnes. 2 vols. (Princeton: Princeton University Press, 1984). 29 As Aristotle summarizes: Our account does not rob the mathem a ticia n s o f their science, by disproving the actual existence o f the in fin ite in the direction o f increase, m the sense o f the untraversable. hi point o f fact they do not need the infinite and do not use it. They postulate only that a fin ite straight line may be produced as far as they wish. It is possible to have divided into the same ratio as the largest quantity another magnitude o f any size you like. Hence, for the purposes o f p roof it w ill make no difference to them whether the infinite is found among existent magnitudes. {Physics IIL7,207b27—34.) 30 Physics IH.6,206a25—29. A slightly more compressed version may be found in Physics HL6,207a7-8: “something is infinite i f taking it quantity by quantity, we can always take something outside."

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successively operated upon (i.e., repeatedly augmented or divided) will, at each stage, be finite and at no stage will achieve actual infinity.31 Although later mathematicians would eschew Aristotle’s physical examples in favor o f more abstract illustrations (e.g., psychological examples were especially prevalent in the nineteenth century, the mathematical infinity o f the natural numbers being described as the enumeration o f successive thoughts), the conceptual connection with some sort o f process remained. Now, in its connection with a notion o f process, the infinite was hardly unique as a mathematical concept: a vivid, dynamic strain o f mathematical reasoning is evident throughout the history o f mathematics, present everywhere from Newton’s development o f the calculus as a theory o f “fluxions” to contemporary elementary geometry texts that explain the congruency of figures as the ability to lift one figure out o f the plane and superimpose it upon another figure without remainder.32 What is peculiar about pre-Cantorian mathematical speculation about the infinite is the repeated insistence that only a process-based account is appropriate. For instance, in a well-known letter the great mathematician Carl Friedrich Gauss addresses Heinrich Christian Schumacher thus: I must protest most vehemently against your use o f the infinite as something consummated; this use is never permitted in mathematics. The infinite is but

31 As Aristotle writes: “By addition then, also, there is potentially an infinite, namely, what we have described as being in a sense the same as the infinite in respect o f division. For it will always be possible to take something ab extra. Yet the sum o f the parts taken will not exceed every determinate magnitude, just as in the direction o f division every determinate magnitude is surpassed and there will always be a sm aller part." (Physics IH.6,206b 16-20) 32 Neither o f these examples would meet the standards o f rigor demanded o f contemporary m ath em atical practice. Nevertheless, both approaches have heuristic value. I have encountered texts written in the mid^O* century that still explain the differential calculus as “slope finding” (a notion much alrin to Newton’s fluxions). The example o f congruent figures is adapted from a popular geometry text that explains reflections through a line in this way: triangle ABC is a proper reflection o f triangle DEF if and only if it is possible to lift ABC out o f the plane and flip it over onto DEF. From a contemporary perspective this is a shockingly loose explanation, but the student gets the point readily enough. Moreover, it is quite plausible to argue that a dynamic understanding o f mathematics is a valuable aid to mathematical discovery.

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a faqon de parler indicating a limit to which certain ratios may approach as closely as desired when others are permitted to increase indefinitely.33 Interestingly, contemporary mathematicians have defended Gauss’ view—at least in part. The situation regarding the interpretation o f infinity that currently prevails is nicely captured by Fraenkel: In almost all branches o f mathematics, especially in analysis (for instance, in the theory o f series and in calculus, also called ‘infinitesimal calculus”), the term “infinite” occurs frequently. However, mostly this infinite is but a faqon de parler...the statement Iim l/n = 0 n-Ko

asserts nothing about infinity (as the ominous sign oo seems to suggest) but is just an abbreviation for the sentence: '/„ can be made to approach zero as closely as desired by sufficiently increasing the positive integer n. In contrast herewith the set o f all integers is infinite (infinitely comprehensive) in a sense which is “actual” (proper) and not only “potential.”34 In short, standard mathematical practice dictates that one should dispense with appeals to the actual infinite whenever possible. This is an understandable strategy, for the legitimacy of mathematical explanations based on the potential

33 C.F. Gauss, Briefwechsel, ed. C-A.F. Peters, 6 vols., voL 2 (Altona: Gustav Esch, 1860-1865), 269. The letter is dated 12 July 1831. To make his own view more palatable Cantor is willing to employ the traditional language o f “approaching a limit” to explain the theory o f transfinite numbers: “It is even permissible to think o f the newly and [sic] created number QOp. Contrary to what die formula asserts, modal status is not always necessary. There is no antecedent necessity that God create a world compatible with the possible existence o f unicorns, dragons, rocks, mosquitoes, or men. 49 Ibid, 168. In an earlier discussion o f Hume, Braine observes: There is a sense o f the word “contingent”, in which it is intuitively plain, anyway in the case o f most things, that their existence is contingent, namely the sense expressed when, for instance, it is said that you or I “m ight not have existed”, an assertion which one would naturally justify by reference to such facts as that one’s mother might easily have died before one was even conceived. To say that X might not have existed in this sense seems to mean that some prior or, as it were, “ancestral” situation was such as to have causally left it open whether or not X should exist. And in this sense, it is evidently false or nonsensical to

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The upshot is that the free-wheeling notion of causation in terms o f logical possibility (as advocated e.g. by Hume) is a non-starter. It simply is not the case that anything can be the cause o f anything else. Rather, causes produce effects in accordance with the particular factual necessities contextually present. To anticipate the results o f chapter 4, the factual necessities alluded to arise from the specific natures o f the particular substances that are brought into causal relation with one another. Interpreting Braine’s position in metaphysical terms, one can say that for Braine act is absolutely prior not only to potency but to possibility as well. (In this respect Braine’s view has some affinity to a position developed by James Ross.50) Applying the results o f Braine’s analysis to the criticism of the KCA advocated by Oppy, it may be noted that Oppy’s appeal to bare logical possibility (as e.g. in his suggestion that there might be a physically extended infinitely dense entity) is not well founded. As a non-theist Oppy is limited to evaluating the KCA from within the factual modalities appertaining to this universe we inhabit. Appeals to other logically possible universes wherein actual infinities might (or might not) obtain are neither well-founded nor strictly relevant. In his defense o f the KCA, Craig is not asking whether we may infer the existence o f a creator by applying the KCA’s thought experiments to any logically possible world whatsoever. Rather, Craig is asking whether we must posit a creator for this world.

say that God might not have existed, and, if one rejected theistic belief, false or nonsensical to say that the Universe might not have existed. (IbicL, 155.) 50 See James F. Ross, “God, Creator o f Kinds and Possibilities: Requiescant universalia ante r e s in Rationality, Religious Belief, and M oral Commitment.- New Essays in the Philosophy o f Religion, ecL Robert Audi and W illiam J. Wainwright (Ithaca & London: Cornell University Press, 1986), 315-34. Ross develops his position in “The Crash o f Modal Metaphysics,” Review o f M etaphysics 43 (1989): 251-80; and in “Aquinas’s Exemplarism; Aquinas’s Voluntarism,” Am erican Catholic Philosophical Q uarterly 64 (1990): 171-98.

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Answering that question, which is factual in nature, will require a careful and patient investigation o f the factual possibilities that obtain in this world. So, to take but one example, whereas Craig’s comments regarding the nature o f the Big Bang singularity appeal to factual possibilities present in the early universe, and hence retain some degree of legitimacy, the sort of global “it might have been otherwise” imagined by Oppy is philosophically inadmissible. 14. Thought experiments and the KCA In this section three tasks are performed. First, I show that the KCA arguments against the actual infinite can be regarded as thought experiments. Second, having established that the KCA arguments against the actual infinite are thought experiments, I argue that their status as thought experiments entails certain interpretive requirements, among which is the need for evaluating any given thought experiment within its appropriate modal context. To accomplish these two goals I will draw upon the work o f Roy Sorensen, who has proposed one o f the more philosophically sophisticated and appealing accounts of thought experiments to date.51 Third, I evaluate Oppy’s criticism o f the KCA thought experiments.

51 The account I follow is drawn from Sorensen’s Thought Experim ents. Although Sorensen is an excellent

source o f examples o f thought experiments and provides a plausible account o f their general structure and use, I do not accept his position in its entirety. For example, a significant part o f Sorensen’s book is dedicated to articulating a biological/evolutionary model o f die development o f thought experiments: skiU in thought experiments developed in conjunction with the evolutionary development o f the human species. While Sorensen may be right about this, the analogy upon which he bases his argument is weak and the available evidence scanty. (Sorensen has subsequently expanded his evolutionary account: see Sorensen, “Thought Experiments and the Epistemology o f Laws,” Canadian Journal o f Philosophy 22, no. I [1992]: 15-44.) For an insightful critique o f Sorensen by another philosopher who has done important work on the subject o f thought experiments see James Robert Brown, “Critical Notice o f Roy Sorensen Thought Experim ents,” Canadian Journal o f Philosophy 25, no. I (1995): 135-42.

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As a first approximation, the Oxford Companion to Philosophy offers the following account o f thought experiments: thought experiments are employed both by philosophers and by theoretical scientists to examine the implications o f theories and to explore the boundaries o f concepts. They are controlled exercises o f the imagination in which test cases are envisaged with a view to establishing their conceptual coherence or their compatibility with some proposed theory.52 Sorensen refines this insight in several steps. First, he defines what is meant by an “experiment”: “An experiment is a procedure for answering or raising a question about the relationship between variables by varying one (or more) o f them and tracking any response by the other or others.”53 Sorensen asserts that there is a continuity between ordinary experiments and thought experiments, and defends the thesis that “thought experiments evolved from ordinary experiments by a process o f attenuation.. ..[T]hought experiments are limiting cases o f experiment just as circles are limiting cases o f ellipses.”54 Sorensen further notes that experiments are essentially topic-neutral55 and that actual performance is not a necessary feature o f experiments.56 With these precisions in hand, Sorensen is ready to define “thought experiment” as “an experiment...that purports to achieve its aim without the benefit o f execution.”57 To clarify what he means by “purports to achieve its aim without benefit o f execution,” Sorensen writes: “I mean that the experimental design is presented in a certain way to the audience. The audience is being invited to believe that

52 The Oxford. Companion to Philosophy, ed. Ted Honderich (Oxford & New York: Oxford University Press,

1995), s.v. “thought experiments." (The definition is due to E J. Lowe.) 53 Sorensen, Thought Experim ents. 186. 54 Ibid. 55 Ib id , 187-88. 56 Ibid.. I90ff. 57 Ib id , 205. Sorensen addresses the subsequent questions o f “W hat makes for a good thought experiment?”

and “W hat are common flaws o f bad thought experiments?" in ib id , ch. 10.

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contemplation o f the design justifies an answer to the question or (more rarely) justifiably raises its question.”58 At this level o f generality it appears that the KCA arguments qualify as thought experiments. Sorensen, however, does not stop at this level of generality, but goes on to distinguish, based upon their underlying logical form, two basic types o f thought experiment. It is the second o f these types, which Sorensen names “possibility refiiters,” that interests us here. The purpose o f any possibility refuter is to establish that some alleged possibility (e.g., that an actual infinite can exist) is not a possibility after all. Sorensen’s method calls for the construction o f a quintet o f jointly inconsistent propositions. Rejecting one or more o f these will render the group of propositions consistent; the trick, of course, lies in convincing one’s opponent to give up the correct proposition. Following the possibility refuter model Sorensen suggests, Craig’s infinite library thought experiment might be expressed thus:59 1) “Libraryism” is the view that a library containing a denumerably infinite quantity o f books could really exist. 2) If Libraryism is correct, then a collection o f Ko real books can exist. 3) If a collection o f Ko real books can exist and people attempt to subtract books from that collection then they will be unable to borrow books from the library. (This is because the logical conditions o f Cantorian mathematics apply and under that system inverse operations are prohibited for transfinite cardinals.) 4) But it is not possible that people will be unable to borrow books from the library. (In a real library people can simply remove whatever books they wish from the shelf and then check them out at the front desk.) 5) I f it is possible that a collection o f Ko real books can exist then it is possible that people attempt to subtract books from that collection. 58 Ibid., 206. For instance, “w e find ethicists wondering what would happen if no one kept their promises,

linguists wondering how a language free o f vagueness would work, and political theorists concentrating on the ‘state o f nature’ to arrive at the function o f government.” (Ibid., 238.) 59 For Sorensen’s discussion o f the logical form o f possibility refiiters see ibid., I53ff. His discussion o f premises that remain the same between possibility refiiters and the other kind o f thought experiments (called “necessity refiiters”) may be found at 135ff.

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To render this group o f propositions consistent at least one proposition must be rejected. A proponent o f the KCA would opt for rejecting Libraryism. Given that Oppy appears to be committed to the position that Cantorian mathematics can supply an adequate model for physically instantiated actually infinite collections, it seems that he will probably accept the truth o f the third proposition. This leaves him with the task o f deciding which o f the remaining propositions to jettison. Although I will not recast all o f the KCA arguments in this form, there seems to be no reason why they should not be amenable to such treatment. Since the KCA arguments can be translated into the canonical form Sorensen identifies, it is reasonable to assert that the KCA arguments for the impossibility o f instantiating an actual infinite are indeed thought experiments. To link the genre o f thought experiments to the modal issues raised earlier in this chapter, it is useful to consider why thought experiments are used at all. There are in fact a number o f reasons why one might turn to a thought experiment instead o f performing an actual experiment. For instance, the experiment might be unethical (think of Judith Jarvis Thomson’s violinist60 or various thought experiments directed against utilitarians), too costly (if both a wound and an unwound watch are dissolved in acid, what happens to the wound watch’s potential energy?61), or simply unnecessary (Galileo did not have to drop tied weights off the tower o f Pisa to disprove the Aristotelian notion that heavier weights fall faster). Another legitimate reason for employing a thought experiment is that actual performance o f the experiment is impossible. For instance, there is an entire class o f non-

60 The thought experiment is recounted in Judith Jarvis Thomson, “A Defense o f Abortion,” Philosophy and

Public A ffairs 1 (1971): 47-68. 61 This example is suggested by Sorensen, Thought Experiments, 200.

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performable operations studied in crystallography, namely, those involving reflection symmetry, that are impossible to perform in three-dimensional space.62 Note that in this list some of the thought experiments are actually performable, others are difficult to perform, and still others are not performable at all. Taking a cue from the previous observation, and consistent with his gradualist account o f thought experiments, Sorensen is perfectly willing to talk about degrees of impossibility.63 He writes: To say that something is impossible is to say that it violates a constraint. Impossible is relative to one’s means. Since one’s means vary over time, what was once impossible can become possible. Low-gravity experiments began as impossible experiments because we did not have the means to reduce the influence of gravity. Once we determine that the deed cannot be done, we ask, “How impossible?”64 With this view o f relative possibility and impossibility, it is not surprising that Sorensen emphasizes the importance of correctly identifying the sort o f possibility or impossibility appropriate for a given thought experiment. For instance, suppose we were to be confronted with a thought experiment that purports to demonstrate that attaining speeds faster than light is possible. One way o f undermining this thought experiment would be to argue that the situation we are asked to entertain is impossible.65 But we must be careful to choose the right sense of impossibility in our rebuttal:

62 See ibid., 201. 63 “The depth o f the impossibility is proportional to how different the world would have to be for the

procedure to be executed. Difference in detail is not much difference. So a procedure rendered infeasible by our position hi space or tim e is still a ‘realistic’ case. The transition from these shallow impossibilities to deep ones is gradual...” (Ibid., 201.) w Ibid., 200. 65 An example o f this sort o f thought experiment, along with its solution, are reported by Sorensen: [One] proposal for transcending the speed o f light begins with a long rigid rod growing out into space from the equator. The longer the rod, the fester its tip whips about, because the earth is a rotating sphere. Therefore, if die rod continues to grow, the tip must eventually move fester than the speed o f light. Physicists counter with close questioning. Where does

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Although the impossibility response is one o f the legitimate resolutions of a thought experiment...people tend to equivocate by latching on to the wrong kind o f impossibility. ‘Impossible’ has to be relativized to the proper background constraints. It is a practical impossibility for all the oxygen molecules to segregate to one comer o f the room, thereby suffocating me. But it is physically possible. An attack on a thought experiment that shows the supposition to be logically impossible is sure to be successful. But the choice o f a weaker impossibility courts the danger o f too weak a response.66 Sorensen is quite explicit about the need for being sensitive to the context within which a thought experiment is to be evaluated.67 Thus, if one were to propose a thought experiment in sociology it would be appropriate to assume (or at least appeal to) the general methods and results already established within that field. It would be inappropriate, for instance, to reject some particular sociological law because it might fail to apply to a logically possible Martian community. This is because the domain o f sociological study is restricted to human beings. On the other hand, if human beings could evidence interpersonal relations of some extreme type (as, for instance, in Thomas More’s Utopia, or in the Ancient Greek city of Sparta, or in an Israeli kibbutz) then such examples might legitimately be adduced in the evaluation o f a specific sociological thought experiment (e.g., suppose someone developed a quasi-Marxist thought experiment designed to show that material possessions are the sole the material for the rod come from? I f it is being drawn from the earth, the conservation o f angular momentum requires that the angular velocity o f the earth-rod mass decreases in the way a skater slows down as he extends his arms. As more o f the earth turns into the rod, the tip slows; once all o f the earth is converted into a celestial wand, the tip will be very slow. On the other hand, if there is an extraterrestrial source for the rod’s material, then the additional mass must be given extra kinetic energy to keep it moving in pace with the angular velocity o f the earth. But we will run out o f energy before the tip reaches the speed o f light. Hence, the appearance o f possibility is a product o f intellectual law less. ( Thought Experim ents, 149-50.) 66 Thought Experim ents, 278. An interesting application o f the idea that different sorts o f possibility must be recognized is developed in Sorensen’s analysis o f thought experiments in ethics: see ibid., 279. There are other dimensions one needs to consider when trying to achieve a proper fit in one’s response to a thought experiment: “I have already trumpeted the importance o f relativizing thought experiments to the intentions of their presenters. It is also important to relativize them to a standard o f complexity.’’ (Ibid., 210.) Oppy’s responses to Craig do not meet the first condition Sorensen mentions, for Oppy’s replies do not occupy the same modal space as die original KCA thought experiments. 67 “Thought experiments rely crucially on our sense o f absurdity.’*(IbicL, 252-53.)

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criterion o f social status). Now contrast this well-grounded approach with someone who objected to our quasi-Marxist thought experiment by adducing the example o f the ant community in T Jf. White’s The Once and Future King. The account in White is both interesting and instructive; nevertheless, the ant colony does not serve to rebut the thought experiment in the way More’s Utopia does. This is not because magic is employed to transform the young Arthur into an ant, for such details are irrelevant here. Rather, adducing the ant community as a counterexample is not effective because the colony White describes does not represent a possible form o f human community. Among the ants young Arthur is decidedly an external observer, and what ultimately prevents his inclusion within the ant community are ineradicable features o f his essential humanness. To clarify Sorensen’s position let us apply his insights to the famous thought experiment in the philosophy o f law known as “The Case o f the Speluncean Explorers.”68 Briefly, in this carefully described thought experiment a group o f amateur cave explorers on the planet Newgarth have the misfortune o f being trapped by a rockslide at the entrance of the cave they are exploring. By the wonders o f wireless technology the trapped explorers manage to contact a rescue team assembled outside the cave. Unfortunately for the trapped explorers, the rescue operation is dangerous and slow, and they have run out o f supplies. Upon discussing their medical condition with a doctor who is part o f the rescue team, it is determined that the condition o f the explorers is such that they will not survive until the time o f their rescue unless they have some food. After protracted consultation with outside authorities and amongst themselves, a decision is made by the explorers to eat one of their 48 The thought experiment was originally proposed in Lon L. Fuller, “The Case o f the Speluncean Explorers,”

H arvard Law Review 62 (1949): 616-45. The case has generated a tremendous body o f literature and is often employed in philosophy o f law classes to illustrate the main schools o f thought within the philosophy o f law.

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number to ensure the survival o f the rest o f the team. A hapless individual named Roger Whetmore is selected by a random throw o f dice, and Whetmore is duly killed and eaten. When the remaining members o f the exploration party are rescued they are charged with murder. If convicted, the relevant Newgarth statute admits o f only one penalty: murderers are to be hung. It is decided that the facts o f the case do meet the formal criteria necessary for application o f the murder statute. Should the spelunkers be hung? It would be absurd to suggest that the case overlooks the logical possibility that the cave-in might suddenly vanish into thin air and thus the trapped explorers could walk out unharmed. Clearly the purpose o f the thought experiment is to raise certain sorts of questions regarding the philosophy o f law, and saying that the decision o f the explorers to eat one o f their number would be vitiated by the possibility o f a sudden disappearance of the cave-in would prevent those very questions from being asked. With respect to this thought experiment, appeals to alternative logical possibilities in the description o f the facts o f the case would indicate a fixed intention on the part o f the objector not to deal with the question; i.e., the raising o f logically possible alternatives would indicate a fixed design to squelch certain types o f question from being asked. Now, there are a number o f ways in which one might legitimately challenge the thought experiment. For instance, it might be the case that the question the thought experiment asks is not well formulated. Perhaps the thought experiment leaves out important details or is vague in some important respect. Criticism along such lines could very well be legitimate, and it is incumbent upon the individual who proposes a thought experiment to ensure that reasonable objections to the construction o f the experiment are addressed. However, unless the proper argumentative space o f a given thought experiment

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is reasonably construed as that o f mere logical possibility, every effort must be made by those who would challenge the thought experiment’s results to underm ine the thought experiment from within the restricted domain o f possibility in which the thought experiment is supposed to operate. If the wrong notion o f possibility is used in the thought experiment itself, it is the duty o f the objector to provide an argument for the appropriateness o f an expanded or contracted notion o f possibility. If no effort is made to show that the thought experiment’s original logical domain is inappropriate, and no internal reasons are given for rejecting the results of the thought experiment, then such objections to the thought experiment are guilty o f an ignoratio elenchL In short, neither raising questions o f possibility from the standpoint o f a modal domain that is wider than that employed within the thought experiment, nor offering another thought experiment that operates within a different logical space than the original, serves to undermine the original thought experiment. Thought experiments trade upon our ability to bring just the right modal facts into play. The factual possibilities open to human beings are presumably different from the factual possibilities o f ants or Martians. If a thought experiment is offered to illu m in a te some feature of human sociology or legal interaction, it is the factual modalities concerning human beings that will be relevant; the factual modalities of ants and Martians will (at best) be tangential to the evaluation o f the thought experiment, hi a parallel fashion, if a thought experiment is offered to illuminate some principle o f physics, then we are obliged to focus our attention upon the subdomain o f factual modality that applies to the entities o f physics. Neglecting to situate evaluations o f thought experiments within their proper modal domain results in an ignoratio elenchL

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Is Oppy guilty o f the error just described? On the one hand, there appears to be ample evidence to convict him of this charge. Despite Craig’s repeated insistence that the thought experiments employed by the KCA are situated within a restricted domain of factual possibility, Oppy repeatedly frames his objections in terms o f logical possibility. Without attempting to show that Craig’s thought experiments are poorly constructed or offering an argument to the effect that it is inappropriate for Craig to appeal to factual possibility as an interpretive standard, Oppy simply asserts that Craig’s thought experiments have failed to convince him and proceeds to offer his own logically possible thought experiments that lead to contrary conclusions. If nothing else, this sort o f response betrays a wooden insensitivity to the formal demands of evaluating thought experiments.69 On the other hand, Oppy’s transgressions do have some significant mitigating circumstances. In a revealing footnote, Oppy confesses that he is unable to make sense o f what Craig means by factual possibility.70 It may be admitted that despite his heroic efforts in other areas Craig has left the important notion o f factual possibility unhelpfully vague. Granted, Craig does discuss causation in various places, and he does suggest that causal connections restrict the domain o f factual possibilities in ways that mere logical possibility does not. These are, however, just hints. How does causation define the limits o f the 69 Oppy’s unsympathetic approach to the KCA thought experiments falls far short o f the interpretive ideaL As Sorensen remarks: Ordinary standards for interpreting thought experiments are generous. In addition to seeking interpretations that sidestep the inventor’s m inor mistakes, we rescue ’the mam point’ from substantive error and ignorance. Plato’s Ring o f Gyges, for instance, has serious run-ins with contemporary opthamology. To see; the eye lens must bend light to form an image on the retina- But a transparent lens has the same index o f refraction as the air (and so cannot bend light) and a transparent retina cannot absorb light. Hence, the invisible man could not see! But an ethicist who tried to rebut Plato by stressing the disadvantages o f blindness would be laughed down. {Thought Experim ents, 287.) 70 “I think it should be noted that other readers found it equally hard to make sense o f Craig’s talk o f ’real possibility’.” (“Kalam Cosmological Arguments: Reply to Professor Craig,” 27-28 n. 3.) Oppy follows this remade with a reference to W illiam Wamwright’s review ofTKCA.

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factually possible? Until a more detailed account is forthcoming, it would be presumptious to claim that all o f Oppy’s difficulties with the KCA have been satisfyingly resolved. In conclusion, the thought experiments crucial to the KCA are intended to be situated within a context o f factual possibility, not logical possibility. Provided that the domain o f factual possibility can be adequately characterized, objections to the KCA thought experiments that are insensitive to this restriction fail to hit their target. The next chapter begins to fill in some o f the necessary details by developing an account o f substantial possibility, a subdomain o f factual possibility whose relevance to the evaluation o f many KCA thought experiments is clear.

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Chapter 4 15. Elements o f a theory o f substantial possibility In this chapter I provide a basis for the theory o f substantial possibility introduced in chapter 3. The relationship that obtains between substantial possibility and factual possibility is one o f part to whole. It is my position that what is substantially possible is factually possible; what is substantially necessary is factually necessary. Since there may be other subdomains o f factual modality, the converse relations do not necessarily obtain. For instance, something may be factually possible without being substantially possible because the reasons for its factual possibility are not to be found in the subdomain of substantial possibility but in some other subdomain of factual possibility. In providing an account o f substantial possibility I am elucidating the range of factual possibilities that hold for a class o f entities I call substances. More precisely, I identify substantial possibility with the domain o f possible causal relations open to substances possessing natures, the nature o f any substance being understood to determine the causal relations into which that substance may enter.1 The account of substantial possibility that emerges is developed entirely from within and by employing the resources o f analytic philosophy.2 While the range and complexity o f metaphysical issues raised in

1 Craig does not offer many hints as to his own position on the question o f how causation and possibility are connected. The most detail I have been able to extract is contained within the following brief remark: insofar as natural laws are inductive generalizations, they are merely descriptions o f what does or does not happen in the universe; and insofar as they are invested with nomic necessity, such necessity derives solely from the causal powers and dispositions o f things that actually exist. (“Graham Oppy on the Kalam Cosmological Argument,” 7.) 2 Which is not to say that historical considerations do not enter into the account. The particular analytic philosophers I discuss in this chapter are all sensitive to the philosophical contributions made by Aristotle, and their positions are often developed in dialog with the historical positions o f Aristotle and Aristotelianism generally. It is not my purpose here to evaluate the accuracy o f the historical interpretations these analytic

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this chapter preclude the sort o f in-depth analysis to which they are naturally amenable, I hope to provide a sketch o f the various elements embedded in the notion of substantial possibility that indicates how a more complete account o f substantial possibility could be elaborated. If a sufficiently clear understanding o f substantial possibility emerges from this chapter, I will then be in a position to apply that notion o f substantial possibility in chapter S, where a strengthened version o f the KCA is developed. The theory o f substantial possibility is built up in stages. In the first stage, I describe how adopting a substance-based metaphysics can be motivated from within analytic philosophy and how the general notion o f substance can be defended from some common objections and misunderstandings. In the second stage, I elaborate the notion o f "‘nature,” which I understand to be the intrinsic character o f a substance that makes the substance to be what it is. It is my position that causal powers flow from and are always in conformity with the given nature o f a substance. The third and final stage draws the notions o f substance, nature, and causation together into a unified theory of substantial possibility. The necessary connection between the nature o f a substance and its causal activity provides the foundation for the restricted notion o f substantial possibility required for accurate assessment o f the KCA. Each o f the stages mentioned is developed by drawing upon the work o f previous philosophers. G.E.M. Anscombe provides valuable guidance regarding the kind o f substance account that is to be preferred, steering us away from problematic accounts o f philosophers offer. As has been my practice throughout the dissertation I will accept then interpretations without comment and assess the positions they develop on their own merits. I recognize, however, that the positions o f some o f these philosophers has proven to be controversial. For instance, in order to illuminate her interpretation o f Aristotle, Anscombe occasionally appeals to W ittgenstein’s Tractatus. This maneuver, while philosophically fruitful, certainly brings with it the threat o f anachronism. See e.g. G.E.M. Anscombe and P.T. Geach, Three Philosophers (Oxford: Basil Blackwell & M ott Ltd., 1961), 44-46.

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substance such as that offered by Locke. Sarah Broadie (nee Waterlow) suggests connections between the account o f substance I endorse and the resources o f the philosophy o f language. David Braine deepens our understanding o f the relation between a substancebased metaphysics and the philosophy o f language, and emphasizes the connection between substantial existence and the manifestation o f active power. Rom Harre and E.H. Madden develop a sophisticated account o f causal powers, which they see as emerging from the natures o f substances and as delimiting the scope o f modal attributions.3 It may be noted here that these five philosophers do not agree in several important details, nor would they be likely to agree with the final position articulated here. However, a consistent account of substantial possibility can be developed through a judicious selection o f their numerous individual insights; the project o f mediating the dispute among these thinkers is left to another occasion. 16. A metaphysics of substances This section lays out, in three steps, the general parameters o f an analytic theory of substance. First, since there have been a number o f contrasting accounts o f substance in the history o f philosophy, some indication must be given regarding the sort o f substance theory endorsed. The purpose of this first move in the argument is not to conclusively establish the truth o f a substance-based metaphysics but rather to give the reader some idea o f where the argument is headed. Second, I offer some evidence in support o f a metaphysics of substances, drawing upon the philosophy o f language and the philosophy o f nature. I argue

3 W ith the possible exception o f Braine, all o f the philosophers mentioned are likely to find some part o f the account I develop objectionable. For instance, Anscombe would have difficulties with the accounts o f causation and modality I endorse, and Harre and Madden would object to the account o f substances and natures that I suggest should be used to undergird the notion o f substantial possibility.

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that introducing a substance-based metaphysics permits the solution o f otherwise intractable problems surrounding the ordinary practice o f predication. It is also argued that another advantage o f a substance metaphysics is that it affords the desirable result that identity can be maintained through change. Third, I answer some standard questions and objections to the substance metaphysics advocated. For example, I defend my position against reductionist attacks, arguing that I have indeed located substances at the right ontological level. 16.1

Which theory of substance? Before taking up the question o f why an analytic philosopher might accept a

substance-based metaphysics it is useful to have some idea of the particular theory of substances advocated. To begin with, I should like to state what my position is not. It is not my position that a substance is a characterless bare particular or unknowable substrate upon which properties are layered like winter clothing on children. This Lockean view of substance as “something, I know not what,” has rightly been criticized, and I have great sympathy for those who complain that they rind it difficult to either make sense of or see the need for a bare particular.4 It is ultimately at his own expense that Locke jests about the poor Indian Philosopher (who imagined that the Earth also wanted something to bear it up) [: had he] but thought o f this word Substance, he needed not to have been at the trouble to find an Elephant to support it, and a

4 Since in what follows substances are linked to a particular account o f causation, it is appropriate to mention the following criticism o f Lockean substances: on Locke’s account it is impossible to develop a satisfactory theory o f agency. As I P . Moreland notes: The bare substratum view pictures agents as simple, bare I’s to which various properties are externally related. This view does allow fo ra distinction between the agent and its various properties, the former being a bare particular. But since bare substrata are simples with no internal capacities or powers, it is hard to see how bare agents can have the capacity to act or refrain from acting. (“Naturalism and Libertarian Agency,” 356.)

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Tortoise to support his Elephant: The word Substance would have done it effectually.5 Pace Locke, the substance of, say, a man is not that something substat, staying under, the man; rather, it is just the man himself. This man, this cow, this tree, and this stone are substances. This position is in accord with the common-sense position of Aristotle, “who defined individual substance as what exists without either being predicated o f or existing in anything else.”6 Putting the same point another way, we say of a substance F that it is (p, but (leaving the interesting phenomenon o f nam ing aside) we do not say of