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THE CATHOLIC UNIVERSITY OF AMERICA
The Kalam Cosmological Argument in Contemporary Analytic Philosophy
A DISSERTATION
Submitted to the Faculty of the
School of Philosophy
of The Catholic University of America
In Partial Fulfillment of the Requirements
For the Degree
Doctor of 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
t h c K j t j c —
MMiicchhaaeell (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 of 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 of 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 of 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 of the KCA, namely, that the past
existence of the universe is finite. Reflection upon the implications of using Cantorian
transfinite mathematics to model physical processes allowed Craig to develop a
distinctively philosophical version of the KCA which is relatively independent of changes
in contemporary scientific cosmology. This dissertation is intended as a critical
investigation and development of this philosophical strand of the KCA. The literature
relating to the KCA has grown however to a significant bulk, and there is now danger of
duplication and misassessment due to the plurality of interpretations that the argument has
received. Part I of the dissertation addresses this need by laying bare the underlying logical
structure of the KCA (chapter 1) and by providing a comprehensive “state of the question”
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(chapter 2). Part II of the dissertation, comprising chapters 3 through 6, focuses upon an
important species of objection made to the KCA. This species of 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 of substances. In the course
of presenting a systematic response I develop an interpretation of the notion of substance
that is useful for analytic philosophy, present a general account of the logical requirements
of KCA thought-experiments, and outline a theory of logical modality suited to the
metaphysical requirements of 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 of this work;
Dean Kurt Pritzl, for providing the underlying presence of the School of Philosophy;
Professors Ronald Calinger and Douglas Gropp, for their generous contributions during the
dissertation defense;
Ingrid Genzel and Gretchen Gusich, for being the kind of 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 of treatment..................................................................................................6
PARTI_________________________________________________________________ XI
Chapter 1.......................................................................................................................II
4. Craig’s version of the KCA as presented in TKCA.............................................11
4.1 Craig on premise I: Whatever comes to be has a cause of its coming to be 11
4.2 Craig on premise 2: The universe came to be...............................................15
4.2.1 Preliminary remarks and terminology........................................................16
4 J2J2 Exposition of Cantorian transfinite number theory...................................20
4.2.2.1 Brief history of mathematical speculation on infinite............................21
4.2.2.2 Cantor and the development of set theory..............................................24
4.2.3 Reflections on and reactions to Cantor......................................................37
4.2.3.1 Taxonomy of 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) of 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 of its coming to be 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) of the KCA...........................................94
8. Division III - Objections to premise (2) of the KCA.........................................100
8.1 Division Hl.a - Objections to argument (A) of the KCA.............................101
8.1.1 Objections to premise (i) of argument (A)...............................................101
8.1.2 Objections to premise (ii) of argument (A)..............................................104
8.2 Division m.b - Objections to argument (B) of the KCA......................112
8.2.1 Objections to premise (a) of argument (B)...............................................113
8.2.2 Objections to premise (b) of argument (B)...............................................118
8.3 Division m.c - Objections to argument (C) of the KCA............................129
8.3.1 Objections to premise (a) of argument (C)...............................................129
8.3.2 Objections to premise (p) of argument (C)_______________________ 131
9. Division IV - Objections to conclusion (3) of the KCA....................................132
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PART II_______________________________________________________________ 136
Chapter 3......................................................................................................................136
10. Appeals to logical possibility in objections to the KCA.................................136
11. Outline of 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 of a theory of substantial possibility................................................168
16. A metaphysics of substances............................................................................170
16.1 Which theory of substance?........................................................................171
16.2 Why an ontology of substances?...............................................................175
16.3 Reply to common objections......................................................................182
17. Substantial nature and the manifestation of 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 of substantial possibility and a substance-based metaphysics ..202
20. Why evaluation of the KCA requires substantial possibility.........................202
21. Events and temporal marks..............................................................................206
21.1 Clarification of the notion of “event”........................................................206
21.2 Clarification and defense of “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 of the actual infinite...............................................................240
26. Operations with transfinite numbers................................................................251
BIBLIOGRAPHY.______________________________________________________ 257
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