One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must have (...) a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of (...) part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason. (shrink)

In ‘Professor Mackie and the Kalam Cosmological Argument’ , 367–75), Professor William Lane Craig undertakes to demonstrate that J. L. Mackie's analysis of the kalam cosmological argument in The Miracle of Theism is ‘superficial’, and that Mackie ‘has failed to provide any compelling or even intuitively appealing objection against the argument’ . I disagree with Craig's judgement; for it seems to me that the considerations which Mackie advances do serve to refute the kalam cosmological argument. Consequently, the purpose of this (...) paper is to reply to Craig's criticisms on Mackie's behalf. (shrink)

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must have (...) a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

In defense of his claim that the universe must have been created, William Lane Craig gives two distinct philosophical arguments against the possibility of an infinite past. The first appeals to various paradoxes allegedly generated by the idea of an actual infinite. The second appeals to a dynamic theory of the nature of time, and tries to show on that basis that an infinite series of events could not have been “formed by successive addition.” The present paper is concerned with (...) the second of these two arguments. I try to show that it cannot stand on its own independently of the first argument, that Craig does not succeed in defending it against standard objections, and that even those who are inclined to accept a dynamic theory of time should not be convinced by what Craig says in its defense. (shrink)

The late John L. Mackie, formerly of University College, Oxford.

infinite, and offer several arguments in sup port of this thesis. I believe their arguments are unsuccessful and aim to refute six of them in the six sections of the paper. One of my main criticisms concerns their supposition that an infinite series of past events must contain some events separated from the present event by an infinite number of intermediate events, and consequently that from one of these infinitely distant past events the present could never have been reached. I (...) introduce.. (shrink)

Of all the major philosophical works, Kant's Critique of Pure Reason is one of the most rewarding, yet one of the most difficult. Norman Kemp Smith's Commentary elucidates not only textural questions and minor issues, but also the central problems which arise, he contends, from the conflicting tendencies of Kant's own thinking. Kemp Smith's Commentary continues to be in demand with Kant scholars, and it is being reissued here with a new introduction by Sebastian Gardner to set it in its (...) contemporary context. (shrink)

The Preface and the General Introduction to the book set the debate within the wider philosophical context and show why the subject of temporal becoming is a perennial concern of science, religion, language, logic, and the philosophy of ...

Central to classical theism is the conception of God as the sole ultimate reality, the creator of all things apart from Himself. Such a doctrine is rooted in Hebrew-Christian scripture and unfolded by the ante-Nicene church fathers. Platonism, which postulates the existence of uncreated abstract objects, is therefore theologically objectionable. In order to overcome the presumption which anti-Platonism enjoys theologically, the Platonist would have to show that all other positions, both realist and nonrealist, are rationally untenable. No one has even (...) attempted so audacious a project, nor is there any reasonable expectation that it could be carried out. (shrink)

This chapter contains sections titled: * Platonism * The Indispensability Argument for Platonism * Challenge to the Truth of Mathematical Statements: Fictionalism * Challenges to the Customary Semantics for Mathematical Discourse * Challenges to the Customary Semantics in General * Theological Objection to Platonism * Conclusion * Notes * References * Further Reading.