• William Lane Craig
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Temporal Series Infinite Series Infinite Time Monthly Notice Personal Letter 
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  14. W. I. Matson similarly asserts that since there is no logical inconsistency in an infinite series of numbers, there is no logical inconsistency in an infinite series of events, and therefore the first cause argument is incurably fallacious. (Wallace I Matson, The Existence of God [Ithaca, N.Y.: Cornell University Press, 1965], pp. 58–60.) Matson fails to understand that the kaldm argument holds that the existence of an actual infinite is really, not logically, impossible. 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 of an actual infinite is really impossible, even if it may not involve logical contradiction.Google Scholar
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  23. It might be protested that we need not bring in the notion of actual infinity when speaking of past events; we may simply say that the series of temporal events is beginningless. This does not appear to be counter-intuitive and avoids the problems of the actual infinite. But such an escape route is easily barred: for it is in analysing what a beginningless series of events involves that the absurdities become manifest. As G. E. Moore indicates, if we grant that events really occur in time, then only two alternatives are possible: either there was a first event or there has been an actually infinite series of events prior to the present one. For if there was no first event, then there must have been an event prior to any given event; since this one also could not be first, there must be an event prior to it, and so on ad infinitum. (George Edward Moore, Some Main Problems of Philosophy Muirhead Library of Philosophy [London: George Allen & Unwin, 1953; New York: Macmillan Co., 1953], pp. 174–5.) Therefore, a beginningless series involves the existence of an actual infinite.Google Scholar
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  27. Russell’s fallacy is also discerned by G.J. Whitrow, The Natural Philosophy of Time (London and Edinburgh: Thomas Nelson & Sons, 1961), p. 149. Whitrow argues that Russell presupposes the incompletable series of events in question may be regarded as a whole, when in fact it is not legitimate to consider the events of Tristram Shandy’s life as a completed infinite set, since the author could never catch up with himself.Google Scholar
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  104. This serves to effectively rebutt the objection of Julian Wolfe to the kalām cosmological argument. (Julian Wolfe, ‘Infinite Regress and the Cosmological Argument’, International journal for Philosophy of Religion 2 [1971]: 246–9.MathSciNetCrossRefGoogle Scholar
  105. The crucial premiss is, in Wolfe’s opinion, that an infinite time cannot elapse. He argues that this is incorrect because prior to causing the first effect, the uncaused cause existed for infinite time. Since the first event did occur, then an infinite time must have elapsed. But in the first place, Wolfe’s formulation of the argument is defective, for the contention is that an infinite number of events cannot elapse, not that an infinite time cannot elapse. The Newtonian could hold that if God is changeless prior to creation, then an undifferentiated, measureless, infinite time could elapse before the first event, but that an infinite temporal series of definite and distinct events could not elapse. Because the argument concerns events, not time, Wolfe’s analysis is inapplicable, since prior to creation there were no events at all. Second, if the relationist is correct, then an infinite time does not elapse prior to creation because time begins at creation. God is simply timeless before the first event. As Harris urges, ‘A persistent state of affairs which is not contrasted with any series of changes, either internal or external to it..., could not be conceived as enduring..., because there would be nothing (no lapse) through which it could be thought to endure.’ (Errol E. Harris, ‘Time and Eternity’, Review of Metaphysics 29 [1976]: 467.)Google Scholar

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