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338 BOOK REVIEWS necessary propaedeutic for what follows, and some help is needed for the student to accomplish this successfully. The expanded Companion might also touch more on matters of political philosophy and might note the polemic surrounding Popper's attack on the Republic. No Companion to the Republic, however rich in informative explanation and interpretation, can ever exhaust its great subject, and there is much need for a Companion which is as rich as possible. The Catholic University of America Washington, D.C. DOMINIC O'MEARA The Kaliim Cosmological Argument. By WILLIAM LANE CRAIG. New York: Harper & Row, 1979. Contemporary discussions of the cosmological argument generally follow the philosophical model provided by Aristotle and Aquinas, which first invokes an empirical fact about the world (contingent beings exist; there is something in motion) , seeks for a cause or explanation of that fact, notes that an infinite series of causal conditions ordered transitively cannot provide an adequate explanation of that fact, and concludes to the existence of a necessary being or first cause. William Craig helpfully reminds us that this constitutes only one general form the cosmological argument has taken, a form originated by the Arabic practitioners of falsafa. His interest lies in another form developed by practitioners of kaliim, a " whole movement within Arabic thought that might best be called Arabic scholasticism" (4). Craig summarizes the lcaliim cosmological argument, which contrary to the above is concerned with the temporal sequence of events, as follows: 1. Everything that begins to exist has a cause of its existence. 2. The universe began to exist. 3. Therefore the universe has a cause of its existence. (63) The first sixty pages of his book present the kaliim cosmological argument as defended by the 9th and 11th century Arabic philosophers al-Kindi and al-Ghiizali and the 10th century Jewish philosopher Saadia. His concern is to provide a clear presentation of the argument as originally and most forcefully developed, particularly with respect to the defense of premise 2, rather than a detailed critique of it. The remainder of the book is devoted to presenting and defending a contemporary version of the kaliim cosmological argument. With respect to the argument given above, premise 1 is taken by Craig as intuitively obvious. " The first premise is so intuitively obvious, especially when applied to the universe, that probably no one in his right mind really believes it to be false" (141). The villain of the piece is BOOK REVIEWS 889 always Hume, and in reply to Hume's critique Craig argues that " all Hume has really shown is that the [causal] principle ... is not analytic and that its denial, therefore, does not involve a contradiction or a logical absurdity." But it" seems intuitively to be really, if not logically, absurd" (145). Craig's defense of the principle is not so much a defense as an appeal. It would have been profitable to develop a critique of Hume's argument, for example, to show that Hume has confused epistemological with ontological conditions in his argument. The critical premise, however, in the argument is the second, and to this Craig devotes the bulk of his energies. He presents four arguments in its support, two of which are philosophical and two empirical. The first argument is: 4. An actual infinite cannot exist. 5. An infinite temporal regress of events is an actual infinite. 6. Therefore an infinite temporal regress of events cannot exist. (69) Craig spends most of his time defending premise 4, arguing that the actual infinite of mathematics-found especially in Cantor's system and set theory -does not describe the real world. It concerns the mathematical world and was never meant to apply to the real world. Indeed, he argues, were it so applied, absurdities of all sorts result. His argument here is painstaking and (to my mind) unexceptionable. Much less time is devoted to the defense of premise 5. Basically he contends that "the fact that the events do not exist simultaneously is wholly irrelevant to the issue at hand; the fact remains that since past events, as determinate parts of reality, are definite and distinct and can be numbered, they can be conceptually collected into a totality...

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