1. See James T. Cushing, Arthur Fine, and Sheldon Goldstein, Bohmian Mechanics and Quantum Theory: An Appraisal in Boston Studies in the Philosophy of Science 184 (Dordrecht: Kluwer Academic Publishers, 1996).
2. See John Barrow and Frank Tipler, The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986), 441.
3. See Bernulf Kanitscheider, “Does Physical Cosmology Transcend the Limits of Naturalistic Reasoning?” in Studies on Mario Bunge’s “Treatise, ” ed. P. Weingartner and G. J. W. Dorn (Amsterdam: Rodopi, 1990), 346–347.
4. Robert Deltete, Critical notice of Theism, Atheism, and Big Bang Cosmology, by William Lane Craig and Quentin Smith, Zygon 30 (1995): 656. (N. B. the review was attributed to J. Leslie due to an editorial mistake at Zygon.
5. See, for example, Abraham Robinson, “Metamathematical Problems, ” Journal of Symbolic Logic 38 (1973): 500–516.
6. See Alexander Abian, The Theory of Sets and Transfinite Arithmetic (Philadelphia: W. B. Saunders, 1965), 68; B. Rotman and G. T. Kneebone, The Theory of Sets and Transfinite Numbers (London: Oldbourne, 1966), 61.
7. See I. D. Novikov and Ya. B. Zeldovich, “Physical Processes near Cosmological Singularities, ” Annual Review of Astronomy and Astrophysics 11 (1973): 401-402; A. Borde and A. Vilenkin, “Eternal Inflation and the Initial Singularity, ” Physical Review Letters 72 (1994): 3305, 3307.
8. Christopher Isham, “Creation of the Universe as a Quantum Process, ”in Physics, Philosophy and Theology: A Common Quest for Understanding, ed. R. J. Russell, W. R. Stoeger, and G. V. Coyne (Vatican City: Vatican Observatory, 1988), 385–387.
9. See John D. Barrow, Theories of Everything (Oxford: Clarendon Press, 1991, 67-68.
10. Stephen Hawking and Roger Penrose, The Nature of Space and Time, The Isaac Newton Institute Series of Lectures (Princeton, N. J.: Princeton University Press, 1996), 20.
11. David Hilbert, “Über das Unendlische, ” Mathematische Annalen 95 (Berlin, 1926): 161–90. Craig cites a reprint of a translation.
12. Kurt Gödel, “Über formal unendscheidbare Sätze der Principia Mathematica und verwandter Systeme I, ” Monatshefte für Mathematik und Physik 38 (1931).
13. For more detailed criticisms of Craig’s mathematical arguments, Quentin Smith, “Infinity and the Past” in William Lane Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Clarendon Press, 1993.
14. Quoted in Marcelo Gleiser, The Dancing Universe: From Creation Myths to the Big Bang (New York: Penguin, 1997), 287.
15. S. W. Hawking, “Breakdown of Predictability in Gravitational Collapse, ” Physical Review D14 (1976): 2460 (my emphasis).
16. On the reality of a singularity, see Quentin Smith in Craig and Smith, Theism, Atheism, and Big Bang Cosmology, p. 208.

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