Infinity

References and further reading

My thanks are due to Dartmouth publishers for permission to re-use material from the introduction to my book Infinity.

	Aristotle (c. mid 4th century ) Physics, Books III and IV, trans. E. Hussey, Oxford: Oxford University Press, 1983. (Book III, sects 4–8, presents the main elements of Aristotle’s account of the infinite.)
	Benardete, J.A. (1964) Infinity: An Essay in Metaphysics, Oxford: Oxford University Press. (Entertaining and wide-ranging discussion of the infinite, with particular emphasis on its paradoxes.)
	Bennett, J. (1971) ‘‘The Age and Size of the World’’, in A.W. Moore (ed.) Infinity, Aldershot: Dartmouth, 1993. (Excellent discussion of Kant’s antinomies.)
	Bolzano, B. (1851) Paradoxes of the Infinite, trans. D.A. Steele, ed. F. Prihonsky, London: Routledge & Kegan Paul, 1950. (Anticipates some of Cantor’s ideas, though with much less rigour. Historically significant.)
	Brouwer, L.E.J. (1913) ‘‘Intuitionism and Formalism’’, trans. A. Dresden, in P. Benacerraf and H. Putnam (eds) Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press, 1983. (Classic statement of some of the fundamental tenets of intuitionism.)
	Cantor, G. (1895–7) Contributions to the Founding of the Theory of Transfinite Numbers, trans. P.E.B. Jourdain, New York: Dover, 1955. (Cantor’s second major publication, in which he establishes transfinite arithmetic. Of ground-breaking importance, but very technical.)
	Hegel, G.W.F. (1812–16) Science of Logic, trans. A.V. Miller, London: Allen & Unwin, 1969. (Pages 116–57 and 225–38 provide the main elements of Hegel’s views.)
	Heidegger, M. (1927) Being and Time, trans. J. Macquarrie and E. Robinson, Oxford: Blackwell, 1978. (Locus classicus of existential thought on human finitude, but exceedingly difficult.)
	Hilbert, D. (1925) ‘‘On the Infinite’’, trans. S. Bauer-Mengelberg, in J. van Heijenoort (ed.) From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press, 1967. (A modern classic which defends ‘finitism’, a position according to which all references to the infinite are strictly meaningless though they can serve a useful function.)
	Kant, I. (1781) Critique of Pure Reason, trans. N. Kemp Smith, London: Macmillan, 1933. (The section entitled ‘Transcendental Dialectic’ up to Book II, ch. 2 and omitting Book II, ch. 1 (A293/B349–A340/B398 and A405/B432–A567/B595) presents the antinomies and their solution.)
	Lear, J. (1979–80) ‘‘Aristotelian Infinity’’, in A.W. Moore (ed.) Infinity, Aldershot: Dartmouth, 1993. (Helpful and instructive account of Aristotle’s views, including a superb discussion of the problem of infinite past time.)
	Moore, A.W. (1990) The Infinite, London: Routledge. (Introductory and partly historical study of all aspects of the infinite.)
	Moore, A.W. (1993) Infinity, Aldershot: Dartmouth. (Collection of the most important and influential articles on infinity published since 1950, with an extensive annotated bibliography and an introduction which expands on the material in this entry.)
	Owen, G.E.L. (1957–8) ‘‘Zeno and the Mathematicians’’, in A.W. Moore (ed.) Infinity, Aldershot: Dartmouth, 1993. (Thorough and scholarly discussion of Zeno’s paradoxes.)
	Rucker, R. (1982) Infinity and the Mind: The Science and Philosophy of the Infinite, Sussex: Harvester Wheatsheaf. (Lively and fascinating account of the more mathematical aspects of the infinite. Defends a kind of mysticism.)
	Russell, B. (1926) Our Knowledge of the External World as a Field for Scientific Method in Philosophy, London: Allen & Unwin. (Chapters 5–7 provide a vigorous defence of Cantor.)
	Salmon, W.C. (1970) Zeno’s Paradoxes, Indianapolis, IN: Bobbs-Merrill. (Collection of some of the best known articles on Zeno’s paradoxes.)
	Williams, B. (1973) ‘‘The Makropulos Case: Reflections on the Tedium of Immortality’’, in A.W. Moore (ed.) Infinity, Aldershot: Dartmouth, 1993. (Superb defence of the ambivalent attitude to death advocated in §7 above.)
	Wittgenstein, L. (1975) Philosophical Remarks, trans. R. Hargreaves and R. White, ed. R. Rhees, Oxford: Blackwell. (Section XII and pages 304–14 provide a good representative sample of Wittgenstein’s views.)