Paradoxes of set and property

DOI: 10.4324/9780415249126-Y024-1
Version: v1,  Published online: 1998
Retrieved September 21, 2020, from

References and further reading

  • Benthem, J.F. van (1978) ‘Four Paradoxes’, Journal of Philosophical Logic 7: 49–72.

    (Analyses the interrelations between the paradox of the largest cardinal, Russell’s paradox, Curry’s paradox about self-reference without negation, and Löb’s version of the liar paradox.)

  • Beth, E.W. (1964) The Foundations of Mathematics, Amsterdam: North Holland.

    (Part 6 has an older, but still useful, summary of the paradoxes.)

  • Cantor, G. (1991) Briefe (Letters), ed. H. Meschkowski and W. Nilson, Berlin: Springer.

    (Includes Cantor’s 1899 letters to Dedekind and 1897–1900 letters to Hilbert relating to the paradoxes.)

  • Church, A. (1971) ‘Logic, History of, IV: Modern Logic’, in Encyclopaedia Britannica vol. 14: 231–237.

    (A general discussion, including the paradoxes.)

  • Fraenkel, A.A., Bar-Hillel, Y. and Levy, A. (1973) Foundations of Set Theory, Amsterdam: North Holland.

    (A careful analysis of the various solutions of the logical paradoxes, including axiomatic set theory, the theory of types, and metamathematics.)

  • Garciadiego, A. (1985) ‘The Emergence of the Non-Logical Paradoxes of the Theory of Sets, 1903– 1908’, Historia Mathematica 12: 337–351.

    (The early history of the semantic paradoxes.)

  • Grelling, K. and Nelson, L. (1908) ‘Bemerkungen zu den Paradoxieen von Russell und Burali-Forti’ (Remarks on the Paradoxes of Russell and Burali-Forti), Abhandlungen der Fries’schen Schule, new series, 2 (3): 301–334.

    (Grelling’s paradox.)

  • Heijenoort, J. van (1967) From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press.

    (Translates relevant articles by Burali-Forti, Gödel, König, Richard, von Neumann and Zermelo. Includes Russell’s 1902 letter announcing his paradox to Frege and mentioning that he had previously sent the paradox to Peano but received no reply.)

  • Hessenberg, G. (1906) Grundbegriffe der Mengenlehre (Fundamental Concepts of Set Theory), Göttingen: Vandenhoeck & Ruprecht.

    (The earliest textbook of set theory.)

  • Hughes, P. and Brecht, G. (1975) Vicious Circles and Infinity: A Panoply of Paradoxes, Garden City, NY: Doubleday.

    (A popular anthology of many paradoxes.)

  • Moore, G.H. (1978) ‘The Origins of Zermelo’s Axiomatization of Set Theory’, Journal of Philosophical Logic 7: 307–329.

    (The role of the axiom of choice and the paradoxes in axiomatization.)

  • Moore, G.H. (1982) Zermelo’s Axiom of Choice: Its Origins, Development, and Influence, New York: Springer.

    (The second chapter indicates how the paradoxes were intertwined with Zermelo’s proof that every set can be well-ordered.)

  • Moore, G.H. (1988) ‘The Roots of Russell’s Paradox’, Russell: The Journal of the Bertrand Russell Archives, new series, 8: 146–156.

    (The connection between Russell’s paradox and his antinomy of infinite number.)

  • Moore, G.H. and Garciadiego, A. (1981) ‘Burali-Forti’s Paradox: A Reappraisal of its Origins’, Historia Mathematica 8: 319–350.

    (Detailed historical treatment of this paradox.)

  • Peckhaus, V. (1990) Hilbertprogramm und kritische Philosophie: das Göttinger Modell interdisziplinarer Zusammenheit zwischen Mathematik und Philosophie (Hilbert’s Programme and Critical Philosophy), Göttingen: Vandenhoeck & Ruprecht.

    (Includes reaction to the paradoxes by the neo-Friesian school.)

  • Rang, B. and Thomas, W. (1981) ‘Zermelo’s Discovery of the ‘‘Russell Paradox’’’, Historia Mathematica 8: 15–22.

    (How Zermelo found Russell’s paradox, prior to Russell, and discussed it with Husserl.)

  • Russell, B.A.W. (1898) ‘An Analysis of Mathematical Reasoning, Being an Inquiry into the Subject Matter, the Fundamental Conceptions, and the Necessary Postulates of Mathematics’, in The Collected Papers of Bertrand Russell, vol. 2, Philosophical Papers 1896–99, ed. N. Griffin and A.C. Lewis, London: Routledge, 1990, 155–242.

    (Includes the contradiction of relativity.)

  • Russell, B.A.W. (1899) ‘The Fundamental Ideas and Axioms of Mathematics’, in The Collected Papers of Bertrand Russell, vol. 2, Philosophical Papers 1896–99, ed. N. Griffin and A.C. Lewis, London: Routledge, 1990, 261–305.

    (Includes the antinomy of infinite number.)

  • Russell, B.A.W. (1903) The Principles of Mathematics, Cambridge: Cambridge University Press; 2nd edn, London: Allen & Unwin, 1937; repr. London: Routledge, 1992.

    (First publication of Russell’s paradox, the paradox of the largest cardinal and the paradox of the largest ordinal.)

  • Russell, B.A.W. (1906) ‘Les paradoxes de la logique’, Revue de métaphysique et de morale 14: 627–650; trans. ‘On ‘‘Insolubilia’’ and their Solution by Symbolic Logic’, in Essays in Analysis, ed. D. Lackey, London: Allen & Unwin, 1973.

    (Analysis of the paradoxes, including the semantic ones.)

  • Russell, B.A.W. (1993) The Collected Papers of Bertrand Russell, vol. 3, Toward the ‘Principles of Mathematics’ 1900–02, ed. G.H. Moore, London and New York: Routledge.

    (See ‘The Principles of Mathematics (Draft of 1899–1900)’ (3–180) on the antinomy of infinite number; and ‘Part I of the Principles, Draft of 1901’ (181–208) for the earliest extant version of Russell’s paradox.)

  • Rüstow, A. (1910) Der Lügner (The Liar), Leipzig: Teubner.

    (The liar paradox.)

  • Zermelo, E. (1904) ‘Beweis, daß jede Menge wohlgeordnet werden kann’, Mathematische Annalen 59: 514–516; trans. S. Bauer-Mengelberg, ‘Proof that Every Set can be Well-Ordered’, in J. van Heijenoort (ed.) From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press, 1967, 139–141.

    (Zermelo’s proof of the well-ordering theorem.)

Citing this article:
Moore, Gregory H.. Bibliography. Paradoxes of set and property, 1998, doi:10.4324/9780415249126-Y024-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2020 Routledge.

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