Essay Review

References

• Cantor , G . 1872 . ‘Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen’ . Mathematicshe Annalen , 5 : 123 – 132 . in Cantor, G. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, E. Zermelo, ed., Berlin: Springer pp. 92–102
   Google Scholar
• Cantor , G. 1880 . ‘Über unendliche, lineare Punktmannigfalitgkeiten’, Part 2 . Mathematische Annalen , 17 : 355 – 358 .
   Google Scholar
• Cantor , G. 1883 . Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen 600 – 612 . Leipzig: B.G. Teubner; in G. Cantor 1932, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, E. Zermelo, ed., Berlin: Springer, pp. 165–208. See also Grattan-Guinness 2005
   Google Scholar
• Benacerraf , P. 1965 . ‘What numbers could not be’ . Philosophical Review , 74 : 47 – 73 .
   Web of Science ®Google Scholar
• Benacerraf , P. 1973 . ‘Mathematical truth’ . The Journal of Philosophy , 70 : 661 – 679 .
   Google Scholar
• Dauben , J. W. 1979 . Georg Cantor. His Mathematics and Philosophy of the Infinite , Cambridge, MA : Harvard University Press . [Repr. Princeton, NJ: Princeton University Press, 1990.]
   Google Scholar
• Dauben , J. W. 1988 . Review of [Purkert and Ilgauds 1987] . Isis , 79 : 700 – 702 .
   Google Scholar
• Dauben , J. W. 2005 . “ ‘1883. Georg Cantor. Paper on the “Foundations of a general set theory”’ ” . In Landmark Writings in Western Mathematics 1640–1940 , Edited by: Grattan-Guinness , I. 600 – 613 . Amsterdam : Elsevier .
   Google Scholar
• Dummett , M. 1991 . Frege: Philosophy of Mathematics , Cambridge, MA : Harvard University Press .
   Google Scholar
• Gödel , K. 1995 . Collected Works, Volume III, Unpublished Essays and Lectures , Oxford : Oxford University Press . S. Feferman, J.W. Dawson, W. Godlfarb, C. Parsons, and R.N. Solovay, eds
   Google Scholar
• Grattan-Guinness , I. 1970 . ‘An unpublished paper by Georg Cantor: “Principien einer Theorie der Ordnungstypen. Erste Mittheilung”’ . Acta Mathematica , 124 : 65 – 107 .
   Google Scholar
• Grattan-Guinness , I. 1971 . ‘Towards a biography of Georg Cantor’ . Annals of Science , 27 : 345 – 391 .
   Web of Science ®Google Scholar
• Hallett , M. 1984 . Cantorian Set Theory and Limitation of Size , Oxford : Oxford University Press .
   Google Scholar
• Hersh , R. 1997 . What is Mathematics, Really? , Oxford : Oxford University Press .
   Google Scholar
• Hilbert , D. 1925 . ‘Über das Unendliche’ . Mathematische Annalen , 95 : 161 – 190 .
   Google Scholar
• Hilbert , D. and Bernays , P. 1934–1939 . Grundlagen der Mathematik , Berlin : Springer .
   Google Scholar
• Ignjatovic , A. 1994 . ‘Hilbert's program and the omega rule’ . The Journal of Symbolic Logic , 59 : 322 – 343 .
   Google Scholar
• Kreisel , G. 1958 . “ ‘Ordinal logics and the characterization of informal notions of proof’ ” . In Proceedings of the International Congress of Mathematicians 289 – 299 . Edinburgh
   Google Scholar
• Kreisel , G. 1970 . “ ‘Principles of proof and ordinals implicit in given concepts’ ” . In Intuitionism and Proof Theory , Edited by: Kino , A. , Myhill , J. and Vesley , R. E. 489 – 516 . Amsterdam : North-Holland .
   Google Scholar
• Kripke , S. 1982 . Wittgenstein on Rules and Private Languages: An Elementary Exposition , Cambridge, MA : Harvard University Press .
   Google Scholar
• Lavine , S. 1994 . Understanding the Infinite , Cambridge, MA : Harvard University Press .
   Google Scholar
• Meschkowski , H. 1967 . Probleme des Unendlichen. Werk und Leben Georg Cantors , Braunschweig : Vieweg .
   Google Scholar
• Purkert , W. 1989 . “ ‘Cantor's views on the foundation of mathematics’ ” . In The History of Modern Mathematics. Ideas and Their Reception , Edited by: Rowe , D. and McCleary , J. Vol. 1 , 49 – 65 . San Diego, CA : Academic Press .
   Google Scholar
• Purkert , W. and Ilgauds , H. J. 1985 . Georg Cantor 1845–1918 , Leipzig : Teubner .
   Google Scholar
• Purkert , W. and Ilgauds , H. J. 1987 . Georg Cantor 1845–1918 , Basel : Birkhäuser .
   Google Scholar
• Tait , W. 1968 . “ ‘Constructive Reasoning’, ” . In Logic, Methodology and Philosophy of Science III , Edited by: van Rootselaar , B. and Stall , J. 185 – 199 . Amsterdam : North Holland .
   Google Scholar
• Tait , W. 1981 . ‘Finitism’ . Journal of Philosophy , : 21 – 42 . 78, 524–556; in Tait (2005)
   Google Scholar
• Tait , W. 1983 . ‘Against intuitionism: Constructive mathematics is part of classical mathematics’ . Journal of Philosophical Logic , 12 : 175 – 195 .
   Google Scholar
• Tait , W. 1986a . ‘Plato's second best method’ . Review of Metaphysics , : 155 – 177 . 39, 455–482; in Tait 2005
   Google Scholar
• Tait , W. 1986b . ‘Truth and proof: the Platonism of mathematics’ . Synthese , : 61 – 88 . 69, 341–370; in Tait (2005)
   Google Scholar
• Tait , W. 1986c . “ ‘Wittgenstein and the “Skeptical Paradoxes”', ” . In Journal of Philosophy 198 – 211 . 9, 475–488; in Tait (2005)
   Google Scholar
• Tait , W. 1994 . “ ‘The law of excluded middle and the axiom of choice’ ” . In Mathematics and Mind 105 – 132 . A. George, ed., Oxford: Oxford University Press, pp. 45–70; in Tait (2005), pp
   Google Scholar
• Tait , W. 1997 . “ ‘Frege versus Cantor and Dedekind: On the concept of number’ ” . In Early Analytic Philosophy: Frege, Russell, Wittgenstein. Essays in Honor of Leonard Linsky 212 – 251 . W. Tait, ed., Chicago: Open Court, pp. 213–248; in Tait (2005)
   Google Scholar
• Tait , W. 2000 . “ ‘Cantor's Grundlagen and the Paradoxes of Set Theory’ ” . In Between Logic and Intuition. Essays in Honor of Charles Parsons 252 – 295 . G. Sher and R. Tieszen, eds., New York: Cambridge University Press; in Tait (2005)
   Google Scholar
• Tait , W. 2001a . ‘Beyond the Axioms: The Question of Objectivity in Mathematics’ . Philosophia Mathematica , : 89 – 104 . 9, pp. 21–36; in Tait (2005)
   Google Scholar
• Tait , W. 2001b . ‘Gödel's Unpublished Papers on Foundations of Mathematics’ . Philosophia Mathematica , : 276 – 313 . 9, pp. 87–126; in Tait (2005)
   Google Scholar
• Tait , W. 2002a . “ ‘Noēsis: Plato on exact science’ ” . In Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics 178 – 197 . D.B. Malament, ed., Chicago: Open Court; in Tait 2005
   Google Scholar
• Tait , W. 2002b . “ ‘Remarks on finitism’ ” . In Reflections on the Foundations of Mathematics. Essays in Honor of Solomon Feferman 43 – 53 . W. Sieg, R. Sommer, and C. Talcott, eds., Natick, MA: A.K. Peters; in Tait (2005)
   Google Scholar
• Tait , W. 2005 . The Provenance of Pure Reason. Essays in the Philosophy of Mathematics and Its History , New York : Oxford University Press .
   Google Scholar
• Tapp , C. 2005 . Kardinalität und Kardinäle: Wissenschaftshistorische Aufarbeitung der Korrespondenz zwischen Georg Cantor und Katholischen Theologen seiner Zeit , Stuttgart : Steiner Verlag .
   Google Scholar
• Wittgenstein , L. 1953 . Philosophical Investigations , New York : Macmillan . G.E.M. Anscombe, trans
   Google Scholar
• Zach , R. 1998 . ‘Numbers and functions in Hilbert's finitism’ . Taiwanese Journal for Philosophy and History of Science , 10 : 33 – 60 .
   Google Scholar
• Zach , R. Hilbert's finitism: historical, philosophical, and metamathematical perspectives , University of California, Berkeley 2001 dissertation
   Google Scholar
• Zach, R. 2006. ‘Richard Zach—Research’, http://www.ucalgary.ca/∼rzach/research/
   Google Scholar