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Epistemic logicism & Russell's regressive method

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References

  • Ayer, Alfred Jules: 1936, Language, Truth and Logic, second edition (New York, Dover), 1946.

    Google Scholar 

  • Bonola, Roberto: 1907, La Geometria Non-Euclidea. Translated by H. S. Carslaw as Non-Euclidean Geometry (New York, Dover), 1955.

    Google Scholar 

  • Carnap, Rudolf: 1931, ‘Die logizistische Grundlegung der Mathematik’, Erkenntnis, 2, 91–105. Translated by Erna Putnam & Gerald J. Massey as ‘The Logicist Foundations of Mathematics’, in Paul Benacerraf & Hilary Putnam, Philosophy of Mathematics, second edition (Cambridge, Cambridge University Press), 1983, 41–52.

    Google Scholar 

  • Dedekind, Richard: 1901, Essays on the Theory of Numbers, revised edition, translated by Wooster Woodruff Beman (New York, Dover), 1963.

    Google Scholar 

  • Frege, Gottlob: 1884, Die Grundlagen der Arithmetik, (Breslau: Köbner). Translated by J. L. Austin as The Foundations of Arithmetic, second revised edition (Oxford, Blackwell), 1980.

    Google Scholar 

  • Frege, Gottlob: 1893, 1903, Grundgesetze der Arithmetik, 2 volumes, (Jena: Pohle). Abridged and translated by Montgomery Furth as The Basic Laws of Arithmetic (Berkeley & Los Angeles, University of California Press), 1964.

    Google Scholar 

  • Frege, Gottlob: 1914, ‘Logic in Mathematics’, translated by Peter Long & Roger White in Frege, Posthumous Writings, (edited by Hans Hermes, Friedrich Kambartel & Friedrich Kaulbach) (Chicago, University of Chicago Press), 1979, 203–250.

    Google Scholar 

  • Gödel, Kurt: 1944, ‘Russell's Mathematical Logic’, in Paul Arthur Schilpp, The Philosophy of Bertrand Russell, third edition, New York: Tudor, 1951, 123–153. Reprinted in Paul Benacerraf & Hilary Putnam, Philosophy of Mathematics, second edition (Cambridge, Cambridge University Press), 1983, 447–469. Page numbers refer to the former.

    Google Scholar 

  • Gödel, Kurt: 1947, ‘What is Cantor's Continuum Problem?’, American Mathematical Monthly 54, 515–525. Revised and reprinted in Paul Benacerraf & Hilary Putnam, Philosophy of Mathematics, second edition (Cambridge, Cambridge UniversityPress), 1983, 470–485. Page numbers refer to the latter.

    Google Scholar 

  • Haack, Susan: 1978, Philosophy of Logics (Cambridge, Cambridge University Press).

    Google Scholar 

  • Hahn, Hans: 1929, ‘Empirismus, Mathematik, Logik’, Forschungen und Fortschritte 5. Translated as ‘Empiricism, Mathematics and Logic’, in Hahn, Empiricism, Logic, and Mathematics (edited by Brian McGuinness) (Dordrecht, Holland, Reidel), 1980, 39–42.

    Google Scholar 

  • Hahn, Hans: 1930, ‘Superfluous Entities, or Occam's Razor’, in Hahn, Empiricism, Logic, and Mathematics (edited by Brian McGuinness) (Dordrecht, Holland, Reidel), 1980, 1–19.

    Google Scholar 

  • Hamming, R. W.: 1980, ‘The Unreasonable Effectiveness of Mathematics’, American Mathematical Monthly 87, 81–90.

    Google Scholar 

  • Hempel, Carl Gustav: 1945, ‘On the Nature of Mathematical Truth’, American Mathematical Monthly 52, 543–556. Reprinted in Paul Benacerraf & Hilary Putnam, Philosophy of Mathematics, second edition (Cambridge, Cambridge University Press), 1983, 377–393. Page numbers refer to the latter.

    Google Scholar 

  • Hubert, David: 1925, ‘Über das Unendliche’, Mathematische Annalen 95 (1926), 161–190. Translated by Erna Putnam & Gerald J. Massey as ‘On the Infinite’, in Paul Benacerraf & Hilary Putnam, Philosophy of Mathematics, second edition (Cambridge, Cambridge University Press), 1983, 183–201. Also translated by Stephan Bauer-Mengelberg as ‘On the Infinite’, in Jean van Heijenoort, From Frege to Gödel (Cambridge, Mass., Harvard University Press), 1967, 369–392. Page numbers refer to Benacerraf & Putnam.

    Google Scholar 

  • Kitcher, Philip: 1979, ‘Frege's Epistemology’, The Philosophical Review 88, 235–262.

    Google Scholar 

  • Kitcher, Philip: 1983, The Nature of Mathematical Knowledge (Oxford, Oxford University Press).

    Google Scholar 

  • Lakatos, Imre: 1962, ‘Infinite Regress and Foundations of Mathematics’, Aristotelian Society: Supplementary Volume 36, 155–184. Reprinted in Lakatos, Mathematics, Science and Epistemology (edited by John Worral & Gregory Currie) (New York, Cambridge University Press), 1978, 3–23. Page numbers refer to the latter.

    Google Scholar 

  • Lakatos, Imre: 1976, ‘A Renaissance of Empiricism in the Recent Philosophy ofMathematics’, British Journal for the Philosophy of Science 27, 201–223. Reprinted in Lakatos, Mathematics, Science and Epistemology (edited by John Worral & Gregory Currie) (New York, Cambridge University Press), 1978, 24–42.

    Google Scholar 

  • Lind, Richard W.: 1984, ‘Microphenomenology and Numerical Relations’, The Monist 67, 29–45.

    Google Scholar 

  • Maddy, Penelope: 1980, ‘Perception and Mathematical Intuition’, Philosophical Review 89, 163–196.

    Google Scholar 

  • Maddy, Penelope: 1984, ‘Mathematical Epistemology: What is the Question?’, The Monist 67, 46–55.

    Google Scholar 

  • Mehlberg, Henryk: 1960, ‘The Present Situation in the Philosophy of Mathematics’, Synthese 12, 380–412. Reprinted in B. H. Kazemier & D. Vuysje, Logic and Language (Dordrecht, Holland, Reidel), 1962, 69–103. Page numbers refer to the latter.

    Google Scholar 

  • Parsons, Charles: 1967, ‘Mathematics, Foundations of’, in Paul Edwards, The Encyclopedia of Philosophy, Vol. 5 (New York & London, Macmillan & The Free Press), 188–213.

    Google Scholar 

  • Poincaré, Henri: 1905, Science and Hypothesis (New York, Dover, 1952).

    Google Scholar 

  • Quine, Willard Van Orman: 1953, ‘Logic and the Reification of Universals’, in Quine, From a Logical Point of View, second edition (Cambridge, Mass., Harvard University Press), 1961, 102–129.

    Google Scholar 

  • Resnik, Michael David: 1975, ‘Mathematical Knowledge and Pattern Cognition’, Canadian Journal of Philosophy 5, 25–39.

    Google Scholar 

  • Resnik, Michael David: 1981, ‘Mathematics as a Science of Patterns: Ontology and Reference’, Noûs 15, 529–550.

    Google Scholar 

  • Resnik, Michael David: 1982, ‘Mathematics as a Science of Patterns: Epistemology’, No∭ 16, 95–105.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1900, A Critical Exposition of the Philosophy of Leibniz (London, Cambridge University Press.)

    Google Scholar 

  • Russell, Bertrand Arthur William: 1901 ‘Recent Work on the Principles of Mathematics’, The International Monthly 4, 83–101. Reprinted with revisions as “Mathematics and the Metaphysicians”, in Russell [1918a], 74–96. Page numbers refer to the former. (In the reprint the original article is miscited as “Recent Work in the Philosophy of Mathematics”.)

    Google Scholar 

  • Russell, Bertrand Arthur William: 1903, The Principles of Mathematics, second edition (London, George Allen & Unwin), 1937.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1904, ‘The Axiom of Infinity’, Hibbert Journal 2, 809–812. Reprinted in Russell [1973], 256–259.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1906, ‘Les paradoxes de la logique’, Revue de Métaphysique et de Morale 14, 627–650. Translated by Russell as “On ‘Insolubilia’ and Their Solution by Symbolic Logic”, in Russell [1973], 190–214.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1907a, ‘The Study of Mathematics’, New Quarterly 1, 29–44. Reprinted in Russell [1910], 71–86 (first edition only), in Russell [1918a], 58–73, and in Russell [1985], 85–93. Page numbers refer to the New Quarterly.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1907b, ‘The Regressive Method of Discovering the Premises of Mathematics’, read before the Cambridge Mathematical Club, 09 March 1907. Published in Russell [1973], 272–283.

  • Russell, Bertrand Arthur William: 1910, Philosophical Essays (London, Longmans, Green & Co.)

    Google Scholar 

  • Russell, Bertrand Arthur William: 1911, ‘L'importance philosophique de la logistique’, Revue de Métaphysique et de Morale 19, 281–291. Translated by P. E. B. Jourdain (with revisions by Russell) as ‘The Philosophical Implications of Mathematical Logic’, The Monist 23 (1913), 481–493 and reprinted in Russell [1973], 284–294. Page numbers refer to the The Monist.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1918a, Mysticism and Logic (London, Longmans Green).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1918b, 1919, ‘The Philosophy of Logical Atomism’, The Monist 28, 495–527; 29, 32–63, 190–222, 345–380. Reprinted in Russell [1956a], 177–281. Page numbers refer to the former.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1919, Introduction to Mathematical Philosophy (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1924, ‘Logical Atomism’, in J. H. Muirhead, Con-temporary British Philosophy, first series (London, George Allen & Unwin), 1924, 357–383. Reprinted in Russell [1956a], 323–343. Page numbers refer to the former.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1940, An Inquiry Into Meaning and Truth, (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1944a, ‘My Mental Development’, in Paul Arthur Schilpp, The Philosophy of Bertrand Russell, third edition (New York, Tudor), 1951, 1–20.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1944b, ‘Reply to Criticisms’, in Paul Arthur Schilpp, The Philosophy of Bertrand Russell, third edition (New York, Tudor), 1951, 679–741.

    Google Scholar 

  • Russell, Bertrand Arthur William: 1956a, Logic and Knowledge, edited by Robert Charles Marsh (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand Arthur William 1956b, Portraits From Memory (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1959, My Philosophical Development (New York, Simon & Schuster).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1967, 1968, 1969, The Autobiography of Bertrand Russell, 3 volumes (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1973, Essays in Analysis (edited by Douglas Lackey) (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand Arthur William: 1985, Contemplation and Action, 1902–14, (The Collected Papers of Bertrand Russell, Vol. 12) (London, George Allen & Unwin).

    Google Scholar 

  • Russell, Bertrand & Alfred North Whitehead: 1910, 1912, 1913, Principia Mathematica, 3 volumes, second edition (New York, Cambridge University Press), 1925 (Vol. 1), 1927 (Vol. 2 & 3).

    Google Scholar 

  • Steiner, Mark: 1975, Mathematical Knowledge (Ithaca, N.Y. & London, Cornell University Press).

    Google Scholar 

  • Wang, Hao: 1957, The Axiomatization of Arithmetic’, Journal of Symbolic Logic 22, 145–158.

    Google Scholar 

  • Whitehead, Alfred North & Bertrand Russell: 1910, 1912, 1913, Principia Mathematica, 3 volumes, second edition (New York, Cambridge University Press), 1925 (Vol. 1), 1927 (Vol. 2 & 3).

    Google Scholar 

  • Wittgenstein, Ludwig: 1956, Bermerkungen über die Grundlagen der Mathematik. Translated by G. E. M. Anscombe as Remarks on the Foundations of Mathematics (edited by G. E. M. Anscombe, R. Rhees & G. H. von Wright), Oxford: Blackwell, 1956.

    Google Scholar 

  • Wood, Allan: 1959, ‘Russell's Philosophy: A Study of its Development’, in Russell [1959], 255–277.

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  1. Department of Philosophy, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    A. D. Irvine

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Work on this paper began while I was a Visiting Fellow at the University of Pittsburgh's Center for Philosophy of Science and continued later at the University of Toronto. During this time, financial support was gratefully received from the Social Sciences and Humanities Research Council of Canada.

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Irvine, A.D. Epistemic logicism & Russell's regressive method. Philosophical Studies 55, 303–327 (1989). https://doi.org/10.1007/BF00355328

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