Primary Literature

• Russell, Bertrand, [PoM] 1903, The Principles of Mathematics, Cambridge: Cambridge University Press. [PoM available online] (Scholar)
• –––, 1905, “On Denoting”, Mind, 14(4): 479–493. doi:10.1093/mind/xiv.4.479 (Scholar)
• –––, 1911, “On the Axioms of the Infinite and of the Transfinite”, printed in Logical and Philosophical Papers 1909–1913: The Collected Papers of Bertrand Russell, Vol. 6, John G. Slater (ed.), London and New York: Routledge, 1992, 41–53. (Scholar)
• –––, 1919, Introduction to Mathematical Philosophy, London: George Allen & Unwin. (Scholar)
• –––, 1948, “Whitehead and Principia Mathematica”, Mind, 57(226): 137–138. doi:10.1093/mind/lvii.226.137 (Scholar)
• –––, 1959, My Philosophical Development, London: George Allen and Unwin, and New York: Simon and Schuster; reprinted London: Routledge, 1993. (Page numbers are to the 1959 edition.) (Scholar)
• –––, 1967, 1968, 1969, The Autobiography of Bertrand Russell, 3 vols., London: George Allen and Unwin; Boston: Little Brown and Company (Vols 1 and 2), New York: Simon and Schuster (Volume 3). (Scholar)
• Whitehead, Alfred North, 1898, A Treatise on Universal Algebra, Cambridge: Cambridge University Press. [Whitehead 1898 available online] (Scholar)
• –––, 1906, “On Mathematical Concepts of the Material World”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 205(387–401): 465–525. doi:10.1098/rsta.1906.0014 (Scholar)
• –––, 1926, “Notes: Principia Mathematica”, Mind, 35(137): 130. doi:10.1093/mind/xxxv.137.130-a (Scholar)
• Whitehead, Alfred North, Bertrand Russell, and M.R. James, 1910, Contract for the First Edition of Principia Mathematica, reprinted in “Illustrations: Manuscripts Relating to Principia Mathematica”, Russell: The Journal of Bertrand Russell Studies, 31(1): 82. doi:10.15173/russell.v31i1.2199 (Scholar)
• Whitehead, Alfred North and Bertrand Russell, 1910, 1912, 1913, Principia Mathematica, 3 volumes, Cambridge: Cambridge University Press; 2nd edition, 1925 (Vol. I), 1927 (Vols II, II); abridged as Principia Mathematica to ∗56, Cambridge: Cambridge University Press, 1956. (Page numbers are to the second edition.) (Scholar)

Secondary Literature

• Borel, Émile, 1898, Leçons Sur La Théorie Des Fonctions, Paris. (Scholar)
• Bernays, Paul, 1926, “Axiomatische Untersuchungen des Aussagen-Kalkuls der Principia Mathematica”, Mathematische Zeitschrift, 25: 305–320. doi:10.1007/bf01283841 (Scholar)
• Blackwell, Kenneth, 2005, “A Bibliographical Index for Principia Mathematica”, Russell: The Journal of Bertrand Russell Studies, 25(1): 77–80. doi:10.15173/russell.v25i1.2072 (Scholar)
• –––, 2011, “The Wit and Humour of Principia Mathematica”, in Griffin, Linsky, and Blackwell 2011: 151–160. doi:10.15173/russell.v31i1.2198 (Scholar)
• Boolos, George, 1971, “The Iterative Conception of Set”, Journal of Philosophy, 68(8): 215–231. doi:10.2307/2025204 (Scholar)
• –––, 1994, “The Advantages of Honest Toil over Theft”, Mathematics and Mind, Alexander George (ed.), Oxford: Oxford University Press, 27–44. (Scholar)
• Burgess, John P., 2005, Fixing Frege, Princeton: Princeton University Press. (Scholar)
• Cantor, Georg, 1883 [1996], Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen, Teubner, Leipzig. Printed as “Foundations of a General Theory of Manifolds: A Mathematico-Philosophical Investigation into the Theory of the Infinite” in From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Vol. II, William Ewald (trans.), Oxford: Oxford University Press, 1996, 878–920. (Scholar)
• –––, 1895 & 1897 [1915], “Beiträge zur Begründung der transfiniten Mengenlehre”, Mathematische Annalen, (1895) 46(4): 481–512 & (1897) 49(2): 207–246. Translated as Contributions to the Founding of the Theory of Transfinite Numbers, Philip E.B. Jourdain (trans), Chicago: Open Court, 1915. doi:10.1007/BF02124929 (de) doi:10.1007/BF01444205 (de) (Scholar)
• Chihara, Charles S., 1973, Ontology and the Vicious Circle Principle, Ithaca, NY: Cornell University Press. (Scholar)
• Church, Alonzo, 1974, “Russellian Simple Type Theory”, Proceedings and Addresses of the American Philosophical Association, 47: 21–33. doi:10.2307/3129899 (Scholar)
• –––, 1976, “Comparison of Russell’s Resolution of the Semantical Antinomies with That of Tarski”, The Journal of Symbolic Logic, 41(04): 747–760. doi:10.2307/2272393 (Scholar)
• Chwistek, Leon, 1912 [2017], “Zasada sprzeczności w świetle nowszych badań Bertranda Russella”, Rozprawy Akademii Umiejętności (Kraków), Wydzial   historyczno-filozoficzny, Series II. 30: 270–334. Translated by Rose Rand as “The Law of Contradiction in the Light of Recent Investigations of Bertrand Russell”, in The Significance of the Lvov-Warsaw School in the European Culture, Anna Brożek, Friedrich Stadler, and Jan Woleński (eds.), Cham: Springer International Publishing, 2017, 227–289. doi:10.1007/978-3-319-52869-4_13 (Scholar)
• –––, 1921 [1967], “Antynomie logiki formalnej”, Przegla̧d Filozoficzny, 24: 164–171. Printed as “Antinomies of Formal Logic”, Z. Jordan (trans.), in Polish Logic 1920-1939, Storrs McCall (ed.), Oxford: Clarendon Press, 1967, 338–345. (Scholar)
• Collins, Jordan E., 2012, A History of the Theory of Types: Developments after the Second Edition of Principia Mathematica, Saarbrücken: Lambert Academic Publishing. (Scholar)
• Copi, Irving M., 1950, “The Inconsistency or Redundancy of Principia Mathematica”, Philosophy and Phenomenological Research, 11(2): 190–199. doi:10.2307/2103637 (Scholar)
• –––, 1971, The Theory of Logical Types, London: Routledge and Kegan Paul. (Scholar)
• Dedekind, Richard, 1872 [1901], Stetigkeit und irrationale Zahlen, Braunschweig: Vieweg. Translated 1901, “Continuity and Irrational Numbers”, Wooster Woodruff Beman (trans.), in Essays on the Theory of Numbers Chicago: Open Court. doi:10.1007/978-3-322-98548-4 (Scholar)
• Eliot, T.S., 1927, “A Commentary”, The Monthly Criterion, 6(4), 289–291. (Scholar)
• Enderton, Herbert B., 1977, Elements of Set Theory, New York: Academic Press. (Scholar)
• Ewald, William and Wilfried Sieg (eds), 2013, David Hilbert’s Lectures on the Foundations of Arithmetic and Logic 1917–1933, Berlin: Springer Verlag. doi: doi:10.1007/978-3-540-69444-1 (Scholar)
• Frege, Gottlob, 1879 [1967], Begriffsschrift: Eine Der Arithmetische Nachgebildete Formelsprache des Reinen Denkens, Halle a/S: Louis Nebert. Translated by Stefan Bauer-Mengelberg as “Begriffsschrift, A Formula Language, Modeled Upon that of Arithmetic, for Pure Thought” in Jean van Heijenoort (ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Cambridge, MA: Harvard University Press, 1967, 1–82. [Frege 1879 available online (de)] (Scholar)
• –––, 1884 [1950], Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl, Breslau: Koebner, translated by J.L. Austin as The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number, Oxford: Basil Blackwell, 1950. (Scholar)
• –––, 1892 [1984], “Über Sinn und Bedeutung”, Zeitschrift für Philosophie und philosophische Kritik 100, 25-50, translated by Max Black as “On Sense and Meaning” in Gottlob Frege: Collected Papers on Mathematics, Logic, and Philosophy, Brian McGuinness, ed., Oxford: Basil Blackwell, 1984, 157–177. (Scholar)
• –––, 1893/1903 [2013], Grundgesetze der Arithmetik, Band I (1893), Band II (1903), Jena: Verlag Hermann Pohle. Translated (preserving the original pagination) by Philip A. Ebert & Marcus Rossberg with Crispin Wright as Basic Laws of Arithmetic, Oxford: Oxford University Press, 2013. (Scholar)
• –––, 1980, Philosophical and Mathematical Correspondence, G. Gabriel, et al. (eds.), Chicago: University of Chicago Press. (Scholar)
• Gabbay, Dov M. and John Woods (eds.), 2009, Handbook of the History of Logic, Volume 5: Logic From Russell to Church, Amsterdam: Elsevier/North Holland. (Scholar)
• Gandon, Sébastien, 2008, “Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics”, History and Philosophy of Logic, 29(1): 1–30. doi:10.1080/01445340701398530 (Scholar)
• –––, 2011, “Principia Mathematica, part VI: Russell and Whitehead on Quantity”, Logique et Analyse, 54(214): 225–247. [Gandon 2011 available online] (Scholar)
• –––, 2012, Russell’s Unknown Logicism, New York: Palgrave Macmillan. (Scholar)
• Gödel, Kurt, 1933 [1995], “The Present Situation in the Foundations of Mathematics”, lecture delivered to the Mathematical Association of America and the American Mathematical Society, Cambridge, MA, December 1933. Printed in Kurt Gödel: Collected Works, Vol. II, Solomon Feferman, et al. (eds.), Oxford and New York: Oxford University Press, 1995, 45–53. (Scholar)
• –––, 1944 [1951], “Russell’s Mathematical Logic”, in The Philosophy of Bertrand Russell, Paul Arthur Schilpp (ed.), first edition, Chicago: Northwestern University, 1944; third edition, New York: Tudor, 1951, 123–153. (Scholar)
• Grattan-Guinness, I., 2000, The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel, Princeton and Oxford: Princeton University Press. (Scholar)
• Griffin, Nicholas and Bernard Linsky (eds.), 2013, The Palgrave Centenary Companion to Principia Mathematica, London: Palgrave Macmillan. doi:10.1057/9781137344632 (Scholar)
• Griffin, Nicholas, Bernard Linsky and Kenneth Blackwell (eds.), 2011, Principia Mathematica at 100, Hamilton, ON: Bertrand Russell Research Centre; also published as a special issue of Russell: The Journal of Bertrand Russell Studies, 31(1). [Griffin, Linsky, and Blackwell 2011 available online] (Scholar)
• Guay, Alexandre (ed.), 2012, Autour de Principia Mathematica de Russell et Whitehead, Dijon: Editions Universitaires de Dijon. (Scholar)
• Hale, Bob and Crispin Wright, 2001, The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, Oxford: Oxford University Press. doi:10.1093/0198236395.001.0001 (Scholar)
• Hausdorff, Felix, 1906, “Untersuchungen über Ordnungstypen”, Berichte der Königlichen Sächsische Akademie der Wissenschaft (Leipzig), 58: 106–169; 59: 84–159. (Scholar)
• Hilbert, David and W. Ackermann, 1928, Grundzüge der theoretischen Logik, Berlin: Julius Springer Verlag. Translated as “Principles of Mathematical Logic”, Providence: American Mathematical Society, 1958. (Scholar)
• Hilbert, David and Paul Bernays, 1934, Grundlagen der Mathematik, Berlin: Julius Springer Verlag. (Scholar)
• Hinkis, Arie, 2013, Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion, New York, Dordrecht, London: Birkhäuser. (Scholar)
• Hintikka, Jaakko, 2009, “Logicism”, in Irvine 2009: 271–290. doi:10.1016/b978-0-444-51555-1.50010-9 (Scholar)
• Irvine, Andrew D. (ed.), 2009, Philosophy of Mathematics (Handbook of the Philosophy of Science), Amsterdam: Elsevier. doi:10.1016/b978-0-444-51555-1.x0001-7 (Scholar)
• Kahle, Reinhard, 2013, “David Hilbert and Principia Mathematica in Poland”, in Griffin and Linsky, 2013: 21–34. (Scholar)
• Kanamori, Akihiro, 2009, “Set Theory from Cantor to Cohen”, in Irvine 2009: 395-459. doi:10.1016/b978-0-444-51555-1.50014-6 (Scholar)
• Kleene, S.C., 1952, Introduction to Metamathematics, Princeton: Van Nostrand. (Scholar)
• Landini, Gregory, 1998, Russell’s Hidden Substitutional Theory, New York and Oxford: Oxford University Press. (Scholar)
• –––, 2011, Russell, London and New York: Routledge. (Scholar)
• –––, 2016, “Whitehead’s (Badly) Emended Principia”, History and Philosophy of Logic, 37(2): 114–169. doi:10.1080/01445340.2015.1082063 (Scholar)
• Link, Godehard (ed.), 2004, One Hundred Years of Russell’s Paradox, Berlin and New York: Walter de Gruyter. (Scholar)
• Linsky, Bernard, 1990, “Was the Axiom of Reducibility a Principle of Logic?” Russell, 10: 125–140; reprinted in A.D. Irvine (ed.), 1990, Bertrand Russell: Critical Assessments, 4 vols., London: Routledge, vol. 2, 150–264. doi:10.15173/russell.v10i2.1775 (Scholar)
• –––, 1999, Russell’s Metaphysical Logic, Stanford: CSLI Publications. (Scholar)
• –––, 2002, “The Resolution of Russell’s Paradox in Principia Mathematica”, Philosophical Perspectives, 16: 395–417. doi:10.1111/1468-0068.36.s16.15 (Scholar)
• –––, 2003, “Leon Chwistek on the No-Classes Theory in Principia Mathematica”, History and Philosophy of Logic, 25(1): 53–71. doi:10.1080/01445340310001614698 (Scholar)
• –––, 2004, “Classes of Classes and Classes of Functions in Principia Mathematica”, in Link 2004: 435–447. (Scholar)
• –––, 2009, “From Descriptive Functions to Sets of Ordered Pairs”, in Alexander Hieke and Hannes Leitgeb, Reduction-Abstraction-Analysis, Vol. 11 of Publications of the Austrian Ludwig Wittgenstein Society, new series, Frankfurt: Ontos Verlag, 259-272. (Scholar)
• –––, 2011, The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition, Cambridge: Cambridge University Press. doi:10.1017/cbo9780511760181 (Scholar)
• –––, 2016, “Propositional Logic from The Principles of Mathematics to Principia Mathematica”, in Early Analytic Philosophy: New Perspectives on the Tradition, Sorin Costreie (ed.), Cham: Springer International Publishing, 213–229. doi:10.1007/978-3-319-24214-9_8 (Scholar)
• Linsky, Bernard and Kenneth Blackwell, 2005, “New Manuscript Leaves and the Printing of the First Edition of Principia Mathematica”, Russell: The Journal of Bertrand Russell Studies, 25(2): 141–154. doi:10.15173/russell.v25i2.2084 (Scholar)
• Mares, Edwin D., 2007, “The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility”, Notre Dame Journal of Formal Logic, 48(2): 237–251. doi:10.1305/ndjfl/1179323266 (Scholar)
• Mayo-Wilson, Conor, 2011, “Russell on Logicism and Coherence”, in Griffin, Linsky, and Blackwell 2011: 63–79. doi:10.15173/russell.v31i1.2206 (Scholar)
• Myhill, John, 1974, “The Undefinability of the Set of Natural Numbers in the Ramified Principia”, in Bertrand Russell’s Philosophy, George Nakhnikian (ed.), London: Duckworth, 19-27. (Scholar)
• Proops, Ian, 2006, “Russell’s Reasons for Logicism”, Journal of the History of Philosophy, 44(2): 267–292. doi:10.1353/hph.2006.0029 (Scholar)
• Quine, W.V.O., 1951, “Whitehead and Modern Logic”, in The Philosophy of Alfred North Whitehead, P.A. Schilpp (ed.), New York: Tudor Publishing, 125-163. (Scholar)
• –––, 1960, Word and Object, Cambridge: MIT Press. (Scholar)
• –––, 1963, Set Theory and Its Logic, Cambridge: Harvard University Press (Scholar)
• –––, 1966a, Selected Logic Papers, New York: Random House. (Scholar)
• –––, 1966b, Ways of Paradox, New York: Random House. (Scholar)
• Ramsey, Frank, 1931, “The Foundations of Mathematics”, in his The Foundations of Mathematics and Other Essays, London: Kegan Paul, Trench, Trubner, 1-61. (Scholar)
• Rodriguez-Consuegra, Francisco, 1991, The Mathematical Philosophy of Bertrand Russell, Boston: Birkhäuser Press; repr. 1993. (Scholar)
• Shapiro, Stewart (ed.), 2005, The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford: Oxford University Press. doi:10.1093/oxfordhb/9780195325928.001.0001 (Scholar)
• Sheffer, Henry M., unpublished, Notes on Bertrand Russell's Lectures (Cambridge, MA 1910), in Harvard University Archives: Henry Maurice Sheffer Personal Archive [accessions], 1891–1970. For further information see URL = <http://id.lib.harvard.edu/alma/990138368470203941/catalog>. (Scholar)
• Solomon, Graham 1989, “What became of Russell's ‘relation arithmetic’?”, Russell: The Journal of Bertrand Russell Studies, 9(2): 168 –173. (Scholar)
• Stevens, Graham, 2011, “Logical Form in Principia Mathematica”, in Griffin, Linsky, and Blackwell 2011: 9–28. doi:10.15173/russell.v31i1.2203 (Scholar)
• Suppes, Patrick, 1960, Axiomatic Set Theory, Princeton: van Nostrand. (Scholar)
• Tarski, Alfred, 1956, Ordinal Algebras, Amsterdam: North Holland. (Scholar)
• Urquhart, Alasdair, 1988, “Russell’s Zigzag Path to the Ramified Theory of Types”, Russell: The Journal of Bertrand Russell Studies, 8(1): 82–91. doi:10.15173/Russell.v8i1.1735 (Scholar)
• –––, 2012, Review of Bernard Linsky’s The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition, Notre Dame Philosophical Reviews, [Urquhart 2012 available online]. (Scholar)
• –––, 2013, “Principia Mathematica: The First 100 Years”, in Griffin and Linsky 2013: 3–20. (Scholar)
• Wahl, Russell, 2011, “The Axiom of Reducibility”, in Griffin, Linsky, and Blackwell 2011: 45–62. doi:10.15173/russell.v31i1.2205 (Scholar)
• Wiener, Norbert, 1914, “A Simplification of the Logic of Relations”, Proceedings of the Cambridge Philosophical Society, 17: 387–90. [Wiener 1914 available online] (Scholar)
• Wittgenstein, Ludwig, 1922, Tractatus Logico-Philosophicus, C.K. Ogden (trans.), London: Routledge & Kegan Paul. (Scholar)
• Wolenski, Jan , 2013, “Principia Mathematica in Poland”, in Griffin and Linsky, 2013: 35–55. (Scholar)
• Wright, Crispin, 1983, Frege’s Conception of Numbers as Objects, Aberdeen: Aberdeen University Press. (Scholar)
• Wrinch, Dorothy, 1919, “On the Exponentiation of Well-Ordered Series”, Proceedings of the Cambridge Philosophical Society, 19: 219-233. [Wrinch 1919 available online] (Scholar)
• Zermelo, Ernst, 1908 [1967], “Neuer Beweis für die Möglichkeit einer Wohlordnung”, Mathematische Annalen, 65(1): 107–128. Translated by Stefan Bauer-Mengelberg as “A New Proof of the Possibility of a Well-Ordering”, in Jean van Heijenoort (ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Cambridge, MA: Harvard University Press, 1967, 183–198. doi:10.1007/BF01450054 (de) (Scholar)