Volume I: Historical Readings in the Philosophy of Mathematics 1. Plato (early 4th century BC). From E. Hamilton & H. Cairns (eds. 1963 corrected reprint., Bollingen Foundation):Meno 80b-86b, W.K.C. Guthrie (trans.), pages 363-371 2. Plato (early 4th century BC). From B. Jowett (ed.), The Dialogues of Plato (1953), Oxford University Press: Phaedo 72e-77d, B. Jowett (trans.), pages 425-431 3. Plato (early 4th century BC). From John Cooper (ed.), Plato: Complete Works (1997), (trans.) G.M.A. Grube & C.D.C. Reeve, Hackett: Republic Book 6, 507a-511e, pages 1126-1133. 4. Plato (early 4th century BC). From John Cooper (ed.), Plato: Complete Works (1997), (trans.) G.M.A. Grube & C.D.C. Reeve, Hackett: Republic Book 7, 525a-527c, pages 1140-1145. 5. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book B, part ii, pages 1574-1575. 6. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book E, part I, page 1619. 7. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book Z, part x-xi, pages 1633-1637. 8. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book Th , part ix, page 1660. 9. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book I, parts i-ii, pages 1662-1665. 10. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book K, parts ii-iv and vii, pages 1675-1677 and 1680-1681. 11. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Metaphysics Book M, parts i-iii, pages 1701-1705 12. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), (trans.) R.P. Hardie and R.K. Gaye, Princeton University Press.Physics, Book B, part ii, pages 330-332. 13. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Princeton University Press:Physics, Book C, parts vi-viii-8, pages 351-354. 14. Aristotle (mid-4th century BC). From Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), (trans.) J.A. Smith, Princeton University Press: De Anima (On the Soul), Book C, parts vi-viii, pages 684-687. 15. Rene Descartes (1637) Part 2 of Discourse on Method, J. Cottingham, R. Stoothoff and D. Murdoch (trans. & eds.) Descartes: Selected Philosophical Writings, pages 25-31. 16. John Locke (1689), from An Essay Concerning Human Understanding, R.S. Woolhouse (ed.) (1997), Penguin: Book I, Chapter II, pages 59-75. 17. John Locke (1689), from An Essay Concerning Human Understanding, R.S. Woolhouse (ed.) (1997), Penguin: Book IV, Chapter II, pages 471-479. 18. George Berkeley (1710), Treatise Concerning the Principles of Human Knowledge, 118-134, pages 131-139, D. M. Clarke (ed) (2008), Cambridge University Press. 19. Gottfried Leibniz (1716), from R.S. Woolhouse and R. Francks (trans. and eds.) G.W. Leibniz: Philosophical Texts (1998), Oxford University Press. Sections 23 to 25 of Reply to Bayle's Note L, pages 252-253. 20. Gottfried Leibniz (1714), from R.S. Woolhouse and R. Francks (trans. and eds.) G.W. Leibniz: Philosophical Texts (1998), Oxford University Press. Sections 28 to 38 of Monadology, pages 271-273. 21. Gottfried Leibniz (1685), from P. Wiener (ed.) Leibniz: Selections (1951), Charles Scribner's Sons. "The Art of Discovery" pages 50-58. 22. D'Alembert, J. L. (1751), Preliminary Discourse to the Encyclopedia of Diderot (1995), R.N.Schwab (transl), University of Chicago Press, pages 16-29. 23. Immanuel Kant (1787), from N. Kemp Smith (transl. and ed.) Critique of Pure Reason (B) (1929), Macmillan. Introduction and Transcendental Aesthetic, B1-73, pages 41-91. 24. Immanuel Kant (1783), from P. Carus & J. W. Ellington Prolegomena to any future metaphysics that will be able to come forward as science (1977), Hackett. Sections 6-13 (inc. Remarks I and II), pages 25-33. 25. John Stuart Mill (1843), from A System of Logic, volume 7 of Collected Works of John Stuart Mill, J.M. Robson (ed.) (1973), University of Toronto Press: Book II, Chapter VI, pages 252-261. 26. John Stuart Mill (1843), from A System of Logic, volume 7 of Collected Works of John Stuart Mill, J.M. Robson (ed.) (1973), University of Toronto Press: Book III, Chapter XXIV, pages 604-621. 27. Richard Dedekind (1888), "On the nature and meaning of numbers" in Essays on the Theory of Numbers (1963), pages 31-115, transl. by W.W. Beman, Dover. 28. Albert Einstein (1921), "Geometrie und Erfahrung", transl. by S. Bargmann as "Geometry and Experience" and repr. in his Ideas and Opinions (1954), Condor, pp. 232-46. Volume II Early 20th Century Philosophies: Logicism, Logical Empiricism, Intuitionism and Formalism Logicism and its critics 29. Gottlob Frege (1884), Foundations of Arithmetic, transl. by J. Austin (Blackwell, 1950), sections 55-109, pages 67e-119e. 30. Gottlob Frege (1893), from The Basic Laws of Arithmetic, transl. and ed. by P. A. Ebert & M. Rossberg with C. Wright, Oxford University Press. Introduction and Part I (sections 1 to 52), pp. 1-69 and Appendices to Volume I, pp. 239-251. 31. Bertrand Russell's letter to Frege and Frege's reply to Russell, transl. by B. Woodward, in J. van Heijenoort (ed.), From Frege to Godel, a source book in Mathematical Logic 1879 -1931, Harvard UP, pp 124-128. 32. Alfred North Whitehead & Bertrand Russell, B. (1910-13), Introduction to the 2nd ed. and Introduction, Principia Mathematica, pp. xii-xlvi and 1-84 of Principia Mathematica to *56 (1997), Cambridge University Press. 33. Henri Poincare (1906), "Mathematics and Logic III" transl. by G.B. Halsted & W. Ewald and repr. in Ewald (1996), pp. 1052-1071. 34. Bertrand Russell (1919), Introduction to Mathematical Philosophy , Spokesman, Chapters 1 (pp.1-10), 2 (pp.11-19), 3 (pp.20-28), 12 (pp.117-130), 13 (pp.131-143), and 18 (pp.194-206). 35. Crispin Wright (1997), "On the Philosophical Significance of Frege's Theorem", in R.G. Heck (ed.), Language, Thought and Logic: Essays in Honour of Michael Dummett. Pages 201-244. 36. George Boolos (1997), "Is Hume's Principle Analytic?", in R.G. Heck (ed.), Language, Thought and Logic: Essays in Honour of Michael Dummett. Pages 245-261. Intuitionism 37. L.E.J. Brouwer, "On the significance of the principle of excluded middle in mathematics, especially in function theory" incl. Addenda & Corrigenda, transl. by S. Bauer-Mengelberg, repr. in van Heijenoort (1967), pp. 335-45. 38. Arend Heyting, (1931), "The intuitionist foundations of mathematics" (1931), transl. by E. Putnam & G.J. Massey and repr. in P. Benacerraf & H. Putnam (eds), Philosophy of Mathematics: selected readings 1983, Cambridge University Press, pp 52-61. 39. Arend Heyting (1956), "Disputation", in P. Benacerraf & H. Putnam (eds), Philosophy of Mathematics: selected readings 1983, Cambridge University Press, pp. 66-76. 40. Michael Dummett (1973), "The philosophical basis of intuitionistic logic", in his Truth and Other Enigmas (Duckworth, 1978), pages 215-47. Formalism 41. David Hilbert (1925), "On the infinite", trans. by S. Bauer-Mengelberg, in van Heijenoort (1967), pp. 367-392. 42. William Tait (1981), "Finitism", Journal of Philosophy 77, pp. 524-46. Logical Empiricism 43. A.J. Ayer (1936), Chapter IV of Language, Truth and Logic, Penguin, pages 64-83 44. Moritz Schlick (1925), 7 (pp.31-39) and 38 (pp.348-358) of General Theory of Knowledge (1974), transl. by A. E. Blumberg, Springer-Verlag. 45. Rudolf Carnap (1950), "Empiricism, Semantics and Ontology", repr. in Benacerraf & Putnam (1983), pp. 241-257. Volume III Contemporary Foundations, Set Theory and Structuralism 46. Ernst Zermelo (1908), "Investigations in the Foundations of Set Theory I" trans. by S. Bauer-Mengelberg as and repr. in J. van Heijenoort (ed.) (1967), From Frege to Godel, Harvard University Press, pp. 199-215. 47. Willard V. Quine (1960), Chapter 7 of Word and Object (pages 233-76), MIT Press. 48. Paul Benacerraf (1965), "What Numbers Could Not Be", Philosophical Review 74, pp. 47-73. 49. Paul Benacerraf (1973), "Mathematical Truth", The Journal of Philosophy 70, pp. 661-679. 50. Penelope Maddy (1990), Chapter 2 of Realism in Mathematics, pages 36-80, Oxford University Press. 51. Hilary Putnam (1967), "Mathematics without Foundations", The Journal of Philosophy 64, pp. 5-22. 52. Geoffrey Hellman (1989), Introduction and Chapter 1 (pp. 1-52) of Mathematics without Numbers, Oxford University Press. 53. Charles Parsons (1990), "The Structuralist View of Mathematical Objects", Synthese 84, pp. 303-46. 54. David Lewis (1993), "Mathematics is Megethology", in his Philosophical Papers (1998), Cambridge University Press, pp. 203-229. 55. Geoffrey Hellman (2001), "Three Varieties of Mathematical Structuralism", Philosophia Mathematica 9, pp. 184-211. 56. Alex Oliver & Timothy Smiley (2006), "What are sets and what are they for?", Philosophical Perspectives 20, pp. 123-55. 57. Oystein Linnebo and Richard Pettigrew (2011), "Category Theory as an Autonomous Foundation", Philosophia Mathematica 19, pp. 227-54. Volume IV: Proof and Mathematical Justification 58. Kurt Godel (1931), "On formally undecidable propositions of Principia mathematica and related systems I", , transl. by J. van Heijenoort and repr. in vol. I of his Collected Works, S. Feferman et al. (eds), Oxford University Press (1990), pp. 144-195. 59. Kurt Godel (1964), "What is Cantor's Continuum Problem?", repr. in vol. II of his Collected Works, pp. 254-270. 60. George Boolos (1971), "The Iterative Conception of Set", Journal of Philosophy 68, pp. 215-231. 61. Imre Lakatos (1976), "A renaissance of empiricism in the recent philosophy of mathematics", The British Journal for the Philosophy of Science 27, pp. 201-223. 62. Daniel Isaacson (1987) "Arithmetical Truth and Hidden Higher-Order Concepts", in W.D. Hart (ed.), The Philosophy of Mathematics, Oxford University Press (1996), pp. 203-224. 63. Penelope Maddy (1988), "Believing the Axioms I", Journal of Symbolic Logic 53, pp. 481-511. 64. Penelope Maddy (1993), "Does V = L?", Journal of Symbolic Logic 58, pp. 15-41 65. Don Fallis (1997), "The Epistemic Status of Probabilistic Proof", Journal of Philosophy 94, pp. 165-186. 66. Mic Detlefsen (2008), "Purity as an Ideal of Proof", in P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford University Press, pp. 179-197. 67. Peter Smith (2013), Chapters 44 and 45 (pages 338-66) of An Introduction to Godel's Incompleteness Theorems (2nd ed.), Cambridge University Press. 68. A.C. Paseau (2015) "Mathematical Knowledge without Proof", The British Journal for the Philosophy of Science, pp.1-25. Volume V: The Indispensability Argument 69. Willard V. Quine (1951), "Two Dogmas of Empiricism" in his From A Logical Point of View, pages 20-46. 70. Willard V. Quine & Nelson Goodman (1947), "Steps Towards a Constructive Nominalism", Journal of Symbolic Logic 12, pp. 105-22. 71. Hilary Putnam (1971), Philosophy of Logic, Harper & Row, repr. in his Mathematics, Matter and Method: Philosophical Papers 1, pages 323-357, Cambridge University Press. 72. Hartry Field (1980), Preliminary Remarks and Chapters 1-5 (pp. 1-46) of Science without Numbers, Blackwell. 73. Hartry Field (1984), "Is Mathematical Knowledge just Logical Knowledge?", Philosophical Review 93, pp. 509-52. 74. George Boolos (1985), "Nominalist Platonism", Philosophical Review 94, pp. 327-44. 75. Elliot Sober (1993), "Mathematics and Indispensability", Philosophical Review 102, pp. 35-57. 76. Penelope Maddy (1997), Chapter II.6 of Naturalism in Mathematics, pages 133-157, Oxford University Press. 77. John Burgess & Gideon Rosen (1997), A Subject With No Object, Oxford University Press, pages 3-66 (Introduction) and pages 205-44 (Conclusion). 78. Mark Colyvan (2001), Chapters 4-6 (pp. 67-140) of The Indispensability of Mathematics, Oxford University Press. 79. Alan Baker (2005), "Are there genuine mathematical explanations of physical phenomena?", Mind 114, pp. 223-238. 80. A.C. Paseau (2007), "Scientific Platonism", in M. Leng, A.C. Paseau & M. Potter (eds), Mathematical Knowledge, Oxford University Press, pp. 123-149.

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