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. Øystein 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.