Towards a philosophy of real mathematics

Towards a Philosophy of Real Mathematics

Volumn , Issue , 2003, Pages 1-288

  Corfield, David ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84929719536     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511487576     Document Type: Book

References (287)

1. Abramsky, S., 1997, ‘Games in the Semantics of Programming Languages’, in Proceedings of the 11th Amsterdam Colloquium, P. Dekker, M. Stokhof and Y. Venema (eds.), University of Amsterdam: 1-6.
2. Adams, F., 1978, Infinite Loop Spaces, Princeton University Press.
3. Albert, M., 2001, ‘Bayesian Learning and Expectations Formation: Anything Goes’, in Corfield and Williamson (eds.): 341-62.
4. Alexanderson, G., 2000, The Random Walks of George Pólya, The Mathematical Association of America.
5. Alon, A., Bourgain, J., Connes, A., Gromov, M. and Milman, V. (eds.), 2000, GAFA 2000 Visions in Mathematics: Towards 2000, Birkhäuser.
6. Arnold, V., 1963, ‘Small Denominators and Problems of Stability of Motion’, Russian Mathematical Surveys, 18(6): 85-192.
7. Arnold, V., (ed.), 1988, Dynamical Systems III, Springer-Verlag.
8. Arnold, V., 2000, ‘Polymathematics: Is Mathematics a Single Science or a Set of Arts?’, in Arnold et al. (eds.): 403-16.
9. Arnold, V., Atiyah, M., Lax, P. and Mazur, B. (eds.), 2000, Mathematics: Frontiers and Perspectives, American Mathematical Society.
10. Ashtekar, A., 2002, ‘Quantum Geometry in Action: Big Bang and Black Holes’, preprint math-ph/0202008 available at xxx.arXiv.cornell.edu.
11. Aspray, W. and Kitcher, P. (eds.), 1988, History and Philosophy of Modern Mathematics, University of Minnesota Press.
12. Atiyah, M., 1974, ‘How Research is Carried Out’, Bulletin of the Institute of Mathematics and its Applications, 10: 232-4, reprinted in Atiyah (1987): 213-15.
13. Atiyah, M., 1976, ‘Global Geometry’, Proceedings of the Royal Society of London A, 347: 291-9, reprinted in Atiyah (1987): 217-28.
14. Atiyah, M., 1977, ‘Trends in Pure Mathematics’, in H. Athen and H. Kunle (eds.), Proceedings of Third ICME: 61-74, reprinted in Atiyah (1987): 263-76.
15. Atiyah, M., 1978, ‘The Unity of Mathematics’, Bulletin of the London Mathematical Society, 10: 69-76, reprinted in Atiyah (1987): 277-86.
16. Atiyah, M., 1984, ‘An Interview with Michael Atiyah’, Mathematical Intelligencer, 6(1), reprinted in Atiyah (1987): 297-307.
17. Atiyah, M., 1987, Collected Works, Vol. 1: Early Papers, General Papers, Oxford University Press.
18. Atiyah, M., 1995, ‘Quantum Theory and Geometry’, Journal of Mathematical Physics, 36(11), 6069-72.
19. Audi, R., 1995, Cambridge Dictionary of Philosophy, Cambridge University Press.
20. Bacon, F., 1620, Novum Organum, trans. R. Ellis and J. Spedding (eds.), The Philosophical Works of Francis Bacon, Routledge, 1905: 212-387.
21. Baez, J., 1999, ‘An Introduction to Spin Foam Models of BF Theory and Quantum Gravity’, preprint gr-qc/9905087 available at xxx.arXiv.cornell.edu.
22. Baez, J., 2001a, ‘Higher-Dimensional Algebra and Planck-Scale Physics’, in Callender and Huggett (eds.): 177-95.
23. Baez, J., 2001b, ‘Week 169’, available at http://math.ucr.edu/home/baez.
24. Baez, J., 2002, ‘The Octonions’, Bulletin of the American Mathematical Society, 39(2): 145-205.
25. Baez, J. and Dolan, J., 1995, ‘Higher-Dimensional Algebra and Topological Quantum Field Theory’, Journal of Mathematical Physics, 36: 6073-6105.
26. Bailey, D. and Borwein, J., 2001, ‘Experimental Mathematics: Recent Developments and Future Outlook’, in Engquist and Schmid (eds.): 51-66.
27. Bailey, D., Borwein, P. and Plouffe, S., 1997, ‘On the Rapid Computation of Various Polylogarithmic Constants’, Mathematics of Computation, 66(218): 903-13.
28. Bailey, D. and Crandall, R., 2001, ‘On the Random Character of Fundamental Constant Expansions’, Experimental Mathematics, 10(2): 175-90.
29. Barnes, B., Bloor, D. and Henry, J., 1996, Scientific Knowledge: A Sociological Analysis, University of Chicago Press.
30. Barnes, E., 1999, ‘The Quantitative Problem of Old Evidence’, British Journal for the Philosophy of Science, 50(2): 249-64.
31. Barrow-Green, J., 1997, Poincaré and the Three Body Problem, American Mathematical Society.
32. Bell, J. and Machover, M., 1977, A Course in Mathematical Logic, North-Holland.
33. Bellissard, J., 1992, ‘Gap Labelling Theorems for Schrödinger Operators’, in Waldschmidt et al. (eds.): 538-631.
34. van Bendegem, J., 2000 ‘Analogy and Metaphor as Essential Tools for the Working Mathematician’, in F. Hallyn (ed.), Metaphor and Analogy in the Sciences, Kluwer: 105-23.
35. Berger, M., 2000, ‘Encounter with a Geometer, Part I’, Notices of the American Mathematical Society, 47(2): 183-94.
36. Bergeron, F., Labelle, G. and Leroux, P., 1997, Combinational Species and Tree-Line Structures, Cambridge University Press.
37. Bloor, D., 1976, Knowledge and Social Imagery, Routledge.
38. Booss, B. and Bleecker, D. D., 1985, Topology and Analysis: The Atiyah-Singer Index Theorem and Gauge Theoretic Physics, Springer-Verlag.
39. Borel, A., 1983, ‘Mathematics, Art and Science’, Mathematical Intelligencer, 5(4): 9-17.
40. Boumans, M., 1999, ‘Built-In Justification’, in Morgan and Morrison (eds.): 66-96.
41. Brady, G. and Trimble, T., unpublished, ‘A String Diagram Calculus for Predicate Logic’.
42. Brandt, H., 1926, ‘Über eine Verallgemeinerung des Gruppenbegriffes’, Mathematische Annalen, 96: 360-6.
43. Breger, H., 1992, ‘A Restoration that Failed: Paul Finsler’s Theory of Sets’, in Gillies (ed.): 248-64.
44. Browder, F. (ed.), 1983, The Mathematical Heritage of Henri Poincaré, American Mathematical Society.
45. Brown, J., 1999, Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures, Routledge.
46. Brown, R., 1987, ‘From Groups to Groupoids: A Brief Survey’, Bulletin of the London Mathematical Society, 19: 113-34.
47. Brown, R., 1992, ‘Out of Line’, Proceedings of the Royal Institution, 64: 207-43.
48. Brown, R., 1994, ‘Higher Order Symmetry of Graphs’, Bulletin of the Irish Mathematical Society, 32: 46-59.
49. Brown, R., 1999, ‘Groupoids and Crossed Objects in Algebraic Topology’, Homology, Homotopy and Applications, 1(1), 1-78.
50. Bundy, A., 1999, ‘Proof Planning Methods as Schemas’, Journal of Symbolic Computation, 11: 1-25.
51. Butterfield, J. and Isham, C., 2001, ‘Spacetime and the Philosophical Challenge of Quantum Gravity’, in Callender and Huggett (eds.): 33-89.
52. Callender C. and Huggett N. (eds.), 2001 Physics meets Philosophy at the Planck Scale, Cambridge University Press.
53. Carnap, R., 1950, Logical Foundations of Probability, 2nd edn., University of Chicago Press, 1963.
54. Carter J., Kauffman, L. and Saito, M., 1996, ‘Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories’, preprint math.GT/9806023 available at xxx.arXiv.cornell.edu.
55. Carter, J. and Saito, M., 1998, Knotted Surfaces and Their Diagrams, American Mathematical Society.
56. Cartier, P., 1992, ‘An Introduction to Zeta Functions’, in Waldschmidt et al. (eds.): 1-63.
57. Cartier, P., 2001, ‘A Mad Day’s Work: From Grothendieck to Connes and Kontsevich - The Evolution of Concepts of Space and Symmetry’, Bulletin of the American Mathematical Society, 38(4): 389-408.
58. Cartwright, N., 1999a, The Dappled World, Cambridge University Press.
59. Cartwright, N., 1999b, ‘Models and the Limits of Theory: Quantum Hamiltonians and the BCS Model of Superconductivity’, in Morgan and Morrison (eds.): 241-81.
60. Chalmers, A., 1982, What is This Thing Called Science?, 2nd edn., Open University Press.
61. Collingwood, R. G., 1940, An Essay on Metaphysics, Clarendon Press.
62. Collingwood, R. G., 1946, The Idea of History, Oxford University Press.
63. Collingwood, R. G., 1999, The Principles of History, Clarendon Press.
64. Collins, H. and Kusch, M., 1998, The Shape of Actions, MIT Press.
65. Colton, S., 1999, ‘Refactorable Numbers - A Machine Invention’, Journal of Integer Sequences, 2, article 99.1.2.
66. Connes, A., 1994, Noncommutative Geometry, Academic Press.
67. Connes, A., Lichnerowicz, A. and Schützenberger, M., 2000, Triangle of Thoughts, trans. J. Gage, American Mathematical Society.
68. Corfield, D. and Williamson, J. (eds.), 2001, Foundations of Bayesianism, Kluwer.
69. Corry, L., 1996, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser.
70. da Costa, N. and French, S., 2000, ‘Theories, Models and Structures: Thirty Years On’, Philosophy of Science, 67, Supplement: Proceedings of PSA 1998: S116-S127.
71. Crane, L., 1994, ‘Topological Field Theory as the Key to Quantum Gravity’, in J. Baez (ed.), Knots and Quantum Gravity, Oxford University Press: 121-32.
72. Crane, L., 1995, ‘Clock and Category: Is Quantum Gravity Algebraic?’, Journal of Mathematical Physics, 36: 6180-93.
73. Crowe, M., 1975, ‘Ten “Laws” Concerning Patterns of Change in the History of Mathematics’, Historia Mathematica, 2: 161-6, reprinted in Gillies (ed.) (1992): 15-20.
74. Crowe, M., 1990, ‘Duhem and the History and Philosophy of Mathematics’, Synthese, 83: 431-47.
75. Crowell, H. and Fox, R., 1977, Introduction to Knot Theory, Springer-Verlag.
76. Davis, P. J. and Hersh, R., 1981, The Mathematical Experience, Birkhäuser.
77. Deninger, C., 1994, ‘Evidence for a Cohomological Approach to Analytic Number Theory’, in A. Joseph et al. (eds.), First European Congress of Mathematics, Vol. 1, Birkhäuser: 491-510.
78. Dieudonné, J., 1969, ‘Richard Dedekind’, Encyclopaedia Universalis, Vol. 5: pp. 373-5.
79. Dieudonné, J., 1972, ‘The Historical Development of Algebraic Geometry’, American Mathematical Monthly, 79: 827-66.
80. Dieudonné, J., 1975a, ‘Poincaré’, in C. C. Gillispie (ed.), Dictionary of Scientific Biography, Charles Scribner’s Sons: 52.
81. Dieudonné, J., 1975b, ‘L’Abstraction et l’intuition mathématique’, Dialectica, 29(1): 39-54.
82. Dieudonné, J., 1989, A History of Algebraic and Differential Topology: 1900-1960, Birkhäuser.
83. Earman, J., 1992, Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory, MIT Press.
84. Edwards, H. M., 1977, Fermat’s Last Theorem - A Genetic Introduction to Algebraic Number Theory, Springer.
85. Edwards, H. M., 1989, Divisor Theory, Birkhäuser.
86. Eilenberg, S. and Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton University Press.
87. Eisenbud, D., 2001, ‘Mathematics Comes from Many Sources’, in Engquist and Schmid (eds.): 647-54.
88. Engquist, B. and Schmid, W. (eds.), 2001, Mathematics Unlimited - 2001 and Beyond, Springer-Verlag.
89. Ewald, W. (ed.), 2000, From Kant to Hilbert: A Sourcebook in the Foundations of Mathematics, Oxford University Press.
90. Fallis, D., 1997, ‘The Epistemic Status of Probabilistic Proof’, Journal of Philosophy, 94(4): 165-86.
91. Feferman, S., 1981, ‘The Logic of Mathematical Discovery vs. the Logical Structure of Mathematics’, in P. D. Asquith and I. Hacking (eds.), PSA 1978, 2, Philosophy of Science Association: 309-27.
92. Ferreirós, J., 2001 ‘The Road to Modern Logic - An Interpretation’, Bulletin of Symbolic Logic, 7(4): 441-84.
93. Feyerabend, P., 1976, ‘On the Critique of Scientific Reason’, in Problems of Empiricism, Philosophical Papers, 2, Cambridge University Press, ch. 10.
94. Field, H., 1980, Science Without Numbers, Blackwell.
95. de Finetti, B., 1974, Theory of Probability: A Critical Introductory Treatment, 1, trans. by A. Machi and A. Smith, Wiley.
96. Fitelson, B., 1998, ‘Using Mathematica to Understand the Computer Proof of the Robbins Conjecture’, Mathematica in Education and Research, 7(1): 17-26.
97. Franklin, A., 1986, The Neglect of Experiment, Cambridge University Press.
98. Freed, D. and Uhlenbeck, K. (eds.), 1995, Geometry and Quantum Field Theory, American Mathematical Society.
99. Friedman, M., 1992, Kant and the Exact Sciences, Harvard University Press.
100. Friedman, M., 2001, Dynamics of Reason, CSLI Publications.
101. Galison, P., 1987, How Experiments End, University of Chicago Press.
102. Galison, P., 1997, Image and Logic: A Material Culture of Microphysics, University of Chicago Press.
103. Gannon, T., 2001, ‘Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine’, preprint QA/0109067 available at xxx.arXiv.cornell.edu.
104. Gardner, H., 1983, Frames of Mind, Paladin.
105. Gilbert, G. and Mulkay, M., 1984, Opening Pandora’s Box: A Sociological Analysis of Scientists’ Discourse, Cambridge University Press.
106. Gilbert, N. and Porter, T., 1994, Knots and Surfaces, Oxford University Press.
107. Gillies, D. (ed.), 1992, Revolutions in Mathematics, Oxford University Press.
108. Gillies, D., 1996, Artificial Intelligence and Scientific Method, Oxford University Press.
109. Giorello, G., 1980, ‘Intuition and Rigor: Some Problems of a “Logic of Discovery” in Mathematics’, in M. L. Dalla Chiara (ed.), Italian Studies in the Philosophy of Science, Reidel, 113-35.
110. Giventhal, A., 1996, ‘Equivariant Gromov-Witten Invariants’, International Mathematical Research Notices, 13: 613-63.
111. Glas, E., 1989, ‘Testing the Philosophy of Mathematics in the History of Mathematics, Part II: The Similarity Between Mathematical and Scientific Growth of Knowledge’, Studies in History and Philosophy of Science, 20: 157-74.
112. Glas, E., 1993, ‘Mathematical Progress: Between Reason and Society, I. The Methodological Model and its Alternatives’, Journal of General Philosophy of Science, 1: 43-62.
113. Glas, E., 1995, ‘Kuhn, Lakatos, and the Image of Mathematics’, Philosophia Mathematica, 3: 225-47.
114. Gowers, W. T., 2000a, ‘The Two Cultures of Mathematics’, in Arnold et al. (eds.): 65-78.
115. Gowers, W. T., 2000b, ‘Rough Structure and Classification’, in Alon et al. (eds.): 79-117.
116. Grosholz, E., 1985, ‘Two Episodes in the Unification of Logic and Topology’, British Journal for the Philosophy of Science, 36: 147-57.
117. Hacking, I., 1967, ‘Slightly More Realistic Personal Probability’, Philosophy of Science, 34: 311-25.
118. Hacking, I., 1979, ‘Lakatos’s Philosophy of Science’, British Journal for the Philosophy of Science, 30: 381-410.
119. Hacking, I., 1983, Representing and Intervening: Introductory Topics in the Philosophy of Natural Science, Cambridge University Press.
120. Hacking, I., 1992, ‘“Style” for Historians and Philosophers’, Studies in History and Philosophy of Science, 23: 1-20.
121. Hacking, I., 1996, ‘The Disunities of the Sciences’, in P. Galison and D. Stump (eds.), The Disunity of Science: Boundaries, Contexts and Power, Stanford University Press.
122. Hacking, I., 1999, The Social Construction of What?, Harvard University Press.
123. Hallett, M., 1979, ‘Toward a Theory of Mathematical Research Programmes’, British Journal for the Philosophy of Science, 30: 1-25, 135-59.
124. Hardy, G. H., 1940, A Mathematician’s Apology, Cambridge University Press.
125. Hasse, H., 1980, Number Theory, Springer-Verlag.
126. Hempel, C., 1945, ‘On the Nature of Mathematical Truth’, in P. Benacerraf and H. Putnam (eds.), Philosophy of Mathematics: Selected Readings, Prentice-Hall, 1964.
127. Herrnstein Smith, B. and Plotnitsky, A. (eds.), 1997, Mathematics, Science, and Postclassical Theory, Duke University Press.
128. Hersh, R., 1979, ‘Some Proposals for Reviving the Philosophy of Mathematics’, Advances in Mathematics, 31(1): 31-50.
129. Hersh, R., 1991, ‘Mathematics has a Front and a Back’, Synthèse, 88: 127-33.
130. Hesse, M., 1974, The Structure of Scientific Inference, Macmillan.
131. Hestenes, D., 1986, ‘A Unified Language for Mathematics and Physics’, in J. Chisholm and A. Commons (eds.), Clifford Algebras and their Applications in Mathematical Physics, Reidel: 1-23.
132. Higgins, P., 1971, Notes on Categories and Groupoids, Van Nostrand Reinhold Co.
133. Hirsch, M., 1994, ‘Responses to “Theoretical Mathematics”, by A. Jaffe and F. Quinn’, Bulletin of the American Mathematical Society, 30(2): 187-91.
134. Hitchin, N., 2001, ‘Global Differential Geometry’, in Engquist and Schmid (eds.): 577-91.
135. Howson, C., 2000, Hume’s Problem, Oxford University Press.
136. Howson, C. and Urbach, P., 1989, Scientific Reasoning: The Bayesian Approach, Open Court.
137. Hughes, R., 1999, ‘The Ising Model, Computer Simulation, and Universal Physics’, in Morgan and Morrison (eds.): 97-145.
138. Hume, D., 1739, A Treatise of Human Nature, Clarendon Press, 1978.
139. Jackendoff, R., Bloom, P. and Wynn, K. (eds.), 1999, Language, Logic, and Concept: Essays in Memory of John Macnamara, MIT Press.
140. Jackson, A., 2001, ‘Interview with Raoul Bott’, Notices of the American Mathematical Society, 48(4): 374-82.
141. Jaffe, A. and Quinn, F., 1993, ‘“Theoretical Mathematics”: Towards a Cultural Synthesis of Mathematics and Theoretical Physics’, Bulletin of the American Mathematical Society, 29: 1-13.
142. Jardine, N., 2000, The Scenes of Inquiry, revised edn., Oxford University Press.
143. Jaynes, E., forthcoming, Probability Theory: The Logic of Science, available at http://bayes.wustl.edu.
144. Jeffrey, R., 1992, Probability and the Art of Judgment, Cambridge University Press.
145. Johnstone, P., 1977, Topos Theory, Academic Press.
146. Johnstone, P., 1982, Stone Spaces, Cambridge University Press.
147. Johnstone, P., (1984), ‘Open Locales and Exponentiation’, in J. W. Gray (ed.), Mathematical Applications of Category Theory, American Mathematical Society.
148. Joyal, A. and Street, R., 1991, ‘The Geometry of Tensor Calculus II’, Advances in Mathematics, 88(1): 55-112.
149. Kac, M., Rota, G.-C. and Schwartz, J., 1986, Discrete Thoughts: Essays in Mathematics, Science, and Philosophy, Birkhäuser.
150. Kaminker, J., 1998, ‘Conference Announcement: Groupoids in Physics, Analysis and Geometry’, at http://www.ams.org/meetings/src-kaminker.html (8 December 1998).
151. Kapranov, M., 1995, ‘Analogies between the Langlands Correspondence and Topological Quantum Field Theory’, in S. Gindikin, J. Lepowsky, and R. Wilson, (eds.), Functional Analysis on the eve of the 21st Century, 1, Birkhäuser: 119-51.
152. Kapranov, M., 2001, ‘Review of Gröbner Deformations of Hypergeometric Differential Equations’, Bulletin of the American Mathematical Society, 38(4): 481-8.
153. Katz, N. and Sarnak, P., 1999, ‘Zeroes of Zeta Functions and Symmetry’, Bulletin of the American Mathematical Society, 36(1): 1-26.
154. Kauffman, L., 1991, Knots and Physics, World Scientific.
155. Kauffman, L., 2000, ‘The Robbins Problem - Computer Proofs and Human Proofs’, available at http://www.math.uic.edu/∼kauffman/Papers.html.
156. Kerber, M., Kohlhase, M. and Sorge, V., 1998, ‘Integrating Computer Algebra into Proof Planning’, Journal of Automated Reasoning, 21(3): 327-55.
157. Kitcher, P., 1983, The Nature of Mathematical Knowledge, Oxford University Press.
158. Kitcher, P., 1993, The Advancement of Science, Oxford University Press.
159. Klainerman, S., 2000, ‘PDE as a Unified Subject’, in Alon et al. (eds.): 279-315.
160. Kline, M., 1972, Mathematical Thought from Ancient to Modern Times, Oxford University Press.
161. Koetsier, T., 1991, Lakatos’ Philosophy of Mathematics: A Historical Approach, North-Holland.
162. Krattenthaler, C., 1999, ‘Advanced Determinant Calculus’, Séminaire Lotharingien de Combinatoire, 42: article B42q.
163. Kreimer, D., 2000, Knots and Feynman Diagrams, Cambridge University Press.
164. Kreisel, G. and MacIntyre, A., 1982, ‘Constructive Logic Versus Algebraization I’, in A. Troelstra and D. van Dalen (eds.), The L. E. J. Brouwer Centenary Colloquium, North-Holland.
165. Kuhn, T., 1962, The Structure of Scientific Revolutions, University of Chicago Press.
166. Kuhn, T., 1977, The Essential Tension, University of Chicago Press.
167. Kumpera, A., 1988, Review of [Mackenzie 1987], Bulletin of the American Mathematical Society, 19(1): 358-62.
168. Ladyman, J., 1998, ‘What is Structural Realism?’, Studies in History and Philosophy of Science, 29: 409-24.
169. Lagarias, J., 1992, ‘Number Theory and Dynamical Systems’, in S. Burr (ed.), The Unreasonable Effectiveness of Number Theory, American Mathematical Society: 35-72.
170. Lakatos, I., 1968, ‘Changes in the Problem of Inductive Logic’, in Lakatos (1978b): 128-200.
171. Lakatos, I., 1976, Proofs and Refutations, The Logic of Mathematical Discovery, J. Worrall and E. Zahar (eds.), Cambridge University Press.
172. Lakatos, I., 1978a, The Methodology of Scientific Research Programmes, Philosophical Papers, Vol. 1, J. Worrall and G. Currie (eds.), Cambridge University Press.
173. Lakatos, I., 1978b, Mathematics, Science and Epistemology, Philosophical Papers, Vol. 2, J. Worrall and G. Currie (eds.), Cambridge University Press.
174. Lang, S., 1970, Algebraic Number Theory, Addison-Wesley.
175. Larvor, B., 1998, Lakatos: An Introduction, Routledge.
176. Larvor, B., 2001, ‘What is Dialectical Philosophy of Mathematics?’ Philosophia Mathematica, 9(2): 212-29.
177. Laudan, L., 1984, Science and Values, University of California Press.
178. Laugwitz, D., 1999, Bernhard Riemann, 1826-1866: Turning Points in the Conception of Mathematics, Birkhäuser.
179. Lawvere, F. W. and Schanuel, S., 1997, Conceptual Mathematics, A First Introduction to Categories, Cambridge University Press.
180. Lefschetz, S., 1971, Selected Papers, Chelsea.
181. Leinster, T., 2002, ‘A Survey of Definitions of n-Category’, Theory and Applications of Categories, 10: 1-70, preprint math.CT/0107188 available at xxx.arXiv.cornell.edu.
182. Macintyre, A., 1989, ‘Trends in Logic’, in R. Ferro, C. Bonotto, S. Valentini and A. Zarnardo (eds.), Logic Colloquium ‘88, North-Holland.
183. MacKenzie, D., 2001, Mechanizing Proof: Computing, Risk, and Trust, MIT Press.
184. Mackenzie, K., 1987, Lie Groupoids and Lie Algebroids in Differential Geometry, Cambridge University Press.
185. Mackenzie, K., 1992, ‘Double Lie Algebroids and Second-Order Geometry, II’, Advances in Mathematics, 92(2): 180-239.
186. Mackenzie, K., 1995, ‘Lie Algebroids and Lie Pseudogroups’, Bulletin of the London Mathematical Society, 27: 97-147.
187. Mackey, G. W., 1992, The Scope and History of Commutative and Noncommutative Harmonic Analysis, American Mathematical Society.
188. Mac Lane, S., 1971, Categories for the Working Mathematician, Springer-Verlag.
189. Mac Lane, S., 1978, ‘Origins of the Cohomology of Groups’, L’Enseignement Mathématique, XXX: fasc. 1-2.
190. Mac Lane, S., 1986, Mathematics: Form and Function, Springer-Verlag.
191. Mac Lane, S., 1988, ‘Concepts and Categories in Perspective’, in P. Duren, R. Askey and U. Merzbach (eds.), A Century of Mathematics in America, Part I, American Mathematical Society: 323-65.
192. Mac Lane, S., 1992, ‘The Protean Character of Mathematics’, in J. Echeverria, A. Ibarra and T. Mormann (eds.), The Space of Mathematics: Philosophical, Epistemological and Historical Explorations, Walter de Gruyter: 3-13.
193. Macnamara, J. and Reyes, G. (eds.), 1994, The Logical Foundations of Cognition, Oxford University Press.
194. Maddy, P., 1997, Naturalism in Mathematics, Clarendon Press.
195. Majid, S., 1995, Foundations of Quantum Groups, Cambridge University Press.
196. Makkai, M., 1999 ‘On Structuralism in Mathematics’, in R. Jackendoff et al. (eds.): 43-66.
197. Mancosu, P., 1996, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press.
198. Markopoulou F., 2002 ‘Coarse Graining in Spin Foam Models’, preprint gr-qc/0203036 available at xxx.arXiv.cornell.edu.
199. Marquis, J.-P., 1997, ‘Abstract Mathematical Tools and Machines for Mathematics’, Philosophia Mathematica, 5: 250-72.
200. Martin, U., 1999, ‘Computers, Reasoning and Mathematical Practice’, in Proceedings of the 1997 NATO ASI Summer School on Logic and Computation, Springer Verlag.
201. McIntyre, M. and Trimble, T., forthcoming, ‘The Geometry of Gray-Categories’, Advances in Mathematics.
202. McLarty, C., 1990, ‘The Uses and Abuses of the History of Topos Theory’, British Journal for the Philosophy of Science, 41: 351-75.
203. McLarty, C., 2000, ‘Voir-dire in the Case of Mathematical Physics’, in E. Grosholz and H. Breger (eds.), The Growth of Mathematical Knowledge, Kluwer: 269-80.
204. Mehrtens, H., 1976, ‘T. S. Kuhn’s Theories and Mathematics’, Historia Mathematica, 3: 297-320, reprinted as ch. 2 of Gillies (ed.) (1992).
205. Mehrtens, H., 1990, Moderne-Sprache-Mathematik, Suhrkamp.
206. Mehrtens, H., 1992, Appendix (1992): Revolutions Reconsidered, in Gillies (ed.) (1992): 42-8.
207. Melis, E., 1998, ‘The Heine-Borel Challenge Problem: In Honor of Woody Bledsoe’, Journal of Automated Reasoning, 20(3): 255-82.
208. van Mill, J. and Reed, G. (eds.), 1990, Open Problems in Topology, North Holland-Elsevier.
209. Mill, J. S., 1843, A System of Logic, Ratiocinative and Inductive, 3rd edn., Longmans, Green & Co.
210. Moerdijk, I. and Reyes, G., 1991, Models for Smooth Infinitesimal Analysis, Springer-Verlag.
211. Morgan, M. and Morrison, M. (eds.), 1999, Models as Mediators, Cambridge University Press.
212. Morrow, G., 1970, Proclus: A Commentary on the First Book of Euclid’s Elements, Princeton University Press.
213. Muggleton, S., 1999, ‘Scientific Knowledge Discovery using Inductive Logic Programming’, Communications of the ACM, 42(11): 42-6.
214. Needham, T., 1998, Visual Complex Analysis, Oxford University Press.
215. Netz, R., 1999, The Shaping of Deduction in Greek Mathematics, Cambridge University Press.
216. Okasha, S., 2000, ‘Van Fraassen’s Critique of Inference to the Best Explanation’, Studies in History and Philosophy of Science, 31(4): 691-710.
217. Oldfield, A., 1995, ‘Metaphysics and History in Collinwood’s Thought’, in D. Boucher, J. Connelly and T. Modood (eds.), Philosophy, History and Civilisation: Interdisciplinary Perspectives on R. G. Collingwood, Univerity of Wales Press: 182-202.
218. Papert, S., 1978, ‘The Mathematical Unconscious’, in J. Wechsler (ed.), On Aesthetics in Science, MIT Press: 105-20.
219. Paris, J., Watton, P. and Wilmers, G., 2000, ‘On the Structure of Probability Functions in the Natural World’, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8: 311-29.
220. Pearl, J., 1988, Probabilistic Reasoning in Intelligent Systems, Morgan Kaufman.
221. Pearl, J., 2000, Causality: Models, Reasoning and Inference, Cambridge University Press.
222. Pearl, J., 2001, ‘Bayesianism and Causality, or, Why I am Only a Half-Bayesian’, in Corfield and Williamson (eds.): 19-36.
223. Penrose, R. and Rindler, W., 1984, Spinors and Space-Time Volume 1: Two-Spinor Calculus and Relativistic Fields, Cambridge University Press.
224. Pickering, A., 1997, ‘Concepts and the Mangle of Practice: Constructing Quaternions’, in Herrnstein Smith and Plotnitsky (eds.): 40-82.
225. Poincaré, H., 1895, Analysis Situs, Oeuvres, 6, Gauthier-Villars, 1953: 193-288.
226. Poincaré, H., 1905, Science and Hypothesis, Dover.
227. Poincaré, H., 1921, Analyse de ses travaux scientifique, Acta Mathematica, 38, reprinted in Browder: 257-357.
228. Polanyi, M., 1958, Personal Knowledge: Towards a Post-Critical Philosophy, Routledge & Kegan Paul.
229. Pólya, G., 1941, ‘Heuristic Reasoning and the Theory of Probability’, American Mathematical Monthly, 48(7): 450-65.
230. Pólya, G., 1954a, Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics, Vol. 1, Princeton University Press.
231. Pólya, G., 1954b, Mathematics and Plausible Reasoning: Patterns of Plausible Inference, Vol. 2, Princeton University Press.
232. Popper, K., 1963, Conjectures and Refutations, Routledge & Kegan Paul.
233. Propp, J., 1999, ‘Enumeration of Matchings: Problems and Progress’, in L. Billera (ed.), New Perspectives in Geometric Combinatorics, Cambridge University Press: 255-91.
234. Quine, W. V., 1955, Mathematical Logic, Harvard University Press.
235. Quine, W. V., 1977, ‘Review of Proofs and Refutations’, British Journal for the Philosophy of Science, 28: 81-2.
236. Rabin, J., 1995, ‘Introduction to Quantum Field Theory for Mathematicians’, in Freed and Uhlenbeck (eds.): 183-269.
237. Rav, Y., 1999, ‘Why Do We Prove Theorems?’, Philosophia Mathematica, 7: 5-41.
238. Ravenel, D., 1986, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press.
239. Reid, M., 1988, Undergraduate Algebraic Geometry, Cambridge University Press.
240. Restivo, S., 1992, Mathematics in Society and History: Sociological Inquiries, Kluwer.
241. Reyes, G., 1980, ‘Logic and Category Theory’, in E. Agazzi (ed.), Modern Logic: A Survey, Reidel.
242. Roberts, D., 1973, The Existential Graphs of Charles S. Peirce, Mouton.
243. Rosenkrantz, R., 1977, Inference, Method, and Decision: Towards a Bayesian Philosophy of Science, Reidel.
244. Rota, G.-C., 1991, ‘The Concept of Mathematical Truth’, Review of Metaphysics, 44: 483-94.
245. Rotman, B., 1997, ‘Thinking Dia-grams: Mathematics, Writing, and Virtual Reality’, in Herrnstein Smith and Plotnitsky (eds.): 17-39.
246. Rovelli, C., 2001, ‘Quantum Spacetime: What do we Know?’ in Callender and Huggett (eds.): 101-22.
247. Ruelle, D., 1988, ‘Is our Mathematics Natural? The Case of Equilibrium Statistics’, Bulletin of the American Mathematical Society, 19: 259-68.
248. Ruelle, D., 1991, Chance and Chaos, Princeton University Press.
249. Sharpe, R., 1997, Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program, Springer.
250. Sklar, L., 2000, ‘Interpreting Theories: The Case of Statistical Mechanics’, British Journal for the Philosophy of Science, 51: 129-42.
251. Solomon, R., 2001, ‘The Classification of the Finite Simple Groups’, Bulletin of the American Mathematical Society, 38(3), 315-52.
252. Spencer-Brown, G., 1969, Laws of Form, Allen & Unwin.
253. Stanley, R., 1999, Enumerative Combinatorics, Vol. 2, Cambridge University Press.
254. Stark, H., 1992, Galois Theory, Algebraic Numbers and Zeta Functions, in Waldschmidt et al. (eds.): 313-89.
255. Steiner, M., 1975, Mathematical Knowledge, Cornell University Press.
256. Steiner, M., 1983, ‘The Philosophy of Imré Lakatos’, Journal of Philosophy, 80(9): 502-21.
257. Steiner, M., 1998, The Applicability of Mathematics as a Philosophical Problem, Harvard University Press.
258. Stewart, I., 1987, The Problems of Mathematics, Oxford University Press.
259. Stewart, I., 1997, Does God Play Dice?: The New Mathematics of Chaos, 2nd edn., Penguin.
260. Sussman, G. and Wisdom, J., 1992, ‘Chaotic Evolution of the Solar System’, Science, 257: 56-62.
261. Tappenden, J., 1995, ‘Extending Knowledge and “Fruitful Concepts”: Fregean Themes in the Foundations of Mathematics’, Nous, 29(4): 427-67.
262. Taylor, P., 1999, Practical Foundations of Mathematics, Cambridge University Press.
263. Thomas, R., 1998, ‘An Update on the Four-Color Theorem’, Notices of the American Mathematical Society, 45(7): 848-59.
264. Thurston, W., 1982, ‘Three Dimensional Manifolds, Kleinian Groups and Hyperbolic Geometry’, Bulletin of the American Mathematical Society, 6(3): 357-81.
265. Thurston, W., 1994, ‘On Proof and Progress in Mathematics’, Bulletin of the American Mathematical Society, 30(2): 161-77.
266. Vafa, C., 1998, ‘Geometric Physics’, Documenta Mathematica, Extra Volume ICM, I: 537-56.
267. Vafa, C., 2000, ‘On the Future of Mathematics/Physics Interaction’, in Arnold et al. (eds.): 321-8.
268. Waldschmidt, M., Moussa, P., Luck, J.-M. and Itzykson C. (eds.), 1992, From Number Theory to Physics, Springer-Verlag.
269. Weil, A., 1940, ‘Une lettre et un extrait de lettre à Simone Weil’, in Collected Papers, 1: 244-55.
270. Weil, A., 1950, ‘Number-Theory and Algebraic Geometry’, in Collected Papers, 2: 90-100.
271. Weil, A., 1960, ‘De la Métaphysique aux Mathématiques’, in Collected Papers, 2: 408-12.
272. Weil, A., 1974, ‘Two Lectures on Number Theory, Past and Present’, in Collected Papers, 3: 279-302.
273. Weil, A., 1979, Collected Papers, Springer-Verlag.
274. Weinstein, A., 1996, ‘Groupoids: Unifying Internal and External Symmetry’, Notices of the American Mathematical Society, 43(7): 744-52.
275. Weyl, H., 1932, ‘Topology and Abstract Algebra as Two Roads of Mathematical Comprehension’, trans. A. Shenitzer, in American Mathematical Monthly, 102(5): 453-60, and 102(7): 646-51.
276. Weyl, H., 1940, Algebraic Number Theory, Princeton University Press.
277. Weyl, H., 1951, ‘A Half Century of Mathematics’, American Mathematical Monthly, 58: 523-53.
278. Wilson, M., 1999, ‘To Err is Humean’, Philosophia Mathematica, 7(3): 247-57.
279. Wise, M., 1979, ‘William Thomson’s Mathematical Route to Energy Conservation: A Case Study of the Role of Mathematics in Concept Formation’, Historical Studies of the Physical Sciences, 10, JHU Press.
280. Wittgenstein, L., 1978, Remarks on the Foundations of Mathematics, revised edn., MIT Press.
281. Wos, L., 1988, Automated Reasoning: 33 Basic Research Problems, Prentice-Hall.
282. Wos, L. and Fitelson, B., forthcoming, ‘The Automation of Sound Reasoning and Successful Proof Finding’, to appear in D. Jacquette (ed.), Blackwell Companion to Philosophical Logic.
283. Wos, L. and Pieper, G. W., 1999, A Fascinating Country in the World of Computing: Your Guide to Automated Reasoning, World Scientific.
284. Wussing, H., 1984, Genesis of the Abstract Group, MIT Press.
285. Zahar, E., 1973, ‘Why did Einstein’s Programme Supersede Lorenz’s?’, British Journal for the Philosophy of Science, 24: 95-123, 223-62.
286. Zahar, E., 1983, ‘Logic of Discovery or Psychology of Invention?’, British Journal for the Philosophy of Science, 34: 243-61.
287. Zahar, E., 1989, Einstein’s Revolution: A Study in Heuristic, Open Court.