Mathematics and fiction II: Analogy

Logique et Analyse

Volumn 45, Issue 177-178, 2002, Pages 185-228

  Thomas, Robert ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

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[No Author keywords available]

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EID: 60449084980     PISSN: 00245836     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (105)

1. Akiba, Ken [2000]: 'Indefiniteness of mathematical objects', PhilosophiaMathematica (3) 8, 26-46
2. Azzouni, Jody [1994]: Metaphysical Myths, Mathematical Practice. NewYork: Cambridge University Press
3. Azzouni, Jody [1997]: 'Applied Mathematics, Existential Commitment andIndispensability Thesisthe Quine-Putnam Indispensability Thesis' Philosophia Mathematica (3) 5, 193-209
4. Azzouni, Jody [2000]: 'Stipulation, Logic, and Ontological Independence'Philosophia Mathematica (3) 8, 225-243
5. Bach, Kent [1987]: Thought and reference. Oxford: Oxford University Press
6. Balaguer, Mark [1996]: 'A fictionalist account of the indispensableapplications of mathematics', Phil. Stud. 83, 291-314
7. Balaguer, Mark [1998]: Platonism and Anti-Platonism in MathematicsOxford: Oxford University Press
8. Benacerraf, P. [1983]: 'Mathematical Truth', in Benacerraf and Putnam[1983], pp. 403-420
9. Benacerraf, P., and H. Putnam [1983]: Philosophy of mathematics: Selectedreadings. Second edition. Cambridge: Cambridge University Press
10. Brown, J. R. [1999]: Philosophy of mathematics. London: Routledge
11. Buchanan, Scott [1962]: Poetry and Mathematics, second edition (firstedition, 1929). Chicago: Chicago University Press
12. Bueno, Otavio [1997]: 'Empirical adequacy: A partial structuresapproach', Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys. 28,585-610. Mathematical Reviews 99c:00004
13. Carnap, R. [1956]: 'Empiricism, Semantics, and Ontology', in Meaning andPutnamNecessity. 2nd ed. Chicago: University of Chicago Press. Reprinted in Benacerrafand Putnam [1983]
14. Chihara, Charles [1973]: Ontology and the Vicious Circle PrincipleIthaca: Cornell University Press
15. Chihara, Charles [1989]: Tharp's "Myth and Mathematics'" Synthèse 81, 153-165
16. Coffa, J. Alberto [1991]: The semantic tradition from Kant to Carnap: Tothe Vienna Station. Cambridge: Cambridge University Press
17. Crittenden, Charles [1991]: Unreality: The Metaphysics of FictionalObjects. Ithaca: Cornell University Press
18. Currie, Gregory [1990]: The Nature of Fiction. Cambridge: CambridgeUniversity Press
19. Dales, H. G. [1998]: 'The mathematician as a formalist', in H. G. Dalesand G. Oliveri, eds., Truth in Mathematics. Oxford: Clarendon Press, pp. 181-200
20. Devitt, M. [1980]: Designation. New York: Columbia University Press
21. Donaldson, Margaret [1993]: Human minds. London: Penguin
22. Dummett, Michael [1977]: Elements of Intuitionism. Oxford: OxfordUniversity Press
23. Dummett, Michael [1991]: Frege: Philosophy of Mathematics. CambridgeMass.: Harvard University Press
24. Eco, Umberto [1979]: The role of the reader: Explorations in thesemiotics of texts. Bloomington, Indiana: Indiana University Press
25. Evans, Gareth [1982]: Varieties of Reference. John McDowell, ed. OxfordClarendon Press
26. Feferman, Solomon [1997]: 'Is CH a definite mathematical problem?' FOM[1997-], 1997 11 24
27. Feldhay, Rivka [2000]: 'Mathematical entities in scientific discourse' inLorraine Daston, ed. Biographies of scientific objects. Chicago: University ofChicago Press, pp. 42-66
28. Field, Hartry [1980]: Science without numbers: A defence of nominalismPrinceton: Princeton University Press
29. Field, Hartry [1989]: Realism, mathematics and modality. OxfordBlackwell
30. FOM [1997-2002], an automated e-mail list for discussing foundations ofmathematics, created by H. Friedman and S. G. Simpson. (The messages arearchived at http://www.cs.nyu.edu/mailman/listinfo/fom/.)
31. Grandy, Richard E. [1996]: 'Shadows of Remembered Ancestors: MathematicsStorytellingas the Epitome of Storytelling', in A. Morton and S. P. Stich [1996], pp.167-189
32. Grice, Paul [1989]: Studies in the Way of Words. Cambridge, Mass.Harvard University Press
33. Hersh, Reuben [1997]: What is mathematics, really? New York: OxfordUniversity Press
34. Hodes, Harold T. [1984]: 'Logicism and the ontological commitments ofarithmetic', J. Phil. 81, 123-149
35. Hodes, Harold T. [1990]: 'Ontological commitment: Thick and thin', in GBoolos, ed. Meaning and method: Essays in honor of Hilary Putnam. Cambridge:Cambridge University Press, pp. 235-260
36. Hoffman, S. [1999] 'Mathematics as Make-Believe', Ph.D. thesisUniversity of Alberta
37. Kitcher, Philip [1984]: The Nature of Mathematical Knowledge. New YorkOxford University Press
38. Körner, Stephan [1966]: Experience and Theory: An Essay in thePhilosophy of Science. London: Routledge & Kegan Paul
39. Körner, Stephan [1967]: 'On the relevance of post- GödelianMuller and Y. Bar-Hillel and reply, pp. 133-137mathematics to philosophy', in I. Lakatos, ed. Problems in the Philosophy ofMathematics. Amsterdam: North-Holland, pp. 118-132, with discussion by Gert H.Muller and Y. Bar-Hillel and reply, pp. 133-137
40. Lakatos, Imre [1976]: Proofs and Refutations: The Logic of MathematicalDiscovery. Cambridge: Cambridge University Press
41. Lewis, C. S. [1982]: 'On Stories', in W. Hooper, ed. Of This and OtherWorlds. London: Collins, pp. 25-45
42. Lewis, David [1983]: 'Truth in fiction', in Philosophical Papers. OxfordOxford University Press, pp. 261-275, and postscripts pp. 276-280
43. Linsky, B., and E. N. Zalta [1995]: 'Naturalized platonism versusplatonized naturalism', Journal of Philosophy 92, 525-555
44. Liston, Michael [1993]: 'Taking mathematical fictions seriously'Synthese 95, 433-458
45. Mac Lane, Saunders [1986]: Mathematics: Form and function. New YorkSpringer
46. Margolis, Howard [1987]: Patterns, Thinking, and Cognition. ChicagoUniversity of Chicago Press
47. Menne, Albert [1982]: 'Concerning the logical analysis of"existence" ', The Monist 65, 415-419
48. Mitchell, W. J. T., ed. [1981]: On Narrative. Chicago: University ofChicago Press
49. Mortensen, Chris [1995]: Inconsistent Mathematics. Dordrecht: Kluwer
50. Morton, Adam [1996]: 'Mathematics as Language' in A. Morton and S. PStich [1996], pp. 213-227
51. Morton, A., and S. P. Stich, eds. [1996]: Benacerraf and his CriticsOxford: Blackwell
52. Netz, Reviel [1999]: The Shaping of Deduction in Greek Mathematics: AHistoryStudy in Cognitive History. Cambridge: Cambridge University Press
53. Opie, I. A., and P. Opie [1969]: Children's games. New York: OxfordUniversity Press
54. Parsons, Charles [1982]: 'Objects and logic', The Monist 65, 491-516
55. Parsons, Terence [1980]: Nonexistent objects. New Haven: Yale UniversityPress
56. Paulos, John Allen [1998]: Once upon a number: The hidden mathematicallogic of stories. New York: Basic Books
57. Putnam, Hilary [1971]: Philosophy of Logic. New York: Harper and RowReprinted in his [1975], pp. 323-357
58. Putnam, Hilary [1975]: Philosophical Papers. Vol. 1. Cambridge: CambridgeUniversity Press
59. Quine, W. V. O. [1969]: 'Ontological Relativity', in OntologicalRelativity and Other Essays. New York: Columbia University Press, pp. 26-68
60. Quine, W. V. O. [1961]: 'On what there is', in From a logical point ofview. 2nd edn. Cambridge, Mass.: Harvard University Press, 1961
61. Resnik, Michael [1980]: Frege and the Philosophy of Mathematics. IthacaCornell University Press
62. Resnik, Michael [1993]: 'A Naturalized Epistemology for a PlatonistMathematics EducationPressMathematical Ontology', in S. Restivo, J. P. Van Bendegem, and R. Fischer, eds.,Math Worlds: Philosophical and Social Studies of Mathematics and MathematicsEducation, Albany, N. Y: SUNY Press, pp. 39-60
63. Resnik, Michael [1997]: Mathematics as a Science of Patterns. OxfordClarendon Press
64. Ricoeur, Paul [1981]: 'Narrative Time', in W. J. T. Mitchell [1981], pp165-186
65. Rosen, Gideon [1990]: 'Modal Fictionalism' Mind 99, 327-354
66. Rotman, Brian [1988]: 'Toward a semiotics of mathematics', Semiotica 721-35, updated in Rotman [2000], pp. 1-43
67. Rotman, Brian [1993]: Ad Infinitum: The Ghost in Turing's MachineStanford: Stanford University Press
68. Rotman, Brian [2000]: Mathematics as sign: Writing, imagining, countingStanford: Stanford University Press
69. Routley, Richard [1980]: Exploring Meinong's Jungle and Beyond: Anthe theory of itemsinvestigation of noneism and the theory of items. Canberra: PhilosophyDepartment, Australian National University
70. Russell, Bertrand [1905]: 'On Denoting' Mind 14, 479-493. Reprinted in[1956], pp. 41-56
71. Russell, Bertrand [1956]: Logic and Knowledge, R. C. Marsh, ed. LondonAllen and Unwin
72. Sainsbury, Mark [1998]: 'Sense without Reference', in Albert NewenStanford, Calif.: Center for the Study of Language and InformationUlrich Nortmann, and Rainer Stuhlmann-Laeisz, eds. Building on Frege: New Essayson Sense, Content, and Concept. Stanford, Calif.: Center for the Study ofLanguage and Information, 2001, pp. 211-230
73. Sainsbury, Mark [1999]: 'Names, Fictional Names, and "Really" 'Aristotelian Society Supplementary Volume LXXIII, pp. 243-269
74. Searle, John [1979]: 'The logical status of fictional discourse', inExpression and Meaning. New York: Cambridge University Press
75. Searle, John [1969]: Speech Acts. Cambridge: Cambridge University Press
76. Shapiro, Stewart [1997]: Philosophy of mathematics: Structure andontology. New York: Oxford University Press
77. Sherry, David [1999]: Thales's Sure Path', Stud. Hist. Phil. Sci. 31621-650
78. Simons, Peter [1999]: 'On what there isn't: The Meinong-Russell Dispute'Worldin A. D. Irvine, ed. Bertrand Russell: Critical Assessments. Volume III:Language, Knowledge, and the World. London: Routledge, pp. 69-100
79. Steiner, Mark [1998]: The Application of Mathematics as a PhilosophicalProblem. Cambridge, Mass.: Harvard University Press
80. Stoll, Avrum [1998]: 'Proper names, names, and fictive objects', Journalof Philosophy 95, 522-534
81. Tait, W. W. [1986]: 'Truth and Proof: The Platonism of Mathematics'Synthese 69, 341-370
82. Reprinted in W. D. Hart, ed., The Philosophy of Mathematics. OxfordOxford University Press, 1996, pp. 142-167
83. Tait, W. W. [2001]: 'Beyond the Axioms: The Question of Objectivity inMathematics', Philosophia Mathematica (3) 9, 21-36
84. Tharp, Leslie [1989]: 'Myth and Mathematics: A Conceptualistic Philosophyof Mathematics I', Synthese 81, 167-201
85. Tharp, Leslie [1991]: 'Myth & Math, Part II (Preliminary Draft)'Synthese 88, 179-199
86. Thomas, R. S. D. [2000]: 'Mathematics and fiction I: Identification'Logique & Analyse 43, 301-340
87. Torretti, Roberto [1981]: 'Three kinds of mathematical fictionalism' inJ. Agassi and R. S. Cohen, eds. Scientific Philosophy Today. Dordrecht: Reidel,pp. 399-414
88. Turner, Mark [1996]: The literary mind. New York: Oxford University Press
89. Vaihinger, Hans [1924]: The Philosophy of 'As If', abridged translationby C. K. Ogden. London: Kegan Paul, Trench, Trubner
90. van Fraassen, Bas [1975]: review of H. Putnam's Philosophy of LogicCanadian J. Phil. 4, 731-743
91. van Inwagen, Peter [1977]: 'Creatures of fiction', American PhilosophicalQuarterly 14, 299-308
92. Vico, G. [1710]: De antiquissima Italorum sapientia
93. (available in translation, On the most ancient Wisdom of the ItaliansIthaca: Cornell University Press, 1988)
94. von Glasersfeld, Ernst [1984]: 'An introduction to radicalconstructivism', in P. Watslawick, ed., The invented reality. New York: Norton,pp. 13-40
95. Wagner, Steven [1982]: 'Arithmetical Fiction', Pacific PhilosophicalQuarterly 63, 255-269
96. Walton, Kendall L. [1990]: Mimesis as Make-Believe: On the Foundations ofthe Representational Arts. Cambridge, Mass.: Harvard University Press
97. Wang Hao [1974]: From Mathematics to Philosophy. London: Routledge &Kegan Paul
98. Wang Hao [1986]: Beyond Analytic Philosophy. Cambridge, Mass.: MIT Press
99. Warnock, Mary [1994]: Imagination and Time. Oxford: Blackwell
100. White, Hayden [1981a]: 'The Narrativization of Real Events', in Mitchell[1981], pp. 249-254
101. White, Hayden [1981b]: 'The value of narrativity in the representation ofreality' in Mitchell [1981], pp. 1-23
102. Woods, John [1969]: 'Fictionality and the logic of relations', SouthernJournal of Philosophy 7, 51-63
103. Woods, John [1974]: The logic of fiction: A philosophical sounding ofdeviant logic. The Hague: Mouton
104. Zalta, Ed [1983]: Abstract Objects: An Introduction to AxiomaticMetaphysics. Dordrecht: Reidel
105. Zemach, Eddy [1998]: 'Tom Sawyer and the beige unicorn', British Journalof Aesthetics 38, 167-179