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68Confronting Ideals of Proof with the Ways of Proving of the Research MathematicianStudia Logica 96 (2): 273-288. 2010.In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Following Cellucci, we call the prevailing view the “axiomatic conception” of proof. The conception includes the ideas that: a proof is finite, it proceeds from axioms and it is the final word on the matter of the conclusion. This received view can be traced back to Frege, Hilbert and Gentzen, amongst others, and is prevalent in both mathematical text books and logic text boo…Read more
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51On the epistemological significance of the hungarian projectSynthese 192 (7): 2035-2051. 2015.There are three elements in this paper. One is what we shall call ‘the Hungarian project’. This is the collected work of Andréka, Madarász, Németi, Székely and others. The second is Molinini’s philosophical work on the nature of mathematical explanations in science. The third is my pluralist approach to mathematics. The theses of this paper are that the Hungarian project gives genuine mathematical explanations for physical phenomena. A pluralist account of mathematical explanation can help us wi…Read more
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45Are Mathematicians Better Described as Formalists or Pluralists?Logic and Philosophy of Science 9 (1): 173-180. 2011.In this paper we try to convert the mathematician who calls himself, or herself, “a formalist” to a position we call “meth-odological pluralism”. We show how the actual practice of mathe-matics fits methodological pluralism better than formalism while preserving the attractive aspects of formalism of freedom and crea-tivity. Methodological pluralism is part of a larger, more general, pluralism, which is currently being developed as a position in the philosophy of mathematics in its own right.1 H…Read more
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28Pluralism and “Bad” Mathematical Theories: Challenging our PrejudicesIn Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications, Springer. pp. 277--307. 2013.
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IntroductionIn Pluralism in Mathematics: A New Position in Philosophy of Mathematics, Springer. 2013.
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50An Analysis of the Notion of Rigour in ProofsLogic and Philosophy of Science 9 (1): 165-171. 2011.We are told that there are standards of rigour in proof, and we are told that the standards have increased over the centuries. This is fairly clear. But rigour has also changed its nature. In this paper we as-sess where these changes leave us today.1 To motivate making the new assessment, we give two illustra-tions of changes in our conception of rigour. One, concerns the shift from geometry to arithmetic as setting the standard for rig-our. The other, concerns the notion of effective proof or c…Read more
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Areas of Specialization
Science, Logic, and Mathematics |
Metaphysics and Epistemology |
Philosophy, Misc |