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60The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart from conside…Read more
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3Leigh S. Cauman, First-order Logic, an Introduction Reviewed byPhilosophy in Review 20 (4): 240-244. 2000.
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42Confronting 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
Washington, District of Columbia, United States of America
Areas of Specialization
Science, Logic, and Mathematics |
Metaphysics and Epistemology |
Philosophy, Misc |