David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 88 (2):119 - 126 (1991)
The distinction between analytic and synthetic propositions, and with that the distinction between a priori and a posteriori truth, is being abandoned in much of analytic philosophy and the philosophy of most of the sciences. These distinctions should also be abandoned in the philosophy of mathematics. In particular, we must recognize the strong empirical component in our mathematical knowledge. The traditional distinction between logic and mathematics, on the one hand, and the natural sciences, on the other, should be dropped. Abstract mathematical objects, like transcendental numbers or Hilbert spaces, are theoretical entities on a par with electromagnetic fields or quarks. Mathematical theories are not primarily logical deductions from axioms obtained by reflection on concepts but, rather, are constructions chosen to solve some collection of problems while fitting smoothly into the other theoretical commitments of the mathematician who formulates them. In other words, a mathematical theory is a scientific theory like any other, no more certain but also no more devoid of content.
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References found in this work BETA
Gottlob Frege (1953/1968). The Foundations of Arithmetic. Evanston, Ill.,Northwestern University Press.
Nicolas D. Goodman (1990). Mathematics as Natural Science. Journal of Symbolic Logic 55 (1):182-193.
Nicolas D. Goodman (1981). The Experiential Foundations of Mathematical Knowledge. History and Philosophy of Logic 2 (1-2):55-65.
Philip Kitcher (1983). The Nature of Mathematical Knowledge. Oxford University Press.
Imre Lakatos (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
Citations of this work BETA
Thomas Tymoczko (1991). Mathematics, Science and Ontology. Synthese 88 (2):201 - 228.
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