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Full-Text Articles in Logic and Foundations of Mathematics
Hilary Putnam's Consistency Objection Against Wittgenstein's Conventionalism In Mathematics, Pieranna Garavaso
Hilary Putnam's Consistency Objection Against Wittgenstein's Conventionalism In Mathematics, Pieranna Garavaso
Philosophy Publications
Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can explain the consistency of T and suggest that an analogous explanation can be provided for the consistency of Peano arithmetic.
On Frege’S Alleged Indispensability Argument, Pieranna Garavaso
On Frege’S Alleged Indispensability Argument, Pieranna Garavaso
Philosophy Publications
The expression ‘indispensability argument’ denotes a family of arguments for mathematical realism supported among others by Quine and Putnam. More and more often, Gottlob Frege is credited with being the first to state this argument in section 91 of the Grundgesetze der Arithmetik. Frege's alleged indispensability argument is the subject of this essay. On the basis of three significant differences between Mark Colyvan's indispensability arguments and Frege's applicability argument, I deny that Frege presents an indispensability argument in that very often quoted section of the Grundegesetze.