Mathematical instrumentalism, Gödel’s theorem, and inductive evidence

Studies in History and Philosophy of Science Part A 42 (1):140-149 (2011)
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Abstract

Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem.

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A. C. Paseau
University of Oxford

Citations of this work

Knowledge of Mathematics without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.

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References found in this work

Content preservation.Tyler Burge - 1993 - Philosophical Review 102 (4):457-488.
The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.

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