Article ID: CBB001024149

Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence (2011)

unapi

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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Authors & Contributors
Gambetta, Emanuele
Heijenoort, Jean van
Gödel, Kurt
Feferman, Solomon
Dawson, John W., Jr.
Kennedy, Juliette
Concepts
Mathematics
Philosophy of mathematics
Logic
Philosophy
Incompleteness theorems
Philosophy of science
Time Periods
20th century
19th century
20th century, early
Places
Germany
Institutions
Universität Göttingen
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