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Formalism in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

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One common understanding of formalism in the philosophy of mathematics takes it as holding that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than playing ludo or chess are normally thought to have. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the practice of advanced mathematicians in some periods—for example, the treatment of imaginary numbers for some time after Bombelli’s introduction of them, and perhaps the attitude of some contemporary mathematicians towards the higher flights of set theory. Finally, it is often the position to which philosophically naïve respondents will gesture towards, when pestered by questions as to the nature of mathematics. Not surprisi

--> Formalism in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy Menu Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Navigation Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top Formalism in the Philosophy of Mathematics First published Wed Jan 12, 2011; sub

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