In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 236--317 (2005)

Authors
Michael Detlefsen
University of Notre Dame
Abstract
A comprehensive historical overview of formalist ideas in the philosophy of mathematics.
Keywords formalism  Hilbert  axiomatic method  Gödel's theorems  Hilbert's Program  Hilbert's formalism  genetic method  creativism (mathematical)  ideal elements  ideal methods
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DOI 10.1093/0195148770.003.0008
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Frege, Hankel, and Formalism in the Foundations.Richard Lawrence - forthcoming - Journal for the History of Analytical Philosophy.
Structuring Logical Space.Alejandro Pérez Carballo - 2016 - Philosophy and Phenomenological Research 92 (2):460-491.
Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - 2016 - British Journal for the Philosophy of Science:axw006.
Pasch’s Philosophy of Mathematics.Dirk Schlimm - 2010 - Review of Symbolic Logic 3 (1):93-118.

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