::Philosophy of mathematics


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{{ safesubst:#invoke:Unsubst||$N=Refimprove |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

The terms philosophy of mathematics and mathematical philosophy are frequently used as synonyms.<ref>{{#invoke:Citation/CS1|citation |CitationClass=journal }}. For example, when Edward Maziars proposes in a 1969 book review "to distinguish philosophical mathematics (which is primarily a specialised task for a mathematician) from mathematical philosophy (which ordinarily may be the philosopher's metier)", he uses the term mathematical philosophy as being synonymous with philosophy of mathematics.</ref> The latter, however, may be used to refer to several other areas of study. One refers to a project of formalizing a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labors of scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some understand the term "mathematical philosophy" to be an allusion to the approach to the foundations of mathematics taken by Bertrand Russell in his books The Principles of Mathematics and Introduction to Mathematical Philosophy.

Philosophy of mathematics sections
Intro  Recurrent themes  History  Major themes  Contemporary schools of thought  Arguments  Aesthetics  See also  Notes  Further reading  External links  

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