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. The latter, however, may be used to refer to several other areas of study. One refers to a project of formalising a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labours 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 taken by Bertrand Russell in his books The Principles of Mathematics and Introduction to Mathematical Philosophy.
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Famous quotes containing the words philosophy and/or mathematics:
“A writer must always try to have a philosophy and he should also have a psychology and a philology and many other things. Without a philosophy and a psychology and all these various other things he is not really worthy of being called a writer. I agree with Kant and Schopenhauer and Plato and Spinoza and that is quite enough to be called a philosophy. But then of course a philosophy is not the same thing as a style.”
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