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.
Other articles related to "philosophy of mathematics, philosophy, mathematics, of mathematics":
... Editing help is available Philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and ... character of a mathematical proposition? What is the relation between logic and mathematics? What is the role of hermeneutics in mathematics? What kinds of inquiry play a role in mathematics? What are the ...
... Platonism and Anti-platonism in mathematics Benacerraf, B ... Philosophy of mathematics selected reading Boolos, G ...
... the sentiment that mathematicians would like to leave philosophy to the philosophers and get back to mathematics — where, presumably, the beauty lies ... and understanding someone else's proof of a theorem of mathematics to that of a viewer of a masterpiece of art — the reader of a proof has a similar sense of exhilaration ... By the same token, however, philosophers of mathematics have sought to characterize what makes one proof more desirable than another when both are logically sound ...
Famous quotes containing the words mathematics and/or philosophy:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we dont happen to have all the data. In mathematics we have all the data ... and yet we dont understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (19091943)
“You may decry some of these scruples and protest that there are more things in heaven and earth than are dreamt of in my philosophy. I am concerned, rather, that there should not be more things dreamt of in my philosophy than there are in heaven or earth.”
—Nelson Goodman (b. 1906)