Philosophy Of Mathematics
Wikipedia Reference Information
Philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics.
Recurrent themes include:
What are the sources of mathematical subject matter?
What does it mean to refer to a mathematical object?
What is the 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 objectives of mathematical inquiry?
What gives mathematics its hold on experience?
What are the human traits behind mathematics?
What is mathematical beauty?
What is the source and nature of mathematical truth?
What is the relationship between the abstract world of mathematics and the material universe?
The terms philosophy of mathematics and mathematical philosophy are frequently used as synonyms. The latter, however, may be used to mean at least three other things. One sense 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 sense 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 book Introduction to Mathematical Philosophy.
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