Foundations Study Guide: Philosophy of Mathematics
by David Ross
The philosophy of mathematics is the philosophical study of the concepts and methods of mathematics. It is concerned with the nature of numbers, geometric objects, and other mathematical concepts; it is concerned with their cognitive origins and with their application to reality. It addresses the validation of methods of mathematical inference. In particular, it deals with the logical problems associated with mathematical infinitude.
Among the sciences, mathematics has a unique relation to philosophy. Since antiquity, philosophers have envied it as the model of logical perfection, because of the clarity of its concepts and the certainty of its conclusions, and have therefore devoted much effort to explaining the nature of mathematics....
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