What is the philosophy of mathematics?

The reasoning used in mathematics is often regarded as the embodiment of rational

thought. However, mathematics also provides a rich source of philosophical problems that

have been at the center of epistemology and metaphysics since the beginning of Western

philosophy. Do numbers and other mathematical entities exist independently of human

cognition? If not, then how do we explain what kind of things are they and how can we

know about them? What is the relationship between mathematics and logic? How does

abstract mathematics relate to the external world around us? The modern analytic tradition

begins with the work of Frege and Russell (among others) for both of whom mathematics

was a central concern. Some of the most important philosophical developments of the 20th

century were instigated by the profound developments that have taken place in

mathematics and logic.

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