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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