ABSTRACT
This chapter provides the interaction between the philosophy of mathematics and the development of mathematical logic. Frege formalized pure logic, proposed a reduction of arithmetic to logic thereby inviting the broader thesis of the reducibility of all mathematics to logic, and broadened Kant's concept of analytic propositions. Frege's inclination to include set theory under logic was in part responsible for the interest of mathematical logicians in Cantor's intuitive and mathematical set theory. The place of mathematics in human knowledge seems to be more interesting than that of pure logic. The overemphasis on logic and the ambiguous identification of logic with mathematics in contemporary philosophy tend to evade many substantial philosophical issues such as the relation between mathematics and physics. The use of formal axiomatic systems is a familiar feature of mathematical logic. Abstract structures enable us to prove once and for all different theorems in different theories which share the same structure.
