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Catalyzed by the failure of Frege's logicist program, logic and the foundations of mathematics first became a philosophical topic in Europe in the early years of the twentieth century. Frege had aimed to show that logic constitutes the foundation for mathematics in the sense of providing both the primitive concepts in terms of which mathematical concepts were to be defined and the primitive truths on the basis of which mathematical truths were to be proved. This article describes three trends in the philosophy of mathematics as it is currently practiced in the United States.

*Keywords: *mathematical concepts;
logicist program;
foundations of mathematics;
primitive truths;
mathematical truths;
United States

*Article.*
*14590 words.*

*Subjects: *Philosophy
; History of Western Philosophy
; Philosophy of Mathematics and Logic

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