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The purpose of Mathematical Philosophy by Cassius J. Keyser is to delve into some of the more essential and significant relations between mathematics and philosophy. To see this relation, one must gain insight into the nature of mathematics as a distinctive type of thought. The standard of excellence in the quality of thinking to which mathematicians are accustomed is called "logical rigor;" clarity and precision are essentials. The demands of logic, however, cannot be fully satisfied even in mathematics, but it meets the requirements much more nearly than any other discipline. Thus, the amount of mathematical training essential to education is the amount necessary to give one a fair understanding of the strict logical standards involved. Mathematics, which is identical to logic, therefore, is not completely separate from philosophy but is, strictly speaking, one of its principle divisions. Whenever a mathematician compares two branches of mathematics, his attitude becomes that of the philosopher. the student of philosophy, on the other hand, needs to acquire that knowledge of mathematics which will bring him into sympathy with it.



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