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Full-Text Articles in Logic and Foundations
Mathematical Philosophy, Janie Ferguson
Mathematical Philosophy, Janie Ferguson
Honors Theses
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 …
Mathematics And Logic, Janet Moffett
Mathematics And Logic, Janet Moffett
Honors Theses
Mathematics is interested in the methods by which concepts are defined in terms of others and statements are inferred from others. It therefore uses a primarily deductive form of reasoning. It is almost impossible to distinguish where logic leaves off and mathematics begins. "... logic is the youth of mathematics and mathematics is the manhood of logic." Mathematics starts from certain premises and, by a strict process of deduction, arrives at the various theorems which constitute it.
In order to understand the congruence of mathematics and deductive logic, one must understand the principles of each and the relation between them. …