Date of Award
Dr. D.M. Seward
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. The ancients called logic the instrument of science and considered it as a preparatory to all science.
Moffett, Janet, "Mathematics and Logic" (1967). Honors Theses. 264.