PHIL 3910 Lecture Notes - Lecture 2: Pythagorean Theorem, Odysseus, Nazi Germany
13 Mar 2016
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Frege thought that everything in math needed to be verifiable, to avoid making mistakes and letting theorems rest on fallacies. In order to do this, he invented modern logic. If an argument is a good one, if a conclusion follows from its premises, it"s because of the form, not the content. Even though people thought that logic was already finished developing as a science, frege thought that some of math was not treatable logically using the theories that aristotle and others had established. But what if: all horses are mammals => all tails of horses are tails of mammals (frege) If the premises are true, then the conclusion must be true (formal logic). (likewise, if the premises are false, the conclusion is also false) Frege invented a new logic to systematize more complicated arguments than those of. He hopes he has captured all possible forms of reasoning. However, frege doesn"t exactly capture notions of necessity or possibility.
