Beginning Mathematics/Logic and Deductive Reasoning

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Logic has a long history, and is one of the central tenets of western thought. Going back to the ancient philosophers, logic has been the attempt to devise a system for ascertaining truth via thought. Logic falls under the category of deductive reasoning, meaning it is used to establish truth based upon already established truths, called postulates or axioms.

The oldest and most influential axiom system would be from Euclid's Elements, the classic geometry text, which ranks as one of the most important books of all time. Euclid starts off his first book with 23 definitions and 5 postulates. The postulates basically describe what can be done with an unmarked ruler and a compass. For instance, the first postulate says that a line can be drawn between two points. The second says that lines can be extended, and the third says that circles can be drawn with a center and a given radius.