Deductive Logic

Deductive Logic

Deductive Logic

Deductive Logic

Synopsis

This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.

Excerpt

Logic is the study of principles of reasoning. It is concerned not with how people actually reason, but rather with how people ought to reason if they wish to ensure the truth of their results. That is, by “principles of logic” we mean those that yield correct reasoning. Moreover, the principles of logic are general: they do not govern reasoning in one specific subject matter or another, but with reasoning as it applies to any and all areas of study.

Reasoning is a matter of drawing conclusions, or inferring. Hence in logic we are often concerned with arguments, that is, inferences from premises to conclusions. An example familiar since antiquity is this:

All persons are mortal.
Socrates is a person.
Therefore, Socrates is mortal.

The first two statements are the premises; the third is the conclusion. (Of course, in everyday life, arguments are seldom laid out quite so neatly. That is a rhetorical matter, and not our concern here.) The argument is a deductive argument: the conclusion follows logically from the premises. This fea-

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