Socratic Logic - Reasoning

The following are the notes I have taken from Peter Kreeft's wonderful Socratic Logic textbook. I highly recommend you buy it. This is a book which deals with classical logic (as opposed to modern symbolic logic.) It is easily the best overall book on logic I have ever read and one of the few I have that are worth making notes from. I even have a small duotang with these notes in it I can carry around and reference on a regular basis.

Evaluating Syllogisms

Textbook uses two methods of evaluation:

A. Euler's Circles

B. Aristotle's Six Rules of Syllogisms

Euler's Circles

Euler's circles are simpler and quicker to work with than Aristotle's rules.

Note: Euler's circles do not work for some syllogisms with I or O premises.

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eg. All men are mortal.

Socrates is a man.

Socrates is mortal.

euler image here....

Socrates (Man) (Mortal)

Valid!!

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Aristotle's Six Rules of Syllogisms

A. A syllogism must have three and only three terms.

B. A syllogism must have three and only three propositions.

C. The middle term must be distributed at least once or commit the Fallacy of the Undistributed Middle.

D. No term that is undistributed in the premises can be undistributed in the conclusion.

E. No syllogism can have two negative premises.

F. If one premise is negative, the conclusion must be negative.