Aristotle'’s Syllogisms

The most famous, and rightly so, of Aristotle'’s logical work is the codification of the syllogism, the “if...then” statements that he believed were the core of logic. By using these statements in combination with certain very basic assumptions about the nature of classes, Aristotle was able to construct a very wide-ranging logical language that is still quite impressive to this day.

There were two parts to describing this language: the first was the general nature of propositions in general, the second was describing how those propositions could like together to form logical arguments.

Classes

Basic to many logical system is the idea of classes, or sets. The classic example of the use of sets in logic is the famous syllogism:
  1. Socrates is a man.
  2. All men are mortal.
  3. Therefore, Socrates is mortal.
There is much more even to this simple syllogism than at first meets the eye, and Aristotle pointed out the similarity of this structure to another kind of logical structure often used in argumentation:
  1. If Socrates is a man, then Socrates is mortal.
  2. Socrates is a man.
  3. Therefore, Socrates is mortal.
Statement 1 of the second structure seems to correspond to Statement 2 of the first, and vice versa. Statement 3 is identical in both structures. Aristotle’s claim was that there was something fundamentally the same (and fundamentally valid) about both structures. He called these structures syllogisms.

Categorical Statements

Aristotle divided categorical propositions into four different kinds: these four “forms” formed the basis for medieval analysis of logic. They divided propositions into universal and particular, affirmative and negative:
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Jason Corley -- corleyj@cobweb.scarymonsters.net