Aristotle's Logic

(Originally written July 14, 2006 in Book 4)

The History of Western Philosophy
Bertrand Russell

Chapter 22: Aristotle's Logic

Aristotle's greatest influence was in the field of logic.

The syllogism is an argument consisting in three parts:
1) A major premise
2) A minor premise
3) A Conclusion

There are a number of different kinds of syllogisms, each with a name. But the most familiar is the 'Barbara':

All men are mortal (major premise)
Socrates is a man (minor premise)
Therefore, Socrates is mortal (conclusion)

Celarent Syllogism:

No fishes are rational.
All sharks are fishes.
Therefore, no sharks are rational.

Darii Syllogism:

All men are rational.
Some animals are men.
Therefore, some animals are rational.

Ferio Syllogism:

No Greeks are black.
Some men are Greeks.
Therefore, some men are not black.

The 'Barbara', 'Celarent', 'Darii', and 'Ferio' make up the first figure. The second and third figures were later added by Aristotle and the fourth figure was added by his followers. But these three could be reduced to match the first.

Aristotle held that all deductive inferences, when properly stated, were syllogisms. By stating everything in syllogisms he held that it was possible to avoid all fallacies.

As the beginning of formal logic this is crucial and admirable.

If this wis the end of formal logic it is open to three types of criticism.
1) Formal defects within the system itself.
2) Over-estimation of the syllogism as compared to other forms of deductive argument.
3) Over-estimation of deduction as a form of argument.

There are 10 Categories for Aristotle
1) Substance
2) Quantity
3) Quality
4) Relation
5) Place
6) Time
7) Position
8) State
9) Action
10) Affection

A category is "an expression which is in no way composite signify" (Russell, 200). Basically a category is a word whose meaning is not a mere compilation of other words.

How are the first premises obtained? Deductive arguments must begin with a non-demonstrable truth.

Aristotle states an individual thing's essence is a non-demonstrable truth.

An essence is a thing's properties that cannot change without that thing losing its identity.

Russell: Essences are linguistic convinces and utterly meaningless. Substances are the same thing. "Substance, in a word, is a metaphysical mistake, due to transference to the world-structure of sentences composed of a subject and a predicate" (Russell, 202).