SYLLOGISM
Syllogism, in logic, a valid deductive argument having two premises and a conclusion. The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate): “All men are mortal; no gods are mortal; therefore no men are gods.” The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself.A categorical syllogism consists of three parts:
Major premise
Minor premise
Conclusion
Each part is a categorical proposition, and each categorical proposition contains two categorical terms. In Aristotle, each of the premises is in the form "All A are B," "Some A are B", "No A are B" or "Some A are not B", where "A" is one term and "B" is another:
"All A are B," and "No A are B" are termed universal propositions;
"Some A are B" and "Some A are not B" are termed particular propositions.
More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion).
For example:
Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
Each of the three distinct terms represents a category. From the example above, humans, mortal, and Greeks: mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, humans. Both of the premises are universal, as is the conclusion.
Major premise: All mortals die.
Minor premise: All men are mortals.
Conclusion: All men die.
Here, the major term is die, the minor term is men, and the middle term is mortals. Again, both premises are universal, hence so is the conclusion.
A syllogism takes the form (note: M – Middle, S – subject, P – predicate.):
Major premise: All M are P.
Minor premise: All S are M.
Conclusion: All S are P.
The premises and conclusion of a syllogism can be any of four types, which are labeled by letters as follows. The meaning of the letters is given by the table:
| Code | Quantifier | Subject | Copula | Predicate | Type | Example |
|---|---|---|---|---|---|---|
| A | All | S | are | P | universal affirmative | All humans are mortal. |
| E | No | S | are | P | universal negative | No humans are perfect. |
| I | Some | S | are | P | particular affirmative | Some humans are clever. |
| O | Some | S | are not | P | particular negative | Some humans are not clever. |
