Philosophy 103 - Introduction to Logic: Critical Thinking

Categorical Syllogisms



I. A syllogism is a two premise deductive argument. Since the Middle Ages, the parts of a categorical syllogism are labeled as follows:

All beagles are mammals (major premise)
All dogs are beagles (
minor premise)
All dogs are mammals (

"Mammals" is the major term since it is the predicate of the conclusion.
"Dogs" is the
minor term since it is the subject of the conclusion.
"Beagles" is the
middle term since it is the term which occurs in both of the premises but not in the conclusion.



II. A categorical syllogism has these features:



III. The mood of a categorical syllogism consists of the letter names of the propositions which make it up. Hence the mood of our example is AAA. The figure of the syllogism depends on the location of the middle term. Refer to the chart on page 262.



IV. Syllogisms are unconditional valid if, and only if, they are valid from both the Aristotelian and Boolean standpoints. They are conditionally valid if they are valid only on the condition that the Aristotelian standpoint is taken and they do not commit the existential fallacy.


Some helpful hints (also see Hurley, pp. 269-270)


1. Label the left circle for the minor term, the right circle for the major term, and the middle circle for the middle term.

2. Only the premises are diagrammed.

3. Always diagram A and E premises first.

4. When diagramming I or O premises: If one part of the relevant area is already shaded, then place the "X" in the unshaded area. If more than one part of the relevant area is not shaded, then place an "X" on the line between the sub-areas in question.