Categorical Syllogisms

I decided to review my Categorical Syllogisms. Since I am a Philosophy major I think its important to stay current in logic as its crucial in any philosophical discussion; perhaps I can go as far as saying logic is the fundamental of any worthwhile discussion. The next few posts will relate to Philosophy and Argumentative Logic.

Today I am reviewing Categorical Syllogism as there are only 5-7 rules of Syllogisms depending on your source. Some sources like to combine syllogistic rules.

A Categorical Syllogism is represented by three terms, a major term (P), a minor term (S) and a middle term (M). The major term is the predicate of the conclusion and the minor term is the subject of the conclusion. The predicate modifies the subject. Traditionally the major term is written first, followed by the minor term and a conclusion. It can be represented as such.

All M are p
All S are M
________
All S are P

To understand how premises are defined we must understand how they are distributed. I have borrowed the list of distributions from Wikipedia and added my own Venn diagrams for ease of learning.

• In "All A are B"-propositions the subject (A) is distributed.
• In "No A are B"-propositions both the subject (A) and the predicate (B) are distributed.
• In "Some A are B"-propositions neither the subject nor the predicate are distributed.
• In "Some A are not B"-propositions the predicate is distributed.

Distribution of Terms

Fallacy 1: Undistributed Middle
The middle term must be distributed at least once.
Fallacy 2: Illicit Major/Illicit Minor
If a term is distributed in the conclusion, then it must be distributed in a premise.
Fallacy 3: Exclusive Premises
If a term is distributed in the conclusion, then it must be distributed in a premise.
Fallacy 4: Drawing an affirmative conclusion from a negative premise, or drawing a negative conclusion from an affirmative premise.
A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise. (Alternate rendering: Any syllogism having exactly one negative statement is invalid.)
Fallacy 5: Existential Fallacy
If both premises are universal, the conclusion cannot be particular.


Other useful resources:
Lander Edu
Csunx