1. Critical Thinking Lecture 11 The Syllogism
By David Kelsey

2. The syllogism A syllogism is a two premise deductive argument.
A syllogism is deductive so is an argument that is intended to be valid.
Socrates is Mortal and The moon is made of green cheese…

3. Categorical syllogisms
A categorical syllogism is:
A syllogism
Each of the syllogisms claims is a standard form categorical claim.
So its 2 premises and its conclusion are all A,E, I or O standard form categorical claims.
It has three terms, which occur exactly twice in exactly two of the argument’s claims.
Remember that each standard form categorical claim has 2 terms.
A categorical syllogism then shares 3 and only 3 terms between its 2 premises and its conclusion.
Thus, each of these three terms occurs in two different claims in the argument.

4. The terms of a syllogism
There are three terms in a categorical syllogism and each term occurs in 2 of the arguments claims.
The major term is the term that occurs as the predicate term of the syllogism’s conclusion. We can call this term P (for predicate.)
The minor term is the term that occurs as the subject term of the syllogism’s conclusion. We can call this term S (for subject.)
The middle term is the term that occurs in both of the premises but not at all in the conclusion. We can call this term M (for middle.)

5. Which is the Categorical Syllogism?
Which of the following arguments is a categorical syllogism? 1.
All cats are mammals
Not all cats are domestic
Thus, not all mammals are domestic. 2.
All soccer players are athletes.
Some basketball players are athletes.
Thus, some soccer players are not basketball players. 3.
Some voters are not students.
All voters are local people.
Thus, some local people are non-students.

6. The First argument The first argument is not a categorical syllogism:
Neither the second premise nor the conclusion is a standard form categorical claim. Do you see why?

7. The Third argument
The third argument is not a categorical syllogism either:
Notice that the conclusion contains the term non-students and yet this term doesn’t occur anywhere in the premises of the argument.

8. The Second argument
The second argument is a categorical syllogism though!
The premises and conclusion are all standard form categorical claims.
The first premise is an A claim: All soccer players are athletes.
The second premise is an I claim: Some basketball players are athletes.
And the conclusion is an O claim: Some soccer players are not basketball players.
And notice the 3 terms are soccer players, athletes and basketball players.
The major term is basketball players, the minor term is soccer players and the middle term is athletes because it is the term occurring in both premises.