1. Critical Thinking Lecture 10 The Syllogism
By David Kelsey

2. The syllogism A syllogism: is a two premise deductive argument.
A syllogism is intended to be valid and it is either sound or unsound.
Socrates is mortal:
The moon orbits the Earth:

3. Categorical syllogisms
A categorical syllogism is:
A syllogism
Each of its claims
It has three terms, which occur exactly twice in exactly two of the claims.

4. The terms of a syllogism
There are three terms in a categorical syllogism: each term occurs in two different propositions of the argument.
The major term:
Call this P
The minor term:
Call this S
The middle term:
Call this M

5. 3 arguments: which is the Categorical Syllogism?1.
All cats are mammals
Not all cats are domestic
Thus, not all mammals are domestic. 2.
All valid arguments are good arguments.
Some valid arguments are boring arguments.
Thus, some good arguments are boring arguments. 3.
Some people on the committee are not students.
All people on the committee are local people.
Thus, some local people are non-students.

6. The rules method of testing the validity of a categorical syllogism
The rules method gives us three simple rules.
If a categorical syllogism breaks any of the three rules then it isn’t valid.
The three rules are:
1) The number of negative claims in the premises must be the same as the number of negative claims in the conclusion.
2) At least one premise must distribute the middle term.
3) Any term that is distributed in the conclusion must be distributed in its premises.

7. Distributing a term
The 2nd and 3rd rules of the rules method mention a claims distributing a term:
Claims distribute terms: A categorical claim’s terms are either distributed or undistributed.
A claim distributes a term if and only if the claim says something about every member of the class the term names.
Consider an A claim: All Monkey’s are mammals
Now let’s do the same for an E, I and O claim:

8. 4 rules about distribution
4 distribution rules: each rule tells us whether or not a categorical claim distributes a term.
This can be found in Moore and Parker, chapter 8. Anyone know which page?
1) An A claim distributes ____________.
All _________ are ___________:
2) an E claim distributes ___________.
No __________ are _________:
3) An I claim distributes ___________.
Some ____________ are ______________.
4) An O claim distributes only its _____________.
Some ___________ are not ___________

9. 2 examples Drummers, keyboard players & Singers:
1. All drummers are keyboard players.
2. Some keyboard players are not singers.
3. Thus, some drummers are not singers.
This example breaks rule
Bars and Pizza Places:
1. No Pizza places are bars.
2. Some bars are restaurants.
3. Thus, some pizza places are restaurants.

10. One final example Futsal, soccer and surfing:
1. No futsal players are surfers.
2. All futsal players are soccer players.
Thus, 3. No soccer players are surfers.
This syllogism breaks which rule?