Lesson 25Distributed Terms
A term is distributed in a statement if it is referring to the entire class.
Example 1: In ‘ All dogs are living beings’.
The term ‘dogs’ is distributed, whereas the term ‘living beings’ is not (the statement does not have us think about ALL living beings, just some of them)
Example 2: Some dogs are mammals.
Neither terms are distributed. Why?
In the 4 types of categorical statements, identify which terms are distributed:
All A are B.
No C are D.
Some E are F.
Some G are not H.
Look at pg 141 and circle all distributed terms.
Lesson 26 Testing Syllogisms by Rules
Rule 1. In at least one premise, the middle term must be distributed. (Otherwise, the syllogism is invalid.)
Example: The following breaks Rule 1. Why?
Some S are M
All P are M
Therefore, Some S are P
If Rule 1 is broken, this is called the Fallacy of the Undistributed middle.
Give another syllogism in standard form which has the Fallacy of the Undistributed middle:
Major premise:
Minor Premise:
Conclusion:
Rule 2. If a term is distributed in the conclusion, it also must be distributed in the premises. . (Otherwise, the syllogism is invalid.)
Example: The following breaks Rule 2. Why?
Some S are M
Some P are not M
Therefore, Some S are not P
When Rule 2 is broken AND the major term in the conclusion is distributed, but not distributed when it appears in the major premise, this is called the Fallacy of the Illicit Major.
When Rule 2 is broken AND the minor term in the conclusion is distributed, but not distributed when it appears in the minor premise, this is called the Fallacy of the Illicit Minor.
Give another syllogism in standard form which has the Fallacy of the Illicit Minor:
Major premise:
Minor Premise:
Conclusion:
Rule 3. One premise must be affirmative (so both premises cannot be negative).
Example: The following breaks Rule 3. Why?
Some S are not M
Some P are not M
Therefore, Some S are not P
When Rule 3 is broken, this is called the Fallacy of two negative premises.
Example: EEA-1 is invalid. Why?
Rule 4. A valid syllogism with an affirmative conclusion must have all its premises also affirmative (it can’t have any negative premise).
Example: The following breaks Rule 4. Why?
Some S are not M
No P are M
Therefore, Some S are P
When Rule 4 is broken, this is called the Fallacy of a negative premise and an affirmative conclusion.
Example: AEA-1 is invalid. Why?
Rule 5. A valid syllogism with a negative conclusion must have one of its premises also negative (it can’t have both affirmative premises).
Example: The following breaks Rule 5. Why?
Some S are M
All P are M
Therefore, Some S are not P
When Rule 5 is broken, this is called the Fallacy of a two affirmative premises and anegative conclusion.
If a syllogism breaks ANY of the rules, it is INVALID.
If a syllogism satisfies all 5 rules, it is VALID!
Exercise:Test the following using the 5 rules
Write Pass/Fail
AEO-1: Rule 1______Rule 2______Rule 3______Rule 4______Rule 5______
AEO-2: Rule 1______Rule 2______Rule 3______Rule 4______Rule 5______
IAE-4: Rule 1______Rule 2______Rule 3______Rule 4______Rule 5______
EOA-2: Rule 1______Rule 2______Rule 3______Rule 4______Rule 5______
OAO-1: Rule 1______Rule 2______Rule 3______Rule 4______Rule 5______