Module 3: Aristotelian Logic
Quick Reference Summary for Aristotelian Logic
Proposition Types and Their Characteristics
- Type A: All S are P.
- Meaning: Every member of S class is a member of P class; S class is included in P class.
- Quantity: Universal
- Quality: Positive
- Type E: No S are P.
- Meaning: No member of S class is a member of P class; S class is excluded from P class.
- Quantity: Universal
- Quality: Negative
- Type I: Some S are P.
- Meaning: At least one member of the S class is a member of the P class.
- Quantity: Particular
- Quality: Positive
- Type O: Some S are not P.
- Meaning: At least one member of the S class is not a member of the P class.
- Quantity: Particular
- Quality: Negative
Relationships in the Square of Opposition
- Contradictories – Have opposite truth values.
- Contraries – At least one is false, both cannot be true.
- Subcontraries – At least one is true, both cannot be false.
- Subalterns – Truth flows down, falsehood flows up
Operations on Categorical Propositions
Conversion
Steps:
1. Switch the subject and predicate terms.
Resulting truth value:
A – Undetermined
E – Same as given statement
I – Same as given statement
O – Undetermined
Obversion
Steps:
1. Change the quality of the statement.
2. Replace the predicate with its term complement.
Resulting truth value:
A – Same as given statement
E – Same as given statement
I – Same as given statement
O – Same as given statement
Contraposition
Steps:
1. Replace the subject with the complement of the predicate.
2. Replace the predicate with the complement of the subject.
Resulting truth value:
A – Same as given statement
E – Undetermined
I – Undetermined
O – Same as given statement
Categorical Syllogisms
Venn Diagram Symbolization
- S circle: Subject Term/Class (subject of the conclusion)
- P circle: Predicate Term/Class (predicate of the conclusion)
- M circle: Middle Term/Class (occurs in both premises)
Major Term is the predicate of the conclusion, occurs in Major Premise.
Minor Term is the subject of the conclusion, occurs in Minor Premise.
Middle Term occurs in both premises, does not occur in the conclusion.
Required sequence of standard form syllogisms:
- Major premise (contains major term)
- Minor premise (contains minor term)
- Conclusion (contains minor term as subject, major term as predicate; does not contain middle term.)
The mood of a syllogism is expressed as the letter/name (A, E, I. O) for each of the three propositions, in standard sequence.
The figure of a syllogism reflects the location the middle term in the premises.
