Syllogistic Logic 1. C Categorical Propositions 2. V Venn Diagram 3. The Square of Opposition: Tradition / Modern 4. C Conversion, Obversion, Contraposition 5. Syllogisms: Mood / figure / Validity Syllogism

Categorical Proposition A (universal affirmative) : All S are P E (universal negative): No S are P I (particular affirmative): Some S are P O (particular negative): Some S are not P

A: All men E: No cats are mortal. are dogs. I: Some books O: Some birds are good. are not red. Quantity Universal Particular Quality Affirmative Negative Categorical Propositions

123 S P 4 SP Venn Diagram SPSP SP

The Square of Proposition: Tradition All S are P A No S are P E I Some S are P O Some S are not P T T F F Contrary C o n t r a d i c t o r y Contradictory C o n t d i c t o r y S u b a t e r n a t e s S u b a t e r n a t e s

Contrary ( 反對關係 ) A E When two propositions are contrary to each other, they could not both be true, but could both be false. When the one is true, the other must be false. When the one is false, the other is indeterminate.

Suncontrary ( 次反對關係 ) I O When two propositions are subcontrary to each other, they could not both be false, but could both be true. When the one is false, the other must be true. When the one is true, the other is indeterminate.

Contradictory ( 矛盾關係 ) A O E I When the one is true, the other must be false. When the one is false, the other must be true. When two propositions are contradictory, they always have the opposite true value.

Subalternation ( 從屬關係 ) A I E O True False True False When A is true, I must be true. When E is true, O must be true. When I is false, A must be false. When O is false, E must be false.

123 S P 4 A: All S are P (Tradition)

123 S P 4 E: No S are P (Tradition)

123 S P 4 I: Some S are P

123 S P 4 O: Some S are not P

123 S P 4 A: All S are P

123 S P 4 E: No S are P

The Square of Proposition: Modern All S are P A No S are P E I Some S are P O Some S are not P C o n t r a d i c t o r y C o n t d i c t o r y

Conversion s p A: s s s p p p E: I: O: s s s s p p p p conversion conversion conversion conversion 123 4

Obversion s p A: s s s p p p E: I: O: s s s s p p p p obversion obversion obversion obversion 123 4

Contraposition s p A: s s s p p p E: I: O: s s s s p p p p contraposition contraposition contraposition contraposition 123 4

Mood C.P. (A,E,I,O) Q M C P Major premise ( 大前提 ) C.P. (A,E,I,O) Q S C M Minor premise ( 小前提 ) C.P. (A,E,I,O) Q S C P 叫我 Middle term ( 中詞 ) 叫我 minor term ( 小詞 )

Figure M PP MM PP M S MS MM SM S S PS PS PS P F1 F2 F3 F4 Collar figure