Syllogistic LogicSyllogistic Logic

1. Categorical Propositions2. Venn Diagram3. The Square of Opposition: Tradition /

Modern4. Conversion, Obversion, Contraposition5. Syllogisms: Mood / figure / Validity

Syllogism

Categorical PropositionCategorical 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 PropositionsCategorical Propositions

1 2 3

S P

4

SP

Venn DiagramVenn Diagram

SP SP

SP

The Square of Proposition: TraditionThe 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

Contradict

ory

Contradictory

Cont dictory

Suba

tern

ates

Subaternates

Contrary (Contrary ( 反對關係反對關係 ))

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 (Suncontrary ( 次反對關係次反對關係 ))

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 (Contradictory ( 矛盾關係矛盾關係 ))

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 (Subalternation ( 從屬關係從屬關係 ))

A I

E O

True

False

True

FalseWhen 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.

1 2 3

S P

4

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

1 2 3

S P

4

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

1 2 3

S P

4

I: Some S are PI: Some S are P

1 2 3

S P

4

O: Some S are not PO: Some S are not P

1 2 3

S P

4

A: All S are PA: All S are P

1 2 3

S P

4

E: No S are PE: No S are P

The Square of Proposition: ModernThe 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

Contradict

oryCont dictory

ConversionConversion

s pA:

1 2 34

s

s

s

p

p

p

E:

I:

O:

s

s

s

s

p

p

p

p

1 2 3

4

1 2 34

1 2 34

conversion 1 2 34

conversion 1 2 34

conversion 1 2 3

4

conversion 1 2 3

4

ObversionObversion

s pA:

1 2 34

s

s

s

p

p

p

E:

I:

O:

s

s

s

s

p

p

p

p

1 2 3

4

1 2 34

1 2 34

obversion 1 2 34

obversion 1 2 34

obversion 1 2 3

4

obversion 1 2 3

4

ContrapositionContraposition

s pA:

1 2 34

s

s

s

p

p

p

E:

I:

O:

s

s

s

s

p

p

p

p

1 2 3

4

1 2 34

1 2 34

contraposition1 2 3

4

contraposition1 2 3

4

contraposition 1 2 3

4

contraposition 1 2 3

4

MoodMood

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 )

叫 我 major term( 大 詞)

FigureFigure

M P P M M P P MS M S M M S M SS P S P S P S P

F1 F2 F3 F4

Collar figure