Syllogistic Logic 1. C Categorical Propositions 2. V Venn Diagram 3. The Square of Opposition:...
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Transcript of Syllogistic Logic 1. C Categorical Propositions 2. V Venn Diagram 3. The Square of Opposition:...
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