LOGICAL
OPPOSITION
Of Categorical Propositions
LOGICAL OPPOSITION
Mutual exclusivity between
concepts
Relations existing in between propositions
with the same subject and predicate, but
differing in quantity and/or quality
Some of fruits are fresh.
CONTRARIES
superaltern
superaltern
I
SUB CONTRARIES
subaltern
subaltern
CONTRADICTION
CONTRADICTION
Differ in quantity and quality
If 1st is TRUE, the 2nd is FALSE
If 1st is FALSE, the 2nd is TRUE
CONTRARY
CONTRARY
Both are UNIVERSAL
Differ in quality (+,-)
If 1st is TRUE, the 2nd is FALSE
If 1st is FALSE, the 2nd is DOUBTFUL
EXAMPLES
All soaps are cleansers. TRUE
All soaps are not cleansers. FALSE
No women are married. FALSE
All women are married. DOUBTFUL
Possible: Some women are married.
Exercise: Identify the contrary
proposition and the truth value.
1.
2.
3.
4.
All diamonds are gems. (T)
No apples are mangoes. (F)
All flowers are roses. (F)
No Bikolanos are Filipinos. (T)
Exercise: Identify the contrary
proposition and the truth value.
1. All diamonds are gems. (T)
CT: All diamonds are not gems.
TV: FALSE
2. No apples are mangoes. (F)
CT: All apples are mangoes.
TV: DOUBTFUL
Exercise: Identify the contrary
proposition and the truth value.
3. All flowers are roses. (F)
CT: All flowers are not roses.
TV: DOUBTFUL
4. No Bikolanos are Filipinos. (T)
CT: All Bikolanos are Filipinos.
TV: FALSE
SUBCONTRARY
SUBCONTRARY
Both are PARTICULAR
Differ in quality (+,-)
If 1st is TRUE, the 2nd is DOUBTFUL
If 1st is FALSE, the 2nd is TRUE
EXAMPLES
Some soaps are cleansers. TRUE
Not all soaps are cleansers. DOUBTFUL
Possible: All soaps are cleansers.
Some women are married. FALSE
Some women are not married. TRUE
Exercise: Identify the subcontrary
proposition and the truth value.
1.
2.
3.
4.
Some triangles are squares. (F)
Some students are not present. (F)
Some basketball players are tall. (T)
Some scholars are not dumb. (T)
Exercise: Identify the subcontrary
proposition and the truth value.
1. Some triangles are squares. (F)
SCT: Some triangles are not squares.
TV: (T)
2. Some students are not present. (F)
SCT: Some students are present.
TV: (T)
Exercise: Identify the subcontrary
proposition and the truth value.
3. Some basketball players are tall. (T)
SCT: Some basketball players are not tall.
TV : (D)
4. Some scholars are not dumb. (T)
SCT: Some scholars are dumb.
TV: (D)
SUBALTERNATION
SUBALTERNATION
Both in QUALITY
Differ in quantity (U,P)
If U is TRUE, P is TRUE
If U is FALSE, P is DOUBTFUL
If P is TRUE, U is DOUBTFUL
If P is FALSE, U is FALSE
EXAMPLES
Some soaps are cleansers. TRUE
All soaps are cleansers. DOUBTFUL
Possible: Some soaps are not cleansers.
All women are married. FALSE
Some women are married. TRUE
Possible: No women are married.
EXAMPLES
Some men are not spiritual. FALSE
No men are spiritual.
Some devils are not good. FALSE
All devils are good.
EXAMPLES
Some oranges are sweet. TRUE
All oranges are sweet.
Not all athletes are not swimmers. FALSE
No athletes are swimmers.
Give the SUBALTERN of the following propositions and
their truth value.
1. Some drivers are blind. (F)
2. Not all professionals are educated. (F)
3. Some teachers are late. (F)
4. All of those who came enjoyed. (T)
5. No policeman is corrupt. (F)
SUMMARY
• CONTRADICTORY(Always opposite)
•
If 1st is T, the 2nd is F
•
If 1st is F, the 2nd is T
• CONTRARY (Cannot be both TRUE)
•
If 1st is T, the 2nd is F
•
If 1st is F, the 2nd is DOUBTFUL
• SUBCONTRARY(Cannot be both FALSE)
•
If 1st is F, the 2nd is T
•
If 1st is T, the 2nd is DOUBTFUL
• SUBALTERN
•
If Universal is T, Particular is T
•
If Universal is F, Particular is Doubtful
•
If Particular is T, Universal is Doubtful
•
If Particular is F, Universal is F
Examples
1. Contrary : No whales are fishes.(F)
2. Contradictory: Not all animals are aquatic. (T)
3. Subcontrary: Some spiders are eightlegged.(T)
4. Subaltern: No whales are fishes. (F)
5. Subcontrary: All spiders are eight-legged.(F)
LOGICAL
OPPOSITION
Of Categorical Propositions