logical opposition

LOGICAL OPPOSITION OF PROPOSITION

LOGICAL OPPOSITION OF PROPOSITION

It refers to the different relations that exists between propositions having the same subject & predicate, but differing in quantity or quality, or both.

1. Contradiction – a relation which exists between propositions that differ both in quantity & quality.

a. A & O

- (UA) All humans are mortal.

(PN) Some humans are not mortal.

- (PN) Some politicians are not celebrities.

(UA) All politicians are celebrities.

b. E & I

- (UN) No humans are angels.

(PA) Some humans are angels.

- (PA) Some lawyers are boastful.

(UN) No lawyers are boastful.

2. Contrariety – a relation which exists between universal propositions that differ in quality only.

a. A & E

- (UA) All Koreans are Asians.

(UN) No Koreans are Asians.

b. E & A

- (UN) No soldiers are coward.

(UA) All soldiers are coward.

3. Subcontrariety – a relation which exists between particular propositions that differ in quality only.

a. I & O

- (PA) Some teachers are males.

(PN) Some teachers are not males.

b. O & I

- (PN) Some politicians are not honest.

(PA) Some politicians are honest.

3. Subalternation – a relation which exists between two propositions having the same quality, but differing in quantity.

a. A & I or I & A

- (UA) All doctors are professionals.

(PA) Some doctors are professionals.

b. E & O or O & E

- (UN) No engineers are egoists.

(PN) Some engineers are not egoists.

*The universal proposition is called the superaltern.

* The particular proposition is called the subaltern.

SQUARE OF OPPOSITION

LAWS OF CONTRADICTION If one is true, the other is false. If one is false, the other is true.

a. (UA) All soaps are cleansers. – True

(PN) Some soaps are not cleansers. – ?

b. (UN) No women are married. – False

(PA) Some women are married. - ?

c. (PA) Some apples are oranges. – False

(UN) No apples are oranges. – ?

d. (PN) Some prisoners are not guilty. – True

(UA) All prisoners are guilty. - ?

LAWS OF CONTRARIETY If one is true, the other is false. If one is false, the other is doubtful.

a. (UA) All diamonds are gems. – True

(UN) No diamonds are gems. – ?

b. (UN) No apples are oranges.– True

(UA) All apples are oranges. - ?

c. (UA) All students are lazy. – False

(UN) No students are lazy. – ?

d. (UN) No politicians are rich. – False

(UA) All politicians are rich. - ?

LAWS OF SUBCONTRARIETY If one is false, the other is true. If one is true, the other is doubtful.

a. (PA) Some Filipinos are lazy. – False

(PN) Some Filipinos are not lazy. – ?

b. (PN) Some students are not present.– False

(PA) Some students are present. - ?

c. (PA) Some students are persons who passed the exam. – True

(PN)Some students are not persons who passed the exam . – ?

d. (PN) Some scholars are not nerd. – True

(PA) Some scholars are nerd. - ?

LAWS OF SUBALTERNATIONI. If U (True), P (True). If U (False), P (doubtful).

a. (A/UA) All surgeons are doctors. - True

(I/PA) Some surgeons are doctors . – ?

b. (E/UN) No beauty title-holders are ugly.– True

(O/PN) Some beauty title-holders are not ugly . - ?

c. (A/UA) All students are scholars. – False

(I/PA) Some students are scholars. – ?

d. (E/UN) No students are lazy . – False

(O/PN) Some students are not . - ?

LAWS OF SUBALTERNATIONII. If P (False), U (False). If P (True), U (doubtful).

a. (I/PA) Some devils are good. - False

(A/UA) All devils are good . – ?

b. (O/PN) Some angels are not spiritual .– False

(E/UN) No angels are spiritual. - ?

c. (I/PA) Some teachers are holy – True

(A/UA) All teachers are holy. – ?

d. (O/PN) Some athletes are not swimmers. – True

(E/UN) No athletes are swimmers. - ?

1. If A is true, E is false, I is true & O is false.

2. If E is true, A is false, I is false, O is true.

3. If I is true, E is false, A is doubtful, & O is doubtful.

4. If O is true, A is false, E is doubtful, & I is doubtful.

5. If A is false, O is true, E is doubtful, & I is doubtful.

6. If E is false, I is true, A is doubtful, & O is doubtful.

7. If I is false, A is false, E is true, & O is true.

8. If O is false, A is true, E is false, & I is true.

a. Contradictionc. Subalternation

b. Contrariety d. Subalternation

1. All lawyers are ethical practitioners. (F)

a. Some lawyers are not ethical practitioners. (T)

b. No lawyers are ethical practitioners. (d)

c. N.A.

d. Some lawyers are ethical practitioners. (d)

2. Some carpenters are professionals. (T)

a. No carpenters are professionals. (F)

b. N.A.

c. Some carpenters are not professionals. (d)

d. All carpenters are professionals. (d)