Under the traditional square of opposition with existential import, if the…
2022
Under the traditional square of opposition with existential import, if the statement “All women are honest” is given as true, which of the following propositions can be inferred from it?
(A) 'No woman is honest' is false.
(B) 'Some women are honest' is true.
(C) 'No woman is honest' is undetermined.
(D) 'Some women are not honest' is false.
Choose the correct answer from the options given below:
Answer: A. A, B, D only — CONCEPTIn the traditional square of opposition, an A-proposition (“All S are P”) is contrary to an E-proposition (“No S is P”), contradictory to an…
- A.
A, B, D only
- B.
B and D only
- C.
B, C and D only
- D.
C and D only
Attempted by 2 students.
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Correct answer: A
CONCEPT
In the traditional square of opposition, an A-proposition (“All S are P”) is contrary to an E-proposition (“No S is P”), contradictory to an O-proposition (“Some S are not P”), and has an I-proposition (“Some S are P”) as its subaltern.
With existential import, truth descends from A to I; contraries cannot both be true, and contradictories must have opposite truth values.
APPLICATION
The given universal affirmative proposition “All women are honest” is the A-proposition and is stipulated to be true.
Its contrary, “No woman is honest,” is therefore false; this establishes statement A.
By traditional subalternation with existential import, “Some women are honest” is true; this establishes statement B.
The original A-proposition’s contradictory, “Some women are not honest,” is false; this establishes statement D.
CONTRAST
“B and D only” leaves out the falsity of the contrary E-proposition.
“B, C and D only” treats the E-proposition as undetermined instead of applying the traditional contrary relation.
“C and D only” both treats the E-proposition as undetermined and leaves out the I-proposition obtained by subalternation.
Therefore, the inferred set is A, B and D only.