Which of the following statements are true ? Choose from the codes given…
2011
Which of the following statements are true ? Choose from the codes given below.
Some arguments, while not completely valid, are almost valid.
A sound argument may be invalid.
A cogent argument may have a probably false conclusion.
A statement may be true or false.
Codes:
Answer: C. 4 alone — ConceptFour technical terms of Western logic decide this item, and each is fixed by definition rather than by degree. Validity is a property of a deductive…
- A.
1 and 2
- B.
1, 3 and 4
- C.
4 alone
- D.
3 and 4
Show answer & explanation
Correct answer: C
Concept
Four technical terms of Western logic decide this item, and each is fixed by definition rather than by degree. Validity is a property of a deductive argument: the argument is valid exactly when it is impossible for its premises to be true and its conclusion false at the same time. Because that condition is an impossibility claim, it either holds or it does not, so validity admits no degrees. Soundness is a compound property, defined as validity together with premises that are in fact all true. On the inductive side, strength plays the part that validity plays in deduction, and cogency is defined as strength together with premises that are in fact all true, which makes the conclusion probably true. A statement, or proposition, is a sentence that asserts something and therefore carries exactly one truth value.
Application
Each numbered claim in the stem invokes one of those definitions, so each can be settled directly against it.
Claim | Definition it invokes | Truth value |
|---|---|---|
Some arguments, while not completely valid, are almost valid. | Validity is an impossibility claim, so it holds or fails outright and has no degrees. | False |
A sound argument may be invalid. | Soundness is defined as validity plus all-true premises, so validity is already part of it. | False |
A cogent argument may have a probably false conclusion. | Cogency is defined as strength plus all-true premises, and a strong argument makes its conclusion probably true. | False |
A statement may be true or false. | A statement is defined as a sentence that bears exactly one truth value. | True |
Cross-check
Reading each offered code by value against that result confirms the match.
The code “1 and 2” would need the “almost valid” claim and the invalid-but-sound claim to hold, but validity has no degrees and soundness already contains validity.
The code “1, 3 and 4” would need the “almost valid” claim and the cogency claim as well, and both are ruled out by their own definitions.
The code “3 and 4” would need the cogency claim, but a cogent argument has true premises and a strong inference, so its conclusion is probably true.
The code “4 alone” names exactly the one claim that the definitions leave standing.
So only the fourth claim, that a statement may be true or false, is true, and the correct code is “4 alone”. Note the trap hidden in the third claim: the conclusion of a cogent argument may still turn out false in fact, but that is not the same as being probably false, which is exactly what cogency rules out.