Question

Explain whether or not an argument can be sound but not valid.

a) Yes, if premises are true but do not logically lead to the conclusion
b) No, as soundness implies both true premises and a valid logical structure
c) Yes, if the conclusion is true but not logically derived from the premises
d) No, as validity ensures a logically sound argument

Answer 1

An argument cannot be sound without being valid because soundness entails both the validity of the argument's structure and the truth of its premises.

Step-by-step explanation:

An argument cannot be sound but not valid. The correct answer is b) No, as soundness implies both true premises and a valid logical structure. To clarify, an argument is considered valid if its conclusion logically follows from its premises. Soundness, however, is a broader concept that not only requires validity but also that all the premises of the argument are actually true. Therefore, if an argument is sound, it is by definition also valid.

Let us examine a simple example of a valid deductive argument using a Disjunctive Syllogism:

1. X or Y.
2. Not Y.
3. Therefore X.

If the premises in this argument are true, then the conclusion must also be true, making the argument valid. However, for the argument to be sound, the truth of both premises -- 'X or Y' and 'Not Y' -- is required. This means that a sound argument automatically fulfills the conditions of validity but additionally assures the truth of its premises. If you can imagine a scenario where the premises are true, but the conclusion is false, then the argument is deemed invalid, which also means it cannot be sound.

Therefore, the relationship between validity and soundness is that soundness includes validity as a necessary but not a sufficient condition and also requires truth in premises.