Question

In strict propositional logic, suppose an argument has a set of premises that is logically unsatisfiable (or inconsistent), meaning they cannot all be True simultaneously. Must the argument be valid since there are no cases where all premises are True and the conclusion is False? If so, can it automatically follow that the argument is unsound, because soundness is defined as validity plus trueness of all premises and the given premises cannot all be True? This is confusing because normally when examining the soundness of an argument, we need to know the particular truth of the premises in the world

Answer 1

In strict propositional logic, an argument is considered valid if its premises cannot all be true simultaneously. However, for an argument to be sound, it must be both valid and have true premises. The truth of the premises is usually determined by considering real-world facts and evidence.

Step-by-step explanation:

In strict propositional logic, if an argument has a set of premises that is logically unsatisfiable or inconsistent, it means that the premises cannot all be true simultaneously. In this case, the argument is considered valid because there are no cases where all the premises are true and the conclusion is false. However, it does not automatically follow that the argument is sound, as soundness requires both validity and the truth of all premises. Since the given premises cannot all be true, the argument is unsound.

Soundness is typically determined by examining the truth of the premises in the real world.This highlights the distinct consideration of validity and truth in evaluating arguments, where the former concerns the structural integrity of the argument and the latter involves assessing the actual truth value of the premises involved.