Final answer:
In logic, a conditional statement with a contradictory antecedent is always considered true because the antecedent cannot be true, which makes the conditional vacuously true.
Step-by-step explanation:
The student's question involves understanding the nature of a conditional statement in logic. The claim made is that a conditional statement with an antecedent that is a contradiction (a statement that is always false) is always true. This is a principle related to the concept of vacuous truth, where a conditional statement is considered true if its antecedent cannot be true.
In formal logic, a contradiction is a statement that is always false. Consequently, the conditional statement 'If P, then Q' is always true if 'P' is a contradiction, because for a conditional to be false, its antecedent must be true and its consequent must be false. Since the antecedent cannot be true, the whole conditional cannot be false. This idea is rooted in the principles of deductive reasoning.
It is important to distinguish this from fallacious reasoning. For instance, an emotional appeal or a fallacy of diversion may incorrectly assert the truth of a conclusion based on irrelevant or misleading premises.