Final answer:
One cannot rationally accept two arguments with conclusions that are known to be in conflict because of the principle of mutual exclusivity, which stipulates that contradictory conclusions cannot both be true. Logical consistency and empirical evidence dictate that at least one of the conflicting arguments must be false.
Step-by-step explanation:
The question regarding whether one can accept two arguments with conclusions that are in conflict pertains to the nature of logical reasoning and valid deductive inferences. In a disjunctive syllogism, which is a common form of argument, if the premises are true, then the conclusion logically follows. However, when two arguments present conclusions that contradict each other, at least one of the premises must be false because two contradictory statements cannot both be true simultaneously. This is an application of the mutual exclusivity in logical terms, where P(A AND B) = 0. Thus, one cannot rationally accept both arguments if their conclusions are genuinely in conflict, as mutual exclusivity dictates that the acceptance of one implies the rejection of the other.
The student's question is essentially addressing logical consistency and the possibility of two conflicting conclusions being true. If we apply this to an example involving the famous philosophical argument by Moore against skepticism, he argues that the premise of having two hands is more credible than the skeptical hypothesis purely on common sense, because the evidence is tangible. In this context, accepting a conflicting argument that denies the existence of one's hands would be illogical and inconsistent with empirical evidence. Therefore, while it's possible to entertain multiple hypotheses, it is only rational to accept the premise that is backed by evidence and reasoning.