Can philosophy prove/disprove anything or it is just inconclusive and useless?

One of philosophy's most important uses is in helping us to spot bad questions. It's better to diagnose the defect in a bad question than to try to answer a bad question straight up.

Take your question, for instance. Its defect is your false dichotomy: your assumption that any discipline either can prove or disprove things or else is inconclusive and useless. It might be neither of those. Historians of Tudor England can't prove or disprove things, if that means answering historically interesting questions with absolute certainty: their historical evidence doesn't allow them to do that. But of course that doesn't make the history of Tudor England a useless area of inquiry, and if it's not useless then it's not inconclusive and useless.

Your false dichotomy aside, philosophy does prove some things, such as the principles of logical reasoning. Less abstractly, philosophy often proves that some theory consisting of specific propositions A, B, C (say) is logically committed to some other proposition D that seems implausible. When that happens the theory in question faces a dilemma: revise away at least one of A, B, C; or explain why D isn't as implausible as it seems.

Yes, many of the most interesting claims in philosophy remain both unproven and unrefuted. But the same goes for many of the most interesting claims in any discipline, including physics. In the absence of proof, some claims are nevertheless better-supported by evidence and argument than others.

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