This is actually quite incorrect. If you had to give a percentage of mathematical statements that boiled trivially down to A=A, they would comprise literally 0% of all of mathematics. There are simple examples… (a+b)^2 = a^2 + 2ab + b^2. Sure, the END RESULT is that they’re the same thing, but that isn’t trivially true at all - you need axioms of the real numbers to prove this. (Incidentally, even 1+1=2 doesn’t have its justification in A=A. There are numerical systems in which 1+1=0. Thus, in order to prove 1+1=2, you need to know what number system you’re in.)
So yeah, few metaphysical arguments are justified by A=A, but that’s meaningless.
I think you’re focusing too heavily on sociological philosophy. I’m not making a broad sweeping statement that we should look for final answers in all of philosophy – although I think we should – but rather that there are areas of philosophy where it’s obvious we should seek (and could easily find) those final answers. Given the definition of free will where I have free will if and only if “I, myself, could have acted otherwise than how I did,” one can prove conclusively that free will doesn’t exist. Given other definitions, it’s also often possible to arrive at a final, conclusive answer. These answers should be sought, and should be found - that’s the whole point of the debate.
Sure, in other cases - cases pretty much exclusively described by moral, sociological debates - you can make a good case for seeking but never finding a final answer being the best way to go about things. But even as my “remain hostile towards final viewpoints” turnaround demonstrates, this isn’t the case for ALL of philosophy. Which you seem to accept. I propose that we’re agreed on this much.
But as far as the rest of your examples go, I think they’re incorrect. Let’s continue with slavery as an example. Or, hell, something more basic, like sexual repression. (I think this last one is a good example, because although society often has strong views on it, a dispassionate analysis is less likely to reveal an obvious answer. We are biologically hard-wired to respond to sexuality, and so being overly sexual really does carry harm with it in many cases. However, sexual repressiveness also can be harmful. Where do they balance?)
You may argue that we shouldn’t seek final answers, because presumably a “final answer” to sociological issues would be too limiting. It would take away our ability to grow, and may lock us into a stance that might be best overall, but might not be best given our particular society. (Please let me know if I’m unfairly summarizing your stance.) However, none of these are valid concerns.
First, while purely metaphysical issues like Free Will and Identity are usually manageable using pure logic, sociological issues are RIDICULOUSLY more complex, and do not easily lend themselves to mathematical analysis. A proof that free will (given the above definition) is impossible is easy; I have no idea how you’d generate a real PROOF that slavery is bad, as opposed to just an argument. Those issues are way too complex to be manageable with the tools we currently have.
Second, even if we could prove the answer to such things – even if we could prove that slavery was bad – it would be meaningless without context. For example, what if we had some (stupid) hypothetical society that required slavery in order for the human race to continue? Putting aside the utter implausibility of such a scenario, we can agree that slavery in such a society is good, because no slavery means we all die. What constitutes “good” or “bad” depends entirely on the context of the situation. So even if we could prove that slavery was bad, it would be in the context of certain assumptions. If we found ourselves in a society where those assumptions didn’t hold, then the conclusion that slavery was bad may also not hold.
Third, if we COULD prove that slavery was bad, either in all cases, or in a particular society on which we wished to focus, why would it be bad for us to reach that conclusion? If slavery is always bad, then it’s good to know that so that we can never attempt it again, and can immediately put aside any pro-slavery arguments propounded by others. If slavery is bad given our society, we can rest assured that as long as we have that sort of society, slavery is always wrong, and know that we won’t have to re-evaluate until our society changes beyond the assumptions of the given proof.
The facts are always there, even if they’re difficult to prove beyond a doubt, and even if they’re not of the form we suspect they are. I don’t think there are any areas where knowledge of the facts is Always bad. Thus, it seems we should strive for final answers with the goal of achieving them, rather than just wallowing in the search. For all of the examples you have named, I think the risk of actually achieving any final answer is essentially zero - but if we did actually come upon such a final answer, it seems that that would solve more problems than it would create.