I can talk about how actually, Logical Positivism isn’t actually closely related to the scientific method. Even though you can ragebait people by saying, “Well, logical positivism says that only mathematical truths and scientific truths matter; what’s wrong with that?”, that’s not correct as a specific instantiation onto a century-old philosophy designed to also try and solve other problems.
I could talk about how actually, practice-based philosophies, or even just engaging with science / math properly is a better use of time.
I could talk about how Carnap and Quine had arguments, the issues with Carnapian L-language architecture.
None of this matters to an actual scientist or mathematician though. Even if the conclusion to all this philosophy is discussing the very meta-level issues with trying to formulate such an abstract philosophy, that’s not the same as doing the thing. Discussing all the issues with creating a meta-level solution for doing the thing is not the same as doing the thing, interestingly enough.
I don’t think it’s a requirement that you should be expected to “hold the torch”, so to speak, in order to truly engage with something. Because you could obviously be diving into something for the ‘wrong reasons’, but think you had the right reasons. Your search could lead you to conclude that you didn’t want to do it and it wasted your time. Sometimes the search itself is the journey and you upgraded your thinking, in an unquantifiable way. Not every math major wants to become a pure mathematician.
But it’s a very strong heuristic. To actually create. And I noticed that this is different from creativity - I can come up with non-obvious observations in a variety of ways - open or closed - but actually instantiating that into a longer term, higher-order goal, is hard.