Gertie wrote
What the scientific method relies on is that there is a real world of stuff which our mental experience relates to, and we can know something about that stuff. Not perfectly or comprehensively, but well enough to pass the tests of inter-subjective agreement and predictability.
And that has given us an incredibly complex, coherent and useful working model of a material world we share.
But you're right to say science doesn't know how to go about explaining mental experience - which all its claims are based in. Bit of a paradox that one. And imo suggests the fundamental nature of the universe is uncertain. Philosophy of mind is coming up with all kinds of speculations about the mind-body problem, but they remain inaccessible to testing - unless you have a surefire method?
Materialism has its own untestable philosophical hypotheses about how mental experience might be reducible to material processes, including philosophical thinking. If you think you have a better philosophical case, can you lay it out as simply and clearly as poss? (Serious request)
Because it's easy to spot the flaws with the all the hypotheses, not so easy to conclusively argue which one should be accepted as correct.
It is not about testing and verification and reliability and the like. These are fundamental to all we do (put your socks on. How did you do that? A repeatedly confirmed theory about the way physical things behave, about moving the arm and hands in this way to produce a specific event. The method of science is unassailable and is simply the method of living and breathing.
And to the waste bin with mind body matters. This is a false ontological problem because it can only make sense if you can say what mind and body are such that they would be different things ontologically--but the very nature of an ontological question goes to a question of Being, what IS, and here, there are no properties to distinguish. In existence there are many different things, states, all distinguished by what we can say about them. We don't believe these differences constitute differences OF Being, just differences IN Being.
Regarding the serious request:
To establish a truly foundational ontology, one has to look where things that assume a foundation have there implicit assumptions. All science is a construct of language and logic before it is ever even gets to constructing tests tubes and telescopes, so the question then is, what is language and logic? the OP says these belong to experience, and experience has a structure, and this structure is one of time. Past, present future. Thought and its "method" has a temporal structure, the anticipating of results when specified conditions are in place (hence, the success in repeatedly tying my shoes properly). Science is, technically speaking, all about what-will-happen if there is this, or that in place, or if one does this or that. Science doesn't have a problem; we ARE the scientific method in a very real way, in every anticipation of our lives there is a history of a learned associations between what we do and what will happen. This is what cognition is.
Time is the foundation of Being, but it is not Einstein's time (an empirical concept based on observation) but structural time, the structure of Being itself in the experience that produces existence, OUR existence, that is, which is a temporal one. time that structures our experience is not beyond experience and Einstein conceived of relativity in the temporally structured world of experience. Outside of this structure this time does not exist (unless it is in some other such experientially structured time, as with God, but this is an arbitrary idea).
Science's failure to be sufficient for philosophical thinking is not in the method, but in the content. I mean, even if I went full subjective into the deep recesses of my interiority and actually found God and the soul, this would be IN time, in an ability to anticipate the next moment, bring up memories, see that the usual is not the case here in order to have a contextual setting that I can recognize God as God. The rub lies with science's paradigms that are exclusively specialized and empirical and ignore the phenomenon of experience as it is. It takes parts of experience and reifies them into being-foundations. To me this is akin to taking knitting, a specialized "part" as well, and defining the existence in terms of the yarn and needle.
Philosophy is supposed to take the most basic and inclusive perspective in which one has pulled away from the "parts" and attempts to be about the whole, and the whole is experience structured in time, and then the matter turns to WHAT is there. Everything. Nothing excluded: love affairs, hatreds, our anxieties, our ethics, tragedies, and so on: all conceived structurally in time and as the WHAT of existence. All is, to use a strange term, equiprimorlial, meaning no one is reducible to any other. Our affairs are not reducible to physical realities, but physical realities belong to a specialized language scientists use, or we all use in a casual way. Evolution is not in any way held suspect, to give an example. It is a very compelling theory. But other actualities are not reducible to this, do not have their explanatory basis in this.
It is science's hegemony that leads us to a position that denies the world's "parts" their rightful ontological status. And if any hegemony should rise, it should be based on what it IS, its "presence" as an irreducible actuality. Of course, this is the presence of affectivity (affect), the very essence of meaning itself.
Science is not applicable to metaphysics, morality or religion, for a start. That's not a shortcoming of science. No tool can address every task.