I would look up pragmatism. Here's a post of mine on pragmatism with a few pointers/links at the beginning to some stuff by known pragmatists. Foundationalism doesn't have any foundation, and coherentism is incoherent. Pragmatism, on the other hand, is pragmatic itself. It says, 'use what works', and, by gosh, that just happens to work.
Unfortunately, typical intro texts on philosophy tend to spend little if any time covering pragmatism, possibly due to its being considered an 'American' philosophy, though that's pretty silly considering that its close cousin science has no national affiliation.
Pragmatism is not a structure of knowledge. It may be a strategy used within one or another of the belief structures, but by itself it does not answer the question of what our belief structures look like. Pragmatism says believe in what works, which is another way of saying that we use our experiences to verify our beliefs. But what justifies our beliefs in our experiences? If the answer is merely, as you put it, that we believe what we believe because it works, we have gone around in a vicious circle, in which whatever it is we have come to believe works justifies our beliefs which support our beliefs which led us to that conclusion in the first place. Rookie mistake. As it is, if we ground our beliefs in our experiences alone, then we believe that our experiences are a justifiable source of knowledge and this gives foundationalism its impetus. Of course, if one understands reason and experience to be distinct, then coherentism is plenty coherent. I agree with pragmatism in spirit, but when it comes to serious epistemology there is a reason why it is not discussed much in intro texts - it does not approach the deeper questions of justification of our belief structures.
It may be a strategy used within one or another of the belief structures
It is the only strategy available to bootstrap any belief system, including either foundationalism or coherentism.
by itself it does not answer the question of what our belief structures look like
Moving goal posts and/or straw man. There is nothing that, by itself, answers the question of what our belief structures look like. The question pragmatism answers is: How can we know anything at all?
which is another way of saying that we use our experiences to verify our beliefs.
Of course. What else could there be? Even foundationalists and coherentists must use their experiences to verify their beliefs. Everyone does this. It is no fault in pragmatism that it points out this basis.
But what justifies our beliefs in our experiences? If the answer is merely, as you put it, that we believe what we believe because it works, we have gone around in a vicious circle, in which whatever it is we have come to believe works justifies our beliefs which support our beliefs which led us to that conclusion in the first place. Rookie mistake.
Read the post I linked to. I clarify 'what works' as 'what makes the best predictions'. There is no vicious circle. It either works or it doesn't. You can clearly differentiate what works from what doesn't (our brains have this as an evolved innate ability), at least to an approximate degree, or else you wouldn't be able to function in this universe.
if we ground our beliefs in our experiences alone, then we believe that our experiences are a justifiable source of knowledge and this gives foundationalism its impetus.
Unfortunately, our experiences are not justifiable in the sense that foundationalists would wish them to be. They are only justifiable in a pragmatic sense. They are only justified to the extent that they are actually useful, i.e. actually make good, accurate predictions of the future. Foundationalists seek a stronger justification than that, and that is where they fail, because -- unless they acknowledge that they ultimately rely on pragmatic justification, just like everyone else -- then they do not have a foundationalist-level justification for their epistemological choice in (any) foundation.
Of course, if one understands reason and experience to be distinct, then coherentism is plenty coherent.
But they aren't. How could they be? Our sense of reason is a part of our experience. Without a way to detect the difference between 'reasonable' vs. 'not reasonable', we would be unable to reason at all. It is this sense of reason, which is an evolved innate ability of the brain, which is the ultimate basis for all human understanding. But we should only trust that sense to the extent that it actually is useful, i.e. makes good predictions.
This is the guiding 'force' or 'impetus' which gives rise to science out of superstition. It is ultimately a pragmatic basis. What actually works, vs. what we wish would work.
but when it comes to serious epistemology ... it does not approach the deeper questions of justification of our belief structures.
Sure it does. In fact it addresses the deepest level of the question of justification. Anyone, everyone, ultimately relies on a pragmatic justification for their beliefs. It is just that some people are better at finding what actually works than others, and so they are able to make more pragmatic choices. Science is the prime example of this.
What works = what makes the best predictions, this is a tautology.
No, it isn't.
Yes, you and I believe that our brains have evolved the ability to approximate the outside world, but this assumes that we know we have evolved and that there is an outside reality.
No, it doesn't assume either of those. Both of those beliefs are derived from pragmatism itself. Specifically, we have science to thank for the knowledge that our brains arose via evolution. That's an a posteriori fact, not a priori. Second, we believe the hypothesis that there's an outside world because this hypothesis best predicts our experiences (e.g. our experiences of interactions with what appear to be other minds). Again, this is a posteriori. First we experience, then we compare those experiences to the possible explanations. For example, in my interactions with you, the most useful hypothesis is that you are an actual other mind, and that we both share a common 'world' of phenomena between us, or otherwise our communication would be meaningless gibberish which could not make any predictions at all.
Of course, we both believe these to be true, but what grounds these beliefs?
Their abilities to make good predictions, of course.
Eventually we end up right back at our experiences. If it "works", that just means we have the experience that this is so. Either we end up going around in circles, or we begin with the belief that our experiences are foundational to our beliefs.
Of course our beliefs depend crucially on our experiences. How could it be otherwise? Having random beliefs?
But how do you distinguish between experiences which point towards truth and those which don't? We've all experienced such illusions, whether perceptual (optical illusions) or conceptual (delusions and confirmation bias).
The only way to distinguish is to evaluate them using our innate abilities. We have an innate sense of what is likely to happen, and future experiences either confirm or disconfirm those prior experiences (of perceived likelihood). The hypotheses which made the best predictions are the ones we naturally tend to prefer (though not perfectly, of course). This is the basis of all knowledge, and it is fundamentally a pragmatic enterprise.
This describes the basic, unconscious pragmatism that all people use every waking moment of their lives. The philosophical stance called 'pragmatism' just puts this process into words and turns it into a conscious process. Instead of blindly following our basic intuitions, we realize that even these intuitions can be mistaken, and there may be 'more true' hypotheses out there to be discovered. So we apply our innate pragmatism to our own beliefs and begin consciously investigating which ones are most true, and which ones are least true.
Of course it is self-referential, in the 'meta' sense. All epistemology is. This does not make it circular, because we can recognize that there is a root, basic assumption, namely the assumption of an innate ability to make pragmatic distinctions based on experience. However, this is an inescapable assumption. All epistemologies, whether they acknowledge it or not, rely on the assumption that our knowledge must ultimately rest on our experiences. Or else, we cannot have any knowledge at all. Even epistemological nihilists or skeptics rely on pragmatism to operate in day-to-day life, such as when crossing the street. Failure to acknowledge (at least subconsciously) the difference between knowledge that works vs. knowledge that doesn't, is, quite literally, fatal.
The problem with foundationalism is that it takes a core set of beliefs as an unjustified basis for everything else. But how do we choose this core set? Why pick set A over set B? Ultimately, it will come down to a personal judgment of whether A is 'better' than B or vice versa. This judgment will either be unconsciously pragmatic, or it will be consciously pragmatic. But no one can escape that this judgment is at basis pragmatic. It's just a question of whether one is aware of it or not.
So, the foundation for foundationalism, if there is such a foundation, is in fact pragmatism, whether conscious or unconscious.
Nobody said foundationalists (like myself) believe that our experiences are completely justifiable. However, they do seem to be the best we've got. Of course, you are right now jumping up shouting "aha, pragmatism!". Well, this is why I said I agree with pragmatism in spirit. I would be more than happy to incorporate pragmatism into my foundationalism, perhaps even as a first step.
It's not really a question of whether to incorporate or not. It is a fact that you must base your foundationalism in pragmatism, or else it will have no connection to reality. You will quickly discover the limits of such foundationalism.
Note that there are Christian foundationalists who try (and fail) to justify their beliefs in a Christian 'foundation', which, obviously, is not a very useful idea, though they believe it is. How can a foundationalist, such as yourself, argue against such Christian foundationalists? You can't. You have no way to determine whether your system A is better than their system B, unless you resort to arguments based in pragmatism.
And let's say that both you and the Christian foundationalists have 'incorporated' pragmatism into your respective foundational sets. But you still disagree, e.g. whether prayer works or not. The Christian says, "Prayer is 'useful' to me, and pragmatism is part of my foundation, so it is justified for me to believe in it." And you say, "But it's not 'useful' to me, and I don't believe it is 'useful' to you either, so I don't think it's justified for you to believe that (or at least, not for me to believe that)."
But this is just a stalemate! Foundationalism has nowhere to go from here. The only way to resolve the debate is to set up a test in the real world, and see if the prediction that prayer works actually works. And the only way to check that prediction is to compare our experiences of the test with our prior experiences of the predicted outcome.
When our experiences don't match what was expected if prayer had actually worked, we mark a notch in the 'prayer doesn't actually work' tally.
The Christian is just wrong when he claims that prayer 'works' for him. He's wrong because his predictions fail.
All conflicts between belief systems must be resolved in this way, if there is to be any resolution at all. It is not the idea that pragmatism is part of some foundational set of beliefs or not. It is that pragmatism is the only tool we have to even decide whether foundationalism is worthwhile or not. I don't actually have to believe in pragmatism to make this choice. It is an innate ability. It is a given. I didn't even have to assume it. I just have it, and so does everyone else.
It's not: "Assuming pragmatism is true, yadda yadda yadda." It's: "The idea of 'truth' at all only makes sense to the extent that I can actually distinguish between 'true' and 'not true'." It turns out that we do happen to have this ability. It's not perfect, but it's pretty good. It got us this far. Let's become conscious of it so that we can apply it even more intelligently than our basic intuitions provide by themselves.
But this does not approach the question of the structure of our knowledge.
Before you can get to the 'structure of knowledge', the question remains: How can we know anything at all? That's the most basic question of epistemology.
Without first saying that our experiences are grounded in our experiences, pragmatism has no foothold, no basis in justification.
"Our experiences are grounded in our experiences"? Ummm, how could it even be otherwise? What else could they be grounded in? Without experiences, what have you got? How do you even know you exist? No epistemology can escape this problem.
We would be at the impasse described earlier, when one can appeal to faith, for example, then say that "it works", then justify their entire epistemology by continually resorting to justifying their beliefs on faith, despite overwhelming "evidence" to the contrary (while remaining perfectly consistent in their belief sets).
But does it actually work? Saying 'it works' doesn't magically make it work. Pragmatism doesn't say, "Use what you wish would work." It says, "Use what works." Faith does not actually work. Pragmatism is the only way to show that.
This is the reason why we need to begin with the structure of our justificatory systems.
What good is a 'justificatory system' if it leads to nonsense beliefs? How do you know whether justificatory system A is better than justificatory system B? What is the only way to tell the difference? I'll give you a hint: It starts with a 'p'. ;-)
Did you do a philosophy degree? Then I suppose, with you therefore being consistently out of work, you must get through a lot of books. Whether or not that true, I wholeheartedly recommend "Pooh and the Philosophers".