I know I've talked about it before, but I'm going to do it again, damnit.
In the world of truth and justification, there are... actually, I don't know why we combine truth and justification. While, yes, it's true that if we could ascertain what is true we would be perfectly justified. So, in that sense, a quest for truth coincidentally ends with the attainment of justification.
But even if you disagree on all other points, you have to admit that absolute truth has yet to be attained as we speak, and as such it seems reasonable to separate truth and justification.
But regardless, in truth and justification, there are two opposing views: coherentism and foundationalism. In coherentism, a person is justified in a belief if that belief is coherent with their current set of beliefs. This leads to some interesting problems, such as if I live in a bubble and have never seen grass, I can say that grass is purple and be justified in the coherentist view. I actually don't see any reason to say this is even a problem. I think it's perfectly acceptable to say that anyone is justified in a belief if they have no beliefs in contradiction with that.
As an outside observer, we can say a belief in purple grass is wrong, but we know that because of other beliefs. And remember, saying it's unreasonable to believe anything without evidence, such as of purple grass in the yard, is a belief itself that affects our entire system of beliefs. In the bubble example, you must also eliminate beliefs like skepticism and empiricism. If I only have two beliefs, hypothetically, of purple grass and cows that bark, both beliefs are justified. They aren't neccessarily true, but there's some major problems with that.
What's true? I can define very well what it is to be justified in a coherentist view: no beliefs contradict. It's that simple. Nothing else must be assumed. No deductive or inductive connections must be made between them, because that implies a more complex set of processes going on than just coherency. DO any two beliefs result in a logical contradiction? If one does, then the assumption must be made that the idea which contradicts the fewest beliefs must be held up as justified.
But for foundationalism, they must be positively concerned with truth. But what is true? What makes the statement "grass is green" true? Does it correspond to reality? Well what does that mean? Correspond to our perceptions of reality? Or to actual reality. What's reality?! I don't mean to fly off into some bizarre and esoteric philosophical black hole, but you can see why the nature of foundationalism is difficult to accept, for me. Coherentism is simple and requires nothing more than our beliefs. It requires no sense perception; no sight, hearing, or taste. It only requires beliefs of any nature and a lack of logical contradiction.
And even if we are to say that for useful applications of a coherentist theory, such as in science, the size and complexity of the underlying belief set must be judged to be adequate, that itself is a belief. A belief that affects all other beliefs in a system that makes us question what we see and know that it, because of our limitations, results in an inherent and irrevocably non-zero chance that our belief system will be incoherent in the future. This is science! And look at what that's done for us.
For example, archaeologists were perfectly justified in believing that dinosaurs looked a particular way in the salad days of the science in the 1800's. We now know that they were wrong, or at least less accurate than we are. In all likelihood, we will discover that we are totally inaccurate on some aspects of our beliefs, but that doesn't mean we aren't justified in those beliefs now. That's why scientific theories are so strong. They are coherent beliefs that do not contradict lots and lots of other experimentally confirmed beliefs. We can feel decently secure in them because if a contradictory belief does arise, it must also contradict all of the other beliefs and as I mentioned earlier, whichever belief contradicts the most beliefs must be held the most suspect.
That doesn't mean that one contradictory idea isn't the right idea. Einstein's theory of special relativity was like that, but it resulted in a massive, new scientific system that is even more coherent than the old one.
I also disregard the argument that a larger coherent system is more likely to be correct than a smaller system. I think any coherent system is equally justified. What we add to our own system is a belief that if a belief system is large, it's better than one that is small because in the past larger belief systems, for example scientific theories, have proven to be accurate. That itself is a belief that must be included in our belief system that is based on things other than raw beliefs. It includes sense perception, and interactions with our environment. We're not talking about experiment. We're talking about beliefs and nothing more.
In many cases, we have coherent systems of belief that are perfectly coherent with the world, equal in size and complexity, but completely contradictory. There are cases of this in theoretical physics and mathematics all the time. Again, I don't see any problems here. You just continue building up coherent beliefs in both systems until one falls apart. Again, that happens in math and physics all the time. Personally, I also think cases like those happen because of our own problems in divvying up reality into packets of information called numbers.
So I find problems with all arguments against practical coherentism. The scientific argument, where we need to define justification outside of mere non-contradiction, implies the application of a skeptical stance which is itself a belief that results in a non-coherent belief system when certain parameters have been met, e.g. a belief system of insufficient size. If we remove that scientific belief, our belief system is totally coherent.
Obviously, that sort of "scientific" coherentism, where beliefs are of low justification when nascent, is very useful for everyday use, but it requires a belief on top of the raw belief system that affects the entirety of the system. For example, I am sitting at a table and believe my foot is now mauve. It is totally coherent for me to believe that my foot has spontaneously turned mauve. But I have other beliefs which make me doubt that. I've never seen a foot turn mauve. Bodily systems would prevent it.
As such, I believe that feet never turn spontaneously mauve. This belief is non-contradictory with all of my other beliefs. If I then look and see that my foot has turned mauve, after calling a doctor, I must reassess my belief system. Where is the contradiction happening? Perhaps my friend secretly painted my foot while I wasn't looking. Perhaps I missed a recent scientific article documenting the thousands of previously unknown cases of mauve feet.
In all but the most extreme case, the scientific system is not thrown away because the system is so large and throwing it away would result in countless contradictions. So in the end, I fall back to a raw coherentist quest. I must find where the contradiction is taking place. My scientific system says feet do not turn mauve, so my first order of business is to acquire new beliefs that help to explain the seeming contradiction.
There is one more attack that foundationalists can muster, namely that our confidence in our own beliefs is in fact a foundation that coherentists implicitly rely upon. Nonsense, says I!
There is a concept in psychology stating that there is no homunculus. This neo-foundationalist implies a homunculus, where a little person exists somewhere in the mind which is inherently separate from body, memory, and even beliefs. That we are separate from our body is acceptable. If I lose my arms and legs, I am still me. That we are separate from our memories is a bit less acceptable, but still adequate. If I forget everything, the effects of my memories on me can remain, so I am still here even if I forget most everything about my past. But separating "me" from my beliefs is distilling "me" down to something that's basically non-existent.
I think that beliefs about beliefs, so-called metabeliefs, are not a special class of belief. If I say "I believe in God," then say "I believe I believe in God," is not only needlessly repetitive, but also problematic. How do I know I'm holding a belief about a belief? Am I merely holding a belief about a memory of a belief? And if that's the case, memories are subject to the skeptical argument, and as such cannot be foundational.
And even if we say that our beliefs are the foundation we can trust, it doesn't matter. Foundationalism is a quest for truth, not justification. Cogito ergo sum is a foundationalist statement. It is a logically self-sufficient statement. Saying "I know what I think" is a statement of startlingly little power. It cannot be used as a foundation because I think it's only slightly disconnected from just saying "I think what I think." And even if it is a powerful statement about knowing what I know, how does that extend to be a foundation upon which to build knowledge? It doesn't. Unless we want to take the position that reality is merely our experience of it, a phenomenalist approach, knowing what we know is just that. It has no connection with reality which is what truth is supposedly after.
Coherentism is real. It's what we use on a day-to-day basis. It can be taught, learned, and applied. Foundationalism, and in fact any other system of justification, fails. By sticking to coherentism in justification it gains power in the real world. It succeeds in science and in law.