Is the epistemic regress infinite or finite? It is often assumed to be infinite, but was there any discussion about how some epistemic regress may not be infinite in certain cases, or a endpoint where everything is explained and no further question within the same epistemic line can b?
An explanation is analogous to data compression. We have a large amount of data, that we explain with a short, simple rule. For example, you may plot a lot of (x, y) points and draw a regression line y = Ax + B through them. The regression line can be described just by two numbers, A and B, even if you have thousands of (x, y) points; we have compressed the data (lossily), and also partially explained it.
The laws of physics are a few simple equations that describe the behavior of many different phenomena. They are data compression as well; it is much simpler to write down the equations than to write down all the details of the phenomena they describe.
The more fundamental the laws, the greater the compression, and the more fundamental the explanation is. Newtonian physics works in a limited domain, so it would not be able to compress all the phenomena explained by quantum mechanics or general relativity. Newtonian physics can be seen as a special case of QM or GR; QM and GR give about the same results as Newtonian physics, over the scales and energies that Newtonian physics was designed for. Thus, QM and GR can be understood as explanations of Newtonian physics - an explanatory regress, concurrent with improved compression of natural phenomena.
There is a limit to how much compression is possible, and thus a limit to how many such explanatory regresses you can do. You can't compress every possible file down to 0 bytes; mathematically, it's not possible due to the pigeonhole principle. We would expect a "minimum length" explanation of the universe - a Theory of Everything - which cannot be described in terms of any more fundamental theory, because any other theory consistent with it would be more verbose and thus less fundamental.
This "minimum length" description would thus be an end to the explanatory regress.
Regarding your "a endpoint where everything is explained and no further question within the same epistemic line", as in classic propositional logic, it's easy to show B→(A→B) is a tautological theorem via material implication substitution, meaning if anything (B) is true then there's always something else (A) may cause it though not definitely so since this is just a material condition, but you cannot rule out such possibility. So within our actual world it's always possible not to have an endpoint as you wished. Of course many philosophers such as Aristotle posited metaphysically there might be an unmoved mover outside our cosmological world to move it as a first cause.
Regarding your "how some epistemic regress may not be infinite in certain cases", according to Münchhausen trilemma:
In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions... The Münchhausen trilemma is that there are only three ways of completing a proof:
- The circular argument, in which the proof of some proposition is supported only by that proposition
- The regressive argument, in which each proof requires a further proof, ad infinitum
- The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended
The trilemma, then, is the decision among the three equally unsatisfying options.
So apparently some epistemic regress may form a finite closed circle, and this kind of epistemology is called coherence theory of justification.
As an epistemological theory, coherentism opposes dogmatic foundationalism and also infinitism through its insistence on definitions. It also attempts to offer a solution to the regress argument that plagues correspondence theory. In an epistemological sense, it is a theory about how belief can be proof-theoretically justified.
The Münchhausen trilemma is a logical reasoning resting on the assumptions that "there are only three ways of completing a proof". However, reality is what it is and does not depend on any logical argument, and there is a fourth possibility which is that we just happen to know stuff. And, guess what, we do. Or at least, I certainly do. I know for example that I am in pain whenever I am in pain and I know pain as whatever I feel when I am in pain. I don't need to prove to myself that I am really in pain. The Münchhausen trilemma is falsified and there is no regress in this case.
The Münchhausen trilemma does apply, however, to objective facts simply because we certainly have no actual knowledge of any objective facts. All we can do is reason on our beliefs to derive other beliefs logically from the first ones. And since we have to use logical reasoning, we are faced with an infinite regress whenever we try to prove all our assumptions. We cannot do that and so knowledge of objective facts is a dead proposition.
To answer the first comment below which is missing the point, there is another way to say it. The Münchhausen trilemma is a fallacy. Namely, it is the fallacy of equivocation. The reasoning of the Münchhausen trilemma is that there are only three ways to prove. As I said, this is false.
More explicitly, the Münchhausen trilemma equivocates between knowledge and logical proof. It assumes without saying so that knowledge ought to be proven to be knowledge. No, it ought not. I know that I am in pain whenever I am in pain and I know pain as whatever I feel when I am in pain, and I don't need to prove to myself that I am really in pain. I don't need any proof, logical or not, to known that I am in pain whenever I am in pain.
And contrary to what the comment suggests, this is not an axiom, or at least, this is not an axiom in the usual, mathematical sense, i.e., something we arbitrarily take as true and could assume instead that it is false. It is instead an axiom in the original sens of being self-evident, and what is self-evident is of course, by definition, true, not just assumed true. I hope this clarify my point.
The Trilemma's equivocation is between subjective knowledge and objective knowledge. The Münchhausen trilemma equivocates between the two. Logical proof is used to derived conclusions from our beliefs about things we don't know. We don't need to prove things we already know. The Münchhausen trilemma only proves there is no objective knowledge. Sure, we have admitted as much since the Ancient Greeks. So the Trilemma fails to prove, and it could not possible prove, that there is no knowledge at all.
I don't see any way out of an infinite epistemic regress, unless you accept Kant's illustration of unresolvable antinomies once you allow reasoning to proceed without empirical content.The limit is pragmatic not logical.
The regress will end empirically in experience or "common sense." I believe it was Gregory Bateson who used the maxim in information theory that meaning is "a difference the makes a difference." And likewise an explanation regresses to a lingering difference "that makes no difference."
This is like the limit in calculus that can proceed to any degree or precision until... well, it doesn't matter. Or like Hume's speck that can get smaller and smaller until one cannot say whether it is "really" there or not.
All this is simply a pragmatist's approach to the problem, in which one can argue or "explain" down to the "belief one is willing to act on." So, this epistemic regress looks to me like a form of Kantian antinomy to which, crudely put, the limit is "show me."