# Is the epistemic regress infinite or finite?

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?

• The Munchausen Trilemma, says it can take three forms: finite, back to some axiomatic basis, which is actually what has been generally assumed; infinite, but only due to circularity, which gives one some footing, but no basis -- you can cover the domain to be explained, because it is limited, but no viewpoint is best; or it is infinite and there is unlimited variation is how things may be connected. Throughout most of history, we have not assumed that last one. That is a new thing. May 27 at 16:41
• I think this relates: ' “Why ask why” and its scions' philosophy.stackexchange.com/questions/79366/… Fundamentally: "The meaning and purpose of dancing is the dance." - Alan Watts May 27 at 18:01

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.

• This is a good, useful explanation, but it is really axiomatic or a reduction to many unstated presuppositions, isn't it? Compression can either arrive at abstractions empty of actual empirical content or continue infinitely in "meta" renderings, as when a physical explantation by means of an equation with a million digits can be "compressed" into the 27 characters in the words "an equation with a million digits," simply recontextualizing the "explanation" into a new epistemic web, which is a very real evidential problem, as in: "if the glove don't fit you must acquit..." May 29 at 17:15
• You can't get to the end of a regress by going forward. The explanation is not the compression algorithm here. It is the decompression algorithm, that takes your conclusion back to the source data. So this is a great answer, but to an entirely different question. Science just accepts a circular regression, theory to data back to theory back to data... And then it can ignore the question. May 29 at 18:16
• Changing the meaning of 'explain' does not remove the regress. It just declares it beside the point. If you decide that whenever the theory and data get closer together and the expression of the derivation does not mushroom in size, then you throw out your previous basis and accept this new one, that does not remove the idea there are an infinite chain of older provisional bases... It just means deduction is not the tool you intend to use. Testing is. May 29 at 18:45
• @NelsonAlexander if you "compress" an equation with million digits into the words "an equation with a million digits," you haven't actually compressed it because you can't recover the original. Equivalently, you've just done very very lossy compression, which is not a good explanation of the data at all because it's so lossy. May 29 at 21:45
• @hide_in_plain_sight Well, what is the meaning of "explain" then, if it is not to represent complicated data using a simple theory? What alternative definition do you have in mind? May 29 at 21:48

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:

1. The circular argument, in which the proof of some proposition is supported only by that proposition
2. The regressive argument, in which each proof requires a further proof, ad infinitum
3. 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.

• The assumptions? No, it is an argument. It does not just presume its conclusion. And yes, just knowing something is one of the options. Some things need to be taken as axiomatic. That you have a natural way of knowing that you are in pain can be taken as axiomatic, it can be derived from other assumptions, or it cannot be used in reasoning. Before you 'falsify' something, know what it means... May 28 at 18:15
• @hide_in_plain_sight "The assumptions? No, it is an argument. It does not just presume its conclusion." ??? I didn't say it wasn't an argument. And all arguments rest on some assumptions. And this is exactly what I said: The Münchhausen trilemma is a logical reasoning resting on the assumptions that "there are only three ways of completing a proof". You seem to be missing the main point of my explanation, though. May 29 at 9:54
• It is not resting on those assumptions. It reaches those conclusions. To say that it rests on the assumption of its conclusion would make it a matter of begging the question, and it isn't. This is an attack, not an argument. May 29 at 17:36
• I clearly don't agree with your conclusion that objective knowledge simply does not exist. Epistemic regress does not equal nihilism. It equals some kind of counter-foundationalism. May 29 at 17:43
• What you are ignoring is that the argument is about deriving kowledge, within the same structure where this 'trilemma' comes from initially, there are two other options where we just receive and do not derive knowledge: direct experience and transmitted information. To derive further understanding from those, you need to accept an axiom about how to judge the reliability of received knowledge. May 29 at 18:00

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."