In the IEP article on infinitism, §4b, an objection to infinitism called "the proof of concept objection" is described. The problem is: if potentially endless nonrepeating sequences of reasons constitute knowledge, where are these sequences?

But scientific reasoning seems to work this way, doesn't it? We come up with a model of some phenomenon, this ends up leading to further questions about the subject, we discover further mysteries that invite new models that lead to more questions... Like, we knew about electromagnetic and gravitational forces, discovered the strong and weak nuclear ones, later discerned that these involve quarks, applied all this cosmologically to infer the existence of dark matter, then found out that there's an apparent acceleration to spatial expansion involving dark energy, presumably we'll have to refine all these concepts again and again as time goes on, and given the potential infinity of possible experience and experiment, is this sequence of scientific development a "proof of concept" of infinitism?

  • It may well be that science produces potentially endless series of reasons that can serve as basis of beliefs, but that is beside the point. To be justified in any belief on this model now we need to have this series of reasons available now, and we don't. The proof of concept asks for an actually endless series of available reasons. – Conifold Mar 11 at 21:01

It's conceivable that science will go through an infinite series of progressively finer explanations as you say (or potentially infinite but actually only during the finite time humans exist). This possibility assumes that the universe has no "base level" we can discover.

On the subject of progressively finer scientific explanations, Asimov's essay, "The Relativity of Wrong", makes some good points.

If there is a "base level" - a most fundamental description of the universe from which all else follows - then it's possible science would eventually discover it. And the regress would stop there. For example, Conway's game of life has a "base level" in terms of its simple cellular evolution rules, and if a scientist existed as a pattern within Conway's game of life, we would expect it to eventually discover those rules.

Nothing inherently prevents infinite regress in the universe. Nothing inherently requires causation in the universe. Whether the universe has infinite regress or causation is entirely a contingent matter. The universe might be any kind of object at all. At the very least, it might be any mathematical object we can conceive of, and we can certainly conceive of mathematical objects with or without infinite regress, and with or without causation. The only way to distinguish among these possibilities is by scientific investigation. Any armchair declarations about what the universe "must" do are liable to be proven wrong by someone who goes out and takes a look and gets a different experimental result. People used to think that space was Euclidean a priori, or that "no action at a distance" was a necessary law. Now we don't think those things.

  • How could a finite number of experiments prove that an infinite number of experiments will give the same result? Or, how could there be a decisive experiment that tested a "base level" hypothesis? – Kristian Berry Mar 11 at 19:35
  • @KristianBerry Things are not proved perfectly, only as a matter of probability. If the candidate "base level" hypothesis seems to be simple enough that it has a high prior probability under Occam's razor, and if we can use it to accurately predict every phenomenon we're aware of, then we would have fairly good evidence that this hypothesis is correct. We'll never reach certainty but we can reach confidence. – causative Mar 11 at 19:49
  • I think the infinitist would object to this way of putting these points, but I guess that would be a discussion for chat... – Kristian Berry Mar 11 at 19:51
  • By your definition a carton of eggs is infinite since we could always pile on more "as long as humans exist." No finite sequence of scientific revolutions could possibly be infinite if it's finite. – user4894 Mar 11 at 22:30
  • @user4894 well yes, of course, as I mentioned it would be "potentially" infinite but actually only during the finite time humans exist. By "potentially" infinite in this case I mean that if (counterfactually) the process of investigation could continue forever, perhaps there would be no bottom to the sequence of finer and finer theories. And in fact we don't know human society won't continue forever - odds seem against it, but it's possible. – causative Mar 11 at 23:10

Infinitism is one of three factions of epistemology, other 2 are foundationalism and coherentism, and none of the three epistemic theories are satisfactory as summarized in the classic "Münchhausen trilemma". From its wikipedia, infinitism is the view that knowledge may be justified by an infinite chain of reasons. It's certainly possible as we can easily imagine in a Platonic ideal world like a convergent series but since it's not physically realizable thus not useful in practice, and Pyrrhonists used it as an argument for their knowledge skepticism. If one needs an infinite amount of reasons to justify a knowledge, it sounds hopeless for an intellectually eager person to get satisfied and completed within his or her limited life.

For me this type of cautious skepticism actually hints philosophy's "ultimate" goal should not be avarice or erudition to acquire all possible knowledge in this world, but rather to choose what level of a foundation you ought to rest upon, meaning philosophy's essence is about ethics, valuation, judgement and eventually free will. Acquiring more knowledge is certainly one of several possible ways to help clarify one's goal but by no means the goal itself...

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