Aristotle describes the regress problem in his logical work Posterior Analytics I.2:

b5. Some hold that, owing to the necessity of knowing the primary premisses, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premisses.

b8. The first school [agnostics?], assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand — they say — the series terminates and there are primary premisses, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since thus one cannot know the primary premisses, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premisses are true.

b15. The other party [sophists?] agree with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal.

b18. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premisses is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premisses from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition we maintain that besides scientific knowledge there is its originative source which enables us to recognize the definitions.

cf. also St. Thomas Aquinas's Commentary on Aristotle's Metaphysics IV l. 6 [¶607] for a conciser resolution of the regress problem

Aristotle's conclusion is that, analogous to Gödel, there are truths which cannot be demonstrated.

For example, there are laws of reasoning that are true but cannot be proven to be true, like the principle of non-contradiction, which is the "first indemonstrable principle" (Summa Theologica I-II q. 94 a. 2 c.):
quoted here

[A] certain order is to be found in those things that are apprehended universally. For that which, before aught else, falls under apprehension, is "being," the notion of which is included in all things whatsoever a man apprehends. Wherefore the first indemonstrable principle is that "the same thing cannot be affirmed and denied at the same time," which is based on the notion of "being" and "not-being": and on this principle all others are based, as is stated in Metaph. iv, text. 9.

Is the regress problem a problem in other, non-Aristotelian logics?

  • Note that the conclusion is not analogous to Gödel's. All that Aristotle is saying is that any chain of deduction must start from somewhere. Gödel's first incompleteness theorem, on the other hand, tells us about statements that are unprovable no matter how many extra premises we add or whatever else we do. – duplode Oct 14 '16 at 20:01
  • The meaning of "logic" has evolved to exclude demonstration, and to require axiomatization or set premises. So the answer is literally 'no' -- simple First Order Logic does not face infinite regresses, because it takes Aristotle's advice and states its premises. But I think what Aristotle means here is more what we mean by 'science', in which case the answer is yes, deciding premises is necessarily circular, or at least dialectical. Can we separate these two questions? – jobermark Oct 14 '16 at 21:37
  • I think the climax of what started with Aristotle and this objection had been reached at the end of the 18th century, where Lessing and Jacobi agreed upon the fact that Spinozism (i.e. holistic unity of Being) is the best possible philosophical solution to the Agrippan Trilemma directly evolving out of Aristotelian logics. Since then, philosophy tends to evolve towards what maybe called historical holism, i.e. realism paired with the insight that justifications change and evolve through history, omitting the idea of actually reaching absoute perfection. See Tim Button, Limits of Realism. – Philip Klöcking Dec 9 '16 at 14:03

Terminology changed somewhat, and much of what used to be called "logic" as late as early 20th century is now called epistemology, for more details see What are the differences between philosophies presupposing one Logic versus many logics? Posterior Analytics covers mostly that epistemological part of logic. What Aristotle describes is what later was coined into Agrippa's trilemma from the exposition of Pyrrhonism in Sextus Empiricus (more recently also Münchhausen trilemma): any justification of knowledge (episteme, Latinized as scientia) either rests on "first principles", or is circular, or involves an infinite regress (technically, this is not a trilemma because the possibilities are not mutually exclusive). Agrippa, according to Sextus, does not have "first principles", but adds three more possibilities, not considered by Aristotle: knowledge is merely hypothetical (this is closest to the "first principles"), knowledge is relative, and knowledge is uncertain and reduces to opinions.

The position Aristotle staked out for himself is now called foundationalism (after the "first principles" being the foundation of knowledge), and the regress of justifications is a classical argument in its support. In modern times foundationalism was reasserted by Descartes, and came in two flavors, rationalist and empiricist, depending on whether the source of "first principles" was purely sensual (Locke, Hume, Mill, Mach) or some sort of rational insight was involved (Descartes, Leibniz, Kant, Husserl).

The outright rejection of foundationalism now came to dominate both current analytic and continental philosophy, including philosophy of science (in the modern sense). Its origin is associated with Hegel, who incidentally also called epistemology Logic, or Science of Logic. Hegel rejected foundations in his famous dialectic of immediate/mediated. In "Agrippa's" terms, he is opting for the infinite regress of sublations of "immediate" givens (albeit denouncing the "bad infinity"):

The facility we attain in any sort of knowledge, art, or technical expertness, consists in having the particular knowledge or kind of action present to our mind in any case that occurs, even, we may say, immediate in our very limbs, in an outgoing activity. In all these instances, immediacy of knowledge is so far from excluding mediation, that the two things are linked together - immediate knowledge being actually the product and result of mediated knowledge [...] Abstract immediacy is no doubt a first; yet in so far as it is abstract it is, on the contrary mediated, and therefore if it is to be grasped in its truth its foundation must first be sought. Hence this foundation, though indeed an immediate, must have made itself immediate through the sublation of mediation.

Heidegger abandoned his early Husserlian foundationalism in late works, and Adorno explicitly employed Hegelian anti-immediacy arguments in his broad "meta-critique" Against Epistemology, which anticipates many postmodernistic themes.

On the analytic side anti-foundationalism was assimilated through Peirce ("My philosophy resuscitates Hegel, though in a strange costume", "[science] is not standing upon the bedrock of fact. It is walking upon a bog, and can only say, this ground seems to hold for the present. Here I will stay till it begins to give way"), Lewis, and his perhaps better known students Quine and Sellars, see Misak's Exploding a Myth. Quine's naturalized epistemology is perhaps the most influential form of analytic anti-foundationalism today, and it openly admits that all knowledge is hypothetical and undergoes potentially unending revision of its "foundations", including methodology. It embraces even the element of circularity the latter entails. Philipse's paper Edmund Husserl and the History of Classical Foundationalism (in Husserl and the Sciences volume) is a good historical survey:

"According to many present-day epistemologists, the justification of scientific theories is relative in at least two respects... New empirical data may top the balance in favour of an existing rival theory, or a new rival theory may be designed that performs better... The model of justification by competition must be applied also at the meta-level of justifying epistemological theories [...] in Heidegger's time, the research programme of classical foundationalism had reached the stage of its final decline, dragging down in its bankruptcy the notion that philosophy is fundamental to the sciences. Its most promising rival as an epistemology of the empirical sciences is not coherentism [e.g. Hegel's], but competitive empiricism... Within the framework of competitive empiricism, the problem of the first principles simply does not arise."

P.S. I do not think there is much of an analogy between Aristotle's reasoning and Gödel's. Aristotle concludes that "axioms" are needed to support deductive chains that derive truths of knowledge (and he was an empiricist about their source). Gödel shows that (sufficiently rich but first order) axiomatic system can not derive all (Platonist) "truths" due to self-reference issues. The reasons involved are completely different, and Aristotle might even reject Gödel's form of the conclusion of the incompleteness theorem on anti-Platonist grounds, as intuitionists did.

  • Just wondering, how do you possibly deny foundationalism? By assuming the very basics when trying to refute it: that logic exists, that you are thinking right now, etc, aren't you always accepting some sort of foundationalism? – APCoding Dec 8 '16 at 3:46
  • @APCoding First, there is no need to refute it if you did not accept it in the first place, but failed attempts over the centuries to produce a "foundation" for anything non-trivial is "refutation" enough. Second, people acted and reasoned long before they learn about logic and other theoretical notions, those evolved later and continue to, which means they "presuppose" a background of practice, not the other way around. If some theoretical "shell" within which we are expected to reason is assumed from the beginning then foundationalism is a natural result, but that is circular. – Conifold Dec 8 '16 at 18:45

Aristotelian logic isn't the reason for the regress problem. The demand for justification is the reason for the regress problem. Any argument uses premises and rules of inference and the truth of the conclusion is dependent on the truth of the premises and the correctness of the rules of inference. If you want to say the argument shows the conclusion is true then you have to do one of two things.

(1) Assert that the premises and rules of inference are correct and can't be questioned.

(2) Try to prove the premises and rules of inference are correct.

Option (1) is bad since it would stop you from spotting mistakes. Option (2) is impossible since it leads to the infinite regress.

There is another option: reject the demand for justification. You look for problems, guess solutions to the problems, criticise the proposed solutions until only one is left and then look for a new problem. The criticism takes the form of working out the consequences of your ideas and then comparing those consequences to reality: if the consequences don't match reality the theory is wrong. You can make various kinds of mistakes in the comparison, so the comparison and so on are also guesses that might be eliminated by criticism.

If you want to know more, see "Objective Knowledge" by Karl Popper Chapter 1, "Realism and the Aim of Science" by Popper, chapter I, "The Fabric of Reality" by David Deutsch chapters 3 and 7, "The Beginning of Infinity" by Deutsch chapters 1,2,4.

  • Why "Option (2) is impossible."? – Geremia Dec 9 '16 at 12:24
  • Option (2) leads to infinite regress. You can't do an infinite amount of stuff, so it is impossible. – alanf Dec 9 '16 at 13:23

Yes in some sense. The problem cannot be gotten away from. The structure of justification and warrant is such that it is indexical to a standard-relative conceptual framework, which can be vetted through the considerations of the Münchhausen trilemma.

  • 1
    This is barely an answer. It's more just an assertion. Why exactly do you think that other approaches like anti-foundationalism must fail? – wolf-revo-cats Dec 23 '16 at 0:50
  • I'm an anti-foundationalist. – Lothrop Stoddard Dec 23 '16 at 0:51
  • @wolf-revo-cats – Lothrop Stoddard Jan 14 '17 at 15:58

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