An infinite regress in a series of propositions arises if the truth of proposition P1 requires the support of proposition P2, and for any proposition in the series Pn, the truth of Pn requires the support of the truth of Pn+1. There would never be adequate support for P1, because the infinite sequence needed to provide such support could not be completed.
Distinction is made between infinite regresses that are "vicious" and those that are not. One definition given is that a vicious regress is "an attempt to solve a problem which re-introduced the same problem in the proposed solution. If one continues along the same lines, the initial problem will recur infinitely and will never be solved. Not all regresses, however, are vicious." [1]
The infinite regress forms one of the three parts of the Münchhausen Trilemma.
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Aristotle argued that knowing doesn't necessitate an infinite regress because some knowledge does not depend on demonstration:
| “ | Some hold that, owing to
the necessity of knowing the primary premises, 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 premises. The first school, 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 premises, 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
premises, 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 premises are true. The other
party 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.
Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premises 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. |
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— Aristotle, Posterior Analytics (Book 1,
Part 3)
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Infinite regress in consciousness is the formation of an infinite series of "inner observers" as we ask the question of who is observing the output of the neural correlates of consciousness in the study of subjective consciousness.
Infinite regress in optics is the formation of an infinite series of receding images created in two parallel facing mirrors.
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