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 P_n, the truth of P_n requires the support of the truth of P_n+1. There would never be adequate support for P₁, because the infinite sequence needed to provide such support could not be completed. In Mathematics, a sequence is an ordered list of objects (or events

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. The Münchhausen-Trilemma, also called Agrippa's Trilemma (after the eponymous Greek Skeptic) is a philosophical term coined to stress the purported impossibility

Aristotle's answer

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 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. 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 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. 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 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.	”
	— Aristotle, Posterior Analytics (Book 1, Part 3)

Optics

Infinite regress in optics is the formation of an infinite series of receding images created in two parallel facing mirrors. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. The Posterior Analytics is a text from Aristotle 's Organon that deals with demonstration, Definition, and Scientific knowledge A mirror is an object with a surface that has good Specular reflection; that is it is smooth enough to form an Image.

See also

• Cosmological argument
• Regress argument
• Turtles all the way down
• Münchhausen Trilemma and Fallibilism
• Self-evidence

The cosmological argument is an Argument for the Existence of God or a " First Cause " The regress argument (also known as the diallelus) is a problem in Epistemology and in general a problem in any situation where a statement has to be justified "Turtles all the way down" refers to an Infinite regression Belief about Cosmology, the nature of the Universe. The Münchhausen-Trilemma, also called Agrippa's Trilemma (after the eponymous Greek Skeptic) is a philosophical term coined to stress the purported impossibility In Epistemology (theory of knowledge a self-evident proposition is one that is known to be true by understanding its meaning without proof.

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