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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 series 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." The infinite regress forms one of the three parts of the
Munchhausen-Trilemma.
Aristotle's answer
Aristotle argued that knowing doesn't necessitate an infinite regress because some knowledge does not depend on demonstration:{{cquote2|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 (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.
See also
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 series 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." The infinite regress forms one of the three parts of the Munchhausen-Trilemma.
Aristotle's answer
Aristotle argued that knowing doesn't necessitate an infinite regress because some knowledge does not depend on demonstration:{{cquote2|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 (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.
See also
