How do you measure circular reasoning?

  • Since one trip through the loop has the same effect as five or ten or a million, I would assume you cannot measure it. There is so much proof then some number of cycles of unproductive nonsense, and then more proof. The number of cycles is exactly what doesn't matter. – user9166 Aug 21 '19 at 13:37
  • Perhaps by the number of distinct elements in the smallest self-referential chain. A->A has length 1, A->B->A has length 2, A->B->C->A has length 3, etc. – user4894 Aug 21 '19 at 18:06
  • What exactly does it mean to "measure" circular reasoning? – Noah Schweber Aug 22 '19 at 4:31

Douglas Walton provides a brief assessment of circular reason which may help to suggest "measures" of its use.

Walton first notes that one should not assume circular reason is always fallacious:

Circular reasoning is very important and characteristic of all kinds of everyday argumentation where feedback is used. So it is often quite correct and useful — not fallacious, as traditionally portrayed in the logic textbooks.

So a first step in measuring circular reason is to determine if it is fallacious or not. If we suspect it is fallacious we need criteria supporting that judgement.

Walton describes a fallacious use of circular reasoning as follows:

Arguing in a circle becomes a fallacy of petitio principii or begging the question where an attempt is made to evade the burden of proving one of the premises of an argument by basing it on the prior acceptance of the conclusion to be proved (See Walton, 1991). So the fallacy of begging the question is a systematic tactic to evade fulfillment of a legitimate BURDEN OF PROOF by the proponent of an argument in dialogue by using a circular structure of argument to block the further progress of dialogue and, in particular, to undermine the capability of the respondent, to whom the argument was directed, to ask legitimate critical questions in reply.

This suggests criteria on how to measure or justify an assessment that an argument using circular reasoning is actually fallacious.

  • To what extent is the use of circular reasoning a tactic that involves evasion of burden of proof?
  • To what extent does this tactic block further progress of dialogue?
  • Does this prevent the one subjected to a circular argument from asking legitimate critical questions?

Walton, D. "Circular Reasoning" entry in A Companion to Epistemology, ed. Jonathan Dancy and Ernest Sosa, Oxford, Blackwell, 1992, p. 66 Retrieved from Douglas Walton's site on August 21, 2019 at https://www.dougwalton.ca/papers%20in%20pdf/92CircReas.pdf

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    Do you have any example of how a circular argument would not be fallacious? Your link doesn't say. And there seems to be a very large consensus that it is always fallacious. – Speakpigeon Aug 21 '19 at 14:45
  • @Speakpigeon In proof systems such as natural deduction using the reiteration inference rule is a form of circular reasoning that is valid. It is not fallacious. In general, referencing a previously agreed upon premise to clarify it or confirm it would not be fallacious. In cross examinations a witness may be asked to confirm repeatedly their commitments to previously made statements to make sure they actually agree with them. The cross examination cannot stop there, but must drive home a contradiction between those prior commitments and something else. – Frank Hubeny Aug 21 '19 at 15:00
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    Maybe some logicians call reiteration "circular" but it's clearly not circular in the same sense as the commonly used "circular" in the discussion of fallacious circular arguments. This seems a case of equivocation. I don't even understand what would be circular in reiteration. – Speakpigeon Aug 21 '19 at 15:33
  • Even the very best uses of circular reasoning, for instance analyses that just embed the concept in multiple domains without achieving a grounding (a la the observations of 'strange loops' via category theory in math, etc.) are logically inconclusive, but they increase the number of circumstantial observations. So in that case the circular argument is not the reasoning, the application of different kinds of leverage to the problem is. The value of the outcome is not dependent on the circles, but on the number of other dependencies noted through the embeddings. – user9166 Aug 21 '19 at 16:04
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    @Frank hubney, the reiteration rule is NOT an example of circular reasoning. In the inference rule you are not justifying another proposition but just repeating what was stated above in a lengthy line proof. I am positive that if you have an 8 line proof you would use reiteration. Repeating the same proposition does nothing in terms of argument. Circular reasoning is arriving at a conclusion based on synonymous premises to the conclusion. In this way the conclusion is not established ever. If the premise was true the conclusion would have to be true by definition. – Logikal Aug 21 '19 at 17:21

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