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I'm studying circularity in arguments and was wondering if there is any acceptable circularity possible in a good philosophical argument. For instance, I gather that some regard rule-circularity as being generally less vicious than premise-circularity - is this the case, and so, would it still be generally unaccceptable in argument? I was also wondering whether circular arguments are always vicious - I've seen "virtuous circularity" mentioned and wanted to know if that was possible? It seems odd that circular reasoning could be non-vicious. thank you!

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I think that the non-vicious quality proposed for some circular arguments is well-described at the Stanford Encyclopedia of Philosophy's entry on Abduction:

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Stathis Psillos (1999, Ch. 4) has responded by invoking a distinction credited to Richard Braithwaite, to wit, the distinction between premise-circularity and rule-circularity. An argument is premise-circular if its conclusion is amongst its premises. A rule-circular argument, by contrast, is an argument of which the conclusion asserts something about an inferential rule that is used in the very same argument. As Psillos urges, Boyd’s argument [in defense of inference to the best explanation] is rule-circular, but not premise-circular, and rule-circular arguments, Psillos contends, need not be viciously circular (even though a premise-circular argument is always viciously circular).

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It is fair to note that for Psillos, the fact that a rule-circular argument does not guarantee a positive conclusion about the rule at issue is not sufficient for such an argument to be valid. A further necessary condition is “that one should not have reason to doubt the reliability of the rule—that there is nothing currently available which can make one distrust the rule” (Psillos 1999, 85). And there is plenty of reason to doubt the reliability of IWE; in fact, the above argument supposes that it is unreliable. Two questions arise, however. First, why should we accept the additional condition? Second, do we really have no reason to doubt the reliability of abduction? Certainly some of the abductive inferences we make lead us to accept falsehoods. How many falsehoods may we accept on the basis of abduction before we can legitimately begin to distrust this rule? No clear answers have been given to these questions.

Be this as it may, even if rule-circularity is neither vicious nor otherwise problematic, one may still wonder how Boyd’s argument is to convert a critic of abduction, given that it relies on abduction. But Psillos makes it clear that the point of philosophical argumentation is not always, and in any case need not be, to convince an opponent of one’s position. Sometimes the point is, more modestly, to assure or reassure oneself that the position one endorses, or is tempted to endorse, is correct. In the case at hand, we need not think of Boyd’s argument as an attempt to convince the opponent of abduction of its reliability. Rather, it may be thought of as justifying the rule from within the perspective of someone who is already sympathetic towards abduction; see Psillos 1999 (89).

[bracketed expressions added by Elliot]

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On Self-Reference, Fractal Ontology, and the Nature of Consciousness

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Preface:--

Those desiring a more technical "Sources and References" section of this writing.

Douglas Hofstadter claimed that phenomenon such as consciousness arose from fractal(-like) strange loops, and, that circularity, not only was not pejorative in this context, but was actually an exposition of much of the structure of reality.

Certain structures such as Gödel's Incompleteness Theorems give rise to self-circuality.

"Douglas Hofstadter, in his books Gödel, Escher, Bach and I Am a Strange Loop, cites Gödel's theorems as an example of what he calls a strange loop, a hierarchical, self-referential structure existing within an axiomatic formal system. He argues that this is the same kind of structure which gives rise to consciousness, the sense of "I", in the human mind. While the self-reference in Gödel's theorem comes from the Gödel sentence asserting its own unprovability within the formal system of Principia Mathematica, the self-reference in the human mind comes from the way in which the brain abstracts and categorises stimuli into "symbols", or groups of neurons which respond to concepts, in what is effectively also a formal system, eventually giving rise to symbols modelling the concept of the very entity doing the perception. Hofstadter argues that a strange loop in a sufficiently complex formal system can give rise to a "downward" or "upside-down" causality, a situation in which the normal hierarchy of cause-and-effect is flipped upside-down. In the case of Gödel's theorem, this manifests, in short, as the following:" — (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)

"Merely from knowing the formula's meaning, one can infer its truth or falsity >> without any effort to derive it in the old-fashioned way, which requires one to >> trudge methodically "upwards" from the axioms. This is not just peculiar; it is >> astonishing. Normally, one cannot merely look at what a mathematical conjecture >> says and simply appeal to the content of that statement on its own to deduce whether the statement is true or false." (I Am a Strange Loop.) — (https://publicism.info/philosophy/strange/14.html)

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