Another one: let's pretend that some philosopher offered you a really convincing argument that all arguments are ultimately circular. How would you pick out the vicious ones? — Pneumenon

When you call something a vicious circle, you are not talking about an argument, you're talking about a situation e.g. climate change. Warming temperatures lead to greater releases of greenhouse gasses from thawing permafrost, loss of reflective ice, etc. This leads to more heating and accelerating releases.

There are two different occasions that you talk about a vicious circle in philosophy.

First one refers to Russell's Paradox or some similar instances. Russell himself describe the Paradox as a vicious circle. This is basically about negative self reference and its effect on logic.

The other example is when we talk about a vicious circle opposite a virtuous circle, basically when elements intensify and aggravate each other and lead inexorably to a worsening of the situation, which T Clark above mentions.

What makes a circular argument viciously circular? I see philosophers doing this thing where they claim that such-and-such argument is circular, yes, but it's not viciously circular. But I haven't been able to find any work on the difference between the two. What is it about a viciously circular argument that makes it vicious, and what makes a virtuous circle virtuous? I've seen philosophers appeal to this, but I don't know what the basis is.

Let's say I claim that P is true. Let's say you claim that P is false. Neither of us can justify our argument without it being circular. What does that mean?

Another one: let's pretend that some philosopher offered you a really convincing argument that all arguments are ultimately circular. How would you pick out the vicious ones? — Pneumenon

Some of this, not all, probably points to the differences between deductive arguments and inductive arguments.

One could also give the example of A proving B, then later one might argue that B proves A. This can be seen in some mathematical proofs, which aren't necessarily seen as circular or fallacious.

One could also argue that some statements are just so foundational that they need no justification, thus the argument may be seen by some as circular, but because the of the nature of these basic propositions, they fall outside the parameters of justification.

If someone makes the claim that all arguments are circular, then I would claim that they don't understand circularity as presented in most logic courses. However, some people try to define circularity in a peculiar way.

I've never heard of a case where circular reasoning was "virtuous" since circularity in general is considered fallacious. Can you provide any examples where people called something circular "virtuous" or at the very least "non-vicious"? You said that you heard philosophers using this language, so it'll help if you offer up the passages where they mention such things so we can interpret for ourselves.

Perhaps this is related to the difference between vicious and benign infinite regresses? That is what comes to mind when I read your title, since both concepts sound similar enough. I actually made a thread about that topic a while back actually, though it didn't take off.

A book on logic I read says that there isn't such a thing as a circular argument.

According to the book, an argument requires at least two different statements. One is the premise and the second is the conclusion. A circular "argument" has only one statement which is the premise and is repeated in the conclusion. This, by definition, isn't an argument.

Note however, that if we consider circularity as an "argument" then it's a perfectly valid argument. If the premise is true then the conclusion, a repetition of the premise, is necessarily true. Circularity is an informal fallacy.

The bigger the circle - more the number of logical steps to the conclusion - the more difficult it is to detect the circularity.

I don't know about circular arguments, but concepts are sometimes said to have a circular dependency. (Specifically, we are talking here about a "tight" circle, involving only a few concepts.) The dependency is not vicious if it is unavoidable on the one hand, and on the other hand the whole construct works reasonably well.

For example, it is argued that time and clock have such a virtuous circular dependency. Neither concept can be understood without the other, but together they seem to make sense.

I'd say that there's always something additive about what are called virtuous cycles: the move from A to B to A again 'adds' something to A, or sustains it in a way. Whereas vicious cycles would not have this additive element: every iteration of the cycle lands you back at the beginning, without any 'increase' along any particular dimension. Conceptually, the key difference here is temporal asymmetry: strictly speaking, vicious cycles have no 'time', they are temporally neuter, purely 'logical', whereas virtuous cycles always have a forward temporal momentum to them.

An example: in democratic theory, there's sometimes what's referred to as the democratic paradox - the idea that you can't have a democracy without a citizenry trained in democratic values, but you can't cultivate a democratically educated citizenry without a democracy. The 'solution' to this paradox that is generally given is that democracies are not 'binary' values: democracy is always something that is being worked upon and worked out, that democracies are always in the process of their own establishment, which is never given or completed once and for all.

Another element that might be relevant is the gestalt nature of virtuous cycles: they come packaged as a 'whole', as a 'form' with a function. To use another example drawn from somewhere else entirely: creationists often used to argue that the eye was an example of 'irreducible complexity': every part of the eye, taken together, is necessary for the eye to work, so the eye could not have evolved in a piecemeal fashion, as biology would have it. The argument here is of a vicious kind: for any part of the eye to have evolved, it would have had to rely on another part, without which it could not have evolved, and vice versa.

The common response to that argument is that the eye was always a 'whole' from the very beginning, that it evolved as a unit to begin with, and not as bits added to other bits over time (early eyes were - and remain in some cases - simple light receptors that can only pick out vague differences in darkness and lightness for example, which might have helped a marine animal gauge how far it might be from the water's surface or something like that). The lesson being that vicious cycles rely on part-to-part thinking, while virtuous cycles are always part-to-whole-and-back-again thinking. Another relevant example of a virtuous cycle is something like the hermenutic cricle, which I won't go into, but is worth reading about, insofar as it exhibits both the part-whole nature of virtuous cycles and their temporality.

Perhaps we can say: virtuous cycles are always bound to 'real life': they are never purely formal-logical.

Your answer was the best. Many thanks.

An argument is viciously circular if its grounding premise is identical with what it purports to prove.

The conclusions of all valid deductive arguments are entailed by their premises. In that sense all deductive arguments might be said to be circular. The conclusion of a virtuously circular argument will tell us something that is entailed by, but is not obviously, to a superficial scrutiny at least, "in", the premises. Valid arguments (proofs) in mathematics would be a good example of this.

Vicious circularity is when one is face with some issue, and one's solution to the problem has the same issue and the problem propagates when they try to apply the solution.