I used to think that circular reasoning should be one of the rarest of fallacies. Would not someone notice that their argument demands the conclusion as a premise? Since then, two things have surprised me: the prevalence of circular reasoning, and the difficulty of its definition. Here I shall restrict myself to practical reasoning,1 under the definition of “using a premise not granted by one’s opponent to demonstrate to him the falsity of his beliefs”. Thus, while a circular argument may be valid, it has (or should have) no persuasive value.
One of the most pervasive examples I have encountered is Hume’s argument against miracles: because a miracle is, by definition, a violation of natural laws, it is of infinitely low probability, and so any explanation consistent with natural laws is of higher probability. Therefore, no report of a miracle can prove their existence, for it is always better explained without resort to miracles. This argument seems to have dominated secular understandings of miracles, but does it actually prove anything? Note the hidden premise: that all violations of natural laws are of infinitely low probability. I, for one, do not grant the premise, and neither, I suspect, do any who believe in miracles (except, perhaps, for Kierkegaard and his followers, but I can make little sense of his intellectual system and thus cannot speak for him): I hold that divine action is unconstrained by the principles that God has chosen to follow in most circumstances, and thus that miracles are not of infinitely low probability. Since the argument thus depends on proof that miracles are of infinitely low probability (which, rather ironically, science cannot demonstrate), it cannot be used independently to discredit reports of miracles.2
The other place I often see such circular reasoning used is in maintaining the necessity of government. I frequently encounter arguments that the credit crisis proves the necessity of government restraints, or that the thalidomide tragedy proves the necessity of the FDA. In neither case was the market free; the banks were regulated in the first case; the FDA existed in the second. Therefore, for the arguments to validly reject the perfectly free market, one must accept the unstated premise that all regulations reduce the probability of problems. Brought to light, this premise should seem absurd to all people, for it is utterly implausible that all government regulation, whatever its form or intention, is beneficial. But even granting that those who make the argument accept that premise, I doubt that very many supporters of the free market would accept it. I would explain the matter differently: each crisis occurred because the government regulation was insufficient (possibly necessarily so) to avert the problem, but was sufficient to cause people to forsake their own responsibilities of monitoring risks. Thus, I would argue the matter in reverse: the existence of such crisis under a regulatory regime indicates the difficulty (although not, prima facie, the impossibility) of effective regulation. These examples only prove the need for government regulation if one assumes its superior effectiveness, which those who would controvert its need would almost certainly deny.
I must note that use of circular arguments (under this definition) is not itself irrational; I think that all people do and even must use them continually to themselves to address challenges to their position. If any challenge to my belief required me to reprove my positions a nihilo, I would never accomplish anything else(actually, I would never accomplish even this). Thus, it is perfectly reasonable to respond to an argument against one’s position with an argument drawing on the position as a premise, thus maintaining the consistency of one’s beliefs even in the face of the counterargument.3 However, what suffices to maintain one’s own position against a counter-argument does not necessarily suffice as an argument against another’s position. Proper form in an informal debate requires basing all of one’s arguments on premises that one’s opponent accepts. If neither can do so, then the debate must remain inconclusive. Above all, one must not declare irrational one who does not agree with one’s conclusions because he does not believe in one’s premises; unless one can object to his premises on some lower common ground,4 one cannot question the rationality or truth of his opinions. However, this seems to be the form of almost all modern debate (from both sides, I must note; this is why I cannot stand Coulter), particularly in religion and politics. It is possible to demonstrate that miracles are impossible, if one assumes that they are impossible; but what does this prove concerning the rationality of those who hold them to be possible?
1 Circular reasoning has no firm place in classical two-truth value logic, most formulations being trivial or proscribing all valid arguments.
2 Does it even prove that much? It seems to me that Aristotle’s dictum that an impossible plausibility is preferable to a plausible possibility applies to life, not merely poetry. Take the example of Christ’s resurrection: to admit the possibility of resurrection seems less momentous than to admit that so many people would lie with expectation of harm. On the other hand, I must acknowledge that this argument is, itself, somewhat circular, for to admit the possibility of resurrection would be far more momentous to an atheist.
3 However, one must be careful to avoid using one’s position to reject the argument: I believe A, P implies not A, therefore not P. Instead, one must either disprove P without reference to A or prove that P is consistent with A. The statist who holds that state regulation of drugs is beneficial can, while maintaining local rationality, state that failures of state regulation do not disprove its utility because it might be worse without the state control (to dispute which would be to commit the nirvana fallacy). However, if it is then demonstrated that conditions would have been better without the state agency, he may not say that because that contradicts his belief in the state system, the demonstration must be false; he must address the demonstration itself.
4 Which will, I believe, always exist, but may be very difficult to find. Of course, one could merely deny all points of agreement to avoid “losing” a debate, but one hopes that one who does so would still question his beliefs. I would also dispute that he has really avoided losing, for the only way to lose a discussion is to fail to aspire to the truth.