A striking instance of reasoning in a circle is that of some ethical writers, who first take for their standard of moral truth what, being the general, they deem to be the natural or instinctive sentiments and perceptions of mankind, and then explain away the numerous instances of divergence from their assumed standard, by representing them as cases in which the perceptions are unhealthy. Some particular mode of conduct or feeling is affirmed to be unnatural; why? because it is abhorrent to the universal and natural sentiments of mankind. Finding no such sentiment in yourself, you question the fact; and the answer is (if your antagonist is polite), that you are an exception, a peculiar case. But neither (say you) do I find in the people of some other country, or of some former age, any such feeling of abhorrence; “ay, but their feelings were sophisticated and unhealthy.”
One of the most notable specimens of reasoning in a circle is the doctrine of Hobbes, Rousseau, and others, which rests the obligations by which human beings are bound as members of society, on a supposed social compact. I waive the consideration of the fictitious nature of the compact itself; but when Hobbes, through the whole Leviathan, elaborately deduces the obligation of obeying the sovereign, not from the necessity or utility of doing so, but from a promise supposed to have been made by our ancestors, on renouncing savage life and agreeing to establish political society, it is impossible not to retort by the question, Why are we bound to keep a promise made for us by others? or why bound to keep a promise at all? No satisfactory ground can be assigned for the obligation, except the mischievous consequences of the absence of faith and mutual confidence among mankind. We are, therefore, brought round to the interests of society, as the ultimate ground of the obligation of a promise; and yet those interests are not admitted to be a sufficient justification for the existence of government and law. Without a promise it is thought that we should not be bound to that which is implied in all modes of living in society, namely, to yield a general obedience to the laws therein established; and so necessary is the promise deemed, that if none has actually been made, some additional safety is supposed to be given to the foundations of society by feigning one.
§ 3. Two principal subdivisions of the class of Fallacies of Confusion having been disposed of; there remains a third, in which the confusion is not, as in the Fallacy of Ambiguity, in misconceiving the import of the premises, nor, as in Petitio Principii, in forgetting what the premises are, but in mistaking the conclusion which is to be proved. This is the fallacy of Ignoratio Elenchi, in the widest sense of the phrase; also called by Archbishop Whately the Fallacy of Irrelevant Conclusion. His examples and remarks are highly worthy of citation.
“Various kinds of propositions are, according to the occasion, substituted for the one of which proof is required; sometimes the particular for the universal; sometimes a proposition with different terms; and various are the contrivances employed to effect and to conceal this substitution, and to make the conclusion which the sophist has drawn, answer practically the same purpose as the one he ought to have established. We say, ‘practically the same purpose,’ because it will very often happen that some emotion will be excited, some sentiment impressed on the mind (by a dexterous employment of this fallacy), such as shall bring men into the disposition requisite for your purpose; though they may not have assented to, or even stated distinctly in their own minds, the proposition which it was your business to establish. Thus if a sophist has to defend one who has been guilty of some serious offense, which he wishes to extenuate, though he is unable distinctly to prove that it is not such, yet if he can succeed in making the audience laugh at some casual matter, he has gained practically the same point. So also if any one has pointed out the extenuating circumstances in some particular case of offense, so as to show that it differs widely from the generality of the same class, the sophist, if he finds himself unable to disprove these circumstances, may do away the force of them, by simply referring the action to that very class, which no one can deny that it belongs to, and the very name of which will excite a feeling of disgust sufficient to counteract the extenuation; e.g., let it be a case of peculation, and that many mitigating circumstances have been brought forward which can not be denied; the sophistical opponent will reply, ‘Well, but after all, the man is a rogue, and there is an end of it;’ now in reality this was (by hypothesis) never the question; and the mere assertion of what was never denied ought not, in fairness, to be regarded as decisive; but, practically, the odiousness of the word, arising in great measure from the association of those very circumstances which belong to most of the class, but which we have supposed to be absent in this particular instance, excites precisely that feeling of disgust which, in effect, destroys the force of the defense. In like manner we may refer to this head all cases of improper appeal to the passions, and every thing else which is mentioned by Aristotle as extraneous to the matter in hand (ἔξω τοῦ πράγματος).”
Again, “instead of proving that ‘this prisoner has committed an atrocious fraud,’ you prove that the fraud he is accused of is atrocious; instead of proving (as in the well-known tale of Cyrus and the two coats) that the taller boy had a right to force the other boy to exchange coats with him, you prove that the exchange would have been advantageous to both; instead of proving that the poor ought to be relieved in this way rather than in that, you prove that the poor ought to be relieved; instead of proving that the irrational agent—whether a brute or a madman—can never be deterred from any act by apprehension of punishment (as, for instance, a dog from sheep-biting, by fear of being beaten), you prove that the beating of one dog does not operate as an example to other dogs, etc.
“It is evident that Ignoratio Elenchi may be employed as well for the apparent refutation of your opponent’s proposition, as for the apparent establishment of your own; for it is substantially the same thing, to prove what was not denied or to disprove what was not asserted. The latter practice is not less common, and it is more offensive, because it frequently amounts to a personal affront, in attributing to a person opinions, etc., which he perhaps holds in abhorrence. Thus, when in a discussion one party vindicates, on the ground of general expediency, a particular instance of resistance to government in a case of intolerable oppression, the opponent may gravely maintain, ‘that we ought not to do evil that good may come;’ a proposition which of course had never been denied, the point in dispute being, ‘whether resistance in this particular case were doing evil or not.’ Or again, by way of disproving the assertion of the right of private judgment in religion, one may hear a grave argument to prove that ‘it is impossible every one can be right in his judgment.’ ”
The works of controversial writers are seldom free from this fallacy. The attempts, for instance, to disprove the population doctrines of Malthus, have been mostly cases of ignoratio elenchi. Malthus has been supposed to be refuted if it could be shown that in some countries or ages population has been nearly stationary; as if he had asserted that population always increases in a given ratio, or had not expressly declared that it increases only in so far as it is not restrained by prudence, or kept down by poverty and disease. Or, perhaps, a collection of facts is produced to prove that in some one country the people are better off with a dense population than they are in another country with a thin one; or that the people have become more numerous and better off at the same time. As if the assertion were that a dense population could not possibly be well off; as if it were not part of the very doctrine, and essential to it, that where there is a more abundant production there may be a greater population without any increase of poverty, or even with a diminution of it.