§ 2. We have now sufficiently exemplified one of the principal Genera in this Order of Fallacies; where, the source of error being the ambiguity of terms, the premises are verbally what is required to support the conclusion, but not really so. In the second great Fallacy of Confusion they are neither verbally nor really sufficient, though, from their multiplicity and confused arrangement, and still oftener from defect of memory, they are not seen to be what they are. The fallacy I mean is that of Petitio Principii, or begging the question; including the more complex and not uncommon variety of it, which is termed Reasoning in a Circle.
Petitio Principii, as defined by Archbishop Whately, is the fallacy “in which the premise either appears manifestly to be the same as the conclusion, [pg 571] or is actually proved from the conclusion, or is such as would naturally and properly so be proved.” By the last clause I presume is meant, that it is not susceptible of any other proof; for otherwise, there would be no fallacy. To deduce from a proposition propositions from which it would itself more naturally be deduced, is often an allowable deviation from the usual didactic order; or at most, what, by an adaptation of a phrase familiar to mathematicians, may be called a logical inelegance.[264]
The employment of a proposition to prove that on which it is itself dependent for proof, by no means implies the degree of mental imbecility which might at first be supposed. The difficulty of comprehending how this fallacy could possibly be committed, disappears when we reflect that all persons, even the instructed, hold a great number of opinions without exactly recollecting how they came by them. Believing that they have at some former time verified them by sufficient evidence, but having forgotten what the evidence was, they may easily be betrayed into deducing from them the very propositions which are alone capable of serving as premises for their establishment. “As if,” says Archbishop Whately, “one should attempt to prove the being of a God from the authority of Holy Writ;” which might easily happen to one with whom both doctrines, as fundamental tenets of his religious creed, stand on the same ground of familiar and traditional belief.
Arguing in a circle, however, is a stronger case of the fallacy, and implies more than the mere passive reception of a premise by one who does not remember how it is to be proved. It implies an actual attempt to prove two propositions reciprocally from one another; and is seldom resorted to, at least in express terms, by any person in his own speculations, but is committed by those who, being hard pressed by an adversary, are forced into giving reasons for an opinion of which, when they began to argue, they had not sufficiently considered the grounds. As in the following example from Archbishop Whately: “Some mechanicians attempt to prove (what they ought to lay down as a probable but doubtful hypothesis)[265] that every particle of matter gravitates equally: ‘why?’ ‘because those bodies which contain more particles ever gravitate more strongly, i.e., are heavier:’ ‘but (it may be urged) those which are heaviest are not always more bulky;’ ‘no, but they contain more particles, though more closely condensed:’ ‘how do you know that?’ ‘because they are heavier:’ ‘how does that prove it?’ ‘because all particles of matter gravitating equally, that mass which is specifically the heavier must needs have the more of them in the same space.’ ” It appears to me that the fallacious reasoner, in his private thoughts, would not be likely to proceed beyond the first step. He would acquiesce in the sufficiency of the reason first given, “bodies which contain more particles are heavier.” It is when he finds this questioned, and is called upon to prove it, without knowing how, that he tries to establish his [pg 572] premise by supposing proved what he is attempting to prove by it. The most effectual way, in fact, of exposing a petitio principii, when circumstances allow of it, is by challenging the reasoner to prove his premises; which if he attempts to do, he is necessarily driven into arguing in a circle.
It is not uncommon, however, for thinkers, and those not of the lowest description, to be led even in their own thoughts, not indeed into formally proving each of two propositions from the other, but into admitting propositions which can only be so proved. In the preceding example the two together form a complete and consistent, though hypothetical, explanation of the facts concerned. And the tendency to mistake mutual coherency for truth—to trust one’s safety to a strong chain though it has no point of support—is at the bottom of much which, when reduced to the strict forms of argumentation, can exhibit itself no otherwise than as reasoning in a circle. All experience bears testimony to the enthralling effect of neat concatenation in a system of doctrines, and the difficulty with which people admit the persuasion that any thing which holds so well together can possibly fall.
Since every case where a conclusion which can only be proved from certain premises is used for the proof of those premises, is a case of petitio principii, that fallacy includes a very great proportion of all incorrect reasoning. It is necessary, for completing our view of the fallacy, to exemplify some of the disguises under which it is accustomed to mask itself, and to escape exposure.
A proposition would not be admitted by any person in his senses as a corollary from itself, unless it were expressed in language which made it seem different. One of the commonest modes of so expressing it, is to present the proposition itself in abstract terms, as a proof of the same proposition expressed in concrete language. This is a very frequent mode, not only of pretended proof, but of pretended explanation; and is parodied when Molière (Le Malade Imaginaire) makes one of his absurd physicians say,
Mihi a docto doctore,
Demandatur causam et rationem quare
Opium facit dormire.