On this Mill remarks that such a process, wherein there is an actual attempt to prove two propositions reciprocally from one another, is seldom resorted to, at least in express terms, by any person in his own speculations, but is more likely to be committed by one who, being hard pressed by an adversary, is forced into giving reasons for an opinion of which, when he began to argue, he had not sufficiently considered the grounds. Hence another way to expose a Diallelon: challenge the reasoner to prove his premise, which if he undertakes to do, his whirl is evolved."

A notable example of reasoning in a circle is the argument of Edwards and other metaphysicians for a necessitated will. The will, they affirm, must be subject to the law of necessity, because its determinations are always, as a matter of fact, in accordance with the strongest motive, the greatest apparent good. The strongest motive determines the choice, hence the will is necessitated. But what do you mean by the strongest motive? It is, of course, the motive that prevails. We know that it is the strongest because it does prevail. If it were not the strongest, the will would not have followed it; and being the strongest, the will must follow it. Then that is to say, the will must follow the strongest motive, because the strongest motive is the one the will must follow.

The second mode of petitio principii is that in which a universal is assumed to prove a particular. For example: "Is William, King of Germany, in any respect tyrannical? Of course he is; for all men possessing power are more or less tyrannical."

It is remarkable that this does not differ in form from the legitimate syllogism. It seems to give new ground for the charge, already discussed," that the Aristotelic syllogism is essentially petitio principii. But observe that the fault here indicated is not a formal fault; it does not lie within the syllogism itself, but precedes it. It lies in the assumption of a principle by the reasoner, from which the conclusion truly follows, but which stands in need of proof as much or even more than the conclusion itself, and therefore cannot establish it, the whole

30 Logic, p. 571. That every particle of matter gravitates equally will not be granted by those who accept the atomic theory, according to which the particles have different specific combining weights. It is true, however, that these particles, though they may be real minima for the purposes of chemical combination, may not be the ultimate particles of the substance; and this doubt renders the hypothesis of equal weights admissible as an hypothesis.

" Part 4th, ii, § 8.

question being still afloat. This, then, is not at all a formal fallacy. Its fault lies solely in taking that for granted which is not granted. It would be petitio principii to prove to a Mohammedan the divinity of Christ from texts in the New Testament, for he does not admit the authority of the Bible; but it would be a valid argumentum ad hominem to prove to him from the Koran the prophetic mission of Jesus, for the authority of the Koran he acknowledges.

The phrase petitio principii, the unwarranted assumption of a principle, or the begging the question, is properly and specifically applied to designate this second mode of the sophism. It is not, however, to be understood as if every probation in which anything is presupposed and not proved were at once to be rejected as worthless. If so, it would be necessary in every case to ascend to the ultimate principles of human knowledge, and these themselves, being incapable of proof, might be rejected as unwarranted assumptions. Were this the meaning, there could be no probation whatever." A probation is guilty of this sophism only when a proposition which may be doubted on the ground on which the thesis itself is doubted is assumed as a principle of proof, and we thus attempt to prove the uncertain by the equally uncertain. Sound probation must depart from such principles as are either immediately given as ultimate, or mediately admit of proof from other sources than the proposition itself in question.” “It is allowed," says Aristotle, " that when assumptions are closely connected with the issue, we may deny them, and refuse them as premises, on the plea that they beg the question." "

34

Among the schoolmen this second mode of the sophism was of peculiar interest. The philosophy of their time consisted largely of certain general propositions (principia) established by authority, and supposed to be ultimately derived from intrinsic evidence. Among these tenets were the doctrines of Aristotle, which were regarded with a reverence due only to inspired Scriptures. Stultum est dicere Aristotelem errare. Others were propositions which were considered as

32 "The main principles of reason are in themselves apparent. For to make nothing evident of itself to man's understanding were to take away all possibility of knowing anything. And herein that of Theophrastus is true, 'They that seek a reason of all things do utterly overthrow reason.'”—Hooker, Eccl. Pol, i, 8, 5.

33 Hamilton's Logic, p. 371. He further observes that a saltus in probation is a special case of petitio; for, by an ellipsis of an intermediate link, we use a proposition which is actually without its proof.

34 De Soph. xvii.

having been fully established by demonstrations as rigorous as those of Euclid. None were ever questioned; except, perhaps, in rare cases, when, consequently, as in the nominalist controversy, society was shaken to its foundations by a moral earthquake. These principia, being universally admitted, were at the command of every disputant. The syllogism in Barbara had properly a principium for its sumption, and an exemplum for its subsumption. The petitio principii occurred when any one, to prove his case, made it an example under a principle which was not among those received, and which was assumed without offering to bring it under their logical empire. Thus, were one to argue from "Every being void of reason must perish" that therefore the brutes perish, it would be denounced as petitio principii, this sumption not being found among the acknowledged principia. Again, suppose one to argue that since "Entire liberty is essential to well-being and happiness," civil law, being an abridgment of liberty, is therefore detrimental and should be abolished. To this would be replied, Of course, if your major is true; but unless you offer preliminary proof, you beg the question. We may illustrate further by the reply of Cardinal Richelieu to an applicant for clemency who thought to reason the matter, saying, “Mais, monsieur, il faut vivre." Said his Grace, "Je n'en vois pas la nécessité." There is, perhaps, a breath of inhumanity in this, but logically it means that the postulate was not among the principles admitted by him as Cardinal, and that one might reasonably beg his life, but not the question.

The third mode of petitio principii assumes the particular to prove the universal. Aristotle himself seems to be guilty of this when he maintains that slavery is in accord with natural law, on the ground that the neighboring barbarians, being inferior in intellect, are the born bondsmen of the Greeks.35

The fourth and fifth modes need no special illustration. Concerning the latter, however, we will remark how easy it is to frame propositions apparently different by the use of opposed or correlative terms. For example, "Everywhere the light of life and truth was lacking, for darkness covered the land, and gross darkness the people." Again, "Alexander was the son of Philip; therefore Philip was the father of Alexander." The last example is cited by Dr. Reid as a case of "simple reasoning" for which Logic does not provide. Truly so; but, on the other hand, Logic has been careful to provide against it.

§ 6. The sixth class is Non causa pro causa (rò μù aïriov we aïTLOV TIOÉVAL). "We mistake," says Aristotle," 36 for a cause what is not a cause [meaning, a reason for what is not a reason] when an irrelevant proposition has been foisted into an argument as if it were one of the necessary premises." His example is a reductio ad impossibile to prove that "Life and the soul are not identical;" thus:

We assume that the opposite of destruction is generation;

Therefore the opposite of a particular destruction is a particular generation. But death is a particular destruction, and its opposite is life;

Life, therefore, is generation, and to live is to be generated.—This is absurd. Therefore life and the soul are not identical.-Q. E. D.

The absurd conclusion may be a proper sequence, and its absurdity justify the contradiction of a premise. But here an unexpressed premise, that "Life and the soul are identical," is mentally foisted into the train, and its contradictory stated as the Q. E. D. It is treated as if it were the cause of the absurd conclusion, which it is not, and so we have the fallacy of false cause, or non causa pro causa. Aristotle afterwards says" that to detect this fallacy we must examine whether the suppression of this premise would interrupt the sequence. If it does not, then we know that it is a superfluous proposition foisted in and treated as the cause of the absurd conclusion; and this is the fallacy in question. In the Prior Analytics, he says, "The most obvious case of the irrelevance of the thesis to the conclusion is when the thesis is not connected by any middle term with the conclusion, as was said in the Topica when discussing the sophism of non causa pro We should exemplify this if, to disprove the commensurateness of the side of the square to the diagonal, we appended an argument for Zeno's theorem that there is no such thing as locomotion, pretending thereby to establish a reductio ad absurdum." "

causa. 1

It is clear that Aristotle intended to designate by non causa pro causa the pretence that the proposition we wish to refute is the cause, in a reductio ad impossibile, of the false conclusion which in fact flows from other premises; that is, the sophism consists in maintaining that the conclusion is false because that particular premise is false. It is a case of sheer impertinence. It arises in dialectic disputation from the practice of asking the opponent to grant certain premises. An unnecessary proposition is asked and granted among the rest, and afterwards it is selected as the false assumption."

36 De Soph. v. 37 Id. ch. xxix. 38 Anal. Prior. ii, 19. "See Mansel, in notes on Aldrich, Appendix, § 4, 4.

Aristotle does not, however, limit the sophism of false cause to cases of reductio ad impossibile, but includes under it all cases wherein a conclusion is declared to exist by virtue of a premise that does not necessitate it. He himself is not guiltless of this vice. For instance, he insists that there are three kinds of simple motion, because body has three dimensions, but hardly makes it clear how the one follows from the other, i. e., gives us no middle term to connect these propositions. He would prove also that the heavens are unalterable and incorruptible, because they have a circular motion, and there is no motion contrary to circular motion. But what has the contrariety of motion to do with the corruption or alteration of body? And is not rectilinear motion contrary to circular?

This sophism has been misunderstood, or at least misstated, by perhaps all recent writers on Logic. We have already noticed several common misapprehensions, deviations from the Aristotelic sense more or less grave. In this case the error is of sufficient importance to require that the common view be set aside and the original one restored. It is needful to explain the deviation and to justify this

statement.

Let us first note a distinction drawn by the old logicians. The Causa essendi is that which determines the existence of a fact. When rain falls upon the ground, the ground is wet; the rain is the cause of the ground's being wet. The cause of there being an eclipse of the sun is that the moon interposes between it and the earth. The Causa cognoscendi is the cause of our knowing a fact. It has rained, therefore I know that the ground is wet. Here the same thing is the cause both of the existence of the fact and of my knowing the fact. But what is effect in the first sense may be cause in the other. E. g., The ground is wet, therefore I know it has rained. There is an eclipse. of the sun, hence the moon must be between it and the earth." The causa cognoscendi, then, is the logical ground; it is the cause determining, not the fact, but the judgment. This we now commonly call the reason for, or sign of, a thing, and use the word cause only in the specific sense of causa essendi."

There can be no doubt that Aristotle, in the title of the sophism under consideration, intended exclusively the causa cognoscendi, or rea

40 In this inversion, reasoning from effect to cause, we should note that we are liable to the fallacy of Plurality of Causes. An effect may be due to a variety of causes, perhaps to a cause other than any that have been observed.

"The illative "because" is still used generically.