that this man is fallible because he is fallible, which is certainly demonstrative enough.

A. Of course the reason really meant to be assigned is, that all other men, as far as observation has extended, have been found to be fallible.

B. That is to say, all men, excluding this man, have been found to be fallible, therefore this excluded man is fallible. Now this is a good material or contingent reason, but it is not a demonstratively conclusive one. In the case of every demonstrated truth, the opposite or negative proposition would be a contradiction in terms. That this man is not fallible would be a contradiction to the proposition that all men are fallible, but not to the proposition that all other men are fallible. Thus, if you include this man you beg the question: if you do not include him your reason is a material or contingent one, very highly probable, engendering almost complete certainty, but not demonstratively conclusive.

What has been said in this chapter may appear on a first glance to correspond with the wellknown distinction made by Aristotle between demonstrative and dialectical syllogisms; but there is a fundamental difference, which it may be well His words are," The syllogism is a form of language in which certain things being laid down, another thing different from those laid down necessarily results from them. Now demonstration takes place when a conclusion is drawn from

to note.

things true and primary, or from those of which the knowledge has been derived from the true and primary. But in a dialectical syllogism, the conclusion is drawn from probable things. The true and primary are such things as are believed of themselves, and not on account of other things: for it behoves not that in the principles of a science the reason why should be sought for, but every principle should be certain in itself."

This is in truth merely saying that when the premises are only probable, the conclusion will be so too, and giving the appellation of dialectical to syllogisms in which they occur.

* Ἔστι δὴ συλλογισμὸς λόγος ἐν ᾧ τεθέντων τινῶν ἑτερόν τι τῶν κειμένων, ἐξ ἀνάγκης συμβαίνει διὰ τῶν κειμένων. Απόδειξις μὲν οὖν ἐστίν, ὅταν ἐξ ἀληθῶν καὶ πρώτων ὁ συλλογισμὸς ᾖ, ἢ ἐκ τοιούτων ἃ διά τινων πρώτων καὶ ἀληθῶν τῆς περὶ αὐτὰ γνώσεως τὴν ἀρχὴν εἴληφεν· διαλεκτικὸς δὲ συλλογισμὸς ὁ ἐξ ἐνδόξων συλλογιζόμενος. ̓́Εστι δὲ ἀληθῆ μὲν καὶ πρῶτα τὰ μὴ δι' ἑτέρων ἀλλὰ δι' αὑτῶν ἔχοντα τὴν πίστιν· οὐ δεῖ γὰρ ἐν ταῖς ἐπιστημο νικαῖς ἀρχαῖς ἐπιζητεῖσθαι τὸ διὰ τί, ἀλλ ̓ ἑκάστην τῶν ἀρχῶν αὐτὴν καθ' ἑαυτὴν εἶναι πιστήν. — Topicorum lib. i. cap. 1.

The same point is thus explained by Wallis.

“Syllogismus Topicus (qui et Dialecticus dici solet, et Didascalicus) talis haberi solet syllogismus (seu syllogismorum series) qui firmam potius præsumptionem, seu opinionem valdè probabilem creat, quam absolutam certitudinem. Non quidem ratione forma (nam syllogismi omnes, si in justa forma, sunt demonstrativi ; hoc est, si præmissa vera sint, vera erit et conclusio), sed ratione materia seu præmissarum; quæ ipsæ, ut plurimum, non sunt absolute certæ et universaliter veræ; sed saltem probabiles, atque ut plurimum veræ."-Institutio Logica, lib. iii. cap. 23.

But this is not all that is maintained in the present chapter, nor even the material part of it.

My doctrine is, that all such reasoning as consists in inferring unobserved facts from general propositions, although strictly demonstrative in form, is in reality contingent, how certain and indisputable soever the general propositions may be; and that it is represented by the formula,

All other men have been found fallible;
Therefore this man (whose fallibility has never

been observed) is fallible.

According to my view, consequently, many syllogisms would rank in the class of arguments demonstrative in form but contingent in reality, besides those which, in the popular use of the term probable, have only probable premises. If I understand Aristotle aright, the latter alone would fall under his denomination of dialectical.

It has been well observed by Mr. Stewart in reference to this distinction in the first book of the Topics, that there is an impropriety in such an employment of the epithets demonstrative and dialectical, inasmuch as it implies, or seems to imply, that one species of syllogism may be more conclusive and cogent than another*, which is at variance with Aristotle's own doctrine in other places, and of course was not intended here.

* Elements of the Philosophy of the Human Mind, vol. ii. p. 262. 8vo. ed.

CHAP. V.

THE INTERMIXTURE OF CONTINGENT AND DEMONSTRATIVE REASONING.

It seems necessary, in order to complete our survey of the two great divisions of the subject, to advert more particularly to a circumstance already indicated in some of the examples introduced into the preceding exposition; viz. that demonstrative reasoning, even when non-syllogistic, is by no means confined to mathematics or the science of quantity; but it is perpetually intermixed with contingent reasoning on matters of a moral or a physical nature.

This might be exemplified by a thousand instances in common life. Take, for example, the course pursued by an advocate in defending his client from a criminal accusation. If he relies, as he is sometimes compelled to do, upon testimony to his client's character, the argument is purely contingent he attempts to establish the moral excellence of the man, and then infers that a person of such estimable qualities would not be likely to commit the offence of which he is accused. But if, instead of this, he endeavours to prove an alibi, the logical procedure is altered. The crime (we will suppose) was committed in London, and he

produces several credible witnesses who swear, that at the very moment when the deed was perpetrated, they saw the accused in Edinburgh. In this hypothetical case, the reasoning of the defence is mixed. When from the number, and respectability, and concurrence of the witnesses the advocate infers that their testimony is true, he employs a contingent argument; but when he proceeds further, and concludes from the attested fact of his client's being in Edinburgh that he could not have committed a crime at the same moment in London, this step in the reasoning is demonstrative.

We may observe a similar intermixture of reasoning on very various occasions, and, amongst the rest, on the common occasion of making indirect comparisons between objects and qualities of all kinds.

If two substances, for example, which could not be brought into juxtaposition, are attested to have been successively compared with a third substance and found to be respectively of the same colour with it, we conclude that they agree in colour with each other.

In this case, while the inference that the two mutually unapproachable substances are each of the same colour with the third (resting as it does on testimony) is contingent, the conclusion that therefore the two former substances resemble each

other in colour, is necessary. A demonstrated conclusion, however, from a premise which has been obtained by contingent reasoning, must itself