relating to Natural Philosophy, assumes many different shapes, and in some of them does not possess the same absolute certainty as in others; e. g. when, from having always observed a certain sheep ruminating, we infer that this individual sheep will continue to ruminate, we assume that "the property which has hitherto belonged to this sheep will remain unchanged;" when we infer the same property of all sheep, we assume that "the property which belongs to this individual belongs to the whole species:" if, on comparing sheep with some other kinds of horned animals, and finding that all agree in ruminating, we infer that "all horned animals ruminate," we assume that "the whole of a genus or class are likely to agree in any point wherein many species of that genus agree; " or in other words, " that if one of two properties, &c. has often been found accompanied by another, and never without it, the former will be universally accompanied by the latter: " now all these are merely different forms of the maxim, that "nature is uniform in her operations," which, it is evident, varies in expression in almost every different case where it is applied, and admits of every degree of evidence, from absolute moral certainty, to mere conjecture.

The same may be said of an infinite number of principles and maxims appropriated to, and employed in, each particular branch of study. Hence, all such Reasonings are, in comparison of Mathematics, very complex; requiring so much more than that does, beyond the process of merely deducing the conclusion Logically from the Premises so that it is no wonder that the longest Mathematical demonstration should be so much more easily constructed and understood, than a much shorter train of

just Reasoning concerning real facts. The former has been aptly compared to a long and steep, but even and regular flight of steps, which tries the breath, and the strength, and the perseverance only; while the latter resembles a short, but rugged and uneven, ascent up a precipice, which requires a quick eye, agile limbs, and a firm step; and in which we have to tread now on this side, now on that-ever considering, as we proceed, whether this or that projection will afford room for our foot, or whether some loose stone may not slide from under us. There are probably as many steps of pure Reasoning in one of the longer of Eucl d's demonstrations, as in the whole of an argumentative treatise on some other subject, occupying perhaps a considerable volume.

As for those Ethical and Legal Reasonings which were lately mentioned as in some respects resembling those of Mathematics, (viz. such as keep clear of all assertions respecting facts,) they have this difference; that not only men are not so completely agreed respecting the maxims and principles of Ethics and Law, but the meaning also of each term cannot be absolutely, and for ever, fixed by an arbitrary definition; on the contrary, a great part of our labor consists in distinguishing accurately the various senses in which men employ each term, ascertaining. which is the most proper, and taking care to avoid confounding them together.

CHAP. III.

Of Inference and Proof.

§ 1.

SINCE it appears, from what has been said, that universally a man must possess something else besides the Reasoning-faculty, in order to apply that faculty properly to his own purpose, whatever that purpose may be ; it may be inquired whether some theory could not be made out, respecting those "other operations" and "intellectual processes, distinct from Reasoning, which it is necessary for us sometimes to employ in the investigation of truth; and whether rules could not be laid down for conducting them.

Reasoning.

Something has, indeed, been done in this Different Apway by more than one writer; and more might plications of probably be accomplished by one who should fully comprehend and carefully bear in mind the principles of Logic, properly so called; but it would hardly be possible to build up any thing like a regular Science respecting these matters, such as Logic is, with respect to the theory of Reasoning. It may be useful, however, to observe, that these "other operations" of which we have been speaking, and which are preparatory to the exercise of Reasoning, are of two kinds, according to the nature of the end proposed; for Reasoning comprehends Inferring and Proving; which are not two different things, but the same thing regarded in two different points of

* D. Stewart,

view: like the road from London to York, and the road from York to London. He who infers,* proves; and he who proves, infers; but the word "infer" fixes the mind first on the Premiss, and then on the Conclusion; the word "prove," on the contrary, leads the mind from the conclusion to the Premiss. Hence, the substantives derived from these words respectively, are often used to express that which, on each occasion, is last in the mind; Inference being often used to signify the Conclusion, (i. e. Proposition inferred,) and Proof, the Premiss. We say, also, "How do you prove that?" and "What do you infer from that?" which sentences would not be so properly expressed if we were to transpose those verbs. One might, therefore, define Proving, "the assigning of a reason or argument for the support of a given proposition ;" and Inferring, "the deduction of a Conclusion from given Premises." In the one case our Conclusion is given, (i. e. set before us,) and we have to seek for arguments; in the other, our Premises are given, and we have to seek for a Conclusion: i. e. to put together our own propositions, and try what will follow from them; or, to speak more Logically, in the one case, we seek to refer the Subject of which we would predicate something, to a class to which that Predicate will (affirmatively or negatively) apply; in the other, we seek to find comprehended, in the Subject of which we have predicated something, some other term to which that Predicate had not been before applied. Each of these is a definition of Reasoning.

* I mean, of course, when the word is understood to imply correct Inference.

"Proving" may be compared to the act of putting away

§ 2.

Investigator and Advo

To infer, then, is the business of the Philosopher; to prove, of the Advocate; the former, cate. from the great mass of known and admitted truths, wishes to elicit any valuable additional truth whatever, that has been hitherto unperceived; and perhaps, without knowing, with certainty, what will be the terms of his Conclusion. Thus the Mathematician, e. g. seeks to ascertain what is the ratio of circles to each other, or what is the line whose square will be equal to a given circle; the Advocate, on the other hand, has a Proposition put before him, which he is to maintain as well as he can : his business, therefore, is to find middle terms (which is the inventio of Cicero); the Philosopher's, to combine and select known facts, or principles, suitably, for gaining. from them Conclusions which, though implied in the Premises, were before unperceived: in other words, for making Logical Discoveries."

6.6

To put the same thing in another point of view, we may consider all questions as falling under two classes; viz. "What shall be predicated of a certain Subject; and which Copula, affirmative or negative, shall connect a certain Subject and Predicate: we inquire, in short, either, 1st, "What is A?" or, 2d, "Is A, B, or is it not?" The former class of questions belongs to the Philosopher; the latter to the Advocate.* (See Rhet. Appendix G. p. 387.)

any article into the proper receptacle of goods of that description; "inferring," to that of bringing out the article when needed.

* The distinction between these two classes of questions is perhaps best illustrated by reference to some case in which our