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for doubt concerning either. On the other hand, in all Reasonings which regard matters of fact, we introduce, almost at every step, fresh and fresh propositions (to a very great number) which had not been elicited in the course of our Reasoning, but are taken for granted; viz. facts and laws of Nature, which are here the principles of our Reasoning, and maxims, or “elements of belief,” which answer to the axioms in Mathematics. If, at the opening of a Treatise, for example, on Chemistry, on Agriculture, on Political Economy, &c. the author should make, as in Mathematics, a formal statement of all the
propositions he intended to assume, as granted throughout the whole work, both he and his readers would be astonished at the number;
and, of these, many would be only probable, - and there would be much room for doubt as
to the degree of probability, and for judgment, in ascertaining that degree.
Moreover, Mathematical axioms are always employed precisely in the same simple form; e. g. the axiom that “
things equal to the same are equal to one another,” is cited, whenever there is need, in those very words ; whereas the maxims employed in the other class of subjects, admit of, and require, continual modifications in the application of
“ the stability of the laws of
them : e. g.
Nature,” which is our constant assumption in inquiries 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
There are probably as many steps of pure Reasoning in one of the longer of Eu> clid'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 labour 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.
Of Inference and Proof.
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.
Something has, indeed, been done in this different Apway by more than one writer; and more might Reasening. 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 anything 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 Rea-X soning comprehends Inferring and Proving ;
which are not two different things, but the
and the road from York to London. He Х
who infers,p proves; and he who proves, infers; but the word “infer” fixes the mind
* D. Stewart.
+ I mean, of course, when the word is understood to imply correct Inference.