very awkwardly the hammer and the trowel. But it is alike incumbent on the orator to design and to execute. He must, therefore, be master of the language he speaks or writes, and must be capable of adding to grammatic purity those higher qualities of elocution, which will render his discourse graceful and energetic.

So much for the connexion that subsists between rhetoric and these parent arts, logic and grammar.

CHAP. V.

Of the different sources of Evidence, and the dif ferent Subjects to which they are respectively adapted.

LOGICAL truth consisteth in the conformity of our conceptions to their archetypes in the nature of things. This conformity is perceived by the mind, either immediately on a bare attention to the ideas. under review, or mediately by a comparison of these with other related ideas. Evidence of the former kind is called intuitive; of the latter, deductive.

SECTION I.

Of Intuitive Evidence.

PART I.-Mathematical Axioms.

OF intuitive evidence there are different sorts. One is that which results purely from intellection*. Of this kind is the evidence of these propositions, One and four make five. Things equal to the same thing are equal to one another. The whole is greater than a part;' and, in brief, all axioms in arithmetic and geometry. These are, in effect, but so many different expositions of our own general notions, taken in different views. Some of them are no other than definitions, or equivalent to definitions. To say, 'One and four make five,' is pre

* I have here adopted the term intellection rather than perception, because, though not so usual, it is both more apposite and less equivocal. Perception is employed alike to denote every immediate object of thought, or whatever is apprehended by the mind, our sensations themselves, and those qualities in body, suggested by our sensations, the ideas of these upon reflection, whether remembered or imagined, together with those called general notions, or abstract ideas. It is only the last of these kinds which are considered as peculiarly the object of the understanding, and which, therefore, require to be distinguished by a peculiar name. Obscurity arising from an uncommon word is easily surmounted, whereas ambiguity, by misleading us, ere we are aware, confounds our notion of the subject altogether.

6

cisely the same as to say, We give the name five ' to one added to four.' In fact, they are all, in some respect, reducible to this axiom, Whatever ' is, is.' I do not say they are deduced from it, for they have in like manner that original and intrinsic evidence, which makes them, as soon as the terms are understood, to be perceived intuitively. And if they are not thus perceived, no deduction of reason will ever confer on them any additional evidence. Nay, in point of time, the discovery of the less general truths has the priority, not from their superior evidence, but solely from this consideration, that the less general are sooner objects of perception to us, the natural progress of the mind in the acquisition of its ideas, being from particular things to universal notions, and not inversely. But I affirm, that, though not deduced from that axiom, they may be considered as particular exemplifications of it, and coincident with it, inasmuch as they are all implied in this, that the properties of our clear and adequate ideas can be no other than what the mind clearly perceives them to be.

But, in order to prevent mistakes, it will be necessary further to illustrate this subject. It might be thought, that if axioms were propositions perfectly identical, it would be impossible to advance a step, by their means, beyond the simple ideas first perceived by the mind. And it must be owned, if the predicate of the proposition were nothing but a

6

repetition of the subject, under the same aspect, and in the same or synonymous terms, no conceivable advantage could be made of it for the furtherance of knowledge. Of such propositions as these, for instance, Seven are seven,' eight are eight,' and 'ten added to eleven, are equal to ten added to eleven,' it is manifest, that we could never avail ourselves for the improvement of science. Nor does the change of the name make any alteration in point of utility. The propositions Twelve are a dozen,'' twenty are a score,' unless considered as explications of the words dozen and score, are equally insignificant with the former. But when the thing, though in effect coinciding, is considered under a different aspect; when what is single in the subject, is divided in the predicate, and conversely; or when what is a whole in the one, is regarded as a part of something else in the other; such propositions lead to the discovery of innumerable, and apparently remote relations. One added to four may be accounted no other than a defi nition of the word five, as was remarked above. But when I say, Two added to three are equal to "five,' I advance a truth, which, though equally clear, is quite distinct from the preceding. Thus, if one should affirm, Twice fifteen make thirty," and again, Thirteen added to seventeen make thirty,' no body would pretend that he had repeated the same proposition in other words. The

cases are entirely similar. In both, the same thing is predicated of ideas which, taken severally, are different. From these again result other equations, as, One added to four are equal to two added to 'three,' and 'twice fifteen are equal to thirteen added to seventeen.'

Now it is by the aid of such simple and elementary principles, that the arithmetician and the algebraist proceed to the most astonishing discoveries. Nor are the operations of the geometrician essentially different. By a very few steps you are made to perceive the equality, or rather the coincidence of the sum of the two angles, formed by one straight line falling on another, with two right angles. By a process equally plain, you are brought to discover, first, that if one side of a triangle be produced, the external angle will be equal to both the internal and opposite angles, and then, that all the angles of a triangle are equal to two right angles. So much for the nature and use of the first kind of intuitive evidence, resulting from pure intellection.

PART II.-Consciousness.

THE next kind is that which ariseth from con sciousness. Hence every man derives the perfect assurance that he hath of his own existence. Nor is he only in this way assured that he exists, but that he thinks, that he feels, that he sees, that he