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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

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say,

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 precisely the same as to "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

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, erę we are aware, confounds our notion of the subject altogether.

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.

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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 repetition of the subject, under the same aspect, and in the same or synonimous terms, no conceivable advantage could be made of it for the furtherance of knowledge. Of such propositions as these, for instance, "Seven are 66 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 term 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 forBut 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 o

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mer.

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ther; such propositions lead to the discovery of innumerable, and apparently remote relations. One added to four may be accounted no other than a definition 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, “ Thir"teen 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 แ 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 tellection.

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PART II....Consciousness.

THE next kind is that which ariseth from consciousness. 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 hears, and the like. Hence his absolute certainty in regard to the reality of his sensations and passions, and of every thing whose essence consists in being perceived. Nor does this kind of intuition regard only the truth of the original feelings or impressions, but also many of the judgments that are formed by the mind, on comparing these one with another. Thus the judgments we daily and hourly form, concerning resemblances or disparities in visible objects, or size in things tangible, where the odds is considerable, darker or lighter tints in colours, stronger or weaker tastes or smells, are all self-evident, and discoverable at once. It is from the same principle, that in regard to ourselves we judge infallibly concerning the feelings, whether pleasant or painful, which we derive from what are called the internal senses, and pronounce concerning beauty or deformity, harmony or discord, the elegant or the ridiculous. The difference between this kind of intuition and the former, will appear on the slightest reflection. The former concerns only abstract notions or ideas, particularly in regard to number and extension, the objects

purely of the understanding; the latter concerns only the existence of the mind itself, and its actual feelings, impressions or affections, pleasures or pains, the immediate subjects of sense, taking that word in the largest acceptation. The former gives rise to those universal truths, first principles or axioms, which serve as the foundation of abstract science; whereas the latter, though absolutely essential to the individual, yet, as it only regards particular perceptions, which represent no distinct genus or species of objects, the judgments resulting thence cannot form any general positions to which a chain of reasoning may be fastened, and consequently are not of the nature of axioms, though both similar and equal in respect of evidence.

PART III....Common Sense.

THE third sort is that which ariseth from what hath been termed properly enough, common sense *, as be

* The first among the moderns who took notice of this principle as one of the genuine springs of our knowledge, was Buffier, a French philosopher of the present century, in a book intitled Traité des premiéres véritez; one who, to an uncommon degree of acuteness in matters of abstraction, added that solidity of judgment which hath prevented in him, what had proved the wreck of many great names in philosophy, his understanding becoming the dupe of his ingenuity. This doctrine hath lately, in our own country, been set in the clearest light, and supported by invincible force of argument, by two very able writers in the science of man, Dr Reid, in his Inquiry into the human mind, and Dr Beattie, in his Essay on the immutability of truth. I beg leave to remark in this place, that,

though