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this confideration, that the lefs general are fooner objects of perception to us, the natural progress of the mind in the acquifition of its ideas, being from particular things to univerfal notions, and not inverfely. But I affirm, that, though not deduced from that axiom, they may be confidered as particular exemplifications of it, and coincident with it, inafmuch 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 neceffary further to illuftrate this fubject. It might be thought, that if axioms were propofitions perfectly identical, it would be impoffible to advance a step, by their means, beyond the fimple ideas first perceived by the mind. And it must be owned, if the predicate of the propofition were nothing but a repetition of the fubject, under the fame afpect, and in the fame or fynonymous terms, no conceivable advantagè could be made of. it for the furtherance of knowledge. Of fuch propofitions as thefe, for inftance, Seven are feven,' eight are eight,' and ten added to eleven, are equal to ten added

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to eleven,' it is manifeft, that we could never

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avail ourselves for the improvement of science. Nor does the change of the term make any alteration in point of utility. The propofitions • Twelve are a dozen,' twenty are a fcore,' unless confidered as explications of the words dozen and score, are equally infignificant with the former. But when the thing, though in effect coinciding, is confidered under a different afpect; when what is fingle 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 fomething else in the other; fuch propofitions 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 fay, Two added to three are equal to 'five,' I advance a truth, which, though equally clear, is quite diftinct from the preceding. Thus, if one thould affirm, Twice fifteen make

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thirty,' and again, Thirteen added to seventeen make thirty,' no body would pretend that he had repeated the fame propofition in other words. The cafes are entirely fimilar. In both, the fame thing is predicated of ideas which, taken severally, are different. From these again refult other equations, as, One added to four

' are

are equal to two added to three,' and 'twice fifteen are equal to thirteen added to feventeen.'

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Now it is by the aid of fuch fimple and elementary principles, that the arithmetician and the algebraist proceed to the most astonishing difcoveries. 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 fum of the two angles, formed by one ftraight line falling on another, with two right angles. By a process equally plain, you are brought to difcover, firft, that if one fide of a triangle be produced, the external angle will be equal to both the internal and oppofite angles, and then, that all the angles of a triangle are equal to two right angles. So much for the nature and ufe of the first kind of intuitive evidence, refulting from pure intellection.

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THE next kind is that which arifeth from confcioufnefs. Hence every man derives the perfect affurance that he hath of his own exiftence. Nor is he only in this way affured that he exifts, put that he thinks, that he feels, that he sees, that

he

Hence his abfolute cerreality of his fenfations

he hears, and the like. tainty in regard to the and paffions, and of every thing whose effence confifts in being perceived. Nor does this kind of intuition regard only the truth of the original feelings or impreffions, 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 vifible objects, or fize in things tangible, where the odds is confiderable, darker or lighter tints in colours, ftronger or weaker tastes or smells, are all felfevident, and difcoverable at once. It is from the fame 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 fenfes, and pronounce concerning beauty or deformity, harmony or difcord, the elegant or the ridiculous. The difference between this kind of intuition and the former, will appear on the flightest reflection. The former concerns only abftract notions or ideas, particularly in regard to number and extenfion, the objects purely of the understanding; the latter concerns only the existence of the mind itself, and its actual feel

ings, impreffions or affections, pleasures or pains, the immediate fubjects of fenfe, taking that word in the largest acceptation. The former gives rise to those univerfal, truths, first principles or axioms, which ferve as the foundation of abftract fcience; whereas the latter, though abfolutely effential to the individual, yet, as it only regards particular perceptions, which represent no distinct genus or fpecies of objects, the judgments refulting thence cannot form any general pofitions to which a chain of reafoning may be faftened, and confequently are not of the nature of axioms, though both fimilar and equal in refpect of evidence.

PART III. Common fenfe.

THE third fort is that which arifeth from what hath been termed properly enough, common fenfe, as being an original fource of know

ledge

+ The first among the moderns who took notice of this prin. ciple as one of the genuine fprings of our knowledge, was Buffier, a French philofopher of the prefent 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 philofophy, his underftanding becoming the dupe of his ingenuity. This doctrine hath lately, in our own country, been fet in the cleareft light, and

fupported

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