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.
Of intuitive evidence there are different sorts. One is that which results purely from intellection.55 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 precisely the same as to say, "We give the name of 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, it the predicate of the proposition were nothing but a 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 of them 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 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, "Thirteen added to seventeen make thirty," nobody 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, I 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.
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 and 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.
The third sort is that which ariseth from what hath been termed properly enough, common sense,56 as being an original source of knowledge common to all mankind. I own, indeed, that in different persons it prevails in different degrees of strength; but no human creature hath been found originally and totallydestitute of it, who is not accounted a monster in his kind; for such, doubtless, are all idiots and changelings. By madness, a disease which makes terrible havoc on the faculties of the mind, it may be in a great measure, but is never entirely lost.
It is purely hence that we derive our assurance of such truths as these: "Whatever has a beginning has a cause"- "When there is in the effect a manifest adjustment of the several parts to a certain end, there is intelligence in the cause." "The course of nature will be the same to-morrow that it is to-day; or, the future will resemble the past"- "There is such a thing as body; or, there are material substances independent of the mind's conceptions"-"There are other intelligent beings in the universe besides me"-"The clear representations of my memory, in regard to past events, are indubitably true." These, and a great many more of the same kind, it is impossible for any man by reasoning to evince, as might easily be shown, were this a proper place for the discussion. And it is equally impossible, without a full conviction of them, to advance a single step in the acquisition of knowledge, especially in all that regards mankind, life, and conduct.
I am sensible that some of these, to men not accustomed to inquiries of this kind, will appear at first not to be primary principles, but conclusions from other principles; and some of them will be thought to coincide with the other kinds of intuition above mentioned. Thus the first, "Whatever hath a beginning hath a cause," may be thought to stand on the same footing with mathematical axioms. I acknowledge that in point of evidence they are equal, and it is alike impossible, in either case, for a rational creature to withhold his assent. Nevertheless, there is a difference in kind. All the axioms in mathematics are but the enunciations of certain properties in our abstract notions, distinctly perceived by the mind, but have no relation to any thing without themselves, and can never be made the foundation of any conclusion concerning actual existence; whereas, in the axiom last specified, from the existence of one thing we intuitively conclude the existence of another. This proposition, however, so far differs, in my apprehension, from others of the same order, that I cannot avoid considering the opposite assertion as not only false but contradictory; but I do not pretend to explain the ground of this difference.
The faith we give to memory may be thought, on a superficial view, to be resolvable into consciousness, as well as that we give to the immediate impressions of sense. But on a little attention one may easily perceive the difference. To believe the report of our senses doth indeed commonly imply to believe the existence of certain external and corporeal objects, which give rise to our particular sensations. This, I acknowledge, is a principle which doth not spring from consciousness, (for consciousness cannot extend beyond sensation,) but from common sense, as well as the assurance we have in the report of memory. But this was not intended to be included under the second branch of intuitive evidence. By that firm belief in sense, which I there resolved into consciousness, I meant no more than to say, I am certain that I see, and feel, and think, what I actually see, and feel, and think. As in this I pronounce only concerning my own present feelings, whose essence consists in being felt, and of which I am at present conscious, my conviction is reducible to this axiom, or coincident with it, "It is impossible for a thing to be and not to be at the same time." Now when I say, I trust entirely to the clear report of my memory, I mean a good deal more than, "I am certain that my memory gives such a report, or represents things in such a manner," for this conviction I have indeed from consciousness; but I mean, "I am certain that things happened heretofore at such a time, in the precise manner in which I now remember that they then happened." Thus there is a reference in the ideas of memory to former sensible impressions, to which there is nothing analogous in sensation. At the same time it is evident, that remembrance is not always accompanied with this full conviction. To describe, in words, the difference between those lively signatures of memory, which command an unlimited assent, and those fainter traces which raise opinion only, or even doubt, is perhaps impracticable; but no man stands in need of such assistance to enable him in fact to distinguish them, for the direction of his own judgment and conduct. Some may imagine that it is from experience we come to know what faith in every case is due to memory. But it will appear more fully afterwards, that unless we had implicitly relied on the distinct and vivid informations of that faculty, we could not have moved a step towards the acquisition of experience. It must, however, be admitted, that experience is of use in assisting us to judge concerning the more languid and confused suggestions of memory; or, to speak more properly, concerning the reality of those things, of which we ourselves are doubtful whether we remember them or not.
In regard to the primary truths of this order, it may be urged that it cannot be affirmed of them all at least, as it may of the axioms in mathematics, or the assurances we have from consciousness, that the denial of them implies a manifest contradiction. It is, perhaps, physically possible that the course of nature will be inverted the very next moment; that my memory is no other than a delirium, and my life a dream; that all is mere illusion; that I am the only being in the universe, and that there is no such thing as body. Nothing can bejuster than the reply given by Buffier, "It must be owned," says he,57"that to maintain propositions, the reverse of the primary truths of common sense, doth not imply a contradiction; it only implies insanity." But if any person, on account of this difference in the nature of these two classes of axioms, should not think the term intuitive so properly applied to the evidence of the last mentioned, let him denominate it, if he please, instinctive: I have no objection to the term; nor do I think it derogates in the least from the dignity, the certainty, or the importance of the truths themselves. Such instincts are no other than the oracles of eternal wisdom.
For, let it be observed further,.that axioms of this last kind areas essential to moral reasoning, to all deductions concerning life and existence, as those of the first kind are to the sciences of arithmetic and geometry. Perhaps it will appear afterwards that, without the aid of some of them, these sciences themselves would be utterly inaccessible to us. Besides, the mathematical axioms can never extend their influence beyond the precincts of abstract knowledge, in regard to number and extension, or assist us in the discovery of any matter of fact: whereas, with knowledge of the latter kind, the whole conduct and business of human life is principally and intimately connected. All reasoning necessarily supposes that there are certain principles in which we must acquiesce, and beyond which we cannot go-principles clearly discernible by their own light, which can derive no additional evidence from any thing besides. On the contrary supposition, the investigation of truth would be an endless and a fruitless task; we should be eternally proving, whilst nothing could ever be proved; because, by the hypothesis, we could never ascend to premises which require no proof. "If there be no first truths," says the author lately quoted, 58"there can be no second truths, nor third, nor indeed any truth at all."
So much for intuitive evidence, in the extensive meaning which
hath here been given to that term, as including every thing whose
evidence results from the simple contemplation of the ideas or
perceptions which form the proposition under consideration, and
requires not the intervention of any third idea as a medium of proof.
This, for order's sake, I have distributed into three classes, the
truths of pure intellection, of consciousness, and of common sense.
The first may be denominated metaphysical, the second physical, the
third moral; all of them natural, original, and unaccountable.
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