the test of the senses, by laying a few halfpence and farthings upon the table; but the evidence of sense is not more unquestionable, than that of abstract intuitive truth; and therefore the former evidence, though to one ignorant of the meaning of the terms, it might serve to explain and illustrate the latter, can never prove it. But not to rest any thing on the signification we affix to the word proof, and to remove every possibility of doubt as to this matter, let us suppose, that the evidence of external sense is more unquestionable than that of abstract intuitive truth, and that every intuitive principle in mathematics may thus be brought to the test of sense; and if we cannot call the evidence of sense à proof, let us call it a confirmation of the abstract principle: yet what do we gain by this method of illustration? We only discover, that the evidence of abstract intuitive truth is resolvable into, or may be illustrated by, the evidence of sense. it will be seen in the next section, that we believe in the evidence of external sense, not because we can prove it to be true, but because the law of our nature determines us to believe in it without proof. So that in whatever way we view this subject, the point we mean to illustrate appears certain, namely, "That all "mathematical truth is founded in certain first principles, which common sense, or instinct, compels us "to believe without proof, whether we will or not."

And

Nor would the foundation of mathematics be in the least degree more stable, if these axioms did admit of proof, or were all resolvable into one primary axiom expressed by an identical proposition. As the case now stands, we are absolutely certain of their truth; and absolute certainty is all that demonstration can produce. We are 'convinced by a proof, because our

constitution is such, that we must be convinced by it: and we believe a self-evident axiom, because our constitution is such, that we must believe it. You ask, why I believe what is self-evident. I may as well ask, why you believe what is proved. Neither question admits of an answer; or rather, to both questions, the answer is the same, namely, Because I must believe it.

Whether our belief in these cases be agreeable to the eternal relations and fitnesses of things, and such as we should entertain if we were perfectly acquainted with all the laws of nature, is a question which no person of a sound mind can have any scruple to answer, with the fullest assurance, in the affirmative, Certain it is, our constitution is so framed, that we must believe to be true, and conformable to universal nature, that which is intimated to us, as such, by the original suggestions of our own understanding. If these are fallacious, it is the Deity who makes them so; and therefore we can never rectify, or even detect the fallacy. But we cannot even suppose them fallacious, without violating our nature; nor, if we acknowledge a God, without the most absurd and most audacious impiety; for in this supposition it is implied that we suppose the Deity a deceiver, Nor can we, consistently with such a supposition, acknowledge any distinction between truth and falsehood, or believe that one inch is less than ten thousand miles, or even that we ourselves exist.

SECT. II.

Of the Evidence of External Sense.

NOTHER class of truths producing conviction,

A are

and absolute certainty, are those which depend

upon the evidence of the external senses; Hearing, Seeing, Touching, Tasting, and Smelling. On this evidence is founded all our knowledge of external or material things; and therefore all conclusions in Natural Philosophy, and all those prudential considerations which regard the Preservation of our body, as it is liable to be affected by the sensible qualities of matter, must finally be resolved into this principle, That things are as our senses represent them. When I touch a stone, I am conscious of a certain sensation, which I call a sensation of hardness. But this sensation is not hardness itself, nor any thing like hardness: it is nothing more than a sensation or feeling in my mind; accompanied, however, with an irresistable belief, that this sensation is excited by the application of an external and hard substance to some part of my body. This belief as certainly accompanies the sensation, as the sensation accompanies the application of the stone to my organ of sense. I believe, with as much assurance, and as unavoidably, that the external thing exists, and is hard, as I believe that I receive and am conscious of the sensation of hardness; or, to speak more strictly, the sensation which by experience I know to be the sign of my touching a hard body. Now, why do I believe that this sensation is a real sensation, and really felt by me? Because my constitution is such that I must believe so. And why do I believe, in consequence of my receiving this sensation, that I touch an external object, really existing, material, and hard? The answer is the same: the matter is incapable of proof: I believe, because I must believe. Can I avoid believing, that I really am conscious of receiving this sensation? No.

* See Dr Reid's Inquiry into the human mind, chap. 5. sect. 3.

Can I avoid believing, that the external thing exists, and has a certain quality, which fits it, on being applied to my hand, to excite a certain feeling or sensation in my mind? No; I must believe this, whether I will or not. Nor could I divest myself of this belief, though my life and future happiness depended on the consequence. -To believe our senses, therefore, is according to the law of our nature; and we are prompted to this belief by instinct, or common sense. I am as certain, that at present I am in a house, and not in the open air; that I see by the light of the sun, and not by the light of a candle; that I feel the ground hard under my feet; and that I lean against a real material table,— as I can be of the truth of any geometrical axiom, or of any demonstrated conclusion; nay, I am as certain of all this as of my own existence. But I cannot prove by argument, that there is such a thing as matter in the world, or even that I myself exist: and yet I know as assuredly, that I do exist, and that there is a real material sun, and a real material world, with mountains, trees, houses, and animals, existing separately, and independently on me and my faculties; I say, I know all this with as much assurance of conviction, as the most irrefragable demonstration could produce. Is it unreasonable to believe in these cases without proof? Then, I affirm, it is equally unreasonable to believe in any case, with proof. Our belief in either case is unavoidable, and according to the law of our nature; and if it be unreasonable to think, according to the law of our nature, it must be equally unreasonable to adhere to the earth, to be nourished with food, or to die when the head is separated from the body. It is indeed easy to affirm any thing, provided a man can reconcile himself to hypocrisy and

falsehood. A man may affirm, that he sees with thẻ soles of his feet, that he believes there is no material world, that he doubts of his own existence. He may as well say, that he believes one and two to be equal to six, a part to be greater than a whole, a circle to be a triangle; and that it may be possible for the same thing, at the same time, to be and not to be.

But it is said, that our senses do often impose upon us; and that by means of reason we are enabled to detect the imposture, and to judge rightly even where our senses give us wrong information; that therefore our belief in the evidence of sense is not instinctive or intuitive, but such as may be either confuted or confirmed by reasoning. We shall acknowledge that our senses do often impose upon us: but a little attention will convince us, that reason, though it may be employed in correcting the present fallacious sensation, by referring it to a former sensation, received by us, or by other men, is not the ultimate judge in this matter; for that all such reasoning is resolvable into this principle of common sense, That things are what our external senses represent them. One instance will suffice at present for illustration of this point *.

After having looked a moment at the sun, I see a black, or perhaps a luminous, circle swimming in the air, apparently at the distance of two or three feet from my eyes. That I see such a circle, is certain ; that I believe I see it, is certain; that I believe its appearance to be owing to some cause, is also certain

thus far there can be no imposture, and there is no supposition of any. Suppose me from this appearance to conclude, that a real, solid, tangible, or visible. round substance, of a black or yellow colour, is ac

*See part 2. chap. 1. sect. 2.

F