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appears certain, namely, "That all mathe66 matical truth is founded in certain first principles which common sense, or inftinct, or the conftitution of the human understanding, or the law of rational nature, compels us to believe without proof, "whether we will or not."

Nor would the foundation of mathematics be in the leaft degree more ftable, if these axioms did admit of proof, or were all refolvable into one primary axiom expreffed by an identical propofition. As the cafe now ftands, we are abfolutely certain of their truth; and abfolute certainty is all that demonftration can produce. We are convinced by a proof, because our conftitution is fuch, that we must be convinced by it and we believe a felf-evident axiom, because our constitution is fuch, that we must believe it. You afk, why I believe what is felf-evident? I may as well afk, why you believe what is proved? Neither question admits . of an answer; or rather, to both questions the answer is the fame, namely, Because I muft believe it.

Whether our belief in these cafes be agreeable to the eternal relations and fitneffes of things, and fuch as we fhould entertain if we were perfectly acquainted with all the laws of Nature, is a queftion which no perfon of a found mind can have any fcruple to anfwer, with the fulleft affurance, in the affirmative. Certain it is, our conftitution is

fo framed, that we must believe to be true, and conformable to univerfal nature, that which is intimated to us, as fuch, by the original fuggeftions of our own understanding. If these are fallacious, it is the Deity who makes them fo; and therefore we can never rectify, or even detect, the fallacy. But we cannot even fuppofe them fallacious, without violating our nature; nor, if we acknowledge a God, without impiety; for in this fuppofition it is implied, that we fuppose the Deity a deceiver. Nor can we, confiftently with fuch a fuppofition, acknowledge any distinction between truth and falfehood, or believe that one inch is lefs than ten thousand miles, or even that we ourselves exist.

I am inclined to think, though I have not as yet fo thoroughly examined the notion as to be able to prove it, that all mathematical truth is refolvable into identical propofitions. But yet I do not fee, that there is any impropriety in saying, (according to my ufe of the terms), that mathematical truth rests on certain principles (or fome one principle) of common fenfe, which the law of our nature (or of rational nature) determines us to believe. For, might we not have been fo framed, as not to perceive the coincidence of the predicate, with the fubject, of an identical propofition? And if fo, is not our power of perceiving that coincidence a part of the constitution of our nature? All beVOL. I.

G

ings

ings endued with reafon have this power as well as we; for we cannot conceive understanding or reason to be, where this power is not. But the existence of rational creatures is an effect of that constitution of things, which the good providence of God has been pleased to establish *.

SECT. II.

Of the evidence of External Senfe.

Another clafs of truths producing convic

tion, and abfolute certainty, are thofe which depend upon the evidence of the external fenfes; Hearing, Seeing, Touching, Tafting, and Smelling. On this evidence is founded all our knowledge of external or material things; and therefore all conclufions in Natural Philofophy, and all those prudential confiderations which regard the preservation of our body, as it is liable to be affected by the fenfible qualities of matter, must finally be refolved into this principle, That things are as our fenfes reprefent them. When I touch a stone, I am confcious of a certain fenfation, which I call a fenfation of hardness. But this fenfation is not hardness itself, nor

*See part 2. chap. 1. fect. 3.

any

I.:

as

er

ver

any thing like hardness: it is nothing more
than a sensation or feeling in my mind; ac-
companied, however, with an irresistible be-
lief, that this fenfation is excited by the ap-
plication of an external and hard fubftance
to a certain part of my body. This belief as
certainly accompanies the fenfation, as the
fenfation accompanies the application of the
ftone to my organ of fenfe. 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 confcious of,
the fenfation of hardness; or, to speak more
ftrictly, the fenfation which by experience I
know to be the fign of my touching a hard
body *. Now, why do I believe that this
fenfation is a real fenfation, and really felt by
me? Because
Because my conftitution is fuch that I
must believe fo. And why do I believe, in
confequence of my receiving this fenfation,
that I touch an external object, really exist-
ing, material, and hard? The answer is
the fame: the matter is incapable of proof:
I believe, because I muft believe. Can I a-
void believing, that I really am conscious of
receiving this fenfation? No. 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 feel-
ing or fenfation in my mind? No; I must

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

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Nor

believe this, whether I will or not. could I diveft myself of this belief, though my life and future happiness depended on the confequence. To believe our fenfes, therefore, is according to the law of our nature; and we are prompted to this belief by instinct, or common fenfe. I am as certain, that at prefent I am in a house, and not in the open air; that I fee by the light of the fun, 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 demonftrated conclufion; 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 affuredly, that I do exist, and that there is a real material fun, and a real material world, with mountains, trees, houses, and animals, existing separately, and independently on me and my faculties; I fay, I know all this with as much affurance of conviction, as the moft irrefragable demonftration could produce. Is it unreafonable to believe in these cafes without proof? Then, I affirm, it is equally unreasonable to believe in any cafe with proof. Our belief in either cafe is unavoidable, and according to the law of our nature; and if it be unreafonable to think according to the law of our

nature,

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