most strange, that supposing her fallacious, we should think ourselves capable of detecting the cheat. Common sense tells me, that the ground on which I stand is hard, material, and solid, and has a real, separate, independent, existence. BERKELEY and HUME tell me, that I am imposed upon in this matter for that the ground under my feet is really an idea in my mind; that its very essence consists in being perceived; and that the same instant it ceases to be perceived, it must also cease to exist in a word, that to be, and to be perceived, when predicated of the ground, the sun, the starry heavens, or any coporeal object, signify precisely the same thing. Now if my com. mon sense be mistaken, who shall ascertain and correct the mistake? Our reason it is said. Are then the inferences of reason in this instance clearer, and more decisive, than the dictates of common sense? By no means; I still trust to my common sense as before and I feel that I must do so. But supposing the inferences of the one faculty as clear and decisive as the dictates of the other, yet who will assure me, that my reason is less liable to mistake than my com mon sense? and if reason be mistaken, what shall we say ? Is this mistake to be rectified by a second reasoning, as liable to mistake as the first ?-In a word, we must deny the distinction between truth and falsehood, adopt universal scepticism, and wan der without end from one maze of error and uncertainty to another; a state of mind so miserable, that Milton makes it one of the torments of the damned

or else we must suppose, that one of these faculties is naturally of higher authority than the other; and that either reason ought to submit to common sense, or common sense to reason, whenever a variance happens between them.

It has been said, that every inquiry in philosophy ought to begin with doubt;-that nothing is to be taken for granted, and nothing believed, without proof. If this be admitted, it must also be admitted, that reason is the ultimate judge of truth, to which common sense must continually act in subordination. But this I cannot admit; because I am able to prove the contrary by the most incontestable evidence. I am able to prove, that "except we believe many things without proof, we never can believe any thing at all; for that all sound reasoning must ultimately rest on the principles of common sense; "that is, on principles intuitively certain, or intuitively probable; and, consequently, that common "sense is the ultimate judge of truth, to which rea"son must continually act in subordination."-This I shall prove by a fair induction of particulars.

CHA P. II.

All reasoning terminates in first principles. All evidence ultimately intuitive. Common Sense the Standard of Truth to Man.

N this induction, we cannot comprehend all sorts

of evidence, and modes of reasoning; but we shall endeavour to investigate the origin of those *

That the induction here given is sufficiently comprehensive, will appear from the following analysis.

All the objects of the human understanding may be reduced to two classes, viz. Abstract Ideas, and Things really existing.

Of Abstract Ideas, and their Relations, all our knowledge is certain being founded on MATHEMATICAL EVIDENCE (a); which compre hends, 1. Intuitive Evidence; and, 2. The Evidence of strict de. monstration.

(a) Sect. 1.
E

which are the most important, and of the most extensive influence in science, and common life; beginning with the simplest and clearest, and advancing gradually to those which are more complicated, or less perspicuous.

TH

SECTION I

Of Mathematical Reasoning.

pure

HE evidence that takes place in mathematics, produces the highest assurance and certainty in the mind of him who attends to, and understands it; for no principles are admitted into this science, but such as are either self-evident, or susceptible of demonstration. Should a man refuse to believe a demonstrated conclusion, the world would impute his obstinacy either to want of understanding, or to want of honesty for every person of understanding feels, that by mathematical demonstration he must be

We judge of Things really existing; either, I. From our own experience; or, 2. From the experience of other men.

1. Judging of Real Existences from our own experience, we attain either Certainty, or Probability. Our knowledge is certain when supported by the evidence, 1. Of SENSE EXTERNAL (b) and INTERNAL (c). 2. Of MEMORY (d); and, 3. Of Legitimate Inferences of THE CAUSE from the Erfect (e).————Our knowledge is probable, when, from facts already experienced, we argue, 1. to facts or THE SAME KIND (ƒ) not experienced; and, 2. to facts OF A SEMILAR KIND (g) not experienced. This knowledge, though called probable, often rises to moral certainty.

2. Judging of Real Existences from the experience of other men, we have the EVIDENCE OF THEIR TESTIMONY (h). The mode of understanding produced by that evidence is properly called Faith; and this faith sometimes amounts to probable opinion, and sometimes rises even to absolute certainty.

(1) Sect. 2.
(f) Sect. 6.

(+) Sect. 8.

(d) Sect. 4.

(g) Sect. 7.

(Sect. 5. (b) Sect. 8.

There are two

convinced whether he will or not. kinds of mathematical demonstration. The first is called direct; and takes place, when a conclusion is inferred from premises that render it necessarily true: and this perhaps is a more perfect, or at least a simpler kind of proof, than the other; but both are equally convincing. The other kind is called indirect, apagogical, or ducens ad absurdum; and takes place when by supposing a proposition false, we are led into an absurdity, which there is no other way to avoid, than by supposing the proposition true. In this manner it is proved, that the proposition is not, and cannot be false; in other words, that it is a certain truth. Every step in a mathematical proof either is self-evident, or must have been formerly demonstrated; and every demonstration does finally resolve itself into intuitive or self-evident principles, which it is impossible to prove, and equally impossible to disbelieve. These first principles constitute the foundation of mathematics: if you disprove them, you overturn the whole science; if you refuse to believe them, you cannot, consistently with such refusal, acquiesce in any mathematical truth whatsoever. But you may as well attempt to blow out the sun, as to disprove these principles: and if you say, that you do not believe them *, you will be charged either with falsehood or with folly; you may as well hold your hand in the fire, and say

that

* Si quelque opiniastre les nie de la voix, on ne l'en scauriot empescher; mais cela ne luy est pas permis interieurement en son esprit parce que sa lumier naturelle y repugne, qui est la partie où se rap. porte la demonstration et le syllogisme, et non aux paroles externes. Au moyen de quoy s'll se trouve quelqu'un qui ne les puisse entendre, cettuy-là est incapable de discipline.

Dialectique de Boujou, liv. 3. ch. 3.

you feel no pain. By the law of our nature, we must feel in the one case, and believe in the other; even as by the same law, we must adhere to the earth, and cannot fall headlong to the clouds.

But who will pretend to prove a mathematical axiom, That a whole is greater than a part, or, That things equal to one and the same thing are equal to one another? Every proof must be clearer and more evident than the thing to be proved. Can you then as sume any more evident principle, from which the truth of these axioms may be consequentially inferred? It is impossible; because they are already as evident as any thing can be *. You may bring the matter to

* Different opinions have prevailed concerning the nature of these geometrical axioms. Some suppose, that an axiom is not self-evident, except it imply an identical proposition; that therefore this axiom, It is impossible for the same thing, at the same time, to be and not to be, is the only axiom that can properly be called intuitive; and that all those other propositions commonly called axioms, ought to be demonstrated by being resolved into this fundamental axiom. But if this could be done, which I fear is not possible, mathematical truth would not be one whit more certain than it is. Those other axioms produce absolute certainty, and produce it immediately, without any process of thought or reasoning that we can discover. And if the truth of a proposition be clearly and certainly perceived by all men without proof, and if no proof whatever could make it more clear or more certain, it seems captious not to allow that proposition the name of Intuitive Axiom.-Others suppose, that though the demonstration of mathematical axioms is not absolutely necessary, yet that these axioms are susceptible of demonstration, and ought to be demonstrated to those who require it. Dr Barrow is of this opinion. So is Apollonius; who, agreeably to it, has attempted a demonstration of this axiom, That things equal to one and the same thing, are equal to one another.-But whatever account we make of these opinions, they affect not our doctrine. However far the demonstration of axioms may be carried, it must at last terminate in one principle of common sense, if not in many; which principle we must believe without proof, whether we will or no.