The latitude with which the word metaphysics is frequently used, makes it necessary for me to remark, with respect to the foregoing passage from D'Alembert, that he limits the term entirely to an account of the origin of our ideas. "The generation of our ideas," he tells us, "belongs to metaphysics. It forms one of the principal objects, and perhaps ought to form the sole object of that science." If the meaning of the word be extended, as it too often is in our language, so as to comprehend all those inquiries which relate to the theory and to the improvement of our mental powers, some of his observations. must be understood with very important restrictions. What he has stated, however, on the inseparable connexion between perspicuity of style and soundness of investigation in metaphysical disquisitions, will be found to hold equally in every research to which that epithet can, with any colour of propriety, be applied.

1 "La génération de nos idées appartient à la métaphysique; c'est un de ses

objets principaux, et peut-être devroit elle s'y borner."—Elém. de Philosophie.

CHAPTER I.

OF THE FUNDAMENTAL LAWS OF HUMAN BELIEF; OR THE PRIMARY ELEMENTS OF HUMAN REASON.

THE propriety of the title prefixed to this chapter, will I trust be justified sufficiently by the speculations which are to follow. As these differ, in some essential points, from the conclusions of former writers, I found myself under the necessity of abandoning, in various instances, their phraseology; but my reasons for the particular changes which I have made, cannot possibly be judged of, or even understood, till the inquiries by which I was led to adopt them be carefully examined.

I begin with a review of some of those primary truths, a conviction of which is necessarily implied in all our thoughts, and in all our actions, and which seem on that account rather to form constituent and essential elements of reason, than objects with which reason is conversant. The import of this last remark will appear more clearly afterwards.

The primary truths to which I mean to confine my attention at present are-1. Mathematical Axioms: 2. Truths, (or, more properly speaking, Laws of Belief,) inseparably connected with the exercise of Consciousness, Perception, Memory, and Reasoning. Of some additional laws of Belief, the truth of which is tacitly recognised in all our reasonings concerning contingent events, I shall have occasion to take notice under a different article.

SECTION 1.-OF MATHEMATICAL AXIOMS.

I have placed this class of truths at the head of the enumeration, merely because they seem likely, from the place which

they hold in the elements of geometry, to present to my readers a more interesting, and, at the same time, an easier subject of discussion, than some of the more abstract and latent elements of our knowledge, afterwards to be considered. In other respects, a different arrangement might perhaps have possessed some advantages, in point of strict logical method.

[SUBSECTION 1.-Of the Nature of Mathematical Axioms.]

On the evidence of mathematical axioms it is unnecessary to enlarge, as the controversies to which they have given occasion are entirely of a speculative or rather scholastic description, and have no tendency to affect the certainty of that branch of science to which they are supposed to be subservient.

It must, at the same time, be confessed, with respect to this class of propositions, (and the same remark may be extended to axioms in general,) that some of the logical questions connected with them continue still to be involved in much obscurity. In proportion to their extreme simplicity is the difficulty of illustrating or of describing their nature in unexceptionable language; or even of ascertaining a precise criterion by which they may be distinguished from other truths which approach to them nearly. It is chiefly owing to this, that in geometry there are no theorems of which it is so difficult to give a rigorous demonstration, as those of which persons unacquainted with the nature of mathematical evidence are apt to say, that they require no proof whatever. But the inconveniences arising from these circumstances are of trifling moment; occasioning at the worst some embarrassment to those mathematical writers, who are studious of the most finished elegance in their exposition of elementary principles, or to metaphysicians anxious to display their subtlety upon points which cannot possibly lead to any practical conclusion.

It was long ago remarked by Locke, of the axioms of geometry, as stated by Euclid, that although the proposition be at first enunciated in general terms, and afterwards appealed to, in its particular applications, as a principle previously examined and admitted, yet that the truth is not less evident

in the latter case than in the former. He observes farther, that it is in some of its particular applications that the truth of every axiom is originally perceived by the mind; and, therefore, that the general proposition, so far from being the ground of our assent to the truths which it comprehends, is only a verbal generalization of what, in particular instances, has been already acknowledged as true.

The

The same author remarks, that some of these axioms "are no more than bare verbal propositions, and teach us nothing but the respect and import of names one to another. whole is equal to all its parts; what real truth, I beseech you, does it teach us? What more is contained in that maxim, than what the signification of the word totum, or the whole, does of itself import? And he that knows that the word whole stands for what is made up of all its parts, knows very little less than that the whole is equal to all its parts.' And upon the same ground, I think that this proposition, A hill is higher than a valley, and several the like, may also pass for maxims."

Notwithstanding these considerations, Mr. Locke does not object to the form which Euclid has given to his axioms, or to the place which he has assigned to them in his Elements. On the contrary, he is of opinion that a collection of such maxims is not without reason prefixed to a mathematical system, in order that learners, "having in the beginning perfectly acquainted their thoughts with these propositions made in general terms, may have them ready to apply to all particular cases, as formed rules and sayings. Not that if they be equally weighed, they are more clear and evident than the instances they are brought to confirm; but that being more familiar to the mind, the very naming of them is enough to satisfy the understanding." In farther illustration of this, he adds very justly and ingeniously, that "although our knowledge begins in particulars, and so spreads itself by degrees to generals, yet afterwards the mind takes quite the contrary course, and having drawn its knowledge into as general propositions as it can, makes them familiar to its thoughts, and accustoms itself to

have recourse to them, as to the standards of truth and falsehood."

But although in mathematics some advantage may be gained without the risk of any possible inconvenience, from this arrangement of axioms, it is a very dangerous example to be followed in other branches of knowledge, where our notions are not equally clear and precise, and where the force of our pretended axioms, (to use Mr. Locke's words,) "reaching only to the sound, and not to the signification of the words, serves only to lead us into confusion, mistakes, and error." For the illustration of this remark I must refer to Locke.

Another observation of this profound writer deserves our attention while examining the nature of axioms;-" that they are not the foundations on which any of the sciences is built, nor at all useful in helping men forward to the discovery of unknown truths."1 This observation I intend to illustrate afterwards, in treating of the futility of the syllogistic art. At present I shall only add, to what Mr. Locke has so well stated, that even in mathematics it cannot with any propriety be said, that the axioms are the foundation on which the science rests, or the first principles from which its more recondite truths are deduced. Of this I have little doubt that Locke was perfectly aware; but the mistakes which some of the most acute and enlightened of his disciples have committed in treating of the same subject, convince me, that a further elucidation of it is not altogether superfluous. With this view I shall here introduce a few remarks on a passage in Dr. Campbell's Philosophy of Rhetoric, in which he has betrayed some misapprehensions on this very point, which a little more attention to the hints already quoted from the Essay on Human Understanding might have prevented. These remarks will, I hope, contribute to place the nature of axioms, more particularly of mathematical axioms, in a different and clearer light than that in which they have been commonly considered.

"Of intuitive evidence," says Dr. Campbell, "that of the following propositions may serve as an illustration :-' One and 1 Book iv. chap. vii. 3 11, (2, 3.)