other intellectual processes which it is necessary for us to employ in the investigation of truth. That it is frequently of essential importance to us, in our speculations, to withdraw our attention from words, and to direct it to the things they denote, I am very ready to acknowledge. All that I assert is, that in so far as our speculations consist of that process of the mind which is properly called reasoning, they may be carried on by words alone; or, which comes to the same thing, that every process of reasoning is perfectly analogous to an algebraical operation. What I mean by "the other intellectual processes distinct from reasoning, which it is necessary for us sometimes to employ in the investigation of truth," will, I hope, appear clearly from the following remarks.

In algebraical investigations, it is well known that the practical application of a general expression, is frequently limited by the conditions which the hypothesis involves, and that in consequence of a want of attention to this circumstance, some mathematicians of the first eminence have been led to adopt the most paradoxical and absurd conclusions. Without this cautious exercise of the judgment, in the interpretation of the algebraical language, no dexterity in the use of the calculus will be sufficient to preserve us from error. Even in algebra, therefore, there is an application of the intellectual powers perfectly distinct from any process of reasoning, and which is absolutely necessary for conducting us to the truth.

In geometry we are not liable to adopt the same paradoxical conclusions as in algebra, because the diagrams to which our attention is directed, serve as a continual check on our reasoning powers. These diagrams exhibit to our very senses, a variety of relations among the quantities under consideration, which the language of algebra is too general to express, in consequence of which we are not conscious of any effort of the judgment distinct from a process of reasoning. As every geometrical investigation, however, may be expressed algebraically, it is manifest that in geometry, as well as in algebra, there is an exercise of the intellectual powers distinct from the logical process, although in the former science

it is rendered so easy by the use of diagrams as to escape our

attention.

The same source of error and of absurdity which exists in algebra, is to be found in a much greater degree in the other branches of knowledge. Abstracting entirely from the ambiguity of language, and supposing also our reasonings to be logically accurate, it would still be necessary for us, from time to time, in all our speculations, to lay aside the use of words, and to have recourse to particular examples or illustrations, in order to correct and to limit our general conclusions. To a want of attention to this circumstance, a number of the speculative absurdities which are current in the world, might, I am persuaded, be easily traced.

Besides, however, this source of error, which is in some degree common to all the sciences, there is a great variety of others from which mathematics are entirely exempted, and which perpetually tend to lead us astray in our philosophical inquiries. Of these, the most important is that ambiguity in the signification of words, which renders it so difficult to avoid employing the same expressions in different senses, in the course of the same process of reasoning. This source of mistake, indeed, is apt in a much greater degree to affect our conclusions in metaphysics, morals, and politics, than in the different branches of natural philosophy, but, if we except mathematics, there is no science whatever in which it has not a very sensible influence. In algebra, we may proceed with perfect safety through the longest investigations, without carrying our attention beyond the signs, till we arrive at the last result. But in the other sciences, excepting in those cases in which we have fixed the meaning of all our terms by accurate definitions, and have rendered the use of these terms perfectly familiar to us by very long habit, it is but seldom that we can proceed in this manner without danger of error. In many cases, it is necessary for us to keep up during the whole of our investigations, a scrupulous and constant attention to the signification of our expressions; and in most cases, this caution in the use of words is a much more difficult effort of the mind

than the logical process. But still this furnishes no exception to the general doctrine already delivered; for the attention we find it necessary to give to the import of our words, arises only from the accidental circumstance of their ambiguity, and has no essential connexion with that process of the mind which is properly called reasoning, and which consists in the inference of a conclusion from premises. In all the sciences, this process of the mind is perfectly analogous to an algebraical operation; or, in other words, (when the meaning of our expressions is once fixed by definitions,) it may be carried on entirely by the use of signs, without attending during the time of the process to the thing signified.

The conclusion to which the foregoing observations lead, appears to me to be decisive of the question, with respect to the objects of our thoughts when we employ general terms; for, if it be granted that words, even when employed without any reference to their particular signification, form an instrument of thought sufficient for all the purposes of reasoning, the only shadow of an argument in proof of the common doctrine on the subject, (I mean that which is founded on the impossibility of explaining this process of the mind on any other hypothesis,) falls to the ground. Nothing less, surely, than a conviction of this impossibility, could have so long reconciled philosophers to an hypothesis unsupported by any direct evidence, and

1

[This argument against the existence of universals, founded on the inutility of such a supposition in explaining the intellectual operations, was considered by the Nominalists of the twelfth century as the strength of their cause. The force of the argument, however, was much weakened by the manner in which they stated it; for, instead of considering it as a complete refutation of the hypothesis of the Realists, (which had nothing to support it but the explanation it was supposed to afford of some phenomena believed to be otherwise inexplicable,) they attempted to demonstrate that universals had no existence,

from the general axiom that nature does nothing in vain; or, as they expressed themselves, "Entia non sunt multiplicanda præter necessitatem." "C'étoit soutenir une bonne thèse," says Condillac, "par une assez mauvaise raison; car c'étoit convenir que ces réalités étoient possibles, et que pour les faire exister, il ne falloit que leur trouver quelque utilité. Cependant ce principe étoit appelé le Razoir des Nominaux.” -Condillac, Cours d'Etude, tom. iv. p. 88.

The argument is better stated by Leibnitz, vol. iv. p. 60, Ed. Dutens. Generalis autem regula est, &c. See Note I.]

acknowledged even by its warmest defenders to involve much difficulty and mystery.

It does not fall within my plan to enter, in this part of my work, into a particular consideration of the practical consequences which follow from the foregoing doctrine. I cannot, however, help remarking the importance of cultivating, on the one hand, a talent for ready and various illustration; and, on the other, a habit of reasoning by means of general terms. The former talent is necessary, not only for correcting and limiting our general conclusions, but for enabling us to apply our knowledge, when occasion requires, to its real practical use. The latter serves the double purpose of preventing our attention from being distracted during the course of our reasonings, by ideas which are foreign to the point in question; and of diverting the attention from those conceptions of particular objects and particular events which might disturb the judgment, by the ideas and feelings which are apt to be associated with them, in consequence of our own casual experience.

This last observation points out to us, also, one principal foundation of the art of the orator. As his object is not so much to inform and to satisfy the understandings of his hearers, as to force their immediate assent, it is frequently of use to him to clothe his reasonings in that specific and figurative language, which may either awaken in their minds associations favourable to his purpose, or may divert their attention from a logical examination of his argument. A process of reasoning so expressed, affords at once an exercise to the judgment, to the imagination, and to the passions; and is apt, even when loose and inconsequential, to impose on the best understandings.

It appears farther, from the remarks which have been made, that the perfection of philosophical language, considered either as an instrument of thought, or as a medium of communication with others, consists in the use of expressions, which, from their generality, have no tendency to awaken the powers of conception and imagination; or, in other words, it consists in its approaching, as nearly as possible, in its nature, to the lan

guage of Algebra. And hence the effects which long habits of philosophical speculation have in weakening, by disuse, those faculties of the mind which are necessary for the exertions of the poet and the orator, and of gradually forming a style of composition, which they who read merely for amusement, are apt to censure for a want of vivacity and of ornament.1

SECT. III.-REMARKS ON THE OPINIONS OF SOME MODERN PHILOSOPHERS ON THE SUBJECT OF THE FOREGOING SECTION.

After the death of Abelard, through whose abilities and eloquence the sect of Nominalists had enjoyed, for a few years, a very splendid triumph, the system of the Realists began to revive; and it was soon so completely re-established in the schools, as to prevail, with little or no opposition, till the fourteenth century. What the circumstances were which led philosophers to abandon a doctrine, which seems so strongly to recommend itself by its simplicity, it is not very easy to conceive. Probably the heretical opinions which had subjected both Abelard and Roscelinus to the censure of the Church, might create a prejudice also against their philosophical principles; and probably, too, the manner in which these principles were stated and defended, was not the clearest, nor the most satisfactory. The principal cause, however, I am disposed to think, of the decline of the sect of Nominalists, was their want of some palpable example, by means of which they might illustrate their doctrine. It is by the use which algebraists make

["Language, like light, is a medium; and the true philosophical style, like light from a north window, exhibits objects clearly and distinctly without soliciting attention to itself. In painting subjects of amusement indeed, language may gild somewhat more, and colour with the dyes of fancy; but where information is of more importance than entertainment, though you cannot throw too strong a light, you should carefully avoid a coloured one. The style of some writers resembles a bright

light placed between the eye, and the thing to be looked at. The light shows itself, and hides the object."—Gilpin. This passage I have transcribed from one of the numerous publications of the ingenious author, but I have neglected to mark the title of the volume.]

The great argument which the Nominalists employed against the existence of universals was:- "Entia non sunt multiplicanda præter necessitatem."