IV.

which, we are not confcious of any effort of the judgment CHAP. diftinct from a procefs of reafoning. As every geometrical in-` veftigation, however, may be expreffed algebraically, it is manifeft, that, in geometry, as well as in algebra, there is an exercise of the intellectual powers, diftinct from the logical procefs; although, in the former fcience, it is rendered fo eafy, by the use of diagrams, as to escape our attention.

THE fame fource of error and of abfurdity, 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 fuppofing alfo our reasonings to be logically accurate, it would ftill be neceffary for us, from time to time, in all our fpeculations, to lay afide the use of words, and to have recourse to particular examples, or illuftrations, in order to correct and to limit our general conclufions.-To a want of attention to this circumftance, a number of the fpeculative abfurdities which are current in the world, might, I am perfuaded, be easily traced.

BESIDES, however, this fource of error, which is in fome degree common to all the fciences, there is a great variety of others, from which mathematics are entirely exempted; and which perpetually tend to lead us aftray in our philofophical inquiries. Of thefe, the most important is, that ambiguity in the fignification of words, which renders it fo difficult to avoid employing the fame expreffions in different fenfes, in the courfe of the fame procefs of reasoning. This fource of miftake, indeed,

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IV.

"CHA P. deed, is apt, in a much greater degree, to affect our conclufions in metaphyfics, morals, and politics, than in the different branches of natural philofophy; but, if we except mathematics, there is no fcience whatever, in which it has not a very fenfible influence. In algebra, we may proceed with perfect safety through the longest investigations, without carrying our attention beyond the figns, till we arrive at the laft refult. But in the other fciences, excepting in thofe cafes 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 feldom that we can proceed in this manner without danger of error. In many cafes, it is neceffary for us to keep up, during the whole of our investigations, a fcrupulous and conftant attention to the fignification of our expreffions; and, in moft cafes, this caution in the use of words, is a much more difficult effort of the mind, than the logical procefs. But ftill this furnishes no exception to the general doctrine already delivered; for the attention we find it neceffary to give to the import of our words, arises only from the accidental circumftance of their ambiguity, and has no effential connection with that process of the mind, which is properly called reasoning; and which consists in the inference of a conclufion from premifes. In all the fciences, this procefs of the mind is perfectly analogous to an algebraical operation; or, in other words, (when the meaning of our expreffions is once fixed by definitions,) it may be carried on intirely by the use of figns, without attending, during the time of the procefs, to the things fignified..

THE

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IV.

179

THE Conclufion to which the foregoing obfervations lead, CHA P. appears to me to be decifive of the queftion, 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 fignification, form an inftrument of thought fufficient for all the purposes of reafoning; the only fhadow of an argument in proof of the common doctrine on the subject, (I mean that which is founded on the impoffibility of explaining this procefs of the mind on any other hypothefis,) falls to the ground. Nothing lefs, furely, than a conviction of this impoffibility, could have fo long reconciled philosophers to an hypothefis unfupported by any direct evidence; and acknowledged even by its warmeft defenders, to involve much difficulty and mystery.

of my

IT does not fall within my plan, to enter, in this part work, into a particular confideration of the practical confequences 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 illuftration; and, on the other, a habit of reafoning by means of general terms. The former talent is neceffary, not only for correcting and limiting our general conclufions, but for enabling us to apply our knowledge, when occafion requires, to its real practical use. The latter ferves the double purpofe, of preventing our attention. from being distracted during the courfe of our reasonings, by ideas which are foreign to the point in question; and of diverting the attention from thofe conceptions of particular objects and particular events which might difturb the judgment, by the ideas

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CHAP. ideas and feelings, which are apt to be affociated with them, in confequence of our own cafual experience.

IV.

THIS laft obfervation points out to us, alfo, one principal foundation of the art of the orator. As his object is not fo much to inform and to fatisfy the understandings of his hearers, as to force their immediate affent; it is frequently of ufe to him to clothe his reasonings in that specific and figurative language, which may either awaken in their minds affociations favourable to his purpose, or may divert their attention from a logical examination of his argument. A procefs of reasoning fo expreffed, affords at once an exercife to the judgment, to the imagination, and to the paffions; and is apt, even when loose and inconsequential, to impose on the best understandings.

IT It appears farther, from the remarks which have been made, that the perfection of philofophical language, confidered either as an inftrument of thought, or as a medium of communication with others, confifts in the ufe of expreffions, which, from their generality, have no tendency to awaken the powers of conception and imagination: or, in other words, it confifts in its approaching, as nearly as poffible, in its nature, to the language of algebra. And hence the effects which long habits of philofophical fpeculation have, in weakening, by difuse, those faculties of the mind, which are neceflary for the exertions of the poet and the orator; and of gradually forming a ftyle of compofition, which they who read merely for amufement, are apt to cenfure for a want of vivacity and of ornament.

CHAP.
IV.

SECTION III.

Remarks on the Opinions of fome modern Philofophers on the
Subject of the foregoing Section.

AFTER the death of Abelard, through whose abilities and eloquence the fect of Nominalifts had enjoyed, for a few years, a very fplendid triumph, the fyftem of the Realifts began to revive; and it was foon fo completely re-established in the schools, as to prevail, with little or no oppofition, till the fourteenth century. What the circumftances were, which led philofophers to abandon a doctrine, which feems fo ftrongly to recommend itself by its fimplicity, it is not very easy to conceive. Probably the heretical opinions, which had fubjected both Abelard and Roscelinus to the cenfure of the church, might create a prejudice alfo against their philosophical principles; and probably too, the manner in which these principles were stated and defended, was not the cleareft, nor the most fatisfactory *. The principal caufe, however, I am difpofed to think, of the decline of the fect of Nominalifts, was their want of fome palpable ex

* The great argument which the Nominalists employed against the existence of univerfals was: "Entia non funt multiplicanda præter neceffitatem."