In geometry, we are not liable to adopt the fame paradoxical conclufions, as in algebra; because the diagrams to which our attention is directed, ferve as a continual check on our reafoning powers. These diagrams exhibit to our very fenfes, a variety of relations among the quantities under confideration, which the language of algebra is too general to exprefs; in confequence of which, we are not confcious of any effort of the judgment diftinct from a procefs of reafoning. As every geometrical investigation, however, may be expressed 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 at tention.

The fame fource of error and of abfurdity, which exifts in algebra, is to be found, in a much greater degree, in the other branches of knowledge. Ab ftracting entirely from the ambiguity of language ; and fuppofing alfo our reafonings to be logically accurate, it would still be neceffary for us, from time to time, in all our fpeculations, to lay afide the use of words, and to have recourfe to particular examples, or illustrations, 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.

Befides, 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

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 course of the fame procefs of reafoning. This fource of mistake, indeed, is apt, in a much greater degree, to affect our conclufions in metaphyfics, 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 fenfible influence. In algebra, we may proceed with perfect fafety through the longest investigations, without carrying our attention beyond the figns, till we arrive at the last refult. But in the other sciences, 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 seldom that we can proceed in this manner without danger of error. 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 most cafes, this caution in the use of words, is a much more difficult effort of the mind, than the logical procefs, But still 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, arifes only from the accidental circumstance of their ambiguity, and has no effential connection with that procefs of the mind, which is properly called reafoning; and which confifts in the inference

N 2

In

ferénce 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 cefs, to the things fignified.

pro

The conclufion to which the foregoing obfervations lead, appears to me to be decifive of the queftion, with refpect 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 fubject, (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 philofophers to an hypothefis unfupported by any direct evidence; and acknowledged even by its warmeft 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 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

and limiting our general conclufions, but for enabling us to apply our knowledge, when occafion requires, to its real practical ufe. The latter ferves the double purpose, of preventing our attention from being dif tracted during the courfe of our reafonings, by ideas which are foreign to the point in queftion; and of diverting the attention from thofe conceptions of particular objects and particular events which might dif turb the judgment, by the ideas and feelings, which are apt to be associated with them, in confequence of our own cafual experience.

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 use to him to clothe his reafonings 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 reafoning fo expreffed, affords at once an exercife to the judgment, to the imagination, and to the paffions; and is apt, even when loofe and inconsequential, to impofe on the best understandings.

"

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 geneṛality, have no tendency to awaken the powers of conception and imagination; or, in other words, it con

fifts 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 difufe, thofe faculties of the mind, which are neceffary for the exertions of the poet and the orator; and of gradually forming a style of compofition, which they who read merely for amufement, are apt to cenfure for a want of vivacity and of ornament.

SECTION III.

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

A

FTER the death of Abelard, through whose abilities and eloquence the fect of Nominalists 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 circumstances 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 Rofcelinus to the cenfure of the church, might create a pre. judice alfo against their philofophical principles; and probably too, the manner in which these principles were stated and defended, was not the cleareft, nor the moft