that whatever is true universally of any fign, muft also be true of every individual which that fign can be employed to exprefs. Admitting, therefore, that every process of reasoning may be refolved into a series of fyllogifms, it follows, that this operation of the mind furnishes no proof of the existence of any thing correfponding to general terms, distinct from the individuals to which these terms are applicable.

These remarks, I am very fenfible, do, by no means, exhaust the fubject; for there are various modes of reasoning, to which the fylogiftic theory does not apply. But, in all of them, without exception, it will be found, on examination, that the evidence of our conclufions appears immediately from the confideration of the words in which the premifes are expreffed; without any reference to the things which they denote. The imperfect account which is given of deductive evidence, in the received fyftems of logic, makes it impoffible for me, in this place, to prosecute the subject any farther.

After all that I have faid on the ufe of language as an inftrument of reasoning, I can eafily foresee a variety of objections, which may occur to the doctrine I have been endeavouring to establish. But without entering into a particular examination of thefe objections, I believe I may venture to affirm, that most, if not all, of them take their rife from confounding reasoning, or deduction, properly so called, with certain other intellectual proceffes, which it is neceffary for us to employ in the inveftigation of truth. That it is frequently of effential importance to us, in our fpeculations, to withdraw our attention from words, and to direct it to the things they denote, I am very ready to acknowl. edge. All that I affert is, that, in so far as our fpeculations confift of that procefs of the mind which is properly called reasoning, they may be carried on

by words alone; or, which comes to the fame thing, that every process of reasoning is perfectly analo gous to an algebraical operation. What I mean by "the other intellectual proceffes diftinct from rea"foning, which it is neceffary for us fometimes to employ in the investigation of truth," will, I hope, appear clearly from the following remarks.

In algebraical inveftigations, it is well known, that the practical application of a general expreffion, is frequently limited by the conditions which the hypothesis involves; and that, in confequence of a want of attention to this circumftance, fome mathematicians of the firft eminence have been led to adopt the most paradoxical and abfurd conclufions. Without this cautious exercise of the judgment, in the interpretation of the algebraical language, no dexterity in the use of the calculus will be fufficient to preferve us from error. Even in algebra, therefore, there is an application of the intellectual powers perfectly diftinct from any process of reasoning; and which is abfolutely neceffary for conducting us to the truth.

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 reasoning 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 process of reasoning. As every geometrical inveftigation, however, may be expreffed algebraically, it is manifeft, that, in geometry, as well as in algebra, there is an exercife of the intellectual powers, diftinct from the logical procefs; although, in the former science, it is rendered fo eafy, by the use of diagrams, as to escape our attention.

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. Abftracting entirely from the ambiguity of language; and fuppofing alfo our reafonings 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 circumstance, a number of the speculative 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 course of the fame procefs of reasoning. 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 philofophy; 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 laft refult. But in the other fciences, excepting in those 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 most cases, 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 reafoning; and which confifts in the inference of a conclufion from premises. 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 conclufion to which the foregoing obfervations lead, appears to me to be decifive of the que tion, 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 purpofes of reasoning; 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 process 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

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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 reasoning by means of general terms. The former talent is neceflary, not only for correcting 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 distracted during the course of our reafenings, 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 and feelings, which are apt to be affociated with them, in confequence of our own cafual experience.

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This laft obfervation points out to us, alfo, one principal foundation of the art of the orator. his object is not so 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 reafonings in that fpecific and figurative language, which may either awaken in their minds affociations favorable to his purpofe, 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 inconfequential, 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 use of expreffions, which from their generality, have no tendency to awaken the powers of conception and imagination; or, in other words, it