the decision of a judge must necessarily be impartial when he is only acquainted with the relations in which the parties stand to each other, and when their names are supplied by letters of the alphabet, or by the fictitious names of Titius, Caius, and Sempronius; so, in every process of reasoning, the conclusion we form is most likely to be logically just, when the attention is confined solely to signs, and when the imagination does not present to it those individual objects which may warp the judgment by casual associations.

To these remarks, it may not be improper to add, that, although in our speculations concerning individuals, it is possible to carry on processes of reasoning, by fixing our attention on the objects themselves, without the use of language, yet it is also in our power to accomplish the same end, by substituting for these objects, words, or other arbitrary signs. The difference between the employment of language in such cases, and in our speculations concerning classes or genera, is, that in the former case the use of words is, in a great measure, optional, whereas, in the latter, it is essentially necessary. This observation deserves our attention the more, that, if I am not mistaken, it has contributed to mislead some of the Realists, by giving rise to an idea, that the use of language, in thinking about universals, however convenient, is not more necessary than in thinking about individuals.

According to this view of the process of the mind, in carrying on general speculations, that IDEA which the ancient philosophers considered as the essence of an individual, is nothing more than the particular quality or qualities in which it resembles other individuals of the same class, and in consequence of which, a generic name is applied to it. It is the possession of this quality, that entitles the individual to the generic appellation, and which, therefore, may be said to be essential to its classi

fication with that particular genus; but as all classifications are to a certain degree arbitrary, it does not necessarily follow, that it is more essential to its existence as an individual, than various other qualities which we are accus tomed to regard as accidental. In other words, (if I may borrow the language of modern philosophy,) this quality forms its nominal, but not its real essence.

These observations will, I flatter myself, be sufficient for the satisfaction of such of my readers as are at all conversant with philosophical inquiries. For the sake of others, to whom this disquisition may be new, I have added the following illustrations.

I shall have occasion to examine, in another part of my work, how far it is true, (as is commonly believed,) that every process of reasoning may be resolved into a series of syllogisms, and to point out some limitations, with which, I apprehend, it is necessary that this opinion should be received. As it would lead-me, however, too far from my present subject, to anticipate any part of the doctrine which I am then to propose, I shall, in the following remarks, proceed on the supposition, that the syllogistic theory is well-founded; a supposition which, although not strictly agreeable to truth, is yet sufficiently accurate for the use which I am now to make of it. Take then, any step of one of Euclid's demonstrations; for example, the first step of his first proposition, and state it in the form of a syllogism." All straight lines, drawn from the centre "of a circle to the circumference, are equal to one ano"ther." "But A B, and C D, are straight lines, drawn "from the centre of a circle to the circumference. There"fore, A B is equal to C D."-It is perfectly manifest, that, in order to feel the force of this conclusion, it is by no means necessary, that I should annex any particular notions to the letters A B, or C D, or that I should comprehend what is meant by equality, or by a circle, its

centre, and its circumference. Every person must be satisfied, that the truth of the conclusion is necessarily implied in that of the two premises; whatever the particular things may be to which these premises may relate. In the following syllogism, too :-"All men must die ;"Peter is a man ;-therefore Peter must die ;"-the evidence of the conclusion does not in the least depend on the particular notions I annex to the words man, and Peter; but would be equally complete, if we were to substitute instead of them, two letters of the alphabet, or any other insignificant characters." All X's must die ;"Z is an X ;-therefore Z must die ;"-is a syllogism which forces the assent no less than the former. It is farther obvious, that this syllogism would be equally conclusive, if, instead of the word die, I were to substitute any other verb that the language contains; and that, in order to perceive the justness of the inference, it is not even necessary that I should understand its meaning.

In general, it might be easily shewn, that all the rules of logic, with respect to syllogisms, might be demonstrated, without having recourse to any thing but letters of the alphabet; in the same manner, (and I may add, on the very same principles,) on which the algebraist demonstrates, by means of these letters, the various rules for transposing the terms of an equation.

From what has been said, it follows, that the assent we give to the conclusion of a syllogism does not result from any examination of the notions expressed by the different propositions of which it is composed, but is in immediate consequence of the relations in which the words stand to each other. The truth is, that, in every syllogism, the inference is only a particular instance of the general axiom, that whatever is true universally of any sign, must also be true of every individual which that sign can be employed to express. Admitting, therefore, that every

process of reasoning may be resolved into a series of syllogisms, it follows, that this operation of the mind furnishes no proof of the existence of any thing corresponding to general terms, distinct from the individuals to which these terms are applicable.

These remarks, I am very sensible, do by no means exhaust the subject, for there are various modes of reasoning, to which the syllogistic theory does not apply. But, in all of them, without exception, it will be found, on examination, that the evidence of our conclusions appears immediately from the consideration of the words in which the premises are expressed, without any reference to the things which they denote. The imperfect account which is given of deductive evidence, in the received systems of logic, makes it impossible for me, in this place, to prosecute the subject any farther.

After all that I have said on the use of language as an instrument of reasoning, I can easily 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 these objections, I believe I may venture to affirm, that most, if not all, of them take their rise from confounding reasoning, or deduction, properly so called, with certain 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 in"tellectual processes distinct from reasoning, which it is

necessary for us sometimes to employ in the investiga"tion 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 errour. 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 errour 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 rea