Abelard. According to thefe philofophers, there are no existences in nature correfponding to general terms; and the objects of our attention in all our general fpeculations are not ideas, but words.

In confequence of this new doctrine, the schoolmen gradually formed themselves into two fects: one of which attached itself to the opinions of Rofcelinus and 'Abelard; while the other adhered to the principles of Aristotle. Of these fects, the former are known in literary history by the name of the Nominalifts the latter by that of the Realifts.

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As it is with the doctrine of the Nominalists that my own opinion on this fubject coincides; and as I propofe to deduce from it fome confequences, which appear to me important, I fhall endeavor to ftate it as clearly and precisely as I am able, pursuing, how. ever, rather the train of my own thoughts, than guided by the reafonings of any particular author.

I formerly explained in what manner the words, which, in the infancy of language, were proper names, became gradually appellatives; in confequence of which extenfion of their fignification, they would exprefs, when applied to individuals, those qualities only which are common to the whole genus. Now, it is evident, that, with refpect to individuals of the fame genus, there are two claffes of truths; the one, particular truths relating to each individual apart, and deduced from a confideration of its peculiar and diftinguishing properties; the other, general truths, deduced from a confideration of their common qualities; and equally applicable to all of them. Such truths may be conveniently expreffed, by means of general terms; fo as to form propofitions, comprehending under them as many particular truths, as there are individuals comprehended under the general terms. It is farther evident, that there are two ways in which fuch general truths may be obtained; either by fixing the

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attention on one individual, in fuch a manner that our reafoning may involve no circumftances but those which are common to the whole genus; or, (laying afide entirely the confideration of things,) by means of the general terms with which language fupplies us. In either of thefe cafes, our inveftigations muft neceffarily lead us to general conclufions. In the first cafe; our attention being limited to thofe circumstances, in which the fubject of our reafoning resembles all other individuals of the fame genus, whatever we demonftrate with refpect to this fubject must be true of every other to which the fame attributes belong. In the second cafe; the fubject of our reasoning being expreffed by a generic word, which applies in common to a number of individuals, the conclufion we form must be as extenfive in its application, as the name of the fubject is in its meaning. The former procefs is analogous to the practice of geometers, who in their most general reafonings, direct the attention to a particular diagram: the latter, to that of algebraifts, who carry on their investigations by means of fymbols.* In cafes of this last fort, it may frequently happen, from the affociation of ideas, that a general word may recal fome one individual to which it is applicable; but this is so far from being neceffary to the accuracy of our reafoning, that, excepting in fome cafes, in which it may be useful to check us in the abuse of general

*These two methods of obtaining general truths proceed on the same principles; and are in fact, much less different from each other, than they appear to be, at first view. When we carry on a process of general reasoning, by fixing our attention on a particular individual of a genus, this individual is to be considered merely as a sign or representative; and differs from any other sign only in this, that it bears a certain resemblance to the things it denotes.-The straight lines which are employed in the fifth book of Euclid to represent magnitudes in general, differ from the algebraical expressions of these magnitudes, in the same respects which picturewriting differs from arbitrary characters.

terms, it always has a tendency, more or lefs, to miflead us from the truth. As the decifion of a judge must neceffarily be impartial, when he is only acquainted with the relations in which the parties ftand to each other, and when their names are supplied by letters of the alphabet, or by the fictitious names of Titius, Caius, and Sempronius; fo, in every process of reasoning, the conclufion we form is moft likely to be logically juft, when the attention is confined folely to figns; and when the imagination does not prefent to it those individual objects which may warp the judgment by cafual affociations.

To these remarks, it may not be improper to add, that although in our fpeculations concerning individuals, it is poffible to carry on proceffes of reasoning, by fixing our attention on the objects themselves, without the use of language; yet it is alfo in our power to accomplish the fame end, by fubftituting for these objects, words, or other arbitrary figns. The difference between the employments of language in fuch cafes, and in our fpeculations concerning claffes or genera, is; that in the former cafe the ufe of words is, in a great measure, optional; whereas, in the latter, it is effentially neceffary. This obfervation deserves our attention the more, that, if I am not mistaken, it has contributed to miflead fome of the Realists; by giving rife to an idea, that the use of language, in thinking about univerfals, however convenient, is not more neceffary than in thinking about individuals.

According to this view of the procefs of the mind, in carrying on general fpeculations, that IDEA which the antient philofophers confidered as the effence of an individual, is nothing more than the particular quality or qualities in which it resembles other individuals of the fame clafs; and in confequence of which, a generic name is applied to it. It is the poffeflion of this quality, that entitles the individual to

the generic appellation; and which, therefore, may be faid to be effential to its claffification with that particular genus; but as all claffifications are to a certain degree arbitrary, it does not neceffarily fol low, that it is more effential to its existence as an individual, than various other qualities which we are accustomed to regard as accidental. In other words, (if I may borrow the language of modern philofophy,) this quality forms its nominal, but not its real effence.

Thefe obfervations will, I flatter myself, be fufficient for the fatisfaction of fuch of my readers as are at all converfant with philofophical inquiries. For the fake of others, to whom this difquifition may be new, I have added the following illuftrations.

I fhall have occafion to examine, in another part of my work, how far it is true, (as is commonly believed,) that every procefs of reafoning may be refolved into a series of fyllogifms; and to point out fome limitations, with which, I apprehend, it is neceffary that this opinion fhould be received.

As it would lead me, however, too far from my present fubject, to anticipate any part of the doctrine which I am then to propof, I fhall, in the following remarks, proceed on the fuppofition, that the fyllogiftic theory is well-founded; a fuppofition which, altho not ftrictly agreeable to truth, is yet fufficiently ac curate for the ufe which I am now to make of it. Take, then, any ftep of one of Euclid's demonftrations; for example, the firft ftep of his firft propofition, and state it in the form of a fyllogifm." All " ftrait lines, drawn from the centre of a circle to the "circumference, are equal to one another." "But A "B, and CD, are straight lines, drawn from the centre "of a circle to the circumference. Therefore, A B "is equal to CD."-It is perfectly manifeft, that, in order to feel the force of this conclufion, it is by no means neceffary, that I fhould annex any particular

notions to the letters AB, or CD, or that I fhould. comprehend what is meant by equality, or by a circle, its centre, and its circumference. Every person must be fatisfied, that the truth of the conclufion is neceffarily implied in that of the two premifes; whatever the particular things may be to which these premises may relate. In the following fyllogifin, too:" All men muft die ;-Peter is a man ;-there"fore Peter muft die ;"-the evidence of the conclufion does not in the leaft depend on the particular notions I annex to the words man, and Peter; but would be equally complete, if we were to fubftitute inftead of them, two letters of the alphabet, or any other infignificant characters." All X's muft die; "-Z is an X ;-therefore Z muft die ;"-is a fyllogifm which forces the affent no less than the former. It is farther obvious, that this fyllogifm would be equally conclufive, if, instead of the word die, I were to fubftitute any other verb that the language contains; and that, in order to perceive the juftnefs of the inference, it is not even neceffary that I should understand its meaning.

In general, it might be easily fhewn, that all the rules of logic, with refpect to fyllogifms, might be demonftrated, without having recourse to any thing but letters of the alphabet; in the fame manner, (and I may add, on the very fame principles,) on which the algebraift demonftrates, by means of thefe letters, the various rules for tranfpofing the terms of an equation.

From what has been faid, it follows, that the af fent we give to the conclufion of a fyllogifm does not refult from any examination of the notions expreffed by the different propositions of which it is composed, but is an immediate confequence of the relations in which the words ftand to each other. The truth is, that, in every fyllogism, the inference is only a particular inftance of the general axiom,