of the fourth figure. It was added by the famous Galen, and is often called the Galenical figure. There is another divifion of fyllogifms according to their modes. The mode of a fyllogifm is determined by the quality and quantity of the propofitions of which it confifts. Each of the three propofitions must be either an univerfal affirmative, or an univerfal negative, or a particular affirmative, or a particular negative. These four kinds of propofitions, as was before observed, have been named by the four vowels, A, E, I, O; by which means the mode of a fyllogifm is marked by any three of thofe four vowels. Thus A, A, A, denotes that mode in which the major, minor, and conclufion, are all univerfal affirmatives; E, A, E, denotes that mode in which the major and conclufion are univerfal negatives, and the minor is an univerfal affirmative.

To know all the poffible modes of fyllogifm, we muft find how many different combinations may be made of three out of the four vowels, and from the art of combination the number is found to be fixty-four. So many poffible modes there are in every figure; confequently in the three figures of Ariftotle there are one hundred and ninety-two, and in all the four figures two hundred and fifty-fix.

Now, the theory of fyllogifin requires, that we fhew what are the particular modes in each figure, which do, or do not, form a juft and conclufive fyl

logifm,

logifm, that fo the legitimate may be adopted, and the fpurious rejected. This Ariftotle has fhewn in the first three figures, examining all the modes one by one, and paffing fentence upon each; and from this examination he collects fome rules which may aid the memory in diftinguishing the false from the true, and point out the properties of each figure.

The first figure has only four legitimate modes. The major propofition in this figure must be univerfal, and the minor affirmative; and it has this property, that it yields conclufions of all kinds, affirmative and negative, univerfal and particular.

The fecond figure has also four legitimate modes. Its major propofition must be univerfal, and one of the premises must be negative. It yields conclufions both univerfal and particular, but all negative.

Its

The third figure has fix legitimate modes. minor must always be affirmative; and it yields conclufions both affirmative and negative, but all particular.

Befides the rules that are proper to each figure, Aristotle has given fome that are common to all, by which the legitimacy of fyllogifms may be tried. These may, I think, be reduced to five. 1. There must be only three terms in a fyllogifm. As each term occurs in two of the propofitions, it must be precisely the fame in both: if it be not, the fyllogifm is faid to have four terms, which makes a

vicious

vicious fyllogifm. 2. The middle term must be taken univerfally in one of the premises. 3. Both premises must not be particular propofitions, nor both negative. 4. The conclufion must be particular, if either of the premises be particular; and negative, if either of the premises be negative. 5. No term can be taken univerfally in the conclufion, if it be not taken universally in the premises.

For understanding the fecond and fifth of these rules, it is neceffary to obferve, that a term is faid to be taken univerfally, not only when it is the fubject of an univerfal propofition, but when it is the predicate of a negative propofition; on the other hand, a term is faid to be taken particularly, when it is either the fubject of a particular, or the predicate of an affirmative propofition.

great

SECT. 3. Of the Invention of a Middle Term. The third part of this book contains rules general and special for the invention of a middle term; and this the author conceives to be of utility. The general rules amount to this, That you are to confider well both terms of the propofition to be proved; their definition, their properties, the things which may be affirmed or denied of them, and those of which they may be af firmed or denied: these things collected together, are the materials from which your middle term is to be taken.

The fpecial rules require you to confider the quantity and quality of the propofition to be pro

ved,

We have likewife precepts given in this book, both to the affailant in a fyllogiftical difpute, how to carry on his attack with art, fo as to obtain the victory; and to the defendant, how to keep the enemy at such a distance as that he shall never be obliged to yield. From which we learn, that Ariftotle introduced in his own fchool, the practice of fyllogiftical disputation, instead of the rhetorical disputations which the fophifts were wont to use in more ancient times.

CHAP. IV.

REMARKS.

SECT. I. Of the Converfion of Propofitions.

W

E have given a summary view of the theory of pure fyllogifms as delivered by Aristotle, a theory of which he claims the fole invention. And I believe it will be difficult, in any fcience, to find fo large a fyftem of truths of fo very abstract and fo general a nature, all fortified by demonstration, and all invented and perfected by one man. It shows a force of genius and la

bour

bour of investigation, equal to the moft arduous' attempts. I fhall now make fome remarks upon

it.

As to the converfion of propofitions, the writers on logic commonly fatisfy themfelves with illuftrating each of the rules by an example, conceiving them to be felf-evident when applied to particular cafes. But Ariftotle has given demonftrations of the rules he mentions. As a fpecimen, I fhall give his demonftration of the firft rule. "Let A B be an univerfal negative pro

66

pofition; I fay, that if A is in no B, it will fol"low that B is in no A. If you deny this con

66

fequence, let B be in fome A, for example, in "C; then the firft fuppofition will not be true; "for C is of the B's.". In this demonstration, if I understand it, the third rule of converfion is affumed, that if B is in fome A, then A must be in fome B, which indeed is contrary to the first fuppofition. If the third rule be affumed for proof of the firft, the proof of all the three goes round in a circle; for the fecond and third rules are proved by the first. This is a fault in reafoning whioh Aristotle condemns, and which I would be very unwilling to charge him with, if I could find any better meaning in his demonftration. But it is indeed a fault very difficult to be avoided, when men attempt to prove things that are felf-evident.

VOL. III.

D

The