A, E, I, O; by which means the mode of a fyllogifm is marked by any three of those four vowels. Thus A, A, A, de notes 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 universal negatives, and the minor is an univerfal affirmative. To know all the possible modes of fyl-. logism, we must 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 fixtyfour. So many possible modes there are in every figure, consequently 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 fyllogifm requires, that we shew what are the particular modes in each figure, which do, or do not, form a juft and conclufive fyllogifm, that so the legitimate may be adopted, and the spuri ous rejected. This Aristotle has shewn in the first three figures, examining all the modes one by one, and paffing fentence upon each; and from this examination he VOL. III. Yy collects collects fome rules which may aid the memory in diftinguishing the false from the true, and point out the properties of each figure. ic The first figure has only four legitimate modes. The major proposition in this figure must be universal, 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 alfo four legitimate modes. Its major proposition must be univerfal, and one of the premises must be negative. It yields conclusions both univerfal and particular, but all negative. Then third figure has fix legitimate modes. Its 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 some that are common to all, by which the legitimacy of fyllogifims may be tried. Thefe may, I think, be reduced to five. 1. There must be only three terms in a fyllogifim. As each term occurs in two of the propofisigns, it must be precisely the fame in both; if it be not, the fyllogifm is faid to have four terms, which makes a vitious fyllogifm. 2. The middle term must Be taken universally in one of the premiles. 3. Both premises must not be particular propositions, 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 second and fifth of these rules, it is necessary to observe, that a term is faid to be taken univerfally, not only when it is the subject of an universal propofition, but when it is the predicate of a negative proposition; 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 proposition. SECT. 3. Of the Invention of a Middie Term. The third part of this book contains rules general and special for the invention of a middle term; and this the author Yy2 conceives conceives to be of great 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 affirmed or denied : these things collected together, are the materials from which your middle term is to be taken, που π" bevor " The special rules require you to confider the quantity and quality of the propofition to be proved, that you may difcover in what mode and figure of fyllogifm the proof is to proceed. Then from the materials before collected, you must feek a middle term which has that relation to the fubject and predicate of the propofition to be proved, which the nature of the fyllogifm requires. Thus, fuppofe the propofition I would prove is an univerfal affirmative, I know by the rules of fyllogifins, that there is only one legitimate mode in which an univerfal affirmative propofition can be proved; and that is the first mode of the first figure. I know likewife, that in this mode, both the premises must be univerfal affirmatives; and that the middle dle term must be the fubject of the major, and the predicate of the minor. Therefore of the terms collected according to the general rule, I feek out one or more which have these two properties; first, That the predicate of the propofition to be proved can be univerfally affirmed of it; and fecondly, That it can be universally affirmed of the fubject of the propofition to be proved. Every term you can find which has those two properties, will serve you as a middle term, but no other. In this way, the author gives special rules for all the various kinds of propofitions to be proved; points out the various modes in which they may be proved, and the properties which the middle term must have to make it fit for answering that end. And the rules are illustrated, or rather, in my opinion, purposely darkened, by putting letters of the alphabet for the several terms. |