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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 thofe of which they may be affirmed or denied: thefe things collected together, are the materials from which your middle term is to 4'' bevera
be taken.es for mag
The special rules require you to consider 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 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 mid
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 dan bé univerfally affirmed of it; and secondly, That it can be univerfally affirmed of the fubject of the propofition to be proved. Every term you can find which has thofe two properties, will ferve you as a middle term, but no other. In this way, the author gives fpecial 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 anfwering that end. And the rules are illuftrated, or rather, in my opinion, purpofely darkened, by putting letters of the alphabet for the feveral terms.
SECT. 4. Of the remaining part of the Firft ! Book.
The refolution of fyllogifms requires no other principles but thefe before laid down
for conftructing them.
However it is
treated of largely, and rules laid down for reducing reasoning to fyllogifms, by supplying one of the premises when it is understood, by rectifying inverfions, and putting the propofitions in the proper or
Here he speaks alfo of hypothetical fyllogifms; which he acknowledges cannot be refolved into any of the figures, although there be many kinds of them that ought diligently to be obferved; and which he promises to handle afterwards. But this promise is not fulfilled, as far as I know, in any of his works that are ex
SECT. 5. Of the Second Book of the First Analytics.
The fecond book treats of the powers of fyllogifms, and fhows, in twenty-feven chapters, how we may perform many feats by them, and what figures and modes are adapted to each. Thus, in fome fyllogifms feveral diftinct conclufions may be drawn from the fame premifes: in fome,
true, conclufions may be drawn from falfe premifes in fome, by affuming the conclufion and one premife, you may prove the other; you may turn a direct fyllogifm
into one leading to an abfurdity.
We have likewife precepts given in this
book, both to the
cal difpute, how to carry on his attack with art, fo as to obtain the victory; and VIS DIM
to the defendant, how to keep the enemy at fuch a distance as that he fhall never be obliged to yield. From which we learn, that Aristotle introduced in his own school, the practice of fyllogistical difputation, inftead of the rhetorical difputations which the fophifts were wont to use in more ancient times.
WE have given a fummary view of the theory of pure fyllogifms as deliver
ed by Ariftotle, 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 labour 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 first rule. "Let A B be an univerfal
negative propofition; I fay, that if A is "in no B, it will follow that B is in no A. "If you deny this confequence, let B be "in fome A, for example, in C; then the "firft fuppofition will not be true; for 65 C is of the B's." In this demonftration, 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 firft fuppofition. If