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for constructing them. However it is treated of largely, and rales laid down for reducing reafoning to fyllogisms, by fupplying one of the premises when it is understood, by rectifying inversions, and putting the propositions in the proper order.
Here he speaks also of hypothetical fyllogisms; which he acknowledges cannot be resolved into any of the figures, although there be many kinds of them that ought diligently to be observed ; 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 extant.
SECT. 5. Of the Second Book of the Firs
The second book treats of the powers
of fyllogisms, and shows in twenty-seven chapters, how we may perform many feats by them, and what figures and modes are adapted to each. Thus, in some fyllogismis several distinct conclufions may be drawn from the fame premises : in some,
un uo 101 true conclusions may be drawn from false
, premises : in fome, by assuming the co clusion and one premise, you may prove
944 the other; you may turn a direct fyllogism into one leading to an absurdity.
We have likewise precepts given in this book, both to the assailant in a fyllogistical dispute, how to carry on his attack
1991 usad with art, fo as to obtain the victory; and
, to the defendant, how to keep the enemy at such a distance as
O ve lhall never be obliged to yield. From which we learn, that Aristotle introduced in his own school, the practice of fyllogistical disputation, in, stead of the rhetorical difputations which the sophists were wont to use in more ancient times. este
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Remarks. sy'97-y} now
at this SECT. 1. Of the Conversion of Propofitions.
WE have given a summary view of the theory of
pure syllogisms as deliver ed by Aristotle, a theory of which he
claims the fole invention. And I believe it will be difficult, in any science, to find so large a system of truths of so
abstract and so 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 most arduous attempts. I shall now make some remarks
it. As to the conversion of propofitions, the writers on logic commonly satisfy themselves with illustrating each of the rules by an example, conceiving them to be felf-evident when applied to particular cases. But Aristotle has given demonstrations of the rules he mentions. As a specimen, I shall give his demonstration of the first rule. “ Let A B be an universal
negative proposition ; I say, that if A is in no B, it will follow that B is in no A. If
you deny this consequence, let B be “ in fome A, for example, in C; then the “ first supposition will not be true; for
C is of the B's.” In this demonstration, if I understand it, the third rule of conversion is assumed, that if B is in fome A, then A must be in some B, which indecd is contrary to the first supposition. If
the third rule be ashamed for proof of the first, the proof of all the three goes round, in a circle ; for the second and third rulesI are proved by the first. This is a fault in reasoning which Aristotle condemns, and which I would be very unwilling to charge him with, if I could find any better meaning in his demonstration. But it is indeed a fault very difficult to be avoided, when men attempt to prove things that are self-evident.
de ad The rules of conversion cannot be applied to all propositions, but only to those that are categorical ; and we are left to
90 the direction of common sense in the con
. version of other propositions. To give an example : Alexander was the son of Philip; therefore Philip was the father of Alexander : A is greater than B; therefore B is less than A. These are conversions which, as far as I know, do not fall within any
rule in logic; nor do we find any loss for want of a rule in such cases.
Even in the conversion of categorical propositions, it is not enough to transpose the subject and predicate. Both must undergo some change, in order to fit thein for their new station : for in every proVOL. III.
position the subject must be a substantive, or have the force of a substantive; and the predicate must be an adjective, or have the force of an adjective. Hence it follows, that when the subject is an individual, the proposition admits not of conversion. How, for instance, shall we convert this propofition, God is omniscient?
These observation's show, that the doctrine of the converfion of propofitions is not so complete as it appears. The rules are laid down without any limitation; yet they are fitted only to one class of propositions, to wit, the categorical; and of these only to such as have a general term for their subject. d
SECT. 2. On Additions made to. Aristotle's
すべット Although the logicians have enlarged the first and second parts of logic, by explaining fome technical words and distinctions which Aristotle has omitted, and by giving names to some kinds of propofitions which he overlooks ; yet in what concerns the theory of categorical fyllo