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exponible; by others imperfectly modal. The rules given with regard to these are obvious, from a just interpretation of the propositions.
The fecond class is that of hypothetical syllogisms, which take that denomination from having a hypothetical proposition for one or both premises. Moft logicians give the name of hypothetical to all complex propositions which have more terms than one fubject and one predicate, I use the word in this large sense; and mean by hypothetical fyllogisms, all those in which either of the premises confits of more terms than two. How many various kinds there
. inay be of fuch fyllogisms, has never been afcertained. The logicians, have given names to fome ;: such as, the copulative, the conditional by some called hypothetical, and the disjunctive. 4. TE VIS.
Such fyllogisms cannot be tried by the rules of figure and mode., Every kind would require rules peculiar to itself. Logicians have given rules for some kinds but there are many that have not fo much as a name.
The Dilemma is considered by most logicians as a species of the disjunctive fyl
logism. A remarkable property of this kind is, that it may sometimes be happily retorted: it is, it seems, like a hand-grenade, which by dextrous management may be thrown back, so as to spend its force upon the assailant.
the assailant. We shall conclude this tedious account of fyllogisms, with a dilemma mentioned by A. Gellius, and from him by many logicians, as infoluble in
to Protagoras, a celebrated fophift, to “ instruct him, promising a great sum of
money as his reward ; one half of which
was paid down the other half he " bound himself to pay as soon as he « should plead a cause before the judges, “ and gain it. Protagoras found him a a
very apt scholar; but, after he had “ made' good progress, he was in no hafte 49. to plead causes. The master, concei
ving that he intended by this means to “ shift off his second payment, took, as “ he thought, a fure method to get the " better of his delay. He fued Euathlus “ before the judges; and, having opened his cause at the bar, he pleaded to this
purpose. O moft foolish young man, “ do you not see, that, in any event, I “ must gain my point ? for if the judges
give fentence for me, you must pay
delay, after having pleaded and gained a “ cause. To which Euathlus answered. 'cs
O most wise master, I might have a“ voided the force of your argument, by
not pleading my own cause. But, giá
ving up this advantage, do you not see, " that whatever sentence the judges pass,
I am safe? If they give sentence for 911 me, I am acquitted by their fentence ; “ if against me, the condition of our bar
gain is not fulfilled, by my pleading a
cause, and losing it. The judges, think"ing the arguments unanswerable on “both-fides, put off the cause to a long
IN N the first Analytics, fyllogisms are con
sidered in respect of their form; they are now to be considered in respect of their
The form lies in the necessary connection between the premises and the conclusion; and where such a connection is wanting, they are said to be informal, or vicious in point of form. ; ;, ROSA * But where there is no fault in the form, there
may be in the matters that is, in the propositions of which they are composed, which may be true or false, probable or improbable. When the premises are certain, and the
, conclusion drawn from them in due form, this iş demonstration, and produces science. Such fyllogifms are called apodic
tical; and are handled in the two books of the Last Analytics. When the premises are not certain, but probable only, such syllogisms are called dialectical; and of them he treats in the eight books of the Topicks. But there are fome syllogisms which seem to be perfect both in matter and form, when they are not really so: as, a face may seem beautiful which is but painted. These being apt to deceive, and produce a false opinion, are called sophistical; and they are the subject of the book concerning Sophisms.
To return to the Last Analytics, which treat of demonstration and of science: We Thall not pretend to abridge these books ; for Aristotle's writings do not admit of abridgement: no man in fewer words can say what he says; and he is not often guilty of repetition. We shall only give some of his capital conclusions, omitting his long reasonings and nice distinctions, of which his genius was wonderfully productive.
All demonftration must be built upon principles already known ; and these upon others of the same kind; until we come at last to first principles, which neither