fell into neglect, if not contempt, even while the doctrine of pure fyllogifms continued in the highest esteem. Moved by thefe authorities, I fhall let this doctrine rest in peace, without giving the leaft disturbance to its afhes.

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SECT. 7. On Syllogifms that do not belong to Figuré and Mode.

Ariftotle gives fome obfervations upon imperfect fyllogifms: fuch as, the Enthimema, in which one of the premifes is not expreffed but understood : Induction, wherein we collect an univerfal from a full enumeration of particulars: and Examples, which are an imperfect induction. The logicians have copied Ariftotle upon these kinds of reafoning, without any confiderable improvement. But to compenfate the modal fyllogifms, which they have laid afide, they have given rules for feveral kinds of fyllogifm, of which Ariftotle takes no notice. Thefe may be reduced to two claffes.

The first class comprehends the fyllogifms into which any exclufive, reftrictive, exceptive, or reduplicative propofition enters. Such propofitions are by fome called exponible, by others imperfectly modal. The rules given with regard to these are obvious, from a juft interpretation of the propofitions.

The fecond clafs is that of hypothetical fyllogifms, which take that denomination from having a hypothetical propofition for one or both premifes. Moft logicians give the name of hypothetical to all complex propofitions which have more terms than one fubject and one predicate. I use

the

the word in this large fenfe; and mean by hypothetical fyllogifms, all thofe in which either of the premises confifts of more terms than two. How many various kinds there may be of fuch fyllogifms, has never been afcertained. The logicians have given names to fome; fuch as the copulative, the conditional by fome called hypothetical, and the disjunctive.

Such fyllogifms cannot be tried by the rules of figure and mode. Every kind would require rules peculiar to itself. Logicians have given rules for fome kinds; but there are many that have not fo much as a name.

A re

The Dilemma is confidered by moft logicians as à fpecies of the disjunctive fyllogifm. markable property of this kind is, that it may fometimes be happily retorted: it is, it feems, like a hand grenade, which by dextrous management may be thrown back, fo as to spend its force upon the affailant. We fhall conclude this tedious account of fyllogifms, with a dilemma mentioned by A. Gellius, and from him by many logicians, as infoluble in any other way.

"Euathlus, a rich young man, defirous of "learning the art of pleading, applied to Protagoras, a celebrated fophift, to inftruct him, promifing a great fum of money as his re"ward; one half, of which was paid down; "the other half he bound himfelf to pay as "foon as he fhould plead a caufe before the judges, and gain it. Protagoras found him a very apt fcholar; but, after he had made "good progrefs, he was in no hafte to plead caufes. The mafter, conceiving that he in"tended by this means to fhift off his fecond payment, took, as he thought, a fure method "to get the better of his delay.

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athlus before the judges; and,

He fued Eu

having open

ed

"ed his caufe at the bar, he pleaded to this "purpose. O moft foolish young man, do you "not fee, that, in any event, I muft gain my "point? for if the judges give fentence for me,

you must pay by their fentence; if against "me, the condition of our bargain is fulfilled, "and you have no plea left for your delay, af"ter having pleaded and gained a caufe. To "which Euathlus answered. O moft wife mafter, I might have avoided the force of your argument, by not pleading my own caufe. "But, giving up this advantage, do you not "fee, that whatever fentence the judges pafs, "I am fafe? If they give fentence for me, I "am acquitted by their fentence; if against me, "the condition of our bargain is not fulfilled, "by my pleading a cause, and lofing it. The "judges, thinking the arguments unanfwera"ble on both fides, put off the cause to a long « day.”

CHAP.

CHAP. V.

Account of the remaining books of the Organon.

SECT. I. Of the Laft Analytics.

IN the first Analytics, fyllogifms are confidered

in respect of their form; they are now to be confidered in respect of their matter. The form lies in the neceffary connection between the premises and the conclufion; and where fuch a connection is wanting, they are faid to be informal, or vicious in point of form.

But where there is no fault in the form, there may be in the matter; that is, in the propofitions of which they are compofed, which may be true or false, probable or improbable.

When the premises are certain, and the conclufion drawn from them in due form, this is demonftration, and produces fcience. Such fyllogifms are called apodictical; and are handled in the two books of the Laft Analytics. When the premises are not certain, but probable only, fuch fyllogifms are called dialectical; and of them he treats in the eight books of the Topicks. But there are fome fyllogifms which feem to be perfect both in matter and form, when they are not really fo as, a face may feem beautiful which is

but

but painted. These being apt to deceive, and produce a falfe opinion, are called fophiftical; and they are the subject of the book concerning Sophisms.

To return to the Laft Analytics, which treat of demonstration and of fcience: We shall not pretend to abridge thefe books; for Ariftotle's writings do not admit of abridgement: no man in fewer words can fay what he fays; and he is not often guilty of repetition. We fhall only give some of his capital conclufions, omitting his long reafonings and nice diftictions, of which his genius was wonderfully productive.

All demonftration must be built upon principles already known; and these upon others of the fame kind; until we come at firft principles, which neither can be demonftrated, nor need be, being evident of themselves.

We cannot demonftrate things in a circle, fupporting the conclufion by the premises, and the premises by the conclufion. Nor can there be an infinite number of middle terms between the first principle and the conclufion.

In all demonftration, the first principles, the conclufion, and all the intermediate propofitions; must be neceffary, general, and eternal truths: for of things fortuitous, contingent, or mutable, or of individual things, there is no demonftration.

Some demonftrations prove only, that the thing is thus affected; others prove, why it is thus affected. The former may be drawn from a remote caufe, or from an effect: but the latter must be drawn from an immediate caufe; and are the most perfect.

The firft figure is bet adapted to demonftration, because it affords conclufions univerfally affirmative; and this figure is commonly used by the mathematicians.

The