ral view of the conclufion drawn, and the argument ufed to prove it, in each of the three figures.

In the first figure, the conclufion affirms or denies fomething, of a certain fpecies or individual; and the argument to prove this conclufion is, That the fame thing may be affirmed or denied of the whole genus to which that species or individual belongs.

In the fecond figure, the conclufion is, That fome fpecies or individual does not belong to fuch a genus; and the argument is, That fome attribute cominon to the whole genus does not belong to that species or in

dividual.

In the third figure, the conclufion is, That fuch an attribute belongs to part of a genus; and the argument is, That the attribute in queftion belongs to a fpecies or individual which is part of that

genus.

I apprehend, that, in this fhort view, every conclufion that falls within the compafs of the three figures, as well as the mean of proof, is comprehended. The rules of all the figures might be eafily deduced from it; and it appears, that there is only one principle of reafoning in all the three; fo that it is not ftrange, that a fyllogifm of one figure should be reduced to one of another figure.

The general principle in which the whole terminates, and of which every categorical fyllogifm is only a particular application, is this, That what is affirmed or denied of the whole genus, may be affirmed or denied of every fpecies and individual belonging to it. This is a principle of undoubted certainty indeed, but of no great depth. Ariftotle and all the logicians affume it as an axiom or first principle, from which the fyllogiftic fyftem, as it were, takes its departure: and after a tedious voyage, and great expence of demonstrations, it lands at laft in this principle as its ultimate conclufion. O curas bominum! O quantum eft in rebus inane !

SECT. 6. On Modal Syllogifms.

Categorical propofitions, befides their quantity and quality, have another affection, by which they are di vided into pure and modal. In a pure propofition, the predicate

predicate is barely affirmed or denied of the fubject; but in a modal propofition, the affirmation or negation is modified, by being declared to be neceffary or contin-gent, or poffible or impoffible. Thefe are the four modes obferved by Ariftotle, from which he denominates a propofition modal. His genuine difciples maintain, that these are all the modes that can affect an affirmation or negation, and that the enumeration is complete. Others maintain, that this enumeration is incomplete; and that when an affirmation or negation is faid to be certain or uncertain, probable or improbable, this makes a modal propofition, no less than the four modes of Ariftotle. We fhall not enter into this dif pute; but proceed to obferve, that the epithets of pure and modal are applied to fyllogifms as well as to propofitions. A pure fyllogifm is that in which both premifes are pure propofitions. A modal fyllogifm is that in which either of the premifes is a modal propofition.

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The fyllogifins of which we have already faid fo much, are thofe only which are pure as well as categcrical. But when we confider, that through all the fgures and modes, a fyllogifmi may have one premife modal of any of the four modes, while the other is pure, or it may have both premifes modal, and that they may be either of the fame mode or of different modes; what prodigious variety arifes from all thefe combinations? Now it is the bufinefs of a logician, to fhew how the conclufion is affected in all this variety of cafes. Ariftotle has done this in his First Analytics, with immenfe labour; and it will not be thought strange, that when he had employed only four chapters in difcuffing one hundred and ninety-two modes, true and falfe, of pure fyllogifms, he fhould employ fifteen upon modal fyllogifms.

I am very willing to excufe myself from entering upon this great branch of logic, by the judgment and example of those who cannot be charged either with want of refpect to Aristotle, or with a low esteem of the fyllogiftic art.

Keckerman, a famous Dantzican profeffor, who fpent his life in teaching and writing logic, in his huge folio fyftem of that fcience, published ann. 1600, calls the doctrine of the modals the crux logicorum. With

regard

regard to the scholaftic doctors, among whom this was a proverb, De modalibus non gustabit afinus, he thinks it very dubious, whether they tortured most the modal fyllogifms, or were most tortured by them. But those crabbed geniuses, fays he, made this doctrine fo very thorny, that it is fitter to tear a man's wits in pieces than to give them folidity. He defires it to be observed, that the doctrine of modals is adapted to the Greek language. The modal terms were frequently used by the Greeks in their difputations; and, on that account, are fo fully handled by Ariftotle; but in the Latin tongue you shall hardly ever meet with them. Nor do I remember, in all my experience, fays he, to have obferved any man in danger of being foiled in a dispute, through his ignorance of the modals.

This author, however, out of refpect to Ariftotle, treats pretty fully of modal propofitions, fhewing how to diftinguish their fubject and predicate, their quantity and quality. But the modal fyllogifmis he paffes over altogether.

Ludovicus Vives, whom I mention, not as a devotee of Aristotle, but on account of his own judgment and learning, thinks that the doctrine of modals ought to be banished out of logic, and remitted to grammar; and that if the grammar of the Greek tongue had been brought to a system in the time of Ariftotle, that most acute philofopher would have faved the great labour he has bestowed on this fubject.

Burgerfdick, after enumerating five claffes of modal fyllogifms, obferves, that they require many rules and cautions, which Aristotle hath handled diligently; but as the use of them is not great, and their rules are very difficult, he thinks it not worth while to enter into the difcuffion of them; recommending to those who would understand them, the most learned paraphrafe of Joannes Monlorius, upon the first book of the First Analytics.

All the writers of logic for two hundred years back that have fallen into my hands, have paffed over the rules of modal fyllogifins with as little ceremony. So that this great branch of the doctrine of fyllogifm, fo diligently handled by Aristotle, fell into neglect, if not contempt,

contempt, even while the doctrine of pure fyllogifins continued in the highest esteem. Moved by thefe authorities, I fhall let this doctrine reft in peace, without giving the least disturbance to its ashes.

SECT. 7. On Syllogifms that do not belang to Figure and Mode

Ariftotle gives fome obfervation upon imperfect fyllogifins: 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 thefe kinds of reafoning, without any confiderable im provement. But to compenfate the modal fyllogifins, which they have laid afide, they have given rules-for feveral kinds of fyllogifm, of which Ariftotle takes no notice. These may be reduced to two claffes.

The first clafs comprehends the fyllogifins 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 thefe are obvious, from a just interpretation of the propofitions.

The fecond clafs is that of hypothetical fyllogifms, which take that denomination from having a hypothe tical propofition for one or both premifes. Moft logi cians give the name of bypothetical to all complex pro→ pofitions which have more terms than one one predicate. I ufe the word in this large fenfe; and fubject 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 con→ ditional, by fome called hypothetical, and the dif junctive.

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

I

The

The Dilemma is confidered by moft logicians as a fpecies of the disjunctive fyllogifm. A remarkable 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 fpend 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 nian, defirous of learning "the art of pleading, applied to Protagoras, a cele"brated fophift, to inftruct him, promifing a great "fum of money as his reward; one half of which was "paid down; the other half he bound himself to pay "as foon as he fhould plead a caufe before the judges, ❝and gain it. Protagoras found him a very apt fcho"lar; but, after he had made good progrefs, he was "in no hafte to plead caufes. The mafter, conceiv"ing that he intended by this means to fhift off his "fecond payment, took, as he thought, a fure me"thod to get the better of his delay. He fued Euath"lus before the judges; and, having opened his caufe. "at the bar, he pleaded to this purpose. O moft fool"ifh young man, do you not fee, that in any event, I "muft gain my point? for if the judges give sentence "for me, you must pay by their fentence; if against 66 me, the condition of our bargain is fulfilled, and you "have no plea left for your delay, after having plead"ed and gained a caufe. To which Euathlus anfwer❝ed. O most wife mafter, I have avoided the force "of your argument, by not pleading my own cause. "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 againft me, the condition of our bar"gain is not fulfilled, by my pleading a caufe, and lofing it. The judges, thinking the arguments un"anfwerable on both fides, put off the cause to a long "day."

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CHAP.