and of fuch we shall afterwards fpeak: but they have nothing to do with the fyftem of figure and mode.

When we go without the circle of the mathema-. tical sciences, I know nothing in which there feems, to be fo much demonftration as in that part of logic which treats of the figures and modes of fyllogifm; but the few remarks we have made, fhew, that it has fome weak places: and befides, this fyftem cannot be used as an engine to rear it self.

The compass of the fyllogiftic fyftem as an engine of fcience, may be difcerned by a compendious and general 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 fpecies 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 common to the whole genus does not belong to that species or individual.

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 question belongs VOL. III. E

to

to a fpecies or individual which is part of that genus.

I apprehend, that in this short view, every conclufion that falls within the compass 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 reasoning in all the three: fo that it is not strange, 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 species and individual belonging to it. This is a principle of undoubted certainty indeed, but of no great depth. Aristotle 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 demonftration, it lands at laft in this principle as its ultimate conclufion. O curas hominum! 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 divided into pure and modal. In a pure pro

pofition,

pofition, the 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 contingent, or poffible, or impoffible. These are the four modes obferved by Aristotle, from which he denominates a propofition modal. His genuine difciples maintain, that thefe 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 difpute; 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 premises are, pure propofitions. A modal fyllogifm is that in which either of the premifes is a modal propofition.

The fyllogifms, of which we have already faid fo much, are thofe only which are pure as well as categorical. But when we confider, that through all the figures and modes, a fyllogifm may have one premise modal of any of the four modes, while the other is pure, or it may have both premises modal, and that they may be either of the fame mode or of different modes; what prodigious variety arises from all these combinations? Now it

is the business 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 firange, that when he had employed only four chapters in difcuffing one hundred and ninety-two modes, true and falfe, of pure fyllogifms, he should employ fifteen upon modal fyllogifms.

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

Keckerman, a famous Dantzican profeffor, who spent his life in teaching and writing logic, in his huge folio fyftem of that science, publifhed anno 1600, calls the doctrine of the modals the crux logicorum. With regard to the fcholaftic doctors, among whom this was a proverb, De modalibus non guftabit afinus, he thinks it very dubious, whether they tortured moft the modal fyllogifms, or were most tortured by them. But thofe crabbed geniuses, says he, made this doctrine so 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 the modals is adapted to the Greek language. The modal terms were frequently used by the Greeks in their difputations; and, on that account, are so fully handled by Aritotle but in the Latin tongue you fhall 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 difpute, through his ignorance of the modals.

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

Ludovicus Vives, whom I mention, not as a devotee of Ariftotle, 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 fyftem in the time of Ariftotle, that moft 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 Ariftotle hath handled diligently; but that, as the ufe of them is not great, and their rules difficult, he thinks it not worth while to enter into the difcuffion of them; recommending to those who would understand them, the most learned paraprafe of Joannes Monlorius upon the firft 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 fyllogifms with as little