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predicate is barely affirmed or denied of the subject ; but in a modal proposition, the affirmation or negation is modified, by being declared to be necessary, or contingent, or possible, or impossible. These are the four modes observed by Aristotle, from which he denominates a proposition modal. His genuine disciples maintain, that there 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 said to be certain or uncertain, probable or improbable, this makes a modal proposition, no less than the four modes of Aristotle. We shall not enter into this dispute ; but proceed to observe, that the epithets of pure and modal are applied to fyllogisms as well as to propositions. A pure syllogisin is that in which both premises are pure propositions. A modal syllogism is that in which either of the premises is a modal proposition.

The fyllogisms of which we have already said so much, are those only, which are pure as well as categorical. But when we consider, that through all the figures


and modes, a fyllogism 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 same mode or of different modes; what prodigious variety arises from all these combinations ? Now it is the business of a logician, to shew how the conclusion is affected in all this variety of cases. Aristotle has done this in his First Analytics, with immense labour; and it will not be thought strange, that when he had employed only four chapters in discussing one hundred and ninety-two modes, true and false, of pure fyllogisms, he should employ fifteen upon modal fyllogisms.

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

Keckerman, a famous Dantzican professor, who spent his life in teaching and writing logic, in his huge folio system of that science, published ann. 1600, calls the doctrine of the modals the crux logi



corum. With regard to the scholastic doctors, among whom this was a proverb, De modalibus non guftabit afinus, he thinks. it very dubious, whether they tortured most the modal fyllogisms, or were most tortured by them. But those 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 desires 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 Aristotle : but in the Latin tongue you shall hardly ever meet with them. Nor do I remember, in all my experience, says he, to have observed any man in danger of being foiled in a dispute, through his ignorance of the modals.

This author, however, out of respect to Aristotle, treats pretty fully of modal propositions, shewing how to distinguish their subject and predicate, their quantity and quality. But the modal fyllogisins he passes over altogether.

Ludovicus Vives, whom I mention, not as a devotee of Aristotle, but on ac



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count of his own judgement 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 Aristotle, that most acute philosopher would have faved the great labour he has bestowed on this subject.

Burgersdick, after enumerating five classes of modal syllogisms, observes, that they require many rules and cautions, which Aristotle hath handled diligently ; but that as the use of them is not great and their rules difficult, he thinks it not worth while to enter into the discussion of théin ; recommending to those who would understand them, the most learned paraphrase 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 passed over the rules of modal fyllogiíms with as little ceremony. So that this great branch of the doctrine of fyllogisın, so diligently handled by Aristotle, fall into negled, if not contempt, even while the doctrine of

púre fyllogifms con


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tinued in the highest esteem. Moved by these authorities, I shall let this doctrine rest in peace, without giving the least difturbance to its afhes.


Sect. 7. On Syllogisms that do not belong

to Figure and Mode.

Aristotle gives fome observations upon imperfect fyllogisms : such as, the Enthimema, in which one of the premises is not expressed but understood : Induction, wherein we collect an universal from a full enumeration of particulars : and Examples, which are an imperfect induction, The logicians have copied Aristotle upon these kinds of reasoning, without any considerable improvement. But to compensate the modal syllogisms, which they have laid aside, they have given rules for several kinds of fyllogifm, of which Aristotle takes no notice.

These may be reduced to two classes,

The first class comprehends the fylloar gisms into which any exclusive, restrictive, exceptive, or reduplicative proposition enters. Such propositions are by fome called 3 C 2


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