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and modes, a fyllogifm may have one premife 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 arifes from all thefe 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 immense 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 false, of pure fyllogifins, he should employ fifteen upon modal fyllogifms.
I am very willing to excufe myself from entering upon this great branch of logic, by the judgement 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 science, published ann. 1600, calls the doctrine of the modals the crux logi
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 most the modal fyllogifms, or were most tortured by them. But thofe crabbed geniufes, fays 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 obferved, that the doctrine of the modals is adapted to the Greek language. The modal terms were frequently ufed by the Greeks in their difputations; and, on that account, are so fully handled by Aristotle 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 respect to Aristotle, treats pretty fully of modal propofitions, fhewing how to distinguish their fubject and predicate, their quantity and quality. But the modal fyllogifins he paffes over altogether.
Ludovicus Vives, whom I mention, not as a devotee of Ariftotle, but on ac
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 fyftem 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 that as the use of them is not great and their rules difficult, he thinks it not worth while to enter into the difcuffion of them; recommending to thofe who would underftand them, the moft 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 fyllogifms 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, even while the doctrine of pure fyllogifms con
tinued in the highest esteem. Moved by these authorities, I fhall let this doctrine reft in peace, without giving the leaft difturbance to its afhes.
SECT. 7. On Syllogifms that do not belong to Figure and Mode.
Ariftotle gives fome obfervations upon imperfect fyllogifms: fuch as, the Enthimema, in which one of the premises 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 reasoning, 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 Aristotle takes no notice. Thefe may be reduced to two claffes.
The first class comprehends the fyllogifms into which any exclufive, restrictive, exceptive, or reduplicative propofition enters. Such propofitions are by fome called exponible,
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 fyllogifins, 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 word in this large fenfe; and mean by hypo-thetical fyllogifms, all those 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 so much
as a name.
The Dilemma is confidered by most logicians as a fpecies of the disjunctive fyllogifm.