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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 syllogisms he passes 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 mo dals 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 saved 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 had 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 them; 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 syllogisms with as little E 3
ceremony. So that this great branch of the doctrine of syllogism, so diligently handled by Aristotle, fell into neglect, if not contempt, even while the doctrine of pure syllogisms continued in the highest esteem. Moved by these authorities, I shall let this doctrine rest in peace, without giving the least disturbance to its ashes.
SECT. 7. On Syllogisms that do not belong to Figure and Mode.
Aristotle gives some observations upon imperfect syllogisms 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 syllogism, of which Aristotle takes no notice. These may be reduced to two classes.
The first class comprehends the syllogisms into which any exclusive, restrictive, exceptive, or reduplicate proposition enters. Such propositions are by some called exponible, by others imperfectly modal. The rules given with regard to these are obvious, from a just interpretation of the propositions.
The second class is that of hypothetical syllogisms, which take that denomination from having a hypothetical proposition for one or both premises. Most logicians give the name of bypothetical to all complex propositions which have more terms than one subject and one predicate. I use the word in this large sense; and mean by hypothetical syllogisms, all those in which either of the premises consists of more terms than two. How many various kinds there may be of such syllogisms, has never been ascertained. The logicians have given names to some; such as, the copulative, the conditional, by some called hypothetical, and the disjunctive.
Such syllogisms cannot be tried by the rules of figure and mode. Every kind would require rules peculiar to itself. Logicians have given rules for some kinds; but there are many that have not so much as a name.
The dilemma is considered by most logicians as a species of the disjunctive syllogism. A remarkable property of this kind is, that it may sometimes be happily retorted: it is, it seems, like a handgrenade, which by dextrous management may be thrown back, so as to spend its force upon the assailant. We shall conclude this tedious account of syllogisms with a dilemma mentioned by A. Gellius, and from him by many logicians, as insoluble in any other way.
"Euathlus, a rich young man, desirous of learning the art of pleading, applied to Protagoras, a "celebrated sophist, to instruct him, promising a great sum of money as his reward; one-half of "which was paid down; the other half he bound "himself to pay as soon as he should plead a cause "before the judges, and gain it. Protagoras found "him a very apt scholar; but, after he had made good progress, he was in no haste to plead causes. "The master, conceiving that he intended by this "means to shift off his second payment, took, as "he thought, a sure method to get the better of "his delay. He sued Euathlus before the judges; "and, having opened his cause at the bar, he
pleaded to this purpose. O most foolish young 66 man, do you not see, that, in any event, I must "gain my point? for if the judges give sentence "for me, you must pay by their sentence; if against me, the condition of our bargain is fulfilled, and you have no plea left for your delay, "after having pleaded and gained a cause. To "which Euathlus answered. O most wise master, "I might have avoided the force of your argu"ment, by not pleading my own cause. But, gi"ving up this advantage, do you not see, that "whatever sentence the judges pass, I am safe? "If they give sentence for me, I am acquitted by "their sentence; if against me, the condition of 68 our bargain is not fulfilled, by my pleading a cause, and losing it. The judges, thinking the 60 arguments
arguments unanswerable on both sides, put off "the cause to a long day."
SECT. 1. Of the Last Analytics.
N the first Analytics, syllogisms are considered in respect of their form; they are now to be considered in respect of their matter. The form lies in the necessary connection between the premises and the conclusion; and where such a connection is wanting, they are said 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 propositions of which they are composed, which may be true or false, probable or improbable.
When the premises are certain, and the conclusion drawn from them in due form, this is demonstration, and produces science. Such syllo