is, that some attribute common to the whole genus does not belong to that species or individual.

In the third figure, the conclusion is, that such an attribute belongs to part of a genus; and the argument is, that the attribute in question belongs to a species or individual which is part of that genus.

I apprehend, that, in this short view, every conclusion 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 easily deduced from it; and it appears, that there is only one principle of reasoning in all the three; so that it is not strange, that a syllogism of one figure should be reduced to one of another figure.

The general principle in which the whole terminates, and of which every categorical syllogism 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 assume it as an axiom or first principle, from which the syllogistic system, as it were, takes it departure: and after a tedious voyage, and great expense of demonstrations, it lands at last in this principle as its ultimate conclusion. O curas hominum! O quantum est in rebus inane!

SECTION VI.

ON MODAL SYLLOGISMS.

CATEGORICAL propositions, besides their quantity and quality, have another affection, by which they are divided into pure and modal. In a pure proposition, the 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 principles 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 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 syllogisms as well as to propositions. A pure syllogism 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 syllogisms 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 syllogism 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 show 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 syllogisms, he should employ fifteen upon modal syllogisms.

I am very willing to excuse myself from entering upon this great branch of logic, by the judgment 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 logicorum. With regard to the scholastic doctors, among whom this was a proverb, De modalibus non gustabit asinus, he thinks it very dubious, whether they tortured most the modal syllogisms, 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 solidity. He desires 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 disputations; 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, showing how to distinguish their sub-ject 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 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 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 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 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 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.

SECTION VII.

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 syllogisms, 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 reduplicative 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 hypothetical 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 it. 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 hand-grenade which, by dexterous management, may be thrown back, so as to speed 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. most foolish young 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 have avoided the force of your argument, by not pleading my own cause. But, giving 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 our bargain is not fulfilled, by my pleading a cause and losing it. The judges, thinking the arguments unanswerable on both sides, put off the cause to a long day."

CHAPTER V.

ACCOUNT OF THE REMAINING BOOKS OF THE ORGANON.

SECTION 1.

OF THE LAST ANALYTICS.

IN 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 connexion between the premises and the conclusion; and where such a connexion 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 sciences. Such syllogisms are called apodictical; and are handled in the two books of the Last Analytics. When the premises are not certain, but probable only, such syllogisms are called dialectical; and of them he treats in the eight books of the Topics. But there are some syllogisms which seem to be perfect both in matter and form, when they are not really so: as, a face may seem beautiful which is but painted. These being apt to deceive, and produce a false opinion, are called sophistical; and they are the subject of the book concerning Sophisms.

To return to the Last Analytics, which treat of demonstration and of science: we shall not pretend to abridge those books; for Aristotle's writings do not admit of abridgment: no man can say what he says in fewer words; and he is not often guilty of repetition. We shall only give some of his capital conclusions, omitting his long reasonings and nice distinctions, of which his genius was wonderfully productive.

All demonstration must be built upon principles already known; and these upon others of the same kind; until we come at last to first principles, which neither can be demonstrated, nor need to be, being evident of themselves.

We cannot demonstrate things in a circle, supporting the conclusion by the premises, and the premises again by the conclusion. Nor can there be an infinite number of middle terms between the first principle and the conclusion.

In all demonstration, the first principles, the conclusion, and all the intermediate propositions, must be necessary, general, and eternal truths; for of things fortuitous, contingent, or mutable, or of individual things, there is no demonstration.