SUBTILTIES OF LOGIC.

Euclid, a native of Megara, and disciple of Socrates, did not follow the taste of his master; for instead of addicting himself chiefly to the doctrine of morality, he set himself to refine the subtilties of logic. He founded a sect which passes for a branch, or rather a continuation of the school of Xenophanes, Parmenides, and Zeno Eleates. Those who followed his method of philosophizing were named Megarians, Megarici, and afterwards Disputers, and at last Dialecticians. His opinions are little known, and it is pretty difficult to comprehend any thing in his doctrine of the nature of good. He made use of nothing but conclusions in his disputes, by which we may judge of the ardour and impetuosity he mixed them with. We may also judge of it by the character of the temper he inspired his disciples with; which was

a rage or fury of disputing. Eubulides, who succeeded him, was the inventor of divers sophisms exceedingly captious and perplexing; these are the names of them: the liar, the deceiver, the electra, the veiled, the sorites, the horned, the bald. You will find in Gassendus a good explanation of all these sophisms, supported by instances. You will find the same in M. Menage. I shall content myself with showing what the liar was. He supposed a man who said I lie, and then he argued in such a manner that from what he said true he concluded that he lied, and from what he lied in, he concluded he spoke truth. ‘ Si dicis te mentiri, verumque dicis, mentiris: dicis autem te mentiri, verumque dicis, mentiris igitur.” Cicero, Acad. Quæst. lib. iv. cap. 28 et 29. ¹³¹ To puzzle the more, they made one consider that, in such reasonings as this, as to the form, the conclusion was true; “how then dare you reject the conclusion of this,” said they, “while you admit that of others?” Cicero observes that Chrysippus, who formed himself these difficulties, could not resolve them. “Qui potes hanc non probare, quum probaveris ejusdem generis superiorem? Hæc Chrysippea sunt ne ab ipso qui dem dissoluta.” They build the same sophism upon that which Epimenides, who was of the isle of Crete, had said, “that all the Cretans were liars.” “He lied then in saying so,” concluded they; therefore the Cretans are not liars, then they deserve to be believed; then the affirmation of Epimenides is to be believed; and then the Cretans are liars. Aristotle has acknowledged that these sophistries are almost inexplicable. Africanus, the civilian, having put a case in which the knot was indissoluble, compares it to the sophism here in question. “I said this argument was one of the insoluble, called by logicians the liar; for whatever is laid down for true, will be found to be false.” Africanus, lib. lxxxviii. ¹³² It is good to see how Seneca laughs at those who lost their time in such vain subtilties: “Quid me destines in eo, quem tu ipse Pseudomenon appellas, de quo tantum librorum compositum est? Ecce tota mihi vita mentitur: hanc coargue, hanc ad verum, si acutus es, redige. Seneca, Epist. xiv. pag. m. 241. ¹³³—Why do you teaze me with your Pseudomenos (liar) on which so many volumes have been composed? Come sir, my whole life is a lie; let me have a specimen of your art in disproving this, and in showing it to be true.”

Some by too intense an application to these kinds of things, contracted a consumptive illness that killed them, and this has been put in their epitaph:

Philetas I; destroy’d by painful toils
In search of subtilties and captious wiles.

Athen, lib. ix.

It might be said then, without hyperbole or figure, that the inventions of Eubulides were murderous sophisms.

Observe, that the school-men have tried their skill upon this matter; you need only see what they say of the propositions which they call se ipsas falsificantes. Alexis, who succeeded Eubulides, was a great lover of dispute, and engaged in it with so much vehemence that he acquired a surname by it. Diodorus, another disciple of Eubulides, was so intoxicated and infatuated with this sort of contest, that he also died with grief, because he could not resolve upon the instant the dialectical questions that Stilpo had put to him. If this sect had contributed any thing to the illustration of truth, it ought to be looked upon as a prodigy; for nothing is more proper to confound and darken things, and to fill the minds of readers and auditors with doubts, than an application to the quintessence and subtilties of controversy, which degenerate almost always into wrangling, obstinacy, fraud and sophistry. Among all the philosophical exercises, there

are none in which a moderation is more necessary than in that of disputation; for no sooner are you passed certain bounds, than you fall into useless trifles and even irregularities, which give the mind an ill turn, and hinder it from finding truth.

A disputation well regulated and confined to proper limits, and where an explanation of things is only intended, is the most useful thing in the world in the search after truth; disputation has not been ill resembled to the striking of two flints together, which fetches out the invisible sparks of fire. But it is very difficult to keep a just medium in this office, and to this chiefly may be applied the observation of Tacitus: “Retinuit quod est difficillimum ex sapientia, or in sapientia modum. Tacit in Vita Agricolæ, cap. iv. ¹³⁴—And what is most difficult, he retained a mean in philosophy.” If this passion for disputing be never so little indulged, it begets a taste of false glory which engages always to find subjects of contradiction, and thenceforward good sense is no more hearkened to, and we are abandoned to the desire of passing for great masters of subtilties. A professor may be excused the pains he takes to awaken by this way, the mind of a young scholar; but Euclid and his successors can never be justified for having made this the principal business of their whole lives, and for attempting to distinguish themselves by inventions that tended only to confound the mind. They were of no service for the correcting of vice or curing any important defect; and besides, they did not in any manner advance the knowledge of speculative truths, but were much more proper to retard it.

A spirit of disputation easily degenerates into a false subtilty; those who cultivate it fall into their own snare, and after having confounded their adversary, they find themselves unable to resist the

sophisms they have invented, and which may be turned against their own doctrines; I have already mentioned Chrysippus, as a great instance of what I have here observed. He professed himself a dogmatical philosopher, and yet laboured almost as much for the interest of scepticism as Carneades, who professed to affirm nothing; both sacrificed chiefly to the subtilties of their own wit; they were in no great pain about truth, provided they had the pleasure to make their objections sparkle and triumph.

Chrysippus, for instance, took extraordinary pains to find out the solution of a sophism which was called sorites, from the Greek word σωρός, which signifies acervus, a heap; hence it is that the Latins thought they might call that sophism Acervalem. Ulpian has thus defined it; “when from positions evidently true, the disputation is led, through the shortest mutations, to positions evidently false.” Cicero describes it so as to make the etymology of the word be understood: “Primùm quidem hoc reprehendendum quod captiosissimo genere interrogationis utuntur. Quod genus minime in Philosophia probari solet, quum aliquid minutatim et gradatim additur aut demitur: Soritas hos vocant qui acervum efficiunt uno addito grano. Cicero, Academ. quæst. lib. iv. p. 65. ¹³⁵ —In the first place this is blameable, that they make use of a most captious kind of interrogation; which method is by no means commendable in philosophy, when any thing is minutely and gradually added or taken away: they call those Sorites who make a heap by the addition of a single grain.” They took, for example, a grain of corn, as you shall see below: and from this true proposition, “one grain of com is not a heap,” they endeavoured to lead one by degrees to this visible falsity,“one grain of corn makes a heap.” You will find some examples in Sextus Empiricus, of the use that was made of this captious

way of interrogating. There is a long and forcible passage by Cicero, whereby it will appear that they pretended to show, by the help of the Sorites, that the mind of man never attains to the knowledge of the fixed point that divides the opposite qualities, or that determines precisely the nature of every thing. This was their question: "wherein consists little, much, length, breadth, smallness, greatness, &c. Do three grains of corn make a heap?” The answer was, “no.” “Do four grains make a heap?” The answer was still the same. They went on in their questions, from grain to grain, without any end; and if you had answered at last, “here is the heap;” they pretended that your answer was absurd, since it supposes that one single grain made the difference between what is not a heap and what is one. I could prove, by the same method, that a great drinker is never drunk. I would ask, “will One drop of wine make him drunk?” “No,” you will say; “will two drops do it?” “by no means; nor three nor four neither?’ I would continue my questions drop by drop, and if you should tell me, when you come to the nine hundred and ninety-ninth drop, “he is not drunk,” and then coming to the next drop, “he is drunk,” I should conclude that one drop of wine makes the specific difference between a great drinker’s being drunk and not being drunk, which is absurd. If the interrogations were made at every three pints, you might easily observe the difference between enough and two much; but the maker of the Sorites has the choice of his weapons, and makes use of the least particles of quantity, and goes from one to the other, to hinder you from finding any fixed point, that separates the not being drunk from the being drunk, little from much, enough from too much, &c. A man, unacquainted with logic, would justly laugh at such cavils; he would appeal to common sense, and to that degree of light which, in the use of civil life, is sufficient to make us discern in general what is little, much, &c.: but a professed logician was not allowed to have recourse to that tribunal; he was obliged to answer in due form; and unless he found a solution according to the rules of his art, he lost the field of battle; his defeat and overthrow were unavoidable. At this time, a Hibernian tutor, who should teaze a professor of Salamanca with a thousand logical cavils, and who should receive for answer, “common sense, notorious evidence sufficiently shows that your consequences are false,” would pass for the conqueror; and it would be said with reason that the professor was worsted: for it was his duty to answer in due form, and according to the rubric of his trade, since his thesis was attacked by that rubric. Chrysippus, who knew his duty very well in that point, plainly saw that the Sorites of the Megaric dialectitians, required a categorical solution, and found no other expedient than to answer a certain number of interrogations, and then to be silent.

Observe well, that Horace fell upon the admirers of the ancients with a Sorites: it is a very fine passage; suffer me to give way to the temptation of placing it here:

Si meliora dies, ut vina poemata reddit,
Scire velim, pretium chartis quotus arroget annus
Scriptor abhinc annos centum qui decidit, inter
Perfectos veteresque referri debet? an inter
Viles atque novos? excludat jurgia finis.
Est vetus atque probus, centum qui perficit annos.
Quid? qui deperiit minor uno mense, vel anno,
Inter quos referendus erit? veteres ne Poetas?
An quos et praesens et postera respuet aetas?
Iste quidem veteres inter ponetur honestè,
Qui vel mense brevi, vel toto est junior anno.
Utor permisso, caudaque pilos ut equinae
Paulatim vello, demo unum, demo etiam unum,
Dum cadat elusus ratione ruentis acervi,
Qui redit ad fastos, et virtutem aestimat annis,
Miraturque nihil, nisi quod Libitina sacravit.

Horat. Epist. 1, lib. 2, ver. 34, et seq.

If verse, like wine, improves, matur’d by age,
What length of years gives value to the page?
Say, shall the bard, who chanc'd to write, we know,
A century, nor more nor less ago,
Stand with the ancients, or the moderns, plac'd?
With these admired, or with those disgrac'd?
A century, sure, so long ago he writ,
Makes him an ancient and a classic wit.
What rank is his, an age who cannot boast,
More modern by a month or year at most?
'Midst bards of old, or those whom, later born,
The present and the future times shall scorn?
Who wants a month, a year at most, may be
Allow'd the priv'lege of antiquity.
This frank concession will my cause avail;
By single hairs, I bare the horse's tail.
One from a hundred years you let me take,
From that another, 'till the heap I break;
Confuting him who values wit by years,
Nor living bards, because alive, reveres.

He who said that by too much disputing we lose sight of truth, was no fool. How many are there who enjoy a profound tranquillity in a firm belief of the doctrine of truth, who would be full of doubts if they were to hear the reasons on both sides of the question? And how many are there, who instead of clearing up their doubts, would involve themselves more deeply therein, if they were to hearken to the answers and replies of two subtle disputants? The former, I mean those who have no doubts, would complain of the ill offices which disputing had done them, would complain that they are much more fluctuating than before, and say to the two antagonists what Terence puts into the mouth of one of his actors: “Fecistes prope; incertior sum multo quam du dum Terentius in Phormione, Act. II, Seen. Ill, ver. 18 & 19. ¹³⁶—Thank you, gentlemen, I am more uncertain than ever.” It was St Ambrose’s opinion that subtle logical disputes were so much to be feared, that the grace of God should be begged by public processions

that we might not be exposed to them. I cannot in this place forbear mentioning what St Ambrose says of St Augustin (a very subtle logician), that public prayers ought to be put up to restrain, or rather extirpate, his furious fondness for disputation. It is an instrument which may be of good use against lies, but it will not stop there, for after having destroyed error it attacks truth; it is like those corrosive powders, which after having eaten the proud flesh of a wound, would prey upon the quick flesh, and eat into the very bones if they were let alone. But not to go so far off, let us be content to consider the ill effect of disputing, for the reasons that Montagne gives us. “Our disputes,” says he, Montagne, Essais, livr. iii, cap. viii, pag. m. 252, 253. ¹³⁷ “ought to be as much prohibited and punished as other verbal crimes. What vices do they not awaken and promote, being always commanded and governed by passion? We quarrel first with the arguments and then with the men; we learn only to dispute that we may contradict, and each contradicting and contradicted, the fruit of disputing is the loss and ruin of truth; therefore Plato in his commonwealth, forbids the exercise of it to unskilful and disingenuous minds. What will be the consequence? One runs to the east, another as far as the west; they lose the principal and put it aside in the crowd of incidents. At the end of an hour’s storming, they know not what they look for; one is high, another low, another wide; one catches at a word or a simile, another is insensible of what is said in opposition to him, so eager is he in his course, and thinks of following himself not you. One finding himself weak, fears every thing, refuses every thing, and in the beginning confounds and puzzles his subject; or in the heat of the debate stops short, and grows silent through a peevish ignorance, affecting an insolent contempt, or a foolish modesty shunning contention. One, provided he strikes, cares not how much he lays himself open; another counts his words, and reckons them for arguments; another makes advantage of his voice and lungs. Here is one that concludes against himself, and another stuns you with prefaces and useless digressions; another falls into downright railing, and picks a quarrel with his adversary to free himself from the society and argument of a wit that bears hard upon him; and this last man sees nothing in reason, but incloses you with his dialectical clauses, and the formularies of his art.” Rohault’s preface to his Physics. ¹³⁸

It may very justly be said that the spirit and character of our Euclid and his successors, have prevailed in the Christian schools ever since the famous dialectician Abelard: but what has been produced by it in favour of truth? What philosophical doctrines have the Nominalists and Realists, the Thomists and Scotists cleared? What have they done but multiply opinions, and found out the art of maintaining, pro and con, by the help of sundry barbarous terms? what one maintains the other denies, and they have all of them distinctions and subterfuges ready at hand to prevent their being put to silence. They have by turns made the most contrary opinions triumph; now this is the most natural consequence of this method of philosophizing. Mr Rohault has admirably well described it: “There is,” says he, “an invincible stubbornness observed in most of those who have gone through their course of philosophy, and who probably are fallen into such a pernicious disposition of mind, only because they have not been used to convincing truths, and see that those who maintain any doctrine whatsoever in public, always triumph over those who endeavour to prove the contrary, so that with them all things pass for probabilities. They do not look upon study as a means to

arrive at the discovery of any new truths, but as a witty sport in which people exercise themselves, the end of which is so to confound true with false, by means of certain subtilties, that they may equally defend one or the other, without ever appearing forced to give, up by any arguments, any extravagant opinion they may maintain; and indeed this is the common success of all public actions, where often in the same pulpit, opinions perfectly contrary are alternately proposed and equally triumph, without the matter in hand being explained, or any truth being better established.”—I say nothing of an evil infinitely more considerable, which this disputing and dialectical spirit has produced. It has passed from the chairs of the philosophers into the schools of divinity, and has turned the most important points of the Christian morality into problems; for what doctrine of morality have not the loose casuists shaken and so obscured, that the only way to arrive at certainty, is to hearken solely to the simplicity of the scriptures, without any manner of regard to the subtle and captious reasonings of those doctors?

“The most lively and subtle wits,” says father Rapin, “are not always the properest for philosophy. The imagination had better be a little heavy, than suffer itself to evaporate into too refined speculations; the plain good sense of Socrates triumphed over all the arts and all the subtlety of the Sophists. Philosophy did not become abstract till it ceased to be solid; they stuck to formalities when they had no longer any thing real to say, nor did they ever think of having recourse to subtilties, till they had no hopes of making pure reason prevail. That Protagoras, who first sought for captious arguments, assumed this subtle air only because he had a wrong turn of mind. They spoiled all, says Seneca, by refining every thing; for in order to make a vain ostentation of wit, they forsook the most essential parts of the

sciences, they began to weaken the truth of things by the artifice of words, making use of sophistry when they were at a loss for good reasons. By this new art, Nausiphanes and Parmenides overthrew every thing; so that the simplicity of reason was corrupted by the artifice of discourse, and they ridiculed truth instead of treating it with respect. This was the error of the Spaniards of the last century; they treated philosophy as they treated politics, both which by their speculative genius they carried up to inconceivable subtilties, every scholar refining upon his master; whence happened such a disorder as Seneca complains of. Disputation became all the fruit of philosophy, and they made use of it, not so much to cure the soul as to exercise the wit.”

Arts. Euclid & Chrysippus.