Hobbes's Quarrels With Dr. Wallis The Mathematician

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Title:     Hobbes's Quarrels With Dr. Wallis The Mathematician
Author: Isaac Disraeli [More Titles by Disraeli]

HOBBES'S passion for the study of Mathematics began late in life--attempts to be an original discoverer--attacked by WALLIS--various replies and rejoinders--nearly maddened by the opposition he encountered--after four years of truce, the war again renewed--character of HOBBES by Dr. WALLIS, a specimen of invective and irony; serving as a remarkable instance how the greatest genius may come down to us disguised by the arts of an adversary--HOBBES'S noble defence of himself; of his own great reputation; of his politics; and of his religion--a literary stratagem of his--reluctantly gives up the contest, which lasted twenty years.

The Mathematical War between HOBBES and the celebrated Dr. WALLIS is now to be opened. A series of battles, the renewed campaigns of more than twenty years, can be described by no term less eventful. Hobbes himself considered it as a war, and it was a war of idle ambition, in which he took too much delight. His "Amata Mathemata" became his pride, his pleasure, and at length his shame. He attempted to maintain his irruption into a province he ought never to have entered in defiance, by "a new method;" but having invaded the powerful natives, he seems to have almost repented the folly, and retires, leaving "the unmanageable brutes" to themselves:

Ergo meam statuo non ultra perdere opellam
Indocile expectans discere posse pecus.

His language breathes war, while he sounds his retreat, and confesses his repulse. The Algebraists had all declared against the Invader.

Wallisius contra pugnat; victusque videbar
Algebristarum Theiologumque scholis,
Et simul eductus Castris exercitus omnis
Pugnæ securus Wallisianus ovat.

And,

Pugna placet vertor--
Bella mea audisti--&c.

So that we have sufficient authority to consider this Literary Quarrel as a war, and a "Bellum Peloponnesiacum" too, for it lasted as long. Political, literary, and even personal feelings were called in to heat the temperate blood of two Mathematicians.

What means this tumult in a Vestal's veins?

Hobbes was one of the many victims who lost themselves in squaring the circle, and doubling the cube. He applied, late in life, to mathematical studies, not so much, he says, to learn the subtile demonstrations of its figures, as to acquire those habits of close reasoning, so useful in the discovery of new truths, to prove or to refute. So justly he reasoned on mathematics; but so ill he practised the science, that it made him the most unreasonable being imaginable, for he resisted mathematical demonstration, itself![A]

His great and original character could not but prevail in everything he undertook; and his egotism tempted him to raise a name in the world of Science, as he had in that of Politics and Morals. With the ardour of a young mathematician, he exclaimed, "Eureka!" "I have found it." The quadrature of the circle was indeed the common Dulcinea of the Quixotes of the time; but they had all been disenchanted. Hobbes alone clung to his ridiculous mistress. Repeatedly confuted, he was perpetually resisting old reasonings and producing new ones. Were only genius requisite for an able mathematician, Hobbes had been among the first; but patience and docility, not fire and fancy, are necessary. His reasonings were all paralogisms, and he had always much to say, from not understanding the subject of his inquiries.

When Hobbes published his "De Corpore Philosophico," 1655, he there exulted that he had solved the great mystery. Dr. Wallis, the Savilian professor of mathematics at Oxford,[1] with a deep aversion to Hobbes's political and religious sentiments, as he understood them, rejoiced to see this famous combatant descending into his own arena. He certainly was eager to meet him single-handed; for he instantly confuted Hobbes, by his "Elenchus Geometriæ Hobbianæ." Hobbes, who saw the newly-acquired province of his mathematics in danger, and which, like every new possession, seemed to involve his honour more than was necessary, called on all the world to be witnesses of this mighty conflict. He now published his work in English, with a sarcastic addition, in a magisterial tone, of "Six Lessons to the Professors of Mathematics in Oxford." These were Seth Ward[2] and Wallis, both no friends to Hobbes, and who hungered after him as a relishing morsel. Wallis now replied in English, by "Due Correction for Mr. Hobbes, or School-discipline for not saying his Lessons Right," 1656. That part of controversy which is usually the last had already taken place in their choice of phrases.[3]

In the following year the campaign was opened by Hobbes with "ΣΤΙΓΜΑΙ; or, marks of the absurd Geometry, rural Language, Scottish Church-politics, and Barbarisms, of John Wallis." Quick was the routing of these fresh forces; not one was to escape alive! for Wallis now took the field with "Hobbiani Puncti dispunctio! or, the undoing of Mr. Hobbes's Points; in answer to Mr. Hobbes's ΣΤΙΓΜΑΙ, id est, Stigmata Hobbii." Hobbes seems now to have been reduced to great straits; perhaps he wondered at the obstinacy of his adversary. It seems that Hobbes, who had been used to other studies, and who confesses all the algebraists were against him, could not conceive a point to exist without quantity; or a line could be drawn without latitude; or a superficies be without depth or thickness; but mathematicians conceive them without these qualities, when they exist abstractedly in the mind; though, when for the purposes of science they are produced to the senses, they necessarily have all the qualities. It was understanding these figures, in the vulgar way, which led Hobbes into a labyrinth of confusions and absurdities.[4] They appear to have nearly maddened the clear and vigorous intellect of our philosopher; for he exclaims, in one of these writings:--

"I alone am mad, or they are all out of their senses: so that no third opinion can be taken, unless any will say that we are all mad."

Four years of truce were allowed to intervene between the next battle; when the irrefutable Hobbes, once more collecting his weak and his incoherent forces, arranged them, as well as he was able, into "Six Dialogues," 1661. The utter annihilation he intended for his antagonist fell on himself. Wallis borrowing the character of "The Self-tormentor" from Terence, produced "Hobbius Heauton-timorumenos (Hobbes the Self-tormentor); or, a Consideration of Mr. Hobbes's Dialogues; addressed to Robert Boyle," 1662.

This attack of Wallis is of a very opposite character to the arid discussion of abstract blunders in geometry. He who began with points, and doubling the cube, and squaring the circle, now assumes a loftier tone, and carrying his personal and moral feelings into a mere controversy between two idle mathematicians, he has formed a solemn invective, and edged it with irony. I hope the reader has experienced sufficient interest in the character of Hobbes to read the long, but curious extract I shall now transcribe, with that awe and reverence which the old man claims. It will show how even the greatest genius may be disguised, when viewed through the coloured medium of an adversary. One is, however, surprised to find such a passage in a mathematical work.

"He doth much improve; I mean he doth, proficere in pejus; more, indeed, than I could reasonably have expected he would have done;--insomuch, that I cannot but profess some relenting thoughts (though I had formerly occasion to use him somewhat coarsely), to see an old man thus fret and torment himself to no purpose. You, too, should pity your antagonist; not as if he did deserve it, but because he needs it; and as Chremes, in Terence, of his Senex, his self-tormenting Menedemus--

Cum videam miserum hunc tam excruciarier
Miseret me ejus. Quod potero adjutabo senem.

"Consider the temper of the man, to move your pity; a person extremely passionate and peevish, and wholly impatient of contradiction. A temper which, whether it be a greater fault or torment (to one who must so often meet with what he is so ill able to bear), is hard to say.

"And to this fretful humour you must add another as bad, which feeds it. You are therefore next to consider him as one highly opinionative and magisterial. Fanciful in his conceptions, and deeply enamoured with those phantasmes, without a rival. He doth not spare to profess, upon all occasions, how incomparably he thinks himself to have surpassed all, ancient, modern, schools, academies, persons, societies, philosophers, divines, heathens, Christians; how despicable he thinks all their writings in comparison of his; and what hopes he hath, that, by the sovereign command of some absolute prince, all other doctrines being exploded, his new dictates should be peremptorily imposed, to be alone taught in all schools and pulpits, and universally submitted to. To recount all which he speaks of himself magnificently, and contemptuously of others, would fill a volume. Should some idle person read over all his books, and collecting together his arrogant and supercilious speeches, applauding himself, and despising all other men, set them forth in one synopsis, with this title, Hobbius de se--what a pretty piece of pageantry this would make!

"The admirable sweetness of your own nature has not given you the experience of such a temper: yet your contemplation must have needs discerned it, in those symptoms which you have seen it work in others, like the strange effervescence, ebullition, fumes, and fetors, which you have sometimes given yourself the content to observe, in some active acrimonious chymical spirits upon the injection of some contrariant salts strangely vexing, fretting, and tormenting itself, while it doth but administer sport to the unconcerned spectator. Which temper, being so eminent in the person we have to deal with, your generous nature, which cannot but pity affliction, how much soever deserved, must needs have some compassion for him: who, besides those exquisite torments wherewith he doth afflict himself, like that

----quo Siculi non invenere Tyranni
Tormentum majus--

is unavoidably exposed to those two great mischiefs; an incapacity to be taught what he doth not know, or to be advised when he thinks amiss; and moreover, to this inconvenience, that he must never hear his faults but from his adversaries; for those who are willing to be reputed friends must either not advertise what they see amiss, or incommode themselves.

"But, you will ask, what need he thus torment himself? What need of pity? If he have hopes to be admitted the sole dictator in philosophy, civil and natural, in schools and pulpits, and to be owned as the only magister sententiarum, what would he have more?

"True, if he have; but what if he have not? That he had some hopes of such an honour, he hath not been sparing to let us know, and was providing against the envy that might attend it (nec deprecabor invidiam, sed augendo, ulciscar, was his resolution); but I doubt these hopes are at an end. He did not find (as he expected) that the fairies and hobgoblins (for such he reputes all that went before him) did vanish presently, upon the first appearance of his sunshine: and, which is worse, while he was on the one side guarding himself against envy, he is, on the other side, unhappily surprised by a worse enemy, called contempt, and with which he is less able to grapple.

"I forbear to mention (lest I might seem to reproach that age which I reverence) the disadvantages which he may sustain by his old age. 'Tis possible that time and age, in a person somewhat morose, may have riveted faster that preconceived opinion of his own worth and excellency beyond others. 'Tis possible, also, that he may have forgotten much of what once he knew. He may, perhaps, be sometimes more secure than safe; while trusting to what he thinks a firm foundation, his footing fails him; nor always so vigilant or quicksighted as to discern the incoherence or inconsequence of his own discourses; unwilling, notwithstanding, to make use of the eyes of other men, lest he should seem thereby to disparage his own; but certainly (though his will may be as good as ever) his parts are less vegete and nimble, as to invention at least, than in his younger days.

"While he had endeavoured only to raise an expectation, or put the world in hopes of what great things he had in hand (to render all philosophy as clear and certain as Euclid's Elements), if he had then died, it might, perhaps, have been thought by some that the world had been deprived of a great philosopher, and learning sustained an invaluable loss, by the abortion of so desired a piece. But since that Partus Montis is come to light, and found to be no more than what little animals have brought forth, and that deformed enough and unamiable, he might have sooner gone off the stage with more advantage than now he is like to do; such is the misfortune for a man to outlive his reputation!

"By this time, perhaps, you may see cause to pity him while you see him falling. But if you consider him tumbling headlong from so great a height, 'twill make some addition to that compassion which doth already begin to work. You are therefore next to consider that when, upon the account of geometry, he was unsafely mounted to that height of vanity, he did unhappily fall into the hands of two mathematicians, who have used him so unmercifully as would have put a person of greater patience into passion, and meeting with such a temper, have so discomposed him that he hath ever since talked idly: and to augment the grief, these mathematicians were both divines--he had rather have fallen by any other hand. These mathematical divines (a term which he had thought incomponible) began to unravel the wrong end; and while he thought they should have first untiled the roof, and by degrees gone downward, they strike at the foundation, and make the building tumble all at once; and that in such confusion, that by dashing one part against another, they make each help to destroy the whole. They first fall upon his last reserve, and rout his mathematics beyond a possibility of rallying; and by firing his magazine upon the first assault, make his own weapons fight against him. Not contented herewith, they enter the breach, and pursue the rout through his Logics, Physics, Metaphysics, Theology, where they find all in confusion."

This invective and irony from this celebrated mathematician, so much out of the path of his habitual studies, might have proved a tremendous blow; but the genius of Hobbes was invulnerable to mere human opposition, unless accompanied by the supernatural terrors of penal fires or perpetual dungeons. Our hero received the whole discharge of this battering train, and stood invulnerable, while he returned the fire in "Considerations upon the Reputation, Loyalty, Manners, and Religion of Thomas Hobbes, of Malmesbury, written by way of Letter to a learned person, Dr. Wallis," 1662.

It is an extraordinary production. His lofty indignation retorts on the feeble irony of his antagonist with keen and caustic accusations; and the green strength of youth was still seen in the old man whose head was covered with snows.

From this spirited apology for himself I shall give some passages. Hobbes thus replied to Dr. Wallis, who affected to consider the old man as a fit object for commiseration.

"You would make him contemptible, and move Mr. Boyle to pity him. This is a way of railing too much beaten to be thought witty: besides, 'tis no argument of your contempt to spend upon him so many angry lines, as would have furnished you with a dozen of sermons. If you had in good earnest despised him, you would have let him alone, as he does Dr. Ward, Mr. Baxter, Pike, and others, that have reviled him as you do. As for his reputation beyond the seas, it fades not yet; and because, perhaps, you have no means to know it, I will cite you a passage of an epistle written by a learned Frenchman to an eminent person in France, in a volume of epistles." Hobbes quotes the passage at length, in which his name appears joined with Galileo, Descartes, Bacon, and Gassendi.

In reply to Wallis' sarcastic suggestion that an idle person should collect together Hobbes's arrogant and supercilious speeches applauding himself, under one title, Hobbius de se, he says--

"Let your idle person do it; Mr. Hobbes shall acknowledge them under his hand, and be commended for it, and you scorned. A certain Roman senator having propounded something in the assembly of the people, which they, misliking, made a noise at, boldly bade them hold their peace, and told them he knew better what was good for the commonwealth than all they; and his words are transmitted to us as an argument of his virtue; so much do truth and vanity alter the complexion of self-praise. You can have very little skill in morality, that cannot see the justice of commending a man's self, as well as of anything else, in his own defence; and it was want of prudence in you to constrain him to a thing that would so much displease you.

"When you make his age a reproach to him, and show no cause that might impair the faculties of his mind, but only age, I admire how you saw not that you reproached all old men in the world as much as him, and warranted all young men, at a certain time which they themselves shall define, to call you fool! Your dislike of old age you have also otherwise sufficiently signified, in venturing so fairly as you have done to escape it. But that is no great matter to one that hath so many marks upon him of much greater reproaches. By Mr. Hobbes's calculation, that derives prudence from experience, and experience from age, you are a very young man; but, by your own reckoning, you are older already than Methuselah.

"During the late trouble, who made both Oliver and the people mad but the preachers of your principles? But besides the wickedness, see the folly of it. You thought to make them mad, but just to such a degree as should serve your own turn; that is to say, mad, and yet just as wise as yourselves. Were you not very imprudent to think to govern madness?"--p. 15.

"The king was hunted as a partridge in the mountains, and though the hounds have been hanged, yet the hunters were as guilty as they, and deserved no less punishment. And the decypherers (Wallis had decyphered the royal letters),[5] and all that blew the horn, are to be reckoned among the hunters. Perhaps you would not have had the prey killed, but rather have kept it tame. And yet who can tell? I have read of few kings deprived of their power by their own subjects that have lived any long time after it, for reasons that every man is able to conjecture."

He closes with a very odd image of the most cynical contempt:--

"Mr. Hobbes has been always far from provoking any man, though, when he is provoked, you find his pen as sharp as yours. All you have said is error and railing; that is, stinking wind, such as a jade lets fly when he is too hard girt upon a full belly. I have done. I have considered you now, but will not again, whatsoever preferment any of your friends shall procure you."

These were the pitched battles; but many skirmishes occasionally took place. Hobbes was even driven to a ruse de guerre. When he found his mathematical character in the utmost peril, there appeared a pamphlet, entitled "Lux Mathematica, &c., or, Mathematical Light struck out from the clashings between Dr. John Wallis, Professor of Geometry in the celebrated University of Oxford (celeberrima Academia), and Thomas Hobbes, of Malmesbury; augmented with many and shining rays of the Author, R. R." 1672.

Here the victories of Hobbes are trumpeted forth, but the fact is, that R. R. should have been T. H. It was Hobbes's own composition! R. R. stood for Roseti Repertor, that is, the Finder of the Rosary, one of the titles of Hobbes's mathematical discoveries. Wallis asserts that this R. R. may still serve, for it may answer his own book, "Roseti Refutator, or, the Refuter of the Rosary."

Poor Hobbes gave up the contest reluctantly; if, indeed, the controversy may not be said to have lasted all his life. He acknowledges he was writing to no purpose; and that the medicine was obliged to yield to the disease.

Sed nil profeci, magnis authoribus Error
Fultus erat, cessit sic Medicina malo.

He seems to have gone down to the grave, in spite of all the reasonings of the geometricians on this side of it, with a firm conviction that its superficies had both depth and thickness.[6] Such were the fruits of a great genius, entering into a province out of his own territories; and, though a most energetic reasoner, so little skilful in these new studies, that he could never know when he was confuted and refuted.[7]

FOOTNOTES:

[A] The origin of his taste for mathematics was purely accidental: begun in love, it continued to dotage. According to Aubrey, he was forty years old when, "being in a gentleman's library, Euclid's Elements lay open at the 47th Propos. lib. i., which, having read, he swore 'This is impossible!' He read the demonstration, which referred him back to another--at length he was convinced of that truth. This made him in love with geometry. I have heard Mr. Hobbes say that he was wont to draw lines on his thighs and on the sheets a-bed."

[1] The author of the excellent Latin grammar of the English language, so useful to every student in Europe, of which work that singular patriot, Thomas Hollis, printed an edition, to present to all the learned Institutions of Europe. Henry Stubbe, the celebrated physician of Warwick, to whom the reader has been introduced, joined, for he loved a quarrel, in the present controversy, when it involved philosophical matters, siding with Hobbes, because he hated Wallis. In his "Oneirocritica, or an Exact Account of the Grammatical Parts of this Controversy," he draws a strong character of Wallis, who was indeed a great mathematician, and one of the most extraordinary decypherers of letters; for perhaps no new system of character could be invented for which he could not make a key; by which means he had rendered the most important services to the Parliament. Stubbe quaintly describes him as "the sub-scribe to the tribe of Adoniram" (i.e. Adoniram Byfield, who, with this cant name, was scribe to the fanatical Assembly of Divines), and "as the glory and pride of the Presbyterian faction."

[2] Dr. Seth Ward, after the Restoration made Bishop of Salisbury, said, some years before this event was expected, that "he had rather be the author of one of Hobbes's books than be king of England." But afterwards he seemed not a little inclined to cry out Crucifige! He who, to one of these books, the admirable treatise on "Human Nature," had prefixed one of the highest panegyrics Hobbes could receive!--Athen. Oxon. vol. ii. p. 647.

[3] It is mortifying to read such language between two mathematicians, in the calm inquiries of square roots, and the finding of mean proportionals between two straight lines. I wish the example may prove a warning. Wallis thus opens on Hobbes:--"It seems, Mr. Hobbs, that you have a mind to say your lesson, and that the mathematic professors of Oxford should hear you. You are too old to learn, though you have as much need as those that be younger, and yet will think much to be whipped.

"What moved you to say your lessons in English, when the books against which you do chiefly intend them were written in Latin? Was it chiefly for the perfecting your natural rhetoric whenever you thought it convenient to repair to Billingsgate?--You found that the oyster-women could not teach you to rail in Latin. Now you can, upon all occasion, or without occasion, give the titles of fool, beast, ass, dog, &c., which I take to be but barking; and they are no better than a man might have at Billingsgate for a box o' the ear.

"You tell us, 'though the beasts that think our railing to be roaring have for a time admired us; yet now you have showed them our ears, they will be less affrighted.' Sir, those persons (the professors themselves) needed not the sight of your ears, but could tell by the voice what kind of creature brayed in your books: you dared not have said this to their faces."--He bitterly says of Hobbes, that "he is a man who is always writing what was answered before he had written."

[4] Dr. Campbell's art. on Hobbes, in "Biog. Brit." p. 2619.

[5] Found in the king's tent at Naseby, and which were written to the queen on important political subjects, in a cypher of which they only had the key. They were afterwards published in a quarto pamphlet, and did much mischief to the royal cause.--ED.

[6] The strange conclusions some mathematicians have deduced from their principles concerning the real quantity of matter, and the reality of space, have been noticed by Pope, in the Dunciad:--

"Mad Mathésis alone was unconfined,
Too mad for mere material chains to bind:
Now to pure space lifts her ecstatic stare;
Now running round the circle, finds its square."
Dunciad, Book iv. ver. 31.

[7] When all animosities had ceased, after the death of Hobbes, I find Dr. Wallis, in a very temperate letter to Tenison, exposing the errors of Hobbes in mathematical studies; Wallis acknowledges that philology had never entered into his pursuits,--in this he had never designed to oppose his superior genius: but it was Hobbes who had too often turned his mathematical into a philological controversy. Wallis has made a just observation on the nature of mathematical truths:--"Hobbes's argumentations are destructive in one part of what is said in another. This is more convincingly evident, and more unpardonable, in mathematics than in other discourses, which are things capable of cogent demonstration, and so evident, that though a good mathematician may be subject to commit an error, yet one who understands but little of it cannot but see a fault when it is showed him."

Wallis was an eminent genius in scientific pursuits. His art of decyphering letters was carried to amazing perfection; and among other phenomena he discovered was that of teaching a young man, born deaf and dumb, to speak plainly. He humorously observes, in one of his letters:--"I am now employed upon another work, as hard almost as to make Mr. Hobbes understand mathematics. It is to teach a person dumb and deaf to speak, and to understand a language."

[The end]
Isaac Disraeli's essay: Hobbes's Quarrels With Dr. Wallis The Mathematician

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