H O B B E S 37 Professors of Mathematics, one of Geometry, the other of Astronomy, in the University of Oxford (E. W., vii. pp. 181-356), in which, after reasserting his view of the principles of geometry in opposi tion to Euclid s, he proceeded to repel Wallis s objections with no lack of dialectical skill, and with an unreserve equal to Wallis s own. He did not scruple, in the ardour of conflict, even to main tain positions that lie had resigned in the translation, and he was not afraid to assume the offensive by a counter criticism of three of Wallis s works then published. When he had thus disposed of the " Paralogisms" of his more formidable antagonist in the first five lessons, he ended with a lesson on "Manners" to the two professors together, and set himself gravely at the close to show that he too could be abusive. In this particular part of his task, it must be allowed, he succeeded very well ; his criticism of Wallis s works, especially the great treatise Arithmctica Infinito- riim (1655), only showed how little able he was to enter into the meaning of the modern analysis. Wallis, on his side, was not less ready to keep up the game in English than he had been to begin it in Latin. Swift as before to strike, in three months time he had deftly turned his own word against the would-be master by admin istering Due Correction for Mr Hobbes, or School Discipline for not saying his Lessons right, in a piece that differed from the Elcnchus only in being more biting and unrestrained. Having an easy task in defending himself against Hobbes s trivial criticism, he seized the opportunity given him by the English translation of the De Corpore to track Hobbes again step by step over the whole course, and now to confront him with his incredible inconsistencies multi plied by every new utterance. But it was no longer a fight over mathematical questions only. Wallis having been betraye l origin ally by his fatal cleverness into the pettiest carping at words, Hobbes had retorted in kind, and then it became a high duty in the other to defend his Latin with great parade of learning and give fresh provocation. One of Wallis s rough sallies in this kind suggested to Hobbes the title of the next rejoinder with which, in 1657, he sought to close the unseemly wrangle. Arguing in the Lessons that a mathematical point must have quantity, though this were not reckoned, he had explained the Greek word tniy^-r), used for a point, to mean a visible mark made with a hot iron ; where upon he was charged by Wallis with gross ignorance for confound ing crriyjUT] and a-Tiy/^a. Hence the title of his new piece : ~S,riyu.a.i A-yea>,ueTpi as ( Aypoi/aas-, Aj/TiTroAireias, Afj.adeias, or M^arks of tlic Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis, Professor of Geometry and Doctor of Divinity (E. W., vii. pp. 357-400). He now attacked more in detail but not more happily than before Wallis s great work, while hardly attempting any further defence of his own positions ; also he repelled with some force and dignity the insults that had been heaped upon him, and fought the verbal points, but could not leave the field without making political insinuations against his adversary, quite irrelevant in themselves and only noteworthy as evidence of his own resignation to Cromwell s rule. The thrusts were easily and nimbly parried by Wallis in a reply (Hobbiani Puncti Dispunctio, 1657) occupied mainly with the verbal ques tions. Irritating as it was, it did not avail to shake Hobbes s determination to remain silent ; and thus at last there was peace for a time. Before the strife flamed up again, Hobbes had published, in 1658, the outstanding section of his philosophical system, and tints com pleted, after a fashion, the scheme he had planned more than twenty years before. So far as the treatise De Hominc (L. W., ii. pp. 1-132) was concerned, the completion was more in name than in fact. It consisted for the most part of an elaborate theory of vision which, though very creditable to Hobbes s scientific insight, was out of place, or at least out of proportion, in a philosophical consideration of human nature generally. The remainder of the treatise, dealing cursorily with some of the topics more fully treated in the Human Nature and the Lcviatlian, has all the ap pearance of having been tagged in haste to the optical chapters (composed years before) 1 as a makeshift for the proper transition required in the system from questions of Body Natural to questions of Body Politic. Hobbes had in fact spent himself in his earlier constructive efforts, and at the age of seventy, having nothing to add to his doctrine of Man as it was already in one form or another before the world, was content with anything that might stand for the fulfilment of his philosophical purpose. But he had still in him more than twenty years of vigorous vitality, and, not conscious matical chapters, in general (not exact) keeping with the English edition of 1(55(5. The Vindex episode, referred to in the Six Lessons, becomes intelligible only by going beyond Molesworth to the original Latin edition of 1655. 1 They were composed originally, in a somewhat different and rather more extended form, as the second part of an English treatise on Optics, completed by the year 1646. Of this treatise, preserved in Harleian MSS. 3360, Molesworth otherwise prints the dedication to the marquis of Newcastle, and the concluding paragraphs (E. W., vii. pp. 467-471). to himself of any shortcoming, looked forward, now his hands were free, to doing battle for his doctrines. Rather than remain quiet, on finding no notice taken of his latest production, he would him self force on a new conflict with the enemy. Wallis having mean while published other works and especially a comprehensive treatise on the general principles of calculus (Ma.tlicsis Univcrsalis, 1657), he might take this occasion of exposing afresh the new-fangled methods of mathematical analysis and reasserting his own earlier positions. Accordingly, by the spring of 1660, he hail managed to put his criticism and assertions into five dialogues under the title Examinatio et Emcndatio Mathematical Hodicrncc qualis explicatur in Libris Johannis Wallisii, with a sixth dialogue so called, con sisting almost entirely of seventy or more propositions on the circle and cycloid. 2 Wallis, however, would not take the bait. Hobbes then tried another tack. Next year, having solved, as he thought, another ancient crux, the duplication of the cube, he had his solu tion brought out anonymously at Paris in French, so as to put Wallis and other critics off the scent and extort a judgment that might be withheld from a work of his. The artifice was successful, and no sooner had Wallis publicly refuted the solution than Hobbes claimed the credit of it, and went more wonderfully than ever astray in its defence. He presently republished it (in modified form), with his remarks, at the end of a new Latin dialogue which he had meanwhile written in defence of another part of his philo sophical doctrine. This was the Dialogics Physicus, sivc De J atura Aeris (L. W., iv. pp. 233-296), fulminated in 1661 against Boyle and other friends of Wallis who, as he fancied, under the influence of that malevolent spirit, were now in London, after the Restora tion, forming themselves into a society (incorporated as the Royal Society in 1662) for experimental research, to the exclusion of him self personally, and in direct contravention of the method of physical inquiry enjoined in the De Corpore. 6 All the laborious manipulation recorded in Boyle s New Experiments touching the Spring of the Air (1660), which Hobbes chose, without the least warrant, to take as the manifesto of the new "academicians," seemed to him only to confirm the conclusions he had reasoned out years before from speculative principles, and he warned them that if they were not content to begin where he had left off their work would come to nought. To as much of this diatribe as concerned himself Boyle quickly replied with force and dignity, but it was from Hobbes s old enemy that retribution came, in the scathing satire Hobbim Hcauton-timorumcnos (1662). Wallis, who had deftly steered his course amid all the political changes of the pre vious years, managing ever to be on the side of the ruling power, was now apparently stung to fury by a wanton allusion in Hobbes s latest dialogue to a passage of his former life (his deciphering for the Parliament the king s papers taken at Naseby), whereof he had once boasted but after the Restoration could not speak or hear too little. The revenge he took was crushing. Professing to be roused by the attack on his friend Boyle, when he had scorned to lift a finger in defence of himself against the earlier dialogues, he tore them all to shreds with an art of which no general description can give an idea. He got, however, upon more dangerous ground when, passing wholly by the political insinuation against himself, he roundly charged Hobbes with having written Leviathan in sup port of Oliver s title, and deserted his royal master in distress. Hobbes seems to have been fairly bewildered by the rush and whirl of sarcasm .with which Wallis drove him anew from every mathe matical position he had ever taken up, and did not venture forth into the field of scientific controversy again for some years, when he had once followed up the physical dialogue of 1661 by eeven shorter ones, with the inevitable appendix, entitled Problcmata Physica, una cum Magnitudine Circuit (L. W., iv. pp. 297-384), in 1662. 4 But all the more eagerly did he take advantage of Wallis s loose calumny to strike where he felt himself safe. His answer to the personal charges took the form of a letter about him- - L. W., iv. pp. 1-232. The propositions on the circle, forty-six in number (shattered by Wallis in 1662), were omitted by Hobbes when he republishcd the Dialogues in 1668, in the collected edition of his Latin works from which Molesworth reprints. In the part omitted, at p. 154 of the original edition, Hobbes refers to his first introduction to Euclid, in a way that confirms the story in Aubrey quoted in an earlier paragraph. 3 Remaining at Oxford, Wallis, in fact, took no active part in the constitution of the new society, but lie had been, from 1645, one of the originators of an earlier association in London, thus continued or re vived. This earlier society had been continued also at Oxford after the year 1649, when Wallis and others of its members received appoint ments there. 4 The Problcmata Physica was at the same time put into English (with some changes and omission of part of the mathematical appen dix), and presented to the king, to whom the work was dedicated in a remarkable letter apologizing for Leviathan. In its English form, as Seven Philosophical Problems and Two Impositions of Geometry (E. W., vii. pp. 1-68), the work was first published in 1682, after
Hobbes s death.
