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Rh appendix entitled The Catching of Leviathan the Great Whale. Hobbes never took any notice of the Castigations, but ten years later replied to the charges of atheism, &c., made in the non-political part of the appendix, of which he says he then heard for the first time (E.W. iv. 279-384). This Answer was first published after Hobbes’s death.

We may now follow out the more troublesome conflict, or rather series of conflicts, in which Hobbes became entangled from the time of publishing his De corpore in 1655, and which checkered all his remaining years. In Leviathan he had vehemently assailed the system of the universities, as

originally founded for the support of the papal against the civil authority, and as still working social mischief by adherence to the old learning. The attack was duly noted at Oxford, where under the Commonwealth a new spirit of scientific activity had begun to stir. In 1654 Seth Ward (1617–1689), the Savilian professor of astronomy, replying in his Vindiciae academiarum to some other assaults (especially against John Webster’s Examen of Academies) on the academic system, retorted upon Hobbes that, so far from the universities being now what he had known them in his youth, he would find his geometrical pieces, when they appeared, better understood there than he should like. This was said in reference to the boasts in which Hobbes seems to have been freely indulging of having squared the circle and accomplished other such feats; and, when a year later the De corpore (L.W. i.) finally appeared, it was seen how the thrust had gone home. In the chapter (xx.) of that work where Hobbes dealt with the famous problem whose solution he thought he had found, there were left expressions against Vindex (Ward) at a time when the solutions still seemed to him good; but the solutions themselves, as printed, were allowed to be all in different ways halting, as he naively confessed he had discovered only when he had been driven by the insults of malevolent men to examine them more closely with the help of his friends. A strange conclusion this, and reached by a path not less strange, as was now to be disclosed by a relentless hand. Ward’s colleague, the more famous (q.v.), Savilian professor of geometry from 1649, had been privy to the challenge thrown out in 1654, and it was arranged that they should critically dispose of the De corpore between them. Ward was to occupy himself with the philosophical and physical sections, which he did in leisurely fashion, bringing out his criticism in the course of next year (In Th. Hobbii philosophiam exercitatio epistolica). Wallis was to confine himself to the mathematical chapters, and set to work at once with characteristic energy. Obtaining an unbound copy of the De corpore, he saw by the mutilated appearance of the sheets that Hobbes had repeatedly altered his demonstrations before he issued them at last in their actual form, grotesque as it was, rather than delay the book longer. Obtaining also a copy of the work as it had been printed before Hobbes had any doubt of the validity of his solutions, Wallis was able to track his whole course from the time of Ward’s provocation—his passage from exultation to doubt, from doubt to confessed impotence, yet still without abandoning the old assumption of confident strength; and all his turnings and windings were now laid bare in one of the most trenchant pieces of controversial writing ever penned. Wallis’s Elenchus geometriae Hobbianae, published in 1655 about three months after the De corpore, contained also an elaborate criticism of Hobbes’s whole attempt to relay the foundations of mathematical science in its place within the general body of reasoned knowledge—a criticism which, if it failed to allow for the merit of the conception, exposed only too effectually the utter inadequacy of the result. Taking up mathematics when not only his mind was already formed but his thoughts were crystallizing into a philosophical system, Hobbes had, in fact, never put himself to school and sought to work up gradually to the best knowledge of the time, but had been more anxious from the first to become himself an innovator with whatever insufficient means. The consequence was that, when not spending himself in vain attempts to solve the impossible problems that have always waylaid the fancy of self-sufficient beginners, he took an interest only in the elements of geometry, and never had any notion of the full scope of mathematical science, undergoing as it then was (and not least at the hands of Wallis) the extraordinary development which made it before the end of the century the potent instrument of physical discovery which it became in the hands of Newton. He was even unable, in dealing with the elementary conceptions of geometry, to work out with any consistency the few original thoughts he had, and thus became the easy sport of Wallis. At his advanced age, however, and with the sense he had of his powers, he was not likely to be brought to a better mind by so insulting an opponent. He did indeed, before allowing an English translation of the De corpore (E.W. i.) to appear in 1656, take care to remove some of the worst mistakes exposed by Wallis, and, while leaving out all the references to Vindex, now profess to make, in altered form, a series of mere “attempts” at quadrature; but he was far from yielding the ground to the enemy. With the translation, in the spring of 1656, he had ready Six Lessons to the Professors of Mathematics, one of Geometry, the other of Astronomy, in the University of Oxford (E.W. vii. 181-356), in which, after reasserting his view of the principles of geometry in opposition 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 maintain positions that he 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 Arithmetica infinitorum (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 administering Due Correction for Mr Hobbes, or School Discipline for not saying his Lessons right, in a piece that differed from the Elenchus 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 multiplied by every new utterance. But it was no longer a fight over mathematical questions only. Wallis having been betrayed originally 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 , used for a point, to mean a visible mark made with a hot iron; whereupon he was charged by Wallis with gross ignorance for confounding  and. Hence the title of his new piece: Στιγμαὶ ἀγεωμετρίας, ἀγροικίας, ἀντιπολιτείας, ἀμαθείας, or Marks of the Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis, Professor of Geometry and Doctor of Divinity (E.W. vii. 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 questions. 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 thus completed, after a fashion, the scheme he had planned more than twenty years before. So far as the treatise De homine (L.W. ii. 11-32) 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 Leviathan, has all the appearance of having been tagged in haste to the optical chapters (composed years before) as