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5.2 With Wallis
Beyond the spat with Bramhall, Hobbes was caught in a series of conflicts from the time of publishing his De Corpore in 1655. In Leviathan he had assailed the system of the original universities. In 1654 Seth Ward (1617-1689), the Savilian professor of astronomy, replying in his Vindiciae academiarum to the assaults by Hobbes and others (especially John Webster) on the academic system. Errors in De Corpore, especially in the mathematical sections, opened Hobbes to criticism from John Wallis, Savilian professor of geometry. Wallis's Elenchus geomeiriae Hobbianae, published in 1655 contained an elaborate criticism of Hobbes's whole attempt to put the foundations of mathematical science in its place within the general body of reasoned knowledge - a criticism which exposed the utter inadequacy of Hobbes's mathematics. Hobbes's lack of rigour meant that he spent himself in vain attempts to solve the impossible problems that often waylaid self-sufficient beginners, his interest was limited to geometry and he never had any notion of the full scope of mathematical science. He was unable to work out with any consistency the few original thoughts he had, and thus was an easy target. Hobbes took care to remove some of the worst mistakes exposed by Wallis, before allowing an English translation of the De Corpore to appear in 1656. But he still attacked Wallis in a series of Six Lessons to the Professors of Mathematics in 1656.
Wallis had an easy task in defending himself against Hobbes's criticism, and he seized the opportunity given him by the English translation of the De Corpore to re-confront Hobbes with his mathematical inconsistencies. Hobbes responded with Marks of the Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis, Professor of Geometry and Doctor of Divinity. The thrusts were easily parried by Wallis in a reply (Hobbiani puncti dispunctio, 1657). Hobbes finally took refuge in silence and there was peace for a time.
Hobbes published, in 1658, the final section of his philosophical system, completing the scheme he had planned more than twenty years before. De Homine consisted for the most part of an elaborate theory of vision, whose fundamental importance in relation to his political philosophy has often been overlooked. The remainder of the treatise dealt cursorily with some of the topics more fully treated in the Human Nature and the Leviathan.
Wallis had meanwhile published other works and especially a comprehensive treatise on the general principles of calculus (Mathesis universatis, 1657). Hobbes, now with time on his hands, took it upon himself to re-spark their clash. He decided once more to attack the new methods of mathematical analysis and by the spring of 1660, he had managed to put his criticism and assertions into five dialogues under the title Examinatio et emendatio mat hematicae hodiernae quaIls explicatur in libris Johannis Wallisii, with a sixth dialogue so called, consisting almost entirely of seventy or more propositions on the circle and cycloid. Wallis, however, would not take the bait. Hobbes then tried another tack having solved, as he thought, another ancient problem, the duplication of the cube. He had his solution brought out anonymously in French, so as to put his critics off the scent. No sooner had Wallis publicly refuted the solution than Hobbes claimed the credit of it, and went more astray than ever in its defence. He republished it (in modified form), with his remarks, at the end of a 1661 Latin dialogue which he had written in defence of his philosophical doctrine. The Dialogus physicus, sive De natura aeris attacked Robert Boyle and other friends of Wallis who were forming themselves into a society (incorporated as the Royal Society in 1662) for experimental research. Hobbes saw this as a direct contravention of the method of physical inquiry enjoined in the De Corpore. The careful experiments recorded in Boyle's New Experiments touching the Spring of the Air (1660), which Hobbes chose 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 naught. To this ill-conceived diatribe Boyle quickly replied with force and dignity, but it was from Wallis that true retribution came, in the scathing satire Hobbius heauton-timorumenos (1662). Hobbes seems to have been "fairly bewildered by the rush and whirl of sarcasm" and wisely kept aloof from scientific controversy for some years.
However, in response to the more personal attacks Hobbes wrote a letter about himself in the third person, Considerations upon the Reputation, Loyalty, Manners and Religion of Thomas Hobbes. In this biographical piece, he told his own and Wallis's "little stories during the time of the late rebellion" with such effect that Wallis did not attempt a reply.
5.3 With geometers
After a time Hobbes began a third period of controversial activity, which he dragged out until his ninetieth year. The first piece, published in 1666, De principiis et ratiocinatione geometrarum, was an attack on geometrical professors. Three years later he brought his three mathematical achievements together in Quadratura circuli, Cubatio sphaerae, Duplicitio cubii, and as soon as they were once more refuted by Wallis, reprinted them with an answer to the objections. Wallis, who had promised to leave him alone, refuted him again before the year was out. The exchange dragged on through numerous other papers until 1678.
