Hobbes–Wallis controversy

The Hobbes–Wallis controversy was a polemic debate that continued from the mid-1650s well into the 1670s, between the philosopher Thomas Hobbes and the mathematician John Wallis. It was sparked by De corpore, a philosophical work by Hobbes in the general area of physics. The book contained not only a theory of mathematics subordinating it to geometry and geometry to kinematics, but a claimed proof of the squaring of the circle by Hobbes. While Hobbes retracted this particular proof, he returned to the topic with other attempted proofs. A pamphleteering exchange continued for decades. It drew in the newly formed Royal Society, and its experimental philosophy, to which Hobbes was (on principle) opposed.

The sustained nature of the exchanges can be attributed to several strands of the intellectual situation of the time. In mathematics there were open issues, namely the priority (pedagogic, or theoretical) to be assigned to geometry and algebra; and the status of algebra itself, which (from an English standpoint) had been pulled together by the text of William Oughtred, as more than a collection of symbolic abbreviations. Socially, the formation of the group of Royal Society members, and the status of the publication Philosophical Transactions, was brought to a point as the quarrel proceeded, with Hobbes playing the outsider versus the self-selecting guild.

Hobbes was an easy target, on the ground chosen by Wallis. The failure of his attempts to solve the impossible problems he set himself were inevitable, but he neither backed down completely, nor applied adequate self-criticism. And on the level of character, Wallis was as intransigent as Hobbes was dogmatic, and this inflicted damage on both of their reputations. Quentin Skinner writes: "There is no doubt that at the personal level Wallis behaved badly (as was widely conceded at the time)."

Part of the significance of the controversy is that Hobbes felt that, in the later stages, the Royal Society was in some way complicit in the attacks from Wallis, despite the fact that he had many friends as Fellows in it. This attitude presented one of the obstacles to Hobbes himself becoming a member, though not the only one.

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