comparing things of two different genera (area with volume, for example) and thus an infinite area could be connected to a finite volume. Others used Torricelli's theorem to bolster their own philosophical claims, unrelated to mathematics from a modern viewpoint. Ignace-Gaston Pardies in 1671 used the acute hyperbolic solid to argue that finite humans could comprehend the infinite, and proceeded to offer it as proof of the existences of God and immaterial souls. Since finite matter could not comprehend the infinite, Pardies argued, the fact that humans could comprehend this proof showed that humans must be more than matter, and have immaterial souls. In contrast, Antoine Arnauld argued that because humans perceived a paradox here, human thought was limited in what it could comprehend, and thus is not up to the task of disproving divine, religious, truths. Hobbes' and Wallis' dispute was actually within the realm of mathematics: Wallis enthusiastically embracing the new concepts of infinity and indivisibles, proceeding to make further conclusions based upon Torricelli's work and to extend it to employ arithmetic rather than Torricelli's geometric arguments; and Hobbes claiming that since mathematics is derived from real world perceptions of finite things, "infinite" in mathematics can only mean "indefinite". These led to strongly worded letters by each to the Royal Society and in Philosophical Transactions, Hobbes resorting to namecalling Wallis "mad" at one point. In 1672 Hobbes tried to re-cast Torricelli's theorem as about a finite solid that was extended indefinitely, in an attempt to hold on to his contention that "natural light" (i.e. common sense) told us that an infinitely long thing must have an infinite volume. This aligned with Hobbes' other assertions that the use of the idea of a zero-width line in geometry was erroneous, and that Cavalieri's idea of indivisibles was ill-founded. Wallis argued that there existed geometrical shapes with finite area/volume but no centre of gravity based upon Torricelli, stating that understanding this required more of a command of geometry and logic "than M. Hobs is Master of". He also restructured the arguments in arithmetical terms as the sums of arithmetic progressions, sequences of arithmetic infinitesimals rather than sequences of geometric indivisibles. Oresme had already demonstrated that an infinitely long shape can have a finite area where, as one dimension tends towards infinitely large, another dimension tends towards infinitely small. In Barrow's own words "the infinite diminution of one dimension compensates for the