Hobbes: The Art of the Geometricians

Hobbes: The Art of the Geometricians WILLIAM SACKSTEDER IT IS OFTEN SUPPOSEDthat the monolithic character of the philosophy of Thomas Hobbes and most of his more egregious misjudgments in scientific thinking result from his belated infatuation with geometry. For, it is argued, he misunderstood the methodological niceties and virtues of that science. And he overestimated its utility and range of application. Hence he allowed a spurious notion of geometry improperly to engulf all other sciences and to usurp the governing role of philosophic principles. Thus our textbook history. I wish here to argue to the contrary that Hobbes precisely separates the art of the geometricians, which he sometimes calls logistica, from all other and distinct methods of science and philosophy. Moreover, he is enabled to do so by exactly defining logistica as the proper analytics of the geometricians. It is a methodology correlated to its own specific science--to a precisely delimited conception of mathematics. His own special notion of geometry may be repugnant to our modem way of regarding that science. And it may not advance ancient traditions as he insisted on its behalf. His mathematics is certainly eccentric to the important accomplishments of his own time. But the geometrical science which is correlated with the logistic method is viable according to its own stipulations. And it is not superaltem to other sciences as they are conceived in his system. It is rather distinguished from them. My thesis is that it is its proper method which effectively defines geometry in Hobbes's strict sense. That method is distinctive, so that it is only one specific case of methodological pronouncements more general to philosophy and to all science. Thus it is prevented from being applied as if sufficient to other and nonmathematical sciences. But in explicating that methodology, Hobbes is troubled by a naming problem. He calls it the "art of the geometricians," as 1 have in my title. He also names it logistica, as I shall for brevity's sake. But he is unwontedly tentative with the latter name, perhaps because it suggests just that identity with logic itself which he wishes to deny. Also the Latin name is plural, rather than singular, although he allows a singular usage similar to our standard singular usage of "mathematics"--a title also plural in origin. He occasionally invokes another antique plural, namely analytica, along with its direct English translation, "the analytics of the geometricians." But these two mislead in another way. For logistica is one complete methodology which includes both analytic and synthetic phases in ways on which I shall insist in a moment. I now adopt his occasional usage whereby the Latin logistica names that whole method which is appropriate to geometry. Besides its problem of nomenclature, Hobbes's explication of this methodology suffers a textual displacement unusual within the careful architectonics of his system. In the chapter entitled "On Method," in the De Corpore, Hobbes presents his compendious I131] 132 HISTORY OF PHILOSOPHY methodological explanations. This passage is a culmination to Part 1, which is called "On Logic or Computation." It might be argued that this chapter is the governing center for his whole philosophy. But logistica as a preeminent method is mentioned only in its final paragraph. There, it merits a succinct but rather opaque summary. More complete explanations are postponed, for reasons which seem feeble and offhand--a lapse rather contrary to Hobbes's usual directness and sense of climax. The more full formulation thus promised appears at the end of Chapter 20, where it is further troubled in several respects. That chapter is surrounded by geometrical proofs, and it contains Hobbes's ill-famed effort to square the circle. For these reasons, only the hardiest modern readers have struggled to decipher it. Partly owing to that taint, no popular reprints provide this text for our study today. I believe it is now available only in the eleven-volume Molesworth edition of his English Works. Moreover, Hobbes's usual clarity is at that place confounded by rhetorical entanglements. He is overly fond and defensive on behalf of his geometrical accomplishments. And he struggles too anxiously to subsume its methods under what he understands to be the tradition...