The relations between different areas of knowledge have been a subject of interest to philosophers as well as to scientists and mathematicians from antiquity. While recent work in this direction has been largely concerned with the question whether one branch of knowledge can be reduced to another , the questions which exercised the Greek philosophers on these matters have a different starting point. Taking for granted that there are a number of distinct areas of knowledge, they proceeded to consider a (...) variety of relations which they observed to hold among the sciences as they knew them; the question of the priority of one science to another is a recurrent theme. In fact, three sorts of orderings were noticed, and the associated conceptions of priority are interesting. Only one of them is the concern of the present paper, though, and I shall briefly describe the remaining two only for purposes of contrast. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 63.3 (2002) 371-397 [Access article in PDF] How the "New Science" of Cannons Shook up the Aristotelian Cosmos Mary J. Henninger-Voss [Figures]Approximately halfway through the "Second Day" of Galileo's Dialogue Concerning the Two Chief World Systems Galileo's mouthpiece, the mathematician Salviati, scoffs at his Aristotelian colleague Simplicio: "I see that you have hitherto been of that herd who, in order to learn how (...) matters such as this [motion] take place, and in order to acquire a knowledge of natural effects, do not betake themselves to ships or crossbows or cannons, but retire to their studies... to see whether Aristotle has said anything about them."1 Silly, simple Simplicio! He has been searching for natural philosophical wisdom in the books of natural philosophers rather than in the world of docks and arsenals. Indeed this quotation appears near the outset of Day Two wherein Salviati offers cannonshot as proof for the opposing Aristotelian position that the experience of projectiles proves the motionless state of the earth. Obviously, if the earth rotates toward the east, cannonballs shot point-blank to the west ought to travel much further than to the east. And clearly this is not so. Simplicio agrees that the new arguments offered by the cannon are excellent, "and now I see with how many elegant experiments nature graciously wishes to aid us in coming to the recognition of the truth," Simplicio enthusiastically enjoins. "What a shame there were no cannons in Aristotle's time!" exclaims the third interlocutor, Sagredo. "With them he would indeed have battered down ignorance, and spoken without [End Page 371] [Begin Page 373] the least hesitation concerning the universe."2 The irony here is not only that Aristotle might have used cannons in order to explain the workings of the universe but also that Galileo does so in the following pages. His demonstrations with reference to artillery demolish the Aristotelian position, but he has had Simplicio open the door for him by recognizing this most violent of artifices as an elegant experiment provided by nature.3The cannon provides a primary referent for Galileo's new mathematical physics of motion from his very first dialogue to his very last. The early De Motu culminated in a series of questions about the shot of cannons, while the conversation in his final masterwork, Discourses Concerning Two New Sciences, was set in the Venetian arsenal, and to it Galileo appended a table of the parabolic paths that could be expected from cannons shot at various elevations.4 In some sense Galileo turned inside-out a much older problem, one that had haunted military engineers of sixteenth-century Italy—and Galileo had been trained, and trained others, in military engineering.5 State organizers of war and captain generals were less interested in the implications the arts of fortifications and artillery held for the existing science of natural motion than in the necessity to reduce to a science, that is, a coherent body of knowledge, the rules for manufacturing cannons, planting artillery battery, aiming guns, and fortifying camps, cities, and castles.What Galileo gives us is recognizable as early physics, as a sophisticated mechanical science, a neat triumph of mathematical method in natural philosophy. But the ways and means by which mathematics came together with natural philosophy to address problems of both technology and nature are by no means neat. My claim is that attention to the military sphere will help us sort out some of those ways and means. The curious thing about the historiography on the relationship between early modern science and warfare is that the fact of a connection seems to have been taken for granted, while the implications have seldom been investigated.6 This essay is an attempt to trace those implications by [End Page 373] looking at a mathematician who specifically tried to reduce to a mathematical science the military arts, Niccolò Tartaglia.7 Tartaglia's story shows how the minutia of Aristotelian philosophy was transmuted in early attempts to understand cannonshot... (shrink)