ABSTRACT
Indeed, high barriers separated the various modes of nature-knowledge from the Greeks onward (p. 18). So different were the intellectual and social worlds of practitioners of mathematical science, of natural philosophy, and of more empiricist approaches that interaction between them was virtually ruled out, even in the rare case where one man was engaged in two modes at a time, as with Ibn Sina or Castro or Descartes. Consequently, the surveys just completed of achievement and limitation between c. 1640 and c. 1700 in all three modes of nature-knowledge in their newly transformed states reveal pronounced differences among them. Even so, connections have also here and there come to light. Some of these betoken nothing but sheer adaptation by natural philosophers of discoveries made in either realistmathematical or fact-finding experimental science, or ‘opportunist’ or ‘eclectic’ uses made of some tenet in natural philosophy. But more genuinely innovative linkages were also at times forged between one mode and another. Here is a list, compiled from chapters 10, 11, and 13 and placed in chronological order.
In the 1630s and 1640s scholars raised in the tradition of mixed mathematics like Mersenne and Riccioli felt inspired by Galileo’s work to conduct ranges of fact-finding experiments directed at measurement in close connection with his laws of falling bodies (pp. 343; 409).
From the late 1640s onward Kircher began to weave a Jesuit synthesis of nature-knowledge from numerous disparate strands (p. 495).
By the 1650s heliocentric common ground between realist-mathematical science and the natural philosophy of kinetic corpuscularianism led to the promotion of heliocentrism in academic circles (p. 396).
In the mid- to late 1650s men like Charleton and Power hoped to make corpuscles distinctly visible. This furthered an outburst of microscopical research in the early 1660s, in the course of which Grew, van Leeuwenhoek, and others adorned carefully observed microscopic phenomena with an arbitrary layer of corpuscles (pp. 385; 454; 503).
In the early 1660s Galileo’s assertion of equal descent in free fall was confirmed empirically in the receiver of Boyle’s air pump (p. 461).
In the early 1660s the telescope was turned from a tool of mathematical science into a tool of fact-finding measurement. As one consequence, the ‘grand schema’ of the measure of the universe underwent drastic revision (p. 451).
From its start in the mid-1660s onward, the Académie joined the repetition and empirical correction of mathematical work pioneered by Galileo and his Italian disciples to its efforts at fact-finding experimental research (ch. 10). It also undertook a somewhat covert testing of Cartesian conceptions (p. 497).
In 1670 Borelli invoked geometrical form and the mathematics of fluid equilibrium as ‘external’ checks upon kinetic corpuscularianism (p. 393).
In 1676 Rømer discovered a way to decide empirically what so far had been a natural-philosophical controversy over whether the velocity of light is finite or infinite (p. 453).
In the 1680s a prolonged controversy on the Reno between two mathematical scientists and their Jesuit, ‘mixed-mathematics’ opponents was alleviated by some cautious rapprochement (p. 312).
In the early 1690s Huygens’ electrical experiments were stimulated by a Cartesian conception of whirlpools (p. 464).
