revolution derives from the metaphysical assumptions of a Neoplatonic cosmology.
It is not only that many of the scientific innovators were not following this
particular metaphysics, or were more concerned with the adequacy of technical
matters (Hatfield, 1990). The numerous competing strands of late scholastic,
Humanist, and occultist philosophies between 1400 and 1600 constituted an
intellectual field without a focus of attention; these are structural conditions for
stagnation rather than for the dynamism of discovery. The main effect of philoso-
phy on the mathematical and scientific revolutions was on the level of social
structures; math and science networks were stimulated to make their arguments
on a higher level of generality when they intersected with the networks of theolo-
gians and philosophers. The importance of this contact is not primarily through
the transmission of philosophical capital into math and science, but in transmission
of the emotional energy of intellectual competition characteristic of the philosophi-
cal networks.- Kangro (1968). Like Harvey, Jungius was a medical doctor from the Padua net-
work. - Upheaval in the material bases of intellectual life fosters creativity in several
directions at once. The last glory of Latin stylistics sprang up in the generations
just before Bacon and Descartes: the anti-Ciceronian and Attic prose movements,
which encompassed Montaigne and his teachers and lasted until the time of Milton
(Croll, 1966). Descartes and especially Bacon were noted Latin prose stylists, along
with their other accomplishments. As we have seen in the case of Greek philosophy,
there is creativity in the moment of closing down an intellectual structure as well
of opening one up. - Viète and Descartes’s father were both members of the Parlement of Brittany, and
Viète was counselor at Tours in the 1590s, near Descartes’s home (DSB, 1981:
4:51, 14:52). The fame of Viète’s mathematics may have made an impression on
Descartes in this way. Notice the parallel instances showing the public prestige of
mathematical puzzle-solving: in 1593 the Dutch ambassador put a mathematical
challenge to the French court involving an equation of the forty-fifth degree, which
Viète solved. Descartes first became interested in mathematics through a challenge
to solve a geometrical problem announced on a public placard in Breda, Holland,
in 1618. It was on this occasion that he met Beeckman (Gaukroger, 1995: 68). - As Michael Mahoney (personal communication) puts it, Descartes’s symbolism
“was essentially different from earlier systems of notation. It was operational. That
is, the symbols revealed through their structure the operations being carried on
them, so that one did the mathematics by manipulating the symbols... Moreover,
unlike cossist algebra, Viéte’s and Descartes’ systems symbolized both knowns and
unknowns, making it possible then to unfold the structure of equations viewed as
general relations.” Descartes had a “drive for generality.” - Hatfield (1990: 159). Descartes does have a place for empirical observation, in the
sense that “the truths that can be deduced from... Principles” include many which
will not be noticed until “certain specific observations” are made. For the advance-
ment of science, experiments must be made by those who know how to unite their
results with a deductive system (Descartes [1644] 1983: xxvii).
998 •^ Notes to Pages 565–568