Routledge History of Philosophy Volume IV

DESCARTES: METHODOLOGY 159
focus. He knew that the standard lens of the time, the biconvex lens, could not do
this, and that the refracting telescope constructed with such a lens was subject to
serious problems as a result. He was convinced on geometrical grounds that the
requisite shape must be a hyperbola but he spent several years pondering the
practical problems of grinding aspherical lenses. In two detailed letters to Jean
Ferrier (a manufacturer of scientific instruments whom Descartes was trying to
attract to Holland to work for him grinding lenses) of October and November
1629, he describes an extremely ingenious grinding machine, with details as to
the materials different parts must be constructed of, exact sizes of components,
instructions for fixing the machine to rafters and joists to minimize vibration,
how to cut the contours of blades, differences between rough-forming and
finishing-off, and so on. These letters leave one in no doubt that their author is an
extremely practical man, able to devise very large-scale machines with many
components, and with an extensive knowledge of materials, grinding and cutting
techniques, not to mention a good practical grasp of problems of friction and
vibration. The rest of his large correspondence, whether it be on navigation,
acoustics, hydrostatics, the theory of machines, the construction of telescopes,
anatomy, chemistry or whatever, confirm Descartes’s ability to devise and
construct scientific instruments and experiments. Is it really possible that
Descartes’s methodological prescriptions should be so far removed from his
actual scientific practice?
Fourth, Descartes has an extremely low view of deduction. He rejects
Aristotelian syllogistic, the only logical formalization of deductive inference he
would have been familiar with, as being incapable of producing any new truths,
on the grounds that the conclusion can never go beyond the premises:
We must note that the dialecticians are unable to devise by their rules any
syllogism which has a true conclusion, unless they already have the whole
syllogism, i.e. unless they have already ascertained in advance the very
truth which is deduced in that syllogism. 6
Much more surprisingly, for syllogistic was generally reviled in the seventeenth
century, he also rejects the mode of deductive inference used by the classical
geometers, synthetic proof. In Rule 4 of the Rules for the Direction of Our Native
Intelligence, he complains that Pappus and Diophantus, ‘with a kind of low
cunning’, kept their method of discovery secret, presenting us with ‘sterile
truths’ which they ‘demonstrated deductively’. 7 This is especially problematic
for the reading of Descartes which holds that his method comprises deduction
from first principles, since this is exactly what he is rejecting in the case of
Pappus and Diophantus, who proceed like Euclid, working out deductively from
indubitable geometrical first principles. Indeed, such a procedure would be the
obvious model for his own method if this were as the quotations above from the
Principles suggest it is.