Routledge History of Philosophy Volume IV

DESCARTES: METHODOLOGY 173
than this, rejecting the need for deductive proof altogether. The reason why he
does this lies ultimately not so much in his rejection of synthetic demonstrations
in mathematics but in his conception of the nature of inference. Before we look at
this question, however, it is worth looking briefly at what role deduction does
play in Descartes’s overall account.
METHODS OF DISCOVERY AND PRESENTATION
In Article 64 of Part II of The Principles of Philosophy, Descartes writes:
I know of no material substance other than that which is divisible, has
shape, and can move in every possible way, and this the geometers call
quantity and take as the object of their demonstrations. Moreover, our
concern is exclusively with the divisions, shape and motions of this
substance, and nothing concerning these can be accepted as true unless it
be deduced (deducatur) from indubitably true common notions with such
certainty that it can be regarded as a mathematical demonstration. And
because all natural phenomena can be explained in this way, as one can
judge from what follows, I believe that no other physical principles should
be accepted or even desired.
Like the passage from the Discourse on Method that I quoted above, there is a
suggestion here that deduction from first principles is Descartes’s method of
discovery. Can we reconcile these and many passages similar to them with
Descartes’s rejection of deductive forms of inference, such as synthesis in
mathematics and syllogistic in logic? I believe we can.
Descartes’s procedure in natural philosophy is to start from problem-solving,
and his ‘method’ is designed to facilitate such problem-solving. The problems
have to be posed in quantitative terms and there are a number of constraints on what
form an acceptable solution takes: one cannot posit ‘occult qualities’, one must
seek ‘simple natures’, and so on. The solution is then tested experimentally
to determine how well it holds up compared with other possible explanations
meeting the same constraints which also appear to account for the facts. Finally,
the solution is incorporated into a system of natural philosophy, and the principal
aim of a work like the Principles of Philosophy is to set out this natural
philosophy in detail. The Principles is a textbook, best compared not with works
like the Optics and the Meteors, which purport to show one how the empirical
results were arrived at, but with the many scholastic textbooks on natural
philosophy which were around in Descartes’s time, and from which he himself
learnt whilst a student. 33 Such a textbook gives one a systematic overview of the
subject, presenting its ultimate foundations, and showing how the parts of the
subject are connected. Ultimately, the empirically verified results have to be
fitted into this system, which in Descartes’s case is a rigorously mechanist system
presented with metaphysical foundations. But the empirical results themselves