Routledge History of Philosophy Volume IV

174 RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM
are not justified by their incorporation within this system: they are justified
purely in observational and experimental terms. It is important to realize this,
because it is fundamental to Descartes’s whole approach that deduction cannot
justify anything. What it can do is display the systematic structure of knowledge
to us, and this is its role in the Principles.
Again, there is something of an irony here, for the kind of misunderstanding
of Descartes’s methodological concerns which has resulted in the view that he
makes deduction from first principles the source of all knowledge is rather
similar to the kind of misunderstanding that Descartes himself fosters in the case
of Aristotle on the one hand and the Alexandrian mathematicians on the other. In
the case of Aristotle, he takes a method of presentation of results which have
already been established to be a method of discovery. In the case of Pappus and
Diophantus, he maintains that a method of presentation is passed off as a method
of discovery. Yet both followers and critics of Descartes have said exactly the
same of him; taking his method of presentation as if it were a method of
discovery, they have often then complained that there is a discrepancy between
what he claims his method is and the procedure he actually follows in his
scientific work. 34
This suggests that there may be something inherently problematic in the idea
of a ‘method of discovery’. If one compares the kind of presentation one finds in
the Geometry with what one finds in the Principles of Philosophy, there is, on the
face of it, much less evidence of anything one would call ‘method’ in the former
than in the latter. Certain basic maxims are adhered to, and basic techniques
developed, in the first few pages of the Geometry, but the former are really too
rudimentary to be graced with the name of ‘method’, and the latter are
specifically mathematical. In the very early days (from around 1619 to the early
1620s), when Descartes was contemplating his grand scheme of a ‘universal
mathematics’, there was some prospect of a really general method of discovery,
for universal mathematics was a programme in which, ultimately, everything
was reduced to mathematics. But once this was (wisely) abandoned, and the
mathematical rules were made specifically mathematical, the general content of
the ‘method’ becomes rather empty. Here, for example, are the rules of method
as they are set out in the Discourse on Method:
The first was never to accept anything as true if I did not have evident
knowledge of its truth: that is, carefully to avoid precipitate conclusions
and preconceptions, and to include nothing more in my judgements than
what presented itself to my mind so clearly and so distinctly that I had no
occasion to doubt it. The second, to divide each of the difficulties I
examined into as many parts as possible and as may be required in order to
resolve them better. The third, to direct my thoughts in an orderly manner,
by beginning with the simplest and most easily known objects in order to
ascend little by little, step by step, to knowledge of the most complex, and