Routledge History of Philosophy Volume IV

178 RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM
syllogism, one scientific because it provided us with knowledge why something
was the case, the other non-scientific because it only provided us with
knowledge that something was the case. The logicians of antiquity were crucially
concerned with the epistemic informativeness of various kinds of deductive
argument, and both Aristotle and the Stoics (founders of the two logical systems
of Antiquity) realized that there may be no logical or formal difference between
an informative and an uninformative argument, so they tried to capture the
difference in non-logical terms, but in a way which still relied on structural
features of arguments, for example the way in which the premises were
arranged. All these attempts failed, and the question of whether deductive
arguments can be informative, and if so what makes them informative, remained
unresolved.
The prevalent seventeenth-century response to this failure was to argue that
deductive arguments can never be epistemically informative. Many critics of
logic right up to the nineteenth century criticized syllogistic arguments for failing
to yield anything new, where what is meant by ‘new’ effectively amounts to
‘logically independent of the premises’. But of course a deductive argument is
precisely designed to show the logical dependence of the conclusion on premises,
and so the demand is simply misguided. Descartes’s response is rather different.
It consists in the idea that the deduction of scientific results, whether in
mathematics or in natural philosophy, does not genuinely produce those results.
Deduction is merely a mode of presentation of results which have already been
reached by analytic, problem-solving means. This is hard to reconcile, however,
with, say, our learning of some geometrical theorem by following through the
proof from first principles in a textbook. Even if Descartes could show that one
can never come to know new theorems in the sense of inventing them by going
through some deductive process, this does not mean that one could not come to
know them, in the sense of learning something one did not previously know, by
deductive means. Indeed, it is hard to understand what the point of the Principles
could be if Descartes denied the latter. But in that case his argument against
deduction as a means of discovery is a much more restricted one than he appears
to think. Moreover, I have already indicated that deduction seems to play a
guiding role in discovery, in the sense of invention or ‘genuine’ discovery, in
Descartes, because his procedures for problem-solving are quite blind as far as
the ultimate point of the exercise is concerned. Finally, the way in which he sets
up the argument in the first place is somewhat question-begging. We are
presented with two alternatives: using his ‘method’, or deduction from first
principles. But someone who has a commitment to the value of deductive
inference in discovery, as Leibniz was to have, will not necessarily want to tie
this to demonstration purely from first principles: Leibniz’s view was that
deduction only comes into use as a means of discovery once one has a very
substantial body of information (discovered by non-deductive means). This is a
possibility that Descartes simply does not account for.