Routledge History of Philosophy Volume IV

DESCARTES: METAPHYSICS AND THE PHILOSOPHY OF MIND 189
1610s, and we know from his letters that a great inspiration during his early
years was the Dutch mathematician Isaac Beeckman, whom he met in Holland in
1618. Beeckman seems to have played for Descartes something of the role which
Hume was later to play for Kant—waking him from his dogmatic slumbers: ‘you
alone roused me from my state of indolence’ wrote Descartes to Beeckman on 23
April 1619 ‘and reawakened the learning that by then had almost disappeared
from my mind’. 12 One of the chief points to strike Descartes was that
mathematics could attain complete clarity and precision in its arguments, and
that the demonstrations it employed were completely certain: no room was
allowed for merely probabilistic reasoning. 13 The mathematical model continued
to influence his scientific work throughout the following decade, 14 leading up to
the composition of his treatise on physics and cosmology, Le Monde, which
announced, at any rate in outline, a comprehensive programme for the
elimination of qualitative descriptions from science in favour of exact
quantitative analysis. 15
Even in this early period, however, Descartes’s interests were never purely
scientific (in the restricted modern sense): right from the start he seems to have
been concerned with how the results achieved in mathematics and physics were
to be related to more fundamental issues about the nature and basis of human
knowledge. In his Regulae ad directionem ingenii (‘Rules for the Direction of our
Native Intelligence’, written in Latin in the late 1620s but not published during
his lifetime), Descartes makes it clear that his interest in subjects like geometry
and arithmetic derives in large part from the fact that they are merely examples
of a more general procedure of potentially universal application:
I came to see that the exclusive concern of mathematics is with questions of
order or measure, and that it is irrelevant whether the measure in question
involves numbers, shapes, stars, sounds or any other object whatever. This
made me realize that there must be a general science which explains all the
points that can be raised concerning order and measure, irrespective of the
subject-matter, and that this science deserves to be called mathesis
universalis. 16
It is important to note that the ‘universal discipline’ described here does not
merely encompass quantitative subject matter. Descartes believes that there is a
formal structure which all valid systems of knowledge manifest, and that this
structure consists essentially in a hierarchical ordering: the objects of knowledge
are to be arranged in such a way that we can concentrate to begin with on the
items which are ‘simplest and easiest to know’, only afterwards proceeding to
the more complex truths which are derived from these basic starting-points. 17
The human intellect, Descartes goes on to explain, has the power to ‘intuit’ these
‘simple natures’ or fundamental starting-points for human knowledge: it simply
‘sees’ them with a simple and direct mental perception which allows for no