Routledge History of Philosophy Volume IV

166 RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM
philosophers wishing to provide a mathematical physics in the seventeenth
century were immense. 21
In the Rules for the Direction of Our Native Intelligence, Descartes outlined a
number of methodological and epistemological proposals for a mathematical
physics. The Rules, the writing of which was abandoned in 1628, is now thought
to be a composite text, some parts deriving from 1619–20 (Rules 1–3, part of
Rule 4, Rules 5–7, part of Rule 8, possibly Rules 9–11) and some dating from
1626–8 (part of Rule 4, part of Rule 8, and Rules 12–21). 22 The earlier parts
describe a rather grandiose reductionist programme in which mathematics is
simply ‘applied’ to the natural world:
When I considered the matter more closely, 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 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
should be termed mathesis universalis. 23
This project for a ‘universal mathematics’ is not mentioned again in Descartes’s
writings and, although the question is a disputed one, 24 there is a strong case to
be made that he abandoned this kind of attempt to provide a basis for a
mathematical physics. The later Rules set out an account of how our
comprehension of the corporeal world is essentially mathematical in nature, but
it is one which centres on a theory about how perceptual cognition occurs.
Throughout the Rules, Descartes insists that knowledge must begin with ‘simple
natures’, that is, with those things which are not further analysable and can be
grasped by a direct ‘intuition’ (intuitus). These simple natures can only be
grasped by the intellect—pure mind, for all intents and purposes—although in
the case of perceptual cognition the corporeal faculties of sense perception,
memory and imagination are also called upon. The imagin ation is located in the
pineal gland (chosen because it was believed to be at the geometrical focus of the
brain and its only non-duplicated organ), it is the point to which all perceptual
information is transmitted, and it acts as a kind of meeting place between mind
and body, although Descartes is understandably coy about this last point. In Rule
14, Descartes argues that the proper objects of the intellect are completely
abstract entities, which are free of images or ‘bodily representations’, and this is
why, when the intellect turns into itself it beholds those things which are purely
intellectual such as thought and doubt, as well as those ‘simple natures’ which
are common to both mind and body, such as existence, unity and duration.
However, the intellect requires the imagination if there is to be any knowledge of
the external world, for the imagination is its point of contact with the external
world. The imagination functions, in fact, like a meeting place between the
corporeal world and the mind. The corporeal world is represented in the intellect