ial and the intellectual
world'[163]; and Reid apparently assumes that he had drawn it correctly.
One characteristic of the Cartesian school is obvious. Descartes, a
great mathematician at the period when mathematical investigations were
showing their enormous power, invented a mathematical universe.
Mathematics presented the true type of scientific reasoning and
determined his canons of inquiry. The 'essence' of matter, he said, was
space. The objective world, as we have learned to call it, is simply
space solidified or incarnate geometry. Its properties therefore could
be given as a system of deductions from first principles, and it forms a
coherent and self-subsistent whole. Meanwhile the essence of the soul is
thought. Thought and matter are absolutely opposed. They are contraries,
having nothing in common. Reality, however, seems to belong to the world
of space. The brain, too, belongs to that world, and motions in the
brain must be determined as a part of the material mechanism. In some
way or other 'ideas' correspond to these motions; though to define the
way tried all the ingenuity of Descartes' successors. In any case an
idea is 'subjective': it is a thought, not a thing. It is a shifting,
ephemeral entity not to be fixed or grasped. Yet, somehow or other, it
exists, and it 'represents' realities; though the divine power has to be
called in to guarantee the accuracy of the representation. The objective
world, again, does not reveal itself to us as simply made up of 'primary
qualities'; we know of it only as somehow endowed with 'secondary' or
sense-given qualities: as visible, tangible, audible, and so forth.
These qualities are plainly 'subjective'; they vary from man to man, and
from moment to moment: they cannot be measured or fixed; and must be
regarded as a product in some inexplicable way of the action of matter
upon mind; unreal or, at any rate, not independent entities.

In Locke's philosophy, the 'ideas,' legitimate or illegitimate
descendants of the Cartesian theories, play a most prominent part.
Locke's admirable common sense made him the leader who embodied a
growing tendency. The empirical sciences were growing; and Locke, a
student of medicine, could note the fallacies which arise from
neglecting observation and experiment, and attempting to penetrate to
the absolute essences and entities. Newton's great success was due to
neglecting impossible problems about the nature of force in
itself--'action