Parallelism, interactionism, identity

In the seventeenth century the great philosophers Descartes, Spinoza, and Leibniz all realized that there was a serious problem about the relation of mind to material body. To some extent, the relation was already a problem for Plato, of course, and for all of the philosophers that came after; but it became much more of a problem with the rise of modern physics. In the seventeenth century, people became aware that the physical world is strikingly causally closed. The way in which it is causally closed is best expressed in terms of Newtonian physics: no body moves except as the result of the action of some force. Forces can be completely described by numbers: three numbers suffice to determine the direction, and one number suffices to describe the magnitude of any force. The acceleration produced by a force has exactly the same direction as the force, and the magnitude of the acceleration can be deduced from the mass of the body and the magnitude of the force according to Newton's First Law, F = ma. When more than one force acts on a body, the resultant force can be computed by the parallelogram law.

It is important to recognize how very different such a physics, stressing number and precise algorithms for computation as it does, is from the essentially qualitative thinking of the middle ages. In medieval thought almost anything could exert an ‘influence’ on anything else. (Our word ‘influenza’ is a survival of this medieval way of thinking.