ABSTRACT
G. J. Whitrow's arguments apply more too Newtonian space than to a plenum. Although he invokes Laplace's equation and the concept of a field, his arguments turn on the possibility of planetary orbits under non-Newtonian gravitational laws, and the fact that we have bodies, and our intelligences can only function on condition of our being a certain sort of thing. The wave equation thus could be viewed as extending the egalitarianism of Laplace to apply over time as well as space—a sort of perpetual equality of opportunity. One reason why space needs to be three-dimensional is because there is the next larger number than two, and two is excellent Pythagoreanly and on the score of reversibility. The inverse square law is therefore the appropriate law for attraction and repulsion in a three-dimensional space, if Laplace's equation is to hold. Therefore if we value the inverse square law, we must have space three-dimensional.
