XIX. WHY THE PHYSICAL SYSTEM IS SUPPOSED TO BE IN OPPOSITION TO PHYSICS.

SOME people will have it that the Physical system is opposed to physics, because the principles of geometry had been believed to show that no body is continuous, each being composed of mathematical points and therefore quite indivisible. This opinion was refuted by Aristotle. The supporters of it said, "What is a solid? The sum of the superficies. And what is the superficies? The sum of lines. And what is the line? The sum of many points. Therefore a solid is constituted by points, and is not continuous."

But the falseness of this reasoning is evident. In geometry a line is not considered as an aggregate of points, which, unless they touched one another, would not form it, and if they did touch, would coincide in one point only; for indivisibilia aut non se tangunt, aut se tangunt juxta se tota. A line is conceived ut excursio puncti, as an imaginary track leaving nothing of itself except the point that slips away. Thus we may suppose geometrically that a superficies is derived from excursion of lines, and a solid from excursion of superficies. But though we may consider a mathematical point as a limit of a line, we may not say that it can exist by itself. These are fictions of the imagination but solid bodies are real, and therefore cannot be constituted by indivisible points.

Hence it is evident that, since the Dynamic system, which supposes the extended and the solid to be constituted by unextended forces in mathematical points, is repugnant to reason: the Physical system, which admits the extended and the real continuous, accords with the sure testimony of the senses, by which we perceive things that are extended, and that, as such, must have a certain continuity.

In attacking the Physical system, the adversaries of St. Thomas and of the Scholastics put forth a specious but sophistical argument. "If," they say, "we grant that a body is extended and continuous, we cannot avoid admitting that a particle of it is infinite which cannot be maintained without an evident contradiction. The real extended, if there is such a thing, must be divisible into the extended whose extension ever decreases. Therefore a small part has an infinite number of parts: and so that small part will be infinite, because an extended thing that includes an infinite number of extended things cannot be said to be finite."

To make this question clear we must clearly understand the divisibility of the continuous extended.