Isaac Newton and the Mathematical Principles of Natural Philosophy

Abstract

The appearance of Isaac Newton’s (1642–1727) Principia Mathematica Philosophiae Naturalis (The Mathematical Principles of Natural Philosophy) in 1687 is taken symbolically as the beginning of the new era of the empirical sciences. Newton’s work laid the foundations for the first part of the new physics—classical mechanics

Appendix: The Mechanistic Image of the World in Newton’s Principia

While Cartesianism was celebrating its triumph in seventeenth century Europe, there was born on the British Isles a system which would shortly shake the very foundations of science. In 1687, Isaac Newton published his landmark Mathematical Principles of Natural Philosophy. The method of the natural sciences which Newton developed was in clear opposition to Descartes’ system of knowledge based on “irrefutable and certain” principles of metaphysics. The Principia pointed the way to a mathematico-empirical method. The structure of the work left no doubt that we are dealing here with a work of central importance. That is evidenced not only by the scientific layer of the work but also by Newton’s philosophical ideas.

The first book of the Principia contains definitions which have as their end precision with respect to the terms of which Newton would make use, and a Scholium, in which the author gives his own interpretation of his mechanics. It is worth taking note of the fact that the definitions of the fundamental quantities which we use in physics even today sprang originally from the pen of Newton himself.

In the second book, the reader finds applications of general principles to concrete cases. We have here to do with scientific analyses and experimental results that follow from the laws of nature.

It is in the third part of the Principia, in which the author, on the basis of general principles, constructs a system of the world, understood above all as a planetary system, where Newton really shows his genius. Beyond that, in this part of the work, the author, taking his own experience into consideration, presents a set of rules of reasoning by which those who study nature should guide themselves.

Among the rules of reasoning which Newton presents in the third part of the Principia, we find interesting ideas concerning the concept of matter. It might seem surprising that the scientist did not put them among the other definitions in the first part of the work. This placement is of course no accident, but is a sign that Newton does not consider the concept of matter to be a part of physics, but rather he understood it to be a part of philosophy. It is impossible to give any operational definition of matter, and one must clearly distinguish the term “matter” from the term “quantity of matter;” the latter term is equivalent to the concept of mass as used in physics, which has a precisely defined, operational meaning. We find the Newtonian definition of matter in the third of the rules of reasoning in philosophy. To be matter, primary (or universal) qualities. Those are extension, hardness, impenetrability, and mobility. To those properties, Newton also adds being subject to inertial motion and to gravitation, although with respect to the latter he has doubts as to whether it should be accepted as a universal quality of bodies. The definition of matter proposed in the Principia stands in explicit contrast to the conception of Descartes, for whom matter means only extension. It is easy to read traces of atomism into Newton’s ideas about matter. He believes that primary qualities belong to the whole of a body because they first belong to its parts. One can seek in Newton roots of the so-called mechanical atomism, according to which matter consists of mechanical atoms which are subject to the same rules of motion as is macroscopic matter. One can see that, thanks to Newton, the concept of matter, removed from physics, becomes the foundation for mechanistic views in philosophy.

Newton was aware that his theory has boundaries, at which the laws of mechanics break down. One can point to three such places:

• 1. the initial conditions for the equations of motion—they do not come from the theory itself, but they must be accepted in order for the theory to function at all;

• 2. the general plan of the system of the world, in which thought and purpose appear;

• 3. the necessity of corrections to the system of the world as disturbances in the system increase over time.

In the face of those difficulties, it was necessary to accept some kind of element which would not only explain that which was not explained by the laws of mechanics, but would allow for the maintenance of continuity in the operation of the world machine. That element was, for Newton, God. Newton was not alone in this approach—putting the Creator in a place to which scientific theories do not reach became a relatively common practice among those scientists who were not content to leave “gaps” in a scientific system even in places that were beyond the reach of science. In Newton’s opinion, God, first, gave the world appropriate initial conditions; second, in accordance with His own design, He created a world governed purposively; third, He “repairs” the world when accidental disturbances disrupt its order. Newton accepted the necessity of divine agency only at the boundaries of his theory, but asserted that because the effects of divine action we have the possibility of knowing God Himself.