NEWTON: Mathematical Principles of Natural Philosophy [Prefaces, Definitions, Axioms, General Scholium]

Newton’s Mathematical Principles of Natural Philosophy was first published in 1687. Two subsequent editions with emendations were published in 1713 and 1726. In the text, Newton lays the foundations for what would be known in the future as classical mechanics – a technical term that simply indicates the study of the behavior of macroscopic bodies when acted upon by forces.

These foundations are Newton’s three laws of motion. The first law states that an object will remain at rest or remain in motion unless acted upon by an external force. That an object will remain at rest unless acted upon by an external force seems intuitive, but Newton’s insight that an object will remain in motion unless acted upon by an external force is truly remarkable considering that he lived on Earth, where air resistance, friction, and a variety of other almost imperceptible forces are constantly affecting the motion of bodies.

The second law of motion states that the force acting upon an object is equal to the objects mass multiplied by its acceleration. Along with Einstein’s E=mc^2, this is one of the simplest and most beautiful laws of physics. Imagine the dread of high school physics students if the formula had been something as complex as nearly any formula of quantum mechanics.

The third law of motion states that for every action there is an equal and opposite reaction. Once again this seems counterintuitive. When we are standing firmly upon the ground, we do not intuitively assume that the ground is exerting a force upon us, but it is. An interesting practical application of this for astronauts is that they can alter their velocity in space by throwing objects. If they throw an object forward, the object will accelerate them backward to the extent of its mass.

In the general scholium at the end of his treatise, Newton asserts that the variety of the world and the order of the universe could not have transpired according to blind chance. He writes “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.” This is a common argument for the existence of god called the “argument from design.” There have been many counterarguments offered by other philosophers. David Hume offered one such argument. And because he is one of the next few authors on the reading list, I will refrain from discussing his counterargument until the relevant blog post. However, I am certain that most of my readers are familiar with Darwin’s theory of evolution. His theory explains how order can arise from purely physical processes. Of course this does not entirely refute the argument; for although Darwin and other philosophers demonstrate that order can arise unaided by a purposeful intelligence, they cannot prove that the order of the universe did arise unaided by a purposeful intelligence. But current physicists are working on answering that question definitively.

“All the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena.”

“Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.”

“The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”

“To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

“Hitherto I have not been able to discover the cause of those properties of gravity from phaenomena, and I frame no hypotheses; for whatever is not deduced from the phaenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.”

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7 thoughts on “NEWTON: Mathematical Principles of Natural Philosophy [Prefaces, Definitions, Axioms, General Scholium]”

  1. Have you written somewhere about how Newton wanted to integrate his findings about science and the beliefs of the church?
    I would love to read your thoughts on it 🙂

    1. Newton asserts that the variety and order of the universe could not have transpired by blind chance, but rather “could only proceed from the counsel and dominion of an intelligent and powerful Being.” Newton’s argument for the existence of God has been challenged by many philosophers. His argument is a variation of the teleological argument.

      Newton certainly was not a Christian who tried to conform his discoveries to the beliefs of Christianity. He was more of a Deist than a Christian. He regarded Christ as a mediator between men and God. He considered the worship of Christ to be akin to idolatry.

      See the following source for more information regarding Newton’s faith:

      Westfall, Richard S. (1994). The Life of Isaac Newton. Cambridge: Cambridge University Press.

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