The selection from Newton is a “scholium” (roughly, a comment) appearing very near the beginning of his Philosophiae Naturalis Principia Mathematica (‘Mathematical Principles of Natural Philosophy’), the work in which Newton presented his laws of motion and law of gravitation. The scholium we will discuss comes immediately after a series of eight definitions concerning matter, motion, and force and just before the statement of his three laws of motion.
The selection from Leibniz consists of parts of his side of an exchange with Samuel Clarke at the end of Leibniz’s life (and about 30 years after the publication of Newton’s Principia), an exchange that Clarke published shortly after Leibniz’s death. (You can find this edition on line under its actual title, “A Collection of Papers, Which passed between the late Learned Mr. Leibnitz, and Dr. Clarke, In the Years 1715 and 1716.”)
Clarke was an associate of Newton, and Newton is known to have read Clarke’s letters before they were sent, but it is not clear how many of the views expressed were Newton’s. Still, the correspondence began as a result of Leibniz’s criticism of some of Newton’s published views, and Leibniz may have thought of the exchange as essentially a dispute with Newton himself. (The letters grew in length as the exchange went on. Leibinz’s “Fifth Paper,” the last, contained 130 numbered paragraphs responding to the Clarke’s replies to the 46 in the fourth, while the third had only 17.)
The best-known parts of the selections from both Newton and Leibniz are certain abstract examples or “thought experiments”; and, while they are not the only things worth discussing, you should make a particular point to think about them.
• Newton describes two, the “rotating bucket” (as it is usually called) described on p. 41 and the two connected spheres described on p. 43. (The phenomena are closely related physically; but, on some interpretations, the presence of the bucket in the first is important for the argument Newton is making at that point.)
• In Leibniz’s case, be sure to think about ¶¶ 5 and 6 of the third paper and ¶ 3 of the fourth.
Most of this discussion is about space most directly and applies to time by analogy, but you can find some remarks specific to time, especially in Leibniz, and you should be on the lookout for those.
Our discussion of Newton and Leibniz may continue on Thursday; but, if you like to prepare for the full week over the weekend, you should also read the start of the selection from McTaggart since we will also begin discussing that on Thursday.