Newton and Leibniz

The controversy between Isaac Newton (1642–1727) and Gottfried Wilhelm von Leibniz (1646–1716) was primarily over their views of space and time. There had been some claims among Newton's followers that Leibniz had plagiarized from Newton, particularly regarding the calculus. It was later proved that there was no plagiarism, but that these two geniuses, standing on the shoulders of those (like Johannes Kepler, for example) who had preceded them, had each made the conceptual leap independently to the calculus. However, Newton (somewhat paranoid) may have retained some feelings of resentment toward Leibniz, and thus does not respond to him directly about their differing views; rather, the differences are aired primarily in the correspondence between Leibniz and Samuel Clarke, a follower of Newton.

Newton had expressed his views on space and time in his Principia Mathematica (1686), in the scholium following the section on definitions. He explains why he did not include in the definitions time, space, place, and motion, because they were well known to everyone. However, people commonly held prejudices regarding these concepts, so he expounds his technical definitions. “Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external.” It is also called duration. Relative, or common, time is a sensible measure of duration (by means of motion). “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.” Relative space is somehow a measure of this absolute space. It is important to look at both concepts together, because they share characteristics that may help in understanding what Newton means. Space (absolute space) is a kind of permanent container in which things may come and go, appear and disappear. Imagine a huge matrix on which one might move pieces (a kind of cosmological chess board); the pieces may move and change, but the board always remains. By analogy, absolute time is always flowing, and does not depend for its existence on the motion or change of bodies. Change implies a before and an after in time, which therefore presupposes time, so it must be more fundamental, an objective reality, according to Newton. He says that absolute time would exist even if there were no motion, or a lapse between motions.

Leibniz denies that space and time are absolute; he argues that they are relative, that they are relations. Space is the order of perceptions of monads (a monad is Leibniz's basic metaphysical, indivisible substance, a concentration of energy, a kind of mind) that coexist; time is the ordering of a monad's different perceptions. Because space and time depend on monadic perceptions (of the world), they are ideal (phenomenal), not real. Just as other relations (such as “smarter than”) do not have an independent existence, but are dependent on the entities compared, neither do space and time have an independent existence. Time is more fundamental; for a monad, the present is represented clearly, the past and the future more obscurely. Space is then the ordering of coexisting monads (or aggregates of monads) at the same time. Leibniz argues that there is a continuum of [Page 914]monads in this best of all possible worlds. (God would have created nothing less; existence is maximized in the best possible world.) If there had not been a best possible world, God would not have had a sufficient reason to create anything.

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