# 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 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.

A controversy between Leibniz and the Newtonians began in 1705 over these serious dis­agreements. It culminated in 1715-1716 with an exchange of letters between Leibniz and Samuel Clarke, a follower of Newton. It began with a criticism of Newton’s position sent by Leibniz to Princess Caroline of Wales; Clarke responded on behalf of Newton, Leibniz wrote back in defense, and so on. There were five letters written by Leibniz, five replies by Clarke, and it ended with­out resolution, at the death of Leibniz.

Leibniz begins his first letter by attacking Newton’s materialism (of atoms and void) and its implications for religion. He argues that Newton’s system implies that God is a kind of unskillful watchmaker who has to fix and adjust his cre­ation periodically and has need of space as his sense organ. Clarke responds that God needs no medium of perception, because he is omnipresent. Clarke argues that a God who does not attend to his creation would be like a king who ignores his kingdom and lets it run on its own. Leibniz responds that God, in his wisdom, foresaw every­thing and has made the best possible world machine, which consequently does not need his intervention; his action, as supreme ruler, is that of continually preserving his creation.

Leibniz’s fundamental principle is that of suffi­cient reason (nothing happens without a sufficient reason why it is so and not otherwise), a rational self-evident truth. If space were a real absolute being, as Newton says, all points in space would be indistinguishable, and there would not be a suf­ficient reason why God placed bodies in one arrangement rather than its opposite (east instead of west, for example). Similarly with absolute time, its parts would be uniform, so there would not have been a sufficient reason why God created everything when he did, and not sooner or later. Clarke replies that God’s will is the sufficient rea­son for creating how and when he did. He attacks the idea of space as relational by saying that if God reversed the position of the stars with that of the moon and Earth, on a relational account, it would be the same, which is contradictory. Or if God moved the material world in a straight line at any speed, on the relational account it would continue in the same place and time (which is absurd).

Leibniz calls Clarke’s examples impossible fic­tions, and says that Clarke did not understand the nature of relational space, by supposing that a world would be moved against an absolute back­ground space and time, which is what is denied. Two indiscernible states are the same state, says Leibniz, and so “’tis a change without a change.” Another fiction is that God might have created the world sooner, because God does nothing without a sufficient reason. Leibniz says that the order of bodies (aggregates of monads) makes space/ situation possible, just as the succession of bodily states makes time/duration possible. If there were no creatures, there would be no space and time. Clarke reiterates that there can be identical parts of space that are yet distinct, and two points in time that are identical; quantity of time can be greater or less, yet the order of temporal events could be the same. Leibniz’s principle of continu­ity denies this; between any two states there must be another state, so greater elapsed time implies more successive, distinct states.

Clarke argues that Leibniz’s universe destroys freedom; everything would be determined. Leibniz replies that he has argued at length, in his Theodicy, that God’s foreknowledge is compatible with free choice. God, in his wisdom, simply created (thought) the one possible world full of free creatures that was the best “actualizing their free natures.” What God did not create, in thinking the best world, is nevertheless possible.

Leibniz argues that absolute space and time would be infinite and eternal and so independent of God, thus possibly greater than God (which is contradictory). If being in space and time is neces­sary to God, he would then be in need of them and thus limited (but God is without limits). Motion depends on a change that can be observed. Time without things, Leibniz says, is only an ideal pos­sibility; to say the created world might have been created sooner is not intelligible (if it could have been created sooner, God would have done so, because that would mean more existence). Space and matter are different, but inseparable; time and motion are distinct, but inseparable, says Leibniz.

Stacey L. Edgar

See also God and Time; Leibniz, Gottfried Wilhelm von; Newton, Isaac; Space, Absolute; Time, Absolute

Ariew, R. (Ed.). (2000). Leibniz and Clarke: Correspondence. Indianapolis, IN: Hackett.

Ariew, R., & Garber, D. (Eds. & Trans.). (1989). Monadology: Principles of nature and grace. In Philosophical essays/G. W. Leibniz. Indianapolis, IN: Hackett. (Original work published 1714)

Newton, I. (1934/1966). Sir Isaac Newton’s mathematical principles of natural philosophy and his system of the world (A. Motte, Trans., 1729; F.

Cajori, Rev., 1966). Berkeley: University of California Press. (Original work published 1687)