Leibniz's Reductionism

Few disputes are more central to the history of the philosophy of space and time than that between substantivalists and reductionists, and no episode is more central to this dispute than the contentious exchange between Leibniz and the Newtonian Samuel Clarke. It is Leibniz, of course, who rejects the philosophical cogency of absolute space and time, arguing instead that they are orders or systems of relations. To contemporary philosophers of science, Leibniz’s disavowal of absolute space and time firmly establishes his legacy as a philosophical and scientific adversary worthy of Isaac Newton, for it is in his views that they find the first profound and systematic instance of reductionism.

All of the above is undoubtedly correct. Leibniz is through and through a reductionist, one who sees substantivalism as a philosophical muddle and a theological danger. He is also a reductionist who promulgates some of the same arguments that to this day continue to be offered in support of reductionism: statements about the world’s position in an absolute time and space are unintelligible in the absence of a procedure for determining that location. But one does a serious injustice to Leibniz’s reductionism if, as is all too often the case, one leaves it at that. Leibniz himself informs Clarke that, apart from the “standard justifications” of reductionism, he has “many demonstrations, to confute the fancy of those who take space to be a substance or at least an absolute being” (LC 14–15). Few readers of Leibniz have taken note of his pronouncement; some have charged him with false advertising. 1 In fact, Leibniz’s boast to Clarke is not hollow rhetoric. It is the aim of this chapter to identify the nature of Leibniz’s reductionism and the many arguments he offers in its favor. In Section 2.6 I will conclude that Leibniz adheres to what Le Poidevin has termed a “non-modal” form of reductionism, one that not only reduces facts about space and time to facts about the relations among spatio-temporal objects, but that also – contrary to a common interpretation of Leibniz – rules out spatial and temporal vacua.