Causal and Temporal Asymmetry

The first sections of this chapter demonstrate that Leibniz believes the direction of causation is given independently of the direction of time. In no uncertain terms, Leibniz disavows a Humean analysis of causation according to which “the cause and effect must be contiguous in space and time … [and] the cause must be prior to the effect” (A Treatise of Human Nature, 1.3.15). Yet if Leibniz’s disavowal of this analysis of causal asymmetry is apparent enough, much less obvious is how he explains the asymmetry by which an effect follows from its cause. By way of illuminating this obscure component of Leibniz’s thought, I examine how he uses what he, in line with a tradition dating back to Aristotle, terms “natural order” and its accompanying relations of “natural priority” and “natural posteriority” to ground causal asymmetry. For Leibniz, causal relations are defined in terms of more primitive relations of natural priority and posteriority, and it is the asymmetry in these latter kinds of relations that accounts for the asymmetry of the former. It may be that no causes are temporally subsequent to their effects, but, for Leibniz, this is neither a defining characteristic of “cause,” nor a fact to which we must have epistemic access in order to determine that something is a cause. This understanding of causation provides Leibniz with the conceptual resources to set forth an atemporal account of causal asymmetry, thus enabling him to explain temporal asymmetry by reference to causal asymmetry.

With this hurdle cleared, I take up Leibniz’s analysis of qualitative temporal relations in terms of non-temporal causal relations. Causal theories of time are often divided into two kinds: (1) those that identify time with causation on purely philosophical or semantic grounds, and (2) those that identify time with causation on empirical or scientific grounds. What quickly becomes apparent is that Leibniz’s causal theory of time is philosophical through and through. The relation between temporal and causal relations for Leibniz is invariably established on semantic, or, better yet, metaphysical, and not merely empirical grounds. In Leibniz’s causal theory of time, we are given a philosophical analysis of what temporal terms mean, and what temporal facts are. Even so, this causal theory of time is not fully congruent with more orthodox variants. Like standard causal theories of time, Leibniz’s identifies time with a structure that is non-temporal; unlike standard causal theories of time, this structure is not causation alone. The causal theory of time adopted by Leibniz more closely resembles what Michael Tooley has recently termed a “spatio- causal theory of time,” a theory of time that identifies temporal facts with spatial and causal facts, not mere causal facts. While such an interpretation might prima facie seem like a distorting rational reconstruction, it is solidly supported – indeed, entailed – by a wide range of texts from the middle and late period. On the basis of his explanation of casual asymmetry and his spatio-causal theory of time, I show how Leibniz provides a non-circular and comprehensive reduction of temporal facts to causal facts.

The chapter concludes by examining a final topological feature of time, its linearity. Given the kind of analysis of causal and temporal asymmetry advanced by Leibniz, he is committed to ruling out the possibility of non-linear time.