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Leibniz, Mach and the C-Series

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According to Carlo Rovelli the (undirected) time orderings of physical states should be given relationally via reference to internal clocks [1]. Internal clocks do not generically provide an always increasing (or decreasing) parameterization of physical states. This means that Rovelli’s internal time proposal allows for violations of ‘temporal monotonicity’. Alternative proposals that retain temporal monotonicity have recently been shown to lead to physically distinct models for quantum cosmology [2]. The status of temporal monotonicity is thus of potential empirical significance.

In this talk we will consider the status temporal monotonicity in a philosophical perspective with reference to three particular historical figures. First, we will examine the extent to which this aspect of time features in Leibniz’s positive account of time, as reconstructed by Arthur [3]. Next, we will considering the relevance of some suggestive remarks from Mach’s Science of Mechanics [4]. Finally, we will consider the extent to which temporal monotonicity is equivalent to McTaggart’s C-series, as reconstructed by Farr [5].

We conclude by briefly considering the challenge to various forms of realism about temporal monotonicity posed by general relativity.

[1] Rovelli, C. (2002) Phys. Rev. D 65 124013.

[2] Gryb, S., & Thébault, K. P. (2018). Physics Letters B 784 324-329.

[3] Arthur, R. T. (1985). Leibniz’s theory of time. In The natural philosophy of Leibniz, pp. 263–313. Springer.

[4] Mach, E. (2013). The Science of Mechanics. Cambridge University Press.

[5] Farr, M. The C Theory of Time. Unpublished draft.

This talk is part of the CamPoS (Cambridge Philosophy of Science) seminar series.

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