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A Relic of a Bygone Age? Causation, Time Symmetry and the Directionality Argument

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Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age” (Russell in Proc Aristot Soc 13:1–26, 1913). This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on the proper interpretation of the ‘time symmetry’ of fundamental physics as it appears in the argument, and offer two alternative interpretations. We argue that: (1) if ‘time symmetry’ is understood as the time-reversal invariance of physical theories, then the crucial premise of the Directionality Argument should be rejected; and (2) if ‘time symmetry’ is understood as the temporally bidirectional nomic dependence relations of physical laws, then the crucial premise of the Directionality Argument is far more plausible. We defend the second reading as continuous with Russell’s writings, and consider the consequences of the bidirectionality of nomic dependence relations in physics for the metaphysics of causation.

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  1. In the literature, some philosophers also endorse the stronger claim that if an entity is physically fundamental, then it is metaphysically fundamental. We do not require the truth of this stronger claim for the rest of the paper, as we are exclusively interested in whether causation is part of the metaphysics of fundamental physics. However, our positive proposal in Sect. 3 is consistent with the truth of the stronger claim.

  2. However, there are challenges to the Directionality Argument that we cannot address in this paper. For example, the combination of the CPT theorem and the experimental CP-violation in neutral K-mesons (cf. Sachs 1987, chs. 8–9) suggests that fundamental physics is not time-symmetric, contra Russell.

  3. This assumption is restricted to a specific part of physical theories: the dynamical laws. However, addressing the Fundamental Commitment Principle, Mathias Frisch argues that “[w]hile the dynamical equations of many of our mature theories of physics are time-reversal invariant, this does not imply that the physical theories as a whole are time symmetric” (Frisch 2012, p. 314; emphases in original). Frisch argues that causal notions can and do play important explanatory and inferential roles in physical theories. We would like to sketch two brief responses to Frisch’s view: Firstly, suppose one accepts that a physical theory can be read as causal only if its dynamical equations have specific causal features. If so, the Directionality Argument is still unsound if one reads ‘time-symmetry’ as time-reversal invariance (as we argue in Sect. 2). Secondly, suppose that Frisch is right and the Fundamental Commitment Principle is rejected. This case poses a challenge to someone who wants to endorse the Directionality Argument in the form presented in Sect. 3. The soundness of the argument crucially depends on the Fundamental Commitment Principle. We acknowledge that a Russellian using the Directionality Argument has to meet Frisch’s challenge of providing a convincing argument for the Fundamental Commitment Principle; see Frisch (2009a, 2009b, 2012) and Norton (2009) for a discussion.

  4. Many Russellians today acknowledge the existence of causal facts as (objective) non-fundamental higher-level facts, as referred to by the causal claims in special science and everyday contexts. One self-declared task of Russellians is to reconcile the existence of higher-level causal facts with an acausal world of fundamental physics (see Sect. 4 for Albert and Loewer’s account).

  5. A referee queries whether we are committed to the rejection of the metaphysical possibility of a world with primitive causal facts in which the physics does not motivate a belief in such facts. We allow for such worlds, but hold merely that the Fundamental Commitment Principle precludes a justified belief in fundamental causation in such a world.

  6. Price (1996, p. 154) presents an earlier version of this argument.

  7. According to hyperrealism (cf. Price 1996, p. 154; Price and Weslake 2010, sec. 1.3), causal facts are fundamental, but not contained within the ontology of fundamental physics. This primitivist metaphysics of causation contrasts with the ontological commitment of the Russellian, as dictated by the Fundamental Commitment Principle.

  8. For instance, Field, although explicitly discussing the bidirectional entailment of past and future states of a system by “time symmetric” laws, also defers to complications concerning ‘time symmetry’ by citing Sklar’s (1977) critical discussion of time-reversal invariance (Field 2003, n. 1). Furthermore, Ney holds that “if the fundamental dynamical laws have the same character in both temporal directions, then there is no temporal asymmetry to be found in fundamental physics” (Ney 2009, p. 748). However, if by ‘sameness of character’ she is referring only to nomic bidirectionality, then this is false, since a law can entail a state’s past and future histories despite being time-reversal non-invariant (we elaborate on this point below), and hence her use of ‘same character’ appears to appeal ambiguously to both nomic bidirectionality and time-reversal invariance. See Sect. 3.2 for further details of the relationship between time-reversal invariance and bidirectional nomic dependence.

  9. See Albert (2000, ch. 1), Earman (2002), Malament (2004) and Arntzenius and Greaves (2009) for important recent discussions of time reversal and the time-reversal operator.

  10. An instantaneous state is a configuration of values of the physical variables of a system at a time.

  11. Albert (2000) does however take such theories to display a ‘curious vestige’ of time-reversal invariance.

  12. Reichenbach holds that in the case of a time-reversal invariant theory, “positive and negative time supply equivalent descriptions, and it would be meaningless to ask which of the two descriptions is true” (Reichenbach 1956, pp. 31–32).

  13. See Price (2011, sec. 3.6) for a recent and illustrative discussion of this controversy.

  14. Maudlin does however argue (Maudlin 2007, pp. 131–135) that positing unidirectional production has explanatory value in the case of the statistical mechanical explanation of the entropy gradient. In order to explain the entropy gradient, Maudlin relies on the notion of typicality in the case of microstates. He claims that primitive production relations explain away part of the atypicality of microstates that lead to lower entropy towards the past. As such, it could be argued that Maudlinian ‘production’ is motivated by the physics, because production features in the best explanation of atypical microstates, and hence positing primitive production satisfies the Fundamental Commitment Principle. See Loewer (2012) and Farr (2013, ch. 7, sec. 7.6) for analyses and criticisms of Maudlin’s argument.

  15. In the case of indeterministic laws, nomic entailment consists in the entailment of a probability that a state A occurs by the laws plus a state B. For a discussion of bidirectional nomic dependence in indeterministic theories see Farr (2012, sec. 4.2–4.4).

  16. Nomic dependence need not be spelled out as nomic entailment. As a referee has pointed out, dependence can be alternatively understood as counterfactual dependence. Given this reading, two states A and B are bidirectionally dependent iff (i) A counterfactually depends on B, and (ii) B counterfactually depends on A. Although we are sympathetic to this approach, we would like to address the question as to whether there is a convincing account of bidirectional counterfactual dependence in a separate paper. One important reason to adopt this strategy is that bidirectional counterfactual dependence implies the controversial claim that earlier states depend on later states (involving so-called backtracking counterfactuals). Due to space constraints we cannot do justice to a counterfactual reading of dependence relations.

  17. Our argument does not depend on Russell’s definition of determinism; see Earman (1986, pp. 10–12) for a critical discussion.

  18. One can nonetheless manufacture a time-reversal operation for the theory such that the value of M is, for example, is taken to −n, such as to ensure that the time reverse of every model of T is a model of T. We take it to be clear as to why this is not to be considered a natural time-reversal operation for T.

  19. Two disclaimers: (1) the realist interpretation is neutral with respect to the question of whether the dependence relation itself is fundamental—a question to which Humeans and anti-Humeans provide different answers; (2) ontic dependence as used here is not to be confused with the notion of metaphysical dependence, which is the subject of the metaphysics literature on supervenience, constitution, and grounding.

  20. It is tenable for a theory to be nomically unidirectional insofar as it holds that states depend only on later rather than earlier states. We ignore this detail since we take the opponent to the Directionality Argument, in general, to hold that causes are earlier than, rather than later than, their effects.

  21. See footnote 3 for a disclaimer.

  22. Or later—recall footnote 20.

  23. Moreover, recall that these symmetric and time-symmetric features of bidirectional dependence are compatible with the relevant theory being time-reversal non-invariant.

  24. In order to assess the nomic dependence version of the Directionality Argument, we suppose, for sake of argument, that the equations of the fundamental physical theories express bidirectional nomic dependence relations. The fact that the dynamical equations of physical theories are routinely used to predict and retrodict suggests that such theories are as a matter of fact bidirectional, and it is this to which Russell makes reference in the case of gravitation. However, whether this is indeed the case is outside of the scope of this paper. We take this to be an open issue, with collapse formulations of quantum mechanics perhaps the most prominent candidates for a nomically unidirectional fundamental physical theory.

  25. Both objections were raised by an anonymous referee.

  26. Aside from violating the Fundamental Commitment Principle, the hyperrealist view does not seem to be viable for all cases of nomically bidirectional theories. For example, the laws of physics could be such that some particular state X of a system is only nomically entailed by the laws conditional upon an earlier state and a later state. The two-state vector formalism (TSVF) of quantum mechanics’ account of the weak value of a system has precisely this form. The hyperrealist must either reject the reality of weak values or adopt an alternative understanding of them to that of TSVF. Neither option is untenable, but each places an a priori constraint on physical explanation that is both physically unmotivated and inconsistent with a currently active research programme. We take the job of the philosopher of physics to be to allow current physics to dictate which philosophical positions are tenable, and not vice versa. See Aharonov et al. (2010) for a summary of recent work on weak values.

  27. However, if one insists that causation can be understood in terms of dependence and that it is also possible that this dependence is bidirectional, then one faces a similar problem to Ney (2009), which we address in Sect. 4.

  28. Alternative strategies are advocated by, for instance, Hitchcock (2007), Ladyman and Ross (2007, ch. 5), Ross and Spurrett (2007), Woodward (2007), Ladyman (2008), and Reutlinger (2013, ch. 6).

  29. Cf. Ney (2009, sec. 5).


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We would like to thank Andreas Hüttemann and James Ladyman, the participants of Andreas Hüttemann’s colloquium in Cologne, and the members of our audiences at the conference Causality and Explanation in the Sciences in Ghent, and in Munich and Vancouver for their comments on earlier versions of the paper. We are also grateful for the comments we received from two anonymous referees for Erkenntnis. Special thanks to Bert Leuridan and Erik Weber for their editorial work. Matt’s research is supported by the John Templeton Foundation grant: New Agendas for the Study of Time: Connecting the Disciplines, at the Centre for Time, University of Sydney. Alex’s research is funded by the DFG Research Group Causation and Explanation (University of Cologne), and the Center for Philosophy of Science (University of Pittsburgh).

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Correspondence to Alexander Reutlinger.

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Farr, M., Reutlinger, A. A Relic of a Bygone Age? Causation, Time Symmetry and the Directionality Argument. Erkenn 78 (Suppl 2), 215–235 (2013).

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