4.2 The incompatibility of causation and physics
4.2.3 The causal directionality argument
As Farr & Reutlinger (2013) point out, the directionality argument based on time reversal symmetry is not the only argument on the incompatibility of causation and physics that can be found in Russell (1913). In the following passage, Russell is making a directionality argument based on a feature of physics different from time reversal symmetry:
16According to Zeh (2006) this is possible, though very unlikely.
17In a more direct fashion, Mirman (1975, p. 496) claims that there “is no relation between
the existence of a direction of time and the existence of time-reversal invariance.” From this perspective, the failure of the directionality argument from time reversal symmetry can hardly be surprising.
In the motions of mutually gravitating bodies, there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula. Certain differential equations can be found, which hold at every instant for every particle of the system, and which, given the configuration and velocities at one instant, or the configurations at two instants, render the configuration at any other earlier or later instant theoretically calculable. That is to say, the configuration at any instant is a function of that instant and the configurations at two given instants. This statement holds throughout physics, and not only in the special case of gravitation. But there is nothing that could be properly called ‘cause’ and nothing that could be properly called ‘effect’ in such a system. (Russell 1913, p. 14)
What Russell is saying is that the laws of physics exhibit determinism in both temporal directions, according to his definition of determinism. That is, given a system in state S1 at time t1, the state of the system at any other time can be
calculated from a function of S1, i.e., S(t) = f(S1). Even though this might not
be the best definition of determinism (cf. Earman 1986, sec. II.5), more important at the moment is that it is not obvious at least, where the conflict with causation lies. Given that Earman (1986, sec. II.2) is correct in claiming that determinism and causation are two concepts that should best be kept separate,18 there is no
direct contradiction between the fact that physics is deterministic in both temporal directions and at the same time describes causal connections. However, following Farr & Reutlinger (2013) I believe that the conflict can be established, if Russell’s statement is read as referring to bidirectional nomic dependence of physics. It is bidirectional nomic dependence that establishes the connection between Russell’s determinism and causation.
According to Lewis nomic dependence can be defined as follows:
The family C1, C2, ... of propositions depends nomically on the family A1, A2,
... iff there are a nonempty set L, of true law-propositions and a set F of true propositions of particular fact such that L and F jointly imply (but F alone does not imply) all the material conditionals A1! C1, A2! C2, ... between
the corresponding propositions in the two families. (Lewis 1986b, p. 167)
Given this analysis, bidirectional nomic dependence of physics follows automatically from Russell’s determinism.19
(PND) Physics and nomic dependence: For a deterministic system it is a law L that S(t) = f (Si), i = 1, 2, ..., and given the right conditions F, and S1 and S2
are two states of the system at times t1< t2, then it follows that S1= f (S2)
and S2 = f (S1), and therefore S2 ! S1 and S1 ! S2, that is S1 and S2
are mutually nomically dependent on each other. A deterministic system therefore exhibits nomic dependence in both temporal directions, under the right conditions F.
18This is not meant to imply that causation and determinism are incompatible. See the discussion
of Mackie (1980), who argues for incompatibility, in Earman (1976, p. 12).
19Without going into detail, I content that a similar analysis can be made for indeterministic
It is important to keep in mind that time reversal symmetry and bidirectional nomic dependence are two different features of a theory. As Farr & Reutlinger (2013, p. 227) conclude: “The key point we wish to stress is that, although it may be the case that a nomically unidirectional theory must also be time-reversal non-invariant, the converse is not true: the time-reversal non-invariance of a theory does not entail that the theory is nomically unidirectional.” Hence, the directionality argument from time reversal symmetry and the argument developed in this section are two different arguments that require different solutions.20
The connection between causation and nomic dependence, however, is less obvious. For Farr & Reutlinger, it is established by a realist reading of nomic dependence: “According to this realist reading, nomic dependencies correspond to ontic depend- encies holding between token states of the actual world, and as such, bidirectional nomic dependence is directly comparable to the features of causation with which the Directionality Argument is concerned.” (Farr & Reutlinger 2013, 227) This realist reading is a necessary condition for constructing the argument against a causal interpretation of physics. Of course, not everyone, especially Humeans, has to agree with such a realist reading. It might be the case, for example, that all relations that exist are spatiotemporal relations. For the sake of the argument, I take the realist reading as given.21
With this presupposition, the directedness of causation then has to correspond to a directedness of nomic dependency. Otherwise it would be the case that a directed relation, causation, corresponds to a symmetric relation, nomic dependence, which would be unclear and against the realist reading of nomic dependence. This is captured in the following principle:
(CND) Causation and nomic dependence: If A causes B then B nomically depends on A, and if A causes B then A does not nomically depend on B.
In what follows, I assume that (CND) is a necessary condition for a causal inter- pretation of physics.
On the basis of the foregoing discussion, the following directionality argument from bidirectional nomic dependence can be made (cf. Farr & Reutlinger 2013, p. 229):
1. If a system is causal, then, by (CND), it does not exhibit bidirectional nomic dependence.
2. If a system is physical, then, by (PND), it exhibits bidirectional nomic dependence.
20It is worth adding that time reversal symmetry implies bidirectional nomic dependence, in so far
a theory is deterministic at all. However, bidirectional nomic dependence does not imply time reversal symmetry (cf. Earman 2002, p. 254).
21However, as Farr & Reutlinger (2013, 228) highlight, Humeanism and a realist reading of nomic
dependence might be compatible, if nomic dependence is seen as a non-fundamental relation. In consequence, Farr & Reutlinger remain neutral with respect to Humeanism.
3. If a system is physical, then it is not causal.22
To end this section, I briefly want to discuss a response to this kind of argument by Ney (2009). Ney’s reaction consists not in attacking the directionality argument, but in the suggestion that causation need not be an asymmetric theory.23 According to
Ney (2009, p. 752) the asymmetry of causation stems from the more anthropomorphic notions of “explanation, prediction, and action”. Thus, a theory of causation at the fundamental physical level, deprived of unnecessary anthropomorphic notions, is not necessarily asymmetric. In particular, Ney (2009, p. 753) claims that even without asymmetry there “is still causation, because there is still physical determination.” However, Farr & Reutlinger (2013, 233) have replied that the confrontation between Russell and Ney “looks like a merely verbal dispute. The parties in the dispute are not really disagreeing about anything.” In particular, they agree on that causation usually is understood as an asymmetric relation and on the validity of the directionality arguments. Only where Russell opts for the abolishment of causation, Ney pleads for a shift in concept. As a consequence, Farr & Reutlinger suggest that it is best to not follow Ney, since in the current debate ‘causation’ is understood as an asymmetric relation, and changing the meaning of the concept will not solve any of the problems around asymmetry, but more likely will only cause confusion. A further problem may arise from Ney’s suggestion to separate causation from explanation. It is not entirely clear what she means here, but given the widely shared view that there are at least some causal explanations, its seems difficult to argue that causation has nothing to do with explanation at all. Hence, Ney might best be interpreted as saying that explanation is not identical or cannot be reduced to causation. In that case, one has three options: First, a top-down approach in which we first identify explanatory relations and on that basis identify causal relations. Second, a bottom- up approach, which takes the reversed direction (cf. Psillos 2002, 282-83). Third, a combination of the two preceding option. For all three options it is problematic to have symmetry at one end, but asymmetry at the other; neither can symmetry be deduced from asymmetry nor the other way round. Ney’s proposal thus leads to the highly questionable consequence that if causation is symmetric, then explanations have to be symmetric as well, which might be regarded as a reductio ad absurdum.
In conclusion, I believe that the directionality argument from bidirectional nomic dependence poses a much bigger challenge for the causal interpretation of physics than the analogous argument from time reversal symmetry. Having said that, I will spend sections 4.3.2 and 4.3.4 arguing that it can be refuted, too.
22The argument is based on a deterministic theory. However, as Field (2003, p. 437) points out, it
works equally well for a theory that is indeterministic in both temporal directions.