Abstract
According to a widespread view, which can be traced back to Russell’s famous attack on the notion of cause, causal notions have no legitimate role to play in how mature physical theories represent the world. In this paper I first critically examine a number of arguments for this view that center on the asymmetry of the causal relation and argue that none of them succeed. I then argue that embedding the dynamical models of a theory into richer causal structures can allow us to decide between models in cases where our observational data severely underdetermine our choice of dynamical models.
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Notes
This remark occurs within the context of a discussion that also involves modal aspects of the causal relation. It is important, however, to keep the two aspects—the putative modality and the asymmetry of the causal relation—distinct. In the present quote van Fraassen unambiguously seems to be concerned with the asymmetry: he examines whether the mathematical formalism of the theory allows us to distinguish asymmetric shovings of brothers by sisters from their inverse, and not whether the shovings in some sense are necessitated.
This point was raised by an anonymous referee for this journal.
Just as models of F = m a are not intrinsically models of Newtonian systems but only if we use F, m, and a to represent force, mass, and acceleration, respectively.
As Richard Healey has reminded me in conversation, one might think that on van Fraassen’s view (or at least according to the view van Fraassen appears to have defended in The Scientific Image (van Fraassen 1980)) a theory does not require an interpretational framework. On that view a theory is true, if it has models that are isomorphic to the phenomena. The problem with that view, however, is that there may be too many isomorphisms and hence that almost all theories come out as (almost) trivially true.
The burgeoning causal modeling literature is evidence that systems of causal relations can be given formally precise representations (see, e.g. Pearl 2009 (2000)). See also Tim Maudlin’s related discussion in (Maudlin 2007, 135ff) of the claim that the passage of time could mathematically be represented by adding a temporal orientation to the spacetime manifold.
See (Newton-Smith 1983) for a proposal of how one might introduce the asymmetry of the causal relations into a Mackie-style account of causation.
“Schon [mit diesem Kontrast] scheint mir das Schicksal der Ereigniskausalität als fundamentaler Gesetzlichkeit besiegelt zu sein.” (the translation into English is my own)
Even though I am following Norton here in expressing the argument in terms of real physical properties of a process, the point I wish to make here is independent of the debate about scientific realism. A defender of a principle of causality can also be an instrumentalist and argue that the causal relations in our models no more represent real properties than other properties or relations in our models. My claim here is that there is no principled reason for treating causal properties differently from other kinds properties and relations of our models (and of the real world systems we are modeling).
This is also what (Field 2003) appears to argue.
Despite what Rohrlich says here, he now seems to believe that there can be good reasons for interpreting a theory with time-reversal invariant laws causally asymmetrically. (See Rohrlich 2006)
Norton’s paper is a response to my (2009a), where I argue that dispersion theory invokes causal assumptions. Norton apparently assumes in his reply that the relevant asymmetry in this case just is an instance of the electrodynamic wave-asymmetry that he discusses. I am less sure than he is, however, that the two cases are as closely related as he suggests. I have two concerns: first, dispersion theory is just one particular application of the general framework of linear response theory, which also has many applications outside of classical electrodynamics; and, second, there appears to be a formal disanalogy between the Green’s functions used in the two cases: while the Green’s function for the wave equation has a temporal inverse, the inverse Green function in the case of linear response theory is not mathematically well-defined. That is, while one can solve the wave-equation both as an initial value problem and a final value problem, one cannot, it seems, represent a linear response system through a final value problem. See also (Frisch 2009b)
In order to bring out the asymmetry as simply and clearly as possible I am adjusting Norton’s specific example slightly. The example of the antenna is discussed in (Earman 2011, 501).
For an argument that causal notions play a role in experimental contexts (see Frisch 2010).
This is not merely a philosopher’s question: see Rohrlich’s discussion of the related question whether there is a local criterion of radiation in his classic text (Rohrlich 1990, sec. 5–2). Rohrlich asks whether there is a local criterion to determine whether a known source radiates or not. His answer is that there is no general local criterion and that we would have to know the field on an entire sphere surrounding the source to be able to determine whether the charge is radiating.
There is an additional problem in CED: due to the problem of self-interactions it is unclear whether there is a well-defined full initial value problem. Thus, radiation phenomena are usually modeled in terms of a modified initial value problem in which the full trajectories of the sources are assumed as given and the time-evolution of the fields is calculated from these and the fields on an initial value surface.
(Pearl 2009, 44: def. 2.2.2) defines a causal model as “a pair M = <C, Θ D > consisting of a causal structure C and a set of parameters Θ D compatible with C. The parameters Θ D assign a function x i = f i (pa i , u i ) to each X i ∈ V and a probability measure P(u i ) to each u i , where PA i are the parents of X i in C and where each U i is a random disturbance distributed according to P(u i ), independently of all other u.” A causal structure is a directed acyclic graph, which in our case is this (Fig. 2):
This point is forcefully argued by Walter Ritz (Ritz 1908).
This is also Pearl’s view, who says: “note that despite its innocent appearance in associational vocabulary, the latter assumption [of initial randomness, Cov(U Y , U X ) = 0,] is causal, not statistical, for it cannot be confirmed or denied from the joint distribution of observed variable, in case U’s are unobservable.” (2009, 704)
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Funding for the research for this paper has been partly provided by the Alexander von Humboldt Foundation. I would like to thank Nancy Cartwright, Chris Hitchcock, Carl Hoefer, Wolfgang Pietsch, and Jim Woodward for extremely helpful discussions and comments on various drafts of this paper.
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Frisch, M. No place for causes? Causal skepticism in physics. Euro Jnl Phil Sci 2, 313–336 (2012). https://doi.org/10.1007/s13194-011-0044-4
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DOI: https://doi.org/10.1007/s13194-011-0044-4