Abstract
This paper offers a new way to evaluate counterfactual conditionals on the supposition that actually, there is no time. We then parlay this method of evaluation into a way of evaluating causal claims. Our primary aim is to preserve, at a minimum, the assertibility of certain counterfactual and causal claims once time has been excised from reality. This is an important first step in a more general reconstruction project that has two important components. First, recovering our ordinary language claims involving notions such as persistence, change and agency and, second, recovering enough observational evidence so that any timeless metaphysics is not empirically self-refuting. However, the project of investigating causation in a timeless setting has a greater relevance than its application to timeless physical theory alone. For, as we show, it can be used to model the assertibility conditions of causal claims more generally.
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Notes
McTaggart (1908) also famously argued for the unreality of time.
Barbour’s view can be thought of as the combination of presentism with modal realism (Butterfield 2002). As Butterfield notes, care is warranted in treating Barbour’s view as a version of presentist modal realism, for two reasons. First, under presentism it is typically thought that the past existed and the future will exist, and thus that which ‘instant’ is present changes as time passes (cf, Tallant 2010; Fiocco 2007). The points in Barbour’s configuration space are static: there is no sense in which the instant that exists will change to a different instant. Each instant exhausts the ontology of its own little universe; all that exists, existed and will ever exist from the perspective of an instant is a single, three-dimensional configuration. Second under Lewis’s (2001) full-blown modal realism, each world is a four-dimensional space-time. However, under Barbour’s view, each world is not a complete space-time as under Lewis’s view; each world is merely a point in a configuration of particles in Riemannian 3-space.
As we discuss later on, this assumption can be given up.
As pointed out to us by an anonymous referee, when applying Lewis’s account to Barbour’s picture and thus to points in Platonia, we are actually moving away from Lewis’s core account. This is so for two reasons. First, because the space of possible worlds to which Lewis appeals is bigger than Platonia. Lewis’s space of worlds includes all possible worlds; Platonia only includes physically possible worlds. Second, Lewis’s space of worlds includes worlds with real past histories (i.e. worlds with a four-dimensional space-time manifold). Platonia, by contrast, includes only three-dimensional configurations—there are no worlds with real past histories. In the current context, however, these differences between Platonia and the space of worlds to which Lewis appeals do not matter, since the same result can be obtained using the unrestricted space of Lewisian worlds just as easily, so long as the actual world is a point in Platonia. Which is to say that even on the unrestricted picture, Lewis’s framework as applied to the actual world treated as a three-dimensional configuration will render counterfactuals trivially false.
Note that the problem is not that there are no dynamical laws, the problem is that there are no dynamical laws. I.e., the problem is not that there are no dynamical generalisations; the problem is that these are not laws. We discuss this issue in more detail in Sect. 4.
We have focused on counterfactual theories of causation, but a similar result can be obtained for process theories. According to the process theory of causation developed by Dowe (1992, 1999) and Salmon (1994), ‘x causes y’ is analysed as follows:
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CAUSPROC \(\quad `\hbox {x}\) causes y’ is true iff (i) x’s worldline in spacetime intersects with y’s and (ii) at the point of intersection x transfers a conserved quantity to y.
Here conserved quantities are things like energy, velocity, and momentum. A causal process is thus the worldline of an object that possesses a conserved quantity. All causal claims analysed via CAUSPROC are trivially false in a Barbour world. Barbour worlds are relative configurations of particles in a 3-space. According to the process theory, however, causation requires the existence of four-dimensional space-time. Since processes are temporal or, at the very least, require the existence of multiple intra-world instants that are appropriately connected to one another, no such processes can occur in a Barbour world and so no causal claim so understood can be true.
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Where ‘\(\le \)’ is a partial order over a set S iff for any points x, y and z such that x \(\in \) S, y \(\in \) S and z \(\in \) S:
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(1)
x \(\le \) x.
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(2)
If x \(\le \) y and y \(\le \) x then x = y.
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(3)
If x \(\le \) y and y \(\le \) z then x \(\le \) z.
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(1)
Where ‘\(\le _\mathrm{\,\,T}\)’ is a total order over a set S iff for any x, y and z such that x \(\in \) S, y \(\in \) S and z \(\in \) S:
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(1)
If x \(\le _\mathrm{\,\, T}\) y and y \(\le _\mathrm{\,\, T}\) x then x = y.
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(2)
If x \(\le _\mathrm{\,\, T}\) y and y \(\le _\mathrm{\,\,T}\) z then x \(\le _\mathrm{\,\,T}\) z.
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(3)
x \(\le _\mathrm{T}\) y or y \(\le _\mathrm{\,\, T}\) x.
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(1)
Once we have come this far, we can also develop a process-like semantics using quasi-worlds to produce a proxy for process causation. Because an actual quasi-world mimics an actual spacetime there will be process-like phenomena within actual quasi-worlds that can underpin a quasi-process semantics. The basic idea would be to use quasi-worlds to recover quasi-world lines through those worlds. We could then reformulate CAUSPROC from footnote 7 to give us assertibility conditions for causation as follows:
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CC3 ‘\(x\) causes \(y\)’ is assertible iff (i) \(x\)’s quasi-world line in a quasi-world intersects with \(y\)’s quasi-world line and (ii) at the point of intersection \(x\) quasi-transfers a conserved quantity to \(y\).
Where ‘quasi-transference’ is a matter of (i) x at a point \(p1\) in Platonia in quasi-world \(h_{1}\) having a conserved quantity C and (ii) at a second point in Platonia \(p_{2}\) in quasi world \(h_{1}\) such that \(p_{2}\) is posterior to \(p_{1}\) in the total order for \(h_{1}\), \(x\) lacks the conserved quantity, and \(y\) possesses that quantity.
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Acknowledgments
The authors would like to thank Huw Price, Jonathan Tallant, Brad Weslake and three anonymous referees for this journal for extremely useful comments on earlier versions of this paper. This research was partly funded by a John Templeton Foundation grant held by Alex Holcombe, Kristie Miller, Huw Price and Dean Rickles entitled: New Agendas for the Study of Time: Connecting the Disciplines.
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Baron, S., Miller, K. Causation in a timeless world. Synthese 191, 2867–2886 (2014). https://doi.org/10.1007/s11229-014-0427-0
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DOI: https://doi.org/10.1007/s11229-014-0427-0