Trans-World Causation Revisited
| Autor | Axel Arturo Barceló Aspeitia |
| Cargo | Instituto de Investigaciones Filosóficas, UNAM |
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CRÍTICA, Revista Hispanoamericana de Filosofía. Vol. 46, No. 136 (abril 2014): 27–41
TRANS-WORLD CAUSATION REVISITED
AXEL ARTURO BARCELÓ ASPEITIA
Instituto de Investigaciones Filosóficas
UNAM
abarcelo@filosoficas.unam.mx
SUMMARY: In a recent paper, García-Ramírez (2012) has argued that Lewis’ counter-factual analysis of causation has the undesirable consequence of making trans-world causation possible. In this paper I argue, against García-Ramírez, that the possibility of trans-world causation cannot be derived from Lewis’ account of in-world causation, since there is no way of extending Lewis’ closeness relation among worlds into a similar closeness relation among pairs of worlds that is neither trivial nor ad-hoc.
KEY WORDS: resemblance, closeness, possible worlds, counterfactuals, Lewis
RESUMEN: En un artículo reciente, García-Ramírez (2012) ha argumentado que el análisis contrafáctico de la causalidad de Lewis tiene la indeseable consecuencia de hacer posible la causalidad transmundana. En este artículo argumento que, contrario a lo que García-Ramírez sostiene, la causalidad transmundana no se deriva de la teoría de Lewis de la causalidad intramundana, ya que no se puede extender la relación de cercanía entre mundos de Lewis a pares de mundo de una manera que no sea trivial o ad hoc.
PALABRAS CLAVE: similitud, cercanía, mundos posibles, contrafácticos, Lewis
1 . Introduction
In a recent paper, Eduardo García-Ramírez (2012) has accused Lewis’ (1973) counterfactual account of causation of entailing the possibility of trans-world causation. Given that one “may think that it is a metaphysical fact about causation that there cannot be trans-world causation, [this] may seem like a terrible consequence of counter-factual theory” (García-Ramírez 2012, p. 82). In finer detail, GarcíaRamírez’s reductio argument against Lewis goes as follows:
1. The counterfactual account of causation: according to Lewis, an event C in a world W causes another event E in the same world W if and only if at the closest worlds to W where C does not occur, E does not occur either.
2. If C causes E in world W if and only if E does not occur at all the closest worlds to W where C does not occur, then an event C in a world WC would cause an event E in a different world WE if and only if E does not occur at the second world of all the closest world-pairs to <WC, WE> such that C does not occur at their first worlds.
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3. There are events E and C, and worlds WC, WE such that C occurs in WC, E occurs in WE and for all the closest world-pairs to <WC, WE> such that C does not occur at the first world of the pair, E does not occur at the second world of the pair.
4. From the previous premises it follows by a couple of Modus Ponens that it is possible for an event in a world to cause an event in a different world, i.e. trans-world causation is possible.
5. Presumably, trans-world causation is impossible.
6. Therefore, we must abandon the counterfactual account of causation.
García-Ramírez presents his argument as a reductio against the conjunction of Lewis’ counterfactual account of causation and his brand of modal realism. However it is clear that, as the reconstruction above shows, his argument does not require that possible worlds be concrete. Consequently, I will take his argument as a reductio of Lewis’ theory of causation, period.
In (1986), Lewis himself had already considered a similar objection, but concluded that, even if we wanted to extend his analysis of counterfactuals to make sense of trans-world cases in something like the way suggested in premise 2 of García-Ramírez’s argument, the most natural way of doing so would not yield any nontrivial trans-world counterfactuals, and instead would make all claims of trans-world causation false. In other words, Lewis had already anticipated García-Ramírez’s objection, and replied by challenging premises 2 and 3. According to Lewis, the above argument is unsound, for it is based on an equivocation in the predicate “being closer to”. For Lewis, the closeness relation relevant for in-world causation is a (three-arguments) relation among worlds, not pairs of worlds, and furthermore, there is no way of extending his closeness relation to develop an analogous relation for pairs of worlds in a way that makes both premises 2 and 3 true, i.e. there is no way of defining a closeness relation among pairs of worlds that is both the most natural extension of the closeness relation governing ordinary in-world causation (so that premise 2 is true) and does not make all relevant counterfactuals trivially false (so that premise 3 is true as well).
García-Ramírez takes Lewis’ claims as setting up a challenge: to extend his counterfactual account of intra-world causation to cover
Crítica , vol. 46, no. 136 (abril 2014)
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TRANS-WORLD CAUSATION REVISITED 29 trans-world causation in a way that is non-trivial and naturally follows from Lewis’ original account. Most of the work on García-Ramírez (2012) is devoted to offering such an account. In this text, I contend that what he offers there is, at best, an incomplete sketch of how such an account could be given and, furthermore, that there is no way of completing it to satisfy the constraints of Lewis’ challenge.
2 . Constraints on a Natural Counterfactual Theory of Trans-World Causation
Before getting on to García-Ramírez’s proposal, it is very important to be clear on what exactly is involved in Lewis’ challenge. The first condition for developing an appropriate counterfactual theory of trans-world causation requires embracing what García-Ramírez calls the fundamental claim of a possible world account of counterfactuals: “Counterfactuals are true if it takes less of a departure from actuality to make the consequent true along with the antecedent than it does to make the antecedent true without the consequent” (Lewis 1973). Also, any account of trans-world causation that aims to be a natural extension of Lewis’ intra-world account must also embrace the following two theses:
Thesis 1: One pair of worlds <X, Y> is closer to another pair <A, B> than another pair <W, Z>, if <X, Y> resembles <A, B> more than <W, Z> does.
Thesis 2: There is causal dependence between an event C in a world WC and another event E in a different world WE iff if C were not to occur in WC, E would not occur in WE. (Lewis 1986)
Combining these two theses with the fundamental claim, we get the following counterfactual account of trans-world causation:
An event C in a world WC causes event E in world WE if and only if, at the closest world-pairs to the pair <WC, WE> where C does not occur at the first world of the pair, E does not occur at the second.
Consequently, Lewis’ challenge is to define a relation of closeness between pairs of worlds that is both non-trivial (it must not make all trans-world causal counterfactuals vacuously false nor vacuously true) and the most natural extension of the closeness relation governing
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intra-world causation. In order to satisfy this second condition, the relevant closeness relation must also satisfy certain constraints, both in its form and its content. From a formal perspective, the closeness relation ought to be a three-place relation among pairs of worlds that is both weak and non-finite;1 regarding its content, Lewis demands that it “be governed by the same sort of closeness that governs ordinary causal counterfactuals” (Lewis 1986, pp. 79–80). Presumably, this requires satisfying at least the following constraints:
Conservativeness: It must not postulate more external relations among worlds or pairs of worlds that those already given in Lewis’ theory.
Homogeneity: Pair <X, X> is closer to <A, A> than <Y, Y> if and only if world X is closer to world A than Y.
However, in order to meet Lewis’ challenge, it is not enough to define a non-trivial closeness relation among pairs of worlds that is conservative and homogenous, or even less to show that developing such a relation is possible (even if showing so would already be a big blow to Lewis’ theory, since he also makes the strong claim that “under a counterfactual analysis of causation, the causal isolation of worlds follows automatically” 1986, p. 78); it is also necessary that the closeness relation defined on pairs of worlds be the most natural extension possible of Lewis’ original proposal. Otherwise, one could not justifiably claim that Lewis’ theory has the possibility of trans-world causation as an undesirable consequence. In other words, in order to meet Lewis’ challenge, one must warrant that the conditional in premise 2 is true, i.e. that one’s closeness relation for pairs of worlds follows naturally from Lewis’ own closeness relation for single worlds. There must not be other, trivial and more natural (or, at least as natural) ways of extending Lewis’ relation. If there were many, equally natural ways of extending Lewis’ closeness relation, some trivial and others not, the conditional in 2 would not be justified, and the Modus Tollens in 6 would not be valid (Lee...
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