Abstract
If one is interested in reasoning counterfactually within a physical theory, one cannot adequately use the standard possible world semantics. As developed by Lewis and others, this semantics depends on entertaining possible worlds with miracles, worlds in which laws of nature, as described by physical theory, are violated. Van Fraassen suggested instead to use the models of a theory as worlds, but gave up on determining the needed comparative similarity relation for the semantics objectively. I present a third way, in which this similarity relation is determined from properties of the models contextually relevant to the truth of the counterfactual under evaluation. After illustrating this with a simple example from thermodynamics, I draw some implications for future work, including a renewed possibility for a viable deflationary account of laws of nature.
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Notes
This prefacing also allows one to separate the question of counterfactual reasoning within a theory from the question of its acceptance, and what that entails, contrary to what the above quotation from van Fraassen suggests. Moreover, it is neutral between the indicative and subjunctive readings because the semantics I propose is independent of the empirical (or metaphysical) adequacy of the theories whose models are employed. See also my discussion of Boyle in Sect. 6.
No assumptions about the metaphysical possibility of the states of affairs represented by the counterfactual antecedent are needed, either. Such a counterfactual will not be vacuous if its antecedent is true in some model. So, the present approach is viable for those who take some aspects of scientific reasoning to involve (metaphysical) counterpossibilities (Jenny 2018; Tan 2018).
Indeed, data from Ciardelli et al. (2018) indicate that at least the general populace does not make counterfactual judgments in accordance with any version of ordering semantics at all. They tended to use simple everyday language counterfactuals, however, so there is still room for the present reforming project when it comes to counterfactuals in physics.
Actually, Muller (2005) slightly modifies the strict conditional to change how it rules in cases of impossible antecedents, but this makes no difference to the point at issue.
See also Lewis (1973, Sect. 1.2) for further discussion of the problems that strict conditionals face as an explication of natural language counterfactual conditionals.
See also van Fraassen (1989, pp. 33–35).
Here I follow Lewis (1981), who gives a modified semantics compared with Lewis (1973, p. 49), allowing the comparative similarity relation to be merely partial. Swanson (2011) then presents a further sophistication based on the concept of a cutset, but I’ve suppressed this innovation since it doesn’t make a significant difference for present purposes.
Because context-independence is here taken only as a necessary condition for objectivity, blocking the argument by itself does not entail that counterfactual conditionals are objective.
This is because of the circularity involved in giving an account of the semantics of counterfactual conditions that invokes the truth of some other counterfactual conditional. Perhaps one could show that this still yielded an implicit definition of the semantics, but I am skeptical of this strategy’s prospects because one conditional appears in the object language and another in the metalanguage. Of course, this sort of circularity would not be a problem if one had other resources to which one could appeal. Indeed, if one were engaged in the project of saving the phenomena of scientific (or everyday) language use, as Muller (2005) [and Lewis (1973), respectively,] is, then one could use basic judgments of competent language users to determine these counterfactuals.
This of course can be greatly generalized; they need only be valued, for example, in some module, in order to define the weighted sum.
Maudlin does develop his account for probabilistic theories, whereas I do not in this essay. The points of comparison thus treat non-probabilistic theories.
On Maudlin’s account, this is a material conditional, not a material biconditional, for he adds that \(\phi \boxright \psi \) is false at w if for all such \(w'\), \(\psi \) is false at \(w'\). If \(\psi \) is true at some \(w'\) and false at others, \(\phi \boxright \psi \) is indeterminate. Thus, Maudlin’s proposal is actually for a three-valued logic. One oddity of this proposal is that it makes \(\phi \boxright \lnot \psi \) and \(\lnot (\phi \boxright \psi )\) logically equivalent. For convenience, I will set these differences aside in the remainder.
Maudlin (2007, p. 33) stresses that “the principal test of a semantic theory is how it accords with our intuitions” not just in evaluation, but in its justification: “the psychological question of how people evaluate counterfactuals, what processes underlie their intuitions” (Maudlin 2007, p. 33). Readers may decide for themselves whether the three-step process Maudlin presents resembles their cognitive processes in evaluating counterfactuals, as Maudlin asserts it does; in any case, what is important is that Maudlin’s goals are distinct from the present ones in this essay.
As Jaramillo and Lam (2018) document, for more complex theories such as general relativity, evaluating counterfactual conditionals is computationally intensive, even without spacetime curvature’s interaction with matter. Despite their claims to the contrary, however, these problems are entirely practical; in principle the same approach developed here applies to general relativity, too.
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Earlier versions of this project, under the title, “Counterfactuals within Scientific Theories,” were presented in Dubrovnik, Istanbul, Helsinki, Munich, Florianópolis, Ames (at Iowa State), Minneapolis, and (under the present title) Kraków, whose audiences I would like to thank for their comments, in addition to those of Chris Willis, David Schroeren, and two encouraging, anonymous referees. This work was supported in part by a Marie Curie International Incoming Fellowship (PIIF-GA-2013-628533).
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Fletcher, S.C. Counterfactual reasoning within physical theories. Synthese 198 (Suppl 16), 3877–3898 (2021). https://doi.org/10.1007/s11229-019-02085-0
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DOI: https://doi.org/10.1007/s11229-019-02085-0