Counterfactual Triviality: A Lewis‐Impossibility Argument for Counterfactuals

Abstract

I formulate a counterfactual version of the notorious ‘Ramsey Test’. Whereas the Ramsey Test for indicative conditionals links credence in indicatives to conditional credences, the counterfactual version links credence in counterfactuals to expected conditional chance. I outline two forms: a Ramsey Identity on which the probability of the conditional should be identical to the corresponding conditional probability/expectation of chance; and a Ramsey Bound on which credence in the conditional should never exceed the latter. Even in the weaker, bound, form, the counterfactual Ramsey Test makes counterfactuals subject to the very argument that Lewis used to argue against the indicative version of the Ramsey Test. I compare the assumptions needed to run each, pointing to assumptions about the time‐evolution of chances that can replace the appeal to Bayesian assumptions about credence update in motivating the assumptions of the argument. I finish by outlining two reactions to the discussion: to indicativize the debate on counterfactuals; or to counterfactualize the debate on indicatives.

Subjunctive Credences and Semantic Humility

“…This exception creates a problem for ( Bridge ): if a subject has some credence that the antecedent of a future subjunctive A □→ C has chance 0, her expectation of the conditional chances ch ( A □→ C | A ) and ch ( C | A ) would also then be undefined. Williams 2010a notes that one could respond to such potential counterexamples by positing primitive conditional chances or by limiting the domain of ( Bridge ):…”

“…The potential objection to my argument is as follows: if that claim is correct and this argument is a reductio of ( Bridge ), then theories of conditionals should not be faulted for yielding verdicts about ordinary subjunctives that are inconsistent with ( Bridge ). For instance, in his discussion of a closely related principle, Williams 2010a suggests that it is not reasonable to expect theories to yield the verdicts entailed by claims like ( Bridge ), since ‘‘it will be very hard to satisfy the Ramsey Bounds for any conditional over a wide range of antecedents and consequents—so hard that consensus opinion in the indicative debate is that the enterprise is quixotic’’ (16).…”

“…Intuitively, ( Bridge ) also fails in such cases. As Williams 2010a acknowledges, if a trusted oracle tells you that a certain fair coin would land heads if it were flipped, you may raise your credence in that conditional without changing your expectations of conditional objective chances involving the coin. For instance, you may remain confident that the coin is fair, so that your expectation of the conditional chance of it landing heads if flipped remains .5.…”

“…Let and be rational credence distributions of hypothetical subjects that are certain that ch ′ and ch ′′ give the actual objective chances, respectively. Here is a slight adaptation of the subjunctive triviality proof in Williams 2010a: …”

“…20 20 This objection was first brought to my attention by Bob Stalnaker in conversation. Here I discuss the objection as developed by Robbie Williams in Williams 2010a. …”