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Contra counterfactism

  • Decision-making and hypothetical reasoning
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Abstract

‘If I were to toss a coin 1000 times, then it would land heads exactly n times’. Is there a specific value of n that renders this counterfactual true? According to an increasingly influential view, there is. A precursor of the view goes back to the Molinists; more recently it has been inspired by Stalnaker, and versions of it have been advocated by Hawthorne, Bradley, Moss, Schulz, and Stefánsson. More generally, I attribute to these authors what I call Counterfactual Plenitude:

For any antecedent A, there is a world wi such that A ☐→ wi is true.

Moreover, some of these authors are also committed to Primitive Counterfacts Realism:

There exist primitive modal facts that serve as truth-makers for counterfactual claims.

Call the conjunction of these italicized theses counterfactism. I clarify it and suggest some of its virtues, while ultimately rejecting it.

Stefánsson’s counterfactism is motivated by and targeted at my “counterfactual skepticism”—I argue that most counterfactuals are false—and counterfactism has various other sources of support. I briefly defend that skepticism, and I seek to undercut those sources of support. I then argue more directly against counterfactism, especially on grounds of its ontological profligacy, and its leading to another kind of skepticism about counterfactuals that I believe is more problematic than my kind. In the process, I discuss how Bradley’s multidimensional semantics bears on counterfactism; I offer some new considerations against some central theses regarding conditionals (Conditional Excluded Middle, Stalnaker’s Thesis, and Skyrms’ Thesis); and I reflect more generally on the epistemology of modality and the choice of primitives in our theorizing.

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Notes

  1. The incompatibility of ‘might nots’ and corresponding ‘woulds’ provides my main reason for regarding most counterfactuals as false, rather than indeterminate. A ◊→ ¬C is easily made true. To be incompatible with A ☐→ C, the latter must false, not merely indeterminate. Upholding bivalence is another reason.

  2. An exception may need to be made for counterlegals.

  3. To be sure, Stefánsson argues that realism about counterfacts goes naturally with the plenitude thesis, but that’s a different matter, to be discussed shortly.

  4. Thinking of propositions as sets of worlds, strictly speaking the consequent should be the singleton set {wi}, rather than the world itself. Take that as read; I want to simplify my notation as much as I can.

  5. All the leading accounts of counterfactuals respect this implication.

  6. I thank him for confirming that this corrects a typo.

  7. Here I will just briefly rehearse the familiar Frege-Geach-style worries about how they embed in various Boolean combinations, modal contexts, and how they iterate, while acknowledging that there are sophisticated replies (much as there are for similar worries about moral expressivism). Especially pressing is how they embed in probabilistic contexts, since no-truth-value theorists appeal to a version of the thesis that probabilities of counterfactuals are corresponding conditional probabilities. But probability is probability of truth: when we say that P(X) = x, it is X’s truth that receives probability x, rather than some other feature of X. As such, X has to have a truth value. ‘X is probable but has no truth value’ is an uneasy combination.

    In this respect, probability is not like desirability: seeking world peace is desirable, but ‘seeking world peace’ does not have a truth value. Desirability can attach to things, and even abstract objects, as well as bearers of truth values. Instead, probability is like possibility: if X is possible, then X has a truth value.

  8. That said, I also wouldn’t be surprised if most of the predictions that we make are false, with a huge transcript of all of the predictions ever made in history containing a majority of falsehoods. (Even putative experts in various areas—the stock market, politics, psychiatry, the law, college admissions—notoriously make false predictions on a regular basis.) If that’s the case, it really should come as no surprise if most of the counterfactuals that we utter are false; but I’ll let that pass.

    We also exchange ‘wills’ for ‘woulds’ when reporting predictions, as Brian Weatherson has pointed out to me. I say: “It will rain tomorrow”. You later report what I said: “Alan said that it would rain tomorrow”. Similarly for conditional versions: “If it rains tomorrow, we will cancel the picnic” later gets reported as “Alan said that if it rained tomorrow, we would cancel the picnic”. Striking though this is, I am not convinced that the latter embeds a counterfactual, even though it superficially appears that way. For “would” is also simply the past tense of “will”.

  9. This is so on the main accounts of counterfactuals.

  10. Strictly speaking, “Humean supervenience” is not the general thesis that all truths supervene on non-modal truths, but rather Lewis’s specific version of that thesis: “all there is to the world is a vast mosaic of local matters of particular fact—all else supervenes on that” (1986b, pp. ix–x).

  11. Contextualists about counterfactuals will seek to uphold folk talk by insisting that in normal contexts, ‘the plate would fall to the floor if dropped’ is true; by drawing attention to the chanciness of the drop, or of your catching the plate, one is changing the context to a more demanding one in which the counterfactual goes false. A proper discussion of contextualism requires another paper (in the works!). But I applaud Stefánsson for attempting to secure the truth of the counterfactual, period—not merely its truth relative to a context. After all, the folk view is that the counterfactual is true, period. Of course, I argue for its falsehood, period.

  12. A plate-itude, one might say.

  13. Actually, I don’t think these are the strongest examples to support her point. One might insist that you really do know that the coin would not land heads each time if it were tossed that many times, since the probability of that happening would be so high. Compare the intuition that you really do know that a given extremely likely thing will happen—for example, you know that your lottery ticket will lose. I do not share this intuition, but a number of people do—see e.g. Bacon (2014). I think that a better example involves just a single toss: “I wonder if this coin would land heads if I were to toss it once. We’ll never know…”.

  14. Thanks to Cory Nichols for the first example.

  15. Stefánsson’s footnote 10 recognizes this.

  16. All my italicizing might make you suspicious that I am drawing your attention to pragmatic rather than semantic phenomena. It’s true that I want to draw your attention to something. I think it is the demandingness of ‘woulds’—a semantic phenomenon. If I’m wrong, it’s still interesting if the ring of truth of CEM can be undermined simply by suitable emphasis. It still becomes a less secure data point to be accommodated.

  17. See also Williamson (1988), who elaborates on the illicit scope shift in negation that may make CEM seem plausible.

  18. Here I follow Stefánsson’s presentation of the Thesis, which is quite standard. Perhaps the chances are time-dependent, in which case we should also index ‘Ch’ with a ‘t’. But it is context-independent what the chance function is at time t.

  19. I am grateful here to a referee for Synthese.

  20. Bradley points out the undeniable truth in an argument that is supposed to defend (his version of) Counterfactual Plenitude, but I think it doesn’t because of the scope issue. Note that David Lewis would agree with the undeniable truth: in each of the closest compatriots-worlds, Bizet and Verdi have some nationality (of course). But Lewis would disagree that there is some nationality such that they have that nationality in each of the closest compatriots-worlds.

  21. Thanks to Justin D’Ambrosio for helpful discussion here. See also Eriksson and Hájek (2007, pp. 205–206).

  22. This is so even though my suggested version 4 presumably requires infinitely many primitive counterfacts (one for each antecedent), and arguably proper class many, just as the alternative versions 1–3 do. This shows that there’s a sense of quantitative parsimony that does not just look at cardinalities.

  23. Thanks to Nick DiBella for this last point.

  24. Baldwin (1996) argues that an entirely empty world is possible.

  25. For the points of this paragraph and the next one I am indebted to Eyal Tal.

  26. Thanks to Cory Nichols for a version of this point.

  27. Evidential probabilities, à la Williamson (2000), might provide a theoretical framework to account for this datum. Arguably, the counter-inductivist’s probability assignment is not justified because it differs wildly from the corresponding evidential probability, given his total evidence.

  28. There’s another problem if the laws are primitive—for example, primitive relations of necessitation between universals, à la Armstrong (1983). Then, it’s unclear how we get an entailment, or indeed any relation of interest, between the primitive laws and what actually happens. See Lewis (1983).

  29. For very helpful comments and discussion, I thank especially Justin D’Ambrosio, Nicholas DiBella, Brian Garrett, John Hawthorne, Boris Kment, Leon Leontyev, Cory Nichols, Wolfgang Schwarz, Orri Stefánsson, Una Stojnic, Eyal Tal, Lee Walters, Brian Weatherson, and audiences at the University of Melbourne (Melbourne Logic Group), Bilkent University, the 2016 Conditionals Conference at Belgrade University, and at the 2019 Australasian Association of Philosophy conference, Wollongong. I also thank two referees for Synthese for their insightful reports, which led to a number of improvements.

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    Alan Hájek

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Hájek, A. Contra counterfactism. Synthese 199, 181–210 (2021). https://doi.org/10.1007/s11229-020-02643-x

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