Abstract
Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic (Reducibility). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference (counterfactual development, or CD) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in a Reducibility-based reply to two kinds of modal skepticism. I argue that its use is entirely dispensable, and that Reducibility makes available replies to modal skeptics which show certain propositions to be metaphysically necessary by deductive arguments from premises the modal skeptic accepts can be known.
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Notes
All reference hereafter to modality is to metaphysical modality unless context indicates otherwise.
I make no claims about the historical accuracy of the labels for the kinds of modal scepticism defined here.
See Yablo (1993) for discussion.
The case of alleged contingent logical truths might seem to preclude the classification of logical and analytic necessity as stricter than metaphysical necessity, contrary to my intention. See §5 below on contingent logical truths. For someone who doubts that there is any necessity stricter than metaphysical necessity, we can define properly metaphysical necessities some other way—e.g., as necessary a posteriori truths (thanks to Margot Strohminger for this suggestion).
Speaking of logical necessity as a property of propositions will appear problematic for the traditional Millian who maintains that ‘Marilyn Monroe = Marilyn Monroe’ and ‘Marilyn Monroe = Norma Jean Baker’ express the same proposition (the first sentence is logically true, the second not; what is the logical status of the proposition expressed?). Although Millians have tended to be sympathetic towards the view that propositions have sentence-like structure, they have not, until recently, made use of all of the distinctions which the conception of propositions as structured allows them to make: see Putnam (1954) and Fine (2007).
Many papers in modal epistemology (see Gendler and Hawthorne 2002 for a sample and references) attempt to rebut this kind of motivation for modal skepticism. Yablo (1993) is a classic example. Hill (2006) is a more recent one. Just like the Humean, Hill worries that “Coherent conceiving is a reliable test for conceptual possibility, but not for metaphysical possibility” (p. 229). This observation motivates his search for an account of modal knowledge based on something other than conceiving alone. Something similar can be said of Williamson himself, who writes that “it is imaginable but not possible that water does not contain oxygen, except in artificial senses of ‘imaginable’ that come apart from possibility in other ways” (PoP, p. 163). The prominence of the Humean’s position in the literature is undeniable, even though it is difficult to find examples of philosophers who explicitly endorse Humean modal skepticism in print. Nevertheless, conversations with philosophers have led me to believe the position to be widespread (a prominent example: Stephen Stich, in conversation, unhesitatingly assented to the Humean position when I described it to him). I suspect that the paucity of textual evidence of widespread commitment to the Humean position is due to the fact that philosophers who subscribe to it generally do not write about modality. What evidence there is typically comes in the form of an explanation of one’s refusal to engage with the topic of the necessary a posteriori, on the grounds that, allegedly, conceivability is the only known way of assessing the modal status of propositions (Segal 2000, p. 15f, is a good example of this). Others (e.g., Fitch 1976; Swinburne 1991) have denied that there are any necessary a posteriori truths. Because one cannot know what is not true, these philosophers are also Humeans.
Malmgren (forthcoming: §3) raises a related worry: that the evaluation of those counterfactuals that, according to Williamson, capture the verdicts issuing from philosophical thought experiments such as Gettier cases might require “rational intuition”. Though this would be bad news for Williamson’s overall metaphilosophical project, it would have no effect on the project of fending off skepticism about modality. I am not concerned with responding to the sort of modal skeptic who (only) thinks we never have knowledge of the necessity of specifically philosophical claims. However, if the reply I develop in §4 is correct, then such a skeptic must be wrong—after all, very many interesting philosophical claims have the form of identity claims: that knowledge is justified true belief; that to have a disposition to R when S is to be such that if one were R-ed, then one would S; and so on.
Up to logical equivalence, at least. One could argue that, because they differ in semantic structure, the two sides of the equivalence in Reducibility are not strictly synonymous (see PoP, p. 160).
The argument relies on the quite innocent rule of Deduction, viz.: if ⊢ p → q then ⊢ p \(\Box\kern-1.2pt \raisebox{1pt}{\(\to\)}\) q, which is common to both Lewis’s and Stalnaker’s counterfactual logics. In Lewis’s system, a more general version of this rule is called “Deduction within Conditionals” (1973, p. 132). In Stalnaker’s system Deduction follows from axiom schema (a1) via Necessitation and the definition of □ (Stalnaker 1968/1981, pp. 105–106).
This proof (and the rule of Deduction) is invalid if there are contingent logical truths. I address this concern in §5.
It is worth noting that paradigm cases of analytic truths can also be shown to be necessary by an extension of this argument. According to one traditional view, all analytic truths can be obtained from logical truths by substituting synonyms for synonyms. Whether or not this is true, at least the paradigm cases of analytic truths have this feature: e.g., ‘All bachelors are unmarried’ is presumably analytic because ‘bachelor’ is synonymous with ‘unmarried man’. To show that it is necessary that all bachelors are unmarried, then, we simply show that ‘All unmarried men are unmarried’, a logical truth, is necessary, and then replace ‘unmarried men’ with ‘bachelors’.
There is good evidence that ‘actually’ does not always (so to speak) take its operand back to the world of the context; rather, the world with respect to which its operand is evaluated can be shifted by other operators. (See Cresswell 1990, Chap. 3. This observation appears to have been made first in Saarinen 1977, pp. 25–27, though using ‘in fact’ instead of ‘actually’.) On ‘I am here now’, see Predelli (1998).
This appears to be Hill’s (2006) suggestion. See his discussion of “two tests” for the necessity of p (pp. 230–231).
Hill (2006) does not consider the case where the antecedent is the negation of the proposition whose necessity we are trying to show.
I would like to thank an anonymous referee for raising this worry.
Of course no advocate of the Essentialist Reply should accept this. The Essentialist must discriminate between intensionally equivalent properties: e.g., humanity may be essential to you, but not the property of being human and Finnish or not Finnish. Since I do not advocate the Essentialist Reply, this is not a problem for me. The only other reason for adopting a hyperintensional conception of properties I am aware of is that one can believe that x is P without believing that x is Q, even when □∀x(Px ↔ Qx); however, on a structured-propositions view the components of content are more fine-grained than properties: e.g., the predicate ‘x is F and G’ contributes to propositions both the properties λxFx and λxGx, whereas ‘x is H’ contributes only λxHx, even if λxHx = λx(Fx ∧ Gx).
It bears noting that not only any PMN, but any true necessity claim at all, is a logical consequence of a true property identity if the standard criterion of property identity is correct. If intensionally equivalent properties are identical and □p, then λx(x = x) = λx(x = x ∧ p), which in turn entails □p.
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Acknowledgments
This paper is a descendant of a paper coauthored with Margot Strohminger, which we presented at various fora in 2009–2010. Even after it became a single-author project, I continued to benefit from enlightening discussions with Margot in writing the paper. My greatest debt of gratitude is to her. In addition, I owe thanks to John Hawthorne and Cian Dorr for helpful comments on earlier drafts, and to Tim Williamson, Sonia Roca-Royes, and audiences (of the coauthored ancestor paper) at the Arché Philosophical Research Centre at the University of St. Andrews, Trinity College Dublin, and the University of Oxford for helpful discussions.
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Yli-Vakkuri, J. Modal skepticism and counterfactual knowledge. Philos Stud 162, 605–623 (2013). https://doi.org/10.1007/s11098-011-9784-4
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DOI: https://doi.org/10.1007/s11098-011-9784-4