Abstract
The chapter defends an evolutionary explanation of modal knowledge from knowledge of counterfactual conditionals. Knowledge of counterfactuals is evolutionarily useful, as it enables us to learn from mistakes. Given the standard semantics for counterfactuals, there are several equivalences between modal claims and claims involving counterfactuals that can be used to explain modal knowledge. Timothy Williamson has suggested an explanation of modal knowledge that draws on the equivalence of ‘Necessarily p’ with ‘If p were false, a contradiction would be the case’. He postulates a cognitive process that draws on this equivalence and that is supposed to underlie our modal judgements. The existence of this cognitive process would, however, have consequences that conflict with results from empirical psychology.
The chapter argues that the equivalence of ‘Necessarily p’ with ‘For all q, if q were true then p would be true’ should instead be used to explain knowledge of necessity. This explanation requires giving an account of how we know truths of the form ‘For all q, if q were true then p would be true’. In order to provide such an account, the chapter draws on a different suggestion by Williamson about knowledge of generalizations. According to this suggestion, we come to know truths of the form ‘All Fs are G’ by imagining a generic F and judging that it is G. Applied to our case, the suggestion would be that we come to know that p is counterfactually implied by all propositions (and hence that p is necessary) by entertaining a generic proposition and judging that it counterfactually implies p. It would even suffice to entertain a generic possible proposition and judge that it counterfactually implies p, for it can be shown that the claim ‘For all possible q, if q were true then p would be true’ is equivalent to the original claim ‘For all q, if q were true then p would be true’ and hence is equivalent to ‘Necessarily p’.
It might seem that, from an evolutionary perspective, probabilistic reasoning is just as useful as reasoning involving counterfactuals. The chapter argues, however, that this would not undermine the envisaged explanation of modal knowledge. The chapter concludes by suggesting avenues of empirical research that might shed light on the cognitive processes that actually underlie our evaluations of modal claims and on the relation between these processes and those involved in counterfactual reasoning. The results of such empirical research would be highly relevant epistemologically, since they will ultimately determine which (if any) equivalence between modal claims and claims involving counterfactuals should be used to explain our modal knowledge.
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Notes
- 1.
Recent discussions of how modal knowledge can be explained include Bealer (2004), Casullo (2010), Chalmers (2002), Cohnitz (2003), Geirsson (2005), Hale (2002), Hill (2006), Kung (2010), Peacocke (1999), Pust (2004), Sosa (2000), Williamson (2007), and Yablo (2008). Williamson’s account of modal knowledge will be discussed in Sect. 10.4.
- 2.
- 3.
The locus classicus of such an evolutionary explanation is Quine’s account of induction: “Creatures inveterately wrong in their inductions have a pathetic but praiseworthy tendency to die before reproducing their kind” (1969: 126). For a more recent discussion of evolutionary explanations in epistemology, see Rescher (1990). For a discussion of evolutionary explanations of modal knowledge, see Fischer (Chap. 14, this volume).
- 4.
See Jackson (1982: 133–134) for a different philosophical application of this point.
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- 6.
Schechter (2010) advocates a similar model for the explanation of modal and other a priori knowledge.
- 7.
Alternatively, knowledge of such iterated necessities could be explained via the S4 principle, according which whatever is necessary is necessarily necessary.
- 8.
For instance, ◊(φ ⊃ □φ), which holds for all φ and hence also for contingently true φ (for which φ ⊃ □φ is false). Proof. It is a truth-functional tautology that □φ ∨ ¬□φ. From the first disjunct, we get φ ⊃ □φ by conditional weakening, which in turn implies ◊(φ ⊃ □φ). The second disjunct yields ◊¬φ, which, too, implies ◊(φ ⊃ □φ). The example is due to Timothy Williamson (personal communication).
- 9.
- 10.
See Epstude and Roese (2008) for an overview.
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- 12.
On the general structure of these similarities, see Adams (1975).
- 13.
For instance, assume that P(p & q & ¬r)=1/10, P(¬p & q & r) = 8/10 and P(¬p & ¬q &¬r)=1/10 while the other conjunctions containing one each of (¬)p, (¬)q and (¬)r as conjuncts have probability 0. Then P(r|q)=8/9 while P(r|p & q)=0.
- 14.
For instance, assume that P(p & q)=3/10, P(¬p & q)=2/10 and P(¬p & ¬q)=1/10. Then P(p|q)=3/5 while P(¬q|¬p)=1/3.
- 15.
- 16.
Sober and Wilson (1999) make a similar point about the psychological mechanisms for altruistic behavior.
- 17.
See Lewis (1973: 21–24) and Williamson (2005). Lange (2005) and Kment (2006) also characterise modality in terms of counterfactuals; however, they differ from the Lewis-Williamson approach by allowing for false counterpossibles (that is, counterfactuals with impossible antecedents). Williamson (2007: 171–174 and ms.) defends the claim that all counterpossibles are true. Epistemological uses of the equivalences are also discussed by Hill (2006).
- 18.
- 19.
See Komatsu and Galotti (1986) and Miller et al. (2000). These studies take care to elicit judgements about genuine metaphysical (im)possibility, and not merely judgements about likelihood or truth by phrasing the questions to their subjects in terms of imaginability (Miller et al. 2000: 388–389) and by using formulations that approximate the possible-worlds criterion for possibility (ibid., 390; Komatsu and Galotti 1986: 414). Shtulman and Carey (2007) establish the similar result that younger children are more prone than older children to falsely judge propositions to be physically impossible.
- 20.
For more detailed discussion of this problem, see Kroedel (2012).
- 21.
The conditional ¬p □→ p that is involved in the not-so-intuitive principle (V) is an instance of ∀q(q □→ p), but by itself this does not affect the claim that the intuitiveness of (Q) suggests that (Q) reflects the cognitive processes that underlie our judgments of necessity (although it shows that we do not live up to ideal standards of rationality).
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- 23.
The judgement r □→ s can be derived from this more general judgement: since for any proposition, cases where it is true are sufficiently similar to themselves, we can infer r □→ s by substituting r for m and s for n in ∀m∀n(((m ∼ r) & (n ∼ s)) ⊃ (m □→ n)).
- 24.
The evolutionary explanation can also account for counterfactuals with nomologically impossible antecedents, that is, antecedents that are not metaphysically compossible with the actual laws of nature; see Kroedel (2012).
- 25.
Proof: Given (Q), the left-to-right direction of (Q′) follows by conditional weakening. To establish the right-to-left direction of (Q′), assume (i) ∀q(◊q ⊃ (q □→ p)) and (ii) ¬□p. (i) implies ◊¬p ⊃ (¬p □→ p); (ii) implies ◊¬p; by modus ponens we get ¬p □→ p. By (V) (which is itself an instance of (Q)), ¬p □→ p yields □p, which contradicts (ii).
- 26.
- 27.
- 28.
Acknowledgements: This chapter incorporates material from Kroedel (2012) and thus inherits the debts of that paper. In addition, I would like to thank Daniel Dohrn, Moritz Schulz, Michael von Grundherr, Marcel Weber, Timothy Williamson, and the participants of a workshop on modal epistemology that took place in Mainz in February 2013.
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Kroedel, T. (2017). Modal Knowledge, Evolution, and Counterfactuals. In: Fischer, B., Leon, F. (eds) Modal Epistemology After Rationalism. Synthese Library, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-319-44309-6_10
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