Abstract
The problem of the source of necessity is the problem of explaining what makes necessary truths necessarily true. Simon Blackburn has presented a dilemma intended to show that any reductive, realist account of the source of necessity is bound to fail. Although Blackburn's dilemma faces serious problems, reflection on the form of explanations of necessities reveals that a revised dilemma succeeds in defeating any reductive account of the source of necessity. The lesson is that necessity is metaphysically primitive and irreducible.
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Notes
I think Blackburn must have meant “explanans” here, instead of “explanandum”. The problem is about whether the fact doing the explaining (explanans) has the same modal status as the original (explanandum).
Cf. Hale (2002, 302).
I am assuming, with Hale, a Lewisian analysis of counterfactuals. On Lewis’ analysis, the counterfactual “if q had not been the case then □p might not have been the case” is true if and only if either □q (the vacuous case) or ¬□p in at least one of the closest ¬q-worlds. Because ◊¬q, ¬□p holds in at least one accessible ¬q-world, and so ◊¬□p. See Lewis (1973a) and Hale (2002, 317). The same result follows on a Stalnakerian analysis of counterfactuals. On Stalnaker’s account, the counterfactual “if q had not been the case then □p might not have been the case” and ◊¬q imply that ¬□p is true in the closest accessible ¬q-world, and hence ◊¬□p. See Stalnaker (1968, 98–112). One reason for preferring Lewis’ account is that, as Lewis points out, Lewis (1973a, 79–80), for Stalnaker, if the antecedent is not impossible, the “would” and “might” counterfactuals come out equivalent. This would obliterate the difference between the Strong and Weak Principles of Explanation. For a response, see Stalnaker (1981).
If q is necessary then the counterfactual is vacuously true.
I am indebted here to Marc Lange and to an anonymous referee. Another problem case for the Weak Principle was suggested to me by Scott Soames. Suppose one explains that Socrates died because he drank the hemlock. Surely this does not commit one to the claim that had he not drank the hemlock then he might not have died.
See Lewis (1973b) for the notion of causal preemption.
Soames’ Socrates example, in note 9, makes a similar point. To say that Socrates died because he drank the hemlock is to give a causal explanation for Socrates’ death.
“The mathematical truths, which you call eternal, have been established by God and depend on him entirely, just as all other creatures do ... he has established these laws in nature as a king establishes laws in his kingdom,” Descartes’ Letter to Mersenne, 15 April 1830, (Kenny 1970). Frankfurt argues that this commits Descartes to the view that nothing is necessary (Frankfurt 1977). Geach and Curley respond that it only commits him to the view that necessities are not necessarily necessary (Geach 1973; Curley 1984). Van Cleve defends the Frankfurt position using the same considerations I have used against the first problem for the contingency horn (Van Cleve 1994).
I intend no interpretive claims about Kant or Wittgenstein. My only claim is a hypothetical one. If Kant tried to explain the source of necessity by appealing to contingent features of our cognitive capacities then he is stuck on the contingency horn (and mutatis mutandis for Wittgenstein and forms of life, cf. Cavell (1979, 118–119)). As Russell read Kant, the antecedent of this conditional is true, and he argued that this commits Kant to the view that the truths of arithmetic and geometry are not necessary Russell (1959, 87). Van Cleve defends Kant with essentially the first problem for Blackburn’s contingency horn, but then rebuts this defense with the same move I have made against the first problem (Van Cleve 1999, 37–41). Thanks to Robert Greenberg for bringing this to my attention.
Cf. Van Cleve (1999, 143).
“What allows us to regard what’s explained as the necessity of p is that fact that the truth of p is explained in a special way, in terms of some fact about what it is to be …, where [being] … is integral to the proposition that p,” (Hale 2002, 312).
Here I have made implicit and essential use of the Strong Principle of Explanation, which, I have argued, applies to the grounding explanations given in accounts of the source of necessity. In the absence of this principle we cannot get from the contingent identity of these properties to the possibility that there are vixens that are not female foxes. The properties might be contingently identical yet necessarily coextensive, in which case it would not be possible for there to be vixens that are not female foxes. The argument here depends not only on the contingent identity of these properties but also the fact that their identity explains the fact that vixens are female foxes, where this explanation is a grounding explanation.
Quine’s regress arises because the conventions that determine what follows logically from what at the same time determine the meanings of logical expressions (Quine 1936). But the conventions must themselves employ logical expressions whose meanings are supposed to be fixed by these same conventions. Hence, these conventions have to be applied to themselves in order to apply them in determining the relation of logical consequence, and this leads to the regress. The problem is not merely epistemic—it is not that we cannot use the conventions to find out what follows from what. The problem is metaphysical—the conventions are incapable of establishing that anything follows from anything else. Thanks to Bill Hanson for clarification on this point.
Ayer goes on to say that “our view must be that what are called a priori propositions do not describe how words are actually used but merely prescribe how words are to be used,” (Ayer 1936, 20). So for example, “Squares necessarily have four sides” is an imperative, dictating how the expressions “square” and “four sides” are to be used. This is a rather idiosyncratic account of conventionalism insofar as it departs from the idea that sentences about necessity are made true by conventions. Imperatives are not made true by anything. In any case, Ayer’s form of conventionalism does ultimately seem to be a claim about the meanings of sentences about necessity, and so it counts as an analysis.
Contrary to Cameron (2008), therefore, Sider’s neo-conventionalism does not solve the problem of the source of necessity.
Here I follow Chihara (1998, 81–82).
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Hanks, P.W. A Dilemma About Necessity. Erkenn 68, 129–148 (2008). https://doi.org/10.1007/s10670-007-9082-x
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DOI: https://doi.org/10.1007/s10670-007-9082-x