Abstract
Can we explain why some propositions are necessary? Blackburn (Fact, science, and value. Blackwell, Oxford, 1987) has presented a dilemma aimed at showing that the necessity of a proposition cannot be explained either in the case where the explanans is another necessary proposition (necessity horn) or in the case where the explanans is a contingent proposition (contingency horn). Blackburn’s dilemma is intended to show that necessary truth is an explanatorily irreducible kind of truth: there is nothing that explains why propositions are necessary, nothing that makes necessary necessary truths. In this paper, I criticize the contingency horn of Blackburn’s dilemma. On the one hand, I show that the official reconstruction of the horn uses a principle that is incompatible with the notion of explanation plausibly needed to explain why propositions are necessary; on the other, I show that a simpler formulation of the horn, which does not make use of such a controversial principle, makes essential use of principles that are incompatible with the idea that possibilities can have explanatory roles. I then defend the view that possibilities can have explanatory roles, and that the explanatory role of possibilities is best represented, within possible worlds, as the existence of trans-world relations of explanation.
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Notes
For simplicity’s sake, I am assuming that p, q, … are propositional atoms. Motivation for this assumption will be discussed below.
One, of course, might believe that there is something that makes certain propositions necessary, without believing that this “something” is itself a proposition. One might say, for example, that the necessity of propositions, if it is explained at all, is explained by the existence of certain sorts of objects or events (on this, see Cameron 2010, pp. 137–38). This view, however, presupposes at least two claims: the first is that an object o, or an event e, explaining the necessity of a proposition, cannot be associated, “salva explanatione”, to some sort of propositional item (in the simplest case: the proposition that o exists or the proposition that e occurs); the second is the assumption that explanatory relations are not uniform relations between propositions, but relations between objects, or events, and propositions. In this paper, I am not going to argue explicitly against these views and I will simply assume that explanatory relations are propositional. To defend this assumption, however, I think that the arguments given by Williamson (2000, pp. 194–200), to the effect that evidential relations (“x constitutes evidence for p”) are propositional, or the arguments given by Lewis (1973a), to the effect that causal dependence among events can be analysed as counterfactual dependence among propositions (by pairing events with propositions) could be adapted to the case at hand.
For a discussion, and a critique, of this horn see Hale (2002, pp. 307–313).
Blackburn (1987, p. 53).
Cfr. Blackburn (1987, p. 53).
In the proof, I have used the expression “p explains \(\square p\)” for “p explains the necessity of q” or “p explains why q is necessary.” Of course, explaining \(\square q\) and explaining why q is necessary are different notions. I could explain the truth of \(\square q\) without explaining why q is necessary. But if I have explained why q is necessary, I surely have explained the truth of \(\square q\). Therefore, an argument, like the one above, that proves that I have not explained \(\square q\), is an argument that also shows that I have not explained why q is necessary.
Cases of causal preemption are about events and the principle we are discussing is about propositions. Trading in events for propositions could be—at least in some cases—quite a risky business. Fortunately, Lewis himself (1973b, p. 166), has shown that—at least in such cases and given some plausible assumptions—it is quite easy to construct a one-to-one correspondence between propositions and events: To any possible event e there corresponds the proposition O(e); O(e) is true in exactly those possible worlds where e occurs.
Hanks (2008, p. 136).
Fodor (1974) famously argued that relations less than identity would render any form of reductionism in principle incompatible with physicalism.
In this respect, showing that necessities cannot be reduced (in the technical sense of being scientifically reduced) to single facts has much in common with showing that the natural kind properties of special sciences (economics, psychology) are not reducible (in the sense of not being identical, or even necessarily equivalent) to natural kind properties of natural sciences.
Of course, there might been other, independent, reasons to deny Axiom 4: Salmon (1986), for example, has claimed that Axiom 4 corresponds to a fallacious modal inference. In particular, he has shown that, in questions having to do with the origins of artifacts, the relation of accessibility among worlds should not be taken to be transitive. In order to show this, Salmon uses a sorities-type construction that he calls “Chisholm paradox”. See also Salmon (1989).
See, for example, Cameron (2010, p. 142).
This is exactly analogous to the standard (i.e., modal) characterization of a property of an object as essential: property F is essential for an object x if and only if x is F in every world in which x exists. What is existence for an object is truth for a proposition.
This conclusion follows from my choice of using propositional atoms in (Truth-Dum) and (Truth-Ans) and all other principles mentioned in the paper. The same conclusion would have been reached if schematic letters for non-modal formulas had been used. The choice was motivated by the assumption that to explain a modal formula is to explain the corresponding non-modal formula in the possible worlds quantified over by the modal operator: “p explains \(\diamond\) q” is true in w i if and only if there is a world w such that p explains q in w. The clause for \(\square q\) is the already discussed principle (Ex-Nec). The same holds for non-atomic and non-modal formulas: I have assumed that “p explains q ∧ r” is true iff p explains q and p explains r. More delicate is the case of negation: it seems, in fact, false that p explains \(\neg q\) iff p does not explain q. The lack of an explanation of q seems necessary to explain \(\neg q\), but not sufficient. Some other condition would be needed. A palusible option is to do as intuitionists do with negation: “p explains \(\neg q\)” is true iff p explains \(q \rightarrow \bot\).
Roughly the same kind of argument, has also been used in questions having to do with material constitution (usually, to defend the “constitution is not identity” view), where the distinctness, for example, of a lump of clay and a clay statue is explained in terms of their different modal properties (namely, in terms of a mere possibility in which they do not share all their properties) Cf. Fine (2003). As it is known, other elements of Kripke’s argument about pain and C-fibers are the view that we are effectively able to imagine/conceive the occurrence of a mental state in absence of its physical counterpart and the principle that (successful) acts of imagining/conceiving imply possibility.
As it is known the “alternate possibilities” model of moral responsibility has been criticized by Frankfurt (1969). For a recent defense of the view that mere possibilities are relevant for responsibility, see Sartorio 2011, p. 1082: in this article, she shows that even for “actual-sequences” views of moral responsibility, there might be cases where the responsibility of an agent would still be grounded on (i.e., explained by) unactualized possibilities.
The symmetry mentioned here is that between the two roles (if something plays the role of explanandum, then it could also play the role of explanans) and it should not be attributed to the relation of explanation itself. The relation of explanation should not to be construed as a symmetric relation. What I am claiming in the text is just that if A and B are connected by a certain explanatory relation in a way that A is the explanans and B the explanandum, there seems to be no logical, or conceptual, reasons to exclude that B may play the role of explanans in another explanatory relation with respect to another proposition C, distinct from A.
I am using \(\diamond\) m p as “p is merely possible”, where “merely possible” means “false, but possibly true”.
Assuming, of course, that w ii is accessible from w i .
For a review of this kind of positions, known as ersatzisms, see Divers (2002). Note, however, that Stalnaker (1976) defends the view that the semantic thesis that ‘actual’ is an indexical does not necessarily correspond to the metaphysical thesis for which actuality is only a relation between a world and the things existing in it. One could thus believe that actuality is an absolute property of a world and that ‘actual’ is an indexical term.
Of course, one can deny that possibilities or possible objects should be conceived as completely specified entities. I myself find this view plausible, especially when non-actually existing objects enter the scene. The claim I am defending here, however, is that if we model modality through a standard conception of possible worlds this is not an option. On the propositional case, there is a function that assigns to every proposition a truth-value in every possible world, on the predicative case, it is determined for every individual, predicate and possible world whether the individual belongs to the extension of the predicate relatively to the possible world. In variable-domains quantified modal logic, the truth-value a formula like Fx, where x is a free variable (under an assignment) is defined even in those worlds where the individual assigned to x does not exist; cf. Kripke (1963, p. 84).
Of course, it might be that we do not have any epistemic interest in modelling explanatory situations like the ones mentioned above; on these matters, however, it is methodologically advisable to be as liberal as possible. Who knows what kind of explanatory situations we might need to model?
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Acknowledgments
Earlier versions of this paper have been presented at the 6th Latin Meeting in Analytic Philosophy (University of Lisbon) and at the COGITO Seminar (University of Bologna). I would like to thank these two audiences for very stimulating comments and discussions. Special thanks go to Andrea Bianchi, Massimiliano Carrara, Giuseppe Spolaore and two anonymous referees.
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Morato, V. Explanation and Modality: On the Contingency Horn of Blackburn’s Dilemma. Erkenn 79, 327–349 (2014). https://doi.org/10.1007/s10670-013-9496-6
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DOI: https://doi.org/10.1007/s10670-013-9496-6