Abstract
Traditional conventionalism about modality claims that a proposition is necessarily true iff it is true by convention. In the wake of the widespread repudiation of truth-byconvention, traditional conventionalism has fallen out of favour. However, a family of theories of modality have arisen that, whilst abandoning truth-by-convention, retain the spirit of traditional conventionalism. These ‘neo-conventionalist’ theories surpass their forebears and don’t fall victim to the criticisms inherited through truth-by-convention. However, not all criticisms levelled at traditional conventionalism target truth-by-convention. Any conventional theory of modality must face the contingency problem. This claims that the contingency of our linguistic conventions jeopardises the necessity of the necessities they determine. I present the contingency problem as relevant to both the traditional conventionalist and the neo-conventionalist. I examine a response from Einheuser that builds upon a response from Wright. I show that the Einheuser response does more to accommodate the conventionalist’s modal beliefs, but that it does not fully satisfy some further conditions that ought to be laid upon such a response. I then suggest how the response can be revised so as to satisfy these conditions. The resulting model of conventionalism is compatible with the validity of S4, and suitably in the spirit of conventionalism.
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Notes
That is, that the S4 axiom is true in every model (where a model is a complete description of the pluriverse).
It is debatable whether the conventionalist should be required to maintain the S4 principle. Both Wright (1980, 1985) and Hale (2002) suggest that to insist upon S4 is to beg the question against the conventionalist. Lewy (1976) argues that the contingency of nec(P) jeopardises the necessity of P, as do Van Cleve (1994) and Sidelle (2009). See also Elder (2006) for a related criticism of conventionalism. Here I assume that if the conventionalist can maintain the validity of S4, then they should.
I phrase my discussion in de dicto linguistic terms for the sake of making it compatible with traditional conventionalism. This allows for bridging between traditional and neo-conventionalism, and highlights the difference in how they work. However, I trust that all that follows could be phrased in terms of non-linguistic necessities. This is compatible with neo-conventionalism, and with the major discussion in the paper. I trust that nothing substantial hangs on this.
One might worry that ‘F is sufficient for M’ is true-by-convention. This is true, but only in so far as it is an object-language formulation of the convention in play. This is truth-by-convention at its most innocuous—equivalent to saying that ‘such-and-such actions are a wedding ceremony’ is true-by-convention because convention determines what constitutes a wedding ceremony. The important point is that M is true not by convention, but because of F, and that truth-by-convention doesn’t feature in the explanation of necessity in any way that is traditionally found to be problematic.
One should not confuse Cameron’s position with a deflationary theory of truth; rather, it provides deflationary truth conditions for modal claims.
This is in fact a mild mischaracterisation. Cameron gives this reasoning as motivation for the conventionalist to sit on the contingency horn of Blackburn’s dilemma, according to which the source of necessary truth must itself be either necessary or contingent. If the source of necessity is itself necessary, then regress ensues; if the source of necessity is contingent, then the necessity of those necessitation claims “has not been explained or identified, so much as undermined” (Blackburn (1993), p.53). However, from Cameron’s arguments I take it that he thinks these considerations are sufficient to dispel the contingency problem (so characterised).
There are some formulations of the contingency problem for which truth-by-convention is a necessary condition. Van Cleve (1994) gives a particularly strong formulation of the problem, and a further argument for the conclusion that everything is contingent. However, Van Cleve’s argument relies on truth-by-convention to apply to conventionalism. The neo-conventionalist is not threatened by the argument because they reject truth-by-convention. As such I will not consider Van Cleve’s argument further here.
It might be that the difference alluded to in A is that there is a necessitation claim P that is actually false that would be true. This would render the actually true necessitation claim nec(¬nec(P)) false, so either way the result is as described in 4. This relies on S5, but for those unwilling to accept S5, A could just as easily stipulate the required change.
Exactly how LINK should be phrased may be debatable, but something like it should hold. Einheuser (2006) p.470 recognises that conventional features of reality must systematically covary with changes in our conventions. Sidelle (2009) p.231 also recognises this need, as does Elder (2006). LINK is in this spirit.
For further discussion motivating RIGIDITY, see Sidelle (2009).
He writes to this effect in (1985), p.192.
For the sake of simplicity, I follow Einheuser in assuming that each world contains only one set of conventional practices. Whilst this is likely false, it makes the following discussion easier, and a full discussion of the consequences of multiple sets of conventional practices is beyond the scope of this paper.
I, Like Einheuser, will have little to say about what exactly a carving is beyond that it is that which our conventional practices give rise to. Einheuser describes it as a theoretical concept that serves as an abstraction from the conventional practices that constitute our conventions. As such, carvings are neither s-features nor c-features, but the bridge between the two.
These are reformulations of Einheuser’s definitions, which state that s supports a feature F iff there is a carving c such that < s,c > has F, and that c carves a c-feature F iff there is a substratum s such that c yields F when applied to s. I take these revisions to be beneficial.
Note that this is not true grounding in the sense popularly discussed in contemporary metaphysics [as discussed in, for example Correia and Schnieder (2012), Fine (2012), and Trogdon (2013)], as even when the substratum and carving ‘match up’ in this respect, the substratum does not genuinely determine the carving. Where Einheuser uses ‘grounding’, one might instead use ‘correspondence’, or ‘correlation’. Recall that there is a world for every substratum/carving combination, and it is this combination that creates diagonal worlds, not any special relationship between the substrata and the carvings. I return to this point in Sect. 6.
I use this term instead of ‘impossible worlds’ because such worlds are still possible relative to different modal notions.
Diagonal A is also true because all diagonal worlds with different conventional practices are counterconventional (assuming that different conventional practices cannot ground the same carving).
Because carvings are functions, any two carvings that produce the same range of c-features (in this case true necessitation claims) from the same s-features are identical.
By ‘actually’ here I don’t mean the rigidifying actuality operator signified by @, but rather actuality as a status that a world may or may not have. This is the kind of actuality that we mean when we say that it might actually have been the case that Curie was not Polish (read as metaphysical and not epistemic modality). We don’t mean that she might have not been Polish in the actual world (as signified by the rigid @ operator), but that a world where she is Czech (say) might have been actual and not merely possible. There is nothing wrong with using these two notions of actuality side by side, just as there is nothing wrong with saying that every world represents itself as being actual but does not represent itself as being the actual world (signified with @). As such, I write both of ‘the actual world’ (w @) and of worlds being actual.
One might think to achieve the desired result using diagonal A. However, it is built into the content of diagonal conditionals that they stipulate change both in conventional practices and in carving. As such, it only trivially maintains LINK′ because, singling out only diagonal worlds, it takes us not from change in conventional practices to change in carving, but from change in conventional practice and carving to change in carving. It fails to capture the determination needed for LINK′. Furthermore, it should be the case of any standard possible world and not just the diagonal worlds that, were it actual, a different range of necessitation claims would be true.
cf. Chalmers (2002).
The consequent requires change in carving because without change in the claims necessitated (which is stipulated against because the antecedent allows only enough substratum change for the conventional practices to differ), the only possible source of modal change is difference in carving.
This assumes that only one set of conventional practices can ground each carving. Whilst this is probably false, it simplifies the discussion and its falsity would not affect the result.
Whilst I do not know of any sources that explicitly endorses such a principle, Wright suggests something like it in (1985), p.186. This principle may be considered controversial. In particular, one might be concerned that it follows from this that if P is necessarily actual, then it is necessary. This however relies on conflating the two ways that P could be necessarily actual. P could be necessarily actual in that, whatever way the world could have been, it would have actually been P, or P could be necessarily actual in that the actual world (interpreted as a rigid designator) is necessarily P. The former is equivalent to necessarily P anyway, and the latter does not allow one to infer necessarily P, so neither is problematic.
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Livingstone-Banks, J. The Contingency Problem for Neo-Conventionalism. Erkenn 82, 653–671 (2017). https://doi.org/10.1007/s10670-016-9837-3
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DOI: https://doi.org/10.1007/s10670-016-9837-3