Some have claimed recently that the laws of nature are necessary truths. What does this claim amount to? It can’t just mean that they hold in any naturally possible world, if natural possibility is analysed a la Lewis in terms of a restricted space of metaphysically possible worlds – otherwise, it would be trivial. This is what I think Kit Fine is getting at in his paper ‘The Varieties of Necessity’ (Fine 2002). (See this post for my objection to the way that Fine uses this point.)
Another approach is called for. Plausibly, the necessity of laws of nature involves at least the claim that Bird in Nature’s Metaphysics calls ‘weak nomic necessitarianism’ (WNN) – the claim that fundamental natural properties have their nomological role essentially, and obey the same laws of nature in every world in which they exist.
Bird describes the thesis of strong nomic necessitarianism (SNN), which goes beyong WNN by adding the further proviso that all fundamental natural properties exist at all worlds (call this claim APAW). To a lot of people this looks too strong. Bird intends APAW to rule out an objection to the necessitarian position which alleges that, while it might be that gravity is necessarily (approximately) an inverse-square law and necessarily acts between masses, there is another possible force, fravitation, just like gravitation in every way except for being an inverse-cube law and acting between schmasses. An acceptance of the possibility of such alien properties (and of alien laws of nature which the alien properties necessarily obey) seems to vindicate the contingentist intuition. But then APAW starts to look like an ad-hoc move to preserve necessitarianism as an interesting and substantive position.
Compare the situation with the debate about alien fundamental natural properties in connection with modal realism. The argument that Lewis finds compelling for the existence of alien natural properties is that it seems parochial to assume that our world is maximal in terms of its inventory of fundamental natural properties. If (as appears intuitively possible) some worlds lack some of the properties found in the actual world, why might the actual world not lack some of the properties found in other worlds? This line of objection tells against the principle APAW which makes SNN stronger than WNN. A more direct line of objection against APAW is the possibility of subtraction itself – it is judged intuitively possible that there could have been no mass, but APAW entails that mass exists at all worlds.
One response to these worries would be to distinguish between existence of a property at a world and instantiation of a property at a world. We could say that mass exists at some worlds but is not instantiated there, and that there are might or might not be unknown properties which exist at the actual world but are uninstantiated here. The problem with this response is that it once again seems to give up on the core of the necessitarian view. Nothing in the picture rules out schmass and fravitation as existent but uninstantiated, and the contingentist can reasonably point to this as vindication of their view. Given that the distinction between instantiation and existence doesn’t help us find a stable form of nomic necessitarianism, I will henceforth assume that they are co-extensive to simplify the rest of the presentation.
Given the problems with APAW mentioned above, it is not surprising that SNN is treated with suspicion by most metaphysicians. But I think that there are ways to uphold necessitarian principles in a non-trivial form without being forced to assert the speculative-looking claim APAW that all natural properties exist in all worlds. One claim we could use to bolster WNN would be the claim that there are a finite number of possible fundamental natural properties. Call this claim FP. While FP is still compatible with our world being maximal in terms of fundamental natural properties, it does not entail this conclusion, avoiding the parochialism objection which afflicts APAW. Indeed, it is compatible with FP that no world be maximal in the sense of containing all natural properties. Maybe two fundamental natural properties exclude one another, for example.
Call the conjunction of WNN and FP Finite Nomic Necessitarianism, or FNN. FNN entails that the actual laws of nature are necessary in that they necessarily apply to the natural kinds which actually exist but it allows for a further sense in which they are necessary – that no world contains any law which is closely similar but still distinct from a given actual law. The actual law may be the only possible law of its type, relating properties of particular types.
This characterization of FNN is obviously very general – but I think it shows there is conceptual room for a brand of nomic necessitarianism in between Bird’s WNN and his SNN. Indeed, there could be many different strengths of this in-between necessitarianism, depending on the details of structural similarities within the set of possible laws. From this perspective, SNN and WNN are different ends of a spectrum, rather than exhaustive exclusive alternatives.