Nomic necessitarianism and counterlegal counterfactuals

One particular class of counterfactuals presents problems for (even weak forms of) nomic necessitarianism: so-called counterlegal counterfactuals, such as ‘if gravity were an inverse-cube law, then the large-scale structure of the universe would be different’ or ‘if the charge on the electron were slightly larger, then atoms would be unstable’*. These are counterfactual forms in which the antecedent is physically impossible; for example, we might say ‘If gravitation were an inverse-cube law, then the solar system could not have formed’. We assess counterlegals of this sort in the process of formulating new scientific theories, and they are frequently asserted in speculative cosmology and science fiction. However, they pose problems for the combination of SNN with any theory of counterfactuals which would ground the truth of counterfactual statements in facts about other possible worlds. According to nomic necessitarianism, there simply are no worlds at which the antecedent of a counterlegal is true; hence, counterlegals cannot be given anything like the standard possible-worlds truth-conditions. How should an advocate of nomic necessitarianism respond to this?

The simplest response would just be to declare counterlegals either trivially false or trivially true, and to say no more about them. But this is unattractive; we want to distinguish between ‘good’ and ‘bad’ counterlegals. For example, consider the following pair.

a) If gravitation were an inverse cube law, the orbit of the Earth would be unstable.

b) If gravitation were an inverse cube law, purple dragons would dance the tango.

a) sounds sensible and assertible; b) does not. If this needs any argument, it is plausible that cosmologists might appeal to a) in discussing knock-on effects of changes in the laws; but I take it to be obvious that they would have no interest whatsoever in b). We could account for this difference between a) and b) in two ways. Either we accept that the semantics of the two statements are similar – that they are both trivially true or trivially false – and give a pragmatic account of the difference in assertibility between them, or we can build the difference into the semantics of the two statements.

The latter approach involves giving a metalinguistic account of the semantics of counterlegal statements. We can interpret statements like a) as concerning our own theories; we could thus analyse a) roughly as ‘if you alter Newtonian gravitational theory so that gravitation is an inverse cube law, then the new theory predicts unstable orbits for objects like the Earth’. This account meshes naturally with the usage of counterlegal statements; they are generally considered in the context of structural relations between alternative possible theories of a particular phenomenon. It also accounts for the difference we feel between a) and b) – it is simply not true that if we modify Newtonian gravitation in the way described, the modified theory implies any particular conclusions about purple dragons.

Taking this latter option does result in a kind of dualism in our interpretation of counterfactuals. Counterfactuals with genuinely possible antecedents will have a different metaphysical status to counterlegals – they will have different truthmakers, or different correctness-makers if you prefer. Furthermore, it need not always be clear whether a given counterfactual is a counterlegal or not. Take the claim ‘if the Higgs boson had been discovered last year, scientists would have celebrated.’ Since we do not know whether the Higgs boson is a (genuinely) possible existent, we do not know whether it would have been (genuinely) possible to discover it last year. Here we have an example of a counterfactual which may or may not be a counterlegal. According to the proposal under consideration, it will either have truth (or correctness) conditions derived from properties of other worlds, or it will have metalinguistic truth (or correctness) conditions. We will not in general be able to know which kind of conditional we are using.

Alternatively, we can take the former line, giving a) and b) the same semantics but locating the difference between them in pragmatic considerations. This might, for example, involve allowing all counterlegals to be trivially true. We could then go on to explain the assertibility or otherwise of counterlegals in terms of metalinguistic phenomena – whether or not our best theory predicts the consequent if it is modified to include the antecedent. Both the semantic and pragmatic approaches can thus account for the felt difference between ‘good’ and ‘bad’ counterlegals along metalinguistic lines.

An objector might press the objection from counterlegals, by pointing to the need for dualism in our analysis of counterfactuals as an undesirable feature of nomic necessitarianism. But a tu quoque response is available here; even if we reject nomic necessitarianism, we still cannot give a uniform philosophical account of counterfactuals. Certain counterpossible conditionals are problematic whether or not we accept nomic necessitarianism: conditionals whose antecedents are logical or mathematical falsehoods. Supposing that there are necessarily-existent abstract objects (among them numbers), consider the counterfactual statement ‘if there were no abstract objects, then there would be no numbers’ and ‘if there were no abstract objects, trees would levitate.’ We would like to be able to give an account according to which the first counterfactual is superior to the second, despite there being no possible world in which the antecedent holds. These conditionals will already require metalinguistic considerations, whether they are eventually located in semantics or pragmatics. Once we take this on board, then clarifying the details of the semantic theory starts to look more like a job for empirical linguistics than a job for metaphysics.

The upshot of this is that whichever semantic theory of counterlegals we end up with, we will need to recognise a metaphysical difference between two types of counterfactual – counterlegals and counterfactuals with possible antecedents – which does not correspond to any surface semantic difference. This need not be any cause for concern. We can explain why there is no surface semantic difference between the two – it is simply because we cannot always tell when we are discussing genuine possibilities and when we are not. Unable to reliably distinguish between genuine possibilities and only apparent possibilities, we ended up using the same form of language for each. As science progresses and rules out more and more apparent possibilities, we are better able to distinguish the two types of counterfactual and to recognise a metaphysical distinction between them. Although the proportion of counterfactuals falling on each side of the dividing line is altered once we adopt nomic necessitarianism, rejecting nomic necessitarianism does not allow us to dispense with the division altogether.

* It may be, as discussed above, that the charge of electrons could have been determined by an indeterministic process in the early universe. In this case, nomic necessitarianism would have no special problems dealing with this ‘counterlegal’, as the antecedent would only be locally physically impossible. The counterfactuals which cause problems for nomic necessitarianism are those with globally physically impossible antecedents. Plausibly, the example involving gravity is just such a counterfactual.

Nomic necessitarianism and counterlegal counterfactuals