1.

Schaffer identifies three types of necessitarianism and two types of contingentism. He presents them in an order that he takes to reflect the range of possible worlds countenanced by each view from most to least restrictive. As such, the set of worlds countenanced by a given view will be a proper subset of those countenanced by the view that follows:

Although not explicitly built into his initial presentation of modal necessitarianism, Schaffer later makes clear that modal necessitarianism rules out the possibility of alien laws (Schaffer Reference Schaffer2005, 3). So, this view countenances only metaphysically possible worlds in which all and only actual laws govern actual properties. Call these ‘MN worlds’.

Schaffer takes nomological roles to be purely structural in nature asserting that ‘[t]he essence of a property, on this view, is its place in the Ramsified lawbook’ (Schaffer Reference Schaffer2005, 2). As he sees it, this view will countenance all of the MN worlds, but will also allow for worlds with alien properties and alien laws. Call the worlds countenanced by nomic necessitarianism ‘NN worlds’.

Here, causal powers are taken to be more robust that mere structural regularities. This view will countenance all of the NN worlds as well as worlds with symmetric laws – ‘laws involving two or more properties in structurally indiscernible roles’ (Schaffer Reference Schaffer2005, 3). Such worlds cannot be countenanced by the nomic necessitarian since if roles r1 and r2 are structurally indiscernible, r1 and r2 are one and the same nomological role and, hence, govern one and the same property. Call the worlds countenanced by causal necessitarianism ‘CN worlds’.

Although he never explicitly argues so, Schaffer seems to hold that the CN worlds are a proper subset of those countenanced by anti-quiddistic contingentism (see Schaffer Reference Schaffer2005, 5). Call the worlds countenanced by the anti-quiddistic contingentist ‘AC worlds’.

This view, which is the view favored by Schaffer, includes all of the AC worlds as well as worlds with merely quiddistic differences. Two worlds w1 and w2 differ quiddistically if they differ only in that, in w1, property p1 has nomological role r1 and property p2 has nomological r2, and in w2, p1 has r2 and p2 has r1. Such world pairs are ruled out by anti-quiddistic contingentism.Footnote ³ So, the AC worlds are a proper subset of those countenanced by quiddistic contingentism. Call the worlds countenanced by quiddistic contingentism the ‘QC worlds’.

Even though it is far from clear that Schaffer has correctly identified the set theoretic relations between the range of worlds countenanced by each of the five views, Footnote ⁴ it would seem that modal necessitarianism, nomic necessitarianism, causal necessitarianism, and anti-quiddistic contingentism all countenance a set of worlds that is a proper subset of the QC worlds. After all, every MN, NN, CN, and AC world will be a world with some set of properties combined with some set of nomological roles and hence among the QC worlds. So, all Schaffer needs for his argument to go through, if it is otherwise successful (a big ‘if’), is for there to be a QC world that is not among the MN, NN, CN, or AC worlds. And that seems eminently plausible.

From here, Schaffer’s argument in broad outline is as follows:

• (1) The set of metaphysically possible worlds countenanced by each of the necessitarian views is a proper subset of the worlds countenanced by (quiddistic) contingentism (the QC worlds).Footnote ⁵

• (2) Our best theories of modality, counterfactuals, propositions, conceivability, and recombination require countenancing all of the QC worlds.

• (3) Thus, (quiddistic) contingentism is the preferable view concerning the relation between properties and laws.

If we accept premises (1) and (2) (and I will not further question either), Schaffer’s argument is prima facie compelling. However, it should also be clear that its plausibility trades on framing the question of which metaphysical view concerning the relation between properties and laws we ought to accept as the question of which range of possible worlds our best theories about modality, counterfactuals, etc. commit us to. It is that very move that I think the necessitarian can and should reject.

2.

To be sure, (quiddistic) contingentism does countenance a wider range of metaphysically possible worlds than do the various types of necessitarianism. However, there is no reason (or at least Schaffer has offered us none) to think that the worlds required by our best theories about modality, counterfactuals, etc. must all be among the metaphysically possible worlds.Footnote ⁶ Thus, the fact (if it is one) that our best theories about modality, counterfactuals, etc. require postulating all of the QC worlds does not entail that all of the QC worlds are indeed metaphysically possible.

One of the first things to note is that an argument analogous to Schaffer’s could be used to establish that the truths of mathematics are contingent. Since, both Goldbach’s conjecture and its negation are epistemically possible (and, hence, plausibly both meaningful and conceivable), we need a range of possible worlds that includes worlds where Goldbach’s conjecture is true and worlds where it is false. So, regardless of whether or not Goldbach’s conjecture is true, the range of worlds required for our best theory of epistemic modality (and of content and conceivability) will outstrip the worlds countenanced by the mathematical necessitarian. Contrary to conventional wisdom on the subject, mathematical statements are contingent! But surely this mathematical contingentism comes too cheaply.Footnote ⁷ Indeed Schaffer’s strategy is so biased toward extreme contingentism that even his preferred quiddistic contingentism would fall prey to it if there is any type of modality requiring worlds that outstrip the QC worlds. (Perhaps our best theory of propositional content would require such worlds.) To be sure, the relationship between properties and laws would still be contingent were that the case, but Schaffer’s quiddistic contingentism would not be the correct view.

What our best theories of modality, counterfactuals, etc. plausibly require is a very broad range of things called ‘worlds’. These need not be possible worlds on any prima facie plausible notion of modalityFootnote ⁸ and a fortiori need not be metaphysically possible worlds.Footnote ⁹ Indeed, these need not be worlds in any intuitive sense at all.Footnote ¹⁰ Different types of modality will specify a different subset of these ‘worlds’ as the possible worlds. So, for example, the metaphysically possible worlds might be specified as the set of worlds consistent with true metaphysical principlesFootnote ¹¹ and the epistemically possible worlds might be specified as the set of worlds consistent with what we (now) know.Footnote ¹² Questions about whether or not such and such is contingent or necessary then arise within this restricted context. So, when we say that (if true) Goldbach’s conjecture is necessary, we are considering only a restricted range of metaphysically possible worlds. We needn’t consider the set of worlds required for epistemic modality which includes both worlds in which Goldbach’s conjecture is true and worlds in which it is false. Plausibly, the same is true with respect to the relevant modality within which the debate about the relation between properties and laws takes place. When we ask whether this relation is contingent or necessary, we are considering only the metaphysically possible worlds. To the extent that it is appropriate to view the metaphysical debate between the various views concerning properties and laws as a debate about the range of possible worlds, it is more properly seen as a debate about the range of metaphysically possible worlds and not about the range of any and all worlds needed for our best theories of modality, counterfactuals, etc.

Wilson (Reference Wilson2013) has recently argued (following Fine (Reference Fine, Hawthorne and Gendler2002) and Bird (Reference Bird2007)) that the (modal) necessitarian should not take physical necessity to be a restriction on metaphysical modality.

For analogous reasons, one might worry that the response to Schaffer that I’ve presented is not a live option for the necessitarian. However, I think that the necessitarian has a ready answer to Wilson’s question. It starts with the realization that the unrestricted set of worlds required for our best theories of modality, counterfactuals, etc. plausibly include worlds that are metaphysically impossible even by the contingentist’s lights (such as worlds in which Golbach’s conjecture is false on the assumption that it is actually true). When we then ask whether the metaphysical relationship between properties and laws is necessary or contingent, we are only interested in the restricted set of metaphysically possible worlds. As such, the restriction is invoked by the very context of the debate.Footnote ¹³ The debate joined, the modal necessitarian will now argue that all of the metaphysically possible worlds are worlds containing actual properties governed by actual laws. In doing so, the necessitarian is making a substantive, non-trivial claim about the metaphysically possible worlds, a claim denied by the contingentist. If the necessitarian is correct, the relation between properties and laws is necessary in the only sense that matters in the context. The fact that it would be contingent on a modality invoking worlds that are not metaphysically possible is irrelevant. The necessitarian would only be guilty of making a cheap and trivial claim if the very debate between necessitarians and contingentists is itself construed as being joined initially in a restricted set of worlds in which the actual laws hold. (I believe that this response is available mutatis mutandis for either the nomic necessitarian or the causal necessitarian).

Thus, metaphysical modality may plausibly be taken by both the necessitarian and the contingentist to be a restricted modality in the sense that it involves only a proper subset of the worlds required by our best theory concerning the varieties of modality (deontic, minimal alethic, conceptual, epistemic, etc.). It should be noted, however, that taking metaphysical modality to be a restricted modality in that sense does not preclude holding that metaphysical modality involves the broadest sense of genuine possibility. The metaphysically impossible ‘worlds’ invoked by other modalities need only be regarded as possible; they need not be in any meaningful sense genuinely possible.Footnote ¹⁴ If this is correct, the mere fact (if it is one) that the QC worlds are invoked by our best theory concerning the variety of modalities provides us no reason for thinking those worlds are among the metaphysically possible worlds. Reaching that conclusion requires an independent argument for quiddistic contingentism.

3.

The previous section focused largely on the use of possible world’s semantics to capture various notions of modality. However, once we distinguish between the set of ‘worlds’ required for our broadest notion of modality and the set of metaphysically possible worlds, the necessitarian can address Schaffer’s other arguments in ways not anticipated. In this section, I will examine Schaffer’s argument from counterfactuals. In Section 4, I will examine his arguments from propositions, conceivability, and recombination. In Section 5, I will examine his argument that the necessitarian is pulled in inconsistent directions such that no single version of the view is adequate.

On one possible worlds semantics for counterfactuals, a counterfactual conditional of the form ‘if it were the case that φ, it would be the case that ψ’ is true (in the world of evaluation) if and only if (i) there is at least one world in which it is the case that φ and (ii) the closest such world (to the world of evaluation) is a world in which it is the case that ψ.Footnote ¹⁵ Now, it is plausible to suppose that there are true counterfactual conditionals with antecedents that run counter to the actual laws (e.g. the conditional ‘if it were the case that like charges attracted, the universe would have a very different structure’). Thus, there must be at least one world in which the antecedent is true (like charges attract). As Schaffer notes, such a world would be a ‘miracle’ world (i.e. a metaphysically impossible world) from the perspective of necessitarianism. If the relevant set of worlds that factors into the truth conditions of counterfactuals is the set of metaphysically possible worlds, the necessitarian will seemingly be forced to say that any counterfactual whose antecedent invokes a miracle will be trivially false. But that contradicts the previous intuition that there are true counter-legal conditionals.

But Schaffer argues that the necessitarian has an even bigger problem. Suppose that we wanted to assert (consistent with Coulomb’s law) that, if there were two like charges instantiated at a given location where there are not in fact two like charges, they would repel. According to Schaffer, this too requires a miracle world. ‘[T]o implement the antecedent that there are like charges at a given location (assuming that this is actually false), we need to imagine some miraculous swerving of say, two electrons, that brings them to said location’ (Schaffer Reference Schaffer2005, 8). If the laws are deterministic, the closest non-miracle world would be one in which the initial state of its universe differed from the actual universe. It would appear that a necessitarian who does not want to assert that any change with respect to what is actual requires a change in the initial state of the universe must hold that all counterfactuals (no matter how plausible) are trivially false.

Wilson (Reference Wilson2013, 660–663) provides a necessitarian response to Schaffer’s argument from counterfactuals. Like Schaffer, Wilson seems to hold that the worlds appealed to in a possible world’s semantics for counterfactuals must be metaphysically possible worlds. He addresses the problem with counterfactuals in general by adopting a modal necessitarianism with indeterministic laws. ‘The assumption that the laws are necessarily indeterministic allows the modal necessitarian to account for counterfactuals without appealing to worlds involving violations of the law’ (Wilson Reference Wilson2013, 661). Provided that modal necessitarians are comfortable adopting indeterminism, it would seem that they can adopt a possible world semantics for a wide range of counterfactuals. Even so, Wilson concedes that explicitly counter-legal conditionals (e.g. ‘if it were the case that like charges attracted, the universe would have a very different structure’) cannot be given a possible world semantics by the necessitarian. However, he argues that this is really of no moment. On the necessitarian view, worlds in which the actual laws do not hold are metaphysically impossible. As such, explicitly counter-legal conditionals are for the necessitarian a species of counter-possible conditional.

If Wilson is correct then, if we continue to assume that our best theory of the truth conditions for counterfactual conditionals involves appeal to possible worlds, it would seem that everyone must acknowledge that some prima facie plausible counterfactual conditionals are trivially false. The only difference between the necessitarian and the contingentist in this regard would be the range of counterfactuals with trivial truth conditions.

While many may find this type of response adequate, others will want to maintain that at least some counter-possible conditionals can be given non-trivial truth conditions. For example, some would regard as non-trivially true the counter-logical conditionals: ‘if it were the case that neither “P”; nor “not-P”; were true, then an intuitionistic logic would be appropriately adopted’Footnote ¹⁶ and ‘if it were the case that both “P”; and “not-P”; were true, then a paraconsistent logic would be appropriately adopted’. On the assumption that metaphysically possible worlds obey a classical logic (or at least do not obey a paraconsistent logic), these conditionals count as counter-possibles for the necessitarian and contingentist alike.Footnote ¹⁷ What is one who both accepts Schaffer’s premise that our best theory of the truth conditions for counterfactuals involves a (so-called) possible worlds semantic and wants to provide non-trivial truth conditions for counter-possible conditionals to do?

It seems to me that an obvious solution is to reject the background assumption (apparently held by both Schaffer and Wilson) that the ‘worlds’ required for a possible worlds semantics for counterfactual conditionals must be metaphysically possible worlds. One can instead hold that the range of ‘worlds’ required is broader than the set of metaphysically possible worlds.Footnote ¹⁸ On such a view, the criteria governing closeness are plausibly taken to be contextually sensitive. One plausible criterion will be: where there is a metaphysically possible world in which the antecedent of the counterfactual is true, that world will be closer to the actual world than any metaphysically impossible world.Footnote ¹⁹ If not, other criteria for judging the closeness of metaphysically impossible worlds to the actual world will have to be brought to bear. To be sure, there will be cases in which necessitarians and contingentists disagree about whether there is a metaphysically possible world in which the antecedent is true. But that would seem to be no more problematic than the fact that, given Alastair Wilson’s approach, the necessitarian and contingentist disagree about which counterfactuals have trivial truth conditions on a possible worlds semantics.

4.

Schaffer’s arguments from our best theories concerning propositions and conceivability trade on the following premises, respectively (see Schaffer Reference Schaffer2005, 10):

According to Schaffer (Reference Schaffer2005, 9), a proposition is best thought of as a set of metaphysically possible worlds (worlds at which p is true). He further asserts that ‘[i]f it is conceivable that p, then there is a possible world at which p is true’ (Reference Schaffer2005, 9). To be sure, if our best theories of propositional content and of conceivability require the postulation of worlds of which the content of the proposition/what is conceived is true, the worlds required to render (8) and (11) true outstrip the MN, NN, and CN worlds.Footnote ²⁰ But so what? Why should our best theory of propositional content or of conceivability entail that the relevant set of worlds is exhausted by the metaphysically possible worlds? Just as the fact that both the proposition expressing Goldbach’s conjecture and the proposition expressing its denial are plausibly conceivable does not show that mathematical statements are in any relevant sense contingent, Footnote ²¹ the fact that the propositions expressing Coulomb’s law and its negation are both conceivable is not germane to whether Coulomb’s law is metaphysically contingent. The necessitarian may (as Handfield Reference Handfield2004 does) legitimately hold that there are conceivably possible worlds that outstrip the metaphysically possible worlds.Footnote ²² With the postulation of conceivably possible worlds and in the absence of cogent reasons to think that these must be genuinely metaphysically possible worlds, the necessitarian can (if so wished) take meaningful propositions to be coarse-grained sets of conceivably possible worlds while accepting both (8) and (11).Footnote ²³

Schaffer’s argument against necessitarianism from recombination is as follows (see Schaffer Reference Schaffer2005, 10):

Premise (13) will arguably be true no matter how we read the modal terms it contains provided that we don’t equivocate between the modalities invoked in its antecedent and consequent.Footnote ²⁴ But, how are we to read ‘possible’ in (14)?

Schaffer wants us to take our cue from what he identifies as the connection between worlds and recombination: ‘if x and y are distinct existences, then there is a possible world with just x, a possible world with just y, and a possible world with both x and y’(Schaffer Reference Schaffer2005, 9). However, this doesn’t really settle the issue once we acknowledge that there are modalities that plausibly outstrip what is metaphysically possible. It is important to note that the antecedent of the recombination principle involves an implicit modal operator that is all by itself ambiguous between various types of modality.Footnote ²⁵. Are x and y being asserted to be metaphysically distinct, conceptually distinct, epistemically distinct, etc.?Footnote ²⁶ How we interpret that modality will dictate how we should interpret the modality implicit in the notion of a possible world in the consequent of the recombination principle and thus how we interpret ‘possible’ in (14). Clearly, on the metaphysical modality reading of the recombination principle, the necessitarian will want to reject (14) on the grounds that charge and acceleration are not metaphysically distinct.Footnote ²⁷ However, I would submit that the necessitarian can accept (14) if the recombination principle is interpreted as involving, e.g. a conceptual modality. If ‘possible’ in (14) just means ‘conceivable’, (15) would then amount to no more than the claim that it is conceivable that there would be a different relationship between properties and their powers. In the absence of cogent reasons to think that the conceivably possible worlds must be metaphysically possible, this conclusion is simply irrelevant to the truth or falsity of necessitarianism.

In order for the argument from recombination to work, we must ensure that the modality invoked is metaphysical modality and that (14) is true on that modality. Quiddistic contingentism holds that (14) is satisfied when ‘possible’ is read as a metaphysical modality. Proponents of each of the three types of necessitarianism will disagree. (14) is plausibly false on anti-quiddistic contingentism as well when taken as invoking metaphysical modality. According to the anti-quiddistic contingentist, properties are world-bound entities that can at best stand in counterpart relations to properties in other worlds. The fact that the counterpart relation is partly determined by laws (or powers) would then seem to place at least some restrictions on the recombination of counterpart properties and laws. So, it would seem that to have reason to believe that (14) is true when taken as invoking metaphysical modality, we would have to have antecedent reason to accept quiddistic contingentism. Schaffer’s argument appears to simply beg the question.Footnote ²⁸

5.

Importantly, unlike the responses Schaffer anticipates or the ones actually provided by Wilson (Reference Wilson2013), none of my responses to his arguments trade on any particular version of necessitarianism. All that is required is an acknowledgment that it is wrong headed to simply assume that all of the worlds required by our best theories of modality, counterfactuals, propositions, etc. will be metaphysically possible worlds. This also allows for a response to Schaffer’s final argument that necessitarianism ‘dissolves, on inspection, into an incoherent heap’ (Schaffer Reference Schaffer2005, 13).

Schaffer first argues that the necessitarian is pulled in the direction of modal necessitarianism on the grounds that two common necessitarian arguments, if valid, fail to support either nomic or causal necessitarianism. However, he immediately goes on to argue that both arguments are invalid (Schaffer Reference Schaffer2005, 6–7). If he is correct on that score, the necessitarian should feel no pressure to adopt modal necessitarianism stemming from these arguments. While, I am sympathetic to his reasons for thinking that what he calls ‘the argument from sustaining counterfactuals’ is invalid, Footnote ²⁹ it is far from clear that what he calls ‘the argument from natural necessity’ is invalid.

As formulated by Schaffer, the argument runs as follows (Schaffer Reference Schaffer2005, 6):

• (1) If the relation between properties and their powers is contingent, then like charges might not repel;

• (2) Like charges must repel;

• (3) Therefore: the relation between properties and their powers is not contingent.

Schaffer (Reference Schaffer2005, 7) suggests that the argument is invalid due to an equivocation between the use of an unrestricted modality in (1) and a more restricted modality of natural necessity in (2). However, it seems to me that the argument could be reformulated so as to remove this equivocation as follows:

• (1*) If the relationship between properties and their powers is contingent on a natural modality, then there will be naturally possible worlds in which like charges do not repel;

• (2*) There are no naturally possible worlds in which like charges do not repel;

• (3*) Therefore, the relationship between properties and their powers is not contingent on a natural modality.

Note that, on this way of reformulating the argument, no assumption is made about which possible worlds are the naturally possible worlds. The argument is thus consistent with all three forms of necessitarianism. Unfortunately, for that very reason, its conclusion does not all by itself obviously establish necessitarianism. Whether or not any form of necessitarianism follows from (3*) depends upon whether or not metaphysical modality outstrips natural modality. For example, suppose that we thought that the naturally possible worlds were simply the worlds in which the actual laws hold. In that case, since contingentists take the metaphysically possible worlds to outstrip the naturally possible worlds, they can cheerfully accept (3*). The same holds true mutatis mutandis if we instead take the naturally possible worlds to be ones with laws that are structurally equivalent to ours or in which the identity of properties is governed by the causal powers of objects that instantiate them. So, we would have to have antecedent reason to think that some version of necessitarianism is true (even if we remain agnostic about which one) in order to think that the reconstructed argument from natural necessity rules out contingentism. So, it isn’t that the argument, if valid, supports modal necessitarianism (as Schaffer would have it); it is that the argument, if valid, provides no independent support for any type of necessitarianism.Footnote ³⁰

Schaffer suggests that, in order to address the arguments from our best theories concerning propositions and conceivability, the necessitarian must appeal to Kripke-style explanations of modal illusions such as its seeming possible that water might not have been H₂O (see Kripke Reference Kripke1980). He asserts that such a response (if successful) would rule out modal necessitarianism, since it requires postulating worlds with alien properties governed by alien laws superficially similar to those exemplified in the actual world. However, he goes on to argue that the Kripke-style response is unsuccessful given disanalogies between ‘water is H₂O’ and ‘charge is governed by Coulomb’s law’ (see Schaffer Reference Schaffer2005, 11–12). If Schaffer is correct that this sort of response fails, then there is no pressure to reject modal necessitarianism on this account. However, it is worth noting that the Kripke-style response does not obviously rule out modal necessitarianism. As we saw above, the modal necessitarian can happily acknowledge conceptually possible worlds involving alien properties governed by alien laws. So, there is no reason to think that the arguments from our best theories of propositions and conceivability pull the necessitarian in the direction of any particular one of the three necessitarian views.

Schaffer notes that ‘it seems intuitively possible to have symmetric laws’ (laws involving two or more properties in structurally indiscernible roles) and even ‘symmetric structures that themselves indicate multiplicity’ and argues that only causal necessitarianism is consistent with symmetric laws (Schaffer Reference Schaffer2005, 12–13). However, it is not clear that there are no actual symmetric laws and, so, no reason to think that such laws are ruled out by modal necessitarianism. While symmetric laws will clearly not be among the NN worlds, the nomic necessitarian can nonetheless maintain that such worlds, while not metaphysically possible, are conceptually possible. Contra Schaffer, the conceptual (or even epistemic) possibility of symmetric laws is no threat to either modal or nomic necessitarianism.Footnote ³¹

Finally, Schaffer argues that skeptical arguments against quiddistic contingentism require nomic necessitarianism (Schaffer Reference Schaffer2005, 16–18). Such arguments trade on the assumption that we only have knowledge of properties via the role that they play in the Ramsified lawbook.Footnote ³² So, if we are to have knowledge of properties, that can only be because the nomological role played fully determines the property (i.e. only if nomic necessitarianism is true). The argument continues that, since we do know what properties exist, properties cannot exchange nomological roles in different worlds – merely quiddistic differences are metaphysically impossible. Even if Schaffer is correct that nomic necessitarianism is required for the skeptical argument against quiddistic contingentism, it remains unclear why the necessitarian would be committed to making such an argument. The necessitarian (perhaps especially of the modal or causal variety, but plausibly also the nomic necessitarian) need not assert that we know what properties exist. There may well be existing properties so beyond our kin that they have no known nomological roles. There may be existing properties that govern multiple laws some of which correspond to known nomological roles and others that do not. While the skeptical argument against quiddistic contingentism may only be available to the nomic necessitarian, this is not all by itself a reason to favor nomic necessitarianism over modal or causal necessitarianism.