Introduction 

In the following pages, I argue for the controversial thesis that the laws of nature are metaphysically necessary. I do this in three stages. First, I defend the thesis from the three most common criticisms raised against it: first, that the laws of nature are a posteriori and that we can conceive of different laws of nature (for reasons that will be seen later, I take these to be equivalent criticisms), second that we can imagine them failing to hold, and third that necessitarianism cannot account for counterfactual truths (throughout, I use the term ‘necessitarianism’ to refer to the viewpoint that natural laws[1] are necessary, and ‘contingentism’ to refer to the viewpoint that natural laws are contingent). Second, I give two positive arguments against the hypothesis that the laws of nature are contingent. I argue that if the laws of nature are contingent, then there will be no adequate explanation for why the laws of nature are the laws that they in fact are. I then argue that if there were different possible variations in the laws of nature, then it would be impossible to determine a probability for any of these variations. Third, I provide some general theoretical benefits entailed by a theory in which natural laws are necessary[2]. I do not, in this essay, presuppose what a law of nature is, but I do assume that there are laws and that their truths and status as laws are mind-independent. Whether chemical, biological or even economic laws should be considered in any sense to be laws of nature, is an interesting question, but this essay focuses on the fundamental physical laws.

A few definitional remarks before we begin. Throughout, I talk about metaphysical possibility and necessity. By ‘metaphysical possibility,’ I mean ‘the way things could have turned out in the broadest sense’. In possible worlds semantics, it is traditional to say that the metaphysically possible worlds are all the worlds. I think this is false. I accept Smith’s (2015) argument that there are worlds beyond the metaphysically possible ones, for reasons that will be seen shortly. If a proposition is metaphysically necessary, then it is true in all metaphysically possible worlds. I also talk about logical possibility. ‘Logical possibility’, as I use the term, is broader than metaphysical possibility (strictly speaking, the term ‘possibility’ is unsuitable because metaphysical impossibilities are impossible in the broadest sense – one can replace, in one’s mind, ‘possibility’ with ‘consistency’). A scenario is logically possible if it involves no a priori contradiction. I believe it to be logically possible for the laws of nature to be violated but I believe it to be metaphysically impossible, thus I think there are metaphysically impossible worlds with different laws of nature. It should be noted that the word ‘logic’ is not being used in the same way that it is used in the phrase ‘formal logic.’ Although there is no formal violation in the term ‘round square’, in the way in which there is a formal violation in the proposition ‘John is both married and unmarried’, I still refer to the former as logically impossible. Thus, I am taking the realm of purely formal possibility to be a subset of logical possibility, and the number of logical necessities to be greater than that of purely formal necessities. It might be useful to regard my use of ‘logical possibility/necessity’ as equivalent to ‘logico-conceptual possibility/necessity.’ I deny the reality of logically impossible worlds. Finally, I will position the sort of necessitarianism I am arguing for in light of Schaffer’s demarcations of the necessitarian thesis (Schaffer, 2005, pp.2-3). He argues that there are three forms of necessitarianism. First, there is the view that the actual laws are the laws in all worlds[3] (modal necessitarianism), second, there is the view that properties have the same nomological roles in all worlds in which they are instantiated (nomic necessitarianism), third, there is the position that properties have the same causal powers in all worlds in which they are instantiated (causal necessitarianism). I defend, and argue for, the first, strongest thesis – modal necessitarianism.  The key distinction between the modal variety and the other two is that the modal variety does not countenance any worlds with different laws whatsoever. The nomic and causal varieties countenance alien laws provided they govern (at least in part) alien properties – that is, properties that don’t exist in the actual world.

Section 1: Defending necessitarianism from the most common criticisms

The three most common criticisms rallied against necessitarianism are a) that natural laws are a posteriori/we can conceive of the laws of nature not obtaining, b) that natural laws can be imagined to be different, and c) that necessitarianism cannot account for the substantial truth of certain counterfactuals.

a)       The laws of nature can only be known a posteriori/we can conceive of the laws of nature being different

I must make clear why I consider these two objections to be equivalent. I appropriate Gendler and Hawthorne’s definition of conceivability: ‘P is conceivable iff it is not a priori that not-P’ (Gendler and Hawthorne, 2002, p.32). According to this definition, if the laws of nature are not a priori then they are conceivably false. This is why I take both these criticisms to be equivalent.

It might be said that the anti-necessitarian argument that appeals to the a posteriority of the laws of nature can be undermined with great swiftness and ease. The swift dispatch of such an argument would go as follows: a prioricity/a posteriority are epistemological notions, whilst metaphysical necessity/contingency are metaphysical notions. There is no logical connection between truths of one kind and truths of another. Kripke will be no doubt be mentioned here, and it will be said that he demonstrated that some a posteriori truths are necessary. The fact that a posteriori truths can be necessary, undermines the argument that the laws of nature must be contingent given their a posteriority. Examples given by Kripke of necessary a posteriori truths include ‘water is H₂O,’ ‘gold has the atomic number 79’ and ‘Hesperus is Phosphorus.’ (Kripke, 1981)

However, I think it can be coherently maintained, although I deny it to be the case, that there is a sense in which these propositions are contingent. Chalmers (1996, 2002, 2010) argues just that. He makes a distinction between a concept’s primary and secondary intensions. The primary intension is a non-rigid description of superficial qualities. Thus, the primary intension of ‘water’ is something like ‘the watery potable liquid in our oceans and lakes.’ The secondary intension, however, is fixed by its referent in the actual world. Since the referent of ‘watery liquid’ is H₂O, it follows that the secondary intension of ‘water’ is ‘H₂O’. The distinction could also be made the following way: primary intensions are extensions from worlds considered as actual, whilst secondary intensions are extensions from worlds considered as counterfactual. If the world in which water is constituted by XYZ is considered as counterfactual, then water is not XYZ in that world. Yet if the same world is considered as actual, then water is XYZ in that world. If the primary intension of ‘water’ is being used, so the argument goes, then ‘water is not H₂O’ is possible. Something other than H₂O could have satisfied the water-role. Assuming that it is actually physically impossible for something other than H₂O to have the superficial qualities of water, I deny that ‘water is not H₂O’ is even primarily possible. That is, if in the actual world, nothing besides H₂O could have the superficial qualities of water, then I deny that there are any worlds in which something other than H₂O has the same superficial qualities as water[4]. Nonetheless, Chalmers’ arguments have persuaded me that a posteriori necessities do not straightforwardly undermine the link between conceivability and possibility. However, the use of a two-dimensional semantic framework similarly doesn’t undermine the view that certain laws are necessary. One can simply deny the primary possibility of certain propositions. One can appeal to two-dimensional semantics to defend the entailment between conceivability and possibility, but one cannot appeal to it to attack views that deny such an entailment without begging the question against these views.

Arguments from conceivability are essentially arguments from non-contradiction. There is no contradiction in the idea of a flying pig, of a frictionless plane, or of an object travelling faster than light. Of course, we cannot test such scenarios to determine if they are possible; after all, we live in the actual world with the actual laws of nature. To confirm the possibility of said scenarios is, simultaneously, to reconceive and rewrite the rule-book of the universe. Although we cannot confirm the possibility of such scenarios, we can note that there is no contradiction involved in said scenarios. Where there is no contradiction, it is assumed that there is no impossibility. Where the bounds of logical possibility are not breached, it is assumed that the bounds of metaphysically possibility are not breached either. I accept that counterlegals are conceivable, and so I must therefore argue that conceivability does not entail possibility. We can appeal to Kripke’s arguments to show that we don’t have to accept the entailment, but it would be best to undermine the entailment.

Certain philosophers, such as Quentin Smith, dismiss arguments from conceivability too quickly (this is partly because he conflates ‘conceivability’ and ‘imaginability’).  For example, he notes that we can conceive of Hesperus not being Phosphorus, despite the fact that Kripke demonstrated that identity statements involving rigid designators are necessary. He also notes that we can conceive of ghosts despite the fact that they involve a logical contradiction because they are both corporeal and incorporeal. He writes, ‘a ghost is popularly understood as a being that is both embodied and disembodied, which is a logical contradiction, and I succeed in imagining and conceiving it only by forming a confused image of some sort of “ethereal body” that hides from me the fact that it has no body and yet has a body.’ (Smith, 2001, p.33) The first example of conceiving Hesperus not being Phosphorus is, of course, an invention of Kripke. He argued that when we think we conceive of Hesperus being non-identical to Phosphorus, what we in fact conceive, is a scenario in which the brightest heavenly body seen in the morning is different from the brightest heavenly body seen in the evening. We really mis-describe what we are conceiving. In truth, nobody ever claimed to be able to conceive the impossible scenario of a heavenly body being distinct from itself. What was conceivable, and what we have little reason to deny possible, is the scenario of two different bodies existing at different locations L and L₁. What was being conceived was possible. Nobody would claim that self-descriptions of what we conceive are guides to possibility, but merely that the conceivings themselves are guides to possibility. Chalmers would, by using a two-dimensional semantic framework, maintain that when using primary intensions, even the proposition ‘Hesperus is not Phosphorus’ is possible. Here the primary intensions are descriptions of the location of particular heavenly bodies at particular times. I think Smith’s ghost is not truly conceivable, or what Chalmers would call ‘ideally conceivable’: ‘S is ideally conceivable when S is conceivable on ideal rational reflection. It sometimes happens that S is prima facie conceivable to a subject, but that this prima facie conceivability is undermined by further reflection showing that the tests that are criterial for conceivability are not in fact passed. In this case S is not ideally conceivable.’ (Chalmers, 2002, p.147) Smith’s ghost is conceivable only on the most superficial level. The contradiction can be easily determined a priori, and thus it follows it is not ideally conceivable.

I will not attempt to provide any arguments directly attacking the thesis that conceivability entails possibility (‘CP’ for short). What I will do is defend criticisms of the negation of CP. My hope is that when the arguments against ¬CP are seen to be misguided, CP will no longer appear so attractive. In the second section of the essay, I will provide reasons to doubt contingentism. If these arguments work, then contingentism is untenable. CP will then be untenable: given that we can conceive of counterlegals, CP renders them possible, but this would validate contingentism which the second section shows to be untenable. Thus, the second section of the essay can be seen as an indirect attack against CP. One thing that should be mentioned from the outset is that it we are rationally obliged to acknowledge that we, as a matter of necessity, do not have overwhelming evidence supporting CP, and as such, it is still an open question whether it is true. The reason we can never have overwhelming evidence, let alone proof, of CP, is obvious. We can never prove that counterlegals are metaphysically possible because they are not nomologically possible, and, by definition, we can never witness states of affairs that violate the laws of the actual world. Thus, we can never determine for certain whether conceivable but nomically impossible scenarios are metaphysically possible. The reasoning for believing in CP is therefore theoretical rather than empirical. The greatest theoretical advantage of CP is that it gives us a fully rationalist account of modality. Anything that is conceivable is possible. No empirical work has to be done. A further virtue of CP is that is makes logical and metaphysical possibilities extensionally identical because logical possibilities, as I define them, are scenarios that are not a priori contradictory. Any logical possibility is thereby a metaphysical possibility. In the final section of the essay however, I outline the theoretical virtues of the view that the laws of nature are necessary. These virtues, I posit, outweigh the virtues of CP.

One might believe there to be inductive reasons for believing in CP. Chalmers writes, ‘why believe in CP?... there are no clear counterexamples to it. Principles linking conceivability and possibility have been widely accepted in the history of philosophy.’ (Chalmers, 2010, p.166) Chalmers mentions many supposed counterexamples to CP that can actually be accommodated by CP (Chalmers, 2010, p.148). Chalmers is right that there are many instances in which supposed counterexamples to CP have been exposed as phony. Smith’s examples provided earlier clearly fail as counterexamples to CP[5]. When we take into account ideal conceivability as well as the distinction between how one self-describes one’s conception, and what one actually conceives[6], then we see that these supposed counterexamples fail.  The inductive argument cannot be made, however. If necessitarianism is true, then each conceivable, nomic impossibility, is a counterexample to CP. These are not of course clear counterexamples to CP, but if one accepts the theoretical arguments for necessitarianism, then one is obliged to accept these as counterexamples. Of course, at the moment this begs the question of whether necessitarianism is true. But to use the inductive argument without providing adequate reason to doubt necessitarianism would be similarly question-begging. Although there are many conceivable and possible scenarios, the necessitarian would deny that there are any conceivable and possible nomically-impossible scenarios. One cannot, therefore, make any inductive inference to the claim that CP holds universally unless one has arguments against necessitarianism. Inductive arguments for CP must therefore fail because they assume success where deniers of CP assume failure, and they assume resistance to failure where deniers of CP assume defeat.

It might be argued that, if CP is false, then we are left with no insight into modality. That is, we will be left with no grounds for determining what is or is not possible (whatever happens, we can know, of course, that the actual is possible, but perhaps nothing else). Thus, Chalmers writes, ‘if we postulate a metaphysical modality that is independent of conceivability, the epistemology of modality becomes quite problematic… if metaphysical modality involves an independent primitive, then it becomes quite unclear why conceivability should be any guide to it at all. Why should there not be just one metaphysically possible world, or thirty-seven?’ (Chalmers, 2010, p.190-191) Epistemological arguments for metaphysical conclusions are often reasonable. These arguments are generally of the form: ‘we have epistemic access to A, if B were the case, then we wouldn’t have epistemic access to A, therefore ¬B.’ A case in point would be a common argument against the conception of numbers as Platonic forms. We know a great deal about the nature of numbers, but arguably we wouldn’t have epistemic access to them if they were Platonic forms, hence they cannot be Platonic forms. For these sorts of arguments to work, we need independent grounds for thinking that we have the epistemic access that we believe we have. It is certainly controversial to say that we have a deep grasp of modality, and that we are not in the dark when it comes to determining what is metaphysically possible. But even if we grant that we do have such epistemic access, the falsity of CP would not undermine this access. By arguing that the falsity of CP renders the epistemology of modality uncertain, Chalmers is assuming that conceivability is the only guide to possibility. If necessitarianism is true, then we still have an effective means of determining metaphysical possibility. We can use the scientific method to determine whether certain scenarios are nomically possible by attempting to observe instances in which such scenarios occur, and scientists can even (and often do) attempt to actualise such scenarios themselves. In thus enumerating a space of nomically possible worlds, we will have thereby enumerated a space of metaphysically possible worlds.

There are a number of reasons why the scientific method would be better for determining possibility than conceivability. First, there is disagreement as to whether conceivability entails, is a strong guide to, is a moderate guide to, or is hardly a guide at all, to metaphysical possibility. However, it is universally accepted (for obvious reasons) that the scientific method is an extremely good guide to nomological possibility. Hence, if the metaphysical and nomological domains are agreed to be coextensive, then there will be no disagreement as to whether the scientific method is a good guide to metaphysical possibility. Second, there is a great deal of disagreement about what is or is not conceivable. A couple of cases in point are ‘philosophical zombies’, and ‘violations of the laws of nature’. Some philosophers (e.g. Dennett in the former case, and Shoemaker in the latter) argue that these scenarios are only prima facie conceivable. The level of disagreement over what is physically possible exists to a much lesser extent since scientific statements can become so well supported by confirming instances that they acquire the status of near fact. Third, wherever there is disagreement in science, this disagreement can in principle be resolved through further observation and further attempts to corroborate or falsify the hypothesis in question. There is no clear analogue of an impartial, objective means of resolving a debate about whether a given scenario is conceivable or not. Of course, we can use reasoning to argue as to whether certain states of affairs would entail a priori contradictions, but this process of reasoning would not be as efficient at producing consensus as the scientific method. Fourth, only ideal conceivability could plausibly entail possibility. A set that contains all and only sets that are not members of themselves is prima facie conceivable. But further thought undermines the notion that such an impossibility is conceivable. It is therefore not ideally conceivable. Unfortunately, there is no objective means of determining at what point a conception is ideal. However, a scientific hypothesis can be disproved by a single disconfirming observation (of course, one can always cast doubts over whether the observation was in fact disconfirming). 

Now, it should be noted that this scientific epistemic access to possibility will still be available for Chalmers and other believers in CP. The scientific method gives them access to what is possible as well since they also accept that nomic possibilities are metaphysical possibilities. Thus, the necessitarian has no greater access to possibility than the believer in CP. It might even be said that the believer in CP has greater access because they can use both the scientific method and conceivability. However, I think that if there is any advantage at all, then it is very slight given the previous issues outlined regarding conceivability. To think that believers in CP are in a much better position when it comes to determining possibility is like arguing that early modern scientists had a much greater advantage when it came to determining the fundamental truths about the chemical elements because not only did they have chemistry, they also had alchemy. Let us assume, however, that the believer in CP comes out on top here. Nonetheless, the necessitarian has a vastly superior means of demarcating metaphysical impossibilities from possibilities. Constant failure to observe or bring about a certain scenario – e.g. the scenario of a massive object travelling faster the speed of light in a vacuum – gives the necessitarian grounds for thinking that no object can travel faster than light in the actual world, and hence in any world[7]. This does not give the believer in CP such grounds because they can still conceive of such a violation. If one accepts the arguments in the previous paragraph for the advantages of the scientific method over conceivability as a guide to possibility, then one should, for the same reasons, also accept the advantages of the scientific method as a guide to necessity over conceivability. The believer in CP perhaps has moderately greater epistemic access to possibility, but she also has a vastly inferior access to necessity. I posit that the necessitarian comes out on top, but at the very least there is a trade-off. Finally, it should be noted that the necessitarian can still use conceivability to some extent as a guide to determining the space of possible worlds because one can apply a posteriori considerations to one’s conceivings. That is, one can hold fixed certain a posteriori scientific truths and see if they conflict with other a priori considerations. Scientific theorising relies heavily on thought experiments, and hence on conceivability, and scientific theorising is the necessitarian’s guide to modality.

In short, although I have not demonstrated that CP is false, I have shown that there is no overwhelming reason to think that conceivability entails possibility. Combined with my arguments in section 2 and 3, we will have reason to reject CP.

b)      We can imagine different laws of nature

Next, we have the argument that the laws of nature can be imagined to be other than they in fact are. I treat ‘being able to imagine P’ as different from ‘being able to conceive P’. I treat imagining P as somewhat akin to forming a mental simulacrum of P. If P is imaginable, then it is possible to form a clear and distinct idea of a situation in which P obtains (to use Cartesian terminology). It is a quasi-sensory ‘imaging’ of a scenario. The distinction that I see between quasi-sensations and sensations is made clear in the distinction between hearing a tune and ‘playing a tune in one’s head’ (of course, Ryle would sneer at the suggestion that there is a genuinely existing ethereal quasi-tune playing in the head, but we can put these considerations aside because I think the distinction is intuitive nonetheless). The definition of conceivability that I use has already been provided: ‘P is conceivable iff it is not a priori that not-P’ (Gendler and Hawthorn, 2002, p.32) The distinction between imagination and conceivability is equivalent to the distinction that Chalmers makes between positive and negative conceivability. He writes, ‘S is negatively conceivable when S is not ruled out a priori, or when there is no (apparent) contradiction in S,’ whilst ‘S is positively conceivable when one can imagine that S: that is, when one can imagine a situation that verifies S.’ (Chalmers, 2002, p.150) Instead of ‘positive’ and ‘negative’ conceivability, I use the terms ‘imaginability’ and ‘conceivability’. To further elucidate the difference, we can point to the greater cognitive constraint on imagination than conceivability. Descartes noted that we can conceive of a chiliagon (a one thousand-sided polygon) but we cannot imagine one. There is no a priori contradiction in such a shape but our cognitive limitations prevent us from depicting to ourselves such a shape.[8] (Descartes, 1996, p.50)

Imaginability poses less of a threat to necessitarianism than conceivability. Alan Sidelle (2002) makes much use of the imaginability of natural laws not obtaining to argue for their contingency. He uses Hume’s example of two billiard balls. We can imagine the first ball hitting the second in ordinary conditions, and we can imagine that the second ‘stays in place, or goes off in another direction, or at a different speed, or turns into a tiger-shaped object and eats the first ball.’ (Sidelle, 2002, p.312) However, it is in fact questionable as to what we are actually imagining here and in other cases in which we imagine violations of natural law. Berkeley noted that whenever we imagine an object or event, we can only ever imagine the object from a particular perspective (Berkeley, 1975). I regard this as an unarguable truth, in the same way in which it is an unarguable truth that conscious experience exists. To imagine an object without imagining it from a perspective is not only impossible, but incoherent[9]. I make the reasonable assumption that to imagine something from a perspective necessitates imagining it experientially. It follows therefore, that in imagining the laws of nature not obtaining, we are, in fact, more precisely imagining an experience in which laws of nature fail to obtain. Note that this argument does not presuppose the existence of a perceiver separate from the perceptions. The argument states that we can only imagine something from a perspective, and hence (with the assumption just made), as an experience. It does not state that there is necessarily a perceiver separate from the perceptions – one can be a Humean bundle-theorist and still accept the argument. Shoemaker (2002) makes a similar point to Berkeley when he notes that that which is in fact being imagined – i.e. certain experiences of the laws of nature being violated – will invariably be nomologically possible, let alone metaphysically possible. He writes, ‘we have abundant empirical evidence that when we can imagine some phenomenal situation, e.g. imagine things appearing certain ways, such a situation could actually exist – things really could appear that way to someone. In days of yore the evidence came from such things as the artistry of stage magicians and tromp l’oeil painters. Now this is supplemented by the production of Hollywood special effects designers, holograms, “virtual reality” devices, and so forth.’ He goes on to write, ‘there is no need here, in the realm of phenomenal states of affairs, to suppose that metaphysical possibility outruns nomological possibility.’ (Shoemaker, 2002, p.73) In short, we can indeed imagine experiences in which the laws of nature are violated, and such experiences are nomologically possible. However, we cannot imagine the laws of nature themselves being violated since all imaginings are imaginings of experiences. Since we cannot imagine the laws of nature being violated, the argument for contingency on the basis of imagination is toothless.

It might be objected that we can in fact imagine events or objects in and of themselves and that we are not confined to imagining experiences of objects or events. However, as I defined ‘imagination’ in the previous paragraph, no such conception of imagination is tenable. Imagination, as I define it, is quasi-sensory. Sensations are clearly experiential. I posit that there is such an intimate link between quasi-sensations and sensations (perhaps the distinction is even unwarranted) that quasi-sensations are experiential. I posit, therefore, that we can only ever imagine experiences.[10] It might be said that we don’t necessarily imagine experiences – we can also imagine experiencing. Hence, I do imagine the laws of nature themselves being violated rather than an experience of such a violation. I imagine these laws being violated through an imaginative experience, I do not imagine the experience itself. But this is only pushing the problem one step back. It may be wrong to say that I imagine the experience per se but rather that I imagine experiencing something (or perhaps that I experience something imaginary). But here one is still imagining something via an experience. One never leaves the realm of experience. One might agree with my arguments that imagination is conceptually linked to experience, such that one cannot imagine something in and of itself. However, one might object that when one says ‘I am imagining a law of nature being violated,’ what one means is ‘I am having a quasi-sensory experience of a law of nature being violated.’ Thus, we can, the objection will go, say truthfully that ‘I am imaging a law of nature being violated.’ This seems to be a perfectly legitimate way of using the term ‘imagination.’ Indeed, it actually fits in better with everyday language use because we often say, without objection, that we can imagine things in and of themselves (not explicitly, but we certainly never qualify by saying ‘I meant to say I can imagine experiencing a tree’). It would be bizarre to object to someone’s assertion ‘I can imagine a tree’ with ‘well actually, you can only imagine an experience of a tree’! I concede this point. But to give up this linguistic ground is only to prove my point because it involves making experience a prerequisite for the imagination. Thus, under this definition of imagination, it will be true to say that we can imagine laws of nature themselves being violated. We will not have to say ‘we can only ever imagine experiences,’ but we will, nonetheless, have to hold that ‘we can only ever imagine experientially.’ Resultantly, we will not be able to draw any modal conclusions from what we can imagine, except perhaps, conclusions about the possible range of experiences.

For those still unconvinced, we can note that imagination consists of a great deal of stipulation, and this undermines its credibility as a guide to possibility. To expand: there are no objective criteria for determining, given a particular imagining, what is in fact being imagined. The imaginative act contains a vital interpretive element within itself. For example, in imagining a struck billiard ball behaving in an untoward manner, we stipulate within our mind’s eye that the ball is an ordinary ball, roughly the same as the ball making the impact, with no strong winds blowing, with no magnets involved etc. In imagining a beach ball travelling faster than light, one might have a quasi-sensory depiction of a round object outpacing a glowing radiant beam. There is nothing inherent in the quasi-sensory element of the beam that objectively determines that it is in fact a beam of light. There is similarly nothing inherent in the quasi-sensory element of the round object that determines that it is distinct from a photon. When we imagine a planet as massive as the earth having a gravitational pull as slender as the moon, we might imagine human beings springing lightly and landing softly on the ground, just as in footage of astronauts on the moon. But again, we construe within our minds that the ground is the part of the surface of a body with the mass of the earth. We do not entertain the idea that the ground being imagined is a surface in freefall. But we could have done, and doing so would not have altered the quasi-sensory nature of the imagined episode. If we take any imagining, it seems almost absurd to ask ‘what is really being imagined?’ There is no answer to this question – there is nothing objectively determinate about what is imagined. Any subjective determinacy is achieved through a silent, unconscious declaration of the status of the imagery. Imaginability, therefore, cannot be a good guide to possibility because the imaginer takes the role of an all-powerful director: that is, the imaginative act is an interpretive act. These considerations hold whether or not one accepts my argument to the effect that we can only ever imagine experiences (or only imagine experientially). Even if we can in fact imagine a reality beyond experience, we can still note that there is no fact of the matter as to what is being imagined beyond the internal interpretation of the imagining. It might be said that this violates our intuitions about what we can imagine. It might be declared obvious that we can imagine Humean billiard balls resisting acceleration, or duplicating, or such-like. Under the account I previously sketched, it doesn’t follow that we can’t imagine such things, rather it follows that there is no determine fact of the matter about whether we can imagine such things. We neither can nor can’t imagine such things. This, I posit, is less unintuitive than denying outright that such things are imaginable. Or, if one likes, one can define ‘imagination’ in such a way that one can still legitimately say that one can imagine such things. But this freedom is a purely linguistic freedom.

It might be protested that imagination must be a guide to possibility since it would otherwise not have been naturally selected. This objection only holds weight if one already believes that the evolutionary ‘function’ of imagination is to determine possibility, or that imagination has no ‘function’ besides determining possibility. What is the evolutionary role that imagination performs? A speculative but plausible example of where imagination would have a survival value is the following: we can imagine a certain scenario obtaining, and from this, imagine further consequences of said scenario. This ‘preps’ us for the future, enabling us to determine whether we should avoid or bring about said scenario. If imagination did not play some evolutionary role of this sort, then it would be difficult to see why nature selected it. Yet there is no reason to think that the imaginative act was what gave the organism knowledge of the possibility of the imagined scenario. Presumably the organism imagined the scenario in the knowledge that it was possible in the relevant sense that it could occur in its future lifetime. The imaginative act didn’t provide this knowledge. It is true that if every imagined scenario were impossible, then imagination would be a useless ‘adaptation,’ and more likely, a harmful one. Yet this does not tell us that imagination is therefore what gives the organism knowledge of what is possible.  Let us say, for the sake of argument, that we can imagine nomically impossible scenarios (as opposed to mere experiences thereof). There is no reason to think that there is any evolutionary advantage to these imaginative acts being possibility-verifying because these possibilities will never be manifested in the organism’s environment (since we are confined to the actual laws). Hence, there is no evolutionary reason to think these imaginings must represent metaphysical possibilities.  Frank Jackson pointed out that the heaviness of the polar bear’s coat is a spandrel, serving no ‘function’ in and of itself. It is simply a necessary bi-product of having the advantage of a warm biological blanket covering the skin. (Jackson, 1982, p.134) Perhaps the capacity to imagine (or, accepting my first argument, seemingly imagine) nomically impossible scenarios is a similar by-product of the capacity for legal imaginings. The latter capacity is useful, the former is useless; the former comes along for the ride on the back of the latter.

c)       Necessitarianism cannot account for certain counterfactual truths

There are two varieties of counterfactuals that pose potential problems for necessitarianism. First, we can invent limitless subjunctive conditionals with antecedents that explicitly violate the laws of nature. Some of these conditionals we should believe to be substantively true. Yet, if necessitarianism is true, then there are no worlds with different laws of nature that could serve as truth-makers for these conditionals. At the very least we will not be able to give an analysis of these truths in terms of possible world semantics. Thus, the argument goes, necessitarianism is false. The second problem comes from the existence of substantively true counterfactuals that do not feature any explicit counterlegal in the antecedent, but that nonetheless, ‘should’ be interpreted as having a counterlegal antecedent if determinism is true. If both determinism and necessitarianism are true, then these counterfactuals will also be vacuously false. I will start with the latter class of counterfactuals because I believe they pose less of a problem for necessitarianism.

i)                    Implicitly counterlegal counterfactuals

Schaffer writes, ‘to implement the antecedent that there are like charges at a given location (assuming this to be actually false), we need to imagine some miraculous swerving of say, two electrons, that brings them to said location. Assuming that the actual laws are deterministic, such a miraculous swerving will require a slight violation of the actual laws.’ (Schaffer, 2005, p.8) We can make a substantively true counterfactual out of this example: ‘if two electrons were to exist at locations L₁ and L₂,  then they would repel.’ The contingentist can provide an account of this truth in terms of possible worlds. She can say that there are worlds in which the laws of nature vary slightly so as to enable such an antecedent. In the nearest such world, the electrons repel. It is not open to the necessitarian to use this analysis since the necessitarian denies the existence of worlds with different laws. Schaffer contemplates a possible necessitarian response of ‘tinkering with the initial conditions instead, in such a way as that the actual laws will evolve into the antecedent.’ (Ibid., p.9, italics original) However, he objects to this, writing, ‘this introduces complete ‘backtracking’, yielding implausible counterfactual dependencies of the initial condition on the present charges.’ (Ibid., p.9) I agree with Schaffer that this does indeed undermine the necessitarian’s appeal to different initial conditions. One might, however, think that these counterfactual dependencies are not implausible. It might be argued that if determinism is true, then it follows that the nature of the initial conditions depends upon truths about the nature of subsequent stages of the universe. One should only think that there is a problem here if one takes the dependency to be a causal one. It needn’t be the case that the initial conditions depend causally upon the latter conditions. The dependence in question is conceptual. Assuming determinism, the initial state of the universe is conceptually linked to facts about future states of the universe, and so depends upon these facts being true. An initial state of the universe S₁ at T₁ depends, as a matter of a priori reasoning, combined with a posteriori facts about the laws of nature, on the truth of S₂ at T₂. However, it is unclear how this dependency is conceptual in a way that temporally-forward dependencies are not. It is certainly unclear how this dependency differs from causal dependency other than in the fact that it is operates by going backwards in time. But to assume that it is not a causal dependency purely on the basis that it operates backwards in time is to beg the question that one hasn’t in fact allowed for earlier events to be causally dependent on later events. Perhaps the necessitarian could simply accept that there is such a thing as backwards causation. Although I do not think this should be rejected out of hand, we need very strong reasons to re-write our conception of causation. Even if one does succeed in doing this, I believe that Swoyer reveals a problem that shows how even that response wouldn’t be able to deal with these counterfactuals.

Swoyer (himself a necessitarian), raises the following, I believe fatal, criticism against the response that relies on different initial conditions: ‘there is in general no guarantee that our laws allow a world to differ just a little from the actual one until a given moment and to differ thereafter in all of the ways we may imagine it to when reasoning counterfactually.’ (Swoyer, 1983, p.221) Indeed, it would be impossible for two worlds to have the same deterministic laws and an identical history up until a given time, t, and then differ at all after t. If the two worlds were to have the same history up until t, then this history must have included their initial conditions, and thus their initial conditions must have been identical. We cannot appeal to different initial conditions to explain the substantive truth of these counterfactuals because we are presupposing those events differ only just before the event captured in the antecedent. Different initial conditions must change the history of the universe before the antecedent. But even if we ignore the difference in history implied by the difference in initial conditions, it is impossible for identical histories flowing from different initial conditions to then diverge (assuming determinism and identical laws). I will return to the problem of counterfactuals and determinism later – it will be dealt with alongside explicitly counterlegal counterfactuals.

Schaffer notes, and I agree, that deterministic Bohmian mechanics is an ‘empirically open possibility’ (Ibid., p.8) But indeterminism is also an empirically open possibility, and it receives no mention from Schaffer. Both interpretations are controversial but both are very much open. If indeterminism is true, then this particular problem of counterfactuals will not undermine necessitarianism. Worlds can have the same laws but differ as to their parts as a result of indeterminacy. Hence, the necessitarian can appeal to worlds just as the contingentist can. There are different worlds that correspond to the different outcomes that indeterminacy permits. Some of these worlds include electrons that are x metres apart. In the closest of these worlds, they repel.

In short, if indeterminism is true, then these counterfactuals can be dealt with by appeal to worlds where indeterminate laws are associated with different outcomes. Thus, the necessitarian does not need to suppose that any of these counterfactuals are counterlegal. If determinism is true, then the necessitarian cannot deal with these counterfactuals by appealing to worlds with different initial conditions. However, in ii), we will see that the solution to explicitly counterlegal counterfactuals will be sufficient to deal with these implicitly counterlegal deterministic cases.

ii)                   Explicitly counterlegal counterfactuals

Handfield provides an example of an explicitly counterlegal counterfactual (call it ‘1’): ‘if gravity had obeyed an inverse cube law, the planets would have very different orbits.’ (Handfield, 2004, p.403) The possible problem for the necessitarian is of the same nature as before. This appears to be a substantively true statement, and yet, if necessitarianism is true, then there are no worlds which obey an inverse cube law, and so there is no means to account for this. Handfield’s approach is to render the statement as equivalent to ‘if it had turned out that mass could have been governed by an inverse cube law of gravitation, then if mass had obeyed an inverse cube law, then planets would have very different orbits.’ (Ibid., 407, italics original) To my mind this is implausibly artificial. It doesn’t capture what we actually mean by (1). When we say ‘if such and such counterlegal, L, were the case, then P would be the case,’ we do not in any sense mean that L is being assumed possible, we are just assuming that L is possible. This is an important difference. We assume the possibility of L, but this assumption makes no semantic difference to what is being asserted. The biggest problem though is that Handfield must analyse metaphysically impossible conditionals differently than metaphysically possible counterfactuals. However, the fact is that we may not know whether a counterfactual’s antecedent is possible. When a scientist debates the consequences of counterfactuals, she cannot mean different things when the counterfactual is possible as when it is impossible if she doesn’t know whether the counterfactual is possible or not. There must be a uniform analysis of these counterfactuals on the basis that in many cases we do not know the modal nature of the counterfactuals we are dealing with.

At this point I shameless steal Smith’s (2015) approach to counterfactuals (she also uses this approach to deal with other objections in Schaffer 2005), and I am hence heavily indebted to her work here. Smith argues that there are worlds beyond the metaphysically possible. By appealing to a range of worlds beyond the metaphysically possible, we can say that the non-trivial truth of these counterfactuals is accounted for by their truth in logically possible, metaphysically impossible, worlds. Thus, the debate between the necessitarian and contingentist, for Smith, is not a debate over the range of worlds per se, but is a debate over the range of metaphysically possible worlds.  If one believes such worlds to be mysterious or theoretically unattractive, her own words should assuage such concerns:

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 modality and a fortiori need not be metaphysically possible worlds. Indeed, these need not be worlds in any intuitive sense at all. (Smith, 2015 p.474)

There is no reason to doubt the plausibility of such worlds; indeed, these worlds could be regarded simply as maximally consistent sets of propositions, and so would be countenanced by modal ersatzists. There is no reason why the set of worlds required for a possible-worlds semantic cannot be greater than that of the metaphysical worlds – to argue this is to weigh the dice heavily in favour of contingentism. It might be objected that these worlds cannot ground counterfactuals because they are not really possible. Metaphysical possibility is the only genuine possibility, and is thus the only possibility that can ground counterfactual truths (with ‘possibility’ here being mind-independent, i.e. not credence). However, we have no a priori grounds to think that worlds that we merely treat as possible, such as counterlegal worlds, cannot ground counterfactuals. In grounding counterfactuals, what we are really doing is providing a semantics that accounts for them. Few people believe in the literal reality of metaphysically possible worlds; even though they provide a semantics for counterfactual truths, it isn’t plausible that they ground the truth of counterfactuals in any stronger sense. Thus, merely logically possible worlds are no worse off – they can provide a semantics for counterlegal counterfactuals despite not being genuinely possible. By appealing to a range of worlds beyond the metaphysical ones, the necessitarian can also account for the substantive truth of implicit counterlegals combined with deterministic laws, thus rounding off the necessitarian response to implicit counterlegal counterfactuals. There are logically possible but metaphysically impossible worlds which violate the laws of nature briefly so as to instantiate the antecedent. Thus, we can appeal to worlds to ground the truth of these conditionals. Hence, we have adequate necessitarian responses to both implicit and explicit counterlegals.

Finally, even if one rejects these solutions, it does not follow that the necessitarian is significantly worse off than the contingentist. It should be pointed out that the contingentist faces the problem of dealing with counter-logical/mathematical counterfactuals just as the necessitarian does. For example, the counterfactual, ‘if 2 plus 2 were to equal 5, then 2 plus 2 would not equal 4’ (3), seems to be substantively true, but there are no worlds, metaphysical or logical, in which the antecedent is true. Contrast this with ‘if 2 plus 2 were equal to 5, then all elephants would be pink’ (4). (3) seems to be substantively true, (4) seems to be trivial. What accounts for this seeming difference? The necessitarian has more of these counterfactuals to deal with (providing the earlier solutions fail), but she does not face a problem which is greater in any qualitative sense. Thus, the problem of counterfactuals is not a problem for necessitarianism per se.

Section 2: A Couple of Arguments against Contingentism

a)       Contingentism is explanatorily weak

One reason for thinking that the laws of nature are metaphysically necessary is the fact that, if true, then, accepting certain assumptions, it follows that there is a clear explanation for why we have the laws we have. We have the laws we have because they are necessary. If the laws of nature are contingent, however, then it follows most plausibly that they have no explanation whatsoever. Less plausibly, it might be held that they are contingent and yet do have an explanation. I argue that any explanation as to why the contingent laws of nature are as they are, will, in turn, be unacceptable.

It might be noted, correctly, that certain necessary truths do in fact have explanations beyond their mere necessity. For example, any mathematical truth that isn’t rudimentary or axiomatic can be explained ultimately in terms of axioms. The truth that an individual A, could not have come from different gametes, or at the very least, gametes with different genetic material, is explained in terms of the identity conditions for personhood (of course, it could be disputed that identity of genes is necessary for identity of person). In short, it is clear that many necessary truths do require, and do have, explanations beyond the fact that they are necessary. It might then be argued that this is true of the laws of nature. If we assume, for the sake of argument, that these laws are necessary, it doesn’t follow that they don’t require an explanation, since many necessary truths require an explanation. I accept that this would be true in the case of less fundamental laws. For example, Boyle’s law must be explained in terms of further laws regarding the nature of gas, which will then be explained in terms of the nature of matter, the nature of motion etc. However, it is implausible to hold that the most fundamental laws would themselves require explanations. If these laws did have explanations, it is mysterious what these explanations would be. It seems doubtful that these laws could be built from logic or mathematics, for example. Take a mathematical analogy: complex mathematical truths are explained in terms of simpler ones, with the simplest being assumed without question. Analogously, physical laws describing complex phenomena are explained in terms of simpler laws. The simplest laws, I posit, require no explanation. Where would the explanation lie? In mathematics? In logic? It seems unreasonable to think that these disciplines could explain the laws. If one did believe that the explanation lay in logic or mathematics, then one would be logically obliged to be a necessitarian on the harmless assumption that mathematical and logical truths are necessary. Thus, although not all necessary truths are explainable only on the grounds of their necessity, the laws of nature, if necessary, would not require further grounds for explanation.

Armstrong considers the objection that the laws of nature, if contingent, lack an explanation. But he writes, ‘the question arises, however, whether we cannot overdo that good thing: explanation.’ (Armstrong, 1978, p.149). Armstrong thinks that in trying to explain the laws of nature, we are taking explanation too far. I cannot prove that something akin to the Principle of Sufficient Reason is true (although I believe it to be), but I certainly needn’t go that far. I will point out only that we should choose explanations over primitives where possible. There are good reasons why certain necessary truths should be regarded as primitive, but these reasons do not apply to any contingent truths. First, it seems difficult to fathom what sort of fact could explain the axioms of mathematics or the basic truths of logic. What sort of fact could explain why A=A? We can accept these necessary truths as primitive on the basis that there doesn’t seem to be any plausible explanation for them. Second, if these seemingly primitive truths do in fact have explanations, then there doesn’t seem to be any principled reason why their explanans would not have their own explandas. If there are explanations even for the truths of logic, then it seems that the requirements for having an explanation are extremely lax. If these truths have explanations, then surely these explanations do too. Here we enter an infinite regress. The regress is not vicious but it is unwanted. This is because, if each explandum requires its own explanan, then it follows that we will never be able to have an absolute understanding of why the axioms of mathematics and the principles of logic are true because we presumably wouldn’t be able to find an infinite number of explanans for an infinite number of explanda. This does not lead to scepticism because we will still have explanations that justify our belief in the fundamental mathematical and logic truths, but we would necessarily lack a complete account of why these propositions are true. It is clear, however, that we could never have such an account on the basis that there is no account – these truths are self-justifying. But if we accept that these truths have explanations, then it follows that there not only is such an account, but that we can never know what it is. A final point to note is that mathematical and logical atoms determine what an explanation is, that is, they determine the nature of explanation and reasoning itself. Thus, it is unreasonable to suggest that they themselves have explanations. In short, we have reason to think that certain necessary truths are primitive, and these reasons are lacking in the case of contingent truths.

One might claim that the laws of nature are contingent but that they have an explanation. I argue that any such explanation would be theoretically unattractive. Clearly such an explanation cannot reside in the laws we are trying to explain. This would be circular: we cannot explain why something, X, has the nature it has, by appealing to the nature of X. It seems unfeasible that logic or mathematics can determine these laws. Even if they could, this option will not be available to the contingentist on the reasonable assumption that the truths of these disciplines are necessary. Perhaps the laws of nature are explained by the initial conditions of the universe. It might be suggested that if one has a similar take regarding natural laws to that of the regularity theorist, such an option is tenable. If laws are merely a subset of universal regularities, then presumably these regularities would be explained by the initial conditions of the universe. However, this is not so. Regularity theory denies nomic necessity. Thus, the initial state of the universe cannot necessitate subsequent regularities and hence subsequent laws. If one believes, however, in genuine nomic necessity, then one similarly cannot hold that the initial conditions determined the laws. This is because, under this approach, the laws of nature explain the nature of the events within the universe; that is, the nature of the way in which the universe unfolds as a result of the initial conditions. In other words, if there is nomic necessity, then what follows from the initial set-up is determined, at least in part, by the laws of nature. It follows, therefore, that we are left with having to posit something beyond the universe itself to explain the nature of natural law. But such an explanation looks like it must be suspiciously theological. We would be left with an explanation that appeals to the whims of God. Perhaps we could posit a Leibnizian best-of-all-possible-worlds explanation. Whatever explanation we give will certainly be very dated to the modern reader, and will rely upon assumptions about the existence and nature of God. I posit that it would be better to accept the brute necessity of the laws of nature, than to accept any explanations that appeal to phenomena beyond the universe itself. The brute contingency of the laws of nature is less attractive than the brute necessity of the laws of nature for the reasons given previously. The reasons we have for believing in certain brute necessities we do not have for believing in brute contingencies.

b)      What probability should we assign each possibility?

In any given world, it is generally assumed, no doubt correctly, that natural laws hold with a probability of 1. For example, it is generally assumed that the laws of nature in the actual world could not at any moment change. This is an inductive principle that Hume argued cannot be rationally justified. Although we may not have to go so far as to say that such a principle cannot be justified, we can at least agree that it clearly cannot be proven. We can assume for the sake of argument, however, that within a given world, laws hold with probability 1 since my arguments do not depend upon this. We therefore have an intra-world notion of probability – the probability of something being the case in a given world. Laws are taken to have an intra-world probability of 1. We can however, conceptualise an inter-world probability. For example, the contingentist would say that, although it is case that laws in the actual world hold with probability 1, there could have been different laws. In possible worlds analysis, what this amounts to, is that other worlds have different laws. Now we have a notion of inter-world probability. Since the laws in the actual world are not metaphysically necessary, there must have been a probability greater than 0 and less than 1 of their being different. This inter-world probability will be determined by the landscape of possible worlds.

If we accept that the laws of nature are contingent on the basis that there is no contradiction in their failing to obtain (which is the primary argument for contingentism), then, following the same principle of accepting the possibility of any non-contradiction, we should accept the possibility of each and every non-contradictory difference in any given law. But there are infinitely many non-contradictory variations that any particular law could undergo. For example, although it is the case that F=ma, there is no contradiction involved in the formula F=ma² or F=m³a etc. If we accept, as the contingentist should, that each of these variations is a genuine possibility, then it follows that we should accept that each variation had a probability (greater than 0 and less than 1) of being true. By ‘probability’ I mean ‘objective likelihood’ rather than ‘credence’. It is also a meta-world, or metaphysical, notion of probability, unlike quantum indeterministic chance. The fact that each possibility must have had a probability greater than 0 and less than 1 is clear. If the probability were 1, then the possibility would have in fact been a necessity. A probability of 0 would have been no possibility at all. But then we are left with the thorny question of which probability each possibility had of being true. Was it most probable that F=ma?  Was each possibility equal in probability? The problem is that there is no way in which to gauge the probability of each possibility, but each possibility must have had a certain probability in order to have been a genuine possibility. There are three problems here that necessitarianism resolves. One is epistemological: there is no means with which to assign credence to any suggested objective probability. If we accept that the laws of nature are metaphysically necessary, however, then this problem is avoided: we are rationally obliged to believe with a credence of 1 that F=ma had a probability of 1. The second is theoretical: a theory in which the laws of nature held with probability 1, is much neater, simpler, and more elegant, theoretically speaking, than a theory in which there are infinite possibilities each with competing probabilities. The third is metaphysical. It might be said that, although we humans could not possibly determine the probabilities corresponding to the possibilities, this does not mean that there are no probabilities corresponding to the possibilities. However, we can ask, rhetorically, ‘what reason could there have possibly been for the possibilities having the probabilities that they had?’ The contingentist here wouldn’t be able to assert that the probabilities were necessary because they could have conceivably been different. For example, although it was the case, let’s say, that F=ma had a probability of 0.7, there would be no a priori contradiction in its having had a probability of 0.8.  Since they rely on the conceivability of different laws of nature to argue against necessitarianism, in order to be consistent, they should also accept that the probabilities in question must not be necessary.

It might be objected here that we shouldn’t compare probabilities of particular laws, but that we should compare probabilities of entire systems of laws. This is because any change to a given law will invariably result in changes to many others. Laws are not autonomous things, but are instead inter-related. This is why, for David Lewis, different collections of truths (i.e. different law-systems) are compared for simplicity and strength; it is not the case that individual laws are pitted against each other, but only entire coherent collections. (Lewis, 1973) However, it still holds that the contingentist should deem any of these coherent systems possible. If they believe laws to be contingent on the basis that there is no contradiction in their failing to hold, then they should also accept as possible any coherent system of laws. But the same issue of determining the possibility of each system arises. The issue is similarly infinite given the infinite number of coherent systems. Was the actual system of laws the most likely one? Again, there is no means with which to assign probabilities to different systems. It should be stressed that the contingentist cannot assign a probability of 1 to the actual system of laws if the probability in question is an inter-world probability. We are not asking, given the laws of nature, whether they could be different, but whether they could have been different in the first place. The necessitarian says no, and so avoids the problem of having to assign probabilities to each of the different possible systems of law.

Section 3: General Theoretical Virtues of Necessitarianism

The most obvious advantage of necessitarianism is that it offers a simpler modal landscape. This is because it reduces the number of necessitation relations. No longer do we need separate metaphysical and nomic necessities, instead nomic necessity becomes a form of metaphysical necessity. If there were a need for this necessity, then this would not be an advantage, but since, as the previous sections have tried to demonstrate, there is no such need, the advantage remains. Further, the picture we have is more elegant in as far as it clears away all metaphysically possible counterlegals. Thus, our modal space is de-cluttered. Moreover, concrete realists, although rare nowadays, can greatly reduce their ontology by removing all metaphysically possible but nomically impossible worlds from their modal universe.

The greatest theoretical virtue of necessitarianism is that it does away with a form of necessity that we have very little understanding of. Nomic necessity, something that isn’t as strong as metaphysical necessity, and yet is more than mere regularity, is mysterious. There is a great problem with the most plausible contingentist views that feature genuine nomic necessitation. The classic accounts are Armstrong 1978, Dretske, 1977, Tooley 1977. These accounts treat the laws of nature as relations of necessitation holding between universals. Such views face the same problem, but Bird sums up this problem in attacking Armstrong’s version specifically: ‘it is unclear what his [Armstrong’s] relation of contingent necessitation is and… it is unclear how it is able to necessitate anything.’ (Bird, 2004, p.261)[11]  It is true that for the regularity theorist, there is no such problem because there is no such thing as nomic necessity. However, I take it to be a reasonable working hypothesis that the regularity theory is false, whether naïve or sophisticated. Much has been written in critique of the regularity theory[12], and it is not the task of this essay to argue for any particular conception of lawhood. In brief, however, regularity theories cannot form the basis of prediction because prior regular conjunctions fail to guarantee future regular conjunctions. They cannot explain natural events given that natural events include regularities. They cannot justify counterfactual claims because all Fs being G does not guarantee that a non-F, if it were an F, would be a G. They cannot allow for laws without positive instances because regularities require instantiation. The more sophisticated regularity theories can distinguish accidental generalisation from laws but can only do so by injecting unattractive epistemological constraints on the laws in question (unattractive because we do not think that laws depend upon humanity). There are many other criticisms that have been rallied against regularity theories, but I think this brief overview justifies why I take it to be a working assumption that the theory fails. If we accept contingentism, then we are either left with a mysterious nomic necessity or we have to accept the regularity theory. This is a dichotomy that necessitarianism avoids. We have a reasonably strong (or at least notably stronger) grasp of the nature of metaphysical and epistemic necessity than of nomic necessity. Under necessitarianism, we do away with this latter enigmatic necessity (or more accurately, we reduce it to metaphysical necessity), and make do with the first two.

Both CP and necessitarianism result in modal dualism. The former has a distinct metaphysical and nomological domain, with the nomological domain occupying a subsection of the metaphysical. Necessitarianism is similarly dualistic – the logical and metaphysical domains come apart, with the metaphysical occupying a subsection of the logical. In my opinion, necessitarian dualism is a preferable dualism. It is a dualism that is born out of the distinction between what can be conceived and what is absolutely possible – that is, it is a dualism that owes its existence to the divide between modal reality in its broadest sense and the ideal epistemic conditions of an ideal mind. However, the dualism of CP is a genuine division that exists ‘out-there’ in the world. Without minded creatures, there would be no dualism of conceivable and metaphysically possible worlds. However, if contingentism is true, then there will still be a modal dualism of nomically and metaphysically possible worlds. If contingentism is true, then no part of reality can be examined, and scrutinised, and be found to reveal the existence of this divide. Nothing in the world can tell us that the laws of nature could have been different, in virtue of the fact that the world is embedded in the laws of nature. Thus, for the contingentist, the only source of modal knowledge is our imagination, and that which we cannot rule out a priori.  For the necessitarian, however, the world dictates what is or is not possible; not the a priori, armchair imaginings or conceptions of our minds, not even of an ideal mind.  

Conclusion

To conclude, the preceding considerations should be enough to remove the knee-jerk repugnance that philosophers feel towards necessitarianism. I do not wish the reader, and I do not believe myself to have given the reader cause to, accepts necessitarianism as true; I wish the reader instead, to regard it as a viable option. The main arguments directed against it range from impotent (e.g. the argument from imaginability) to at least objectionable (e.g. the argument that we can conceive of different laws of nature). My explanatory arguments against contingentism are powerful, but admittedly in need of further development. The mystery of why these laws is better accounted for if we take the laws to be necessary. Further, the means with which to assign objective probabilities to each of the possible systems of law is removed if we accept that there is only one possible system. Finally, necessitarianism is extremely attractive theoretically speaking. It simplifies modal space, it offers a more attractive modal dualism to that of CP, and it subsumes the mysterious nomological necessity into metaphysical necessity.

References

Armstrong, D.M. (1978). What is a Law of Nature? Cambridge: Cambridge University Press.

Berkeley, George. ([1710] 1975) The Principles of Human Knowledge London: Everyman

Bird, Alexander (2004) Strong Necessitarianism: The Nomological Identity of Possible Worlds Blackwell Publishing. Ratio XVII

Carroll, John (1990) The Humean Tradition The Philosophical Review, Vol.99, No.2, pp.185-219

Chalmers, David. (1996) The Conscious Mind Oxford: Oxford University Press

Chalmers, David. (2010) The Character of Consciousness Oxford University Press

Descartes, René. (1996) Meditations on First Philosophy Cambridge University Press; 2Rev Ed edition

Dretske, Fred (1977) Laws of Nature Philosophy of Science 44 pp.248-268

Gendler, Tamar & Hawthorne, John (2002) Conceivability and Possibility Oxford University Press

From the same publication:

-                      Chalmers, David (2002) Does Conceivability Entail Possibility?

-                      Sidelle, Alan (2002) On the Metaphysical Contingency of Laws of Nature

Handfield, Toby (2004) Counterlegals and Necessary Laws The Philosophical Quarterly, Vol. 54, No.216

Jackson, Frank (1982) Epiphenomenal Qualia Philosophical Quarterly 32 pp. 127-136

Jeffrey, Richard. (1983) The Logic of Decision University of Chicago Press

Kneale, W.C. (1949) Probability and Induction Clarendon Press

Kripke, Saul. (1981) Naming and Necessity Blackwell Publishing

Lewis, D. (1973) Counterfactuals, Oxford Blackwell Publishers and Cambridge, MA: Harvard University Press

Lewis D. (1983) New Work for a Theory of Universals Australasian Journal of Philosophy 343-377

Lewis, D. (2002). On the Plurality of Worlds Blackwell Publishing

Schaffer, Jonathan. (2005). Quiddistic Knowledge Philosophical Studies, Springer

Shoemaker, Sydney. (1980) Causality and Properties in Peter van Inwagen (ed.), Time and Cause. D. Reidel. pp. 109-35

Shoemaker, Sydney. (1998) Causal and Metaphysical Necessity Pacific Philosophical Quarterly pp. 59-77

Smith, Deborah. (2015) Properties, Laws and Worlds Canadian Journal of Philosophy pp.471-489

Smith, Quentin. (2001) The Metaphysical Necessity of Natural Laws Philosophica 67 pp.31-55

Tooley, Michael (1977) The Nature of Laws Canadian Journal of Philosophy, Vol 7, No.4 pp.667-698