Necessitarianism about Laws

How does metaphysical necessity relate to the modal force often associated with natural laws? Fine argues that natural necessity can neither be obtained from metaphysical necessity via forms of restriction nor of relativization — and therefore pleads for modal pluralism concerning natural and metaphysical necessity. Wolff, 898–906, 2013) aims at providing illustrative examples in support of applying Fine’s view to the laws of nature with specific recourse to the laws of physics: On the one hand, Wolff takes it that equations (...) of motion can count as examples of physical laws that are only naturally but not metaphysically necessary. On the other hand, Wolff argues that a certain conservation law obtainable via Noether’s second theorem is an instance of a metaphysically necessary physical law. I show how Wolff’s example for a putatively metaphysically necessary conservation law fails but argue that so-called topological currents can nevertheless count as metaphysically necessary conservation laws carrying physical content. I conclude with a remark on employing physics to answer questions in metaphysics. (shrink)

This book deals with an internal theme of metaphysics, which is the metaphysics of the laws of nature. The author presents traditional contemporary theories, as well as his own original theory, and evaluates each one at a time. He also addresses the problem of the modality of the laws of nature and makes some criticism of the standard view of necessity as truth in all possible worlds, and shows an application of his discussion to the metaphysics of physics. / Este (...) livro trata de um tema interno à metafísica, que é a metafísica das leis da natureza. O autor apresenta as teorias tradicionais contemporâneas, tal como também a sua própria teoria original, e avalia cada uma delas por vez. Ele também aborda o problema da modalidade das leis da natureza e apresenta uma certa crítica à visão padrão da necessidade como verdade em todos os mundos possíveis, e mostra uma aplicação da sua discussão à metafísica da Física. (shrink)

The main intent of this thesis is to defend that the laws of nature are better thought as transcendent universals, such as platonic governism suggests, and that they are metaphysically necessary in a strong way, such as the heterodox version of such platonism defends. With this intention, we sustain that physical symmetries are essential consequences of the laws of nature – what solves the challenge of symmetries – thus being metaphysically necessary, without being governist's necessitation laws. First, we will show (...) what laws of nature are and the reasons to reject other metaphysical theories and to accept platonic governism. Soon after, we will present the challenge of symmetries and the reasons to prefer the platonic governist answer over dispositionalist, regularist, aristotelic (governism), counterfatualist and primitivist ones. At last, we will define what is the metaphysical necessity, argue for the strong metaphysical necessity of laws and their consequences, and show why the reasons for the contingency or weak necessity of laws are bad theoretical paths. (shrink)

We intend at this article to show some reasons to think the laws of nature as metaphysically necessary: to distinguish the metaphysical modality from the epistemical modality, and to have an absolute modality to face the relative physical and logical modalities. Lately, we indicate what does it mean to talk about metaphysically necessary laws, distinguishing two kinds of metaphysical modalities, and we account for the question about if the laws of nature are metaphysically necessary. The conclusion we get is that (...) the laws, whichever they are, are metaphysically necessary. (shrink)

In this paper, I intend to argue against Alexander Bird‟s thesis (2001) that the law salt dissolves in water is metaphysically necessary. I briefly indicate Bird‟s argument for the necessity of such law, and then I provide a counter-argument to his thesis. In a general way, Bird wants to show that the existence of certain substances depends on the truth of certain laws, and that because of this the existence of such substances implies the existence of such laws. That would (...) make the laws existing at least while the substance it rules exists; what, for Bird, makes such laws metaphysically necessary. My counter-argument to Bird is that such conception apprehends just what we call “weak necessity”, and not the strong necessity we would like a metaphysically necessary law to have. (shrink)

Law dispositionalism is the doctrine according to which laws of nature are grounded on powers/dispositions. In this article, I shall examine how certain laws of nature can turn out to be contingent on this view. First of all, I shall distinguish between two versions of law dispositionalism (i.e., a weak and a strong one) and I shall also single out two further theses that may be conjoined with it (i.e., strong and weak dispositional essentialism). I shall then define four different (...) sorts of laws of nature. Afterwards, I shall examine five sources of contingency for law dispositionalism: the contingent existence of the relevant entities involved in the laws; the contingent activation, background and possession conditions of the powers at stake; the presence of contingent constants in the laws; the presence of indeterministic powers; the presence of powers that are not essential to the entities involved in the laws. (shrink)

Substantive counterlegal discourse poses a problem for those according to whom the laws of nature are metaphysically necessary. I discern two types of necessitarianism about laws: Dispositional Essentialism and Modal Necessitarianism. I argue that Handfield (2004)’s response to the problem of counterlegals cannot help the Modal Necessitarian, according to whom all possible worlds are identical with respect to the laws. I thus propose a fictionalist treatment of counterlegals. Fictions are not limited by metaphysical possibility, hence, fictionalism affords the Modal Necessitarian (...) the means to account for the apparent substance of counterlegals even granting the metaphysical necessity of the laws. (shrink)

According to contingentism, laws of nature hold contingently. An objection to contingentism is that it implies quidditism, and therefore inherits its implausible consequences. This paper argues that this objection is misguided. Understood one way, quidditism is not an implication of contingentism, hence even if it has implausible consequences, these are not relevant to contingentism. Understood another way, quidditism is implied by contingentism, but it is less clear if this version of quidditism has the same implausible consequences. Whatever the merits of (...) contingentism, the argument from anti-quidditism is not successful in showing that it is false. (shrink)

The question of the metaphysical status of the laws of physics has received increased attention in recent years. Perhaps most well-known among this work are David Lewis’s Humean supervenience and Nancy Cartwright’s dispositionalism, both of which reject the classical conception of the laws of physics as necessary and real independent of the objects they govern, arguing instead that what we call laws are shorthand for the regularities of local states of affairs or the dispositions of objects. The properties of necessity (...) and reality are generally taken to go hand-in-hand when physical laws are concerned; however, this leaves aside the possibility that the laws of physics are independently real yet contingent. This paper will explore this third option which is found in the work of Quentin Meillassoux. We will ask: if laws both exist independent of their objects and are contingent, what happens when laws change? Specifically, the possibility of metaphysical retro-causation becomes a live option. This raises both questions of the ontological status of the past as well as our epistemic access to the past after a change in physical laws. Meillassoux’s ontology of hyper-chaos weathers this challenge with its consistency intact; however, it is an open question of whether or not saving the reality of physical laws by sacrificing their necessity is worth the epistemic limits and metaphysical strangeness that it implies. (shrink)

If the laws of nature are metaphysically necessary, then it appears that miracles are metaphysically impossible. Yet Locke accepts both Essentialism, which takes the laws to be metaphysically necessary, and the possibility of miracles. I argue that the apparent conflict here can be resolved if the laws are by themselves insufficient for guaranteeing the outcome of a particular event. This suggests that, on Locke’s view, the laws of nature entail how an object would behave absent divine intervention. While other views (...) of laws also make miracles counterfactually dependent on God’s will, I show how this view is consistent with the Essentialist commitment to the view that the laws are metaphysically necessary. Further, I argue Locke’s view is a relatively attractive version of Essentialism, in part, because it allows for the possibility of miracles. (shrink)

There have been various attempts to argue from the _success_ of certain aspects of scientific practice to the existence of necessary connections between distinct events. Many of these arguments are based on an inference to the best explanation. I will start by reviewing some of these IBE arguments as well as their recent critique by Helen Beebee. Beebee’s critique is convincing with regard to the particular arguments she criticises. I will, however, present other aspects of scientific practice that need to (...) be explained. More particularly I will argue that the _failure_ of certain manipulatory practices can best be explained in terms of necessary connections. Beebee’s critique does not apply to this IBE-argument. (shrink)

This discussion paper is a reply to Stathis Psillos’ paper “Induction and Natural Necessities” :327–340, (2017), published in this journal. In that paper, he attempts to refute David Armstrong’s solution to the problem of induction. To accomplish this desideratum, he proposes that the best explanation for our observed regularities is a sort of “best before date” necessity. That is, necessary connections may break down and are not by default timeless. He develops arguments against my :67–82, (2014) defence of the necessitarian (...) solution regarding a previous paper by Beebee :504–527, 2011.. He alleges that best before date necessity is no worse than timeless necessity; his proposal does not imply any further inductive generalisation to timeless necessity; and inductive inferences are justified. In this discussion paper, I provide arguments against these three claims. (shrink)

Alexander Bird (2001; 2002; 2007) offers a powerful argument showing that, regardless of whether necessitarianism or contingentism about laws is true, salt necessarily dissolves in water. The argument is that the same laws of nature that are necessary for the constitution of salt necessitate the solubility of salt. This paper shows that Bird’s argument faces a serious objection if the possibility of emergentism – in particular, C. D. Broad’s account – is taken into account. The idea is (roughly) that some (...) emergent laws in some possible worlds may disrupt the solubility of salt without disrupting its constitution. (shrink)

That laws of nature play a vital role in explanation, prediction, and inductive inference is far clearer than the nature of the laws themselves. My hope here is to shed some light on the nature of natural laws by developing and defending the view that they involve genuine relations between properties. Such a position is suggested by Plato, and more recent versions have been sketched by several writers.~ But I am not happy with any of these accounts, not so much (...) because they lack detail or engender minor difficulties, though they do, but because they share a quite fundamental defect. My goal here is to make this defect clear and, more importantly, to present a rather different version of this general conception of laws that avoids it. I begin by considering several features of natural laws and argue that these are best explained by the view that laws involve properties, that this involvement takes the form of a genuine relation between properties, and, finally, that the relation is a metaphysically necessary one. In the second section I start at the other end, and by reflecting on the nature of properties arrive at a similar account of natural laws. In the final section I develop this account in more detail, with emphasis on the nature of the relation between properties it invokes. Along the way several natural objections to the account are answered. (shrink)

I discuss Josef Seifert, a realist phenomenologist, and David Oderberg, an Aristotelian. Both endorse essences, understood as objective quiddities. Both argue that no law of nature is strongly necessary: i.e. true in every possible world. But they disagree about weak necessity of laws: Seifert argues that no law is true in every possible world in which its referring expressions are non-empty, while Oderberg argues that some is. I restate, relate, and review reasons of both authors for each of those theses. (...) Seifert’s reasons include God’s ability to do miracles, conceivability of counterinstances to laws, and many others. Oderberg’s reasons include dependence of laws on particulars, depiction of laws as truths about properties necessarily connected with essences, and explanation of persistent regularities by means of that necessary connection. I argue that no reason of either Seifert or Oderberg is convincing, as its stands. But I also argue that given God and his ability to do miracles, the idea of “meaningful” but non-necessary connection between essences — an idea endorsed but insuffi ciently utilized by Seifert — is a better essentialist explanation of persistent regularities. This explanation implies that no law is necessary, be it weakly or strongly. (shrink)

Dispositionalism is the view that the world is, ultimately, just a world of objects and their irreducible dispositions, and that such dispositions are, ultimately, the sole explanatory ground for the occurrence of events. This view is motivated, partly, by arguing that it affords, while non‐necessitarian views of laws of nature do not afford, an adequate account of our intuitions about which regularities are non‐accidental. I, however, argue that dispositionalism cannot adequately account for our intuitions about which regularities are non‐accidental. Further, (...) I argue that, intuitions aside, if we suppose that our world contains objects along with their irreducible dispositions, we must suppose, on pain of logical incoherence, that it contains laws of nature that are incompatible with a dispositionalist ontology. Indeed, if we suppose a world of objects and irreducible dispositions, we will have to suppose that the most prominent views of laws of nature currently on offer are all inadequate. (shrink)

A key issue concerning the views of Spinoza is whether he is a necessitarian or if he allows for the existence of possibilities. Commentators on Spinoza agree that his metaphysics revolve around, at the very least, a deterministic universe in which the laws of nature, together with all preceding causes, determine everything that occurs. There is also agreement that Spinoza does allow for doxastic possibility, which involves humans being able to imagine different outcomes based on inadequate knowledge of preceding causes. (...) For instance, humans can imagine a particular car existing or not existing. The divide among commentators occurs over the issue of whether Spinoza is a necessitarian or not. For instance, consider the existence of a black car. If Spinoza is a necessitarian, then the car could not be any color other than black; otherwise, the car could have been a different color. Due to Spinoza’s acceptance of a universe based on deterministic laws, the entire causal order would have to be different in order to produce the car in a different color. A major focus of this study, therefore, will be on whether Spinoza allows that the entire causal order could have been different. Views supporting a necessitarian interpretation of Spinoza, those of Garrett and Koistinen, will be examined as well as views supporting a possibilist interpretation of Spinoza, those of Curley and Walski, and Miller. The views of these five commentators will be examined in an attempt to determine their plausibility in regard to Spinoza’s writings as well as their plausibility in regard to the consistency of their arguments. In order to simplify the task of examining the allowance of possibilities other than doxastic in Spinoza’s metaphysics, this study will focus on Miller’s view of nomological possibility. Nomological possibility involves everything that is consistent with the laws of nature when the laws of nature are considered separately from the actual causal order. In the course of this study the shortcomings of the views defending standard necessitarianism will be demonstrated; the problems of the views espousing the allowance of nomological possibilities will also be demonstrated. A major shortcoming of the necessitarian views involves the plausibility of including one particular causal order within God’s essence, while a major shortcoming of the possibilist views will be their inability to handle the parallelism doctrine that Spinoza holds. A major aim of this study is to demonstrate that nomological possibility, when combined with IP17 in the Ethics, yields a result in which all the things consistent with the laws of nature end up actually existing. IP17 declares that “God creates everything that He understands.” If God understands everything consistent with the laws of nature, then He creates everything consistent with the laws of nature. The hybrid view, which is termed “super necessitarianism,” will be examined to sketch a way that it could fit into Spinoza’s metaphysics. The view of super necessitarianism will be considered in three variations, those of eternal, expansive, and concentrated. Eternal super necessitarianism involves all the things consistent with the laws of nature being created over the vast spans of time, while expansive super necessitarianism involves all the things being created over the vast universe. Concentrated super necessitarianism involves all the things being created within the same finite mode but expressed through different attributes. The choice will be made as to which of the three variations of super necessitarianism is most plausible, and finally it will be shown how super necessitarianism avoids some of the problems inherent in the necessitarian and possibilist views. (shrink)

Physicalism holds that the laws of physics are inviolable and ubiquitous and thereby account for all of reality. Laws leave no “wiggle room” or “gaps” for action by numinous agents. They cannot be invoked, however, without boundary stipulations that perforce are contingent and which “drive” the laws. Driving contingencies are not limited to instances of “blind chance,” but rather span a continuum of amalgamations with regularities, up to and including nearly determinate propensities. Most examples manifest directionality, and their very definition (...) encompasses intentionality. Contingencies, via their interactions with laws, can reinforce and maintain one another, thereby giving rise to enduring, ordered configurations of constraints. All of ordered nature thus results from ongoing transactions between mutualistic contingencies that constrain possibilities and entropic chance events that degrade order but diversify opportunities. Laws do not of themselves determine reality; interactions among contingencies do. For believers, the robust abundance of indeterminacies provides ample latitude for divine intervention, free will, and prayer. The priority of contingency also affords some insight into the meaning of suffering and evil. (shrink)

"Accessibility" is a crucial concept of possible worlds semantics. The simplest approach to accessibility is the "magical theory" that construes this relation as analogous to spatial or temporal relations. In this paper I give a nonmagical structural account of the accessibility relation that can be used to give a necessitarian account of kinds and laws. Laws are characterized in a structural way as stable invariants of the world's gestalt. Finally, I point out how the structural approach can be embedded in (...) a general representational theory of modality. (shrink)

In a recent paper (Bird 2001), Alexander Bird argues that the law that common salt dissolves in water is metaphysically necessary - and he does so without presupposing dispositionalism about properties. If his argument were sound, it would thus show that at least one law of nature is meta- physically necessary, and it would do so without illicitly presupposing a position (dispositionalism) that is already committed to a necessitarian view of laws. I shall argue that Bird's argument is unsuccesful.

No one has yet elaborated and defended with so much subtlety, rigour, and depth the exciting new metaphysics of nature that replaces both versions of the traditional categoricalist picture of nature...Reading Bird is highly rewarding: he sheds new light on many problems by analysing them in a new way...Bird's book holds promise to become the authoritative statement of the new dispositionalist metaphysics.

How can the laws of nature, that determine how objects behave, be understood as natural objects themselves? The answer that transpires from the analysis of modern theories of the laws of nature is: laws of nature are due to the causal structure of our world. They express the causal efficiacy of fundamental properties of nature. In contrast to rivaling theories, this answer does justice to the fact that laws of nature determine the course of natural events without having to appeal (...) to the strong assumption of necessarily acting forces. The modal force exerted by the laws of nature instead reflects a fundamental factual constitution of our world: fundamental properties like charge or mass exert their efficiacy in an unperturbed fashion, without influencing each other. The 'necessity' that laws of nature convey is hence compatible with their metaphysical contingency, the possibility of other, nomologically different worlds. The suggested theory connects laws of nature and causality in a new way: only in a temporally asymmetrical world can causality exist, and only in a causal world can fundamental properties exhibit those asymmetric relations that we call laws of nature. (shrink)

In Bird 2001 I argued that a law that might seem to many to be contingent is in fact necessary. In short the argument is this. Given the existence of salt and water, Coulomb’s law of electrostatic attraction is sufficient to make the former dissolve in the latter. So any possible world in which salt failed to dissolve in water would be one in which Coulomb’s law is false. However, it is also the case that the existence of salt depends (...) on Coulomb’s law. If Coulomb’s law is false then salt cannot exist. So there is no possible world in which salt exists and in which it does not dissolve in water. (shrink)

This chapter deals with the main characteristics of natural kinds, and analyzes three approaches to them. The first approach argues that natural kinds are characterized by their essential properties (in a modern, scientific sense), but encounter difficulties even on the physico-chemical level, which is where it seems to be better implemented. On the other hand, the constructivist stance, much more liberal, does not explain why certain kinds are inductively useful and not others. Third, an introduction, with comments, is provided on (...) the approach of Richard Boyd, among others, which understands natural kinds as homeostatic property clusters that accommodate to the causal structure of the world. In this view, natural kinds are usually fuzzy sets with no clear boundaries, subject to time and space limitations, and relative to some perspective. However, it solves the problems of the other approaches mentioned without forgoing a realistic conception of natural kinds. Finally, a proposal is made on how an application of Boyd’s ideas to the analysis of laws of nature can help to solve the old chestnut about the distinction between scientific laws and accidentally true generalizations. (shrink)

Abstract It is argued that the problem of the necessity and projectability of laws may be solved by distinguishing between the fact of necessity and explanations of its nature. This reduces the problem of necessity to that of induction, which in consequences must be solved without reference to necessity using ?self?supporting? arguments. The consequences for the analysis of ?counterfactual conditionals and the problem of language dependence is discussed.

According to the dispositional essentialist account of laws of nature, the latter express the dispositional nature of fundamental natural properties. In this paper I discuss the difficulty that the existence of fundamental constants of nature raises for that account. To this end, I examine a relevant argument against the account and describe how an advocate of the dispositionalist conception may try to undermine it by raising objections to its premises. Then I discuss those objections and show that eventually all fail. (...) I finally conclude that the existence of the fundamental constants remains a “constant” threat to the dispositional essentialist conception of laws. (shrink)

Scientific essentialism holds that: (1) each scientific kind is associated with the same set of properties in every possible world; and (2) every individual member of a scientific kind belongs to that kind in every possible world in which it exists. Recently, Ellis (Scientific essentialism, 2001 ; The philosophy of nature 2002 ) has provided the most sustained defense of scientific essentialism, though he does not clearly distinguish these two claims. In this paper, I argue that both claims face a (...) number of formidable difficulties. The necessities of scientific essentialism are not adequately distinguished from semantic necessities, they have not been shown to be necessities in the strictest sense, they must be relativized to context, and they must either be confined to a subset of scientific properties without warrant or their connection to causal powers must be revoked. Moreover, upon closer examination (1) turns out to be a trivial thesis that can be satisfied by non-kinds, and (2) is inapplicable to some of the most fundamental kinds in the basic sciences. (shrink)

The basic principles of dispositional essentialism do not require that the fundamental spatiotemporal relations are dispositional in nature. Nevertheless, Bird (who defends dispositional monism) argues that they possess dispositional essences in virtue of the fact that the obtaining of these relations can be characterised by the satisfaction of a certain counterfactual. In this paper I argue that his suggestion fails, and so, despite his attempt, the case of the spatiotemporal relations remains the ‘big bad bug’ for the thesis of dispositional (...) monism. (shrink)

In "The Philosophy of Nature," Brian Ellis provides a clear and forthright general summation of, and introduction to, the new essentialist position. Although the theory that the laws of nature are immanent in things, rather than imposed on them from without, is an ancient one, much recent work has been done to revive interest in essentialism and "The Philosophy of Nature" is a distinctive contribution to this lively current debate. Brian Ellis exposes the philosophical and scientific credentials of the prevailing (...) Humean metaphysic as less than compelling and makes the case for new essentialism as an alternative metaphysical perspective in lucid and unambiguous terms. This book develops this alternative metaphysic and considers the consequences for philosophy, and for some other areas of investigation, of working with such a metaphysic. Ellis argues that these consequences are profound and that a new essentialism provides a comprehensive new philosophy of nature for a modern scientific understanding of the world. (shrink)

I look at a recent argument offered in defense of a doctrine which I will call generalized scientific essentialism. This is the doctrine according to which, not only are some facts about substance composition metaphysically necessary, but, in addition, some facts about substance behavior are metaphysically necessary. More specifically, so goes the argument, not only is water necessarily composed of H2O and salt is necessarily composed of NaCl, but, in addition, salt necessarily dissolves in water. If this argument is sound, (...) and if the statement that necessarily salt dissolves in water is a statement of a law of nature, then one conclusion of the argument is that there is at least one metaphysically necessary law of nature. My paper examines the extent to which this kind of argument could be generalized to provide a case for a full-blown scientific essentialism: the doctrine according to which all of the laws of nature are necessary. Or, in terms of dispositions, it is the doctrine according to which natural kinds have all of their powers, capacities and propensities as a matter of necessity. (shrink)

For many years essentialism was considered beyond the pale in philosophy, a relic of discredited Aristotelianism. This is no longer so. Kripke and Putnam have made belief in essential natures respectable once more. Harré and Madden have argued against Hume's theory of causation and developed an alternative theory based on the assumption that there are genuine causal powers in nature. Dretske, Tooley, Armstrong, Swoyer, and Carroll have all developed strong alternatives to Hume's theory of the laws of nature. And Shoemaker (...) has developed a thoroughly non-Humean theory of properties. The "new essentialism" has evolved from these beginnings and can now reasonably claim to be a metaphysic for a modern scientific understanding of the world - one that challenges the conception of the world as comprising passive entities whose interactions are to be explained by appeal to contingent laws of nature externally imposed. (shrink)

This chapter focuses on the dispute between necessitarians and contingentists, mainly addressing the issue as to whether laws of nature are metaphysically necessary or metaphysically contingent with a weaker kind of necessity, commonly referred to as natural, nomological, or nomic necessity. It is assumed here that all fundamental properties are dispositional or role properties, making the dispute a strictly verbal one. The existence of categorical intrinsic properties as well as dispositional properties is also assumed and the relationship between them examined. (...) Finally, the chapter concludes by returning to the debate between necessitarians and contingentists under the assumption that both dispositional and categorical fundamental properties exist. It is argued here that necessitarian positions can be recast as contingentist, but that there are unequivocally contingentist positions preferred because they are less mysterious despite being ontologically more complex. (shrink)

Hume defined ‘cause’ three times over. The two principal definitions (constant conjunction, felt determination) provide the anchors for the two main strands of the modem empiricist accounts of laws of nature 1 while the third (the counter factual definition 2) may be seen as the inspiration of the nonHumean necessitarian analyses. Corresponding to the felt determination definition is the account of laws that emphasizes human attitudes, beliefs, and actions. Latter day weavers of this strand include Nelson Goodman, A. J. Ayer, (...) and Nicholas Rescher. In Fact, Fiction and Forecast Goodman writes: “I want to emphasize the Humean idea that rather than a sentence being used for prediction because it is a law, it is called a law because it is used for prediction” (1955, p. 62). In “What is a law of nature?”, Ayer explains that the difference between ‘generalizations of fact’ and ‘generalizations of law’ “lies not so much on the side of facts which make them true, as in the attitude of those who put them forward” (1956, p. 162). And in a similar vein, Rescher maintains that lawfulness is “mind-dependent”; it is not something which is discovered but which is supplied: “Lawfulness is not found in or extracted from the evidence but superadded to it. Lawfulness is a matter of imputation” (1970, p. 107). By contrast, the constant conjunction definition promotes the view that laws are to be analyzed in terms of the de re characteristics of regularities, independently of the attitudes and actions of actual or potential knowers. (shrink)

I want to examine a possible solution to the problem of induction-one which, as far as I know, has not been discussed elsewhere. The solution makes crucial use of the notion of objective natural necessity. For the purposes of this discussion, I shall assume that this notion is coherent. I am aware that this assumption is controversial, but I do not have space to examine the issue here.