Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (shrink)

1.1 Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tangent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (...) . . . . . . . . . . . 7 1.3 Vector Fields, Integral Curves, and Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Tensors and Tensor Fields on Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 The Action of Smooth Maps on Tensor Fields . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 Lie Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Derivative Operators and Geodesics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.8 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.9 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.10 Hypersurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1.11 Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96.. (shrink)

Focusing on spacetime singularities, Earman engages with a host of foundational issues at the intersection of science and philosophy, ranging from the big bang to the possibility of time travel.

A modest proposal concerning laws, counterfactuals, and explanations - - Why be Humean? -- Suggestions from physics for deep metaphysics -- On the passing of time -- Causation, counterfactuals, and the third factor -- The whole ball of wax -- Epilogue : a remark on the method of metaphysics.

This volume presents a selection of the most influential recent discussions of the crucial metaphysical questions: what is it for one event to cause another? The subject of causation bears on many topics, such as time, explanation, mental states, the laws of nature, and the philosphy of science.

It is commonly supposed that metaphysical modal claims are to be evaluated with respect to a single domain of possible worlds: a claim is metaphysically necessary just in case it is true in every possible world, and metaphysically possible just in case it is true in some possible world. We argue that the standard understanding is incorrect; rather, whether a given claim is metaphysically necessary or possible is relative to which world is indicatively actual. We motivate our view by attention (...) to discussions in Salmon 1989 and Fine 2005, in which various data are taken to support rejecting the transitivity of accessibility and modal monism ; we argue that relativized metaphysical modality can accommodate these data compatible with both standard modal logic and modal monism. Noting an analogy with two-dimensional semantics, we argue that metaphysical modality has a complex structure, reflecting what is counterfactually possible, relative to each indicatively actual world. In arguing for the need for relativization, we are broadly on the same side as Crossley and Humberstone and Davies and Humberstone ; our contribution here is, first, to offer distinctively metaphysical reasons for relativization, and second, to show that relativization can be incorporated in ways minimally departing from standard modal logic. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

Alan Sidelle's Necessity, Essence, and Individuation is a sustained defense of empiricism—or, more generally, conventionalism—against recent attacks by realists. Sidelle focuses his attention on necessity a posteriori, a kind of necessity which contemporary realists have taken to support realism over empiricism. Turning the tables against the realists, Sidelle argues that if there are in fact truths necessary a posteriori, it is not realism, but rather empiricism which provides the best explanation for them.

The Theory of Relativity and A Priori Knowledge will hereafter be cited as "RAK. " The German edition is out of print. 2 H. Reichenbach, The Philosophy of ...

This paper focuses on the concept of collective essence: that some truths are essential to many items taken together. For example, that it is essential to conjunction and negation that they are truth-functionally complete. The concept of collective essence is one of the main innovations of recent work on the theory of essence. In a sense, this innovation is natural, since we make all sorts of plural predications. It stands to reason that there should be a distinction between essential and (...) accidental plural predications if there is a distinction among singular predications. In this paper I defend the view that the concept of collective essence is governed by the principle of Monotonicity: that something is essential to some items only if it is essential to any items to which they belong. (shrink)

Are laws of nature necessary, and if so, are all laws of nature necessary in the same way? This question has played an important role in recent discussion of laws of nature. I argue that not all laws of nature are necessary in the same way: conservation laws are perhaps to be regarded as metaphysically necessary. This sheds light on both the modal character of conservation laws and the relationship between different varieties of necessity.

Summary: The paper provides an argument for modal primitivism, the view that necessity is not defined and is therefore part of the structure of reality. It then raises the explanation-challenge for primitivists: how can modal truths be explained by hyper-intensional truths, if necessity is not defined in terms of hyper-intensional phenomena? To address the challenge, the paper introduces 'sophisticated modal primitivism' which gives a substantive analysis of the notion of a 'source of necessity'. The final part of the paper offers (...) some applications of that novel piece of ideology. (shrink)

ABSTRACT Many phenomena appear to be indeterminate, including material macro-object boundaries and certain open future claims. Here I provide an account of indeterminacy in metaphysical, rather than semantic or epistemic, terms. Previous accounts of metaphysical indeterminacy have typically taken this to involve its being indeterminate which of various determinate states of affairs obtain. On my alternative account, MI involves its being determinate that an indeterminate state of affairs obtains. I more specifically suggest that MI involves an object's having a determinable (...) property, but not having any unique determinate of that determinable. I motivate the needed extension of the traditional understanding of determinables, then argue that a determinable-based account of MI accommodates, in illuminating fashion, both ‘glutty’ and ‘gappy’ cases of MI, while satisfactorily treating concerns about MI stemming from Evans’ argument and the problem of the many. (shrink)

A fundamental entity is an entity that is ‘ontologically independent’; it does not depend on anything else for its existence or essence. It seems to follow that a fundamental entity is ‘modally free’ in some sense. This assumption, that fundamentality entails modal freedom (or ‘FEMF’ as I shall label the thesis), is used in the service of other arguments in metaphysics. But as I will argue, the road from fundamentality to modal freedom is not so straightforward. The defender of FEMF (...) should provide positive reasons for believing it, especially in light of recent views that are incompatible with it. I examine both direct and indirect routes to FEMF. (shrink)

Many are reluctant to accept primitive modality into their fundamental picture of the world. The worry often traces to this thought: we shouldn't adopt any more primitive - that is, unexplained - notions than we need in order to explain all the features of the world, and primitive modal notions are not needed. I examine one prominent rival to modal primitivism, combinatorialism, and show that in order to account for all the modal features of the world the combinatorialist must adopt (...) two additional primitive notions. My own modal primitivist view takes as primitive the notion of incompatibility between properties or relations. I show how the non-modal notions that the combinatorialist must adopt as primitive may be analyzed using my notion. The upshot is that with respect to the number of primitive notions, my modal primitivist theory comes out ahead. (shrink)

This paper is concerned with the question of the truth conditions of nomological statements. My fundamental thesis is that it is possible to set out an acceptable, noncircular account of the truth conditions of laws and nomological statements if and only if relations among universals - that is, among properties and relations, construed realistically - are taken as the truth-makers for such statements. My discussion will be restricted to strictly universal, nonstatistical laws. The reason for this limitation is not that (...) I feel there is anything dubious about the concept of a statistical law, nor that I feel that basic laws cannot be statistical. The reason is methodological. The case of strictly universal, nonstatistical laws would seem to be the simplest case. If the problem of the truth conditions of laws can be solved for this simple subcase, one can then investigate whether the solution can be extended to the more complex cases. I believe that the solution I propose here does have that property, though I shall not pursue that question here.1. (shrink)

Three popular views regarding the modal status of the laws of nature are discussed: Humean Supervenience, nomic necessitation, and scientific/dispositional essentialism. These views are examined especially with regard to their take on the apparent modal force of laws and their ability to explain that modal force. It will be suggested that none of the three views, at least in their strongest form, can be maintained if some laws are metaphysically necessary, but others are metaphysically contingent. Some reasons for thinking that (...) such variation in the modal status of laws exists will be presented with reference to physics. This drives us towards a fourth, hybrid view, according to which there are both necessary and contingent laws. The prospects for such a view are studied. (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)

This paper defends the idea that there might be vagueness or indeterminacy in the world itself---as opposed to merely in our representations of the world---against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague *properties and relations*; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague *objects*; we (...) argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the *world as a whole* might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)

In response to various shortcomings of regularity theories of natural law, some philosophers of a realist bent have recently been drawn to the view that a law of nature is a relation between universals. Heading this group are Michael Tooley and D. M. Armstrong.

Non-Humean accounts of lawhood are said to founder on the Inference Problem, which is the problem of saying how laws that go beyond the regularities can entail the regularities. I argue that the Inference Problem has a simple solution – the Axiomatic Solution – on which the non-Humean only needs to outfit her laws with a law-to-regularity axiom. There is a remaining Epistemic Bulge, as to why one should believe that the posit-so-axiomatized is to be found in nature, but the (...) non-Humean can flatten the bulge. Lawhood serves as a case study of how fundamental posits can do their business. (shrink)

I develop a metaphysical position that is both lawless and anti-Humean. The position is called realist lawlessness and contrasts with both Humean lawlessness and nomological realism – the claim that there are laws in nature. While the Humean view also allows no laws, realist lawlessness is not Humean because it accepts some necessary connections in nature between distinct properties. Realism about laws, on the other hand, faces a central dilemma. Either laws govern the behaviour of properties from the outside or (...) from the inside. If the former, an unacceptable quidditist view of properties follows. But no plausible account of laws within properties can be developed that permits a governing role specifically for laws. I conclude in favour of eliminativism about laws. At the conceptual core, the notion of a law in nature is misleading. It is suggestive of an otherwise static world in need of animation. (shrink)

In his influential article ‘Essence and Modality’, Fine proposes a definition of necessity in terms of the primitive essentialist notion ‘true in virtue of the nature of’. Fine’s proposal is suggestive, but it admits of different interpretations, leaving it unsettled what the precise formulation of an Essentialist definition of necessity should be. In this paper, four different versions of the definition are discussed: a singular, a plural reading, and an existential variant of Fine’s original suggestion and an alternative version proposed (...) by Correia which is not based on Fine’s primitive essentialist notion. The first main point of the paper is that the singular reading is untenable. The second that given plausible background assumptions, the remaining three definitions are extensionally equivalent. The third is that, this equivalence notwithstanding, Essentialists should adopt Correia’s version of the definition, since both the existential variant, which has de facto been adopted as the standard version of the definition in the literature, and the plural reading suffer from problems connected to Fine’s primitive essentialist notion. (shrink)

This paper motivates and defends a principle which captures a systematic connection between essence, truth, and grounding. It says that if a proposition expresses an essential truth, i.e., if it is true in virtue of the nature of some objects, then there are grounds for its truth which involve these objects. Together with the assumption that a fact can only be grounded in facts which are relevant to it, this principle is then applied in an argument against the monotonicity of (...) the Essentialist notion ‘true in virtue of the nature of’. (shrink)

A priori metaphysics has come under repeated attack by naturalistic metaphysicians, who take their closer connection to the sciences to confer greater epistemic credentials on their theories. But it is hard to see how this can be so unless the problem of theory change that has for so long vexed philosophers of science can be addressed in the context of scientific metaphysics. This paper argues that canonical metaphysical claims, unlike their scientific counterparts, cannot meaningfully be regarded as ‘approximately true,’ and (...) that this means that the epistemic progress that science arguably enjoys through episodes of theory change cannot be expected to transfer to its metaphysics. What the value of engaging in metaphysics of science before the emergence of a final theory becomes correspondingly unclear. (shrink)

There cannot be a reductive theory of modality constructed from the concepts of sparse particular and sparse universal. These concepts are suffused with modal notions. I seek to establish this conclusion by tracing out the pattern of modal entanglements in which these concepts are involved. In order to appreciate the structure of these entanglements a distinction must be drawn between the lower-order necessary connections in which particulars and universals apparently figure, and higher-order necesary connections. The former type of connection relates (...) specific entities. By contrast, the latter type of connection is unspecific: it relates entities to some others. I argue that whilst there may be techniques that succeed in providing reductive truth conditions for sentences that say particulars and universals figure in lower-order necessary connections, such techniques cannot succeed in providing reductive truth conditions for sentences that say these entities figure in higher-order necessary connections. I conclude that this situation leaves reductionists with a dilemma. If they wish to affirm that there are particulars and universals then the project of reducing modality by positing these entities must be abandoned. Alternatively, they may continue to deploy their usual reductive techniques but then they must abandon the doctrine that there is more than one fundamental category of entity. (shrink)

s div class="title" a terTwo Notions of Being: Entity and Essence s /div a ter - Volume 62 - E. J. Lowe.

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)

In ‘The Varieties of Necessity’ Fine presents purported counterexamples to the view that a proposition is a naturally necessary truth if and only if it is logically necessary relative to or conditional upon the basic truths about the status and distribution of natural kinds, properties and relations. The aim of this article is to defend the view that natural necessity is relative necessity, and the general idea that we can define other kinds of necessity as relative, against Fine's criticisms.

This paper defends the idea that there might be vagueness or indeterminacy in the world itself--as opposed to merely in our representations of the world--against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague properties and relations ; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague objects (...) ; we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the world as a whole might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)

In a recent paper, Tuomas Tahko has argued for a hybrid view of the laws of nature, according to which some physical laws are metaphysically necessary, while others are metaphysically contingent. In this paper, we show that his criterion for distinguishing between these two kinds of laws — which crucially relies on the essences of natural kinds — is on its own unsatisfactory. We then propose an alternative way of drawing the metaphysically necessary/contingent distinction for laws of physics based on (...) the central kinematical/dynamical distinction used in physical theorising, and argue that the criterion can be used to amend Tahko’s own account, but also that it can be combined with different metaphysical views about the source of necessity. (shrink)

It is widely accepted that necessity comes in different varieties, often called ‘kinds': metaphysical necessity, logical necessity, natural necessity, conceptual necessity, moral necessity, to name but a few – and the same goes for the varieties of possibility. What is usually not fully appreciated, however, is that modal variety is not simply ‘unidimensional': it does not only involve one main variable – kind, whose values are the particular kinds of necessity. Rather, I argue, it is ‘bidimensional', involving two distinct variables (...) – domain and strength. In the first part of the paper, I introduce and develop the proposed bidimensional picture of modal variety, defending it against the common, unidimensional one. In the second part, I consider how the main available accounts of necessities and their relations rely, at least to a significant extent, on the latter picture, pointing out important limitations that they face as a result. I also show how, accordingly, alternative accounts based on a clear and systematic distinction between domain and strength would overcome those limitations. I conclude that, beyond the particular bidimensionalist view defended, our understanding of the modal realm may benefit from more direct debate on whether and how it is multidimensional. (shrink)

Fred Dretske, Michael Tooley, and David Armstrong accept a theory of governing laws of nature according to which laws are atomic states of affairs that necessitate corresponding natural regularities. Some philosophers object to the Dretske/Tooley/Armstrong theory on the grounds that there is no illuminating account of the necessary connection between governing law and natural regularity. In response, Michael Tooley has provided a reductive account of this necessary connection in his book Causation (1987). In this essay, I discuss an improved version (...) of his account and argue that it fails. First, the account cannot be extended to explain the necessary connection between certain sorts of laws—namely, probabilistic laws and laws relating structural universals—and their corresponding regularities. Second, Tooley’s account succeeds only by (very subtly) incorporating primitive necessity elsewhere, so the problem of avoiding primitive necessity is merely relocated. (shrink)

Orthodoxy has it that only metaphysically elite properties can be invoked in scientifically elite laws. We argue that this claim does not fit scientific practice. An examination of candidate scientifically elite laws like Newton’s F = ma reveals properties invoked that are irreversibly defined and thus metaphysically non-elite by the lights of the surrounding theory: Newtonian acceleration is irreversibly defined as the second derivative of position, and Newtonian resultant force is irreversibly defined as the sum of the component forces. We (...) think that scientists are happy to invoke metaphysically non-elite properties in scientifically elite laws for reasons of convenience, such as to simplify the equations and to make them more modular. On this basis, we draw a deflationary moral about laws themselves, as being merely convenient summaries. 1 Introduction2 Orthodoxy2.1 Orthodoxy stated2.2 Orthodoxy explained2.3 A worrisome commitment: Term objectivism3 The Loose View3.1 The argument from practice3.2 Finding the scientifically elite equations3.3 Diagnosing the metaphysically non-elite properties3.4 Situating our challenge4 Newtonian Mechanics4.1 Newtonian acceleration4.2 Newtonian resultant force4.3 A metaphysical discovery?5 Objections5.1 Metaphysically elite after all?5.2 Scientifically non-elite after all?5.3 But our world is not Newtonian!6 Consequences6.1 Consequences for the motivations for link6.2 Consequences for metaphysically elite properties6.3 Consequences for lawhood. (shrink)

We argue that the inference from dispositional essentialism about a property (in the broadest sense) to the metaphysical necessity of laws involving it is invalid. Let strict dispositional essentialism be any view according to which any given property’s dispositional character is precisely the same across all possible worlds. Clearly, any version of strict dispositional essentialism rules out worlds with different laws involving that property. Permissive dispositional essentialism is committed to a property’s identity being tied to its dispositional profile or causal (...) role, yet is compatible with moderate interworld variation in a property’s dispositional profile. We provide such a model of dispositional essentialism about a property and metaphysical contingency of the laws involving it. (shrink)

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional - necessarily, if C then p - where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone, that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, (...) and offer another - considerably simpler - solution. (shrink)