This chapter defends the account of metaphysical indeterminacy of Barnes and Williams against Eklund's objections.

On many currently live interpretations, quantum mechanics violates the classical supposition of value definiteness, according to which the properties of a given particle or system have precise values at all times. Here we consider whether either metaphysical supervaluationist or determinable-based approaches to metaphysical indeterminacy can accommodate quantum metaphysical indeterminacy (QMI). We start by discussing the standard theoretical indicator of QMI, and distinguishing three seemingly different sources of QMI (S1). We then show that previous arguments for the conclusion that metaphysical supervaluationism (...) cannot accommodate QMI, due to Darby 2010 and Skow 2010, are unsuccessful, in leaving open several supervaluationist responses. We go on to provide more comprehensive argumentation for the negative conclusion. Here, among other results, we establish that the problems for supervaluationism extend far beyond the concern that is the focus of Darby's and Skow's discussions (according to which a supervaluationist approach is incompatible with the orthodox interpretation, in light of the Kochen-Specker theorem) to also attach to common understandings of other interpretations on which there is QMI (S2). We then argue that a determinable-based account can successfully accommodate all three varieties of QMI (S3). We close by observing the positive mutual bearing of our results on the coherence and intelligibility of both quantum mechanics and metaphysical indeterminacy (S4). (shrink)

Metaphysicians should pay attention to quantum mechanics. Why? Not because it provides definitive answers to many metaphysical questions-the theory itself is remarkably silent on the nature of the physical world, and the various interpretations of the theory on offer present conflicting ontological pictures. Rather, quantum mechanics is essential to the metaphysician because it reshapes standard metaphysical debates and opens up unforeseen new metaphysical possibilities. Even if quantum mechanics provides few clear answers, there are good reasons to think that any adequate (...) understanding of the quantum world will result in a radical reshaping of our classical world-view in some way or other. Whatever the world is like at the atomic scale, it is almost certainly not the swarm of particles pushed around by forces that is often presupposed. This book guides readers through the theory of quantum mechanics and its implications for metaphysics in a clear and accessible way. The theory and its various interpretations are presented with a minimum of technicality. The consequences of these interpretations for metaphysical debates concerning realism, indeterminacy, causation, determinism, holism, and individuality are explored in detail, stressing the novel form that the debates take given the empirical facts in the quantum domain. While quantum mechanics may not deliver unconditional pronouncements on these issues, the range of possibilities consistent with our knowledge of the empirical world is relatively small-and each possibility is metaphysically revisionary in some way. This book will appeal to researchers, students, and anybody else interested in how science informs our world-view. (shrink)

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

There has been recent interest in formulating theories of non-representational indeterminacy. The aim of this paper is to clarify the relevance of quantum mechanics to this project. Quantum-mechanical examples of vague objects have been offered by various authors, displaying indeterminate identity, in the face of the famous Evans argument that such an idea is incoherent. It has also been suggested that the quantum-mechanical treatment of state-dependent properties exhibits metaphysical indeterminacy. In both cases it is important to consider the details of (...) the metaphysical account and the way in which the quantum phenomenon is captured within it. Indeed if we adopt a familiar way of thinking about indeterminacy and apply it in a natural way to quantum mechanics, we run into illuminating difficulties and see that the case is far less straightforward than might be hoped. (shrink)

Here I compare two accounts of metaphysical indeterminacy (MI): first, the 'meta-level' approach described by Elizabeth Barnes and Ross Cameron in the companion to this paper, on which every state of affairs (SOA) is itself precise/determinate, and MI is a matter of its being indeterminate which determinate SOA obtains; second, my preferred 'object-level' determinable-based approach, on which MI is a matter of its being determinate---or just plain true---that an indeterminate SOA obtains, where an indeterminate SOA is one whose constitutive object (...) has a determinable property, but no unique determinate of that determinable. In S1, I first note an important difference between our accounts, concerning whether MI is taken to induce propositional indeterminacy; in S2, I highlight and defend certain advantages of my account; in S3, I address certain of Barnes and Cameron's objections to my account. (shrink)

In this paper I aim to answer two questions: Can spin be treated as a determinable? Can a treatment of spin as a determinable be used to understand quantum indeterminacy? In response to the first question I show that the relations among spin number, spin components and spin values cannot be captured by a single determination relation; instead we need to look at spin number and spin value separately. In response to the second question I discuss three ways in which (...) the determinables model might be modified to account for indeterminacy, and argue that none of them is fully successful in helping us to understand quantum indeterminacy. (shrink)

It has frequently been suggested that quantum mechanics may provide a genuine case of ontic vagueness or metaphysical indeterminacy. However, discussions of quantum theory in the vagueness literature are often cursory and, as I shall argue, have in some respects been misguided. Hitherto much of the debate over ontic vagueness and quantum theory has centered on the “indeterminate identity” construal of ontic vagueness, and whether the quantum phenomenon of entanglement produces particles whose identity is indeterminate. I argue that this way (...) of framing the debate is mistaken. A more thorough examination of quantum theory and the phenomenon of entanglement reveals that quantum mechanics is best interpreted as supporting what I call the “vague property” construal of ontic vagueness, where vague properties are understood in terms of determinable properties without the corresponding determinates. (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)

What is called ``orthodox'' quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions --- the projection postulate and the eigenvalue-eigenvector link --- that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements and that the eigenvalue-eigenvector link implies that virtually all interesting properties are (...) maximally indefinite pretty much always. I present an alternative way of conceptualising quantum mechanics that does a better job of representing quantum mechanics as it is actually used, and in particular that eliminates use of either the projection postulate or the eigenvalue-eigenvector link, and I reformulate the measurement problem within this new presentation of orthodoxy. (shrink)

A recent theory of metaphysical indeterminacy says that metaphysical indeterminacy is multiple actuality: there is metaphysical indeterminacy when there are many 'complete precisifications of reality'. But it is possible for there to be metaphysical indeterminacy even when it is impossible to precisify reality completely. The orthodox interpretation of quantum mechanics illustrates this possibility. So this theory of metaphysical indeterminacy is not adequate.

This is a prize-winning study of an area of physics not previously explored by philosophy: gauge theory. Gauge theories have provided our most successful representations of the fundamental forces of nature. But how do such representations work? Healey defends an original answer to this question.

Although Bohr's reply to the EPR argument is supposed to be a watershed moment in the development of his philosophy of quantum theory, it is difficult to find a clear statement of the reply's philosophical point. Moreover, some have claimed that the point is simply that Bohr is a radical positivist. In this paper, we show that such claims are unfounded. In particular, we give a mathematically rigorous reconstruction of Bohr's reply to the _original_ EPR argument that clarifies its logical (...) structure, and which shows that it does not rest on questionable philosophical assumptions. Rather, Bohr's reply is dictated by his commitment to provide "classical" and "objective" descriptions of experimental phenomena. (shrink)