Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are (...) false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles, and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity weaker than what we will call individuality : two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory. (shrink)
The symmetries of a physical theory are often associated with two things: conservation laws and representational redundancies. But how can a physical theory's symmetries give rise to interesting conservation laws, if symmetries are transformations that correspond to no genuine physical difference? In this article, I argue for a disambiguation in the notion of symmetry. The central distinction is between what I call "analytic" and "synthetic" symmetries, so called because of an analogy with analytic and synthetic propositions. "Analytic" symmetries are the (...) turning of idle wheels in a theory's formalism, and correspond to no physical change; "synthetic" symmetries cover all the rest. I argue that analytic symmetries are distinguished because they act as fixed points or constraints in any interpretation of a theory, and as such are akin to Poincaré's conventions or Reichenbach's 'axioms of co-ordination', or 'relativized constitutive a priori principles'. (shrink)
This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: (...) in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (shrink)
In a series of recent papers, Simon Saunders, Fred Muller, and Michael Seevinck have collectively argued, against the folklore, that some nontrivial version of Leibniz’s principle of the identity of indiscernibles is upheld in quantum mechanics. They argue that all particles—fermions, paraparticles, anyons, even bosons—may be weakly discerned by some physical relation. Here I show that their arguments make illegitimate appeal to nonsymmetric, that is, permutation-noninvariant, quantities and that therefore their conclusions do not go through. However, I show that alternative, (...) symmetric quantities may be found to do the required work. I conclude that the Saunders-Muller-Seevinck heterodoxy can be saved. (shrink)
How best to think about quantum systems under permutation invariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutation invariance reflects a representational redundancy in the formalism. Under such a proposal, it is far from obvious how a constituent quantum system is represented. Consequently, it is also far from obvious how quantum systems compose to form assemblies, i.e. what is the formal (...) structure of their relations of parthood, overlap and fusion. In this paper, I explore one proposal for the case of fermions and their assemblies. According to this proposal, fermionic assemblies which are not entangled—in some heterodox, but natural sense of ‘entangled’—provide a prima facie counterexample to classical mereology. This result is puzzling; but, I argue, no more intolerable than any other available interpretative option. (shrink)
In this article I expound an understanding of the quantum mechanics of so-called “indistinguishable” systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This understand- ing has heterodox consequences for the understanding of the states of constituent systems in an assembly and for the notion of entanglement. It corrects widespread misconceptions about the inter-theoretic relations between quantum mechanics and both classical particle mechanics and quantum field theory. The most striking (...) of the heterodox consequences are: that fermionic states ought not always to be considered entangled; it is possible for two fermions or two bosons to be discerned using purely monadic quantities; and that fermions may always be so discerned. (shrink)
The purpose of this short article is to build on the work of Ghirardi, Marinatto and Weber and Ladyman, Linnebo and Bigaj, in supporting a redefinition of en- tanglement for “indistinguishable” systems, particularly fermions. According to the proposal, non-separability of the joint state is insufficient for entanglement. The re- definition is justified by its physical significance, as enshrined in three biconditionals whose analogues hold of “distinguishable” systems.
The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives any of the three hypotheses any (...) non-zero credence has strong reasons to reject Causal Decision Theory. However, we concede that no version of the Many Worlds Interpretation (Vaidman, in Zalta, E.N. (ed.), Stanford Encyclopaedia of Philosophy 2014) gives rise to the conflicts that we point out. (shrink)