On Kinds of Indiscernibility in Logic and Metaphysics

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. (These definitions are based on definitions made by Quine and Saunders.) 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 (which will come in two versions), and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity (i.e. non-identity) weaker than what we will call individuality (being an individual): 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.Comment: 55 pages, 21 figures. Forthcoming, after an Appendectomy, in the British Journal for the Philosophy of Scienc

Estruturas lógico-quânticas para partículas semelhantes

In this work we discuss logical structures related to indistinguishable (or similar) particles. Most of the framework used to develop these structures was presented in previous works. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of similar particles, and draw possible philosophical implications. We also review some proposals available in the literature which may be considered within the framework of the quantum logical tradition regarding the problem of indistinguishability. Besides these discussions and constructions, we advance novel technical results, namely, a latticetheoretical structure for identical particles for the finite dimensional case. This approach has not been present in the scarce literature on quantum logic and similar particles.Neste trabalho discutimos estruturas lógicas relacionadas a partículas indistinguíveis (ou semelhantes). A maior parte do quadro teórico usado para desenvolver essas estruturas foi apresentada em trabalhos anteriores. Usamos essas estruturas e construções para discutir possíveis ontologias para partículas idênticas. Em outras palavras, usamos essas estruturas para caracterizar a estrutura lógica de sistemas quânticos para o caso de partículas semelhantes, e traçamos possíveis implicações filosóficas. Também examinamos algumas propostas disponíveis na literatura que podem ser consideradas dentro do quadro da tradição da lógica quântica concernentes ao problema da indistinguibilidade. Além dessas discussões e construções, apresentamos novos resultados técnicos relativos à estrutura da teoria de reticulado para partículas idênticas, no caso de dimensão finita. Esta abordagem não está presente na pequena literatura sobre lógica quântica e partículas semelhantes.Fil: Holik, Federico Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Gomez, Ignacio Sebastián. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaFil: Krause, Décio. Universidade Federal de Santa Catarina; Brasi

Does weak discernibility determine metaphysics?

Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argue that, contrary to part of current literature, it does not provide for a fully naturalistic determination of metaphysics. Underdetermination of the metaphysics still plagues the way of the naturalist

Does weak discernibility determine metaphysics?

Dos entidades son débilmente discernibles cuando entre ellas se mantiene una relación irreflexiva y simétrica. En la actualidad no se discute que la discernibilidad débil se da en la mecánica cuántica. Las consecuencias ontológicas de la discernibilidad débil, sin embargo, no están muy claras. Parte de la literatura al respecto parece implicar que la discernibilidad débil apunta, en la mecánica cuántica, a una metafísica determinada. En este artículo analizaremos la contribución metafísica de la discernibilidad débil a la mecánica cuántica y argumentaremos que, al contrario de lo que se sostiene en parte de la literatura actual, la discernibilidad débil no proporciona una determinación completamente.; Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argue that, contrary to part of current literature, it does not provide for a fully naturalistic determination of metaphysics. Underdetermination of the metaphysics still plagues the way of the naturalist