Quasi-set theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as a non-classical logic (a non-reflexive logic). In this paper we revise and correct some aspects of quasi-set theory as presented in [12], so as to avoid some misunderstandings and possible misinterpretations about the results achieved by the theory. Some further ideas with regard to quantum field theory are also (...) advanced in this paper. (shrink)

This paper discusses the issue of the identity and individuality (or lack thereof) of quantum mechanical particles. It first reconstructs, on the basis of the extant literature, a general argument in favour of the conclusion that such particles are not individual objects. Then, it critically assesses each one of the argument’s premises. The upshot is that, in fact, there is no compelling reason for believing that quantum particles are not individual objects.

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The (...) chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context. (shrink)

What is it that determines the identity of an entity? Processualism is a theoretical perspective that offers a startling answer to this question. The identity of an entity—whether human or nonhuman, animate or inanimate—depends on the set of relations in which this entity is located. And as the sets of relations are several, so are the identities that an entity can take. This article discusses this conclusion by integrating processual accounts from different fields of inquiry, such as relativistic physics and (...) actor-network theory. According to a processual interpretation of relativistic physics, speaking of states of things is but an abstraction. For states come from the introduction of arbitrary breakups of the spacetime continuum. Therefore, processes precede states, a process being a set of relations that confers identity on a physical state. According to a processual interpretation of actor-network theory, the same holds true for actors. Again, speaking of states of actors is but an abstraction. For what really acts is heterogeneous networks. When one describes actors in isolation, one is neglecting a whole array of relations with other actors whereby that actor can act or is made to act in such and such a way. These strands of processualism come to the same conclusion as to the identity of entities. These are not characterized by individuality but by individuality: they can be differently individuated according to the set of relations one is able to take into account. The main methodological consequence is that, if one intends to describe what an entity is, knowledge of this entity—whether human or nonhuman, animate or inanimate—should be based on progressively less narrow localizations and mappings of the relations it has to other entities. (shrink)

Paraconsistent logics are logics that can be used to base inconsistent but non-trivial systems. In paraconsistent set theories, we can quan- tify over sets that in standard set theories, if consistent, would lead to contradictions, such as the Russell set, R = fx : x =2 xg. Quasi-set theories are mathematical systems built for dealing with collections of indiscernible elements. The basic motivation for the development of quasi-set theories came from quantum physics, where indiscernible entities need to be considered. Usually, (...) the way of dealing with indiscernible objects within clas- sical logic and mathematics is by restricting them to certain structures, in a way so that the relations and functions of the structure are not sufficient to individuate the objects; in other words, such structures are not rigid. In quantum physics, this idea appears when symmetry conditions are introduced, say by choosing symmetric and anti-symmetric functions in the relevant Hilbert spaces. But in standard mathematics, such as that built in Zermelo-Fraenkel set theory, any structure can be extended to a rigid structure. That means that, although we can deal with certain objects as they were indiscernible, we realize that from out- side of these structures these objects are no more indiscernible, for they can be individualized in the extended rigid structures: ZF is a theory of individuals, distinguishable objects. In quasi-set theory, it seems that there are structures that cannot be extended to rigid ones, so it seems that they provide a natural mathematical framework for expressing quantum facts without certain symmetry suppositions. There may be situations, however, in which we may need to deal with inconsistent bits of infor- mation in a quantum context, even if these informations are concerned with ways of speech. Furthermore, some authors think that superposi- tions may be understood in terms of paraconsistent logics, and even the notion of complementarity was already treated by such a means. This is, apparently, a nice motivation to try to merge these two frameworks. In this work, we develop the technical details, by basing our quasi-set theory in the paraconsistent system C1. We also elaborate a new hierarchy of paraconsistent calculi, the paraconsistent calculi with indiscernibility. For the finalities of this work, some philosophical questions are outlined, but this topic is left to a future work. (shrink)

The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s11016-010-9463-7 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Castellani, Department of Philosophy, University of Florence, Via Bolognese 52, 50139 (...) Florence, Italy Laura Crosilla, Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT UK Steven French, Department of Philosophy, University of Leeds, Leeds, UK Décio Krause, Department of Philosophy, Federal University of Santa Catarina, 88040-900 Campus Trindade, Florianópolis, SC Brazil Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796. (shrink)

The contextual dimension of ren or li is celebrated in English studies of Confucian ethics. However, it often gives way to the issue of individual practice in studies concerning the relationship be...

Process ontology is making deep inroads into the hard sciences. For it offers a workable understanding of dynamic phenomena which sits well with inquiries that problematize the traditional conception of self-standing, definite, independent objects as the basic stuff of the universe. Process-based approaches are claimed by their advocates to yield better ontological descriptions of various domains of physical reality in which dynamical, indefinite activities are prior to definite “things” or “states of things”. However, if applied to physics, a main problem (...) comes up: the notion itself of process appears to pivot on a conception of evolution through time that is at variance with relativistic physics. Against this worry, this article advances a conception of process that can be reconciled with general relativity. It claims that, within timeless physical frameworks, a process should not be conceived as activities evolving through time. Rather, processes concern the identity that entities obtain within the broader sets of relations in which they stand. To make this case, the article homes in on one of the physical approaches that most resolutely removes time from the basic features of reality, that is, canonical quantum gravity. As a case in point, it addresses Carlo Rovelli’s Evolving Constant approach as a physical paradigm that resolutely rejects time as an absolute parameter and recasts processualism as an inquiry into how physical systems affect one another. (shrink)

The feasibility of establishing a proper notion of a distinguishable object in the context of the de Broglie–Bohm approach to quantum mechanics seems, at first sight, uncontroversial by virtue of the fact that this theory can supposedly be interpreted in terms of a system of objective particles distinguished by individuating properties. However, after conducting a critical revision and evaluation of this trivial interpretation, and having assessed different alternatives that have been proposed in recent literature, I argue that within this theory (...) an appropriate notion of a distinguishable object can only be articulated by means of the following theoretical and metaphysical strategies: firstly, by appealing to a pre-existing, symmetrized Bohmian framework that is empirically indistinguishable but physically distinguishable from the standard Bohmian formulation; and secondly, by suggesting a different interpretation of this symmetrized formulation based upon a relational notion of the distinguishable object that can only be appropriately conceived from a structuralist point of view. (shrink)

In this basically expository paper we discuss the role oflogic and mathematics in researches concerning the ontology of scientific theories, and we consider the particular case of quantum mechanics. We argue that systems of logic in general, and classical logic in particular, may contribute substantially with the ontology of any theory that has this logic in its base. In the case of quantum mechanics, however, from the point of view of philosophical discussions conceming identity and individuality, those contributions may not (...) be welcome for a specific interpretation, and an altemative system of logic perhaps could be used instead of a classical system. In this sense, we argue that the logic and ontology of a scientific theory may be seen as mutually inftuencing each other. On the one hand, logic contributes to shape the general features of the ontology of a theory; on the other hand, the theory also puts constraints on the possible understanding of ontology and, respectively, on possible systems of logic that may be the underlying logic ofthe theory. (shrink)

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on (...) a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. (shrink)

In the philosophy of science, identity over time emerges as a central concern both as an ontological category in the interpretation of physical theories, and as an epistemological problem concerning the conditions of possibility of knowledge. In Reichenbach and subsequent writers on the problem of indistinguishable quantum particles we see the return of a contrast between Leibniz and Aquinas on the subject of individuation. The possibility of rejecting the principle of the identity of indiscernibles has certain logical difficulties, leading us (...) inexorably from ontology into epistemology. For the epistemological problem we attend to the differences that emerged between the (neo-)Kantian and logical empiricist traditions, also saliently displayed in Reichenbach's writings. After examining the contrast between Kant's and Leibniz's conceptions of empirical knowledge, specifically with respect to the irreducibility of spatiotemporal determinations, we explore an application of a neo-Kantian view to the same problem of indistinguishable quantum particles. (shrink)

The aim of this paper is to argue that some objections raised by Jantzen (Synthese, 2010 ) against the separation of the concepts of ‘counting’ and ‘identity’ are misled. We present a definition of counting in the context of quasi-set theory requiring neither the labeling nor the identity and individuality of the counted entities. We argue that, contrary to what Jantzen poses, there are no problems with the technical development of this kind of definition. As a result of being able (...) to keep counting and identity apart for those entities, we briefly suggest that one venerable tradition concerning the nature of quantum particles may be consistently held. According to that tradition, known as the Received View on particles non-individuality, quantum particles may be seen as entities having both features: (i) identity and individuality do not apply to them, (ii) they may be gathered in collections comprising a plurality of them. (shrink)

The concept of natural kind is center stage in the debates about scientific realism. Champions of scientific realism such as Richard Boyd hold that our most developed scientific theories allow us to “cut the world at its joints” (Boyd, 1981, 1984, 1991). In the long run we can disclose natural kinds as nature made them, though as science progresses improvements in theory allow us to revise the extension of natural kind terms.