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)
A investigação de um domínio amplo da realidade, como a evolução dosseres vivos, pode dar origem a diferentes “teorias”, cada uma consoantecom uma particular perspectiva que se considere. Para que se proceda auma análise detalhada dos pressupostos e conceitos que baseiam umadeterminada visão, o método axiomático parece ser a melhor das opções.Neste artigo, são discutidas algumas teorias da biologia evolutiva de umponto de vista axiomático, mostrando-se de que forma se pode apresentarum “predicado de Suppes” para a teoria sintética da evolução, (...) comodetalhado em outro local . Estaformulação é utilizada, dentre outras coisas, para se discutir a noção deaptidão darwiniana, bem como para explorar as relações entre a teoriadarwiniana da seleção natural e a genética de populações.The investigation of a wide field of knowledge, as evolution of living beings,may originate different “theories”, each one acting as a particularperspective we have about the domain. In order to proceed a philosophicalanalysis of the underlying assumptions of a particular view, it seems thatthe use of the axiomatic method is still the better way. Here, we discuss some theories of evolutionary biology from an axiomatic point of view, bymeans of a Suppes predicate for the synthetic theory of evolution, alreadydetailed in MAGALHÃES and KRAUSE . This formulation is hereused, among other things, to deal with the concept of Darwinian fitness, soas to explore the relationships between Darwinian theory and populationgenetics. (shrink)
Contents: I. Philosophical and Methodological Problems of the Process of Cognition. Jenny WADE: Idealizing the Cartesian-Newtonian Paradigm as Reality: The Impact of New-Paradigm Physics on Psychological Theory. Elzbieta HORNOWSKA: Operationalization of Psychological Magnitudes. Assumptions-Structure-Consequences. Thomas BACHMANN: Creating Analogies - on Aspects of the Mapping Process between Knowledge Domains. Harald SCHAUB: Modelling Action Regulation. II. The Structure of Ideal Learning Process. Stellan OHLSON and James J. JEWETT: Ideal Adaptive Agents and the Learning Curve. Bodo KRAUSE: Towards a Theory of Cognitive (...) Learning. Bodo KRAUSE and Ulrich GAUGER: Learning and Use of Invariances: Experiments and Network Simulation. Manuela FRIEDRICH: "Reaction Time" in the Neural Network Module ART 1. III. Control Processes in Memory. Joseph TZELGOV, Vered YEHENE and Moshe NAVEH-BENJAMIN: From Memory to Automaticity and Vice Versa: On the Relations between Memory and Automaticity. H. HAGENDORF, S. FISCHER and B. SÁ: The Function of Working Memory in Coordination of Mental Transformations. IV. Common Sense and Idealization. Leszek NOWAK: On Common-Sense and -Idealization. Izabella NOWAKOWA: On the Problem of Induction. Towards an Idealizational Paraphrase. (shrink)
Denounced by neighbors and scrutinized by demonologists, the early modern French witch also confessed, self-identified as a witch and as the author of horrific deeds. What led her to this point? Despair, solitude, perhaps even physical pain, but most decisively, demonology's two-pronged prosecutorial and truth-seeking confessional apparatus. This book examines the systematic and well-oiled machinery that served to extract, interpret, and disseminate witches' confessions in early modern France. For the demonologist, confession was the only way to find out the truth (...) about the clandestine activities of witches. For the witch, however, trial confessions opened new horizons of selfhood. In this book, Virginia Krause unravels the threads that wove together the demonologist's will to know and the witch's subjectivity. By examining textual and visual evidence, Krause shows how confession not only generated demonological theory but also brought forth a specific kind of self, which we now recognize as the modern subject. (shrink)
According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a parallel between van Fraassen’s (...) modal interpretation of quantum mechanics and Skolem’s relativism regarding set-theoretic concepts, we introduce a distinction between relative and absolute concepts in the context of the models of a scientific theory. And we discuss the significance of that distinction. Finally, by focusing on contemporary particle physics, we raise the question: since there is no general accepted unification of the parts of the standard model (namely, QED and QCD), we have no theory, in the usual sense of the term. This poses a difficulty: if there is no theory, how can we speak of its models? What are the latter models of? We conclude by noting that it is unclear that the semantic view can be applied to contemporary physical theories. (shrink)
Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build (...) a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)
We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist.We analyze that (...) claim by employing the traditional square of opposition.We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them. (shrink)
The concept of non-domination is an important contribution to the study of freedom but it does not comprehend the whole of freedom. Insofar as domination requires a conscious capacity for control on the part of the dominant party, it fails to capture important threats to individual freedom that permeate many contemporary liberal democracies today. Much of the racism, sexism and other cultural biases that currently constrain the life-chances of members of subordinate groups in the USA are largely unconscious and unintentional, (...) and they do not always involve control. Although they constitute real barriers to freedom, these forms of influence are not accurately characterized as domination, and they will require different mechanisms to overcome them. To achieve the more capacious freedoms that liberal democracy promises, we will need to go beyond non-domination and to come to terms with the non-sovereign, socially distributed character of human agency. (shrink)
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 , 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)
It has been suggested that quantum particles are genuinelyvague objects (Lowe 1994a). The present work explores thissuggestion in terms of the various metaphysical packages that areavailable for describing such particles. The formal frameworksunderpinning such packages are outlined and issues of identityand reference are considered from this overall perspective. Indoing so we hope to illuminate the diverse ways in whichvagueness can arise in the quantum context.
El artículo analiza el rol que cumple la confianza en la construcción de la realidad social, argumentando que constituye uno de sus componentes esenciales. Lo es porque hace posible el nacimiento, permanencia y reconocimiento colectivo de las instituciones, así como su iteración y organización en subsistemas.
In this paper we present an overview of Professor Newton C. A. da Costa’s work in logic, emphasizing the main results obtained by him in the several areas of his research activity. The text furnish a detailed bibliographic reference of his works, which are listed in the last section.
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)
Following J.-Y.Béziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in . Our conclusion was that such states are contraries, contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties. In this chapter we bring the issue once again into the center of the (...) stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible. (shrink)
We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by non-relativistic quantum mechanics. There are two central ingredients in the proposal: in the case of non-relativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique principle of individuation. We also hold that even when taken in (...) a loose sense, naturalism does not provide any sense in which one could hold that quantum mechanics endorses primitive individuality over non-individuality. Rather, we argue that non-individuality should be preferred based on the grounds that such a view fits better the claims of the theory. (shrink)
In this paper we discuss some questions proposed by Prof. Newton da Costa on the foundations of quasi-set theory. His main doubts concern the possibility of a reasonable semantical understanding of the theory, mainly due to the fact that identity and difference do not apply to some entities of the theory’s intended domain of discourse. According to him, the quantifiers employed in the theory, when understood in the usual way, rely on the assumption that identity applies to all entities in (...) the domain of discourse. Inspired by his provocation, we suggest that, using some ideas presented by da Costa himself in his seminars at UFSC and by one of us in some papers, these difficulties can be overcome both on a formal level and on an informal level, showing how quantification over items for which identity does not make sense can be understood without presupposing a semantics based on a ‘classical’ set theory. (shrink)
The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.
En este trabajo examinamos el tópico de la responsabilidad en el derecho penal internacional a la luz de la filosofía de John Searle, y del fallo dictado por la Corte Penal Internacional en el caso de Thomas Lubanga. En el primer acápite analizamos la declaración de responsabilidad penal en función de la teoría de actos de habla de Austin y de Searle, tratándola como un acto ilocucionario cuyo significado es dependiente de un marco institucional específico. Luego, en el segundo acápite, (...) mostramos de qué forma tal marco puede reconstruirse como un ejemplo paradigmático de la realidad social construida descrita por Searle, especialmente en virtud del nexo entre mente, lenguaje y sociedad. A nuestro juicio, los conceptos de intencionalidad colectiva, atribución de funciones de estatus y poderes deónticos son fundamentales para entender tal nexo. En efecto, tal como argumentamos en la tercera sección, los sistemas de poderes deónticos asociados al derecho internacional no solo explican la aparición de Tribunales penales internacionales, como la Corte Penal Internacional, sino además el carácter imprescriptible de los crímenes de lesa humanidad. Los acuerdos internacionales que promueven y protegen los derechos humanos, y que tratan la imprescriptibilidad de aquellos crímenes, son objeto de análisis en la sección final, en donde exponemos algunas reflexiones finales a partir del caso Lubanga. (shrink)
This paper develops a formal framework to model a process in which the formation of individual opinions is embedded in a deliberative exchange with others. The paper opts for a low-resolution modeling approach and abstracts away from most of the details of the social-epistemic process. Taking a bird's eye view allows us to analyze the chances for the truth to be found and broadly accepted under conditions of cognitive division of labour combined with a social exchange process. Cognitive division of (...) labour means that only some individuals are active truth seekers, possibly with different capacities. Both mathematical tools and computer simulations are used to investigate the model. As an analytical result, the Funnel Theorem states that under rather weak conditions on the social process, a consensus on the truth will be reached if all individuals possess an arbitrarily small capacity to go for the truth. The Leading the pack Theorem states that under certain conditions even a single truth seeker may lead all individuals to the truth. Systematic simulations analyze how close agents can get to the truth depending upon the frequency of truth seekers, their capacities as truth seekers, the position of the truth (more to the extreme or more in the centre of an opinion space), and the willingness to take into account the opinions of others when exchanging and updating opinions. (shrink)
The ‘ontic’ form of structural realism , roughly speaking, admits a complete elimination of the objects in the discourse of scientific theories, leaving us with structures only. As put by the defenders of such a claim, the idea is that all there is are structures and, if the relevant structures are to be set-theoretical constructs , as it has also been claimed, then the relations which appear in such structures should be taken to be ‘relations without the relata’. As far (...) as we know, there is not a definition of structure in standard mathematics which fits their intuitions, and even category theory seems not to correspond adequately the OSR claims. Since OSR is also linked with the semantic approach to theories, the structures to be dealt with are taken to be set-theoretical constructs. But these are ‘relational’ structures where the involved relations are built from basic objects , and so no complete elimination of the relata is possible, although it would be adequate for characterizing OSR. In this paper we present a definition of a kind of relation that does not depend on the particular objects being related in the sense that the ‘relation’ continues to hold even if the relata are exchanged by suitable objects. Although there is not a ‘complete’ elimination of relata, our definition might be viewed as an alternative way of finding adequate mathematical ‘set-theoretical’ frameworks for describing at least some of the intuitions regarding OSR within a ‘set-theoretical’ framework. (shrink)
Recently, in the debate about the ontology of quantum mechanics some authors have defended the view that quantum particles are individuals in a primitive sense, so that individuality should be preferred over non-individuality (the alternative option). Primitive individuality involves two main claims: (1) every item is identical with itself and (2) it is distinct from every other item. Non-relativistic quantum mechanics is said to provide positive evidence for that position, since in every situation comprising multiple particles there is a well-defined (...) number of them to begin with, and so they must be distinct from each other. We argue that the link between a well-defined number of items and the relation of identity that is being claimed to hold is not imposed by quantum mechanics, but rather by a metaphysical view. Formal evidence is advanced in favor of the thesis that counting may be performed for items without identity (non-individuals), so that quantum mechanics needs not be viewed as endorsing an ontology of individuals. (shrink)
Lowe has recently argued that quantum particles offer examples of vague objects. While accepting the premise of the argument that such particles can be regarded as individuals, we point out that there is a lacuna here, to be filled by a detailed analysis of the nature of the entangled states which they enter into. We then elaborate the alternative view, according to which such particles should be regarded as non- individuals' and situate it in the context of recent developments of (...) a logic of non- individuality. Our conclusion is that it is here that one encounters genuine ontic vagueness. (shrink)
We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have (...) no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)
H. Post's conception of quantal particles as non-individuals is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.
A better appreciation of the material, distributed quality of human agency can illuminate subtle dynamics of domination and oppression and reveal resources for potentially liberatory political action. Materialist accounts of agency nevertheless pose challenges to the notion of personal responsibility that is so crucial to political obligation and democratic citizenship. To guard against this danger, we need to sustain the close connection between agency and a sense of selfhood that is individuated, reflexive, and responsive to norms. Yet we should acknowledge (...) that reflexive selfhood is not the whole of individual agency for the sources of agency extend beyond the individual herself. We also need to recognize the ways that both reflexivity and norm-responsiveness are themselves embodied capacities. When properly conceived, a materialist view of agency can increase awareness of our oftenunwitting contributions to systematic inequalities of power and extend our political responsibilities in emancipatory directions, thus holding great promise for democratic life. (shrink)
In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as non-individuals, then there would be strong reasons (...) to ask for a different mathematical framework for describing the structures that would be the models of the corresponding theory. In departing from the standard frameworks (those worked on within standard mathematics), we hope to bring to the scene, within the scope of the semantic approach, the importance of paying attention to some fundamental concepts usually only superficially touched by philosophers of science (if touched). (shrink)
In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate (...) in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal , for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science. (shrink)
In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a non-classical logic. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize individuals, and then explain in what sense entanglement is a concept which can be applied to individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that this concept is of a fundamental importance, (...) we mention the ‘traditional’ theory of identity of standard logic and mathematics, which underly the basic formalism of quantum theory. Then we propose to call the Problem of Identity the question whether identity of objects can be justified, and under what conditions. As in the Hume’s celebrated Problem of Induction, we conclude that the attribution of transtemporal identity to an object has no logic justification, and must be considered as a metaphysical hypothesis. Numerical identity is also put aside for similar reasons. Then we guess that identity is just an useful concept, but which in certain fields, mainly in the quantum realm, could be substituted by a weaker concept of indiscernibility. This assumption motivates us to look for an interpretation of quantum mechanics based on a non-classical logic, termed non-reflexive, and the corresponding mechanics is called non-reflexive quantum mechanics. (shrink)
The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice (J-lattice), which can be modeled by an algebraic structure built in quasi-set theory Q. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that 'naturally' arises is non distributive.