Skip to main content

Décio Krause

Followers

1,064

Following

38

Co-authors

7

Public Views

Retired as Full Professor, Department of Philosophy, Federal University of Santa Catarina, Brazil. Retired as Full Professor, Department of Mathematics, Federal University of Paraná. Professor at the Graduate Program in Logic and Metaphysics, Department of Philosophy, Federal University of Rio de Janeiro.
Supervisors: Newton C. A. da Costa

less

franciska pramuji lestari

Utrecht University

Jonas R B Arenhart

Universidade Federal de Santa Catarina - UFSC (Federal University of Santa Catarina)

Raimundo Fernández Mouján

Universidad Diego Portales

Matteo Morganti

Università Roma Tre

Juan Pablo Jorge

Universidad de Buenos Aires

École Normale Supérieure

University of Notre Dame

InterestsView All (21)

Uploads

Books by Décio Krause

A obra de Newton C. A. da Costa em lógica

In this paper we present an overview of Professor Newton C. A. da Costa's work inlogic, emphasizi... more

Conceptual Clarifications: Tributes to Patrick Suppes (1922-2014)

by Décio Krause and jean-yves beziau

This is a collection of papers written by people who have worked with Patrick Suppes or have been... more

Brazilian Studies in Philosophy and History of Science: An account of recent works.

This is a collection of papers written by Brazilian philosophers of science. The aim of the book ... more This is a collection of papers written by Brazilian philosophers of science. The aim of the book is to provide a general look about what kind of problems have occupied philosophers of science in Brasil. Of course the book doesn't cover all works that have been developed. but it provides an idea of the subject.

Álgebra Linear com um pouco de Mecânica Quântica

Trata-se de um livro introdutório, destinado principalmente a alunos de filosofia mas que pode se... more

The Logical Foundations of Scientific Theories: Languages, Structures, and Models

Tópicos em Ontologia Analítica

This is a book for a general audience. It starts by revising the main ideas related to ontology i... more

Introdução aos Fundamentos Axiomáticos da Ciência

Prefácio minação 'analítica' segue uma tendência recente (creio que dos anos 1980 para cá) de den... more Prefácio minação 'analítica' segue uma tendência recente (creio que dos anos 1980 para cá) de denominar de ontologia analítica e de metafísica analítica os estudos em ontologia e, mais geralmente, em metafísica, de um ponto de vista 'analítico'. Temas como a ontologia formal de Husserl, as ideias de filósofos como Heiddegger e outros não serão tocadas por dois motivos básicos: porque estenderiam demais o presente volume, não obstante a importância desses autores, e pela minha falta de competência para me atrever a escrever sobre esses filósofos em um livro. Assim, proponho algo mais modesto e, na Introdução, tento delinear este 'viés analítico' um mínimo necessário para que o título deste livro fique justificado.

Identity in Physics: A Historical, Philosophical and Formal Analysis

Papers by Décio Krause

On the Received View Versus the Alternative View Controversy About Quantum (Non)individuality

Foundations of Science, 2025

Some philosophers of physics have addressed criticisms of the so-called Received View (RV) of non... more Some philosophers of physics have addressed criticisms of the so-called Received View (RV) of non-individual quantum objects, also called the orthodox view. Dennis Dieks made a very good resume of these criticisms in Dieks (in: Non-reflexive logics, non-individuals, and the philosophy of quantum mechanics: essays in honor of the philosophy of Décio Krause, Synthese Library, Springer, 2023) and Bigaj (Identity and indiscernibility in quantum mechanics. New directions in the philosophy of science, Palgrave Macmillan, 2022) has a more detailed account. In considering (mainly) these works and with some additional mentions, I hope to dissipate some misunderstandings about the RV and clarify what is happening with such a view. According to Dieks, the RV doesn't fit the practice of physics since, in some situations, the physicist assumes that quantum objects can be treated individually, imitating standard objects (individuals) of classical physics. Dieks also proposes an Alternative View (AV), generally called the heterodox view, which would give a view of the fundamental ontology of quantum physics and which would be more by the way physicists usually proceed. I think that the AV cannot be viewed as the fundamental ontological theory despite being suitable for practical purposes. Furthermore, I think that it does not conflate the RV but is complementary to it, substituting it when quantum objects are sufficiently apart and can be treated in conformity with the classical way. From my point of view, in the practice of physics, one can adopt AV. Still, the RV is more adequate when we are looking for logical and foundational analyses, at least when the supposed metaphysics comprises non-individuals. Keywords Identity • Individuality • Non-individuality • Quantum objects • Received view • Alternative view • Heterodox view If you wish to converse with me, define your terms. Voltaire. Logic [and we could say scientific theories] is founded on a metaphysical conception of the world. Partially supported by CNPq.

THE UNDERLYING LOGIC IS MANDATORY ALSO IN DISCUSSING THE PHILOSOPHY OF QUANTUM PHYSICS

Principia, 2024

Any scientific theory (here we consider physical theories only) has an underlying logic, even if ... more Any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not totally made explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory's principles, mainly when described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory's mathematical and logical concepts. We argue that no physical theory and no philosophical discussion based on the theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just 'relational' and that they cannot be absolutely identified by a monadic property, are fallacious once one remains within a 'standard' logico-mathematical framework, grounded on classical logic. We also discuss the (to us) unjustifiable claim that some properties (such as those that came from logic) would be 'illegitimate' for discerning these entities. Thus, this paper may interest logicians, physicists, and philosophers.

On the Received View vs. the Alternative View controversy about quantum (non)individuality

Preprint, 2024

Some philosophers of physics have addressed criticisms of the socalled Received View (RV) of non-... more Some philosophers of physics have addressed criticisms of the socalled Received View (RV) of non-individual quantum objects, also called the orthodox view. Dennis Dieks made a very good resume of these criticisms in [14] and Tomasz Bigaj in [5] has a more detailed account. In considering (mainly) these works and with some additional mentions, we hope to dissipate some misunderstandings about the RV and clarify what is happening with such a view. According to Dieks, the RV doesn't fit the practice of physics since in some situations the physicist assumes that quantum objects can be treated individually, imitating standard objects (individuals) of classical physics. Dieks also proposes an Alternative View (AV), generally called the heterodox view, which would give a view of the fundamental ontology of quantum physics and which would be more by the way physicists usually proceed. In my view, the AV cannot be viewed as the fundamental ontological theory despite being suitable for practical purposes. Furthermore, we think that it does not conflate the RV, but is complementary to it, substituting it when quantum objects are sufficiently apart and can be treated in conformity with the classical way. From our point of view, in the practice of physics, we can adopt AV. Still, the RV is more adequate when we are looking for logical and foundational analyses, at least when the supposed metaphysics comprises non-individuals.

On identity and quantification of quantum entities

Preprint, 2024

There has been an interesting and relevant discussion about quantification involving quantum enti... more There has been an interesting and relevant discussion about quantification involving quantum entities in the recent literature on the philosophy of quantum physics. It is stressed that the meaning of quantifiers can have a sense if and only if the quantified entities have well-defined identity conditions, so there would be difficulties in supposing that quantum entities can be completely indiscernible: how to quantify over them in such a situation? In this paper, we discuss this topic and argue that we really do quantification over such entities and what we need is a new understanding of the role of quantifiers at least when applied to the quantum domain.

Sobre una teoría `pura' de casi-conjuntos y su aplicación a una ontología cuántica de propiedades

by Décio Krause and Juan Pablo Jorge

Preprint, 2024

In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as ... more In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasi-set can have a cardinal, called its quasi-cardinal, but this is made so that, at least for the finite case, the quasi-cardinal is not an ordinal, and hence the indistinguishable elements of a quasi-set cannot be ordered. In the last sections, we show how the theory can be used to ground a quantum metaphysics of properties, which sees the quantum entities as bundles of properties, and we also introduce a new approach for the use of quantifiers in quantum physics.

Aspectos da indiscernibilidade quântica e da teoria de quase-conjuntos

Perspectivas

A indiscernibilidade das entidades quânticas é considerada como uma das noções centrais das teori... more A indiscernibilidade das entidades quânticas é considerada como uma das noções centrais das teorias quânticas. Neste artigo expositivo, são apontadas algumas das razões para essa alegada importância, bem como as ideias básicas de uma teoria matemática que permite tratar de coleções dessas entidades. O artigo inicia com uma posição geral do autor sobre a filosofia da ciência.

Observações sobre a neutralidade ontológica da matemática

Zenodo (CERN European Organization for Nuclear Research), Dec 1, 2003

Quantifying Over Indiscernibles

Axiomathes

One of the main criticisms of the theory of collections of indiscernible objects is that once we ... more One of the main criticisms of the theory of collections of indiscernible objects is that once we quantify over one of them, we are quantifying over all of them since they cannot be discerned from one another. In this way, we would call the collapse of quanti ers: 'There exists one x such as P ' would entail 'All x are P '. In this paper we argue that there are situations (quantum theory is the sample case) where we do refer to a certain quantum entity, saying that it has a certain property, even without committing all other indistinguishable entities with the considered property. Mathematically, within the realm of the theory of quasi-sets Q, we can give sense to this claim. We show that the above-mentioned 'collapse of quanti ers' depends on the interpretation of the quanti ers and on the mathematical background where they are ranging. In this way, we hope to strengthen the idea that quanti cation over indiscernibles, in particular in the quantum domain, does not conform with quanti cation in the standard sense of classical logic.

Models and Modeling in Science: the role of metamathematics

Principia: an international journal of epistemology

The use of models of scientific theories should not be done without qualifications about the math... more The use of models of scientific theories should not be done without qualifications about the mathematics being used to build the models. This looks obvious, at least for logicians, but generally, it is not to the philosopher of science. Thus, some details about this point seem useful for both. Since any quick revision in the literature shows that in most cases, mainly after the raising of the semantic approach (to scientific theories), the models are taken to be set-theoretical structures, in discussing the issue we shall be concerned more with set theories, the locus where the play is usually developed (yet sometimes unconsciously).

Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics

Nonreflexive quantum mechanics is a formulation of quantum theory based on a nonclassical logic t... more Nonreflexive quantum mechanics is a formulation of quantum theory based on a nonclassical logic termed nonreflexive logic (a.k.a. 'non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are individuals in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical (mainly metaphysical) motivations and consequences of it.

Do `classical' space and time provide identity to quantum particles?

arXiv: Quantum Physics, 2017

Non-relativistic quantum mechanics is grounded on ‘classical’ (Newtonian) space and time (NST). T... more Non-relativistic quantum mechanics is grounded on ‘classical’ (Newtonian) space and time (NST). The mathematical description of these concepts entails that any two spatially separated objects are necessarily different, which implies that they are discernible (in classical logic, identity is defined by means of indiscernibility) — we say that the space is T2, or "Hausdorff". But quantum systems, in the most interesting cases, some- times need to be taken as indiscernible, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an identity to them, which seems to be contra the physical situation. In this paper we discuss this topic for a case study (that of two potentially infinite wells) and con- clude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems...

O gato de Schrödinger não está vivo e morto antes da medição: sobre a interpretação dos resultados quânticos

Seminário Lógica no Avião, 2019

Muitos textos de divulgação que falam da mecânica quântica fazem referência ao "paradoxo" do gato... more Muitos textos de divulgação que falam da mecânica quântica fazem referência ao "paradoxo" do gato de Schrödinger, comentando que, antes da medida do estado do sistema, o gato encontra-se vivo e morto ao mesmo tempo. Outros dizeres referem-se a que uma partícula pode estar em dois (ou mais) lugares ao mesmo tempo, que ela passou por duas fendas simultaneamente, ou ainda que percorreu dois caminhos de uma só vez, e que "interferiu consigo mesma". Na opinião deste autor, tratam-se de exageros conceituais, que podem conduzir o leitor não especializado ao erro e a imaginar situações que nada têm a ver com a mecânica quântica propriamente dita, entendida do modo como o fazemos neste artigo. Este texto de caráter geral, sem mencionar essas fontes, tem a intenção de esclarecer ou ao menos de questionar esses e outros pontos polêmicos na fala comum sobre os resultados da mecânica quântica. "Cats seem to play an important role in physics." B. Kanitscheider (1992)

A obra de Newton C. A. da Costa em lógica

In this paper we present an overview of Professor Newton C. A. da Costa's work inlogic, emphasizi... more

Conceptual Clarifications: Tributes to Patrick Suppes (1922-2014)

by Décio Krause and jean-yves beziau

This is a collection of papers written by people who have worked with Patrick Suppes or have been... more

Brazilian Studies in Philosophy and History of Science: An account of recent works.

This is a collection of papers written by Brazilian philosophers of science. The aim of the book ... more This is a collection of papers written by Brazilian philosophers of science. The aim of the book is to provide a general look about what kind of problems have occupied philosophers of science in Brasil. Of course the book doesn't cover all works that have been developed. but it provides an idea of the subject.

Álgebra Linear com um pouco de Mecânica Quântica

Trata-se de um livro introdutório, destinado principalmente a alunos de filosofia mas que pode se... more

The Logical Foundations of Scientific Theories: Languages, Structures, and Models

Tópicos em Ontologia Analítica

This is a book for a general audience. It starts by revising the main ideas related to ontology i... more

Introdução aos Fundamentos Axiomáticos da Ciência

Prefácio minação 'analítica' segue uma tendência recente (creio que dos anos 1980 para cá) de den... more Prefácio minação 'analítica' segue uma tendência recente (creio que dos anos 1980 para cá) de denominar de ontologia analítica e de metafísica analítica os estudos em ontologia e, mais geralmente, em metafísica, de um ponto de vista 'analítico'. Temas como a ontologia formal de Husserl, as ideias de filósofos como Heiddegger e outros não serão tocadas por dois motivos básicos: porque estenderiam demais o presente volume, não obstante a importância desses autores, e pela minha falta de competência para me atrever a escrever sobre esses filósofos em um livro. Assim, proponho algo mais modesto e, na Introdução, tento delinear este 'viés analítico' um mínimo necessário para que o título deste livro fique justificado.

Identity in Physics: A Historical, Philosophical and Formal Analysis

On the Received View Versus the Alternative View Controversy About Quantum (Non)individuality

Foundations of Science, 2025

Some philosophers of physics have addressed criticisms of the so-called Received View (RV) of non... more Some philosophers of physics have addressed criticisms of the so-called Received View (RV) of non-individual quantum objects, also called the orthodox view. Dennis Dieks made a very good resume of these criticisms in Dieks (in: Non-reflexive logics, non-individuals, and the philosophy of quantum mechanics: essays in honor of the philosophy of Décio Krause, Synthese Library, Springer, 2023) and Bigaj (Identity and indiscernibility in quantum mechanics. New directions in the philosophy of science, Palgrave Macmillan, 2022) has a more detailed account. In considering (mainly) these works and with some additional mentions, I hope to dissipate some misunderstandings about the RV and clarify what is happening with such a view. According to Dieks, the RV doesn't fit the practice of physics since, in some situations, the physicist assumes that quantum objects can be treated individually, imitating standard objects (individuals) of classical physics. Dieks also proposes an Alternative View (AV), generally called the heterodox view, which would give a view of the fundamental ontology of quantum physics and which would be more by the way physicists usually proceed. I think that the AV cannot be viewed as the fundamental ontological theory despite being suitable for practical purposes. Furthermore, I think that it does not conflate the RV but is complementary to it, substituting it when quantum objects are sufficiently apart and can be treated in conformity with the classical way. From my point of view, in the practice of physics, one can adopt AV. Still, the RV is more adequate when we are looking for logical and foundational analyses, at least when the supposed metaphysics comprises non-individuals. Keywords Identity • Individuality • Non-individuality • Quantum objects • Received view • Alternative view • Heterodox view If you wish to converse with me, define your terms. Voltaire. Logic [and we could say scientific theories] is founded on a metaphysical conception of the world. Partially supported by CNPq.

THE UNDERLYING LOGIC IS MANDATORY ALSO IN DISCUSSING THE PHILOSOPHY OF QUANTUM PHYSICS

Principia, 2024

Any scientific theory (here we consider physical theories only) has an underlying logic, even if ... more Any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not totally made explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory's principles, mainly when described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory's mathematical and logical concepts. We argue that no physical theory and no philosophical discussion based on the theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just 'relational' and that they cannot be absolutely identified by a monadic property, are fallacious once one remains within a 'standard' logico-mathematical framework, grounded on classical logic. We also discuss the (to us) unjustifiable claim that some properties (such as those that came from logic) would be 'illegitimate' for discerning these entities. Thus, this paper may interest logicians, physicists, and philosophers.

On the Received View vs. the Alternative View controversy about quantum (non)individuality

Preprint, 2024

Some philosophers of physics have addressed criticisms of the socalled Received View (RV) of non-... more Some philosophers of physics have addressed criticisms of the socalled Received View (RV) of non-individual quantum objects, also called the orthodox view. Dennis Dieks made a very good resume of these criticisms in [14] and Tomasz Bigaj in [5] has a more detailed account. In considering (mainly) these works and with some additional mentions, we hope to dissipate some misunderstandings about the RV and clarify what is happening with such a view. According to Dieks, the RV doesn't fit the practice of physics since in some situations the physicist assumes that quantum objects can be treated individually, imitating standard objects (individuals) of classical physics. Dieks also proposes an Alternative View (AV), generally called the heterodox view, which would give a view of the fundamental ontology of quantum physics and which would be more by the way physicists usually proceed. In my view, the AV cannot be viewed as the fundamental ontological theory despite being suitable for practical purposes. Furthermore, we think that it does not conflate the RV, but is complementary to it, substituting it when quantum objects are sufficiently apart and can be treated in conformity with the classical way. From our point of view, in the practice of physics, we can adopt AV. Still, the RV is more adequate when we are looking for logical and foundational analyses, at least when the supposed metaphysics comprises non-individuals.

On identity and quantification of quantum entities

Preprint, 2024

There has been an interesting and relevant discussion about quantification involving quantum enti... more There has been an interesting and relevant discussion about quantification involving quantum entities in the recent literature on the philosophy of quantum physics. It is stressed that the meaning of quantifiers can have a sense if and only if the quantified entities have well-defined identity conditions, so there would be difficulties in supposing that quantum entities can be completely indiscernible: how to quantify over them in such a situation? In this paper, we discuss this topic and argue that we really do quantification over such entities and what we need is a new understanding of the role of quantifiers at least when applied to the quantum domain.

Sobre una teoría `pura' de casi-conjuntos y su aplicación a una ontología cuántica de propiedades

by Décio Krause and Juan Pablo Jorge

Preprint, 2024

In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as ... more In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasi-set can have a cardinal, called its quasi-cardinal, but this is made so that, at least for the finite case, the quasi-cardinal is not an ordinal, and hence the indistinguishable elements of a quasi-set cannot be ordered. In the last sections, we show how the theory can be used to ground a quantum metaphysics of properties, which sees the quantum entities as bundles of properties, and we also introduce a new approach for the use of quantifiers in quantum physics.

Aspectos da indiscernibilidade quântica e da teoria de quase-conjuntos

Perspectivas

A indiscernibilidade das entidades quânticas é considerada como uma das noções centrais das teori... more A indiscernibilidade das entidades quânticas é considerada como uma das noções centrais das teorias quânticas. Neste artigo expositivo, são apontadas algumas das razões para essa alegada importância, bem como as ideias básicas de uma teoria matemática que permite tratar de coleções dessas entidades. O artigo inicia com uma posição geral do autor sobre a filosofia da ciência.

Observações sobre a neutralidade ontológica da matemática

Zenodo (CERN European Organization for Nuclear Research), Dec 1, 2003

Quantifying Over Indiscernibles

Axiomathes

One of the main criticisms of the theory of collections of indiscernible objects is that once we ... more One of the main criticisms of the theory of collections of indiscernible objects is that once we quantify over one of them, we are quantifying over all of them since they cannot be discerned from one another. In this way, we would call the collapse of quanti ers: 'There exists one x such as P ' would entail 'All x are P '. In this paper we argue that there are situations (quantum theory is the sample case) where we do refer to a certain quantum entity, saying that it has a certain property, even without committing all other indistinguishable entities with the considered property. Mathematically, within the realm of the theory of quasi-sets Q, we can give sense to this claim. We show that the above-mentioned 'collapse of quanti ers' depends on the interpretation of the quanti ers and on the mathematical background where they are ranging. In this way, we hope to strengthen the idea that quanti cation over indiscernibles, in particular in the quantum domain, does not conform with quanti cation in the standard sense of classical logic.

Models and Modeling in Science: the role of metamathematics

Principia: an international journal of epistemology

The use of models of scientific theories should not be done without qualifications about the math... more The use of models of scientific theories should not be done without qualifications about the mathematics being used to build the models. This looks obvious, at least for logicians, but generally, it is not to the philosopher of science. Thus, some details about this point seem useful for both. Since any quick revision in the literature shows that in most cases, mainly after the raising of the semantic approach (to scientific theories), the models are taken to be set-theoretical structures, in discussing the issue we shall be concerned more with set theories, the locus where the play is usually developed (yet sometimes unconsciously).

Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics

Nonreflexive quantum mechanics is a formulation of quantum theory based on a nonclassical logic t... more Nonreflexive quantum mechanics is a formulation of quantum theory based on a nonclassical logic termed nonreflexive logic (a.k.a. 'non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are individuals in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical (mainly metaphysical) motivations and consequences of it.

Do `classical' space and time provide identity to quantum particles?

arXiv: Quantum Physics, 2017

Non-relativistic quantum mechanics is grounded on ‘classical’ (Newtonian) space and time (NST). T... more Non-relativistic quantum mechanics is grounded on ‘classical’ (Newtonian) space and time (NST). The mathematical description of these concepts entails that any two spatially separated objects are necessarily different, which implies that they are discernible (in classical logic, identity is defined by means of indiscernibility) — we say that the space is T2, or "Hausdorff". But quantum systems, in the most interesting cases, some- times need to be taken as indiscernible, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an identity to them, which seems to be contra the physical situation. In this paper we discuss this topic for a case study (that of two potentially infinite wells) and con- clude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems...

O gato de Schrödinger não está vivo e morto antes da medição: sobre a interpretação dos resultados quânticos

Seminário Lógica no Avião, 2019

Muitos textos de divulgação que falam da mecânica quântica fazem referência ao "paradoxo" do gato... more Muitos textos de divulgação que falam da mecânica quântica fazem referência ao "paradoxo" do gato de Schrödinger, comentando que, antes da medida do estado do sistema, o gato encontra-se vivo e morto ao mesmo tempo. Outros dizeres referem-se a que uma partícula pode estar em dois (ou mais) lugares ao mesmo tempo, que ela passou por duas fendas simultaneamente, ou ainda que percorreu dois caminhos de uma só vez, e que "interferiu consigo mesma". Na opinião deste autor, tratam-se de exageros conceituais, que podem conduzir o leitor não especializado ao erro e a imaginar situações que nada têm a ver com a mecânica quântica propriamente dita, entendida do modo como o fazemos neste artigo. Este texto de caráter geral, sem mencionar essas fontes, tem a intenção de esclarecer ou ao menos de questionar esses e outros pontos polêmicos na fala comum sobre os resultados da mecânica quântica. "Cats seem to play an important role in physics." B. Kanitscheider (1992)

Quasi-set theory for bosons and fermions: Quantum distributions

Foundations of Physics Letters, 1999

Abstruct Quasi-set theory provides a mathematical background for dealing with coll ections of in... more Abstruct Quasi-set theory provides a mathematical background for dealing with coll ections of indistinguishable elementary particles. In this paper, we show how to obtain the quantum statistics into the scope of quasi-set theory and we also discuss the Helium atom, which represents the simplest example where indistinguishability plays an important role. One of the advantages of our approach is that one

A finite analog to the l�wenheim-skolem theorem

Studia Logica, 1994

The traditional model theory of first-order logic assumes that the interpretation of a formula ca... more The traditional model theory of first-order logic assumes that the interpretation of a formula can be given without reference to its deductive context. This paper investigates an interpretation which depends on a formula&#x27;s location within a derivation. The key step is to drop the assumption that all quantified variables must have the same range and to require only that the ranges of variables in a derivation must be related in such way as to preserve the soundness of the inference rules. With each (consistent) derivation there is associated a “Buridan-Volpin (orBV) structure” [M, {r(x)}] which is simply a Tarski structureM for the language and a map giving the ranger(x) of each variablex in the derivation. IfLK* is (approximately) the classical sequent calculusLK of Gentzen from which the structural contraction rules have been dropped, then our main result reads: If a set of first-ordered formulas G has a Tarski modelM, then from any normal derivationD inLK* of G ? ? can be constructed aBV modelMD=[M, {r(x)}] of G where each ranger(x) is finite.

The problem of identity and a justification for a non-reflexive quantum mechanics

Logic Journal of IGPL, 2013

In this paper we try to justify our way of looking for an alternative approach to quantum mechani... more 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 (TTI) 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 (either a macroscopic or a microscopic one) 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.

Logical Aspects of Quantum (Non-)Individuality

Foundations of Science, 2010

In this paper I consider some logical and mathematical aspects of the discussion of the identity ... more 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.

Física e Ontologia

Discusiones Filosóficas, 2008

RESUMEN La pregunta de Quine,¢ Qué es lo que hay? µ recibe una caractertstica peculiar en la ftsi... more RESUMEN La pregunta de Quine,¢ Qué es lo que hay? µ recibe una caractertstica peculiar en la ftsica actual, especialmente cuando otorgamos atención al concepto de entidad ftsicaµ, u objeto físico, sobre lo que dicen algo, al menos idealmente, las teorías físicas. En la medida en que la física se ocupa de los constitutivos~ ltimos de la materia, entra en escena la cuestión de los objetos ftsicos de modo esencial. A pesar de que la física actual no se ocupa propiamente de ontologta, sino de explicar por qué el mundo es como es, las ...

Quasi-truth and defective knowledge in science: a critical examination

Manuscrito

Quasi-truth (a.k.a. pragmatic truth or partial truth) is typically advanced as a framework accoun... more

Making Sense of Nonindividuals in Quantum Mechanics

Quantum Worlds

It is only a slight exaggeration to say that good physics has at times been spoiled by poor philo... more It is only a slight exaggeration to say that good physics has at times been spoiled by poor philosophy." (Heisenberg [1998], p. 211) 0. Motivation As the epigraph by Heisenberg suggests, physics and philosophy may both benefit from a beneficial exchange in which one may enlighten the other. Physics can illuminate philosophy, and philosophy can illuminate physics. Of course, some may think that philosophy has nothing to contribute to physics (see Weinberg [1992]), and although we shall not provide a detailed defense of why we take philosophy to be relevant for science in general, we want to defend the relevance of ontology, as a field of metaphysics, to physics and to what physics is about. We stress, in this work, through a case study, the way in which ontology, as a philosophical field, can engage with physics, particularly in clearing the ground for the understanding of the nature of physical reality.

Quasi-set theory: a formal approach to a quantum ontology of properties

Synthese

In previous works, an ontology of properties for quantum mechanics has been proposed, according t... more In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate metalanguage to speak of the proposed ontology of properties and its structure.

On the controversy Received View vs. Alternative View

Preprint, 2025

This chapter discusses some (in my opinion) misunderstandings about the Received View of quantum ... more

A reply to Adonai Sant'Anna and a theory of quasi-sets without atoms

Preprint, 2024

Adonai Sant'Anna made some criticisms to the theory of quasi-sets and in particular he asked why ... more Adonai Sant'Anna made some criticisms to the theory of quasi-sets and in particular he asked why there is no a theory of quasi-sets that does not presuppose the existence of atoms. Furthermore, he claims that in dealing with non-individuals, that is, entities to which the standard notion of identity does not apply, we don't need to go out of standard frameworks; he advocates that permutation models in ZFA can do the job. In this paper we discuss his ideas and present a proposal of a quasi-set theory which does not involve atoms.

On Otávio Bueno on identity and quantification

Preprint, 2024

Otávio Bueno has pointed out an interesting and relevant topic about quantification. He stresses ... more Otávio Bueno has pointed out an interesting and relevant topic about quantification. He stresses that the meaning of quantifiers can have a sense if and only if the entities being quantified have well-defined identity conditions. In this paper we discuss his view and show that this is not the case in all situations, being quite reasonable to quantify also over entities to which identity conditions fail to hold.

On Dieks against the Received View

Preprint, 2024

Dennis Dieks addressed some criticisms of the so-called Received View (RV) of non-individual quan... more Dennis Dieks addressed some criticisms of the so-called Received View (RV) of non-individual quantum objects in a series of papers. His main concern is that the RV doesn't fit the practice of physics since in some situations the physicist assumes that quantum objects can be treated individually, imitating standard objects (individuals) more or less as in classical physics. In this paper, we revise his argumentation, showing that it involves some misunderstandings regarding the objectives of the RV. Dieks also proposes an Alternative View (AV) which he thinks is more in accordance with the way physicists usually proceed. We argue that the AV is not conflating the RV, but is complementary to it, namely, substitutes it when quantum objects are sufficiently apart and can be treated in conformity with the classical way. Thus, from the point of view of the practice of physics, in most cases, we can opt for the Alternative View, but the RV is more adequate when we are looking for logical and foundational analyses.

The underlying logic is mandatory also in discussing the philosophy of quantum physics

It is supposed that any scientific theory (here we consider physical theories only) has an underl... more It is supposed that any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not made explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory's principles, usually described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory's mathematical and logical concepts. We argue that no physical theory and no philosophical discussion on the basis of the theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just 'relationals' and that they cannot be absolutely identified by a monadic property, are fallacious if one remains within a 'standard' logico-mathematical framework, grounded on classical logic. We also discuss the claim that some properties (as those that came from logic) would be 'illegitimate' for discerning these entities is not justifiable. Thus, this paper may be interesting for logicians, physicists, and philosophers.

The underlying logic is mandatory, mainly in discussing the quantum case

It is supposed that any scientific theory (here we consider physical theories only) has an underl... more It is supposed that any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not clearly explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory's principles, usually described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory's mathematical and logical concepts. We argue that no physical theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just relationals and that they cannot be absolutely identified by a monadic property, are fallacious if one remains within a 'standard' logico-mathematical framework, grounded on classical logic. We also discuss the claim that some properties cannot be accepted as individuating properties, suggesting that such distinction between 'legitimate' and 'illegitimate' properties is not justifiable. Thus, this paper may be interesting for both physicists and philosophers. This is to those who are generally unaware of the assumptions they implicitly assume with the underlying logic of their physical theories.

A remark on quasi-automorphisms and deformable structures in quasi-set theory and its account to the logical foundations of quantum theory

Quantum theory is the land of indiscernible things, of things that in some situations cannot be p... more Quantum theory is the land of indiscernible things, of things that in some situations cannot be put apart. This contrasts in much with standard mathematics and classical logic, which were elaborated to deal with individuals, discernible things. Many thinkers, among them the mathematician Yuri Manin, have proposed that a more general theory of 'sets' than standard set theories (where sets are collections of discernible elements) should be elaborated to cope with quantum physics. Quasi-set theory was proposed with such an aim. In this paper, we consider some aspects of this theory and discuss the way we can use such a theory as a framework for constructing deformable (not rigid) structures where indiscernible things can be considered but with one additional and fundamental detail: these structures cannot be extended to rigid structures as it happens in the standard frameworks. Really, the way of dealing with indiscernible (or indistinguishable) elements within a 'standard' framework such as a 'classical' set theory (like the ZFC system) requires the confinement of the discussion to deformable (non-rigid) structures. But in ZFC every structure can be extended to a rigid structure (encompassing only the trivial automorphism-the identity function), so that in the extended structure (or in the whole universe) one can realize that the

UM ROBÔ PODE JULGAR? O USO DA ABDUÇÃO EM DIREITO

Preprint , 2023

This paper (written in Portuguese) analyses two relevant points in the Philosophy of Law, namely,... more This paper (written in Portuguese) analyses two relevant points in the Philosophy of Law, namely, whether a computer program (here termed "robot") can play the role of a judge in certain situations and the use of abductive reasoning in Law. We conclude that yes, a robot can be useful in certain simple situations and that the abductive ways of reasoning should be considered as legitimate in the Theory of Law.

A way to see the interplay of theory vs. reality with a glimpse into the quantum case

Décio Krause, 2023

The purpose of this paper is to argue that neither mathematics nor logic can be applied 'directly... more The purpose of this paper is to argue that neither mathematics nor logic can be applied 'directly' to reality, but to our rational representations (or reconstructions) of it, and this is extended to scientific theories in general. The difference to other approaches (e.g., Nancy Cartwright's, Bueno & Colyvan's or Hughes') is that I call attention to something more than it is involved in such a process, namely, metamathematics. A general schema of 'elaboration' of theories, which I suppose cope with most of them, is presented and discussed. A case study is outlined, the quantum case, whose anchored description, in my opinion, demands a different metamathematics and a different logic.

The underlying logic is mandatory, even in discussing the quantum case

Décio Krause, 2023

It is supposed that any scientific theory (here we consider physical theories only) has an underl... more It is supposed that any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not clearly explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory's principles, usually described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory's mathematical and logical concepts. We argue that no physical theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just relationals and that they cannot be absolutely identified by a monadic property, are fallacious if one remains within a 'standard' logico-mathematical framework, grounded on classical logic. Thus, this paper may be interesting for both physicists and philosophers. This is to those who are generally unaware of the assumptions they implicitly assume with the underlying logic of their physical theories.

Un acercamiento a las semánticas Nmatriciales basadas en QST

by Juan Pablo Jorge and Décio Krause

Principia an international journal of epistemology, Dec 2023

Se introduce la teoría de quaset QST en la base formal de las Nmatrices. El objetivo es construir... more Se introduce la teoría de quaset QST en la base formal de las Nmatrices. El objetivo es construir un sistema Nmatricial reemplazando en su formulación todos los conjuntos estándar por quasets. De esta manera, debido a que QST es una extensión conservativa de ZFA (ZF con átomos), pueden obtenerse Nmatrices generalizadas (Q-Nmatrices). Se presentan diferentes posibles compleciones de la axiomática de QST, ya que la formulación original no cuenta con algunos axiomas necesarios para el objetivo de este trabajo. Una de las consecuencias más atractivas de la axiomática extendida es la existencia de quasets complementarios que admiten elementos comunes con pertenencia indeterminada. Estos elementos pueden interpretarse como sistemas cuánticos en superposición de estados. Presentamos también un vínculo directo entre QST y la teoría de Rough Sets RST, que garantiza la existencia de modelos constituidos por rough sets para QST. Algunas consecuencias de nuestro formalismo son analizadas para las relaciones de consecuencia lógica fundadas en la nueva semántica.

Non-Reflexive Logics: Logics that Derogate the Standard Theory of Identity

In this paper an outline of a class of heterodox logics is presented. These systems, roughly spea... more In this paper an outline of a class of heterodox logics is presented. These systems, roughly speaking, question the standard notion of identity as given by classical logic and standard mathematics. Due to the apparent fundamentality of this notion, it is necessary to provide a strong motivation for the elaboration of such systems, and perhaps the main one comes from quantum mechanics. This link is mentioned, and some references are made, but no details are presented; the references provide more detailed works. We just describe some non-reflexive logics and mathematics, ending with a general discussion about the necessity of identity.