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Décio Krause

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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

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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)