Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1501.02961

Contextual completeness and a classification scheme for theories

George Jaroszkiewicz

Published Jan 13, 2015• 0 citations
arXivHTMLPDF

Abstract

We discuss the role of propositions, truth, context and observers in scientific theories. We introduce the concept of generalized proposition and use it to define an algorithm for the classification of any scientific theory. The algorithm assigns a number 0, 1, 2 or 3 to a given theory, thereby classifying it as of metaphysical, mathematical, classical or quantum class. The objective is to provide an impartial method of assessing the scientific status of any theory.

DOI
10.48550/arxiv.1501.02961

Related papers

A Unified Scientific Basis for Inference

Inge Svein Helland

Every experiment or observational study is made in a context. This context is being explicitly considered in this book. To do so, a conceptual variable is defined as any variable which can be defined by (a group of) researchers in a given setting. Such variables are classified. Sufficiency and ancillarity are defined conditionally on the context. The conditionality principle, the sufficiency principle and the likelihood principle are generalized, and a tentative rule for when one should not condition on an ancillary is motivated by examples. The theory is illustrated by the case where a nuisance parameter is a part of the context, and for this case, model reduction is motivated. Model reduction is discussed in general from the point of view that there exists a mathematical group acting upon the parameter space. It is shown that a natural extension of this discussion also gives a conceptual basis from which essential parts of the formalism of quantum mechanics can be derived. This implies an epistemological basis for quantum theory, a kind of basis that has also been advocated by part of the quantum foundation community in recent years. Born's celebrated formula is shown to follow from a focused version of the likelihood principle together with some reasonable assumptions on rationality connected to experimental evidence. Some statistical consequences of Born's formula are sketched. The questions around Bell's inequality are approached by using the conditionality principle for each observer. The objective aspects of the world are identified with the ideal inference results upon which all observers agree (epistemological objectivity).

arXiv:1206.5075•Jun 22, 2012•2 citations

Is it true; or is it false; or somewhere in between? The logic of quantum theory

Christopher John Isham

The paper contains a relatively non-technical summary of some recent work by the author and Jeremy Butterfield. The goal is to find a way of assigning meaningful truth values to propositions in quantum theory: something that is not possible in the normal, instrumentalist interpretation. The key mathematical tool is presheaf theory where multi-valued, contextual truth values arise naturally. We show how this can be applied to quantum theory, with the ‘contexts’ chosen to be Boolean subalgebras of the set of all projection operators.

Contemporary Physics•May 1, 2005•18 citations

A classification scheme for interpretations of Quantum Mechanics

Gerd Christian Krizek

A physical theory consists of the mathematical formalism and an interpretation, which contains the definition of symbols, measurement assignments, concepts and principles, and an ontology. We present a scheme to classify these different levels of a physical theory and apply it to Newtonian Mechanics and the interpretations of Quantum Mechanics. We show that this classification scheme is embedded in the methodology of philosophy of science. With this scheme, different interpretations of Quantum Mechanics can be compared concerning the formalism and the used conceptions, and it serves as a guidance to identify ontological entities and reality conceptions in the different interpretations. Inspired by the commitments on the ontological level, we propose two heuristics concerning ontological statements.

arXiv:1707.00097•Jul 1, 2017•0 citations

Structures and Models of Scientific Theories: A Discussion on Quantum Non-Individuality

Décio Krause, Jonas R. Becker Arenhart

Abstract. 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, namely, that which sees them as non-individuals, then there would be strong reasons to ask for a different mathematical framework for describ-ing the structures that would be the models of the corresponding theory. In departing from the standard frameworks (that is, 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).

•Oct 1, 2010•2 citations

Some aspectos of quantum physics

Newton C. A. da Costa

I discuss some questions of quantum physics, for instance the validity and limitations of the basic language of set theory to deal with problems related to elementary particles. I also present a sketch of a formalization of a “metaphysics of structures”, which might be useful for a kind of “ontic structural realism”, and briefly review the concept of quasi-truth, which underlies my way of understanding scientific theories and the scientific activity.

•Jan 1, 2007•0 citations

On a New Concept of Truth in Empirical Theories

Jiří Souček

We introduce a new concept of truth in empirical theories based on the experience in the study of quantum mechanics. In this concept a statement can be true, false or undecidable.

•Feb 1, 2016•0 citations
We discuss the role of propositions, truth, context and observers in scientific theories. We introduce the concept of generalized proposition and use it to define an algorithm for the classification of any scientific theory. The algorithm assigns a number 0, 1, 2 or 3 to a given theory, thereby classifying it as of metaphysical, mathematical, classical or quantum class. The objective is to provide an impartial method of assessing the scientific status of any theory.
Every experiment or observational study is made in a context. This context is being explicitly considered in this book. To do so, a conceptual variable is defined as any variable which can be defined by (a group of) researchers in a given setting. Such variables are classified. Sufficiency and ancillarity are defined conditionally on the context. The conditionality principle, the sufficiency principle and the likelihood principle are generalized, and a tentative rule for when one should not condition on an ancillary is motivated by examples. The theory is illustrated by the case where a nuisance parameter is a part of the context, and for this case, model reduction is motivated. Model reduction is discussed in general from the point of view that there exists a mathematical group acting upon the parameter space. It is shown that a natural extension of this discussion also gives a conceptual basis from which essential parts of the formalism of quantum mechanics can be derived. This implies an epistemological basis for quantum theory, a kind of basis that has also been advocated by part of the quantum foundation community in recent years. Born's celebrated formula is shown to follow from a focused version of the likelihood principle together with some reasonable assumptions on rationality connected to experimental evidence. Some statistical consequences of Born's formula are sketched. The questions around Bell's inequality are approached by using the conditionality principle for each observer. The objective aspects of the world are identified with the ideal inference results upon which all observers agree (epistemological objectivity).
The paper contains a relatively non-technical summary of some recent work by the author and Jeremy Butterfield. The goal is to find a way of assigning meaningful truth values to propositions in quantum theory: something that is not possible in the normal, instrumentalist interpretation. The key mathematical tool is presheaf theory where multi-valued, contextual truth values arise naturally. We show how this can be applied to quantum theory, with the ‘contexts’ chosen to be Boolean subalgebras of the set of all projection operators.
A physical theory consists of the mathematical formalism and an interpretation, which contains the definition of symbols, measurement assignments, concepts and principles, and an ontology. We present a scheme to classify these different levels of a physical theory and apply it to Newtonian Mechanics and the interpretations of Quantum Mechanics. We show that this classification scheme is embedded in the methodology of philosophy of science. With this scheme, different interpretations of Quantum Mechanics can be compared concerning the formalism and the used conceptions, and it serves as a guidance to identify ontological entities and reality conceptions in the different interpretations. Inspired by the commitments on the ontological level, we propose two heuristics concerning ontological statements.
Abstract. 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, namely, that which sees them as non-individuals, then there would be strong reasons to ask for a different mathematical framework for describ-ing the structures that would be the models of the corresponding theory. In departing from the standard frameworks (that is, 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).