Semantic Epistemology Redux (original) (raw)

Semantic Epistemology Redux: Proof and Validity in Quantum Mechanics

Definitions I presented in a previous article as part of a semantic approach in epistemology assumed that the concept of derivability from standard logic held across all mathematical and scientific disciplines. The present article argues that this assumption is not true for quantum mechanics (QM) by showing that concepts of validity applicable to proofs in mathematics and in classical mechanics are inapplicable to proofs in QM. Because semantic epistemology must include this important theory, revision is necessary. The one I propose also extends semantic epistemology beyond the 'hard' sciences. The article ends by presenting and then refuting some responses QM theorists might make to my arguments.

DOES QUANTUM MECHANICS REQUIRE NEW FORMS OF THOUGHT? Towards a formal epistemology

In quantum mechanics, the expectations which are induced by the aiming at a traditional type of object, such as the corpuscular bearers of properties, are generally confuted. But this type of object endowed with properties is presupposed by the predicative structure of judgment, as abstracted by classical logic. How can we overcome such discrepancy between quantum expectations and the formal framework of classical logic? Just substituting a quantum logic for classical logic is a cheap move, because it purports to save the formal concept of property somehow. Here, we propose to elaborate a broader formal discipline which can accommodate the structure of quantum expectations without being bound to a standard ontological framework. This new discipline is called a “formal epistemology”.

Quantum mechanics, mathematics, cognition and action: proposals for a formalized epistemology

2002

Preface. Introduction. Part One: Preliminary Explorations: What, Why, How? 1. Remarks about the Program for a Formalized Epistemology F. Bailly. 2. Formalized Epistemology in a Philosophical Perspective H. Barreau. 3. Formalized Epistemology, Logic, and a Grammar M. Bitbol. 4. Epistemic Operations and Formalized Epistemology: Contribution to the Study of the Role of Epistemic Operations in Scientific Theories M. Paty. 5. Mathematical Physics and Formalized Epistemology: Debate with Jean Petitot Interlocutors: F. Bailly, M. Bitbol, M. Mugur-Schachter, V. Schachter. 6. On the Possibility of a Formalized Epistemology R. Vallee. Part Two: Constructive Contributions. 7. Quantum Mechanics Versus a Method of Relativized Conceptualization M. Mugur-Schachter. 8. Mathematical and Formalized Epistemologies R. Vallee. 9. Ago-Antagonistic Systems E.Bernard-Weill. Part Three: Further Explorations. 10. Complexity of the 'Basic Unit' of Language: Some Parallels in Physics and Biology E. And...

A Philosopher's View of the Epistemic Interpretation of Quantum Mechanics

2010

There are various reasons for favouring ψ-epistemic interpretations of quantum mechanics over ψ-ontic interpretations. One such reason is the correlation between quantum mechanics and Liouville dynamics. Another reason is the success of a specific epistemic model , in reproducing a wide range of quantum phenomena. The potential criticism, that Spekkens' restricted knowledge principle is counter-intuitive, is rejected using 'everyday life' examples. It is argued that the dimensionality of spin favours Spekkens' model over ψ-ontic models. van Enk's extension of Spekkens' model can even reproduce Bell Inequality violations, but requires negative probabilities to do so. An epistemic account of negative probabilities is the missing element for deciding the battle between ψ-epistemic and ψ-ontic interpretations in favour of the former. * I owe a special thanks to Dr. Jeremy Butterfield for supervising this paper, generously providing encouragement, comments and advice. I also thank Dr. Alex Broadbent and an anonymous reviewer in the History and Philosophy Department, Cambridge University for helpful comments.

A Semantic Approach to the Completeness Problem in Quantum Mechanics

Foundations of Physics, 2000

The old Bohr-Einstein debate about the completeness of quantum mechanics (QM) was held on an ontological ground. The completeness problem becomes more tractable, however, if it is preliminarily discussed from a semantic viewpoint. Indeed every physical theory adopts, explicitly or not, a truth theory for its observative language, in terms of which the notions of semantic objectivity and semantic completeness of the physical theory can be introduced and inquired. In particular, standard QM adopts a verificationist theory of truth that implies its semantic nonobjectivity; moreover, we show in this paper that standard QM is semantically complete, which matches Bohr's thesis. On the other hand, one of the authors has provided a Semantic Realism (or SR) interpretation of QM that adopts a Tarskian theory of truth as correspondence for the observative language of QM (which was previously mantained to be impossible); according to this interpretation QM is semantically objective, yet incomplete, which matches EPR's thesis. Thus, standard QM and the SR interpretation of QM come to opposite conclusions. These can be reconciled within an integrationist perspective that interpretes non-Tarskian theories of truth as theories of metalinguistic concepts different from truth.

An epistemic interpretation and foundation of quantum theory

arXiv (Cornell University), 2019

The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical inference theory. The approach can be said to have an intuitive basis: The quantum states of a physical system are under certain conditions in one-to-one correspondence with the following: 1) Focus on a concrete question to nature and then 2) give a definite answer to this question. This foundation implies an epistemic interpretation, depending upon the observer, but the objective world is restored when all observers agree on their observations on some variables. The article contains a survey of parts of the author's books on epistemic processes, which give more details about the theory. At the same time, the article extends some of the discussion in the books, and at places makes it more precise. For further development of interpretation issues, I need cooperation with interested physicists.

Quantum Mechanics as a Classical Theory III: Epistemology

2008

The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the formalism’s limitations. In this paper, a Realist Interpretation of quantum mechanics based on these results is elaborated and compared to the Copenhagen Interpretation. We demonstrate that von Neumann’s proof of the impossibility of a hidden variable theory is not correct, independently of Bell’s argumentation. A local hidden variable theory is found for non-relativistic quantum mechanics, which is nothing else than newtonian mechanics itself. We prove that Bell’s theorem does not imply in a non-locality of quantum mechanics, and also demonstrate that Bohm’s theory cannot be considered a true hidden variable theory. 1

The quantum formulation derived from assumptions of epistemic processes

Journal of Physics: Conference Series, 2015

Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is introduced, and for this setting the basic Hilbert space formalism is arrived at under certain technical assumptions. Other aspects of ordinary quantum mechanics will be developed from the same basis elsewhere.

Epistemological and ontological aspects of quantum theory

arXiv (Cornell University), 2021

In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group of observers. These conceptual variables are very often accessible, that is, it is possible to find values of the variables by doing experiments or by making measurements. An important notion is that of maximal accessibility. It is shown here that this new machinery may facilitate the discussion of when a specific quantum state can be given an ontological interpretation, and also the more speculative question whether all states can be given such an interpretation. The discussion here is general, and has implications for the basic problem of how one should look upon information from experiments and measurement, in particularly the question concerning when this information may reflect properties of the real world.