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A Pragmatist–Inferentialist Account of the “Semantics” of Quantum Theory

Richard Healey

Published Jan 25, 2026• 0 citations
Publisher

Abstract

Abstract Models in quantum theory have non-representational uses through which content accrues to claims involved in their application. A promising approach to understanding how is provided not by a referential semantics but by inferentialist pragmatism. In use, a quantum model is applied to physical systems, but not to represent them or their behavior. It is used to issue probabilistic claims about phenomena involving these systems by the Born Rule. Instances of the Born Rule, statements assigning quantum states, and claims about the values of magnitudes all derive their content through their inferential relations, to one another and to other claims.

DOI
10.1093/9780198911586.003.0011

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Abstract Models in quantum theory have non-representational uses through which content accrues to claims involved in their application. A promising approach to understanding how is provided not by a referential semantics but by inferentialist pragmatism. In use, a quantum model is applied to physical systems, but not to represent them or their behavior. It is used to issue probabilistic claims about phenomena involving these systems by the Born Rule. Instances of the Born Rule, statements assigning quantum states, and claims about the values of magnitudes all derive their content through their inferential relations, to one another and to other claims.
Quantum theory involves a novel, indirect use of models to further the aims of fundamental science. It is revolutionary because of the way it improves our use and understanding of representations of the universe we could offer without it. The so-called semantic approach takes a scientific theory to supply a collection of models to be used to represent phenomena: but models of quantum theory are applied more indirectly to provide good advice on the significance and credibility of claims about physical things whose existence is assumable here. Inferentialism takes these claims to derive their content through inferential links to others. They are objective, as are the probabilities they are assigned, and some are objectively true.
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabilities for physical events: both state and probability are objective—not because they represent elements of physical reality, but because each exerts normative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements (about values of magnitudes) that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not “collapse” on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violation of Bell inequalities does not demonstrate “spooky” non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner’s friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inferences. This promises a better treatment of meaning than that of Bohr. Quantum theory models physical systems with no mention of measurement: it is decoherence, not measurement, that licenses application of Born's probability rule. So quantum theory also offers advice on its own application. I show how this works in a simple model of decoherence, and then in applications to both laboratory experiments and natural systems. Applications to quantum field theory and the measurement problem will be discussed elsewhere.
Abstract The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inference. This promises a better treatment of meaning than that offered by Bohr. Quantum theory models physical systems with no mention of measurement: it is decoherence, not measurement, that licenses application of Born’s probability rule. So, quantum theory also offers advice on its own application. After presenting a simple model of decoherence to show how this works, the essay considers applications to both laboratory experiments and natural systems. Applications to quantum field theory and the measurement problem will be discussed in later essays.
Abstract These essays in natural philosophy were all written from a pragmatist point of view developed over the past 15 years. They show what work pragmatism can do in science as well as philosophy. Many essays express a view of quantum theory developed using ideas of contemporary pragmatist philosophers: other essays apply these more widely to science and metaphysics. Quantum models are used not to represent physical systems but to offer good advice on how to represent them. The role of a quantum state is not to describe a system but to yield objective probabilities for alternative outcomes of events involving it. A situated agent could use these probabilities to decide what to do, and one can use them to explain phenomena. They are probabilities for physical events including measurements: pragmatist inferentialism helps one to say what these are, and when they have outcomes, thereby resolving the quantum measurement problem. One can use quantum theory locally to explain non-localized correlations, and why quantum field theory poses no ontological problem. Despite its unrivaled success, quantum theory offers no scientific image of the physical world on which a naturalist could construct a metaphysics. There are structural reasons why the rest of physical theory cannot be reduced to quantum theory. This pragmatist view of quantum theory is not instrumentalist. One essay explains why it should count as realist. Other essays defend pragmatist views of scientific laws and explanations as well as causation, truth, and objectivity.