Is Quantum Logic Really Logic?

  title={Is Quantum Logic Really Logic?},
  author={Michael Robert Gardner},
  journal={Philosophy of Science},
  pages={508 - 529}
  • M. Gardner
  • Published 1 December 1971
  • Philosophy
  • Philosophy of Science
Putnam and Finkelstein have proposed the abandonment of distributivity in the logic of quantum theory. This change results from defining the connectives, not truth-functionally, but in terms of a certain empirical ordering of propositions. Putnam has argued that the use of this ordering ("implication") to govern proofs resolves certain paradoxes. But his resolutions are faulty; and in any case, the paradoxes may be resolved with no changes in logic. There is therefore no reason to regard the… 

Logic, Quantum Logic and Empiricism

This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a

Quantum Logic and Meaning

  • G. Hellman
  • Philosophy
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
  • 1980
Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that

Quantum logic as a dynamic logic

It is concluded that there is no contradiction between classical logic and (the authors' dynamic reinterpretation of) quantum logic, and that the Dynamic-Logical perspective leads to a better and deeper understanding of the “non-classicality” of quantum behavior than any perspective based on static Propositional Logic.

A New Approach to Quantum Logic

  • J. L. Bell
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1986
The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about

Two Deviant Logics for Quantum Theory: Bohr and Reichenbach*

  • M. Gardner
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1972
Foundational studies in quantum theory have consisted in large part of attempts to avoid certain paradoxes. This paper concerns Bohr's and Reichenbach's attempts to avoid some of these seeming

Probability and the Interpretation of Quantum Mechanics*

  • A. Fine
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1973
In concluding a popular exposition of probability in quantum mechanics {QM), Richard Feynman says 'But the deep mystery is what I have described, and no one can go any further today.' Thus Feynman

Why classical logic is privileged: justification of logics based on translatability

In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation

A critique of the disturbance theory of indeterminacy in quantum mechanics

Heisenberg'sgendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a

Logic, Counterexamples, and Translation

It is argued that counterexamples in logic are countereXamples not to particular inferences, but to logics as a whole, and that what counts as a legitimate translation from natural language to formal language is dependent on the background logic being assumed.



Philosophic Foundations of Quantum Mechanics

IN the preface of this work, the author tells us that he “has tried to develop a philosophical interpretation of quantum physics which is free from metaphysics”; a somewhat puzzling sentence, since

The Problem of Hidden Variables in Quantum Mechanics

Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure

The Physical Principles of the Quantum Theory

It is an unusual pleasure to present Professor Heisenberg’s Chicago lectures on “The Physical Principles of the Quantum Theory” to a wider audience than could attend them when they were originally

Statistical Interpretation of Quantum Mechanics.

The published work for which the honor of the Nobel prize for the year 1954 has been accorded to me does not contain the discovery of a new phenomenon of nature but, rather, the foundations of a new

On the Problem of Hidden Variables in Quantum Mechanics

The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. It

Quantum Mechanics without “The Observer”

This thesis is that the observer, or better, the experimentalist, plays in quantum theory exactly the same role as in classical physics.

Matter, Space and Logic

Physics has a warp and a woof, like a fabric stretched across many levels of abstraction and woven out two millenia long. Across the fabric is a pattern persistent over the entire length in which the

Simultaneous measurability in quantum theory

This paper presents a study of what is sometimes regarded as the conceptual heart of quantum theory, namely, the orthodox ‘physical’ interpretation of non-commuting operators as representatives of

Some Conceptual Problems of Quantum Theory

  • Pittsburgh Series in Philosophy of Science
  • 1972