# Is Quantum Logic Really Logic?

@article{Gardner1971IsQL, title={Is Quantum Logic Really Logic?}, author={Michael Robert Gardner}, journal={Philosophy of Science}, year={1971}, volume={38}, pages={508 - 529} }

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…

## 56 Citations

### Logic, Quantum Logic and Empiricism

- PhilosophyPhilosophy of Science
- 1982

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

- PhilosophyPSA: 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

- PhilosophySynthese
- 2010

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.

### Two Deviant Logics for Quantum Theory: Bohr and Reichenbach*

- PhilosophyThe 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*

- PhilosophyThe 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

- PhilosophySynthese
- 2021

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

- Physics
- 1981

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

- PhilosophyJournal of Philosophical Logic
- 2021

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…

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

- PhilosophyJ. Philos. Log.
- 2022

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

- Philosophy
- 2018

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.

## References

SHOWING 1-9 OF 9 REFERENCES

### Philosophic Foundations of Quantum Mechanics

- PhilosophyNature
- 1946

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…

### Simultaneous measurability in quantum theory

- Philosophy
- 1968

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…

### The Problem of Hidden Variables in Quantum Mechanics

- Physics
- 1967

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

- Physics
- 1930

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.

- PhysicsScience
- 1955

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

- Physics
- 1966

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”

- Physics
- 1967

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

- Art
- 1969

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…

### Some Conceptual Problems of Quantum Theory

- Pittsburgh Series in Philosophy of Science
- 1972