# Quantum Logic and Meaning

@article{Hellman1980QuantumLA, title={Quantum Logic and Meaning}, author={Geoffrey Hellman}, journal={PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association}, year={1980}, volume={1980}, pages={493 - 511} }

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 synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth…

## 19 Citations

### Quantum Logic and the Projection Postulate

- PhilosophyPhilosophy of Science
- 1981

This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the…

### 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…

### 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…

### Quantum Logic and the Luders Rule

- PhilosophyPhilosophy of Science
- 1982

In a recent paper, Michael Friedman and Hilary Putnam argued that the Luders rule is ad hoc from the point of view of the Copenhagen interpretation but that it receives a natural explanation within…

### Syntactic and Semantic Distribution in Quantum Measurement

- Physics
- 2005

The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We…

### Quantum Disjunctive Facts

- PhilosophyPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1986

A reformulation of the Kochen and Specker Theorem is used to show how quantum disjunctive facts have presented an insurmountable obstacle to mainstream attempts to motivate quantum logic. The failure…

### Non-Deterministic Semantics for Quantum States

- Computer Science, PhysicsEntropy
- 2020

This work exploits the failure of the principle of truth functionality in the quantum formalism to import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics, allowing to study post-quantum models using logical techniques.

### Quantum Mathematics

- Philosophy, MathematicsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1980

This paper explores the development of mathematics on a quantum logical base when mathematical postulates are taken as necessary truths. First it is shown that first-order Peano arithmetic formulated…

### 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.

### Projection Operators, Properties, and Idempotent Variables in the Modal Interpretations

- Mathematics
- 1998

This paper will discuss the representation of properties in two modal interpretations of quantum mechanics: Richard Healey’s interactive interpretation (Healey, 1989) and the Kochen-Dieks-Clifton…

## References

SHOWING 1-10 OF 20 REFERENCES

### Is Quantum Logic Really Logic?

- PhilosophyPhilosophy of Science
- 1971

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…

### Quantum Logic, Conditional Probability, and Interference

- PhilosophyPhilosophy of Science
- 1982

Friedman and Putnam have argued (Friedman and Putnam 1978) that the quantum logical interpretation of quantum mechanics gives us an explanation of interference that the Copenhagen interpretation…

### Quantum Logic and the Projection Postulate

- PhilosophyPhilosophy of Science
- 1981

This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the…

### Some Reflections on Quantum Logic and Schrödinger's Cat

- PhysicsThe British Journal for the Philosophy of Science
- 1979

The claim that logic is empirical—advanced as a solution to certain conceptual problems of quantum mechanics—is a thesis about the way the world is put together. The proposal that the logic of the…

### Only If Quanta Had Logic

- PhilosophyPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1978

Putnam and others have argued that an examination of structures arising in quantum mechanics can lead to a non-classical propositional logic, quantum logic. In this paper it is argued that the…

### The Physics of Logic

- Philosophy
- 1979

The quantum theory implies a modification of the empirical logic of the real world, a revolution at a deeper level than that of general relativity but analogous in many ways. An operational or…

### If quanta had logic

- PhilosophyJ. Philos. Log.
- 1972

The aims are to provide a formal semantic framework for Putnam's proposals, to investigate alternative ways of realizing his program, and to come to some tentative conclusions concerning the promise and significance of the enterprise.

### Quantum Set Theory

- Philosophy
- 1981

This paper studies set theory based on quantum logic, which is the lattice of all closed linear subspaces of a Hilbert space and shows the fact that there are many complete Boolean algebras inside quantum logic.

### Quantum Mathematics

- Philosophy, MathematicsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1980

This paper explores the development of mathematics on a quantum logical base when mathematical postulates are taken as necessary truths. First it is shown that first-order Peano arithmetic formulated…

### 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…