“Schrodinger” by rptnorris is licensed under CC BY-SA 2.0
The Belnap-Dunn Interpretation of Schrödinger’s Cat
Introduction
The Schrödinger’s cat paradox (1935) illustrates quantum superposition: a cat entangled with unobserved radioactive decay exists as |alive⟩ + |dead⟩ until measured. This binary, two state model is oversimplistic. in so far as it ignores logical complements (alive implies ¬dead (Not-Dead state)) and pre-measurement indeterminacy, creating paradoxes like “how does ¬alive coexist with alive without contradiction explosion?” Classical logic demands exclusivity; binary superposition violates this, leaving “alive AND dead” philosophically unstable.
Solving Binary Oversimplification
We can solve this structural problem by applying the Belnap-Dunn four-valued logic model, where we can see the four values ( 01,10,11, and 00) represented.
Belnap-Dunn four-valued logic (True, False, Both, Neither) resolves this as follows:
Problem solved: Paraconsistency: “Both” (alive ∧ dead) stable; “Neither” captures void state.
Why superior?: This disentangles the Alive/Dead valuations independently, creating 16 accessible states (4×4 tensor), matching Hilbert space richness without explosion.
Hilbert space richness: Refers to quantum mechanics’ infinite-dimensional state space where superpositions span continuous basis states (e.g., all positions/momenta), enabling complex entanglement. Schrödinger’s cat occupies a high-dimensional subspace (|alive⟩ + |dead⟩ + orthogonals), and simply that dual value binary pair.
“Without explosion” contrasts classical logic explosion(contradiction > all statements true) with paraconsistent logic (Belnap-Dunn) preserving coherence.
Paraconsistent logic is a non-classical logic that tolerates contradictory statements without logical explosion, which is unlike classical logic where contradiction derives everything. Core feature: rejects Principle of Explosion, enabling “inconsistent but non-trivial” theories.
Reference: Quantum logicians note that the binary cat two-state model ignores these negation structures; Dunn logic fixes them.
Video Explanation
I found this video that explains what I am suggesting:
Four Core States: Complements Defined
| State | Belnap-Dunn | Logical Form | Fixes Binary Issue |
|---|---|---|---|
| 1 | True | Alive ∧ ¬Dead | Classical alive (exclusive) |
| 2 | False | Dead ∧ ¬Alive | Classical dead (exclusive) |
| 3 | Both | Alive ∧ Dead | Stable superposition |
| 4 | Neither | ¬Alive ∧ ¬Dead | Indeterminate reality. |
16-States Extrapolated
| Binary | Alive (Bit3) | Not-Alive (Bit2) | Dead (Bit1) | Not-Dead (Bit0) | Alive Prob | Dead Prob | Status |
|---|---|---|---|---|---|---|---|
| 0000 | 0% | 0% | 0% | 0% | 50% | 50% | Neither half-dead nor half-alive |
| 0001 | 0% | 0% | 0% | 100% | 50% | 50% | half not alive and half dead |
| 0010 | 0% | 0% | 100% | 0% | 50% | 50% | Half dead and half not alive |
| 0011 | 0% | 0% | 50% | 50% | 50% | 0% | Half alive |
| 0100 | 0% | 100% | 0% | 0% | 0% | 50% | Not-Alive Bias |
| 0101 | 0% | 100% | 0% | 100% | 0% | 50% | half not alive and half not dead |
| 0110 | 0% | 100% | 100% | 0% | 0% | 100% | True Dead |
| 0111 | 0% | 100% | 50% | 50% | 0% | 75% | 100% dead and 50% not dead |
| 1000 | 100% | 0% | 0% | 0% | 50% | 50% | 50% alive and 50% dead |
| 1001 | 100% | 0% | 0% | 100% | 100% | 0% | True Alive |
| 1010 | 100% | 0% | 100% | 0% | 50% | 100% | 50% alive and 50% dead |
| 1011 | 100% | 0% | 100% | 100% | 100% | 50% | 100% Alive and 50% dead |
| 1100 | 100% | 100% | 0% | 0% | 50% | 0% | 100% alive and 50% not alive |
| 1101 | 100% | 100% | 0% | 100% | 100% | 50% | 100% alive and 50% not alive |
| 1110 | 100% | 100% | 100% | 0% | 50% | 100% | 100% Dead 50% not alive |
| 1111 | 100% | 100% | 100% | 100% | 50% | 50% | 100% dead and 100% alive. |
Further Reading
https://en.wikipedia.org/wiki/Schr%C3%B6dinger’s_cat
https://www.wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/
https://aeon.co/essays/no-schrodingers-cat-is-not-alive-and-dead-at-the-same-time
https://www.journals.uchicago.edu/doi/10.1093/bjps/30.1.27
https://en.wikipedia.org/wiki/Four-valued_logic
https://link.aps.org/doi/10.1103/PhysRevA.99.063813
https://arxiv.org/abs/2210.01083
https://www.science.org/doi/10.1126/science.adf7553
https://en.wikipedia.org/wiki/Quantum_superposition
https://en.wikipedia.org/wiki/Quantum_superposition
https://scienceexchange.caltech.edu/topics/quantum-science-explained/quantum-superposition
https://www.reddit.com/r/QuantumPhysics/comments/169orux/can_someone_give_me_an_explanation_of/
https://quantum.microsoft.com/en-us/insights/education/concepts/superposition
https://www.techtarget.com/whatis/definition/superposition
https://quantumatlas.umd.edu/entry/superposition/
https://www.quantum-inspire.com/kbase/superposition-and-entanglement/
https://www.youtube.com/watch?v=mAgnIj0UXLY
https://www.researchsquare.com/article/rs-95171/v1
https://link.aps.org/doi/10.1103/PhysRevA.100.052118
https://www.semanticscholar.org/paper/6762278fdcdef8495b4cc3ded486c22374dcf852
http://link.springer.com/10.1007/BF00730892
http://link.springer.com/10.1007/BF01300547
https://link.springer.com/10.1007/s12596-024-02307-w
https://www.cambridge.org/core/product/identifier/9781316494233%23CN-bp-6/type/book_part
https://www.semanticscholar.org/paper/dea730cc1219f124cd1c8c9545193dba7493de97
https://www.semanticscholar.org/paper/f6fd96cc4efd28f8fb4d9030f16758683301e2ec
http://arxiv.org/pdf/2312.13540.pdf
http://arxiv.org/pdf/1802.05102.pdf
https://arxiv.org/pdf/1703.10943.pdf
http://arxiv.org/pdf/1312.7322.pdf
https://arxiv.org/abs/1311.4275
http://arxiv.org/pdf/1201.0688.pdf
http://arxiv.org/pdf/2210.02398.pdf
https://quantum-journal.org/papers/q-2024-05-06-1335/pdf/
https://en.wikipedia.org/wiki/Schr%C3%B6dinger’s_cat
https://www.wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/
https://en.wikipedia.org/wiki/Four-valued_logic
https://link.aps.org/doi/10.1103/PhysRevA.99.063813
https://www.science.org/doi/10.1126/science.adf7553
https://arxiv.org/html/2510.01120v1
https://arxiv.org/abs/2210.01083
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