Belnap-Dunn Interpretation of Schrödinger's Cat

“Schrodinger” by rptnorris is licensed under CC BY-SA 2.0

Contents

1 The Belnap-Dunn Interpretation of Schrödinger’s Cat
2 Further Reading

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:

[dsgvo-youtube url=”https://youtu.be/zkHFXZvRNns” images=”https://self-transcendence.org/wp-content/uploads/2025/12/Quantum-Superposition.png”][/dsgvo-youtube]

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.