Vehicle/Content Distinction

The vehicle/content distinction explains a central puzzle: how can minds coherently represent contradictions, impossibilities, and $L_3$ violations when reality cannot instantiate them?

The Distinction

A representation has two components:

Vehicle: The physical structure doing the representing—a brain state, quantum state, measurement apparatus, or symbolic inscription. Vehicles must satisfy $L_3$; they are actual configurations.

Content: What is represented—outcome possibilities, measurement alternatives, even contradictions and impossibilities. Contents need not satisfy $L_3$.

This asymmetry is the key insight: the representing is always $L_3$-admissible, even when the represented is not.

The Asymmetry as Evidence

If $L_3$ constrained only representation (as psychologism claims), then:

• Representing violations should be difficult or impossible (vehicles must satisfy $L_3$)
• Instantiating violations should be possible (reality would be unconstrained)

If $L_3$ constrains only instantiation (as Logic Realism claims), then:

• Representing violations should be possible (vehicles satisfy $L_3$ while contents need not)
• Instantiating violations should be impossible ($A_\Omega$ is defined by $L_3$ satisfaction)

The empirical record supports the second pattern. Conceiving contradictions is cognitively trivial; instantiating them has never been observed. This asymmetry is the empirical foundation of Logic Realism Theory.

Superposition as Vehicle

Consider the paradigm case:

This superposition:

• As vehicle: Is a precise, well-defined mathematical object with definite coefficients, inner products, and evolution under unitary operators
• As content: Describes a physical situation that is not yet determinate with respect to “has definite value 0 or 1 in this basis”

The state does not represent a configuration that both has and lacks a definite value (NC violation). It represents a physical situation such that when measurement occurs, exactly one outcome will be recorded—and that record will be $L_3$-admissible.

Layered Representation

The LRT picture has three layers:

Layer 1: $I_\infty$ (Representable configurations) All specifications, including contradictions and impossibilities. No constraint.

Layer 2: Quantum states as representational vehicles Well-defined Hilbert space vectors. These are $L_3$-consistent descriptions within mathematical formalism. They encode outcome-possibilities via probability distributions.

Layer 3: Measurement outcomes as instantiated records Sharp property assignments in stable, public records. Determinately 0 or 1, spin-up or spin-down. Only this layer is directly instantiated as public record.

Layer 2 is the theory’s vehicle for representing how Layer 3 distributions arise from physical situations. The vehicle/content distinction operates at each level.

Why This Matters

The vehicle/content distinction:

1. Explains representation of impossibilities: Minds represent round squares without instantiating them because the vehicle (brain state) is $L_3$-admissible even when the content is not

2. Dissolves superposition paradoxes: Superposition is not a contradiction but a determinate vehicle encoding indeterminate content

3. Grounds probability objectively: The measure over outcomes belongs to the vehicle, not the content—it characterizes how the physical situation is objectively poised toward outcomes

4. Enables the Born rule derivation: Vehicle-invariance (probability assignments independent of mathematically equivalent decompositions) forces the $\lvert\psi\rvert^2$ form via Gleason’s theorem

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