The L₃ Constraints
The Three Fundamental Laws of Logic as Physical Constraints
The Three Fundamental Laws of Logic ($L_3$) form the ontological foundation of Logic Realism Theory:
Determinate Identity (Id)
Every instantiated configuration is determinately what it is, independent of description or decomposition.
\[\text{For any descriptions } d, d' \text{ of the same configuration: } d(i) = d'(i) = i\]This is not the trivial claim that identity is reflexive ($i = i$). It is the substantive claim that instantiated configurations have determinate identity: they are self-identical in a way that does not depend on how they are described, measured, or decomposed.
Consequences:
- Vehicle-invariance (probability assignments cannot depend on basis choice)
- Permutation symmetry for identical particles
- Local tomography (composite states determined by local measurements)
Non-Contradiction (NC)
No instantiated configuration simultaneously possesses and lacks a property in the same respect.
\[\neg(P(i) \land \neg P(i))\]The “in the same respect” qualification is essential. An electron can have spin-up relative to the z-axis and spin-down relative to a rotated axis. But it cannot have spin-up and spin-down relative to the same measurement basis.
Consequences:
- Mutually exclusive measurement outcomes
- Boolean structure of actualized records
Excluded Middle (EM)
For any well-defined property $P$ applicable to an instantiated configuration, either the configuration possesses $P$ or it lacks $P$.
\[P(i) \lor \neg P(i)\]This is a constraint on instantiation for sharply specified properties, not a claim about what an agent can know or prove. The law applies to instantiated configurations with respect to well-defined properties.
Consequences:
- Determinate measurement outcomes
- Temporal ordering from joint inadmissibility
The Two Domains
The $L_3$ constraints define a boundary between two domains:
$I_\infty$ (Representable): All specifications, including contradictions and impossibilities. No constraint.
$A_\Omega$ (Instantiable): The subset satisfying $L_3$. Only these configurations can be physically instantiated as stable records.
\[A_\Omega := \{ i \in I_\infty : L_3(i) \}\]This is the foundational relationship: physics proceeds because its outputs are $L_3$-shaped.
Related Papers
Position Paper
Full development of the $L_3$ framework establishing the foundational ontology.
Read Paper →Born Rule Derivation
Vehicle-invariance from Determinate Identity forces the $\lvert\psi\rvert^2$ probability measure.
Read Paper →Hilbert Space Derivation
Local tomography from Determinate Identity selects complex Hilbert space.
Read Paper →