From Logic to Physics: The L₃ Journey
Here’s a strange fact: across all of experimental science, no laboratory has ever recorded a genuine contradiction.
Not once. Not a single detector that registered “triggered” and “not triggered” at the same moment, in the same respect. Not a single measurement log with “yes” and “no” simultaneously. For over a century of precision physics (quantum mechanics, particle accelerators, gravitational wave detectors), every stable record obeys the same pattern.
This might seem obvious. Of course contradictions don’t show up in lab notebooks. But here’s what makes it interesting: we can imagine contradictions. We can represent them. Philosophers have spent careers exploring scenarios where something could be both P and not-P. Nature refuses to instantiate them.
Logic Realism Theory (LRT) takes this asymmetry seriously.
The Three Laws
Everyone learns the basic logical laws, usually without much fanfare:
Identity (Id): A thing is what it is. Non-Contradiction (NC): Nothing can be both P and not-P at the same time and in the same respect. Excluded Middle (EM): For any well-defined property, either a thing has it or it doesn’t.
Collectively, we call these $L_3$. Most treat them as rules of reasoning, guidelines for clear thinking. LRT makes a bolder claim: these are constraints on what can exist.
The Key Distinction
LRT distinguishes two domains:
$I_\infty$ is everything representable: every concept, configuration, or description you can construct. This includes contradictions, impossibilities, round squares, and married bachelors. You can represent “the electron is both spin-up and spin-down in the z-basis.” You just did.
$A_\Omega$ is the subset of $I_\infty$ that can be physically instantiated. These are the configurations that can show up as stable records: detector clicks, measurement outcomes, permanent states.
The claim: $A_\Omega$ = ${x \in I_\infty : L_3(x)}$.
Only configurations satisfying the three logical laws can be instantiated. The $L_3$ is a constraint on what reality can be.
Why This Matters for Physics
If the $L_3$ constrains what can exist, then physics operates within a pre-shaped space. The question becomes: what does that constraint require?
The answer turns out to be substantial. When you work through what Identity demands of physical systems (especially the requirement that outcomes must be “vehicle-invariant,” the same regardless of how you describe them), you get specific structures:
- The Born rule (the $\lvert\psi\rvert^2$ probability law of quantum mechanics) follows from vehicle-invariance via Gleason’s theorem
- Complex Hilbert space (not real, not quaternionic) is selected by local tomography requirements
- The symmetrization postulate (bosons vs. fermions) follows from Identity applied to indistinguishable particles
These are derivations. The $L_3$ generates quantum mechanics.
It from Bit, Bit from Fit
John Wheeler famously proposed “It from Bit”: physical reality emerges from information. LRT accepts this, then asks: where does information come from?
A bit (a distinction between 0 and 1) only exists if there’s a fact of the matter about which it is. Without Determinate Identity, there’s no such fact. The bit dissolves.
So the complete picture is: It from Bit, Bit from Fit. Physical structure (It) emerges from informational structure (Bit), which emerges from logical admissibility (Fit = $L_3$). The three logical laws ground the entire chain.
What This Is Not
LRT treats logic as ontologically real: describing genuine constraints on what can be instantiated.
LRT does not claim to derive all of physics from logic. Specific field content, coupling constants, and initial conditions remain empirical. What we derive is the framework, the mathematical arena within which physics operates.
LRT is falsifiable. If a laboratory ever produced a stable record instantiating a genuine contradiction (a detector simultaneously registering “yes” and “no” in the same respect) LRT would be refuted. The framework takes empirical risk.
The Journey Ahead
This is the first article in a series exploring Logic Realism Theory for a broader audience. Future pieces will address:
- The Instantiation Barrier Explained: Why some configurations in $I_\infty$ can’t cross into $A_\Omega$
- Why Distinguishability Requires Quantum Mechanics: The path from Identity to Hilbert space
- The Born Rule Is Not Optional: How probability emerges from logical constraint
- Common Objections to Logic Realism: Addressing the skeptics
For the full technical treatment, see the Position Paper. For concept-by-concept breakdowns, explore Topics.
Logic Realism Theory was developed by James (JD) Longmire. This article is part of the LRT documentation at jdlongmire.github.io/logic-realism-theory.