Philosophy Paper Abstract: Deriving the Structure of Existence from a Single Axiom
We propose that the structure of physical reality follows from a single logical axiom: nothing cannot exist (◇N→ ¬N). This claim is not empirical but logical—absolute nothingness is self-undermining, since considering it possible requires a conceptual framework, but any framework is something rather than nothing. From this axiom, we derive that existence requires relation as its minimum structure: a bare "something" with nothing to distinguish it from collapses into the nothingness that cannot exist. Distinguishability is therefore fundamental, and distinguishability is inherently relational.
We identify five necessary constraints for robust distinguishability: boundary (β), pattern (κ), resource (ρ),integration (λ), and ordering structure (τ). These constraints define a five-dimensional configuration space with bounded viable region, where configurations are organized by a potential function Φ = ln(Ω/K)—the logarithm of accessible states over descriptive complexity. This potential emerges not as an additional axiom but as a consequence of the structure of distinguishability itself, connecting at large scales to thermodynamic quantities.
A central result concerns the emergence of time and causality. At N = 2 (the minimum configuration of two distinguishable features), no ordering structure is possible—the configuration is inherently symmetric, and τ = 0necessarily. At N ≥ 3, irreducible structure emerges: three coupling matrices cannot be simultaneously diagonalized, enabling circulation and chirality. This geometric asymmetry is what we experience as temporal ordering; the direction of time aligns with the gradient of Φ, yielding the thermodynamic arrow without special initial conditions.
The framework connects to physics through proposed correspondences: boundary maps to spatial structure, pattern to quantum coherence, resource to energy-momentum, integration to entanglement, and ordering to causality. Physical constants (c, ℏ, G, α, k_B) are conjectured to be geometric properties of constraint space rather than arbitrary parameters. The N = 2 regime corresponds to quantum mechanics (inherently non-factorizable correlations), while the large-N limit yields classical thermodynamics. Parallels to established formalisms—Finster's Causal Fermion Systems, Barandes' indivisible stochastic processes, Jacobson's thermodynamic derivation of Einstein's equations—suggest the framework captures structures already implicit in foundational physics.
We conclude that existence is not a mystery requiring explanation but the resolution of the paradox inherent in nothingness. The framework is offered as natural philosophy: rigorous conceptual analysis pointing toward mathematical formalization and empirical test, with the recognition that the program of deriving physics from logical necessity remains to be completed.