Formal systems are missing a validation layer between syntax and execution.
A string can be syntactically legal and still not executable. A premise set can contain individually well-formed formulas whose conjunction describes a state no evaluation can resolve. A provability request can route through its own verdict without grounding. A halting query can demand an answer from a structure that cannot supply one. In each case the input parses. In each case the engine accepts it. In each case the result is treated as a deep discovery about the limits of logic, computation, or mathematics. The claim of this project is that the result is instead a diagnostic artifact of missing input validation.
The project currently has ten core essays.
Running Comes First argues that the primitive is not invariance, consistency, or any static condition, but self-sustaining process. Persistence, distinction, and selection are increasingly explicit appearances of that running. This is the ontological foundation.
Role-Arity and the Structure of Emergence provides a diagnostic framework. Questions and operations require specific numbers of functionally distinct roles. When a question demands more structure than its target supplies, the surplus generates phantom depth. When it demands less, it forces false dichotomy. The diagnostic predicts which questions dissolve and which resolve.
Why Is There Something Rather Than Nothing applies the diagnostic to a canonical metaphysical question and shows it is structurally overspecified relative to its target.
The Consistency Gate identifies the first species of non-executable input: contradictory premise sets that cancel the substrate needed for discrimination. It argues that explosion is not a defect in classical inference but the correct behavior of an engine fed input that failed a precondition. The fix is a validation layer between syntax and consequence, not a weakened engine. Classical logic with a consistency gate handles every use case attributed to paraconsistent logic, with strictly greater inferential power.
The Executability Gate identifies the second species: evaluative requests whose dependency structures cycle without grounding. It specifies a typed validator over evaluative requests and applies it to the liar, Turing’s D(D), and Gödel’s G as canonical cases of anchor-failure. All three are shown to be instances of one pattern: formally correct derivations from input that should have been rejected at the boundary between expression and execution.
Agency Is Not Added argues that agency is not a property added to non-agentive matter at a complexity threshold. It is what self-sustaining process looks like when selection becomes explicit. The question “how does agency arise from non-agentive matter?” is diagnosed as the same structural error as “why is there something rather than nothing?” — an overspecified question whose foil is fabricated by the question’s own contrastive structure.
Value Is Structural argues that the asymmetry between carry-through and collapse is intrinsic to the running, not projected by an observer. Not all process-states are equivalent. That structural asymmetry is the precondition for any non-arbitrary value claim.
What Carries Through applies the framework to the question “what should I do?” The structural answer: do things whose carry-through you can sustain, under criteria you can own, that produce real distinctions and verdicts you can feed back into further action. The enemy is not failure. The enemy is non-executability.
Why Games Feel Meaningful argues that games feel meaningful not because of their content but because they compress the structural conditions for meaning — persistence, distinction, and selection — into a resolution a human can directly experience. Games are meaning laboratories, not simulations of meaning.
Taken together, the essays develop a philosophy of how process carries through, how malformed requests fail, and how meaningful action becomes possible once selection is made explicit.
The essays are available at tompassarelli.org. All work is released under CC0.