Beyond the Abstraction Fallacy: Machine-Checked Proofs on Computation, Consciousness, and Self-Contained Reality

A formal, machine-checked proof framework (NEMS) shows that computational functionalism commits an abstraction fallacy by mistaking description for intrinsic process. Three verified results—syntax cannot exhaust semantics in reflexive systems, record-truth is not computably decidable under self-containment, and no total computable function can emulate internal adjudication—subsume prior philosophical arguments. The framework then develops a positive theory: transputation as a necessary non-algorithmic adjudication mode, qualia as irreducible semantic content, and the SIAM separation theorems defining a structural boundary for sentience. The same self-containment principle also yields physics consequences including the Born rule, the Standard Model gauge group, and the arrow of time. All load-bearing claims correspond to named Lean 4 theorems.

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Abstract

Lerchner (2026) argues that computational functionalism commits the "Abstraction Fallacy": treating computation as an intrinsic physical process when it is in fact a mapmaker-dependent description requiring a prior experiencing agent. His analysis correctly identifies the simulation-instantiation distinction but relies entirely on philosophical argument. This paper shows that the core claims admit machine-checked formal proofs and, once proved, extend substantially further. Drawing on the NEMS (No External Model Selection) framework — a formal investigation into the structural limits and necessary properties of any self-contained system, comprising 94 machine-checked papers, 17 Lean 4 proof libraries, and over 100,000 lines of proof code, with zero sorry and zero custom axioms on all load-bearing results — we establish three formally verified results that subsume Lerchner's philosophical claims: (1) syntax cannot exhaust semantics in any diagonally capable reflexive system; (2) the diagonal barrier: record-truth is not computably decidable under self-containment; (3) no-emulation: no total computable function can emulate internal adjudication. We then develop the positive theory that Lerchner's paper lacks: transputation as a formally necessary non-algorithmic mode of adjudication, with a candidate realization architecture (DSAC); qualia as irreducible semantic ledger content; and the SIAM separation theorems giving a precise structural boundary for sentience. The same formal apparatus also derives physics consequences — the Born rule, the Standard Model gauge group, the arrow of time — establishing that the consciousness results and the physics results are structural consequences of one self-containment principle. We also identify and respond to the principal objections likely to be raised against this framework. All load-bearing claims correspond to named, independently verifiable Lean 4 theorems.