Refutation of Refutation of Pancomputationalism

A rigorous defense of computationalism against its most sophisticated critics, built on the mathematics of algorithmic information theory rather than hand-waving about silicon brains.

The paper's central move is surgical: it identifies a single conceptual error that runs through ten book-length critiques of computationalism, plus the biological naturalism of Anil Seth and Peter Godfrey-Smith. Every one of these critics, the authors argue, is attacking a straw man. They conflate two very different things: (a) abstract computation in the Church-Turing sense — the mathematical notion that any sufficiently expressive physical process can implement — and (b) von Neumann engineering, meaning the specific stored-program digital architecture in your laptop. Pointing out that today's GPUs lack ion channels or autopoietic self-maintenance is empirically interesting but irrelevant to the in-principle question of what computation can do.

The second error is subtler and arguably more important. The critics assume that a "fixed program" means "fixed behavior." It doesn't. A universal Turing machine runs a fixed program and can produce any computable behavior — open-ended learning, adaptive category formation, self-maintenance, genuine novelty. The program specifies the update rules; the variables evolve without bound. An LLM is a fixed program. A reinforcement learning agent is a fixed program. Adaptivity is not something computation lacks; it is what fixed programs do with their variables. The paper calls this the master error shared by all ten critiques.

Against this backdrop, the authors deploy Kolmogorov Theory (KT), their own research program grounded in algorithmic information theory. The key objects are Kolmogorov complexity (the length of the shortest program that produces a string — a substrate-independent measure of structure), mutual algorithmic information between an agent's model and the world (a formal, observer-independent notion of "aboutness"), and a Good Algorithmic Regulator theorem showing that any system that effectively regulates its environment is exponentially pressured to carry shared structure with that environment. Organizational closure, autonomy, precariousness, organism-environment unity, and open-ended evolution all get precise definitions in this vocabulary. The paper works through each of the ten critiques — Rosen, Kauffman, Deacon, Juarrero, and others — and shows that the property each critic claims is beyond computation turns out to be formally characterizable as an algorithmic property.

One concession is genuine and important. The critics are half-right about the syntax-semantics gap. Mutual algorithmic information gives you objective "aboutness" — a model that provably shares structure with the world — but not experienced meaning, meaning-as-lived. KT's answer is that experienced meaning requires pure experience, a phenomenal ground the framework takes as ontologically fundamental alongside mathematical structure. Algorithmic structure plus pure experience yields structured experience. The missing ingredient is phenomenal, not biological. This is where the paper's commitments go deepest and where the most philosophical work remains.