Abstract:
A common intuition in debates about artificial intelligence, consciousness, and free will is that ordinary Turing computation may be fundamentally insufficient: something about minds or “true” general intelligence is thought to depend on non-computable physical processes or hypercomputation. These claims are rarely grounded in a precise model of what an embedded agent can actually observe and use when interacting with the world.
This paper adopts a deliberately minimal, operational perspective. We model an embedded agent whose only contact with the universe is through finite measurement records, and we define a corresponding space of reality as everything that can possibly be known and abstracted in this sense. Within this measurement-limited framework we provide two main results.
First, we prove an epistemic Turing sufficiency theorem: for any finite measurement history available to an embedded agent, there exists a Turing machine whose observable behavior is indistinguishable from that of the physical universe over that history. Second, we introduce operational definitions of consciousness, sentience, and free will as specific types of policies over finite measurement histories and internal symbolic states, and we show that, under mild effectiveness assumptions, all three processes can in principle be implemented by a Turing machine.
We discuss the implications for artificial general intelligence (AGI) and superintelligence (ASI). Any such system whose behavior supervenes on rules over finite sensor histories and in- ternal states—precisely the setting considered here—does not require more than Turing-powerful
computation to realize the functional structures associated with consciousness, sentience, or exploratory free will in the sense defined. The analysis is agnostic about the ultimate nature of physical law and does not address phenomenal consciousness or qualia. It clarifies, instead, what
can and cannot be demanded of computation at the level of behavior and decision-making for embedded agents.
2025-11-16 | Preprint
Contributors: David Keil