CF Debate

Church Turing Thesis

Key ArgumentMethodologySubstrateBehaviouralOntologyComputational

Overview

All computable functions and physical phenomena can be simulated to arbitrary input/output accuracy on a Turing Machine or any equivalent computational system, including modern digital computers. Given the extremely broad class of such functions, it is highly likely that the functions of consciousness fall within them. If consciousness does not have a function, then it can be hard to understand why we are able to report on it and why consciousness would have been amenable to natural selection (see Natural Selection Argument).

Responses

  1. This argument can be challenged both on its limited definition of computation and its dismissal of non-computable phenomena. On the former, Turing equivalence ensures input-output equivalence of computations, but it is possible that other aspects of computation matter for consciousness. For instance, if the number of computational steps (or underpinning physical mechanisms) in an algorithm is relevant, then Turing Machine simulation does not guarantee capturing all the necessary details. The same goes for the number or nature of inputs and outputs to individual computational steps. Possible motivations can be drawn from theories of consciousness invoking ignition thresholds and phase transitions, pointing to information-processing density requirements that do not carry over in Turing-equivalence. More generally, digital simulations of even fairly simple phenomena break down quite quickly, e.g. the exact development of a system with a few hundred strongly entangled particles. In many cases, the only effective simulation of a complex system long-term is the system itself.

    BUT: These arguments are only suggestive of cases where Turing equivalence is insufficient. Without fully specified candidate algorithms for conscious experience, they are hard to evaluate. There is a reasonable debate about where the burden of proof should lie in this debate.

  2. Not all phenomena are exactly computable and these might be relevant for consciousness (or at least, it is premature to rule them out). For instance, the exact values of many real numbers cannot be computed and such numbers often have special significance in our theories of mathematics and physics (such as pi, phi, e). Likewise, it is not possible to generate exact digital equivalents of continuous or analog physical phenomena (such as quantum mechanics, certain field structures, space-time in general relativity). If those phenomena matter in their own right as physical structures (e.g. quantum entanglement for phenomenal binding or sources of 'true' randomness in some relevant sense) or if their exact functional outputs matter for consciousness (e.g. the sensitivity of chaotic systems to exact initial conditions for the right criticality levels), then Turing Machine simulation would be inadequate.

    BUT: Regarding exact non-computable numbers: If the base layer of physics is discrete (a question which remains open), then non-computable reals cannot be embedded in physical systems either. Even if physics is continuous, the embedding of any real number could not be "read off" in exact terms, given limits such as Bekenstein's bound, placing restrictions on the ways on which such a value could be incorporated into a function.

    BUT: Regarding physical structures: There is an open debate in philosophy of science whether physical structures are exhaustively described by their causal interactions (e.g. ontic structural realism). If they are, it becomes more plausible that all the same properties would inhere in simulations with emergent causal structures that map exactly onto a target causal structure.

  3. It is possible that the same input/output function can be adequately replicated on a Turing Machine in terms of precision, but that there is some other aspect of the function that matters for consciousness. In other words, there might be two functions that broadly (or even precisely) have the same result, but with different causal structures for getting there or with different substrate properties, and that these matter for consciousness. For instance, certain analogue computing methods (such as non-linear optical Ising machines) might be more energy efficient, spatiotemporally concentrated, or amenable to our evolutionary environment than equivalent digital Turing Machine methods. Those functional differences might be directly necessary for consciousness or the physical substrates that enable them might happen to be the only ones capable of consciousness.

    More generally, computations would not give rise to consciousness until they are physically implemented. As soon as they are physically implemented, various physical phenomena and constraints become relevant, such as features of the implementation substrate or the thermodynamics of information processing/storage/correction. It is possible that consciousness depends not only on a computable function but some aspect of its thermodynamics or physical implementation.

Further reading