< Texts on topics cikon.de

A Short Refutation of Computationalism

A possible wording of the computationalist's credo:

"Whatever the functional principle of the mind or intelligence, the computer is guaranteed to be able to accommodate it." (As quoted / stated in Who will win AI: Computer or Brain?, by Christoph von der Malsburg.)

Question: Is this a theorem? In other words: Is the (human) mind (i.e., the totality of  - electro-chemical and electrodynamic - processes supported by the brain and its body interacting with their external environment) provably computable (e.g., Turing realisable)? This looks like an instance of Church's Thesis. What would be required of a rigorous proof?

Remember: Church's Thesis is not a theorem! It  cannot be proven. It can be interpreted as a definition of "computability" and made plausible (as a definition) by proving the equivalence of different formalisms designed to capture the notion of effective computability (e.g., Turing-machines, lamda-calculus, recursive functions, Chomsky-0 grammars, RAMs, Post's rewriting systems, Markov algorithms, etc.).

That's all. Hence, in order to prove a statement such as the above (more reliably than by mere "hand-waving") we have to create a formal (abstract) model of brain-body-systems and prove its Turing-equivalence. But there is no guarantee that our model captures all relevant aspects (or functional principles?) of natural brain-body systems. Whatever model we come up with, it falls short of the "real thing". That's what models do. To claim that we can create an all-encompassing model of natural brain-body systems (let alone implement it) would in all likelihood be an instance of potentially dangerous hubris (see also: Will “intelligent” machines “take over”?).

Of course we know that biological brain-body systems can compute, they are capable of emulating Turing Machines (simply because they were invented by one specific brain-body system, named Alan Turing!). So the reverse of the above stated credo is trivially true: "Whatever the functional principle of the (Turing-equivalent) computer, the human mind or intelligence is guaranteed to be able to accommodate it."

The human mind, unassisted, does it slowly, very slowly. But it is powerful enough to invent devices that speed it up dramatically. We call these devices - products of the human mind - "computers", artificial extensions of the human mind.

(More on The Mind-Body Problem – is it Really a Problem?)

Hans-Georg Stork, 3/2017