Lucas–Penrose argument
In plain wordsAn argument that human minds cannot be computers because, using a famous result in logic, people can see that certain statements are true that no fixed computer program could prove.
An argument from Kurt Gödel's incompleteness theorems that the human mind is not equivalent to any machine. For any consistent formal system strong enough for arithmetic — and so for any computer program regarded as a theorem-proving system — there is a true sentence, its Gödel sentence, that the system cannot prove; a human mathematician, the argument runs, can see that the sentence is true, so the mathematician is not that system and, since the system was arbitrary, not any machine. Roger Penrose added that human understanding must therefore exploit non-computable physical processes. Most logicians and philosophers reject the argument, chiefly because humans cannot in general know that their own reasoning is consistent, and because it credits people with an infallible mathematical insight they lack.
Origin
Alan Turing considered and rejected 'the mathematical objection' in 1950. J. R. Lucas stated the argument in 'Minds, Machines and Gödel' (Philosophy, 1961), and Roger Penrose revived and extended it in The Emperor's New Mind (1989) and Shadows of the Mind (1994).
Usage note
Gödel himself drew only a disjunctive conclusion (1951): either the mind surpasses every machine or there are absolutely unsolvable mathematical problems. Penrose's proposed physical mechanism, developed with Stuart Hameroff as 'orchestrated objective reduction', is a separate and equally contested hypothesis.
Related
- Lovelace objectionLovelace objection, n.: The argument, traced to Ada Lovelace in 1843, that computers cannot be truly creative because they can only do what they have been programmed to do.
- computational theory of mindcomputational theory of mind, n.: The idea that thinking is a kind of computation: the mind processes information by following rules, much as a computer runs a program, and the brain is the machine doing it.
- strong AIstrong AI, n.: Originally, the claim that a computer running the right program would literally have a mind and understand, not just imitate understanding. Today it often simply means AI as capable as humans across the board.
- machine consciousnessmachine consciousness, n.: Whether a machine such as an AI system could have genuine experiences of its own — and the research field that tries to find out, or to build such a machine.
- Computing Machinery and IntelligenceComputing Machinery and Intelligence, prop. n.: Alan Turing's 1950 essay asking whether machines can think. It proposed a conversation test in place of that question, answered objections to thinking machines and suggested that machines might learn like children.
Sources
- Lucas, J. R. (1961). Minds, Machines and Gödel. Philosophy 36(137), 112–127.
- Penrose, R. (1989). The Emperor's New Mind. Oxford University Press.
Mentioned in
Gödel's incompleteness theoremsGödel's incompleteness theorems, n.: Two famous results from 1931 showing that any consistent set of rules for doing arithmetic leaves some true statements unprovable, and cannot prove that it is itself free of contradictions., philosophy of artificial intelligencephilosophy of artificial intelligence, n.: The branch of philosophy that asks what AI is and could be: whether machines can think, understand or be conscious, what intelligence is, and what we owe to and should expect from intelligent machines., Lovelace objectionLovelace objection, n.: The argument, traced to Ada Lovelace in 1843, that computers cannot be truly creative because they can only do what they have been programmed to do., Roger PenroseRoger Penrose, prop. n.: A British mathematical physicist and Nobel laureate who argues that human understanding is not computational, so that no computer, however powerful, could truly think like a mathematician.