The Lucas–Penrose argument
PAPER VIII — COMPUTATION · QUESTION 24 OF 32
In plain terms: The free careful statement of what was proved, against which the anti-mechanist leap is measured.
The question as set
Lucas and Penrose argue from Gödel's incompleteness theorems that the mind is not a formal system. State the argument, and the standard objection that it equivocates on what the human mathematician can know to be consistent.
The question in Paper VIII · Its section on the reference page
The question in context
This is question 24 of the 32 set in Paper VIII — Computation of The Truly Hardest Exam in the World, the examination of The College of All Minds. In the College’s subject index it is filed under Consciousness and mind. Like every question of the College, it carries three references of record, verified live at publication and described twice — technically, and in plain terms — so the ground can be judged before it is walked. The response required is an argument, not a survey, of at most three thousand words, as technical as the question demands and no more.
The references of record
Gödel's incompleteness theorems
The theorems with the hypothesis the argument trades on — consistency — and the standard diagnosis of equivocation.
In plain terms: The free careful statement of what was proved, against which the anti-mechanist leap is measured.
The Lucas–Penrose argument about Gödel's theorem
The argument and objection in dedicated form: outstripping the machine requires knowing one's own consistency — which Gödel denies.
In plain terms: The free entry devoted to the exact exchange the question sets — claim, objection, and the equivocation named.
Gödel's own disjunctive caution — mind exceeding machine or absolutely unsolvable problems — against the argument's confidence.
In plain terms: The free account of what the theorems' author thought they showed about minds: strictly less than Lucas claimed.
Background: Penrose–Lucas argument · Gödel's incompleteness theorems