Theorem: General Intelligence Entails Creativity, Assuming - Computational Creativity Research: Towards Creative Machines - page 58

over basic arithmetic at the level of the truths of arithmetic will not be persuaded. But
I maintain that at the very least it's undeniable that it's not unreasonable to construe
alien-fair gi in such a manner that understanding of one or more

is included. After
all, Earth-bound empirical evidence is on my side, given the remarkable creativity it
has taken to reach some truths. I also maintain that it's not unreasonable to identify

creativity with a process of coming to know some , since invariably this hard-won

knowledge comes via reasoning that is beyond the rigid, mechanistic construction
of standard formal proofs in first-order logic.

3.4.2 A Non-creative Route to a ?

Objection: “But here's a non -creative way to reach the performance you say is cre-
ative, which serves as a counter-example to your so-called theorem: We know that
the set of all formulae reachable from the grammar and alphabet of L A by standard

recursive rules for well-formedness is countably infinite. Even the extensions of the
language to make room for the moves to second-order logic of course stay within
the bound of countably infinite. Hence there is a machine

which prints out (in
accordance with some lexicographic ordering) the first such formula, then the sec-
ond, and so on. In addition,

M

is assumed to be equipped with a random “formula
picker” P such that, given a formula in the relevant class, it returns either

M

true or

M

false 's you're talk-

ing about to be true—and yet clearly this 'agent' is operating in purely mechanistic,
naïve fashion, indeed more so than the searching for proofs in the proof theory

randomly. Clearly, if -plus- P is lucky, it will declare all the

.”
My reply: Multiple problems are fatal to this objection; I mention two here. First, if
this objection worked, then basic incompleteness results like

˄

would in some sense
be surmounted as well, by stunningly “dumb” means. But no one thinks there's a
shortcut here to establishing formulae that are beyond PA ˄ . Second, my tests of
both gi and creativity (in the realm of arithmetic) are such that to pass requires
understanding , and the behavioral correlate to understanding, taken to confirm its
presence, is justification . 13 In other words, and this repeats what has been said above,
to pass

G

T gi , an agent must prove that their answers to basic arithmetic are correct;
and to pass T c must prove at least one truth about arithmetic. The dim contraption

M -plus- P does nothing of the sort.

3.4.3 Mere Mechanical via Ordinal-Logics?

Objection: “You are ignoring perhaps the very earliest systematic attempt to 'sur-
mount' Gödelian incompleteness, one seminally inaugurated by none other than
Turing, in his doctoral dissertation, and soon thereafter published in [ 20 ]: viz., ordinal

13 See footnote 12.