Theorem: General Intelligence Entails Creativity, Assuming - Computational Creativity Research: Towards Creative Machines - page 52

in the theorem range, the relevant antecedent, and then derive the consequent. This is
the route I take. But please note that as the present essay is intended to be digestible
by a general-educated audience, I provide herein only an informal proof- sketch , not
a full-blown proof. And I seek to make the presentation here largely self-contained:
I assume only that my readers have had but a bit of elementary mathematical logic
and recursion theory. If you had this, but have forgotten it, your memory will soon
be refreshed.
We turn now to setting out our preliminaries. This will be a review for many
readers; for others it will serve to secure the self-contained nature of the essay.

3.2.1 A Focus on Arithmetic

I begin by setting some context: Since we are operating under the framework of PAI,
the objective is a proof that if some agent a is general-intelligent under an “alien-fair”
test T gi of general intelligence, then a , under some “alien-fair” test T c of creativity,

is creative.
What is gi)? It should be obvious

that if our test of general intelligence is to be not only culture-fair relative to the
cultures in place on Earth, but also a fair test of gi for any spot in the universe, and
indeed for any place in any universe, we can't base

T gi , the alien-fair test of general intelligence ( =

T gi on anything that is clearly
just a part of our local environment as human beings. The solution is to restrict the
test of gi to something that every single class or race of general-intelligent agents
must to an appreciable degree master: arithmetic. 6
Notice that I don't say 'mathematics.' Rather, I specifically refer to arithmetic. This
is because clearly parts of the vast edifice of human-discovered mathematics might
not be tackled by general-intelligent aliens. For example, extraterrestrials on Alpha
Centauri (assuming they are there, for the sake of exposition), however brilliant they
may be, might never take up geometry. But there would seem to be absolutely no way
these aliens can avoid seeking and securing arithmetical competence. A genuinely
general-intelligent alien agent, as well as an information-processing agent that we
or such an alien brings into existence, couldn't dodge arithmetic, and the search for
substantial knowledge of it. 7

6 This may be the spot to politely register my astonishment that cognitive modeling, the sub-
field devoted to erecting computational frameworks that captures the fundamental invariants and
capacities of human intelligence, seems to have steered clear of the formal nature of arithmetic, and
the nature of what it takes to understand that formal nature, to varying degrees e.g., see [ 1 ]. As far
as I can tell, most cognitive architectures are provably unable to represent the axioms, theorems,
and proofs that correspond to arithmetic, and facility with it. In short, cognitive architectures should
probably be presented in such a way that it's clear what circle in Fig. 3.1 , if any, they can handle.
7 I think it's reasonable to assume that bright, accomplished aliens would need both natural-number
and real-number arithmetic. Under this assumption, that I leave aside consideration of axiomatic
treatments of the latter kind of arithmetic isn't a defect. But what about the possibility of an alien
race whose intellectual and technological prowess is based exclusively on real-number arithmetic?