The point I just made cannot be pursued very far, however, because any
further discussion of it *requires* that someone on the AIXI side
become more specific about why they believe their definition of
"intelligent behavior" should be considered coextensive with the
common sense use of that term. No such justification is forthcoming,
so withot it all I can do is rest my case by asking "Why should I
believe your (re)definition of intelligence?"
Well, actually, the theorems about AIXI work if we define intelligence as
"maximize criterion F"
where F is **any** computable function. At least that's my reading of
the theorems...
So, no matter what definition you specify for "intelligence", so long as
it involves maximizing some computable function, the AIXI theorems will
apply, and the conclusion will be that AIXI is maximally intelligent
according to the definition.
The question, then, is whether maximization of some computable function
is a reasonable definition of "intelligence."
It seems clear that any IQ test ever given to humans **does** fit nicely
into this framework. For instance, "do really well on a long series of
IQ tests" would be a definition of intelligence fitting into the
assumptions of the AIXI theorems. AIXI, given the series of IQ tests,
would gradually learn how to do well on the IQ tests --- consuming a lot
of resources in the process, but doing at least as well as any other
system would, assuming equivalent initial states of knowledge.
OTOH, Pei Wang has proposed that intelligence should be explicitly
defined as something roughly like "achieving complex goals given limited
resources" [not his exact wording]. In this case AIXI would not be
considered intelligent....
But my view is that the natural language concept of intelligence
actually is just about functionality rather than mechanisms. We say
someone is smart because of the problems they can solve, not because of
our understanding of how they go about solving the problems...
Anyway, the NL notion of "intelligence" is not necessarily any more
intrinsically meaningful than the NL concepts of "cup" and "bowl"....
It combines a bunch of deep ideas with some culturally relative and
anthropomorphic stuff that is not so important...
The notion of intelligence embodied in AIXI is an interesting one, which
things can be proved about.... I don't claim that it exhausts the
interesting insights contained in the ambiguous and diverse NL concept
of intelligence...
-- Ben G
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