Ben Goertzel wrote:
Hi,
s.
1) Would anyone currently putting energy into the foundations of
probability discussion be willing to say that this hypothetical human
mechanism could *still* be meaningfully described in terms of a
tractable probabilistic formalism (by, e.g., transforming or
approximating all the nasty nonlinearity I just introduced into a
simpler, more analytic form, without losing anything)?
[My intuition on this question: no way.]
My intuition is completely opposite yours on this issue.
I think that a system like you described above could likely be
described, in terms of its **action selections** and patterns therein,
using probability theory.
This is why, in the theoretical hypotheses I proposed, I was talking
only about probabilistic rules observed by an external agent M2 to
govern a given agent M1's action-selections. I was not making any
committments that M1 has to explicitly use probability theory
internally. I think that explicitly using probability theory internally
is only one among many ways to wind up approximately using probability
theory on the level of patterns in one's action-selections.
Point taken: but I was specifically *not* addressing any of the issues
related to describing an M1 using some other M2 that employed
probability theory. I was strictly confining myself to the question of
whether M1 used any kind of probability theory in its internal
mechanisms. I thought that was obvious, but I guess not. I have no
interest in the M2 arguments.
Also, I don't know why you contrast "analytic" with "nonlinear."
Nonlinear equations are analytic constructs, just as surely as
probabilistic equations. And probabilistic relationships can be nonlinear.
I did not mean the word "nonlinear" to be interpreted in the narrow
sense (again, sorry, but I did not think I needed to explain that usage,
given my known position on these issues): I meant generalized
nonlinearity (which includes realms of "badly behaved" functions), and
when I said "analytic" I meant that there are no *analytic* solutions to
these sorts of beast.
I mean: if the concept units I described are really basing crucial
decisions on such factors as those that came up in the example I gave,
where the decision about raven-blackness depends on the appearance of a
a very particular representation of other concepts in the STM (to wit,
the fact of the interlocutor having weird motives), isn't this a
paradigm case of (generalized) nonlinearity?
2) Suppose that this really *is* the way the human cognitive system
works, and that the reason it works this way is that evolution has
figured out (pardon the teleology: you know what I mean) that any
attempt to build systems that manipulate more tractable types of
"concepts," using simpler types of reasoning formalisms that actually
do allow things to be interpreted in a high level way, simply do not
work. In other words, such system just do not get to be intelligent
(for whatever reason.... but probably because they can never learn
those horribly vague, messy-looking concepts that don't fit very
nicely into logical formalisms, but which are vital to the development
of the system)? My actual question, then: Suppose it just happens
not to be possible to do it any other way than with all the messy,
nonlinear mechanisms described above: what, in that case, would be
the use in trying to keep as close as you can to a formal, tractable
approach to AGI, of the sort that would allow you to prove at least
something about the way the not-quite-probabilities are handled?
It **could** be that the only way a system can give rise to
probabilistically sensible patterns of action-selection, given limited
computational resources, is to do stuff internally that is based on
nonlinear dynamics rather than probability theory.
But, I doubt it...
The human brain may work that way, but it is not the only (nor the
ideal!) cognitive system...
Hmmm.... but what I wanted was to try to get some traction on why you
would say this.
Your answer is only "I don't think so."
Your comment that the human brain "... is not the only (nor the ideal!)
cognitive system" is a direct rejection of the idea that I was asking
you to consider as a hypothesis.
I *know* you don't believe it to be true! ;-) What I was trying to do
was to ask on what grounds you reject it.
Richard Loosemore.
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