Ben,

No, I wasn't intending any weird chips.

For me, the most important way in which you are a constructivist is
that you think AIXI is the ideal that finite intelligence should
approach.

--Abram

On Wed, Oct 29, 2008 at 2:33 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>
> OK ... but are both of these hypothetical computer programs on standard
> contemporary chips, or do any of them use weird
> supposedly-uncomputability-supporting chips?  ;-)
>
> Of course, a computer program can use any axiom set it wants to analyze its
> data ... just as we can now use automated theorem-provers to prove stuff
> about uncomputable entities, in a formal sense...
>
> By the way, I'm not sure the sense in which I'm a "constructivist."  I'm not
> willing to commit to the statement that the universe is finite, or that only
> finite math has "meaning."  But, it seems to me that, within the scope of
> *science* and *language*, as currently conceived, there is no *need* to
> posit anything non-finite.  Science and language are not necessarily
> comprehensive of the universe....  Potentially (though I doubt it) mind is
> uncomputable in a way that makes it impossible for science and math to grasp
> it well enough to guide us in building an AGI ;-) ... and, interestingly, in
> this case we could still potentially build an AGI via copying a human brain
> ... and then randomly tinkering with it!!
>
> ben
>
> On Wed, Oct 29, 2008 at 1:45 PM, Abram Demski <[EMAIL PROTECTED]> wrote:
>>
>> Ben,
>>
>> The difference can I think be best illustrated with two hypothetical
>> AGIs. Both are supposed to be learning that "computers are
>> approximately Turing machines". The first, made by you, interprets
>> this constructively (let's say relative to PA). The second, made by
>> me, interprets this classically (so it will always take the strongest
>> set of axioms that it suspects to be consistent).
>>
>> The first AGI will be checking to see how well the computer's halting
>> matches with the positive cases it can prove in PA, and the
>> non-halting with the negative cases it can prove in PA. It will be
>> ignoring the halting/nonhalting behavior when it can prove nothing.
>>
>> The second AGI will be checking to see how well the computer's halting
>> matches with the positive cases it can prove in the axiom system of
>> its choice, and the non-halting with the negative cases it can prove
>> in PA, *plus* it will look to see if it is non-halting in the cases
>> where it can prove nothing (after significant effort).
>>
>> Of course, both will conclude nearly the same thing: the computer is
>> similar to the formal entity within specific restrictions. The second
>> AGI will have slightly more data (extra axioms plus information in
>> cases when it can't prove anything), but it will be learning a
>> formally different statement too, so a direct comparison isn't quite
>> fair. Anyway, I think this clarifies the difference.
>>
>> --Abram
>>
>> On Wed, Oct 29, 2008 at 1:13 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>> >
>> >>
>> >> >
>> >> > But the question is what does this mean about any actual computer,
>> >> > or any actual physical object -- which we can only communicate about
>> >> > clearly
>> >> > insofar as it can be boiled down to a finite dataset.
>> >>
>> >> What it means to me is that "Any actual computer will not halt (with a
>> >> correct output) for this program". An actual computer will keep
>> >> crunching away until some event happens that breaks the metaphor
>> >> between it and the abstract machine-- memory overload, power failure,
>> >> et cetera.
>> >
>> > Yes ... this can be concluded **if** you can convince yourself that the
>> > formal model corresponds to the physical machine.
>> >
>> > And to do *this*, you need to use a finite set of finite data points ;-)
>> >
>> > ben
>> >
>> > ________________________________
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>
>
> --
> Ben Goertzel, PhD
> CEO, Novamente LLC and Biomind LLC
> Director of Research, SIAI
> [EMAIL PROTECTED]
>
> "A human being should be able to change a diaper, plan an invasion, butcher
> a hog, conn a ship, design a building, write a sonnet, balance accounts,
> build a wall, set a bone, comfort the dying, take orders, give orders,
> cooperate, act alone, solve equations, analyze a new problem, pitch manure,
> program a computer, cook a tasty meal, fight efficiently, die gallantly.
> Specialization is for insects."  -- Robert Heinlein
>
>
> ________________________________
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