On Jun 9, 7:27 am, Bill Taylor <w.tay... at (no spam) math.canterbury.ac.nz> wrote:
Can someone explain to me what this guy is talking
about? I'm sure it's something deep, and interesting...
if I understood it, that is...
http://www.cs.bu.edu/fac/lnd/expo/gdl.htm
I stopped reading at this point, where mysticism is sure to follow:-
For it is just this becoming evident of more and more new axioms
on the basis of the meaning of the primitive notions that
a machine cannot imitate.
This quote, allegedly by Godel in 1961, (though I'm surprised
that he would make such an elementary Lucas-like blunder)
is at the heart of silly old-fashioned thinking.
Whenever one reads a line that purports to say something
about what machines cannot do, pause and reflect that
we too are machines, and can do some of these things.
Of course, we are massively parallel machines, with vast
memory back-up (experience) and multi-port inputs
and possible internal random elements, but nothing in
the above quote (or those like it) discounts any of that.
The distinction between carbon and silicon is utterly
irrelevant. Sandbrains will eventually be made to imitate
meatbrains with great versimilitude, like HAL in 2001.
Though it will take a lot longer to invent them than
sci-fi writers may hope!
If one wishes to *restrict* the sort of things that machines
are *allowed* to do, to perform (or fail to) these various
quoted tasks, then ultimately all one is saying what Godel
proved, that perfect-recursive machines cannot do them,
and so we are no further ahead.
If one wants to say that some new axioms are "self-evident"
to humans, then there is no reason that they should not be
self-evident to mathematically educated sandbrains as well.
Quotes like the above one REALLY STINK!
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Bill Taylor W.Tay... at (no spam) math.canterbury.ac.nz
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The Physical Turing Machine is to computer science
as the perpetual motion machine once was to physics.
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Gödel's statement in the quotation is right for the concept of machine
Gödel was referring to, namely, finite state machines, i.e algorithms
(assuming Church thesis).
And for any sensible concept of 'machine', I'd add.
The reason is that machines have no FUNCTIONAL semantic states, since
they can be fully described by specifying a set of instructions for
symbol manipulation. Note that Gödel writes:
"(...) on the basis of the meaning of (...)"
which sounds as though he meant that grasping meaning is functional.
Gödel insisted on the existence of 'abstract concepts', i.e. concepts
whose possession enables for knowledge that cannot be reduced to
symbol manipulation.
