Re: Incompleteness vs. Mechanical Reasoning

On Apr 4, 8:06 am, Marshall <marshall.spi...@xxxxxxxxx> wrote:
A few times lately I've had the experience of mentioning
something about mechanical reasoning and then having
someone mention incompleteness as if that had anything
to do with what I was saying. In fact the attitude seems
to be akin to that woman in the penguin-on-the-telly sketch
who says "there; I've run rings around you logically."

It's puzzled me a good deal.

A thought just occurred to me: could this possibly be
the result of people thinking that incompleteness is
something that affects mechanical systems but not
our brain? Is the idea floating around that the human
mind is somehow capable of doing things not only
that no *current* computer can do, but also that no
possible future computer could ever do? Is that
what's going on here?

How do I say this: I do not subscribe to that hypothesis.


The human mind has free will and is capable of making a genuinely
random decision. Take a proposition like "X will leave for office at
9-00 AM tomorrow". Not even X can be certain of the truth of or
falsity of this proposition even until a micro-second before 9-00 AM
tomorrow. This, in my opinion, is the difference between a human being
and a machine. Normal machines that we are aware of are predictable,
while human beings are not.

Of course I am talking about machines that take in predictable inputs,
without any interaction with human beings. E.g. I could program a
machine to shut itself down if there are 5 or more users logged in at
5-00 AM tomorrow. Here the machine is taking in unpredictable inputs
and is therefore unpredictable. A human being could be unpredictable
even if all inputs are predictable.

I think that quantum computers are actually capable of picking
genuinely random numbers, just like human beings, and could therefore
be just as unpredictable as human beings. In fact a human mind may
actually be doing quantum computations for all we know. To confirm
this would require a new computability theory, formulated in the logic
NAFL, as noted in the following reference:

http://arxiv.org/abs/math.LO/0506475

Regards, RS

.

Relevant Pages

  • Re: Incompleteness vs. Mechanical Reasoning
    ... something about mechanical reasoning and then having ... someone mention incompleteness as if that had anything ... It is a basic postulate of the logic NAFL. ... declarations made in the human mind. ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... something about mechanical reasoning and then having ... someone mention incompleteness as if that had anything ... possible future computer could ever do? ... random decision. ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... someone mention incompleteness as if that had anything ... possible future computer could ever do? ... mechanical reasoning does not exhaust all the possibilities of logical ... whether human mind can in turn exhaust them (or at least ...
    (sci.logic)
  • Re: Incompleteness vs. Mechanical Reasoning
    ... something about mechanical reasoning and then having ... someone mention incompleteness as if that had anything ... In fact the attitude seems ... possible future computer could ever do? ...
    (sci.logic)
  • Incompleteness vs. Mechanical Reasoning
    ... A few times lately I've had the experience of mentioning ... something about mechanical reasoning and then having ... someone mention incompleteness as if that had anything ... possible future computer could ever do? ...
    (sci.logic)