On Aug 22, 2012, at 1:57 PM, benjayk <benjamin.jaku...@googlemail.com>
wrote:
Jason Resch-2 wrote:
On Wed, Aug 22, 2012 at 1:07 PM, benjayk
<benjamin.jaku...@googlemail.com>wrote:
Jason Resch-2 wrote:
On Wed, Aug 22, 2012 at 10:48 AM, benjayk
<benjamin.jaku...@googlemail.com>wrote:
Bruno Marchal wrote:
Imagine a computer without an output. Now, if we look at what
the
computer
is doing, we can not infer what it is actually doing in terms of
high-level
activity, because this is just defined at the output/input. For
example, no
video exists in the computer - the data of the video could be
other
data as
well. We would indeed just find computation.
At the level of the chip, notions like definition, proving,
inductive
interference don't exist. And if we believe the church-turing
thesis, they
can't exist in any computation (since all are equivalent to a
computation of
a turing computer, which doesn't have those notions), they
would be
merely
labels that we use in our programming language.
All computers are equivalent with respect to computability. This
does
not entail that all computers are equivalent to respect of
provability. Indeed the PA machines proves much more than the RA
machines. The ZF machine proves much more than the PA machines.
But
they do prove in the operational meaning of the term. They
actually
give proof of statements. Like you can say that a computer can
play
chess.
Computability is closed for the diagonal procedure, but not
provability, game, definability, etc.
OK, this makes sense.
In any case, the problem still exists, though it may not be
enough to
say
that the answer to the statement is not computable. The original
form
still
holds (saying "solely using a computer").
For to work, as Godel did, you need to perfectly define the
elements in
the
sentence using a formal language like mathematics. English is too
ambiguous. If you try perfectly define what you mean by
computer, in a
formal way, you may find that you have trouble coming up with a
definition
that includes computers, but does't also include human brains.
No, this can't work, since the sentence is exactly supposed to
express
something that cannot be precisely defined and show that it is
intuitively
true.
Actually even the most precise definitions do exactly the same at
the
root,
since there is no such a thing as a fundamentally precise
definition. For
example 0: You might say it is the smallest non-negative integer,
but
this
begs the question, since integer is meaningless without defining 0
first.
So
ultimately we just rely on our intuitive fuzzy understanding of 0 as
nothing, and being one less then one of something (which again is an
intuitive notion derived from our experience of objects).
So what is your definition of computer, and what is your
evidence/reasoning
that you yourself are not contained in that definition?
There is no perfect definition of computer. I take computer to mean
the
usual physical computer,
Why not use the notion of a Turing universal machine, which has a
rather well defined and widely understood definition?
since this is all that is required for my argument.
I (if I take myself to be human) can't be contained in that definition
because a human is not a computer according to the everyday
definition.
A human may be something a computer can perfectly emulate, therefore a
human could exist with the definition of a computer. Computers are
very powerful and flexible in what they can do.
Short of injecting infinities, true randomness, or halting-type
problems, you won't find a process that a computer cannot emulate.
Do you believe humans are hyper computers? If not, then we are just
special cases of computers. The particular case can defined by
program, which may be executed on any Turing machine.
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