On 22 Aug 2012, at 12:17, benjayk wrote:

Bruno Marchal wrote:

On 22 Aug 2012, at 00:26, benjayk wrote:

meekerdb wrote:

On 8/21/2012 2:52 PM, benjayk wrote:

meekerdb wrote:
On 8/21/2012 2:24 PM, benjayk wrote:
meekerdb wrote:
"This sentence cannot be confirmed to be true by a human being."

The Computer

He might be right in saying that (See my response to Saibal).
But it can't confirm it as well (how could it, since we as
humans can't
confirm it and what he knows about us derives from what we
program into
it?). So still, it is less capable than a human.
I know it by simple logic - in which I have observed humans to be
relatively slow and
error prone.

regards, The Computer

Well, that is you imagining to be a computer. But program an actual
computer that concludes this without it being hard-coded into it.
All it
could do is repeat the opinion you feed it, or disagree with you,
on how you program it.

There is nothing computational that suggest that the statement is
true or
false. Or if it you believe it is, please attempt to show how.

In fact there is a better formulation of the problem: 'The truth-
value of
this statement is not computable.'.
It is true, but this can't be computed, so obviously no computer can
this conclusion without it being fed to it via input (which is
external to the computer). Yet we can see that it is true.

Not really.  You're equivocating on "computable" as "what can be
and "what a
computer does".  You're supposing that a computer cannot have the
reflexive inference
capability to "see" that the statement is true.
No, I don't supppose that it does. It results from the fact that we
get a
contradiction if the computer could see that the statement is true
(since it
had to compute it, which is all it can do).

A computer can do much more than computing. It can do proving,
defining, inductive inference (guessing), and many other things. You
might say that all this is, at some lower level, still computation,

Sorry, but the opposite is the case. To say that computers do proving,
defining, guessing is a confusion of level, since these are interpretation of computations, or are represented using computations, not the computations
itself. If we encode a proof using numbers, then this is not the proof
itself, but its representation in numbers. Just as "Gödel's proof" is not
Gödel's proof just because I say it represents Gödel's proof.
Or just as I say computers the word computers don't compute anything.

That is why when I say that a computer dreams, or that a number dreams, it is a shorthand for a computer having an activity supporting a dream, or a number involved in an arithmetical realization of a dream.
This makes sense in the comp theory.

In arithmetic too we already make the distinction between a number representing a proof and the proof itself, which is the sequence of distinct formula verifying some conditions.
Computers do that distinction.

PA use numbers as language like German use the German language, but both the Germans and PA will distinguish what they talk about and the syntactical terms used to denote them.

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.

That is the reason that I don't buy turings thesis, because it intends to
reduce all computation to a turing machine

... to a Turing machine activity (as defined in math, I don't mean physical activity).

just because it can be
represented using computation. But ultimately a simple machine can't compute the same as a complex one, because we need a next layer to interpret the simple computations as complex ones (which is possible). That is, assembler isn't as powerful as C++, because we need additional layers to retrieve the
same information from the output of the assembler.

That depends how you implement C++. It is not relevant. We might directly translate C++ in the physical layer, and emulate some assembler in the C++. But assembler and C++ are computationally equivalent because their programs exhaust the computable function by a Turing universal machine.

You are right that we can confuse the levels in some way,

Better not to confuse the levels ever, except when using fixed point theorem justifying precisely how to fuse levels.

basically because
there is no way to actually completely seperate them.

When we look at an unknown machine, yes.

But in this case we
can also confuse all symbols and definitions, in effect deconstructing
language. So as long as we rely on precise, non-poetic language it is wise
to seperate levels.

OK. I agree with this.


Bruno Marchal wrote:

but then this can be said for us too, and that would be a confusion of
Only if we assume we are computational. I don't.

Bruno Marchal wrote:

The fact that a computer is universal for computation does not
imply logically that a computer can do only computations. You could
say that a brain can only do electrical spiking, or that molecules can
only do electron sharing.
You have a point here. Physical computers must do more then computation, because they must convert abstract information into physical signals (which
don't exist at the level of computation).
But if we really are talking about the abstract aspect of computers, I think my point is still valid. It can only do computations, because all we defined
it as is in terms of computationl.


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