On 15 Sep 2013, at 18:29, John Clark wrote:
On Sun, Sep 15, 2013 Bruno Marchal <marc...@ulb.ac.be> wrote:
> As long as you suggest that there are things "made of" things, you
are staying in the Aristotelian frame. Other can suggest that there
are no such things at all, just natural numbers relative computations,
So you are suggesting that a thing like broken glass is made of
numbers,
????
I was just saying that things are not made up of things.
A broken glass is NOT made of number. That has no meaning at all.
What happens is that addition and multiplication of natural numbers
emulate dreams, which might be dream of a broken glass.
fine, and who knows it might even be true, but don't tell me there
is no such thing as a thing, that's just more gibberish.
It is a matter of tedious, and not so simple, exercise to see that the
computations exist in some definite sense when we postulate
arithmetic. (This is done in good textbook, and very well done in
Epstein & Carnielli, but also in Boolos & Jeffrey).
Physical things then appears as stable percept by persons living those
dreams.
>> By "machine" I assume you mean a deterministic process.
> A machine is not a process,
Make up your mind! First you say everything is the process of
"natural numbers" in "relative computations" and then you say
"digital machines, which are defined in term of number relations"
are an exception to this because what they do "is not a process".
The sum of number relations is not a process?? None of this makes
any sense to me.
Some number relation defines some machines, or some programs, which
are static entities.
*Other number relations, involving the preceding one, defines
computations, or processes, ...
A machine, in that setting is basically one number, relative to some
universal number.
A computation might be codes by one number, but is better seen as a
sequence of numbers, coding the states corresponding to that
computation.
Bruno
John K Clark
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