# Re: Arithmetical Realism

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Tue, 29 Aug 2006 16:30:40 +0200

Le 28-août-06, à 16:47, 1Z a écrit :

>
>
> Bruno Marchal wrote:
>
>> AR eventually provides the whole comp ontology, although it has
>> nothing
>> to do with any commitment with a substantial reality.
>
> If it makes no commitments about existence,. it can prove nothing about
> ontology.

Absolutely so. But I said that comp makes no commitment about primary
physical stuff. As I said more than 10 times to you is that comp,
through AR makes a commitment about the existence of (non substantial)
numbers.

You tend to beg the question through your assumption that only primary
physical matter exists.
But then comp is false or the UDA reasoning is false, but then just

Tell me also this, if you don't mind: are you able to doubt about the
existence of "primary matter"? I know it is your main fundamental
postulate. Could you imagine that you could be wrong?

> Bruno Marchal wrote:
>
>> In both comp and the quantum, a case can be made that the
>> irreversibility of memory (coming from usual thermodynamics, or big
>> number law) can explain, through physical or comp-physical
>> interactions, the first person feeling of irreversibility.
>> But with comp we do start from a basic "irreversibility": 0 has a
>> successor but no predecessors.
>
> ...among the natural numbers. Does COMP really prove
> that negative numebrs don't exist ?

Who said that? You can already define the negative integer in Robinson
Arithmetic, and prove the existence of each negative integer. The
common algebraical construction of the integer as couple of natural
number togeteher with the genuine equivalence relation can be done in
RA. RA or PA proves only that 0 has no predecessor among the natural
numbers.
Actually, as I have said, RA can already define all partial recursive
functions, i.e. all function which are programmable in your favorite
programming language. (No need of CT here, unless your favorite
programming language belongs to the future).
Despite this RA is very weak and has almost no ability to generalize.
Peano Arithmetic PA, which is just RA + the induction axioms, is much
clever, and most usual mathematics (including Ramanujan's work) can be
done by PA.

Bruno

http://iridia.ulb.ac.be/~marchal/

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Received on Tue Aug 29 2006 - 14:26:57 PDT

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