Re: Arithmetical Realism

From: 1Z <>
Date: Tue, 29 Aug 2006 18:45:03 -0000

Bruno Marchal wrote:
> 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.

It makes no other ontological commitment.

>As I said more than 10 times to you is that comp,
> through AR makes a commitment about the existence of (non substantial)
> numbers.

The version of AR that is supported by comp
only makes a commitment about mind-independent *truth*. The idea
that the mind-independent truth of mathematical propositions
entails the mind-independent *existence* of mathematical objects is
a very contentious and substantive claim.

> You tend to beg the question through your assumption that only primary
> physical matter exists.

AFAICS, I am only asuming that *I* exist.

(I could also you tend to beg the guqestio that ruth is existence...)

> But then comp is false or the UDA reasoning is false, but then just
> show where, please.

Where is it shown the UD exists ?

> 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?

It is possible that I am wrong. It is possible that I am right.
But you are -- or were -- telling me matter is impossible.

> > 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.

But the negative integers exist (or "exist"), so it has
an existing predecessor.

 All you are aying is that in Platoia
there are structures with the same one-way quality as time,
well, of course there are. Every structure exists in Platonia,
if Paltonia exists.

That doesn't explain why we see only one particular structure
(which is still only B-series).

> 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

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Received on Tue Aug 29 2006 - 14:47:57 PDT

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