Re: Arithmetical Realism

From: David Nyman <david.nyman.domain.name.hidden>
Date: Sat, 02 Sep 2006 15:57:34 -0000

1Z wrote:

> Necessary truth doesn't entail necessary existence unless
> the claims in question are claims about existence.

If one claims (which I don't BTW) that something is 'necessarily true'
*independent of contingent existence* then I think for this to be in
any way coherent, one must be making some sort of existence claim for
'necessary truth'. By contrast, within contingent existence, some
things may seem 'necessarily true', but this truth can only be derived
from aspects of contingency (i.e. in virtue of the concept and its
referents being contingently instantiated).

> Not if AR is only a claim about truth. Necessary truth
> can exist in a world of contingent existence -- providing
> all necessary truths in such a world are ontologically non-commital.
> As non-Platonists indded take mathematical statements to be.

I agree insofar as you mean what I'm saying above: i.e. the 'existence'
of 'necessary truth' in a world of contingent existence must itself be
'contingently instantiated'. 'Necessity' in this sense is restricted to
'necessary under ceratin contingencies'. In a world of contingent
existence the behaviour of a logical system must reduce ultimately to
the behaviour of a contingently instantiated system.

> There is also an apriori argument against Pythagoreanism (=everything
> is numbers). If it is a *contingent* fact that non-mathematical
> entities
> don't exist, Pythagoreanism cannot be justified by rationalism (=-
> all truths are necessary and apriori). Therefore the
> Pythagorean-ratioanlist
> must believe matter is *impossible*.

Yes, I agree. That's what I mean about the 'existence' claim of
'necessary truth' - since it rules out 'contingent instantiation', it
must replace it with 'necessary instantiation', or be incoherent as to
ontology.

David

> David Nyman wrote:
> > Bruno Marchal wrote:
> >
> > > Please I have never said that primary matter is impossible. Just that I
> > > have no idea what it is, no idea what use can it have, nor any idea how
> > > it could helps to explain quanta or qualia.
> > > So I am happy that with comp it has necessarily no purpose, and we can
> > > abandon "weak materialism", i.e. the doctrine of primary matter, like
> > > the biologist have abandon the vital principle, or like the abandon of
> > > ether by most physicist.
> > > But with comp it is shown how to retrieve the appearance of it, by
> > > taking into account the differences between the notions of n-person
> > > (and of n-existence) the universal machine cannot avoid.
> >
> > Are we not trying to discriminate two possible starting assumptions
> > here?
> >
> > 1) Necessity
> > 2) Contingency
> >
> > Assumption 1 makes no appeal to fundamental contingency, but posits
> > only 'necessarily true' axioms (e.g. AR).
>
> Things don't become necessarily true just
> because someone says so. The truths
> of mathematics may be necessarily true, but
> that does not make AR a s aclaim about
> existence necessarily true. AR as a claim
> about existence is metaphysics, and highly debatable.
>
> > In this sense there could
> > never be "nothing instead of something" because the 'necessary truth'
> > of AR is deemed independent of contingency - indeed 'contingency' would
> > be seen to emerge from it (hence its 'empiricism' Bruno?)
>
> Necessary truth doesn't entail necessary existence unless
> the claims in question are claims about existence.
>
> Whether mathematical truths are about existence is debatable
> and not "necessary".
>
> > Assumption 2 posits by contrast the ultimate contingency of 'existence'
> > - there might indeed have been 'nothing'. The apparent 'necessity' of
> > AR must consequently be illusory
>
> Not if AR is only a claim about truth. Necessary truth
> can exist in a world of contingent existence -- providing
> all necessary truths in such a world are ontologically non-commital.
> As non-Platonists indded take mathematical statements to be.
>
> > - i.e. AR, CT etc. derive their
> > 'existence' and characteristics from the prior facts of brute
> > contingency.
> >
> > Under assumption 2, therefore, the semantics of 'bare substrate' boil
> > down to a fundamental assertion of 'non-relative contingent existence',
> > and 'primary matter' to 'relative contingent processes/ structures'.
> > Starting from assumption 2 we could see comp as a schema of relative
> > contingent process/ structure within which 'primary matter' is deemed
> > to be 'instantiated', or vice versa (i.e. the 'usual assumption' of
> > physical instantiation).
> >
> > But are assumptions 1 and 2 ineluctably 'theological preferences', or
> > can we discriminate them empirically?
>
> That's what White Rabbits are all about.
>
> There is also an apriori argument against Pythagoreanism (=everything
> is numbers). If it is a *contingent* fact that non-mathematical
> entities
> don't exist, Pythagoreanism cannot be justified by rationalism (=-
> all truths are necessary and apriori). Therefore the
> Pythagorean-ratioanlist
> must believe matter is *impossible*.
>
> (BTW, empiricists can accept *some* apriori arguments).


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Received on Sat Sep 02 2006 - 11:59:27 PDT

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