Re: Arithmetical Realism

From: 1Z <>
Date: Sat, 02 Sep 2006 15:26:06 -0000

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
don't exist, Pythagoreanism cannot be justified by rationalism (=-
all truths are necessary and apriori). Therefore the
must believe matter is *impossible*.

(BTW, empiricists can accept *some* apriori arguments).

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Received on Sat Sep 02 2006 - 11:28:01 PDT

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