Re: Arithmetical Realism

From: Bruno Marchal <>
Date: Mon, 4 Sep 2006 15:18:47 +0200

Le 02-sept.-06, à 17:26, 1Z a écrit :

> 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.

Yes. So let us never do it.

> 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".

Existential mathematical statement are about existence.

> Not if AR is only a claim about truth.

AR is about the truth of arithmetical statements, and among
arithmetical statements, many are existential, so AR makes claim about
the independent truth of existential statements. No need to add
metaphysics at this stage (nor at any other stage by the way, except
the yes doctor, which I prefer to range in "theology" than in

> Necessary truth
> can exist in a world of contingent existence -- providing
> all necessary truths in such a world are ontologically non-commital.

I don't understand.

> As non-Platonists indded take mathematical statements to be.

AR does not ask you for believing in some metaphysical (still less
physical) existence of numbers. It ask you to agree that a proposition
of the type ExP(x) is true or false independently of any cognitive
faculty. Cognitive abilities are needed to believe or know that ExP(x)
is true (or false), but that's all.

> 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,

It is not even a fact. It is an assumption. Nobody has proved that
something non mathematical exists, although comp is quite close in
proving this. Indeed comp shows that no first person can be described
mathematically by herself. So *relatively* to a machine first person,
many things will *appear* non mathematical. It is a consequence of
incompleteness + the theaetetical-plotinian definition of knowledge.

> Pythagoreanism cannot be justified by rationalism (=-
> all truths are necessary and apriori). Therefore the
> Pythagorean-ratioanlist
> must believe matter is *impossible*.

Not impossible. Just useless.


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Received on Mon Sep 04 2006 - 09:20:45 PDT

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