Re: Arithmetical Realism

From: 1Z <>
Date: Mon, 04 Sep 2006 07:08:09 -0700

Bruno Marchal wrote:
> 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.

Debate is what we are here for.

> > Necessary truth doesn't entail necessary existence unless
> > the claims in question are claims about existence.
> Exactly.
> > Whether mathematical truths are about existence is debatable
> > and not "necessary".
> Existential mathematical statement are about existence.

And Sherlock Holmes lives because Sherlock Holmes lives
at 221b Baker Street.

> > 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.

Arithmetical statements use the word "exists", or the symbolic
euivalen thereof. However, it is not to be taken literally
in all contexts.

> No need to add
> metaphysics at this stage

Yes there is. You need metaphysics to answer the question
of whether the existence-claims of mathematics shouldbe takne

> (nor at any other stage by the way, except
> the yes doctor, which I prefer to range in "theology" than in
> "metaphysics").

Is theology better-foudned as a discipline ?

> > 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.

If necessary truths don't refer to contingently
existing things, they cannot be "infected" by their contingency.

> > 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.

Then it does not show the UD exist, and it cannot follow
that I part of its output.

> It ask you to agree that a proposition
> of the type ExP(x) is true or false independently of any cognitive
> faculty.

It may well be true. It may well mean nothing more
than "P(x) is non-contradictory"

> Cognitive abilities are needed to believe or know that ExP(x)
> is true (or false), but that's all.

Quite. So nothing in the argument can tell me about the nature of my

> > 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.

I already said "if"...

> Nobody has proved that
> something non mathematical exists, although comp is quite close in
> proving this.

That isn't the point. The point is the consistency
Pythagorean rationalism as a hypothesis.

> 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.

The Pythagorean rationalist *must* believe mater
is impossible -- the argument becomes inconsistent otherwise.

The argument that matter is "useless" is more akin
to empiricism than rationalism.

> Bruno

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Received on Mon Sep 04 2006 - 10:10:46 PDT

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