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.
> > 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
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
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.
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