"1Z" <peterdjones.domain.name.hidden> wrote on August 29
> The version of AR that is supported by comp
> only makes a commitment about mind-independent *truth*. The idea
> that the mind-independent truth of mathematical propositions
> entails the mind-independent *existence* of mathematical objects is
> a very contentious and substantive claim.
I'm very late in reading this thread. I assume AR is "Arithmetical
Realism" and that *truth* in this thread implies alethic qualification
of some sort. To me, a statement like "only use batteries with the
same rated voltage" would seem only to be qualifiable as true or
otherwise if related to factual content. Such a statement would not be
meaningless and would contain information which could be worth
preserving or using.
I am wondering how much semantic loading Bruno's ideas of
quantification are obliged to carry here. Quantifiers always worry me
as they often seem to come up at a very early stage and they do always
seem to carry with them a similar pattern to "only use batteries with
the same rated voltage" and their meaning if any is never absolutely
clear or clarifiable. Perhaps they cannot entail the aforementioned
"mind-independent *existence* of mathematical objects". Or, at least,
not without further qualification, rendering his theory possibly
incomplete as theories tend to be.
This is not the same as people saying "in spite of all we know about
electricity, we do not know what electricity is", because of course we
do know what electricity is, in context if not in metaphysics.
[Bruno's defintiion of Arithmetic Realism I understand to be
" Arithmetical Realism.
All proposition pertaining on natural numbers
with the form Qx Qy Qz Qt Qr ... Qu P(x,y,z,t,r, ...,u) are true
independently
of me. Q represents a universal or existential quantifier, and P
represents a
decidable (recursive) predicate. That is, proposition like the
Fermat-Wiles
theorem, or Goldbach conjecture, or Euclide's infinity of primes
theorem are
either true or false, and this independently of the proposition "Bruno
Marchal
exists". It amounts to accept, for the sake of my argument, that
classical logic is correct in the realm of positive integers. Nothing
more."]
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Received on Wed Aug 30 2006 - 10:39:20 PDT