David Nyman wrote:
> 1Z wrote:
> > Necessary truth doesn't entail necessary existence unless
> > the claims in question are claims about existence.
> If one claims (which I don't BTW) that something is 'necessarily true'
> *independent of contingent existence* then I think for this to be in
> any way coherent, one must be making some sort of existence claim for
> 'necessary truth'.
But only the sort of abstract "exisence" that
numbers have in the first place, which is
not genuine existence at all for anti-Platonists.
> By contrast, within contingent existence, some
> things may seem 'necessarily true', but this truth can only be derived
> from aspects of contingency (i.e. in virtue of the concept and its
> referents being contingently instantiated).
What things ? Are they really necessarily true,
or only seemingly so ?
> > 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 agree insofar as you mean what I'm saying above: i.e. the 'existence'
> of 'necessary truth' in a world of contingent existence must itself be
> 'contingently instantiated'.
Statements, concepts and beliefs must
be contingently instantiated. That doesn't
mean that their truths-values are logially
> 'Necessity' in this sense is restricted to
> 'necessary under ceratin contingencies'. In a world of contingent
> existence the behaviour of a logical system must reduce ultimately to
> the behaviour of a contingently instantiated system.
But physical possibility is a subset
of logical possibility, so the physical
systems can't do anything its abstract counterpart
cannot do, so what is true of the abstract system
is true of any phsycial systems that really instantiates it.
> > There is also an apriori argument against Pythagoreanism (=everything
> > is numbers). If it is a *contingent* fact that non-mathematical
> > entities
> > don't exist, Pythagoreanism cannot be justified by rationalism (=-
> > all truths are necessary and apriori). Therefore the
> > Pythagorean-ratioanlist
> > must believe matter is *impossible*.
> Yes, I agree. That's what I mean about the 'existence' claim of
> 'necessary truth' - since it rules out 'contingent instantiation', it
> must replace it with 'necessary instantiation', or be incoherent as to
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