# Re: Arithmetical Realism

```
David Nyman wrote:```
```
> 1Z wrote:
>
> > Statements, concepts and beliefs must
> > be contingently instantiated. That doesn't
> > mean that their truths-values are logially
> > contingent.
> >
>
> I'm not sure that in a world of strictly contingent existence one can
> establish a 'logical necessity' that is independent of 'contingent
> instantiation'

Why should the *truth* of a statement be dependent on
the *existence* of an instance of it ?

Moreover, the necessary truth of mathematical statements
follows from their lack or real referents:-

Mathematical statements
are necessarily true because there are no possible circumstances
that make them false; there are no possible circumstances that
would make them false because they do not refer to anything
external. This is much simpler than the Platonist
alternative that mathematical statements:

1) have referents
which are
2) unchanging and eternal, unlike anything anyone has actually seen
and thereby
3) explain the necessity (invariance) of mathematical statements
without
4) performing any other role -- they are not involved in
mathematical proof.

> and thus escapes restriction to 'necessary under certain
> contingencies' (even if these are equivalent to 'any that I can
> imagine').

If one is going to be a 'contingentist', then one might as
> well be a thoroughgoing one.
>
> > 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.
>
> I agree. However what I'm saying is that in a world of contingent
> existence *everything* is contingently instantiated.

What does instantiation have to do with truth ?

> Consequently,
> neither 'physical possibility' nor 'logical possibility' can escape
> dependency on such instantiation.

Logical possibility is defined in terms of contradiciton.
Why should it turn out to be nonetheless dependent
on instantiation ?

>  In a world of contingent existence
> the elevation of any 'necessary truth' above contingency is dubious and
> possibly incoherent.

I don't see why. You just seem to be treating
truth and existence as interchangeable, which
begs the questions AFAICS.

> To be coherent AFAICS one would need to be making
> ontic claims for 'necessary truth' that would constrain 'contingent
> possibility'.

I have no idea what you mean by that. Why would a claim about
necessary truth be ontic rather than epistemic, for instance ?

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