# Re: Arithmetical Realism

```1Z wrote:

> Why should the *truth* of a statement be dependent on
> the *existence* of an instance of it ?```
```
What I mean is that - for a 'thoroughgoing contingentist' -
'statements', 'concepts', 'truths', 'referents' and anything else
whatsoever can exist solely in virtue of their actual contingent
instantiation (i.e. there literally isn't any other sort of
'existence'). Within such a world-view, even apparently inescapable
logical truths are 'necessary' only within a relational system
instantiated solely in terms of a contingent world. They cannot
'transcend' present contingencies, and under different contingencies
(about which we can know nothing) they could be different. This
establishes an 'epistemic horizon' for a contingent world.

> What does instantiation have to do with truth ?

Everything. 'Truth' in contingent terms is (very loosely) something
like:

1) dispositions to believe that certain statements correspond with
putative sets of 'facts'.
2) sets of 'facts'
3) logical/ empirical processes of judgement
4) conclusions as to truths asserted
5) behaviour consequent on this
6) etc.

If any element of this - from soup to nuts - fails to be instantiated
in some form it cannot exist in a purely contingent world. In this
view, 'conceptual existence' is just the instantiated existence of a
concept. AFAICS any other view would have to assert some sort of
transcendent 'conceptual existence' that subsumes 'contingent
existence'.

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

Because 'contradiction' itself depends on instantiation. A statement is
'contradictory' because its referent is impossible to instantiate under
present contingencies. In this world-view, answering such questions is
easy - *everything* depends on such instantiation. Conceptual
'existence' is simply the sum of the instantiations of all (agreed)
instances of a concept - IOW they're all apples if we agree they are.
Any other view is surely already 'Platonic'?

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

No, I'm saying (above) that 'truth' in a contingent world  can only be
*derived* from present contingencies. By this token, truth in any
'transcendent' sense is either impossible (if one believes in a
contingent world), or alternatively *must* be a de facto 'existence'
claim that rules out 'primary contingency' - i.e. the world 'in the
sense that I exist' is supposed to emerge from 'necessity'. So I'm
agreeing with you (I think) in your contention that 'number theology',
to be ontically coherent, must be an existence claim for a priori truth
in this 'strong' sense.

> > 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 ?

For the reasons you yourself have argued - i.e. that claims based on
'Platonic numbers' must be regarded as ontic in a strong sense if they
are supposed to account for a world that exists 'in the sense that I
exist'. Epistemic claims would then follow from this.

David

> 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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