Re: Arithmetical Realism

From: 1Z <>
Date: Sun, 03 Sep 2006 11:24:32 -0000

David Nyman wrote:
> 1Z wrote:
> > Indeed, but the contingentist doesn't have to regard truth
> > as something that exists.
> Fair enough, but even the contingentist needs to express herself
> intelligibly without recourse to a constant blizzard of scare quotes.
> So she still needs something that FAPP corresponds to 'instantiated
> truth', and we can indeed discover such analogs in a contingent world.

Finding something that corresponds to instantiated
truth -- such as knowledge -- does not make truth contingent.

> > That would indicate that logical possibility is a subset
> > of physical possibility, which is counterintuitive. That
> > is one motivation for sayign that truth (along with other
> > abstracta such as numbers) doesn't exist at all.
> Agreed, with the above proviso.
> > No they couldn't, because they do not refer to external
> > contingencies ITFP. Where there is no relation, there
> > is no variation. Invariance is necessity.
> Well, at the level of metaphor you are correct, but in a strictly
> contingentist sense, they implicitly refer to external contingencies,

No. They don't refer at all. Maths isn't empirical.

> because 'conceptual' contingencies must be instantiated in terms of
> those selfsame 'external' ones.

Instantiation isn't reference.

> IOW, 'reference', 'externality' and the
> entire conceptual armamentarium are instantiated in a given contingent
> state of affairs

if they are instantiated at all.

> and consequently are dependent on it for their
> 'logic'.

Clearly not, since we are able to concive physically
impossible worlds. The virtual "logic" isn't determined
by physics. A computer running on real phsyics can
simulate a world where graivity is an inverse cube law.

> Were these contingencies different, white rabbits might become
> quite mundane.

Yes. It is logically possible for what is physically
(im)possible to have been different. Physical
possibillity is a subset of logical possibility.
Logical possibility isn't determined by physical possibility.

> > You seem to be intent on defining truth in
> > the most baggy way possible.
> Yes, but I'm just trying to point out that we can pragmatically deploy
> a variety of means to establish agreement to some level of accuracy
> without having to believe in the 'transcendent existence' of truth.

That is tangential to the discussion. The point
is that anti-Plaotonists can agree with Platonists
100% about the mind-independence of mathemaical
trth, whilst agreeing 0% about the mind-independent
existence of mathematical objects."Transcendent" truth does not
have to be sacrificed to ontological contingency.

> > > In this
> > > view, 'conceptual existence' is just the instantiated existence of a
> > > concept.
> >
> > What has that got to do with truth ?
> Well, the existence of truth is just the instantiated existence of a
> truth, in the contingentist view. Actually, I don't really want to push
> all this too far. FAPP the distinctions you make are valid, and I'd
> much rather agree to deploy a metaphorical sense of the 'existence' of
> truth rather than chase about looking for its multifarious
> contingentist instantiations. I was originally trying to contrast the
> contingent vs. necessary ontic assumptions that seemed to me implicit
> in your dialogue with Bruno. As it happens, my own preference lies on
> the side of contingency.


> 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'?
> >
> > Nope.
> Why isn't it? Do you mean that we can ascribe metaphorical 'existence'
> to a conceptual framework that transcends any or all particular
> instantiated examples, without ascribing literal existence to it? In
> this case, as with 'truth', I would concur.

Mathematical "existence" operates under constraints of logical
non-contradicition, consistency. It is not just a case of conceiving

You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to
To unsubscribe from this group, send email to
For more options, visit this group at
Received on Sun Sep 03 2006 - 07:26:24 PDT

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:12 PST