# Re: Arithmetical Realism

From: David Nyman <david.nyman.domain.name.hidden>
Date: Sun, 03 Sep 2006 00:49:21 -0000

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.

> 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,
because 'conceptual' contingencies must be instantiated in terms of
those selfsame 'external' ones. IOW, 'reference', 'externality' and the
entire conceptual armamentarium are instantiated in a given contingent
state of affairs and consequently are dependent on it for their
'logic'. Were these contingencies different, white rabbits might become
quite mundane.

> 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.

> > 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.

David

> David Nyman wrote:
> > 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').
>
> Indeed, but the contingentist doesn't have to regard truth
> as something that exists.

> > 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.
>
> 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.
>
> > They cannot
> > 'transcend' present contingencies, and under different contingencies
> > (about which we can know nothing) they could be different.
>
> 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.
>
> > 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'.
>
> That is belief, not truth.
>
> > 2) sets of 'facts'
>
> Facts exist. Statements are true. Which do you mean ?
>
> > 3) logical/ empirical processes of judgement
>
> What is judged may be true, since it
> may be a statement or proposition.
>
> Processes of judgement are neither true nor false.
>
> > 4) conclusions as to truths asserted
>
> Defining truth in terms of truth.
>
> > 5) behaviour consequent on this
>
> Behaviour is neither true nr false. It is not a
> statement or proposition.
>
> > 6) etc.
>
> You seem to be intent on defining truth in
> the most baggy way possible.
>
> > If any element of this - from soup to nuts - fails to be instantiated
> > in some form it cannot exist in a purely contingent world.
>
> Hardly anything in your list actually has anythig to
> do with truth. The possible exception is (2), "facts".
> But "fact" is a notoriously[*] ambiguous word.
>
> [*] Not notoriously *enough* , though.
>
> > In this
> > view, 'conceptual existence' is just the instantiated existence of a
> > concept.
>
> What has that got to do with truth ?
>
> > AFAICS any other view would have to assert some sort of
> > transcendent 'conceptual existence' that subsumes 'contingent
> > existence'.
>
> No, because truth and existence are different.
>
> Thus, a proposition can both exist contingently and
> have a necessary truth-value.
>
> > > 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.
>
> No it doesn't.
>
> > A statement is
> > 'contradictory' because its referent is impossible to instantiate under
> > present contingencies.
>
> No, it is contradictory becuase it contains a clause of
> the form [A & ~A] (A and not-A). Contradiciton is a formal,
> logical property.
>
> > 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'?
>
> Nope.
>
> > > 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.
>
> It can also be derived from the interrelation of concepts.
>
> > By this token, truth in any
> > 'transcendent' sense
>
> Could you specify a "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'.
>
> I couldn't make sense of that.
>
> Necessity is an abstract logical property, not a thing.
>
> > 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.
>
> Platonists feel they must reify the supposed referents
> of necessarily true statements in order to explain
> their necessity.
>
> Number theologians only need to reify numbers. I have no
> idea why you are so keen on reifying truth.
>
> > > > 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'.
>
> If you want to finish with the conclusion that we
> assumption that Plato's heaven exists. But I
> don't see what that has to with being coherent.
>
> One can simply deny that we are in Plato's heaven.
>
> Then we don't need to make ontological