Re: Arithmetical Realism

From: 1Z <>
Date: Sun, 03 Sep 2006 00:11:05 -0000

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'?


> > 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
are in Plato's heaven, you must start with the
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
assumptions about mathematical statements.
Nothing else prompts us to, either,

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 Sat Sep 02 2006 - 20:12:57 PDT

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