FOM: Re: Ontology in Logic and Mathematics

[Roger Bishop Jones]

In response to Matt Insall <montez at rollanet.org> Tuesday, September 26, 2000
2:57 AM


> Roger:
> No.
>
> It all hangs on the semantics.
> If the semantics of a language is specified by giving truth conditions for
> sentences then these truth conditions tell you what it means to assert the
> sentence (i.e. asserting a sentence is asserting that the truth conditions
> hold).
>
>
> Matt:
> Let us say for now that I am ontologically committed to the theory
> (ZFC-AxInf)+not(AxInf), which I shall denote by T.  How do I deal with
> semantics in this case?

I'm more interested myself in avoiding absolute ontological claims, so my
most sincere response is - don't, it serves no useful purpose and leads into
a quagmire.

*If* you want a language for exploring the consequences of this absolute
ontological claim, in which the sentences turn out false if the claim is
itself false, then you can just stipulate this in the truth conditions.
i.e. you say in your definition of the semantics something like "a sentence
in L is true (simpliciter) if it is true in all models of
(ZFC-AxInf)+not(AxInf) and if there is at least one such model".

This seems to me like a bad idea even if you are interested in absolute
ontology.
It suffices to make the statement which you have and then explore its
consequences in a normal first order theory.

Alternatively you could do what I suggested previously - have a special
language which is about what *really* exists.
For such a language the formula "a sentence is true (simpliciter) if it is
true in every model of the non-logical axioms" would be replaced by "a
sentence is true (simpliciter) if it is true *in reality*".
If you think this a useless specification of semantics then I would agree
with you.
It does make clear what the sentences of the language are intended to
convey, but doesn't provide any practical clues on how to establish which
are true.