FOM: Re: Ontology in Logic and Mathematics

[Roger Bishop Jones]

In response to Jeffrey Ketland Monday, September 25, 2000 2:37 AM

> Dear Roger
>
> >If you leave open the semantics of the language, then what you assert is
> >also left open.
>
> If I assert something (say, "Cheese is edible"), then have I *not*
> asserted something, until I have previously specified the semantics of
English?

I didn't intend to say that the semantics must be specified by the speaker.

Try: "if the semantics of a language is unclear, then what is asserted by
sentences in that language is unclear".

<snip>

> Following a Tarskian definition, here are the semantics for the language
of
> arithmetic:
>
>     "0" designates the number 0
>     "s" designates the successor operation
>     "+" designates the addition operation
>     "x" designates the multiplication operation
>     "N" designates the set of whole numbers (the closure of {0} under
> successor}
>
> Are you saying that the sentences of arithmetic do *not* have these
> meanings?

No.

<snip>

> What exactly is wrong with Quine's analysis of ontological commitment.
I.e.,
>
>     "There is something x such that x is an F" is true if and only if
there
> is an F?
>
> I.e., Quine's analysis of ontological commitment = the disquotation clause
> for existential quantifiers (in a Tarskian truth definition in the
> metalanguage).
>
> I do not understand your use of the notion "ontological commitment". And I
> do not understand your use of the word "absolute". On standard usage, a
> sentence that starts "There is a ..." is true only if there is such a
thing.
> I don't see what's wrong with that?

The use of the word "absolute" is there to contrast a bald existential claim
of the kind which might be made in metaphysics with a claim in some special
context, which might be called "relative".
A "relative" claim is one in which the existence of some class of entities
is presupposed rather than asserted and in which some other claim is
asserted in that context.
I could make true claims about Sherlock Holmes having a deerstalker, which
are only true in the context that Sherlock Holmes is a fictional character,
and exists only in the novels of Arthur Conan Doyle.
Though I do not hold that the natural numbers are fictional, I do hold that
truths about the natural numbers can properly be enunciated while reserving
judgement about whether the natural numbers exist in any absolute sense
(i.e. other than by supposition).

A "Tarskian" account of the semantics of existential quantification is
relative (the object must exist in the domain of discourse).
Consequently, first order languages need never be construed as making
absolute ontological claims.

You are free of course, to adopt a special semantics for a first order
language so that its assertions are then construed as making absolute
existential claims.
(e.g. fix the domain of discourse as the collection of everything which
"really" exists)

Roger Jones