FOM: No Arbitrary Objects

[Dean Buckner]

Many apologies - I have changed the tools option on MS Outlook EXpress to
plain text - everything still looks the same but assume that is my editor.

Apologies again

Dean


----- Original Message -----
From: Dean Buckner
To: fom at math.psu.edu
Sent: Saturday, February 09, 2002 2:47 PM
Subject: No Arbitrary Objects


Name: Dean Buckner
Institution:  None (Financial derivatives specialist)
Research interests: reference, singular terms, history of logic, Frege,
maths and natural language


I have been following the discussion on arbitrary objects with fascination &
bewilderment.  I'm not a mathematician, I'm not anything at all (I work in
an office).  But is the whole issue as complicated as it's made to seem?
Consider

(1) A soldier was returning home from the war (Andersen)

If the story is true (though it's not, it's a fairy tale) then a soldier
must have existed.  The story is "existentially committed".  Suppose we
describe this existential commitment as follows

(2) Sentence (1) introduces an arbitrary object

We could equally have said it introduces a fictional object, a discourse
entity, a discourse object, an abstract object &c.  The point is that (2) is
also "existentially committed", since if is true, there must exist both a
sentence and an arbitrary object.  Moreover, even if (1) is false, and there
is no soldier, (2) is still true, for it is supposed to be about the meaning
of sentence (1).  Even if there was no soldier, there is still an "arbitrary
object".

Isn't a more economical way of describing this to say

(3) Sentence (1) says that a soldier was returning home from the war


since (3) can be true without anything (apart from sentence (1) itself)
having to exist?  Sentence (3) specifies what a certain sentence means,
without committing us to the existence of arbitrary objects (or discourse
entities or anything like that).  This is exactly why we have sentences like
this in ordinary language.  We sometimes need to specify what a person says,
without committing ourselves to the truth of what they say, or the existence
of what they say to exist, e.g. "Jake says there's some money in the
drawer".

Admittedly it can be useful to go on as if there were such things.  In
literary criticism, e.g. people go on as if the fictional characters really
did exist.  It's very convenient in one sense, because we can omit
expressions like "in the text it is written that", "Melville claims that"
and so on. But it's economical with expression, not economical with reality.
There's an analogy between literary criticism and maths: mathematicians go
on as if there really were four dimensional spaces, points, lines, sets and
classes.  But on the other hand if we want to talk about the meaning of
fiction, ordinary language allows us to do this perfectly well without these
spurious objects.  Is there an analogy in maths?  Could we talk about the
meaning of mathematical symbolism, without talking about some of the weird
things maths is meant to be about?

I've talked more about "objects" than "arbitrary objects".  That's because
part of the puzzle i think is the "object".  If there is an object, (a
soldier), then which member of the class are we talking about?  Which
soldier, which army?  For a proof to work, the object must as it were stand
in for all the objects in a class, without being any of them.  But by now
it's gone wrong.  Once you start on about "objects", the bad thing has
happened.  As I've argued, we can explain the meaning of ordinary sentences
which claim that objects exist, by means of ordinary sentences that make no
such claims.

There's more to say than, but I will read Kit Fine's book, as Charlie
Silvers has just recommended.

Dean Buckner