FOM: Alice, Carol and Leibniz

Dean Buckner Dean.Buckner at
Sat Apr 13 11:42:04 EDT 2002

Occasionally you see an argument in a form that has only to be stated, to be
refuted.  An offline correspondent (who will remain anonymous) has said if
we drop the second-order (Fregean) notion of equality, we are left with
nothing.  We have "Alice and Carol are different people".  But

(i) How could we possibly know they are different people if there is no
predicate U such that U(alice) and not U(carol)?
(ii) If there is no such predicate, then Alice and Carol are totally
(iii) How do we know they are not the same, if they are identical in every
conceivable way?

Well, first of all (to take a hackneyed example) we could have a completely
empty universe except for two atomic particles rotating round each other.
Couldn't they be qualitatively identical, but numerically different?

But this misses the point anyway, which is that, besides getting information
by sight, hearing and the senses, we also get it from language.  That's what
I'm using right now, unless you haven't noticed.  You haven't met me, I
haven't met you.  But through this wonderful medium, we can share thoughts
using these 26 little letters.  Even the amazing thought in the last
sentence, I communicated using a few letters.

And  this information we get from language can be exactly as the objection
it cannot.  Here's some more information.  I just said I had an anonymous
correspondent, who made this Leibnizian objection.  Well, as it happens I
have another correspondent who made exactly the same objection.  I have just
given you the information that there are two people, without supplying any
predicate U such that U the one and not U the other.  All I have said is
that they both made a certain objection.  They are, from your point of view,
indistinguishable.  Yet they are are different.

To take another example, consider:

    There were some whales.  There were (also) some other whales.

Two separate sentences, hence two separate propositions.  If true, they must
be true of two exclusive sets of objects.  Whatever is in the collection of
things that the first is true of, cannot be in the collection of things that
the second is true of.

So these sets are defined by the concept "whale"?  Nonsense!  Whatever you
are able to predicate of any object in the first set, you can say of any in
second (except of course that they are numerically the same).

It's no use arguing that in reality there must be characteristics
distinguishing the things from one another.  Certainly, there will be.  But
the propositions express that, do they?  Is that what we grasp, when we
understand them?  And is that what, if the propositions are true, makes the
two sets of things different?  Rather than the simple assertion, contained
in the proposition, that they just are different?  I don't think so.

In summary:  how do we know that two objects are not the same, if they are
said identical in every conceivable way?  Answer: because they are said to
be different.

Dean Buckner
4 Spencer Walk
London, SW15 1PL

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