FOM: Alice, Bob and Carol

[Dean Buckner]

Judging from the replies (mostly offline) to my posting "And another thing",
what I said was not very clear.  Never mind, it's not necessarily a clear
subject  I'll try if I may to put it a different way.

I give you the information *that* Alice is married, *that*  Bob is married,
and *that* Carol is married.

Then:

1.  Alice, Bob and Carol, if they are different people, certainly have
attributes that mark them out from each other, and that also mark them out
from anyone else.

2.  But the information we have been given does not include any of this.  It
does not even include the information that Alice, Bob and Carol are
different people.

3.  Some people worry about whether we can "abstract" this very limited form
of information.  But surely that's what we are doing just by understanding
what I say, by grasping its meaning.  Moreover, since anyone can understand
it, we shouldn't have to worry about this abstract information being mental
or private - it's not, since it's available to anyone who understands the
sentence.

4.  Suppose we add the information that Alice is a different person from Bob
and Carol.  Now we have the information that at least three people are
married.

5.  Using a very limited number of words, and without any stuff about
properties of collections of objects, we can communicate an important fact
about things, namely how many there are.

And that, surely, is all we need to know about number.  Frege has this idea
that something more is required.  Any collection of objects must have a
property that defines them as a set. So Alice Bob and Carol have some
property F3, that only applies to them, Alice and Bob are marked out by some
F2, Alice by some F1, that uniquely applies to her.

Sure, maybe so.  Leibniz' friend could not find two leaves the same.  But
none of this has to do with the content of the information we receive.  The
information does specify how many people there are, so all this F1..F3 stuff
is irrelevant to number.  It's just an accident, that different things have
different properties.  It's not required for communication.

6.  Moreover, if the information is correct, if it's true, then there are
three married things, it's a fact.  So, once again, this number that we
grasp is something "in the world", if you want to put it that way.
Something says that p, we grasp that p, and it is a fact that p.

7.  So, isn't that all there is to say about number?  There is an object a,
an object b, an object c.  And they are not all the same object, a is
different from b, b from c and c from a.  That fact alone guarantees the
existence of three things, and the information we give by saying this also
includes the information about their number.

Is it any more complicated than that?  Why in particular the idea that there
must be some property possessed by Alice Bob and Carol but no one else,
which has a number, which is the same as the number possessed by the
property of being identical to 0, 1, or 2?  That's crazy.  Moreoever, we
have to add the information that 0 is different from 1, 1 from 2, and 0 from
2, otherwise we are back where we started.

If just saying a bunch of objects are all different from each other is
enough to say they have a number, why not stop right there?

========= Summary ===========

To sum up a very simple argument, we can communicate information about how
many things there are without communicating any information whatsoever of
the sort that Fregean or neo-Fregean number says is essential to our ideas
about number, or about number "itself".

Moreover this information, if correct, reflects the way things are, so
nothing else is relevant to the *fact* that there are a certain number of
things.

>From which I conclude all the Fregean stuff is absolutely irrelevant either
to our ideas about number, or to facts about it.



Dean Buckner
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London, SW15 1PL
ENGLAND

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