FOM: Alice, Bob and Carol
Dean.Buckner at btopenworld.com
Thu Apr 11 15:44:14 EDT 2002
>----- Original Message -----
>Martin Davis <martin at eipye.com> wrote
> At 09:17 PM 4/8/2002 +0100, Dean Buckner wrote:
> >5. Using a very limited number of words, and without any stuff about
> >properties of collections of objects, we can communicate an important
> >about things, namely how many there are.
> >And that, surely, is all we need to know about number. Frege has this
> >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
> >F2, Alice by some F1, that uniquely applies to her.
> Surely what is missing from this is the concept, idea, or (speaking
> extensionally) set of numbers. I believe Frege was trying to explicate
That's a very good point, but I'm not sure it addresses the one I
was trying to make. My target is another Fregean idea that we cannot
away all the properties of objects in a collection, leaving (as it were)
pure numerosity. Frege thinks we would be left with what he calls the
"unfortunate Ones", i.e. "a thing and a thing and a thing", being unable to
grasp whether any of these things is the same as any other.
For the same reason he thinks proper names don't work, since it's not part
of the meaning of a proper name that its bearer is different from the bearer
of another. "Berlin is a city and Munich is a city" does not specify whether
the cities are different! Thus he thinks that each collection has a common
that defines it as that collection. Alice, Bob and Carol must all have some
common property, Alice and Bob must share some different property from what
they share with Carol, and presumably Alice herself must have some property
that distinguishes here from all other things in the universe.
That may well be. But it's no part of the content of "Alice and Bob are
different from Carol" that Alice and Bob have a property distinguishing them
from Carol (for example). The proposition abstracts from all of that
content, by means of the (I would argue) irreducible relation " -- is
different from --". It suffices.
As it happens, I don't like the idea of a set of numbers. You have, a
number of people, a number of plates, a set of dishes. But not a set of
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