# [FOM] Finite Set Theory

slaterbh@cyllene.uwa.edu.au slaterbh at cyllene.uwa.edu.au
Wed Feb 22 06:39:55 EST 2006

```Harvey says, in response to

>> Thus if there is just one pair of things, there are only
>> two things, no third thing.

> This is incorrect. There is a third thing here, in the pair written
> ><x,y>. There is x, there is y, and there is the ordered pair <x,y>.
> (Or >we could do this with the unordered pair).

There is another problem, if one brings in ordered pairs - they do not
differ in their members from the corresponding unordered pairs.  So
where, with two apples, for instance, are the *three* further objects -
the pair of apples, and the two ordered pairs of them?  The bowl must
be quite overflowing! (Note that if one eats both apples, the pair of
them disappear, so one is talking about physical things all the time.)

More centrally, what about even the singleton set of just one of the
apples?  That has been the key problematic case, from a philosophical
point of view, in notable writings by David lewis, Peneope Maddy and
Michael Potter, amongst others. If Harvey could locate that, a great
number of people who have thought very hard about these things would be
very happy.

Hartley

```