Re: Kuratowski Ordered Pair

On Dec 21, 5:58 am, noel etters wrote:


Noel,

First of all, please trim the context of your posts.


If it seems to me that you are blockheadedly failing to
take the point, I should draw the conclusion that I haven't
expressed myself well.

Given the relative uncertainty of the human condition,
I recommend that you should at least have on your
internal list of possibilities the idea that your point
may not actually have any merit to it. Just sayin'.


What we need, to describe pairs, both ordered and unordered,
is the notion of content at a position.

What you need to describe *ordered* pairs is the notion of content
at a position. You don't need that for unordered pairs.


What we require, in either case, is that
there are distinct positions or slots. Call them S and S' (S not= S'). We
cannot identify the slots with their content i.e. S is the slot which has
a, for in the event that a=b, we should again come down to a single slot.
Slots are not reducible to their contents.
A pair, (a, b), is: (a at S, b at S').

This is a fine description of ordered pair. It has nothing to do
with unordered pairs however.


An ordered pair and an
unordered pair have the same conceptual complexity.

For pairs, we have the concept of there being two members.
For the ordered pair, we have the additional concept of
one of the two members being the first one. Did I leave
any concepts out? I don't see how they could be said
to have the same conceptual complexity.

And regardless of conceptual complexity, the information
content of an ordered pair is higher than that of the same
pair, unordered.


The difference is in the stipulation
that (a at S, b at S') equals (a at S', b at S) for an
unordered pair

Unordered pairs do not support the operation of having a value
at S or at S'.


Marshall
.