Re: Kuratowski Ordered Pair

On Dec 20, 3:19 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

Please, ante up already. Please say EXACTLY what the Kuratowski
definition was INTENDED to do but does not do.

the intent is not necessary to an objection

...

maybe i am far too gone

maybe all the objectioners in this thread
are really loons like me
and the only reason i understand is because i'm just as lost

but is it really that hard to see what might be their issues?

a long time ago
i had this conversation with mitch over in sci.logic

http://groups.google.com/group/sci.logic/msg/71b096014e4859ef

in it
some long way down in that post
there was this exchange:

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: I guess I cannot quite understand what people mean by an
: "unordered pair." I can understand not knowing the order of a
: pair and I can understand superposition of all possible orders.
: But, the connectivity of a pair without order is
: incomprehensible to me.

Yes!!! Yes! Yes and yes!!!

I once got into a discussion with my topology teacher about which was
more
primary. He argued that ordered pairs required more definition,
whereas my
point was that on all conceptual levels I could identify (visual,
auditory,
etc.), the ordering seemed to follow most naturally from the input,
and the
act of "unordering" seemed a latter abstraction.

a -> b is much more useful evolutionarily than, say, a = b.

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when presented with a collection of "things"
objects, impressions, ..
we appear to identify the collection through some ordering process

we select an object and pattern recognise it
then another
and so on
a temporal series of conceptual isolations

the same goes for counting

we _choose_ one
then another

these orderings aren't a priori or associated innately with the
objects
and they might change any time an identification is done
but the ordering seems integral to the conceptualisation

we read symbols in some order
giving them some connective mereology as a data structure
something we can iterate through

this is how turing machines work

and then we look at set theory
which takes collections as unordered
and a pair (a, b)
becomes {a, {a, b}}?

and it still assumes the ordering for parsing
but claims an unordered semantics?

when a language mangles a natural concept so horribly
there is plenty to object

no matter the intent

...

i miss mitch

there was one crazy-cool mfer
a real logico-philisophico-mathemagician
always bringing up many-sorted logics
topological logics
numerical and visual patterns
..

a ton of energy which my work always prevented me from keeping up with

he was not one afraid to investigate

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galathaea: prankster, fablist, magician, liar
.