Re: Epistemology 201: The Science of Science

From: aeo6 (aeo6_at_cornell.edu)
Date: 03/15/05 

Date: Tue, 15 Mar 2005 15:27:36 -0500

Daryl McCullough said:
> aeo6 says...
>
> >I looked up "order type" and from what I see it isn't much closer to what I am
> >talking about than measure theory. It seems to be a way of classifying orders,
> >not discerning sizes of relative infinities. Do you have a link by any chance
> >that might make it sound more relevant?
>
> see
> http://mathworld.wolfram.com/OrderType.html
> http://www.absoluteastronomy.com/encyclopedia/o/or/order-embedding.htm
> http://www.absoluteastronomy.com/encyclopedia/o/or/order_theory.htm
>
> In the mathworld article, the following quote appears:
> Every totally ordered set is associated with a so-called order type. Two sets A
> and B are said to have the same order type iff they are order isomorphic
> (Ciesielski 1997, p. 38; Dauben 1990, pp. 184 and 199; Moore 1982, p. 52; Suppes
> 1972, pp. 127-129). Thus, an order type categorizes totally ordered sets in the
> same way that a cardinal number categorizes sets. The term is due to Georg
> Cantor, and the definition works equally well on partially ordered sets.
>
> --
> Daryl McCullough
> Ithaca, NY
>
>
Yes, I found and read the mathworld article before I replied. Can you explain
how this creates finite differences or ratios between sizes of infinite sets,
or defines relative sizes of infinite sets based on the correspondence function
between them?

It's interesting. I mention "measure" as an inherent quality of numbers, and I
get referred to "measure theory", which turns out to have nothing to do with
what I am saying. Now I am making the point that the ordering is important, and
that divergence from the natural quantitative order of numbers causes unnatural
results, and I am referred to "order theory". This seems somewhat related, but
not the answer to my question. If I want responses like this, I'll call Dell
back and spend another hour on the phone asking which pin on their rotten
proprietary ATX power supply is the power-on pin, and see which laptop division
they forward me to. 

-- 
Smiles,
Tony

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