Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity

From: Ross A. Finlayson (raf_at_tiki-lounge.com)
Date: 01/24/05 

Date: 23 Jan 2005 16:01:47 -0800

Hi Tim,

I'm rather ignorant about the paraconsistent logic. When I first heard
about it, some years ago shortly after which I wrote to sci.math about
reading about it, it was in the context of multivalent logics, or
multi-valued logics, in the thread titled "Base", for it has besides
the T and F an indeterminate third truth value, generally U, where that
is often ascribed to Kleene, after Lucasiewicz.

In terms of its intuitionistic slant and excluded middle, that is
considered. In the null axiom or axiom-free set theory, the excluded
middle on the ur-element, the ur-paradox of the assertion of existence,
does and does not apply.

It's considered five years ago in that beginner's post about
multivalent logic, or many other posts on sci.math.

I admit as well to not being as well-studied as I would like, ergo I
study. We here actually basically know what we're discussing, or
"talking about". Being as well a voracious learner and enjoying
knowledge for its own sake, you might understand why I'm very
particular about my own personal logical theory of everything and
demand my own input. This group is full of people who love to have
mathematical knowledge and share it with others, each for their own
reasons. Mathematical logic is somewhat vast, and is hopefully
compressible to three or four pages.

Well, enough of that business. When you say you talk about transfinite
cardinals and functions, do you mean along the lines of the functions
from reals to reals, or computational complexity and Turing, ie
asymptotic finite combinatorics?

Do you use that lambda calculus, theory of functions and types,
Coquand, Luo, Pierce, Martin-Lof? I heard of it, type theory and
lambda calculus, read a couple of those Pierce books. It's cumbersome
to apply it in computer programming unless you're writing a compiler,
where it can be useful.

Basically I want to learn more about you. Do you have a math degree or
is your learning self-directed? It's easy to see what words you write
here, and the rapidity of assimilation of material. What's your
philosophy about mathematics, or mathematical discussion?

When you use the transfinite, as you say, is it transfinite induction
you use?

Regards,

Ross Finlayson

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