Numinus, Dr Who, et al,
The Question here, may in itself, be an anceint "paradox" in a newer form.
(Merely an opinion.)
(Non-Original THOUGHT)
How do we count? What do we mean when something is "uncountable." What is a "set of numbers?"
There are, as I understand it, two lines of thought:
- Mathematical objects are real objects.
- Mathematical objects are concepts.
Thumbnail Source: http://platosheaven.blogspot.com/2005/12/do-numbers-exist.html
I'll be honest, I am one of those few who oppose the Platonic view that numbers are "real" and they exist independently of human thought. The same would go for the set of spectrum detection (colors) and similar formal constructs; or "points" along a continuum (time or dimension).
(COMMENT)
Each question we have, in which we use mathematics is used as a solution tool, is not always going to have an derivable answer through mathematics that fits which other commutations. As we all know, scientifically, we see that individual evaluations of "relativity" and "quantum mechancis" are testable and verifiable. But again, yes --- the unforgiving truth is that, mathematically, they do not match-up (at least not yet).
The concept and implication of a "Null Set" (prove something does not exist) assumes that, in reality, there is such a thing (very real) known as a "Set" (of something).
First we must prove that the concept of a "Set" is even real; and not just a human construct. If it is, merely a human construct, then what does that mean in its application to the concept of a Supreme Being?
While it may seem to be a lower order question, it is actually a question (while very simple) of the highest order.
Most Respectfully,
R
