Jees wrote:Something keeps spooking in my head: despite numbering was born out of the desire to manage size, how much of numbering is solely about "size"?
Is the axioma of numbering = size?
For example if numbering indicates discrepancies in quantum states, the concept of size
as we know it start to slip trough the fingers. Then the numbers start to be more connected to energy states than the literal size it occupies.
If I could squeeze out the thumb sucking reflex 'how big/much' and have them numbers cleared from connotations, they might be free to live in the abstract on their own terms. Then they don't necessarily have to make sense anymore in the real world. Then 'sensibility' can no longer be feeding a prove/disprove discourse.
Feeling puzzled about this
Numbers are not just about 'size,' although they always have at least some value associated with them. We've just been talking pretty much exclusively about cardinality, which does use numbers to represent quantities. If you want to see numbers representing something other than size, go wander over to differential calculus where numbers can represent rates, or linear algebra where numbers can represent vectors in various dimensions.
There is no axiom that numbers equal size, I don't know where you're getting that. None of the axioms of ZFC, for example, make any reference to size. We use numbers to represent sizes, in the same way we use them to represent a lot of other things. They're very useful abstractions in this regard.
I'm not sure what you mean by 'clearing numbers from their connotations.' You could easily create a formal system that makes all numbers have the same value, but you couldn't do much with it.
Blessings
~ND
"There are many paths up the same mountain."