On Hell and Forgiveness

[polymath257]

Suppose I have four plants and you consider one to be a tree and I consider that one to be a bush. You would say there are four trees and I would say there are three. And we could both be correct. The method of counting is the mathematical model: how to apply the abstract language to a particular real world situation. The reality didn't change: it was only our interpretation that differs.

Here you are arguing that they are ontologically objective.  The number of things did not change and was not effected by the subject or their opinions. We are describing something external and not internal to the subject.

No, I *am* saying the number is subjective: it does depend on the observer and their biases.

But, more importantly, the actual identity of the number 4 is not agreed upon. Is it the set {{{{}}}}? Or is it the set {0,1,2,3}, where 3={0,1,2}, 2={0,1}, 1={0}, and 0={}?

Or do we use the notion in the integers (equivalence classes of order pairs of natural numbers)? Or in the rational numbers (equivalence classes of order pairs of integers)? Or in the real numbers (Dedekind cuts? equivalence classes of Cauchy sequences?)? Or maybe in the complex numbers (ordered pairs of real number? Or the algebraic quotient field obtained from real polynomials after modding out by x^2 +1?)

Or do we simply mean SSSS0 in an inductive set with first element 0 and successor function S (in which case, there are many, many, many different specific notions)?