In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> Pi is constructable and computable and definable, because there is a > finite rule (in fact there are many) to find each digit desired. But > as there are only countably many finite rules, there cannot be more > defined numbers.
If there are countably many rules then there are uncountably many lists of rules capable of generating a number.
> Therefore matheologicians have created undefinable > "numbers".
WM mistakes the issue.
In pure mathematics, like in games, one has a set of rules to follow. Differing sets of rules generate differing systems only some of which are of much mathematical interest.
The systems of rules we chose to use need not be subject to the constraints that the system of rules that WM choses to play by are subject to.
For example, in FOL+ZFC, a commonly used system of rules which WM doe not care for, all sorts of things are legitimate that none of WM's systems of rules will allow.
WM tries to force everyone to play only by his rules, but most of us find his system of rules dead boring and of little or no mathematical interest.
Fortunately, outside of those classrooms in which his poor students are compelled to play by his rules, he has no power to impose those rules on anyone.