Re: The set of necessary FISONs

On 04.02.2025 18:51, Jim Burns wrote:

On 2/4/2025 5:11 AM, WM wrote:

On 03.02.2025 20:48, Jim Burns wrote:

On 2/3/2025 1:36 PM, WM wrote:

 

Therefore Peano, Zermelo, or v. Neumann
create ℕ as well as the set of all FISONs
for use in set theory.

>
Axioms describe.
Magic spells create.

>
To describe something
it must be existing.

 To describe something existing,
it must be existing.
 Describing what doesn't exist doesn't create it.

That is Platonism, requiring God's influence. It cannot be excluded. But in my opibion describing non-standard mathematics does not prove that it was existing before.

If ℕ is existing,
we do not need axioms.

 Describing it did not create it.

Then nothing further than stating ℕ would be necessary. That is a wrong opinion.

 

If ℕ is existing,
we do not need axioms.

 If ℕ is described,
its description can have appended to it
not.first.false claims,

Either they did exist or they did not.

If ℕ is existing,
we do not need axioms.

 If the axioms are contradictory,
ℕ is not existing.

And if they are not contradictory, then the ℕ created by them exists.
Regards, WM