> So, conceivably, the concept of 'standard' natural number, and the concept of 'standard' model of Peano arithmetic, are more subjective than most mathematicians think. Perhaps some of my 'standard' natural numbers are nonstandard for you! I think most mathematicians would reject this possibility... but not all.
It's probably worth elaborating why the majority of logicians (and likely most mathematicians) believe that standard natural numbers are not subjective (although my own opinion is more mixed).
Basically the crux is, do you believe that statements of the form using all/never quantifiers such as "this machine will never halt" or "this machine will always halt" have objective truth values?
If you do, then you are implicitly subscribing to a view that the standard natural numbers objectively exist and do not depend on subjective preferences.