There is nothing philosophical about it, actually. It is a matter of definitions and running with them.
Even crazier things start happening in logic when you start assuming certain set theoretic axioms and seeing which other theorems are proved or not proved under these axioms. Look into the Axiom of Choice.
Indeed. This is where the philosophy of mathematics gets tricky and I am sure in no position to delve deeper into it.
There is nothing philosophical about it, actually. It is a matter of definitions and running with them.
Even crazier things start happening in logic when you start assuming certain set theoretic axioms and seeing which other theorems are proved or not proved under these axioms. Look into the Axiom of Choice.
Thanks, I will check it out