That is very reductive view of what constitutes most axioms.
Merriam-Websters has:[1]
>2: an established rule or principle or a self-evident truth
Etymonline has:[2]
>"statement of self-evident truth," late 15c., from French axiome, from Latin axioma, from Greek axioma "authority," literally "that which is thought worthy or fit,"...
So, no, not arbitrary at all. Which particular axioms do you find arbitrary? Is game theory arbitrary?
That is very reductive view of what constitutes most axioms.
Merriam-Websters has:[1]
>2: an established rule or principle or a self-evident truth
Etymonline has:[2]
>"statement of self-evident truth," late 15c., from French axiome, from Latin axioma, from Greek axioma "authority," literally "that which is thought worthy or fit,"...
So, no, not arbitrary at all. Which particular axioms do you find arbitrary? Is game theory arbitrary?
[1] https://www.merriam-webster.com/dictionary/axiom
[2] https://www.etymonline.com/word/axiom