[FOM] Formalization Thesis vs Formal nature of mathematics

[Alex Blum]

In his latest contribution to this thread, Vladimir Sazonov makes
a remark regarding mathematics which no doubt touches the subject on 
most everyone’s account but I wonder if it hits the nail on
the head.

He writes: “The main definitive and distinctive attribute of mathematics
is that it is rigorous. But what means rigorous needs to be explained. I
take rigorous = formal and understand formal in sufficiently general 
sense of this word. The contemporary concept of formal system (FOL, PA, 
ZFC, etc.) is only a limited version of 'formal'.”

Clearly, as he is aware, this covers logic as well. But more
importantly, it is not clear that rigour is not the consequence of the 
abstract subject matter of mathematics. It's scientific methodology 
demands it. It has no other recourse to claim our allegiance, as opposed 
to for example biology, although we have, J.H. Woodger, The Axiomatic 
Method in Biology(1937).

Alex Blum