Take a stupid Italian (Peano) and mix in a Jew (von Neumann) and what you get the spaghetti axioms. :-)
You can know a person by his quotes:
"Young man, in mathematics you don't understand things. You just get used to them."
Yes, we have seen the fruits of that in mainstream mathematics. A sewer of flawed theory.
As for Peano, he got the quote right but the mathematics was a juvenile attempt:
"Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use."
One needs to understand the importance of being well defined.