Undefined Terms, p 93-94
Undefined terms [...] do get defined in a sense: implicitly --by the totality of all propositions in which they occur, rather than explicitly, in a definition.
[...]
A full formalization of geometry would take the drastic step of making every term undefined [...]
[...] symbols automatically pick passive meanings in accordance with the theorems they occur in.
Is Number Theory the Same in All Conceivable Worlds? p 100
It seems to be the consensus of most modern mathematicians and philosophers that there is [...] a core number theory, which ought to be included, along with logic, in what we consider to be "conceivable worlds". The core of number theory, the counterpart to absolute geometry, is called Peano arithmetic [...]