It is clear that the number of "primitive propositions
of logic" is arbitrary, for we could deduce logic from one
primitive proposition by simply forming, for example, the
logical produce of Frege's primitive propositions. (Frege
would perhaps say that this would no longer be immediately
self-evident. But it is remarkable that so exact a thinker as
Frege should have appealed to the degree of self-evidence as
the criterion of a logical proposition.)