[FOM] AXIOM SCHEMATA

[John Corcoran]

1. Who were the earliest to use an axiom schema in the modern sense?
Kneale and Kneale 1962 page 528 says Von Neumann 1927.
2. Who were the earliest to attempt to explain the concept of an axiom
schema?
3. Who were the earliest to purpose the expression ‘axiom schema’?
4. Which other expressions were proposed?  Herbrand 1930 uses ‘matrix’.
5. When was the axiom of mathematical induction first approximated by a
schema? Herbrand 1930?
6. When did logicians start to realize that a sufficiently rich system
of number theory could be constructed on the basis of a first-order
language?
7. Who were the earliest to attempt to use a axiom schema for
mathematical induction in an axiomatization of first-order number
theory? Herbrand 1930?
8. Who objected that infinitely many “axioms” was contrary to the spirit
of the axiomatic method?
9.What else should I be asking about schemata?


PLATONISM IN MATHEMATICS:  To me a Platonism 
 with respect to
mathematical concepts 
 seems to be obvious and its rejection to border
on feeble-mindedness. — Kurt Gödel 1975, BSL 2004.  It is the merest
truism, evident at once to unsophisticated observation, that mathematics
is a human invention. — Percy Bridgman 1946, Kline 1980, 325.