FOM: Combinatorics and Large Cardinals

Joseph Shoenfield jrs at
Mon Apr 20 09:55:41 EDT 1998

   Steve's recent communication states our differences clearly.   He
slightly misrepresents me on one point.   I don't object to discussion
of informal notions; but I think that if the discussion is to serve
the purposes of fom, it must aim at replacing these notions by formal
ones.   Steve shows no interest in replaing the notion of "finite
combinatorial statement" by a formal notion.   If I correctly inter-
pret him, we have an unresolvable difference over the purpose of fom.
     I did not defend my statement that ConZFC is a combinatorial
statement because I didn't think it would be controversial.   Steve
says that a combinatorial statement is a statement about the arrange-
ment of objects in patterns.   ConZFC ia about the arrangement of
sentences of set theory in the patterns of proofs.   Steve's objection
seems to be that ConZFC is not interesting to certain people: people
with little knowledge of logic and specialists in finite combinatorics.
It seems he is replacing "finite combinatorial statement" by "finite
combinatorial statement of interest to certain people".   I do not
regard this informal notion as of much interest, especially with the
peculiar (to me) choice of these people.

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