Bram: It's a mistake to infer the existence of large cardinals from the consistency of large cardinal set theory. I agree that it is likely that large cardinal set theory is consistent, but the falseness`of 'consistency implies existence' follows from thinking about theories like PA+not(con(PA)): if PA is true then it is consistent, and so is PA+not(con(PA)) (by Goedel's incompleteness theorems), but surely this theory isn't true!