Your thoughtless edit When you did this edit did you read the next following sentence If it is discovered that two or more of these conditions hold then all of them hold and ZFC A1 is inconsistent and ZFC A2 is inconsistent in this case these axioms would no longer be considered large cardinal axioms You are supposing that this can not happen that is that none of the large cardinal axioms will ever be found to be inconsistent even though this has repeated happened in the past