So, I am taking a math class and the professor comments on one of my proofs saying that there is an 'inconsistent use' of a variable, he doesn't show how or why it is inconsistent he just said that it was his opinion. I am thinking of replying to him w/ this : "I thought that the essence of Western mathematics was that if a statement is affirmed to be true, then it must follow (according to certain explicit rules) from other true statements and that it doesn't get it's validity by being referred back to the person uttering the statement and their authority, as if they were a priest, a king, or God. Every true statement must be open to examination and discussion. Am I wrong here, or does this math department not see itself as belonging to this tradition?" Is this appropriate for communication between a professor and a student?