This weekend I accidentally stumbled on a page for science teachers. http://digipac.ca/chemical/proof/index.htm
I was appalled by the twisted message, that reduces logic to a suspicious rhetorical device. Money quotes:
Proof does not equal truth
Here's a definition of what it means to prove something: "Proof is arriving at a logical conclusion, based on the available evidence." Notice that this has absolutely nothing to do with being right or wrong.
Proving something does not make it true. It just means that you have convinced other people that the evidence supports your conclusion.
I was particularly stung by the third quote, because I use similar terms to try to explain how to write a proof: I usually say that it should be just formal enough, but not too formal, and that "just formal enough" depends on the recipient - just enough to convince the reader that you indeed have a valid proof.