Yes, you are definitely right, so far as proving things goes in the real world, and so far as how the word "proof" is used in the real world. This is a sticking point for my students, as well: Formal logic employs these terms differently.
In formal deductive logic, the premise "if P then Q" plus the premise "not-Q" together prove the conclusion "not-P." I chose the nouns Paris and France to fill in the P's and Q's, because it makes the logical force of this argument form clearer. But I could choose any nouns. I could say "If Harry is a unicorn, then Harry has gold fur. Harry does not have gold fur. So, Harry is not a unicorn."
Have I said anything true about the real world? No.
Have I "proven" anything about this Harry? No.
But have I constructed valid argument that proves its conclusion by the rules of formal deductive logic? Yes.
So that's why I spoke up about the claim that "It's logically impossible to prove negative statement." This claim is relevant in many real-world situations. For example, it is easier to prove that something exists than to prove that it doesn't exist. But the claim can mislead people about the nature of logic, or at least the nature of formal logic, where we use the words "proof" and "negative statement" in very restricted and sometimes seemingly unrealistic ways. And, of course, since I teach this for a living right now, I couldn't resist saying something :evil_lol: It's the teacher in me coming out....
lol! PuppyFluffer, you can get all this and more in most logic classes in philosophy departments. I wish more of my students thought this stuff was interesting!
