Well, the answer to that is yes. There's almost certainly more to define. We'll have to shore-up our foundation as we go. (And the stove is on as I write this, but I know about it. Don't worry.)
Anna made a good point about probable proofs, in a comment on the last post:
"But when spinning your wheels in a discussion, probable proof is very simply just... dismissed for nothing more than the lack of desire to see the truth.... 'you can't prove that' is often attempting a 'gotcha'..."The person saying "you can't prove that" may mean "you can't provide a deductive argument" or "you can't test that in a lab". There are many things we accept as true but can't provide proof for, if we're using such a narrow definition of "proof".
Can you show me utterly certain, physical evidence that your spouse loves you? I don't want to see examples, I want to see a test that comes back "yes" or "no" from the lab. It doesn't exist. (And if it did, it throws back to the mind/body problem -- is the chemical state it detects the cause or the effect of the love?)
Can you provide certain proof that anything other than yourself exists? That you're not in the Matrix? No, this has to be accepted as a brute fact.
Can you provide a certain proof that the sun will rise tomorrow? No, only a probable proof. If I flip a coin, and it comes up heads, that's normal. If it comes up heads again, that's still normal. After a few more, you might become suspicious. After a thousand heads, you might feel confident that the next flip will come up heads as well. But there is no certainty (unless you peek at my two headed coin). There is only the knowledge that this has worked over and over again, every time. It is going to work again.