Whelp, I see Rhythm that you're very hesitant to even acknowledge there's a discussion front regarding the definition of "logical" in our language. I might have a few ideas as to why that is. But putting all that aside, I'm very much reminded of what one of my philosophy teachers once said - all philosophy problems are essentially problems of language. And the more I try and comprehend things, the more that rings true. I don't think either of us can really prove what we're saying, because it's semantics, and semantics is a big issue in philosophy of language.
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle