I think I understand now. Sorry, but I'll have to be blunt. I promise I don't mean to insult you, but I feel that clarity is more important that politeness here.
You recognize the existence of rather precise (though contradictory) definitions of OO. You probably have a preference for one of them. Yet, you have "chosen to believe" that there is a concept that most programmer agree to call "OO".
Of course, you are unable to put such a concept in writing (or you would have done so by now). Therefore, you dismiss actual definitions of OO as "implementations", saying that the "concept" is above that. The advantage of such a line of thinking is that you don't actually disagree with anyone. The problem is that you hardly say anything when you utter "OO".
I may be wrong. But if you want to convince me, you'll have to write a definition of this OO "concept" you're talking about. Or a sketch. Or at least tell me that it will take too much space and effort.