If you do any inferring at all, you are participating in a social process which you learned from others. Whether or not that inference is considered a correct one is a purely socially determined fact. So, after all, you are being corrected by a social force - you just didn't notice it. I don't understand the distinction you are trying to make.
Conceptions are real.
Actually, I would prefer to say that it is the beliefs that are true or false. That is, they are made up of propositions which are either true or false. I think that propositions, in contemporary philosohpy, are thought to be those things which allow deductions to be made and truth values assigned. The way you describe them, they seem to be mental entites of some kind. I think that they are logical objects.