How can you be confident that you're an open-minded or free thinker? Doesn't it
Good question. Could use some precision in the terms, i.e. what exactly counts as being "open-minded" or "free thinking"? some of these terms might have very specific meaning in certain contexts, but not clear what meaning you're assigning to them here. Also the heart of your second sentence/question is empirical, really -- we'd have to do a carefully devised survey to find out how people generally self-conceive. One of the really deep philosophical questions you have a finger on here might be this: is it possible to reconcile "open-mindedness" with "having reached a firm rational conclusion" -- since the degree to which you are convinced (rationally) by P is the degree to which you are no longer "open to" not-P. So even if you are initially "open" to all sorts of arguments/evidence, once you've made up your mind you are now "closing yourself" with respect to counter arguments/evidence. Of course, one might hold that an "open-minded" thinker is one who continuously revisits the issue, revisits the arguments/evidence, continues to look for new counter arguments/evidence -- but I'm not sure doing that is always really a virtue. (Seems pretty inefficient overall -- once you've investigated something you would never be finished, which will stop you from moving on to other things.) So there are a lot of good things to think about here!