You believe it's not possible to know what you can't prove. I believe it is. It's a different framework, but I wouldn't suggest that my system makes me more intellectual than someone else. Would you say that of yours?
No. I would say the opposite, actually. My ability to say "I don't know" makes my system more intellectual (and intellectually honest as well) than your system in that yours is little more than opinion presented as fact.
History is riddled with people who "knew" they were right that turned out to be wrong. The ability to admit doubt makes for a more intellectual stance.