Smith is a spy but his parents will never find out.This could be true but Smith’s parents could not know it! The proposition above is a blindspot for Smith’s parents, though not for anyone else.
It’s raining outside but I don’t know this.Obviously, this proposition could be true but, equally obviously, I could not know it to be true. This proposition is a blindspot for me and me alone.
There will be an exam tomorrow but you don’t know this.(“There will be a surprise exam tomorrow.”) In this strange case, her announcement is easily shown to be self-defeating, i.e., a blindspot for the class. Although her words may be true, the class cannot know them to be true. This case proves easily assimilable to the birthday case above.