That's a problem right there. Maybe that made sense to the Greeks, but it definitely doesn't make any sense in the 21st century. "Knowing" falsehoods is something we broadly acknowledge that we all do.
To say that this is not "knowing" is (as another commenter noted) hair-splitting of the worst kind. In every sense it is a justified belief that happens to be false (we just do not know that yet).
Not to mention what does it even mean for something to be false. For the hypothetical savage the knowledge that the moon is a piece of cheese just beyond reach is as true as it is for me the knowledge that it's a celestial body 300k km away. Both statements are false for the engineer that needs to land a probe there (the distance varies and 300k km is definitely wrong).