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.
This is something that a lot of Greeks would have had issues with, most probably Heraclitus, and Protagoras for sure. Restricting ourselves to Aristotelian logic back in the day has been extremely limiting, so much so that a lot of modern philosophers cannot even comprehends how it is to look outside that logic.
That's arguably good. If you restrict yourself to something that you know is a valid method of ascertaining truth, then you have much higher confidence in the conclusion. The fact that we still struggle even with getting this restricted method shows that restrictions are necessary and good!
Then you bootstrap your way to a more comprehensive method of discourse from that solid foundation. Like Hilbert's program, which ultimately revealed some incredibly important truths about logic and mathematics.
And to give a concrete example related to this as a whole, people should have known that getting to know something by not knowing it more and more is a valid epistemological take, just look at Christian Orthodox Isichasm and its doctrine about God (paraphrased it goes like this: the more you are aware of the fact that you don’t know God then the more you actually know/experience God”). Christian Orthodox Isichasm is, of course, in direct connection with neo-Platonism/Plotinism, but because the neo-Platonist “doctrine” on truth has never been mathematically formalized (presuming that that would even be possible) then the scientific world chooses to ignore it and only focuses on its own restricted way of looking at truth and, in the end, of experiencing truth.