Well he factually didn't even from the perspective of 'his known world', Alexander both turned back from on campaign, and had planned another campaign he didn't live to initiate.
But regardless it strikes me as a pretty ridiculous claim to make, (especially today) when an estimated 70% of the world population lived in places (they obviously know) that weren't conquered by Alexander. After all there is no 'the' known world. You can find many millions of people who have not a clue of the world beyond a few miles away and you'll thereby find many different people who each rule their known world.
But regardless it strikes me as a pretty ridiculous claim to make, (especially today) when an estimated 70% of the world population lived in places (they obviously know) that weren't conquered by Alexander. After all there is no 'the' known world. You can find many millions of people who have not a clue of the world beyond a few miles away and you'll thereby find many different people who each rule their known world.