Albert Camus in The Myth Of Sisyphus basically says that the absurd contradictory world can’t be explained by the rational mind. Noson Yanofsky in The Outer Limits Of Reason basically says that the world can’t have a contradiction (the cat both on and off the mat) but the human mind can. This is paradoxical.
There are two concepts that might help one get their head around this……. definitions and dualisms.
The definition of a word is done with other words and is therefore circular and is therefore paradoxical.
Dualisms underlie just about everything humans try to understand like black and white (ie-just shades of gray?), or nature and nurture (ie-just the ends and sides of a rectangle?), or discrete vs continuous (ie-pulsatile blood flow out of the aortic valve becomes continuous blood flow in a capillary in a finger). This is also paradoxical.
After bashing my head against the wall more times than I care to think about, my opinion is that Wittgenstein was right…...it’s all just word games.
Drinking martinis in Aristotle's cave And not really even getting a glimpse Of the stuff beneath the brain wave That the random act contradicts All that I know of what is free will It is gonna be a hard night mark Sucking down another sleeping pill To interpret the shadows in the dark As a simple way to rationalize The fact we've escaped to a bigger cave It could have been otherwise