Anticlimax Boss: The Final Boss makes many amateur rhetorical mistakes and repeatedly falls into easily-debunked logical fallacies. Half the argument doesn't even require using anything from the idea slate! Of course, he may actually want you to succeed.
Fridge Brilliance: The Arbiter is actually not very good at logic, and makes a lot of mistakes when arguing with Socrates. This is because Socrates lived and died before the development of formal logic, instead using a methodology focused on trapping his opponents in contradiction.
Immanuel Kant. His arguments are quite complicated; even the characters complain about how incomprehensible he is. To beat him you need to do something that seems foolish and isn't required anywhere else: use his own philosophy (the first idea he gives you) against him. Even then, figuring out exactly where to do it can be tricky.
Which boss counts as That One Boss for the player may, in fact, reflect their own philosophical beliefs. Philosophers they strongly agree with may be harder to take down; for instance, a deeply religious individual may struggle even against Euthyphro. (It's just as likely that being well-versed in their philosophy may allow one to know all the counterpoints in advance, however.)