Philosophers have always admitted contradictions. Saying that they are worthy of our notice. Usually the contradiction is an apparent contradiction, or, put another way, a disagreement of kinds. The Greek word pseudos as is oft mentioned makes no distinction between lie and falsehood, though the distinction was clear to the ordinary Greek. Contradiction in its basic form is a lie or disagreement between two statements taken from our daily dealing. This situation of apparent confusion is a part of daily life. Early on Plato comes to the most extreme contradiction, that not-being is (cf. the Sophist.) The sophists, who in passing one might notice were badly used, as all professors take money, so too the sophist, demonstrated the cataclysmic failure of episteme or science. However, already in Aristotle it was deemed so that whatever was outside the possibilities of the theoria (the glance from without at an alien splendor) of the proper being could not be dealt with, and in this sense Aristotle said the the psuke, the human life, is in a way all of the beings. Thusly, it is clear that the tradition was always aware of this difficulty and all the thinkers of the tradition ponder it. This is the moment of judgement. One must break from the form notice of the contradiction when needed.
Now, in our own day the degeneration occurred because "logic" as in the scholastics was a tool for friendly investigation. Since all were part of the Christian thing seeking the same ends. Maimonides and Averroes et all can also be included in this friendliness with truth that prevented mathematical formality from becoming a loggerhead and obdurate confuser. So long as there is deliberation or reasoning, and at most shared disputation, it is useful to be able to point to all the informal fallices. they are not proof of anything but only helpful signposts. But, when, on the one hand we have mathematics replacing logic, and on the other debate and controversy political and lawyerly replacing deliberation and dialogic, we get an evolutionary mismatch. The devices were not meant to be used in this way. The use in experiment regarding physical law is simply understood as Humean Fictionalism, and so useful. But, it is not useful when carried into the realm of public discussion.