The way I see it, Aristotle used language as a reasoning tool. Logic inference rules, modus ponens, and so on.

Aristotle was also unaware of the incompleteness problem discovered by Gödel, that no reasoning tool of that type can be complete.

There are fundamental contradictions in the nature of language, it however doesn't make them not useful for the entire experience of daily communication, all of literature, and so on.

Just that there are affirmations that are true, but there is no set of rules that can prove them.

I would point you to Gödel, Escher, Bach for a very nuanced discussion about this topic.