I think that Aristotleanism, at least as expressed by present-day Aristotleans, has positivist tendencies. Positivists make a kind of argument from incredulity to the effect that if formal completeness is not possible then definite meaning must be impossible: if it is impossible in principle to specify the essence of a thing formally and completely, it is impossible in principle to say anythingdefinite about the essence of that thing.
The 20th century positivists got blown out of the water by Godel.
Russell made some valiant attempts, but he never developed a good argument against Godel.
Ultimately, the problem is much older than that.
The Neo-Platonists, notably Plotinus, founded their philosophy on non-discursive knowledge.
Aristotelian and post-Aristotelian positivists start by assuming that all knowledge is discursive, and if something is non-discursive, then that thing is not knowledge.
There’s not much common ground for debate between positivists and Neo-Platonists. Competent mathematicians tend to be Neo-Platonists.