Admittedly, there is an anachronism here, but Westphal (in Transcendence and Self-Transcendence) argues that theologians such as Augustine and Aquinas actually provide precursors to the type of argument that becomes the critique of onto-theology in Heidegger, etc. Essentially the critique follows a Kantian path, rather than a Spinozan or Hegelian one. It asserts that no systematic knowledge can be sufficient to establishing a full understanding of the divine. No matter how far it takes us, such a system will always lack more than it gains. Further, this insufficiency also affects our knowledge of other created things. Here is how Westphal describes Aquinas' take on the problem:
"God, in knowing the divine essence, knows all created beings, which participate, however weakly, in that essence. Not knowing the divine essence, we do not know things in this way. We do not know the perfections they imperfectly embody. Once again, human "knowledge" is secondary and human "truth" second-rate...
It is not just that God's knowledge, by contrast with ours, is creative [N.B. - Humans clearly have a creative element to our knowledge.]. We are not defined, strictly speaking, as rational animals but as created rational animals. A paradox emerges from the fact that createdness belongs to the essence of finite things. This fact is what makes them intelligible to us... At the same time, their createdness makes them incomprehensible.
For Aquinas 'it is part of the very nature of things that their knowability cannot be wholly exhausted by any finite intellect, because these things are creatures, which means that the very element which makes them capable of being known must necessarily be at the same time the reason why things are unfathomable.' This is not a quantitative deficiency... Aquinas is talking about our grasp of the essence of things."