This is a question I've been pondering a lot lately, and I have no good answers for you.
On the one hand, I feel fairly certain that a classical understanding of the Trinity leads to the position that what the Father knows, the Son knows, lest their be any division in the Godhead. The great problem then becomes the Incarnation - in what sense do we speak of the knowledge of the divine person of the Christ, in his divine and human natures?
Matthew 24:36 But concerning that day and hour no one knows, not even the angels of heaven, nor the Son, but the Father only.
That seems to me to be a pretty hard sticking-point. Especially for Cappadocian exegesis. They want to consistently refer limitations and humble characterisations to the human nature, which I think is generally quite correct. But then they want to say that when the Scriptures speak of 'the Son', without qualification, then it's referring to the divine nature. That won't wash here, and Cappadocian exegesis of this passage seems very confused, if not a kind of inverted contradiction.
Luke 2:52 seems to definitely give a picture of the incarnate Christ as a person who grows in knowledge and understanding. We must hold on to that if we are to affirm the full humanity.
So, any thoughts? How do we understand and articulate the knowledge of the incarnate Son in a way that affirms Nicaea and Chalcedon?