The first principle and logic

Hello Rabbi
Doesn't the claim that God is incapable of things that lack logic assume logic as a primary existence for God and as something separate from Him? After all, if we assume that God is the primary cause of everything, then we also assume that logic is a result of Him, and it doesn't seem reasonable to me to think that God created logic and denied Himself the option to overcome it.
Now you might come and say that the very statement that God can act contrary to logic is meaningless, and I agree, but does that resolve the contradiction? If so, then I would love to know how, according to how I understand it, at most it means that perhaps the very consideration of God is meaningless by virtue of his being prior to logic (which all our thinking is done only within).
thanks.