I've going to focus on one aspect of Nate Shannon's recent article "The epistemology of divine conceptualism," Int J Philos Relig (2015) 78:123–130.
As no doubt the reader will have noticed, I harbor an openness to the possibility that the laws of logic as we know them do not exist necessarily, in the strong sense in which this is usually taken, but only given a few things (whichever things get us from God’s being uncompelled to create all the way to the actual world). Put more precisely, I think there is rather too much confidence (exaggerated epistemic license, we might say) in the claim that the laws of logic as we know them do in fact exist necessarily, even for God, in the very mind of God.
To suppose that the laws of logic as we know them obtain as we know them in the mind of God is to exaggerate by the force of contingent, fallible intuition the continuity between the creator and the creature to such an extent that no discontinuity is recognized.
i) On one interpretation, Shannon is open to universal possibilism (i.e. there are no necessary truths or necessary falsehoods). If so, there are fundamental problems with that position:
a) It's self-refuting.
b) Orthodox theology requires logical necessity. If logic is relative, then there's no tenable distinction between orthodoxy and heresy.
Given universal possibilism, anything could be the case. Once you denial logical necessity, nothing else can be denied. Everything follows from anything.
ii) On a less radical interpretation, Shannon is distinguishing between human systems of logic and the archetypal logic of divine reason. If so:
a) Welty/Anderson's theistic conceptual realism is referring to logic in general, rather than a specific system. They don't equate a particular human system of logic with the structure of God's mind.
b) At the very least, orthodox theology requires informal logic. Shannon can't avoid that. He can't be noncommittal about logic and retain a commitment to orthodox theology.
Shannon typically tries to take refuge in a buffer zone. But he himself must periodically emerge from the buffer zone to draw lines. To affirm theological truths.
iii) There's a sense in which human systems of logic necessarily inhere in God's mind. Given God's natural knowledge, it is necessary that God know all human systems of logic.