"I'm not so sure we have discovered an a priori Universe. In the sequence of the events we perceive, there is no doubt that thought precedes any discovery. But of course there is the possibility that the Universe preceded the thought."
Let's not confuse 'a priori' and 'preceded' and strictly speaking, I have done so. If we take a look around, we observe and deduce that the universe has been observed before us and not just by humans. This is the temporal statement that uses the 'preceded' sense of order. In the temporal domain, the Universe preceded us. When you invoke a sequence of events, I see Universe, perception, cognition, self-awareness, Decartes. So from our perspective, the Universe temporally preceded us.
The 'a priori' sense gives us a different avenue to explore. Let us suppose a Godhead whose intellect is reflected/channeled in the minds of humans. I forgot the -ism, but this is the view that begat sayings such as, "The lamps are many but the light is one." In this cosmology, the thought, which would be conception in the mind of God and by transference, humans, is a priori to creation which is the utterance of the thought, if you will. Here the temporal dimension is created posteriori to the existence of thought. This occurs in the 'Cosmic time zone', whatever that may mean. Such a process creates a Universe that necessarily (because we have evidence) forces the 'preceded' sense to follow my earlier exposition.
Another way in which the 'a priori' sense can work extemporaneously is through solipsism, but I don't subscribe to that superannuated newsletter.
What is your sense of things?
"'However, if you would have it, I'd grant that where human sentience is insufficient for arithmogeny, God's mind is apt.'
Unless I misunderstand you, I think we have shown that human sentience is sufficient for arithmogeny. (Great word!) But that only strengthens the case for God's aptness."
Yes, my claim is that where humans have not yet calculated a particular number, God may already have.
"'This of course leads back to whether God can conceive the sum of an infinite series and whether such conceptions as the complex field over the reals have already been worked out.'
I think the answers are "Yes", and "Yes"."
Well, if God has worked out the details of complex math, presumably the reals have been as well and thus the rational numbers and lastly the finite sets of integers. In this case, is it not valid for humans to reason about natural logarithms and is it not plausible that reality is a continuum?
"Do [...] transfinite cardinalities, for which you say you have a sense, bring along with them the contradictions and absurdities that Cantor, Russell, and Goedel say they must?"
Here I am at a disadvantage, for I am only moderately aware of the issues around Russell's Paradox and I'm a tyro with Cantor and Goedel. It was my understanding that RP succumbs to Tarski's heirarchical treatment of these kinds of paradoxes, although I've only touched upon those methods. Didn't Russell himself suggest there were problems with categorical predicates and vicious loops?