Okay @swamidass is looking for some sort of Lutheran reflection on the nature of paradox as a way forward with his notion of "Fallacies of Improper Mixture, " the recognition of divine action in the world (miracle), and I suppose a viewpoint on the nature of science and religion – so here we go!
Paradox
The nature of Lutheran paradox is captured in Luther’s tract, “On the Freedom of a Christian,” where he states, “A Christian man is the most free lord of all, and subject to none; a Christian man is the most dutiful servant of all, and subject to every one.” Regarding the Christian in the world, Luther recognizes that we are completely free and completely bound. For anyone who has looked into Luther’s theology, you’ll find affinity with the familiar Lutheran dualisms of Saint/Sinner, the Sacraments of Bread/Body, Wine/Blood, Two Kingdom Theology, etc…
The paradox of practical Christian freedom gives way to more theoretical/metaphyscial paradoxes as we use our freedom to contemplate the nature of God and his creation. Luther is famous for limiting reason to ministerial purposes. Reason must always remain subordinate to scripture. Of course, this is easier said than done and just as demarcating science from pseudoscience is a difficult if not impossible task, so is often the task of recognizing when reason slips from a ministerial into a magisterial role. Easy cases are trying to understand the two natures of Christ. Any attempt to understand how Christ can be fully man and fully God will lead one to reasoning beyond what scripture makes clear – we break with the Reformed on this one. Harder cases are going to be something like discerning a legitimate miracle in the world today.
Divine Action
How this might play out with divine action is looking to Scripture, particularly John 14:6, "Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me.” I would take this to mean that if I’m not somehow talking about Christ, then any talk of the Father is going to be speculative. Do miracles happen? Absolutely, as @swamidass @Andrew_Loke and others have pointed out, scripture surely testifies to these miracles. I trust the reports and thus know that miracles are possible. Do I see miracles around me? Maybe, but alternative explanations will always be possible and the declaration that X is a miracle will always be underdetermined by the data. This is partly due to how God seems to work in the world – he uses his natural creation (water to wine, burning bushes, becoming man). @swamidass has pointed out repeatedly that science simply can’t account for miracles. I think this is correct as even if we could have been at Lazarus’ bedside, with all the medical equipment hooked-up, the facts would have been the same even if more fully described. In medical scenario, at time A Lazarus’ cells were NOT metabolizing, a man named Jesus yelled at Lazarus, and at time B Lazarus’ cells were metabolizing! In biblical scenario, at time A Lazarus is in a tomb, a man named Jesus yelled at Lazarus, and at time B Lazarus walked out of the tomb! Did a miracle take place? Of course, but it was because Jesus declared it to be. However, since Jesus is not walking in his public ministry around us today reversing cellular death and casting out mental illness, I must work from a stance of the hidden God. The hidden God seems to imply that I will have trouble even recognizing a theological miracle apart from scripture.
Hidden God
Some have hit upon the notion of natural and revealed theology. I think, and I admit that I may be idiosyncratic, but Luther would have preferred something more akin to God hidden and God revealed. God revealed would pertain simply to the state of affairs surrounding “in Christ God was reconciling the world to Himself in Christ” (2 Cor. 5:19) versus the hidden or masked God that operates outside of Christ in pillars of fire, burning bushes, tornadoes, pick your favorite OT story where God comes and terrifies his creation through natural means! When talking about discerning a miracle outside of the biblical revelation, we are dealing with the hidden God and any identifying of such a miracle inches closer to magisterial use of reason due to its extra-biblical nature. Again, I’m not saying that identifying a miracle is impossible or a problem of magisterial over ministerial, but my Lutheran theological intuitions and my philosophy of science intuitions align in being more skeptical than not when dealing with extra-biblical divine action.
Of Sandboxes and Fallacies
God gives us freedom to explore and act in this world as we see fit. In fact, a Lutheran picture is that we become masks of God to our neighbors. To be better masks, this means that we also become creative entities in working with the materials around us. We may not be naming animals, but we are discovering functions, laws, whatever and putting them to use for our neighbor. Even the sandboxes that we find ourselves in are our constructions whether science or theology. However, these different sandboxes are overseen or how about undergirded by God with Christ serving as the physical bridge between all the different boxes. Every box or discipline can speak to aspects of God through Christ due to his historical and physical nature. But, as Christ bridges the different boxes, he also allows the boxes to develop independently of each other. This will always promote tension as we want that magisterial view, but it is a view that is always beyond our grasp.
The fallacies provide rules of thumb for interacting between boxes, but are themselves products of creation. However, the second we start employing them, we will run into that humbling experience captured at the end of the thread @jrfarris as we realize that we may not be modeling anything like “how science and religion could interact” or what “disciplines outside of science actually contribute evidence.” It is an intellectual tower of Babel to think we have it figured out. However, as @swamidass made clear, the rules are always provisional and may need reworking as new conversations happen even when we do not have a clear cut methodology or conception of good evidence. We confidently stumble along even after being kicked out of the Garden.
Done for now…
Sorry for the length – it would of been much better to post smaller tidbits in response to different threads as they developed over the last couple of days. However I came late and thus you are given my ramblings as I tried to grab and comment on the big picture. The notion of paradox needs more fleshing out as is along with its relation to epistemic and metaphysical concerns.