I can completely affirm everything you say here.
The Leibnizian Hyper-Calvinist God
Even assuming Leibniz’s clockwork universe, sure it could lead to a deist God, which may sound scary. But I don’t think all versions of deism are necessarily in conflict with orthodox Christianity. You could have a God who preordains the initial conditions and laws of the universe such that they accomplish His will exactly as He wanted it. Into these initial conditions he would include the worldly manifestations of His attributes, including providence, love, justice, redemption, and so on. Such a God would also sustain the laws that are set in motion.
This God would be a hyper-Calvinist sort of God, but in principle it does not conflict with the Bible. From our viewpoint we would see no difference: we would still have free will (of course compatibilism would have to be true), we could still pray to God for His providence. We could even allow, in such a deistic picture, rare times when the laws of the universe are suspended for miracles.
The God of Modern Physics
Despite my defense of the Leibnizian picture, the fact is that science has progressed immensely since that time. We have a host of phenomena we can explain, yet we also know things which seem fundamentally mysterious:
- The inherent randomness of quantum mechanics
- The puzzle of different interpretations of quantum mechanics
- The existence of chaotic phenomena
- The immense fine tuning of the universe
- The persistence of the hard problem of consciousness in philosophy of mind
- The difficulty of explaining the origin of life
- The evidence that the universe had a beginning in time
These are just examples I can think of the top of my head. Now, possibly science or philosophy might eventually be able to explain some of these mysteries away. But it is entirely possible, in my view, that some of God’s providence could be contained in some of these problems. They seem to be of a fundamentally different nature than regular scientific problems. To me, that possibility is just as, if not more exciting than the possibility that science will simply fail to explain less fundamental problems (in my opinion) like evolution and the motions of planets. For you, looking for God’s providence in quantum mechanics is a form of arrogant, reductionist, scientistic deism. But for me, it’s one of the most intriguing scientific-theological investigations there could be.
The Pitfalls of Scientific Agnosticism
You advocate for an agnosticism with regards to what science will ultimately be able to explain. I agree with you in principle. But that should be a stance taken by a philosopher or layman observer, not a scientist working in the field. The scientist’s job is precisely to chase lawlike explanations of unexplained phenomena to the ends of the Earth, especially those that exhibit regularities. (I am reminded of Eddington, whom you admired, conducting experiments as far as West Africa and Brazil in order to test Einstein’s theory of general relativity in 1919).
Scientists, including Christian ones, must continually test the boundaries of God’s laws versus providence (to use Newton’s terms). Otherwise science would have stopped with Newton. A scientist who stops doing that is no longer a scientist anymore. (Of course, I am not speaking of special revelation - miracles.)
Science as a Form of Worship
And far from being a form of atheism, such an attitude is a form of worship towards the Creator who created and sustains these laws in the first place. When I encounter these lawlike regularities I do not see a distant, deistic, clockwork God. Instead I see a God who is kind enough to create a universe whose laws are simple enough to be grasped by limited minds such as my own. He is allowing us a tiny glimpse into the beauty and brilliance of His mind. We see this in the incredible beauty, for example, of quantum electrodynamics, which even as messy as it is, can give us predictions accurate to 12 decimal places. God’s regularities are an expression of His everlasting love and goodness. So why are we scared? Why are we pushing God into the gaps? Why can’t we see Him in the “works of His fingers” that are already in front of us?