I think this is worth expanding upon, and enumerating, before going farther. Then I want to point to one way to start bringing this together, a Lutheran notion of Paradox (@Philosurfer).
The Fallacies of Improper Mixture?
I do not present these as an exposition of Bacon, but as a riff on several failure points that I can common see. Perhaps they are not stated correctly. Feel free to revise if you see need.
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Miracles always implied God acted. Some miracles, however, are coincidences with out any apparent violation law. Especially with Molinism in view, there is no reason to think these are any less miraculous than special acts of God, even if they have less empirical basis to observers.
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Miracles always follow Natural law (or the regular order). God can transcend the regular order whenever He likes, and we are right to believe that the Resurrection of Jesus (and Lazarus) was the special action of God.
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If we personally perceive God’s providence, we should be able to justify it to others. However the direct experience of a miracle gives a different epistemological basis than those that merely hear of it through us. We might expect direct witnesses to be convinced, and others unconvinced.
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If God acted outside natural laws, science should be able to detect such irregularities. This presumes that God is always doing something in a way that is designed to be revealed to scientists thinking in a scientific way. God might (and probably usually does) have other purposes.
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God did not specially act if science provides natural (or scientific) explanations that seem ‘sufficient’ to explain a miracle. God might have acted in a way that is hidden from scientific inquiry. For example, God might have acted supernaturally to give us a religious experience of seeing his providential work.
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God used a miracle to communicate to me, so he is using that miracle to communicate to you. There is an relational difference between our personal experience with a miracle, and a the secondhand report of that miracle. God communicates differently in our personal experience of a miracle, and the testimony of that miracle to others.
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If I have solid grounding to believe a miracle, you also have solid grounding to believe said miracle.* There is an epistemological difference between our personal experience with a miracle, and a the secondhand report of that miracle. Even if we both come to believe a miracle took place, our strength of grounding is different.
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If I have good grounding for believing a miracle, science must be able to demonstrate it, perhaps be showing natural laws insufficient. For all the reasons stated above, a public inquiry by others (no matter what rules are used) would not usually be expected to agree that a miracle took place. Even if natural law was violated, evidence might usually be ephemeral. The miracle might alternate natural explanations.
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We can clearly discern miracles entirely independent of special revelation in any form. There is a collaboration between natural and special revelation that brings us confidence in perceiving a miracle. A strange storm might draw our interest, the light show might be bizarre, but in we could still be considering it a hoax or magic trick, or an unknown law. Something happens when the miracle is connect to special revelation that brings confidence to both. They are mutually reinforcing, such that we might doubt how clearly we could even perceive miracles independent of revelation.
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It is possible to scientifically demonstrate God’s action (or the “insufficiency of nature”). That may or may not be true, depending on the rules of science. The rules as we inherit them, however, seem to preclude this. Even if the rules were changed, our instinct that science (even in revised form) can clearly demonstrate God’s action or miracles might be misguided.
So those are some of the key fallacies I’m thinking. I’ll write more in a moment, exploring these fallacies are avoided in the confidence we have in the Resurrection, and how these fallacies seem to plague discourse on science and theology.
First, to answer a few questions…
Not in a way that would help with divine action.
We can only get at it indirectly, by analogy to our own sense of agency. Even then, it is very difficult to discern intentions of another person by merely looking at their actions. This is particularly true for us, because we have long range goals and purposes.
In a theological context, God has agency, but He goes about things in a manner very different than us. One of @jack.collins good points is that the inner mechanisms of God providence are not usually known. We can’t presume that studying the mechanisms of the world, therefore, that God’s providential governance would be make mathematically apparent.
God is so very different than is. He has a mind, but it is not like our mind. There is no way to know when the analogy breaks down, except to be certain that it certainly does. With things like Molinism and providence over lots in play, it is not clear at all that God’s agency can be detected by any sort of quantitative mathematical means.
First though…
Yes. This abounds in science. We can only explain things partially. So eventually we get to a point where the explanation extends outside our scope and we loose interest.
Take the comet whose impact killed the dinosaurs. How do we explain why it came precisely then at that moment in our history? Without that comet, the “humans,” that we all know and love as ourselves, might never have come into being. It is certainly a rare anomaly to the the natural order that might very well be explained entirely by natural law. It also might be a providential event. It also might have been guided by God’s action. Perhaps God ensured the creation of that comet “somehow” to clear the board for the rise of mammals, and then the rise of us.
Biological evolution is full of unexplained contingencies like this. That is why Gould says that if we were to “rewind the tape”, evolution would produce totally different things. This is seen as an anti-God statement because it is an appeal to randomness. It can just as easily be taken as an appeal to the insufficiency of our knowledge of nature (including both natural law and initial conditions) to explain what we see.
As @jongarvey and have discussed at length in relation to information theory, we have no obvious way to distinguish between: randomness, providential choice, and unknown law.
So that is the PARADOX…we understand a great deal through science, but we also do not understand very much at all. This paradox is important take hold of, and might help with this:
I would suggest we can, but in a paradoxical way. @Philosurfer