Science without an uderlying ground for the cause-effect relationship? Without a justification for the assumption of the continuity of nature (i.e., repeatability)? (ha!)

Science can never be agnostic--it can only proceed by borrowing the capital of Christian theism.

Disagree.

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Causation and motion are the domain of physics (in the Aristotelian sense, certainly, as well as in the more modern sense) rather than metaphysics.

The scientific method is deeply dependent on our epistemology, to be certain, but metaphysics? I'd argue that is a different domain of knowledge.

Physics cannot proceed without metphysical assumptions.

There is no ground to assume the continuity of causation or motion such that we can make reliable predictions without taking for granted that things will be tomorrow as they have been through today. Even probability requires this assumption, which requires a certain metaphysic.

"There is no ground to assume the continuity of causation or motion...without taking for granted that things will be tomorrow as they have been today."

I'd contend that is an epistemological assertion, not a metaphysical one.

Our ability to do physics and metaphysics alike depends on our epistemology.

The Aristotelian distinction worth keeping in mind is physics is the study of that which is real and changes, while metaphysics is the study of that which is real and is unchanging.

With that distinction, it seems clear to me that, while our metaphysics can color our understanding of physics, our ability to study changing things does not wholly depend on whether we have a correct metaphysics.

Our epistemology, also, cannot but presuppose a certain metaphysic.

To channel Van Til, "the unbeliever can count, but he cannot account for counting." This applies to all scientific endeavor.

...and, our ability to do physics relies on an objectively real world and objectively real natural systems and processes--whose persistence itself relies on its Creator and his promise to keep it going that way (at least for a while longer).

Exactly! If we assume that we are just a chemical accident, why should we trust our senses or our logic or assume that we can know anything. If we assume that we are created in the image of God and that God designed everything that is, then it is an obvious conclusion to trust our senses and logic and that the universe works according to certain reliable, trustworthy, continual rules and can be known.