My kneejerk reaction is to agree with everything you've said.
However, the cold, analytical side of me just isn't convinced. When the success or failure of prayer is dependent on the whim of God, there can be no proof.
Though I'd argue that one of the things in the "generic theism" we're assuming here are the notions that God is good and that God is
capable of answering prayers. I think that the idea of a god who grants prayers for larger tomatoes but not the prayer for help for an abused child does speak to the truth of those initial assumptions about the god in question.
OK, mball, MSizer, I'm going to try to explain this again.
By way of example, "Did God cure Mary's cancer" is not the topic. The topic is "if God did cure Mary's cancer, would science be able to tell?"
That depends what you mean. You're right that science hasn't definitively concluded that no gods exist, but I don't think that science is
silent on the issue of god.
Another way of asking your question would be "is science able to tell what cures people's cancer?" The answer to this is something like "yes, but not with absolute certainty."
We do have statistical tests (for instance:
Student's t-test - Wikipedia, the free encyclopedia) that can tell us whether an effect and a hypothesized cause are linked to a significant degree. If some other cause is generally at work besides the one we assume, then this fact shows up in the results. If God were really going around healing people's cancer, then the correlation between, say,
chemotherapy and cancer remission would be a lot worse than the theory would predict.
Pick any issue you want, not just cancer remission. If we can come up with a list of factors that explain the results we see to a very, very high degree in a demonstrable way, then this also
excludes to a very, very high degree the possibility that some other, unknown factor (e.g. God) is at play with any significance.
This doesn't imply absolute certainty, but it does imply more certainty than if we had no information at all.
Now... this still allows the possibility that this unknown factor is at work to an
insignificant degree, but IMO, an insignificant God is not the "generic theistic" God.