The effectiveness of mathematics does imply at least the existence of a halting oracle, so there is something that transcends the physical world, since the laws of physics are Turing reducible.

No it doesn’t.

Plantinga’s argument is better than Craig’s

I’m sorry but I cannot make sense of that.

Mathematics *can’t not* be effective at describing a world in which anything at all exists. How are we to make sense of the idea that mathematics could be ineffective? Try to magine for a moment a world where there are entities that differ in magnitude or quantity. How can mathematics NOT be effective at making sense of these relations?

You are inventing a “problem” that logically cannot exist. Mathematics does not need to be created or designed to be “effective” at describing relations of quantity or magnitude. **It can’t conceivably be otherwise.** It must necessarily be the case that mathematics must be effective at describing such relations.

If there is some possible world in which you cannot count, or enumerate entities, then that world is empty, because in so far as something, anything at all, were to exist in that world, you *could* count it. And if you can count it, then mathematics obtains.

To speak of a world in which there exist any sort of entity that cannot be counted, and which does not stand in some sort of relation of quantity or magnitude to something else, is logically nonsensical.

Or how about the concept of entities that stand in relations that are not of magnitude or quantity? If that can be the case, then mathematics would not be effective at describing their relations. But that is not because mathematics was flawed and would have to be “re-designed”, it would be because the relations between the entities *are not* of magnitude or quantity.