This sounds like a false dilemma to me. Isn't it possible that God sometimes cures cancer, but doesn't choose to regrow limbs (or grow an extra limb, for that matter)?
Yes, it's a false dilemma. As I posted later, please don't be distracted by the soundbite quality of the question. The point is not about amputees
per se, it's that whenever there can be no doubt whether God answers a prayer or not, he never does. When one can confuse a normal event with an answered prayer, there's tons of examples of 'answered prayers'.
I will stipulate that regardless of the "no doubt" scenerio that anyone can think up, we can also make up some counter reason for why God would not answer any prayer in that instance. - "Oh, God doesn't answer prayers when there is an MRI machine being used, along with a xyz chemical protocol. he only answers if one of the two is being used."
The claim is not that we can prove, beyond all doubt, that no prayers are answered. The claim is that we can specify a large number of scenerios where we can reasonably show no prayers are answered. You can move the goal posts by just making up some reason for why a prayer is not answered in that instance, but that's not parsimonious, because the reasons are going to vary based on the scenerio. I.e., in scenerio A God doesn't answer because MRI machines are used, but in scenerio B it's because something else (he just doesn't want to regrow limbs). It's arbitrary, and
just so. So, occam's razor suggests the simpler answer - no prayers are being answered at all.
Also, there is less of a false dilemma in my statement than you might think. I stated "either God really hate amputees, or people are mistaken about God is answering prayers to cure cancer, etc." Just replace "hate" with "chooses not to heal", and I have covered your case.
Why would God choose not to heal an amputee? It makes no sense. Unless no prayers are being answered at all.