How To Destroy Natural Theology in One Fell Swoop
Believers will fallaciously use these augments to their own particular God hypothesis by additionally arguing that in a world inhabited by their God it makes their own miracle claims more probable than not. So in this way Christians argue for a natural theology based on them just as other theists do. But there is no reasonable way to tell in advance if these arguments point to their particular God. So believers cannot use them to establish their respective natural theologies either. For how do they know which God these arguments lead them to in advance of looking at the evidence for their particular religion? They simply cannot reasonably assume these arguments lead them to their particular God. Therefore they cannot approach their own miracle claims as having any more probability to them than other miracle claims, even granting that the arguments work.
In other words, these arguments to God's existence simply do not grant any believer any relevant background knowledge, or “priors,” prior to examining their own particular religious faith. They must still look at the raw uninterpreted data to determine if a miracle took place without using a potentially false presumption that their God performed the particular miracle under investigation. Hence this line of reasoning destroys natural theology in one fell swoop. Even if there is a God of some kind, believers still have no reason to think their particular God did the miracle under investigation. That is, even a world with a God in it does not make their own miracle claims any more probable than not after all. For if Allah exists then Jesus was not raised from the dead, and we all know that the Jews rejected the Christian claim that Yahweh raised him from the dead. And vice versa.
To Christians who respond that the arguments to God's existence open up the possibility of miracles, I simply ask them if they would ever seriously consider the Christian miracles if they were Muslims or Orthodox Jews? Theism does not entail that your particular miracles have any more probability to them than others. I suspect Muslims and Orthodox Jews, even as theists themselves, are no more open to your miracle claims than I am as a non-believer, so you shouldn't be either!
To read more of my criticisms of natural theology click here.
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Edit: You can read a further discussion of this argument right here, which is a response to Christian apologist Victor Reppert's response in the comments below.