Two Types of Weak Arguments for Theism: "God of the Gaps" vs. "Weak Naturalistic Explanations"

1. God of the Gaps Arguments

On my old team blog (Secular Outpost, which was migrated from Patheos and renamed as Secular Frontier), I proposed the following schema for God of the Gaps Arguments (hereafter, "Gap Arguments").

(1) There is some puzzling phenomenon P which science cannot at present explain.

(2) Theism does explain P.

Therefore:

(3) P is more likely on the assumption that God exists than on the assumption God does not exist.

Possible values for P may certainly include, but are not limited to, the origin of the universe, the life-permitting conditions of the universe, the origin of life itself (i.e., not evolution), the origin of consciousness, near-death experiences, and so forth. What is important to note here is that merely referring to alleged "hard" cases for naturalism is not a sufficient condition to make a theistic argument a Gap Argument. Rather, the following are necessary and sufficient conditions for a theistic argument to qualify as a Gap Argument: (a) the argument must refer to scientific ignorance; and (b) the argument must not include a premise about current knowledge (scientific or otherwise) which allegedly favors theism over naturalism. To see this, consider two versions of an argument from consciousness for theism.

Version 1: The Argument from Consciousness (Gap Version)

(1) Science cannot explain consciousness.
(2) Theism does explain consciousness.
Therefore:
(3) Consciousness is more likely on the assumption that God exists than on the assumption God does not exist. 

Version 2: The Argument from Consciousness (Non-Gap Version) 

(1) E ("Human consciousness exists") is known to be true, i.e., Pr(E) is close to 1.
(2) Source physicalism is not hopelessly intrinsically much more probable than theism, i.e., Pr(|N|) is not much greater than Pr(|T|).
(3) Human consciousness is antecedently more probable on the assumption that source physicalism is true than on the assumption that theism is true i.e., Pr(E | T & B) =1 > Pr(E | N & B).
Therefore:
(4) Other evidence held equal, N is probably false, i.e., Pr(N | B & E) < 1/2.

In version 2, premise (3) would then be supported by one or more arguments based on what we do know, rather than appealing to scientific ignorance.

2. Weak Naturalistic Explanations Arguments 

Weak Naturalism Explanation Arguments (hereafter, "Weak Explanation Arguments") are related to Gap Arguments, but represent a distinct type of argument. While the exact details differ, they have the following basic form.

(1) The evidence (E) regarding some known topic T is known to be true.

(2) Naturalistic explanations 1...n are weak explanations because they are ad hoc, have weak explanatory power, or both.
(3) Theism has great explanatory power. 

Therefore:

(4) Theism is true. 

Possible values for T may certainly include, but are not limited to, the origin of the universe, the life-permitting conditions of the universe, the origin of life itself (i.e., not evolution), the origin of consciousness, near-death experiences, the historicity of Jesus' resurrection, and so forth. What is important to note here is that merely referring to alleged "weak" naturalistic explanations is not a sufficient condition to make a theistic argument a Weak Explanation Argument. Rather, the following are necessary and sufficient conditions for a theistic argument to qualify as a Weak Explanation Argument: (a) the argument must refer to the weakness of naturalistic explanations; and (b) the argument must not include a premise about the (alleged) strength of the theistic explanation. To see this, consider two versions of an argument for the historicity of the Resurrection.

Again, let's compare and contrast two versions of an argument for the historicity of the Resurrection. 

Version 1: The Argument for the Resurrection (Weak Explanation Version)

(1) The evidence (E) relevant to the alleged Resurrection of Jesus is known to be true.
(2) Each of the traditional naturalistic explanations 1...n for E are weak explanations because they are ad hoc, have weak explanatory power, or both.
(3) The Resurrection theory is a strong explanation of the evidence.
Therefore:
(4) [probable] Jesus rose from the dead.

Version 2: The Argument for the Resurrection (Non-Weak Explanation Version)

(1) The evidence (E) relevant to the alleged Resurrection of Jesus is known to be true.
(2) Each of the traditional naturalistic explanations 1...n for E are weak explanations because they are ad hoc, have weak explanatory power, or both.
(3) The Resurrection theory is a strong explanation of the evidence because it is neither ad hoc nor has weak explanatory power.
Therefore:
(4) [probable] Jesus rose from the dead.

In version 1, the argument assesses traditional naturalistic explanations by considering their background probability and explanatory power, but does not consider the background probability of the Resurrection theory. In contrast, version 2 considers background probability and explanatory power of all explanations. N.B. I think even version 2 fails, but version 2 is better than version 1. Why does version 2 fail? I'll save that for another time.