CRAIG'S CASE IS DEAD ON ARRIVAL
Before I evaluate the sub-argument for premise (5c) in Craig's core argument, I would like to reiterate my evaluation of the last two inferences in Craig's core argument:
5c. The best explanation for Craig's three key established historical facts concerning Jesus' final fate is the resurrection hypothesis (i.e., God raised Jesus from the dead).
THEREFORE:
8. The best explanation of the established historical facts that are relevant to Jesus' final fate is the resurrection hypothesis (i.e., God raised Jesus from the dead).
THEREFORE:
9. It is more likely than not that God raised Jesus from the dead.
The inference from premise (5c) to premise (8) is weak and dubious because we have no good reason to believe that Craig's selection of his three key established historical facts constitutes a good and representative sample of the general collection of established historical facts that are relevant to Jesus' final fate. Furthermore, in Part 5, I provided a good reason to believe that Craig's selection of three established historical facts was significantly influenced by Confirmation Bias.
This is a serious problem with the inference from premise (5c) to premise (8) that is sufficient to sink Craig's core argument, and to make his case for the resurrection of Jesus Dead on Arrival.
However, there is also a serious problem with the inference from premise (8) to the conclusion (9). In Part 6, I showed that premise (8) does not logically imply the conclusion (9) and that premise (8) also falls short of providing significant inductive confirmation of conclusion (9). This final inference is thus also weak and dubious, providing another sufficient reason to reject Craig's core argument, and another good reason to conclude that his case for the resurrection of Jesus is Dead on Arrival.
Therefore, even if Craig had provided a strong and solid argument for premise (5c), the two weak and dubious inferences at the end of his argument make it a bad argument and cause his case for the resurrection to fail.
CRAIG'S SUB-ARGUMENT FOR PREMISE (5c)
Here is the sub-argument for premise (5c):
3b. IF IT IS NOT THE CASE THAT the resurrection hypothesis (i.e. God raised Jesus from the dead) has been shown to be more implausible than the alternative naturalistic explanations for Craig's three key established historical facts concerning Jesus' final fate, THEN the best explanation for Craig's three key established historical facts concerning Jesus' final fate is the resurrection hypothesis (i.e., God raised Jesus from the dead).
4b. IT IS NOT THE CASE THAT the resurrection hypothesis (i.e. God raised Jesus from the dead) has been shown to be more implausible than the alternative naturalistic explanations for Craig's three key established historical facts concerning Jesus' final fate.
THEREFORE:
5c. The best explanation for Craig's three key established historical facts concerning Jesus' final fate is the resurrection hypothesis (i.e., God raised Jesus from the dead).
The inference here is a modus ponens, so the inference in this sub-argument is a valid deductive inference. Thus, the logic of this sub-argument is fine. If there is a problem with this sub-argument for (5c), it would be a problem with the truth of one or both premises.
INITIAL EVALUATION OF PREMISE (3b)
Craig provides a sub-argument in support of premise (3b), so we need to consider that argument before we form a final evaluation of premise (3b). However, at this point my initial evaluation is that (3b) is FALSE. If I am correct on this point, then that would make this sub-argument an unsound argument for premise (5c), and would give us a third good reason to reject Craig's core argument, and to reject his case for the resurrection of Jesus.
Premise (3b) is a conditional statement. Thus, it asserts that the antecedent of that statement (i.e., IT IS NOT THE CASE THAT the resurrection hypothesis has been shown to be more implausible than the alternative naturalistic explanations for Craig's three key established historical facts concerning Jesus' final fate.) logically implies the consequent of that statement (i.e., The best explanation for Craig's three key established historical facts concerning Jesus' final fate is the resurrection hypothesis.) But it seems clear that the antecedent of (3b) does NOT logically imply the consequent of (3b).
The problem is that the antecedent statement only claims that the resurrection hypothesis is not more implausible than the alternative hypotheses. That does NOT imply that it is more plausible than the alternative hypotheses. But an explanation is "the best explanation" only if it is the most plausible explanation of the available alternatives.
Suppose that the Resurrection Hypothesis and the skeptical alternatives that Craig evaluates all have the same probability:
- There is a 16% chance that the Resurrection Hypothesis is true.
- There is a 16% chance that the Conspiracy Hypothesis is true.
- There is a 16% chance that the Apparent Death Hypothesis is true.
- There is a 16% chance that the Wrong Tomb Hypothesis is true.
- There is a 16% chance that the Displaced Body Hypothesis is true.
- There is a 16% chance that the Hallucination Hypothesis is true.
- There is a 4% chance that some other hypothesis is true.
Craig assumes that there is a correlation between the relative plausability of alternative explanations and the relative probability of those alternative explanations. Given the above scenario where the Resurrection Hypothesis has the same probability as each of the various skeptical hypotheses, we may infer that they have the same relative plausibility.
Thus, if Craig's methodology for determining the relative plausibility of alternative hypotheses leads us to a correct evaluation of the relative plausibility of these hypotheses, then using his methodology would lead us to the conclusion that NONE of these hypotheses would be more plausible than the other alternative hypotheses.
In this scenario, the antecedent of premise (3b) would be true, but the consequent would be false. Although none of the other hypotheses would, in this scenario, be more plausible than the Resurrection Hypothesis, it is also the case that the Resurrection Hypothesis would not be more plausible than any of the skeptical hypotheses. In this scenario, the Resurrection Hypothesis would NOT be "the best explanation" of the relevant facts.
Therefore, the antecedent of (3b) can be true and yet the consequent of (3b) could be false. That means that the conditional statement asserted by premise (3b) is false.
Furthermore, in the above scenario, the chance that the Resurrection Hypothesis is true is 16%, which is far smaller than what the conclusion of Craig's core argument asserts. According to the conclusion (9), the chance that the Resurrection Hypothesis is true is greater than 50%.
Finally, given the above scenario, the chance that one or the other of the five skeptical hypotheses considered by Craig is true is 80% (5 skeptical hypotheses x 16% each = 80%), compared to the small 16% chance that the Resurrection Hypothesis is true. So, in this scenario, it seems much more reasonable to believe that one or the other of the five skeptical hypotheses is true than to believe that the Resurrection Hypothesis is true.
CONCLUSION
Because Craig has provided a sub-argument in support of premise (3b), we should leave open the possibility that my initial evaluation of this premise is incorrect, at least until we consider the sub-argument for (3b). However, if Craig's sub-argument fails to give us a good reason to believe that (3b) is true, then we ought to conclude that premise (3b) is false, based on the above line of reasoning.

