We are rationally justified, according to C. Behan McCullagh, to believe a given statement (the hypothesis) is true about a given event (observable data) if that statement meets the following conditions:
(1)The statement, together with other statements already held to be true, must imply yet other statements describing present, observable data. (We will henceforth call the first statement ‘the hypothesis’, and the statements describing observable data, ‘observation statements’.)
(2)The hypothesis must be of greater explanatory scope than any other incompatible hypothesis about the same subject; that is, it must imply a greater variety of observation statements.
(3)The hypothesis must be of greater explanatory power than any other incompatible hypothesis about the same subject; that is, it must make the observation statements it implies more probable than any other.
(4)The hypothesis must be more plausible than any other incompatible hypothesis about the same subject; that is, it must be implied to some degree by a greater variety of accepted truths than any other, and be implied more strongly than any other; and its probable negation must be implied by fewer beliefs, and implied less strongly than any other.
(5)The hypothesis must be less ad hoc than any other incompatible hypothesis about the same subject; that is, it must include fewer new suppositions about the past which are not already implied to some extent by existing beliefs.
(6)It must be disconfirmed by fewer accepted beliefs than any other incompatible hypothesis about the same subject; that is, when conjoined with accepted truths it must imply fewer observation statements and other statements which are believed to be false.
(7)It must exceed other incompatible hypotheses about the same subject by so much, in characteristics 2 to 6, that there is little chance of an incompatible hypothesis, after further investigation, soon exceeding it in these respects. ( McCullagh 1984: 19 emp. original)
“[I]f the scope and strength of an explanation are very great,” concluded McCullagh, “so that it explains a large number and variety of facts, many more than any competing explanation, then it is likely to be true.” (ibid, 26)
McCullagh & Resurrection of Jesus
Though the Christian hypothesis that God raised Jesus from the dead has a greater explanatory scope and power than its rivals given the observable historical data, McCullagh deemed resurrection hypothesis as less plausible and more ad hoc than its rivals(ibid 21). He argued that “The hypothesis that God exists and cared about Jesus is of questionable plausibility; the hypothesis that he wanted to raise Jesus from the dead and reveal him to the disciples and others is almost entirely ad hoc” (McCullagh 2012: 46).
Thus, though he believes in resurrection of Jesus, McCullagh finds it difficult to decide on the evidence whether it should be accepted or rejected as a best explanation.
Before I address the probability of resurrection of Jesus hypothesis relative to the background knowledge and specific data Pr(R/ B&D) and whether it is the best explanation of the data in a pool of competing rival hypotheses, it is important to bring up the main question that I attempt to answer: Can a Christian, with love, gentleness and respect, present a persuasive historical case to show that it is rationally justified to believe that Jesus rose again from the dead?
My inquiry is less ambitious. It seeks not to convince non-Christians that Jesus rose again leaving an empty tomb but to show that Christians’ belief in Jesus’ resurrection is rationally acceptable. If my task were of convincing non-Christians then McCullagh’s concerns would have had to be addressed. But since the hypothesis that God exists and care about Jesus is neither of questionable plausibility nor is it ad hoc to Christians then I will proceed with the sub-questions I set to answer (see Rationality of The Resurrection of Jesus).
McCullagh, C. Behan (1984) Justifying Historical Descriptions. Cambridge: Cambridge University Press.
__________________________ (2012) ‘The Resurrection of Jesus: Explanation or Interpretation?’ Southeastern Theological Review Vol.3 No. 1: 41-53
 McCullagh is aware of other conditions as simplicity and greater degree of falsifiability than any other, but find them unnnecessary (20)