If we have two valid arguments, each of which entails the conclusion that a particular monotheistic god exists, then we can form a disjunctive argument that also entails the same conclusion. More generally, if we have a large collection of valid arguments, each of which entails the conclusion that a particular monotheistic god exists, then we can form a multiply disjunctive argument that also entails that same conclusion. However, it should not be supposed that a ‘cumulative’ argument that is formed in this way is guaranteed to be a better argument than the individual arguments with which we began (even if we are properly entitled to the claim that the arguments with which we are working are all valid). For, on the one hand, if all of the arguments are defective on grounds other than those of validity — for example, because they have false premises, or because they are question-begging — then the cumulative argument will also be defective. But, on the other hand, if even one of the arguments with which we began is not defective on any other grounds, then it is a cogent argument for its conclusion, and the cumulative argument is plainly worse (since longer and more convoluted). So, at the very least, we have good reason to be suspicious of talk about a cumulative case for the claim that a given monotheistic god does — or does not — exist that is based upon a collection of (allegedly) valid arguments for the claim that the god in question does — or does not — exist. …

Talk about a cumulative case makes much more sense if we suppose that we are dealing with ‘probabilistic’ — or ‘inductive’, or ‘evidential’ — arguments, in which the premises provide ‘probabilistic’ — or ‘inductive’, or ‘evidential’ — support for their conclusions. … However, once we start talking about accumulating evidence in this sense, it seems to me that the only interesting question to consider is how a given proposition stands in the light of all of the relevant available evidence. That a given proposition is probable given a carefully selected part of the total relevant evidence is not an interesting result. But — at the very least — this makes it very hard to be sure that one has succeeded in setting out a good probabilistic argument for any hotly disputed conclusion.