 Of course, even if the two premises of Le Poidevin’s argument are true, it doesn’t follow that the argument is a good one. For the argument also contains two inferences (from steps  1  and  2  to  step 3  and from step 3 to  step 4),  neither of which is obviously correct. Concerning the first inference, suppose, for example, that even though there is no firm basis upon which to judge which of theism and atheism is intrinsically more probable (that is, Le Poidevin’s first premise is true), there is firm basis upon which to judge that theism is not many times more probable intrinsically than some specific version of atheism, say, reductive physicalism. And suppose that, even though there is no firm basis upon which to judge which of theism and atheism is favored by the total evidence (that is, Le Poidevin’s second premise is true), there is firm basis upon which to judge that the total evidence very strongly favors reductive physicalism over theism (in the sense that it is antecedently very many times more probable given reductive physicalism than it is given theism). Then it follows that both of Le Poidevin’s premises are true and yet (3) is false: there is a firm basis (that includes the odds version of Bayes’ theorem applied to theism and reductive physicalism instead of to theism and atheism) to judge that reductive physicalism is more probable or even many times more probable than theism and hence that theism is probably or even very probably false. Arguably, no similar strategy could be used to show that theism is probably true in spite of Le Poidevin’s premises both being true. So it may be that Le Poidevin’s premises, if adequately supported, establish that theistic gnosticism is false (that is, that either agnosticism or atheistic gnosticism is true) even if they don’t establish that agnosticism is true.