In this section we unpack the idea of the supernatural as a counterintuitive world that is not merely counterfactual in the sense of physically implausible or nonexistent. Rather, the supernatural literally lacks truth conditions. A counterintuitive thought or statement can take the surface form of a proposition (e.g., “Omnipotence [i.e., God] is insubstantial”), but the structure of human semantics is such that no specific meaning can be given to the expression and no specific inferences generated from it (or, equivalently, any and all meanings and inferences can be attached to the expression). The meanings and inferences associated with the subject (omnipotence = physical power) of a counterintuitive expression contradict those associated with the predicate (insubstantial = lack of physical substance), as in the expressions “the bachelor is married” or “the
deceased is alive.”
Now, I have no idea whatsoever who the people are who are supposed to be going around saying "Omnipotence is insubstantial" as part of their religious beliefs, but this is an odd sort of passage. "Omnipotence" owes its existence in religious discourse to its being primarily a theological term; that is, it's a technical term, and it does not and has never (as far as I can tell) been used in such a way that it would necessarily imply "physical power". And I don't even know why someone would use 'insubstantial' in this context.
Perhaps it's just a clumsy hypothetical example. But the above passage requires that these counterintuitive statements 1) be taken in a strictly literal sense; 2) imply contradiction. And both of these are surprisingly strong. Since figures of speech can have truth values and definite truth conditions, a statement that 'literally lacks truth conditions' in the sense given above can figuratively have them, e.g., "The bachelor is married to his work" and "The deceased is alive in our memories". Since "omnipotence is insubstantial" would have to be a technical proposition, it would probably be intended to be taken in a strictly literal way; but most of the cases Atran and Norenzayan seem to have in mind (ghosts, gods, goblins, and the like) would not obviously be described in terms that were expected by the describers to be taken in a strictly literal way.
As to implication, the possibility of implying a contradiction depends on the meaning of the terms of the original proposition; i.e., it is only in the sort of statement said above, taken as strictly literal, and interpreted in a clearly contradictory way, that this feature would hold. And in the paper, what plays the major role is not logical contradiction but violation of expectation, which is something very different, even if the expectation is a deep-seated one of an automatic 'intuitive ontology'. And yet, again, no real account seems to be taken in the paper of association, vagueness, and figurative discourse, although they presumably would be relevant. Again, it's perhaps just a clumsy (or excessively concise) discussion; but I'd have to see the analysis on which even talk about ghosts and goblins would actually turn out to be counterintuitive in the above sense. (The psychological effect ascribed to counterintuitive statements does not, as far as I can see, depend on their being counterintuitive in the above sense, but on their being surprising, violations of expectation, etc.; so it might well be that this analysis contributes little to the actual account. And that would be a good thing; people who cite Ayer for their view of religious statements are likely to have dubious views. And just briefly skimming what I can find on counterintuition on the net, it seems that treatment of counterintuitive statements in terms of, effectively, pseudo-propositions, is an unusual characterization.)
Nonetheless, it's an interesting paper, with lots of good stuff, and I'll have to place the book on my reading list. Hume would like it; and I'll have to post at some point on Hume's The Natural History of Religion (which is, in fact, cited in the paper).
