Some Further Points about the Stone Paradox
Once More on the Stone Paradox (This Time with Symbols)
As I've noted before, there's no actual logical paradox in the stone paradox even on the crudest account of omnipotence, unless you make very specific assumptions about what kind of modality does the best work of formalizing abilities, which is a controvertible subject. It is simply not self-evident what the best overall modal account of abilities is. The John case in the first post seems to me not to be parallel at all, because it doesn't have the structure of ability and inability; it would only be parallel if John's inability were itself something directly in John's power to have or not. (Which is why the paralysis-and-antidote scenario mentioned in my post linked to above is a more reasonable structural parallel.) Talk of abilities is counterfactual through and through, but it is a mistake to assume that all counterfactuals are on a level when we are talking about abilities. I am able to type the next letter and I am able to buy milk at the supermarket, but they are not all equally near to the actual situation, where I am far from the supermarket and have my hands on the keyboard. And there are times (like the paralysis-and-antidote case) where the distance and proximity of the counterfactual is crucial. And this is one of them: this difference between remote and proximate counterfactuals is why even a crude account of omnipotence can both say that God is omnipotent and that God is unable to lift a particular stone without contradiction, just as I can perfectly well say both that I am able to buy milk at the supermarket (by going there) and that I am unable to buy milk at the supermarket (because I am at home typing up a post on the stone paradox) without any contradiction whatsoever. As I noted in my previous post on the stone paradox, the only difference in the omnipotence case is that it requires an infinite regress of abilities (which some Cartesians, for instance, have actually argued for). This makes it so there is never any such thing as an ability, simpliciter, which is where the apparent contradiction in the stone paradox comes from; all abilities are relative to whether or not other abilities are being exercised.
But I was interested in the challenge that Burgis poses in the second post. Burgis identifies two possible responses to the stone paradox. In the first, which he calls the Standard Defense, one simply says that omnipotence is the ability to do anything that does not involve a contradiction, rather than just the ability to do anything. The second is what he calls the Mere Possibility Defense ("that God could create such a stone, and if He did so, He wouldn't be omnipotent any more, but so long as he happens to contingently continue to choose not to do so, He's still omnipotent") which is more or less a version of the one I was talking about above. He rejects the Standard Defense (SD) because of its epicycles and the Mere Possibility Defense (MPD), which he rejects for reasons he gives in the first post ("If Object X contingently doesn't happen to exist, that's quite irrelevant to whether Agent Y could perform Action Z to Object X. If Object X exists, that's epistemically relevant--we get to test whether Agent Y has the ability to perform Action Z--but the non-existence of the test doesn't normally entail anything one way or the other about the power.") He then delivers a challenge:
Either (a) explain the relevant disanalogy between the move made by theists who employ the SD and put a logical-consistency epicycle in their new, watered-down definition of omnipotence, and other cases where a general principle generates contradictions, and we all think that the rational response is to reject the general principle rather than stick in a consistency epicycle, (b) provide an argument for theism so devestatingly convincing that it justifies the SD as the overall best explanation even in the face of the ad hocness, (c) explain the relevant disanalogy between the contingent absence of hundred-floor buildings in the John-ruled world (which seems irrelevant to the limits on John's stair-climbing powers) and the contingent absence of an unliftable stone in the God-ruled universe (which, according to partisans of the MPD, is relevant to the limits of God's powers), or (d) provide an alternative way out, thus showing that (a)-(c) aren't jointly exhaustive of the options for defenders of the doctrine of divine omnipotence who want their beliefs to be closed under some sort of (non-paraconsistent) logical consequence relation.
(a), it turns out, is extraordinarily easy to do. Throughout Burgis assumes that the SD is in fact an ad hoc response to problems like the Stone Paradox. It's very clear historically that this is not so. The actual history is somewhat messy, but its basic structure is easy to grasp. The original, and still basic, account of omnipotence is that of power over everything (sovereignty, as it is sometimes called), particularly as required by the more fundamental doctrines of creation and providence. This is true of Christian, Jewish, and Muslim accounts of omnipotence. The doctrine of omnipotence comes from somewhere; people weren't just sitting around one day and suddenly thought that it would be cool to call God omnipotent. There were reasons, and the basic understanding of omnipotence has to take into account those reasons.
The tendency to phrase omnipotence in terms of power to do anything comes later, and was heavily argued over. The 'Standard Defense' wasn't formulated as a defense; it was formulated as a qualification on the sense in which one could take the "power over everything" account of omnipotence and the "power to do everything" account of omnipotence to be effectively equivalent. The latter has advantages: it's actually easier to apply directly to a lot of things and has a more obvious modal structure (it's easier to describe directly in terms of possibilities). But it raised some logical puzzles, of which the stone paradox is a distant descendant. Since these logical puzzles don't seem to exist in the "power over everything" account of omnipotence, which is anchored by the doctrine of creation on one side and doctrine of providence on the other, this means that the "power to do everything" account has to be qualified in order to remain equivalent to the more fundamental account. This is where the qualification comes in. It is indeed an epicycle; it's not an epicycle on the doctrine of omnipotence but an epicycle on one particular formulation of it, which is required to keep it equivalent to a more fundamental formulation. And thus it's not watering down the doctrine of omnipotence, which precedes it by a long shot, and it's not an ad hoc defense of the doctrine. Rather, people who try to ignore the qualification in talking about omnipotence are arbitrarily dropping one of the qualifications that had been introduced as a precondition for making the formulation equivalent to the sort of thing people meant by 'omnipotence' at all. This is clearly disanalogous to the case of taking a general principle and watering it down.
(Medieval discussions of omnipotence are full of these sorts of discussions, by the way. Another major question, for example, was whether formulations of the doctrine of omnipotence in terms of infinite power were actually equivalent to more basic formulations.)
The problem, in other words, arises with the mistake, common among analytic philosophers today, of thinking that arguments and claims just spring out of nowhere and therefore don't need anything other than themselves in order to be understood properly. In actual fact, the interpretation of arguments and claims must be constrained by the reasons for putting them forward in the first place.
Given that (a) can easily be met, (b) can be ignored. But (b) is in any case badly formulated; it's irrelevant whether it is convincing or not (and unclear what it means -- to whom? how would we test whether it was convincing? would it be a purely psychological test). What matters is whether there is good reason to think that there is a God and good reason to think that God is omnipotent, where good reason just means the sort of thing that gives reason to think that at least tentatively accepting the claim will be fruitful for inquiry. If there are good reasons for both, then there would be good reasons for epicycles. This is what epicycles are: they move the discussion forward, not backwards, and the epicycles on the Ptolemaic system improved it rather than deteriorating it. The myth that epicycles are a bad thing is a rather pernicious one; adding epicycles is always the rational response unless there is already in hand a better account without epicycles. And in the broad sense that's being used here, no field of intellectual inquiry can do without them. When we teach students that a method for division works except where it introduces division by zero, we aren't being irrational; it is the most rational thing to do, because we have good reason for the method and good reason for thinking that we need the qualification.
(c) is effectively done by the infinite regress of abilities response; and the response for (d) is already implicit in the points I made with regard to (a). So I don't see that there's any real problem with meeting any of these challenges, for either SD or MPD, except for (b), which is badly formulated anyway (and is otiose if (a) can be met). Possibly I'm missing something, though.