Many people believe that there is: 1) no greatest number, 2) no greatest possible world, and 3) a greatest being (person, agent). The reason many people believe 1 and 2 is that there seems to be procedures to take a number (or world) and return a larger (or better) one. For any number (cardinal), take the powerset to get a larger number. For any world, stick some happy people in a far off corner to get a better world. (Of course, there is far from universal agreement on this second point.) The question arises: Is there any way to take a being, and return a better one?
One way is to try and link beings with the worlds they create. The idea would be that a being who creates a surpassable world is a surpassable being. This line of thought gives rise to a whole body of literature, some quite recent. Going in a different direction, here is another way that any being might be surpassable. Let us imagine that some virtues, e.g. courage, are traits wherein one wants to be at the mean that lies between extremes. We might imagine that ‘courage-level’ runs along a continuum from 0 (totally cowardly) to 1 (totally rash). Then, speaking loosely, somewhere in the middle is best. But, is it clear that any specific point is best? That is, what if the function, F, from courage-level (which runs from 0 to 1) to the value or goodness of the being goes as follows: F(x) = x for x in [0, 0.5] and F(x) = 1.01 – x for x in (0.5, 1]. Then there is no greatest being, as for any being, there is a better one. There is no greatest being, as beings get better as they approach 0.5 from the right on courage-level.
If there is an optimal point on a trait, call that trait ‘closed’. If there is not an optimal point on a trait (for any level a being takes on the trait, there is a better level), as in the courage example above, call that trait ‘open’. The question is, are all traits are closed? Or, what is the best argument to the conclusion that all traits are closed? In the absence of an argument regarding open and closed traits, the principle of indifference might suggest that courage is open with 50% probability and closed with 50% probability.
(One way to respond is to argue along these lines: certain traits/properties are fundamental (e.g., power, knowledge, freedom, goodness), these traits take maximal levels (individually and together), all other traits follow logically from these, and thus all traits take optimal levels and so are closed. Is there a relatively simple and convincing argument along these lines? Also, are there other ways to argue that all traits are closed? In particular, and thinking of approaching the question from a non-theistic angle, am I missing some sort of simple argument or reason as to why all traits are closed?)
The famous Stone Paradox asks, ‘can an omnipotent being make a stone so heavy he can’t lift it?’ A simpler question, and one which I think makes the issues clearer, is, ‘can an omnipotent being fail?’
If a being can fail, then there is something that being doesn’t have the power to do, namely, whatever it is it can fail to do. If a being can’t fail, then there is something it doesn’t have the power to do, namely, to fail.
Now, we sometimes have chancy powers/abilities, as, for instance, in J. L. Austin’s famous example, the power to sink a putt from a certain distance. The possibility of failure is compatible with this sort of power. However, surely when we ascribe omnipotence to God, we don’t mean to say that he has chancy powers of this sort; we mean that he has infallible powers. In fact, I would claim, in ascribing omnipotence to God, part of what we mean is precisely that he can’t fail to do anything he tries to do. (This isn’t all we mean; to avoid some counterexamples, we need some conditions about what he can try to do. In an as-yet-unpublished paper, Alexander Pruss and I argue that this additional condition is perfect freedom of will.)
Call the following property ‘act-omnipotence’:
S is act-omnipotent =df. S can perform a token of any logically possible action-type
We can turn the above reasoning into an argument that act-omnipotence is inconsistent with omnipotence:
- If a being can fail, that being is not omnipotent.
- If a being cannot fail, that being is not act-omnipotent.
- Every being either can fail or cannot fail.
- No being is both omnipotent and act-omnipotent.
In my last post, I discussed Sobel’s proposal that, since the Stone Paradox shows essential omnipotence to be incoherent, the traditional God, since he would have his properties essentially, would have essential ONSLIP, or only necessarily self-limited power, but that this would not amount to omnipotence. Here I want to propose an alternative account of omnipotence, an attribute worthy of that name and which would be had essentially. First, however, we must distinguish power from freedom. To be omnipotent is to be all powerful. God is also supposed to be free in his exercise of power, and this creates a number of problems, some of which were discussed on my personal blog at the beginning of this series. I take it that the relevant type of power, the kind that agents have, is simply the ability to do what one wants, or to bring about one’s ends, whereas freedom is something more complicated. This immediately suggests the following definition of omnipotence:
S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p.
To prevent any ambiguities, here it is in symbols:
S is omnipotent =df. □∀p[(p is a proposition & S wills that p) -> p]
So an omnipotent being’s will would always be fulfilled as a matter of logical necessity. Now that’s power! Furthermore, omnipotence, being a modal property, entails essential omnipotence.
Here are some interesting features/consequences of this definition:
- The definition follows Alexander Pruss‘s suggestion on the earlier post that omnipotence be construed as having to do with the range of states of affairs God can bring about.
- If the value of S substituted into the sentence (e.g. ‘God’) is a rigid designator, and the necessity is interpreted as being of the ‘broadly logical’ type, then omnipotence, being a modal property, entails essential omnipotence.
- The conditional in the definition is intended to be a material conditional. As a result, if there are any necessarily false propositions (and there are), then the definition entails, by the Distribution Axiom of modal logic, that, necessarily, those propositions are not willed by an omnipotent being. That is, □~(2+2=5) and God’s omnipotence (as defined) jointly entail □~(God wills that 2+2=5).
- The definition entails that an omnipotent being’s higher-order volitions (if any) are satisfied, which is thought by some (e.g. Frankfurt) to be important for freedom. That is, if God wills to will what is good, then (necessarily) he wills what is good.
But you might be worried about something (at least if you are not a Humean about causation and/or abilities): what if S wills only things that come about because S’s will is conformed to reality, rather than reality being conformed to S’s will? It is not clear that this is coherent: some philosophers think that the difference between belief and propositional desire/volition is the ‘direction of fit’ – that is, we try to conform our beliefs to the world, but we try to conform the world to our desires. If a being’s (so-called) ‘desires’ were actually conformed to the world, rather than vice versa, they might turn out not to be desires at all, but rather beliefs. But in case this response doesn’t work, we can easily modify the formula:
S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p because S wills it
Now, cashing out the ‘because’ might be tough, but if we are non-Humean enough to care about the problem, then presumably we are non-Humean enough to think that some sense can be given to ‘because’ here.
I cannot see that omnipotence, defined this way, generates any paradoxes by itself. Certainly it is unaffected by Sobel’s objections. It may, however, have complicated interactions with other divine attributes, especially freedom (there are things that God can’t will). The current definition looks like it plays nice with compatibilism, but it is not so clear that it plays nice with libertarianism.
[cross-posted at blog.kennypearce.net.]
Suppose Open Theism (OT) holds. There is a possible world where a demon is better off doxastically than God in respect of future free actions of creatures. On some views of inductive knowledge, there is a possible world where a demon is better off epistemically than God in respect of future free actions of creatures. Hence OT is false. This may be all old hat. But, hey, it's fun to reinvent the wheel–the thrill of discovery, of seeing it roll, etc. Now I need to argue for my above claims.