Omnipotence and Failure
June 13, 2011 — 16:22

Author: Kenny Pearce  Category: Concept of God  Tags: , , , ,   Comments: 12

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 In an as-yet-unpublished paper, Alexander Pruss and I argue that this additional condition is perfect freedom of will.)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:

  1. If a being can fail, that being is not omnipotent.
  2. If a being cannot fail, that being is not act-omnipotent.
  3. Every being either can fail or cannot fail.
  4. Therefore,

  5. No being is both omnipotent and act-omnipotent.

more…

On Omnipotence
October 26, 2010 — 13:10

Author: Kenny Pearce  Category: Concept of God  Tags: , , , , ,   Comments: 27

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:

  1. 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.
  2. 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.
  3. 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).
  4. 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.]