Getting Stoned

The Paradox of the Stone

The paradox, if successful, shows that it is not possible for there to be a being that can perform any task.  Since omnipotence is supposed to entail that there is no task that cannot be performed, it follows that the paradox, if successful, demonstrates that there is no omnipotent being—indeed that there cannot be an omnipotent being.

Already we can see that there is some confusion.  There are plenty of ‘tasks’ that no being can perform for the simple reason that there are plenty of ‘tasks’ that, upon analysis turn out to be impossible tasks.

Impossible Tasks Simpliciter: A task T is an impossible task simpliciter iff (if, and only if) T is either logically or metaphysically impossible.

Examples: making it the case that 2+2 = 5; making a square-circle, making something both red and non-colored; making something both completely red and completely blue; making it the case that water is not identical with H2O (assuming that water = H2O); making it the case that some contingent proposition is necessary; making it the case that some necessary proposition is contingent

Impossible tasks simpliciter are tasks that it is not logically or metaphysically possible to perform and hence no being, not even an omnipotent one can perform such a task.  Hence, we need to clarify what the paradox is supposed to show.  If it is supposed to show that there is some task T such that an omnipotent being cannot perform T, then the paradox is uninteresting, because we already know that there is some T such that an omnipotent being cannot perform T.

Note that to say that there is some T such that an omnipotent being cannot perform T is not yet a problem for the possibility of omnipotence.  At a first approximation, a being is omnipotent only if there is no possible task that the being cannot perform.  But not being able to perform a task that is not possible to perform is no defect or lack of power.


Savage worries (or at least suggests) that not being able to perform self-contradictory tasks may be a limitation of power.

Reply:  this objection is not a serious problem.  First note the following:
1. Either an omnipotent can perform contradictory tasks or it cannot.
2. If it can, and if it is contradictory to suppose that an omnipotent being cannot create a stone that it cannot lift, then such a being can perform this contradictory task.
3. If it cannot, then we argue that the inability to perform contradictory tasks is no limitation of power. 
3a. A contradictory task is a task that is logically impossible to perform.
3b. A logically impossible task is a task that is not possible to perform in any possible world. 
3c. There is no such thing as an impossible world.
3d. Hence, there is no world where a logically impossible task can be performed.
3e. If there is no world where a logically impossible task can be performed, then there is no world where an omnipotent being cannot perform some task that can be performed in that world.
3f. Hence, if x is omnipotent, then there is no world where there is some task that x cannot perform.
3g. But if there is no task that x cannot perform, then there is no limitation to x’s power.
3h. Hence, not being able to perform contradictory tasks is no limitation to an omnipotent beings power.

                  Here is another way to the same conclusion:
Perhaps contradictions are really incoherent or meaningless.  If that is right, then not being able to perform meaningless or nonsensical tasks is no limitation on power.  To think otherwise is to think that not being able to perform such tasks as: making a woobly woley weabley; making a kjshgkjsh; etc. is a limitation of power.  But the above tasks are not even tasks.  They are incoherent strings of letters or incoherent strings of meaningless sounds. 

Argument B
1. Either x can create a stone that x cannot lift or x cannot create a stone that x cannot lift

2. If x can create a stone that x cannot lift, then necessarily there is at least one task that x cannot perform

3. If x cannot create a stone that x cannot lift, then necessarily there is at least one task that x cannot perform

4. Hence, there is at least one task that x cannot perform

5. If x is an omnipotent being, then x can perform any task

6. Hence, x is not omnipotent

Problem
Since I think it is obvious that not being able to perform contradictory tasks is not a limitation of power, I think a premise must be added.

We need 4 to be changed to 4*: Hence there is at least one possible task that x cannot perform.

Savage allows for the above modification.  Let’s make it throughout the argument and see what happens.

Argument C (inclusion of possible task)
1. Either x can create a stone that x cannot lift or x cannot create a stone that x cannot lift

2. If x can create a stone that x cannot lift, then necessarily there is at least one possible task that x cannot perform

3. If x cannot create a stone that x cannot lift, then necessarily there is at least one possible task that x cannot perform

4. Hence, there is at least one possible task that x cannot perform

5. If x is an omnipotent being, then x can perform any possible task

6. Hence, x is not omnipotent


Problem
Consider 2.  We know that 2 is possible for some beings.  I can create a stone (or something) that I cannot lift.  Hence, there is a possible task that I cannot perform.  Hence, I am not omnipotent.

Consider 3: There are some possible tasks that I can perform that you cannot.  You cannot truthfully assert that you are the only son of Charles and Ida.  You cannot truthfully assert that you are identical to me.  But I can truthfully assert both things. 

Application: God cannot truthfully assert either thing as well.  Furthermore, God cannot cease to exist, if He exists.  God cannot sin.  God cannot ask for forgiveness.  God cannot begin to exist.  But I and you can perform these tasks.

Hence, there are possible tasks such that only some being can perform them.  There are possible tasks that God cannot perform because performing them is contradictory upon analysis. 

Consider God cannot cease to exist: Suppose God exists.  If God exists, then God is eternal (or is in time but has no beginning and no end) is conceptually true.  Hence, God can cease to exist means that the being that cannot cease to exist can cease to exist.  But that is contradictory.

So, we need to amend Argument C in some way because we know that there are tasks that I can perform that God cannot but which imply no limitation on God’s part because such tasks—the tasks that I can perform that God cannot—are contradictory. 

The best or most economical way to do this is to replace x in Argument C with God.  But that just brings us right back to Mavrodes’ argument.  

Savage’s Solution
X cannot create a stone that x cannot lift does not entail that there is a task which x cannot perform.

1. [x cannot create a stone that x cannot lift] means [if x can create a stone, then x can lift it.] 
2. But [if x can create a stone, then x can lift it], does not imply any limitation of x’s power. 
3. Hence, [x cannot create a stone that x cannot lift] does not imply any limitation of x’s power.
  

Meaning of statements in C
1. There is a y such that y is a stone and x can create y and it is not the case that x can lift y or it is not the case that there is a y such that y is a stone and x can create y and it is not the case that x can lift y

2. If there is a y such that y is a stone and x can create y and it is not the case that x can lift y, then there is a y such that y is a stone and it is not the case that x can lift y.

3. It is not the case that [if there is a y such that y is a stone and x can create y and it is not the case that x can lift y, then there is a y such that y is a stone and it is not the case that x can create y.]

Second Disjunct in 1:
It is not the case that there is a y such that y is a stone and x can create y and it is not the case that x can lift y

Becomes

For all y, it is not the case that [(y is a stone and x can create y) and (it is not the case that x can lift y)]

Becomes

For all y, it is not the case that (y is a stone and x can create y) or (x can lift y)

Becomes

For all y, if y is a stone and x can create y, then x can lift y.



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