Thursday, June 7, 2018

The Paradox of the Stone


I am sick to death of people defining God's omnipotence by the capacity to do all that is logically possible. That is not a logically self-consistent idea. We can prove it right now.
  1. God is omnipotent (definition).
  2. Omnipotence is the capacity to perform any logically possible task (definition).
  3. Therefore, God has the capacity to perform any logically possible task (from 1, 2). 
  4. If I can imagine some logically possible world wherein some task is being performed, then that task is logically possible to perform (definition of a logically possible action/task).
  5. Given any finite rock, I can imagine a logically possible world wherein it is being lifted (definition of possible worlds---the proposition is self-consistent so it is necessarily possible to imagine).
  6. Therefore, it is logically possible to lift any finite rock (from 4,5). 
  7. Therefore, God can lift any finite rock (from 3,6).
  8. I can create a finite rock such that its own creator cannot lift it (observation---I can only lift so much weight).
  9. If I can create a finite rock such that its own creator cannot lift it, then it is logically possible to create a finite rock such that its own creator cannot lift it (modal axiom B---actual implies necessarily possible). 
  10. Therefore, God can create a finite rock such that its own creator cannot lift it (from 3,9).
  11. If a rock is created by God, then God is the creator of that rock (definition of "creator"). 
  12. If God can create a finite rock such that its own creator cannot lift it, then God can create a finite rock such that God cannot lift it (from 11).
  13. If God can create a finite rock such that God cannot lift it, then there exists a finite rock such that God cannot lift it (definition of create---to bring into existence; the rock does not have to be actual, either; I can simply imagine an element of that set, and the set is officially nonempty).
  14. If there exists a finite rock such that God cannot lift it, then God cannot lift any finite rock (from set theory---there exists an element of the set of finite rocks that is outside of the set of things that God can lift). 
  15. Contradiction with 6: (God can lift any finite rock) and (God cannot lift any finite rock).  

The logic has spoken, guys. Just give it up already and find another definition for omnipotence. I defy anyone to explain which premise they disagree with.


8 comments:

Unknown said...

I'm untrained in modal logic (more comfortable with first-order logic), but it seems to me that the argument, more formally, is that a logical god is that there exists fallacies in logic. Wouldn't this be circumvented if we supposed that God was both logical and sound? Considering specifically points seven and eight:

7. I can create a finite rock such that its own creator cannot lift it (observation---I can only lift so much weight).
8. If I can create a finite rock such that its own creator cannot lift it, then it is logically possible to create a finite rock such that its own creator cannot lift it (modal axiom B---actual implies necessarily possible).

The premises state that the god can lift a rock of mass [0, inf).

7 and 8 seem to imply that a creator can create finite rocks with mass (0, inf). It also implies that an individual i can lift rocks of mass [0, W_i], W_i being the maximum weight that i can lift. It seems conclude to state that there exists some W_g that the god cannot lift, which is weird since our hypothetical god can lift a rock so long as it has a finite mass that is a non-negative real number.

There's this weird line of reasoning that seems to state that creator-ness implies existence of some threshold unliftable weight W_g. I lack the sophistication to know what to do with it, but I think it's there.

James Alan said...

How do you deal with the problem that the definition of "lift" changes with scale? The argument is based on an incomplete understanding of physical law. At some point a finite stone will start to exert a non-negligible gravitational field. Eventually it becomes the planet that the other rocks are being lifted off of. If you continue further, the stone collapses and forms a black hole. At some point "lifting" itself becomes logically impossible, doesn't it?

Unknown said...

I mean, my opinion is that once physics kicks in, it's kind of hard to argue on the side of God. I think that you're absolutely right in your thinking.

Mostly, I found the argument weird from a set theory perspective: the premise seems to be that if there exists a rock in the set of all rocks, God can lift it, yet somehow we find a subset of rocks that God cannot lift, and we derive our contradiction from there.

Tyler Jones said...

As several other people have stated, the ability to actualize all possible worlds is a perfectly coherent, self-consistent definition for omnipotence.

Stephen Weigel said...

Hey man, I know I don't comment on a lot of these, but your videos are great. I made this silly meme of ya, so I hope you like it! XD
https://imgur.com/a/SaqBqR8

AnticitizenX said...

"As several other people have stated, the ability to actualize all possible worlds is a perfectly coherent, self-consistent definition for omnipotence."

Does that mean you admit Premise 2 is a bad definition or what? Just because you prefer some OTHER definition, that does not negate the fact that Premise 2 is a very common expression, nor does it negate the fact that many people publicly hold to it. So don't take it up with me. Take it up with THEM!

AnticitizenX said...

"Wouldn't this be circumvented if we supposed that God was both logical and sound?"

God is not an argument. You need an argument before you can talk about being "sound." God is a word. Words have definitions. Those definitions are either self-consistent and meaningful or they are not.

"It seems conclude to state that there exists some W_g that the god cannot lift, which is weird since our hypothetical god can lift a rock so long as it has a finite mass that is a non-negative real number."

That's why it's called a "contradiction," friend. The definition is NOT self-consistent.

AnticitizenX said...

"How do you deal with the problem that the definition of "lift" changes with scale?"

Two ways:

1) It's not about the physics of lifting. It's about the logical structure of the definition. I can do X, therefore X is logically possible, and therefore God can do it as well.

2) We don't have to lift rocks. We could invent any wacky scenario so long as it contains a self-referential negation. Try standing before a podium and stating truthfully the words "I am not God," or "There are no omnipotent beings." It's still a logical coherent task.