No more rocks for God please

[Alkatran]

Many times you will run into, or use, an argument similar to: "Could God create a rock so heavy even he could not lift it?" The argument is meant to show how omnipotence entails logical contradictions.

The problem with the argument is it muddles up your point by involving infinities. This gives a number of loop holes you can use to counter the statement. For example, in maths, we can ask "What is infinity minus infinity?" and get a variety of answers depending on the context (which is why we say it is an indeterminate form). As x tends to infinity x^2 - x tends to infinity, x - x^2 tends to negative infinity, x-x tends to 0, x-x+23 tends to 23, etc. There is no reason to involve unnecessary calculus in the discussion of God's existence!

If you're going to argue, you should make your arguments clear and to the point. Therefore I suggest using statements such as "Can God subtract exactly 4 from 5 and get 0?" instead of the rock one. It's much clearer what the problem you're pointing out is.

[SezMe]

You have to be kidding. You think fundies are going to be amenable to a mathematical argument? That they are willing to entertain arguments about infinities? It's much more likely that Haggard is not gay.

Period.

[David Swidler]

Could God make women understandable?

[slingblade]

Not to you.

[Alkatran]

You have to be kidding. You think fundies are going to be amenable to a mathematical argument? That they are willing to entertain arguments about infinities? It's much more likely that Haggard is not gay.

Period.

I was thinking more in line with a philosophy class, haha. Debating fundies is just a way to piss you and them off.

[fuelair]

I was thinking more in line with a philosophy class, haha. Debating fundies is just a way to piss you and them off.
As long as it helps give them an ulcer (I already know they're wrong so I don't worry I just irritate them.)

[Glen.Nogami]

You have to be kidding. You think fundies are going to be amenable to a mathematical argument? That they are willing to entertain arguments about infinities? It's much more likely that Haggard is not gay.

Period.

Didn't you hear? He went to Camp Heterosexuality. He's all better now.

[Orangutan]

Could God make you slap me?

(No) Result! "See your god can't even make his followers do something they don't want to."

(Yes) Result! Call the police and press assault charges.

<I'm being facetious by the way>

[Marquis de Carabas]

Could God create a rock so big Marion Barry couldn't smoke it?

[JoeTheJuggler]

What about the contradiction presented by divine omniscience and human free will?

[Marquis de Carabas]

What about the contradiction presented by divine omniscience and human free will?
Oh, please. Christian apologists long ago explained that there was no contradiction between the two. It's not their fault you're not impressed by shoddy logic.

[Mephisto]

Could God create a rock so big Marion Barry couldn't smoke it?

:)

[Darat]

...snip...

If you're going to argue, you should make your arguments clear and to the point. Therefore I suggest using statements such as "Can God subtract exactly 4 from 5 and get 0?" instead of the rock one. It's much clearer what the problem you're pointing out is.

I think the second one is a much weaker attempt at stating the problem - since there is no reason at all why you couldn't come up with some maths that can do that, it just wouldn't be our "common garden" variety of arithmetic. SO you'd have to include a definition of the maths you were using.

The rock is the best way to illustrate this "problem" - which has two simple solutions both of which are fine solutions depending on your faith.

[Darat]

Didn't you hear? He went to Camp Heterosexuality. He's all better now.

We all know he went camp - but what's that got to do with heterosexuality?

[Glen.Nogami]

We all know he went camp - but what's that got to do with heterosexuality?

:D

[Alkatran]

I think the second one is a much weaker attempt at stating the problem - since there is no reason at all why you couldn't come up with some maths that can do that, it just wouldn't be our "common garden" variety of arithmetic. SO you'd have to include a definition of the maths you were using.

The rock is the best way to illustrate this "problem" - which has two simple solutions both of which are fine solutions depending on your faith.

It's extremely clear that subtraction over the integers is meant. If they insist, then specifically state you're using Z.

[Solus]

Here's another one: could god create a curved perfectly straight line?

[Dr Adequate]

Omnipotence Paradox

Not a good argument.

[Solitaire]

Could god make a paper so big that he could not cut it with a pair of scissors?

[Myriad]

I prefer...

Can God learn anything?

Respectfully,
Myriad

[Jimbo07]

Omnipotence Paradox

Not a good argument.

Dr. A, I've always liked the "Omnipotence is Logically Meaningless," argument.

Any God worth his salt (that is, that I would consent to worshipping) must be able to actualize rational absurdities in the blink of an eye... otherwise, he is merely very powerful. ;)

[Alkatran]

Omnipotence Paradox

Not a good argument.

Clearest article I've ever read on it.

Is God more powerful than a Turing machine?

[LawnOven]

All 'god' would have to do in order to make a rock, blah blah blah, would be: make a rock, and then totally turn down his god muscles so he was really weak and could not lift said rock. So I guess the answer is 'yes'.

[Kopji]

it's a mystery

[Mosquito]

Here's another one: could god create a curved perfectly straight line?

I think this was done in "Flatterland", so it is not necessarily a good argument.

It was a question of perspective, I think.


Mosquito - Flatter than thou

[Jekyll]

Clearest article I've ever read on it.

Is God more powerful than a Turing machine?

Yes, he can have an oracle if he wants.

[Darat]

It's extremely clear that subtraction over the integers is meant. If they insist, then specifically state you're using Z.

But you wanted something better. To make your replacement question work you need to include, at a minimum, the above explanation in your question so you end up with in my opinion something more-complicated and less clear which would therefore be less effective then the "Has God got big rocks?"" question. The reason we still have that question in that format is that it's simple and easy to understand and therefore a very good clear example of the paradox problem.

If you want to replace it your replacement has to be, again in my opinion, an even clearer example.

[Darat]

Clearest article I've ever read on it....snip...

It needed a bit of editing ;)

[RandFan]

Aquinus sufficently dealth with this. Can god make a square circle? No, because once a squre becomes a circle it ceases to be a square. Can god make it so that X = ~X? No.

I used to posit the too big rock for god "paradox" until I read Aquinus. Dumb argument. Really dumb argument. Assumes that the abstract concept of omnipotence includes the ability to be not omnipotent.

Now, I differ from Aquinus in that I think the notion of omnipotence to be untenible. A better thought experiment to consider the problems inherent in the idea of omnipotence is to interject omnicence and simply ask if god can change his mind?

Does god know what he will do tomorrow? Yes.
Can he write it down? Yes.
Having written it down can he change his mind and do something else? No.
God is powerless to change.

[RandFan]

Omnipotence Paradox

Not a good argument.:mad: Sure, beat everyone else to the punch. Killjoy.

[Paul C. Anagnostopoulos]

"Can God subtract exactly 4 from 5 and get 0?"
But this immediately brings up the question whether god can do something illogical. We can eliminate this issue if we simply say no, he cannot. Does that then make him not omnipotent?

Edited to add: Oh, according to the Wiki article, modern-day omnipotence cannot defy logic. How convenient. :D

~~ Paul

[Paul C. Anagnostopoulos]

Here's another one: could god create a curved perfectly straight line?
I think the answer here is no, simply by definition.

~~ Paul

[Darat]

I think the answer here is no, simply by definition.

~~ Paul

No just another variant of the paradox.

Whenever this paradox comes up I find myself in a minority here because I can absolutely and 100% accept a believer in a omnipotent God answer to these types of paradoxes i.e. a simple "yes" and that ends the discussion.

To me this is why it is a rather pointless (albeit you can have some fun playing with it) argument because it all depends on how you define "God".

Aquinus like so many others when faced with a tough question about his God just redefined his God so the problem disappeared, you do see signs that he realised he had in fact diminished his God, so like many he tried to put the fault onto humans. In the end his solution was just handwaving and a "Don't ask silly questions" - which is how the "modern theoligians" the SkepticWiki article mentions also try to deal with the problem.

(By the way I am of course being rather disparaging of Aquinus as he was a most remarkable and obviously incredibly intelligent bloke.)

[Megalodon]

The answer to all those questions is "Yes, and also vice versa"

It's a meaningless question, much like "does the friction of Santa's sledge contribute to Global Warming?". But nevertheless, any fundie with a minimal of brain power (rare but existent) will tear it to pieces.

[Bob Klase]

Omnipotence Paradox


As long as we're talking about the christian god, this argument against the omnipotence paradox either proves that the bible is wrong, or it raises the omnipotence paradox against itself:

Most theologians who argue that God (as defined in the Christian religion) is omnipotent mean that he can bring about any state of affairs that are possible".


Matthew 19:26:

With men it is impossible; but to God all things are possible.


So, Matthew 19:26 is wrong. Or all things, including logical contradictions, are possible. (Or logical contradictions are not a part of "all things").

[drkitten]

So, Matthew 19:26 is wrong. Or all things, including logical contradictions, are possible. (Or logical contradictions are not a part of "all things").

Or you're not interpreting Matthew correctly. Recognizing that contradictions are not "things" is a good start.

C.S. Lewis had a good formulation for this. He pointed out (paraphrased), that a meaningless sentence will not gain meaning simply because someone chooses to prepend the phrase "God can." And it is meaningless to speak of creating a rock so heavy an omnipotent being cannot lift it.

[Paul C. Anagnostopoulos]

No just another variant of the paradox.
I'm not convinced. The definitions of "straight line" and "curved" are contradictory. God cannot create such a thing simply because there is no such thing by definition. Once he curves the line, it is no longer a straight line by definition.

But can't we come up with a task for god that isn't ruled out by definition, yet is mathematically or logically impossible?

~~ Paul

[Darat]

I'm not convinced. The definitions of "straight line" and "curved" are contradictory. God cannot create such a thing simply because there is no such thing by definition. Once he curves the line, it is no longer a straight line by definition.



But the answer is easy - "My God can create a curved perfectly straight line." - discussion is over.

You may say "but what about logic" and "but it's a contradiction" and I will answer "for man perhaps not for my God". Discussion over.



But can't we come up with a task for god that isn't ruled out by definition, yet is mathematically or logically impossible?

~~ Paul

But someone with faith would just respond with "Yes God can do that." whatever that "that" is.

This is why I said at the start the "Has God got big rocks" is the best example and why it has the stood the test of time.

There are only two possible (possible of course to us mere humans...) answers "yes" or "no".

If you say "no" then you have to (to keep the faith) come up with an answer like Aquinas did to explain why the limitation you are placing on your omnipotent God isn't really a limitation. In Aquinas case it was to assert the question itself as meaningless.

If you say "yes" then it's again just a matter of keeping the faith. In other words it is not an argument against their God since their God is not limited or constrained as humans are.

[Beerina]

Clearest article I've ever read on it.

Is God more powerful than a Turing machine?

The Church-Turing Thesis proposes there is a legitimate concept of "most powerful computational model that can perform, at most, a finite number of calculations in a finite period of time", and that the Turing machines (and every equivalent computational model like modern logic, math, most computer programming languages, etc.) are that model. This is not proven, which is why it's "only" a thesis.

When Penrose suggested (incorrectly IMHO) that there were tiling problems that humans could solve that a Turing machine could not, this was a fascinating development, because it suggested there either was something infinite in the "computation" the human mind performed, or it was still finite, but there was (at least one) layer greater than a Turing machine that was still finite in nature, and hence the Church-Turing thesis was false. Either development would have been fascinating. So, too, would "quantum computing", should that pan out, because that suggests one could do an infininte number of computations in a finite period of time, solving huge almost-prime factorizations, etc. This in turn would demonstrate the universe itself was on a higher level than a finite computational device.

But it's still all speculation at this time. The Turing machine is still "it" as far as anyone has demonstrated.

[Beerina]

So, Matthew 19:26 is wrong. Or all things, including logical contradictions, are possible. (Or logical contradictions are not a part of "all things").

Yes, but is this in the rock category, or in the camel-thru-the-eye-of-a-needle category of impossible?

Philosophers argue that "all things" means all things logically conceivable. When you ask about a square circle, that is actually a meaningless statement, and that you are not actually conceiving anything, even in the abstract.

[The Kilted Yaksman]

But can't we come up with a task for god that isn't ruled out by definition, yet is mathematically or logically impossible?

~~ Paul
Whose definition? Man's, or your hypothetical god's? If he created everything can't he simply change the rules in the middle of the game? Or does he have to "shake the Etch-a-Sketch" and start over with a new reality in which the definitions are different?

(Not a b'liever, just "asking questions")

[drkitten]

I'm not convinced. The definitions of "straight line" and "curved" are contradictory. God cannot create such a thing simply because there is no such thing by definition. Once he curves the line, it is no longer a straight line by definition.

But can't we come up with a task for god that isn't ruled out by definition, yet is mathematically or logically impossible?

In simplest terms, no. The reason being, the only reason that something is mathematically or logically impossible is because it conradicts other aspects of the discourse. But those other aspects are definitions.

[Mashuna]

Can God create custard so yellow that a wooden filing cabinet marries a goat?

If not, then it's proof that I shouldn't drink at lunchtime on a Friday.

[Paul C. Anagnostopoulos]

But the answer is easy - "My God can create a curved perfectly straight line." - discussion is over.

You may say "but what about logic" and "but it's a contradiction" and I will answer "for man perhaps not for my God". Discussion over.
Ah, I see. I didn't get that you were giving the fundies' argumentation.

If God can defy logic as he see fit, I'd better not hear any arguments about God that employ logic.

~~ Paul

[Paul C. Anagnostopoulos]

In simplest terms, no. The reason being, the only reason that something is mathematically or logically impossible is because it conradicts other aspects of the discourse. But those other aspects are definitions.
Really? There is no distinction between a definition and a theorem?

Consider a stone. God cannot create a stone that "falls upward," because this is impossible by definition. But can God hold a stone in midair, let it go, and have the stone move away from the Earth?

~~ Paul

[drkitten]

Really? There is no distinction between a definition and a theorem?

Not in a practical sense. A theorem is simply a consequence of a (set of) definition(s).

[Paul C. Anagnostopoulos]

Here, let me try another one:

God cannot create a set B containing only elements of set A but not being a subset A, by definition.

But can God create a set that is not a subset of itself?

~~ Paul

[Paul C. Anagnostopoulos]

Not in a practical sense. A theorem is simply a consequence of a (set of) definition(s).
Hmm. We must be approaching this from different directions. My example seems to make a distinction between definitions and theorems:

Consider a stone. God cannot create a stone that "falls upward," because this is impossible by definition. But can God hold a stone in midair, let it go, and have the stone move away from the Earth?

Perhaps this is just trivial, because "falls upward" can easily be restated in the more interesting way?

~~ Paul

[drkitten]

Here, let me try another one:

God cannot create a set B containing only elements of set A but not being a subset A, by definition.

But can God create a set that is not a subset of itself?

I'm sorry.... this may simply be a bad case of the Fridays, but I don't understand what the sentence even means.

Nor, for that matter, do I care. Because you're obviously trying to create a distinction that doesn't matter.

Here's a simple example. We can define a triangle as a three-sided polygon.

Can God create a four-sided triangle? Of course, not -- by definition.

Actually, this isn't true. You'd need some additional machinery to formalize the fact that a polygon cannot have X and Y sides (X and Y distinct) simultaneously.

Can God create a four-angled triangle? Of course, not -- also by definition.

And, of course, this isn't true either, without a separate proof that a polygon of X sides contains X angles as well.

So in neither case is the proof strictly encompassed in the definition. But no mathematician would bat an eye, precisely because there is almost never a single definition, and one can so easily restate a definition to encompass its consequences.... "A triangle is a three-sided and three-angled polygon."

If all you're suggesting is that mathematicians get sloppy with their use of "by definition" -- sure, everyone knows that. "By definition" really means "by definitions and their consequences that are too well-known for me to justify developing a separate proof for."

[drkitten]

Hmm. We must be approaching this from different directions. My example seems to make a distinction between definitions and theorems:

Consider a stone. God cannot create a stone that "falls upward," because this is impossible by definition. But can God hold a stone in midair, let it go, and have the stone move away from the Earth?

Perhaps this is just trivial, because "falls upward" can easily be restated in the more interesting way?

Yup. "Just trivial" is exactly the phrase I would use.

[Paul C. Anagnostopoulos]

Nor, for that matter, do I care. Because you're obviously trying to create a distinction that doesn't matter.
Excuse me, but no I'm not. I'm trying to understand this.

When I ask whether God can create a stone that falls upward, it seems to me that is trivially false by definition, because "falls" means "moves downward toward the center of the Earth" and "upward" contradicts that. Do you think that such a question should be implicitly converted into a more complex question that avoids the obvious contradiction of definitions? I realize "falls upward" sounds silly, but certainly I can construct another question that doesn't sound as silly but is just a contradiction of definitions, too, such as "Can God create two parallel lines that intersect?"

So is there nothing that is more than just a contradiction of definitions? What if it involves an axiom? Can God create two equal sets that don't have the same elements? Is this so close to a definitional contradiction that there is really no distinction?

What if it involves a law of nature? Surely contradicting a law of nature is not the same as contradicting a definition.

~~ Paul

[drkitten]

So is there nothing that is more than just a contradiction of definitions? What if it involves an axiom?

Axioms are in practice definitions. They're just how one defines verbs and adjectives instead of nouns. They define the terms of mathematical discourse.

Can God create two equal sets that don't have the same elements? Is this so close to a definitional contradiction that there is really no distinction?

Er, yes. Or if you think there's a significant distinction there to be drawn, then please draw it.


What if it involves a law of nature? Surely contradicting a law of nature is not the same as contradicting a definition.

Of course not. But I'm not sure that "laws of nature" as they are generally regarded have been thought to be a limitation on God's power. A God who can cause a (human) virgin to conceive, part the waters of the Red Sea, and cause the Sun to stop for an hour over the plains of Jericho is obviously not limited by what we think of as the "laws of nature." A God who can make it rain for forty days continuously and cause water to build up globally to a depth of several thousand meters is obviously not restricted by the conservation of mass-energy.

Now, there are some "laws of nature" that have been suggested to be actual limitations on God's power -- God cannot, for example "create two hills without a valley between." But if you look more closely, that's not a "law of nature" violation, but again a mathematical and definitional impossibility. That doesn't violate a law of nature, but a law of geometry as expressed in the terminology of nature.

[Paul C. Anagnostopoulos]

Axioms are in practice definitions. They're just how one defines verbs and adjectives instead of nouns. They define the terms of mathematical discourse.
Okay, that makes sense.


Er, yes. Or if you think there's a significant distinction there to be drawn, then please draw it.
I'm just wondering whether mathematicians draw it. It certainly seems to be the case that mathematicians draw a distinction between "impossible by definition" and "logically impossible." But perhaps not if it just a question of definition vs. axiom.

Perhaps I'm confusing myself with mathematical questions, as opposed to physical questions.


A God who can make it rain for forty days continuously and cause water to build up globally to a depth of several thousand meters is obviously not restricted by the conservation of mass-energy.
Apparently, but it still makes me ponder whether omnipotence should imply the ability to violate the laws of nature. And certainly this is not just a question of definitions.

~~ Paul

[drkitten]

I'm just wondering whether mathematicians draw it. It certainly seems to be the case that mathematicians draw a distinction between "impossible by definition" and "logically impossible."

Yes, but the distinction unfortunately tends to be whether the path to get back to the definitions is of publishable length or difficulty.


Apparently, but it still makes me ponder whether omnipotence should imply the ability to violate the laws of nature. And certainly this is not just a question of definitions.

Well, I believe that God is routinely cited as having the ability to violate the laws of nature. So the question does not arise in practice.

[Paul C. Anagnostopoulos]

Yes, but the distinction unfortunately tends to be whether the path to get back to the definitions is of publishable length or difficulty.
Aha! That 'splains it.

~~ Paul

[RandFan]

No just another variant of the paradox. Could an omnipotend god make X =~ X? There's nothing to see here. As soon as you turn a square into a circle it stops being a square. There is no such thing as a squared circle and abstractly declaring that god can do it won't solve the logical imposibility.

[Darat]

Could an omnipotend god make X =~ X? There's nothing to see here. As soon as you turn a square into a circle it stops being a square. There is no such thing as a squared circle and abstractly declaring that god can do it won't solve the logical imposibility.

But you know the answer to that one -

Blind faith hand waving answer - "God can do anything; that we conceive it as being a 'logical impossibility' is a limitation of humankind not of God."

Or the Aquinas hand waving answer - "Your question doesn't make any sense - just because you can ask questions that do not make sense is not a limitation of God but a failing of humanity."

Whichever answer a believer (in the type of God this discussion tends to be about i.e. a "Christian" concept of God) chooses makes no difference - when you boil it down it's all mankind's fault.... Christian theology in a nutshell! :duck:

[RandFan]

But you know the answer to that one -

Blind faith hand waving answer - "God can do anything; that we conceive it as being a 'logical impossibility' is a limitation of humankind not of God."

Or the Aquinas hand waving answer - "Your question doesn't make any sense - just because you can ask questions that do not make sense is not a limitation of God but a failing of humanity."

Whichever answer a believer (in the type of God this discussion tends to be about i.e. a "Christian" concept of God) chooses makes no difference - when you boil it down it's all mankind's fault.... Christian theology in a nutshell! :duck: I think most educated Christians would respond simply that the question is non-sensical.

The bottom line is, the fact that the argument proves nothing is favorable to a believer so there is no need for the believer to blame humans for our inability to grasp how X=~X. I'm not saying that there does not exist Christians who hold such a view and your point is fair that in the end it doesn't matter to a believer because all roads lead to Rome (in the end god is omnipotent). So I will grant you that.