The Stone--and other Paradoxes of Infinity

[Antone]

Premise: God can do anything
Question: Can God do A.

Perhaps you misunderstand what a paradox is. It's not about whether god can do something.
It is about whether he can do it without invoking a necessary contradiction.

Your continuous repetitition about God being able to do anything is totally meaningless distraction that does nothing but clutter up this threat.

[Antone]

I'm not convinced there's a god.

Once again, the question of whether there is a God is totally irrelevant. The question of whether or not God is omnipotent is irrelevant. Whether there are observers is irrelevant. The question is, when given the premises, we can create a non-paradoxical way to get an answer. I think I've clearly shown a way that this can be done with logical consistency. Discussion that addresses this--rather than other irrelevant concerns is appreciated.

[altonhare]

Premise: God can do anything
Question: Can God do A.

Perhaps you misunderstand what a paradox is. It's not about whether god can do something.
It is about whether he can do it without invoking a necessary contradiction.

Your continuous repetitition about God being able to do anything is totally meaningless distraction that does nothing but clutter up this threat.

Define God, then, for the purposes of your discussion so we can then talk about what he does. Originally you defined him as omnipotent, which to me means able to do anything. Apparently omnipotent means, to you, that he can do some things and can't do others. So:

God: Can do some things and not others

Question: Can God...

Answer: Maybe, he can do some things but not others.

Done.

But you'll want to proceed with specific examples:

Question: Can God poop?

Answer: Maybe, he can do some things but not others.

Question: Can God make 'an' infinite stone?

Answer: Maybe, he can do some things but not others.

Question: Can God move?

Answer: Maybe, he can do some things but not others.

Question: Can God grow?

Answer: Maybe, he can do some things but not others.

Question: Can God smite ye evil doers?

Answer: Maybe, he can do some things but not others.

Question: Can God restore a woman's virginity?

Answer Maybe, he can do some things but not others.

Question: Can God take a woman's virginity?

Answer: No way that's evil! But.. I guess maybe, he can do some things but not others.

Peter how did you get out again!? *Runs* Oh well, he's no real harm to anyone, as long as they close their ears.

Where does God lie on your omnipotence meter Antone? Does it go from 1 to 10 or 0 to 10? Does it even go to 10? I think you were born in the wrong century, you and Peter could have spent your lives trying to decide where God lies on your omnipotence meter.

[Antone]

Apparently omnipotent means, to you, that he can do some things and can't do others.

Again, you seem to demonstrate your inability to understand what a paradox is. It isn't about what god can or can't do. It's about whether a very specific premise that takes the general form "God can do something that apparently he can't do." is paradoxical or not.

Your singleminded reply that [God can do anything--so he can do anything] addresses neither the paradox itself, nor my argument that the paradox can be resolved. And despite your several posts, I can't think of a single meaningful thing you've said except [god can do anything-so he can do anything]. Which by the way, I understood the first time you said it. For that matter, I understood the principle a priori, or before you even said it. It isn't a very difficult concept to grasp, even if it fails to address the issue.

[altonhare]

Again, you seem to demonstrate your inability to understand what a paradox is. It isn't about what god can or can't do. It's about whether a very specific premise that takes the general form "God can do something that apparently he can't do." is paradoxical or not.

Now you've stuck in "apparently" i.e. you've invoked an observer.

Observer A: God does not appear strong enough to lift this stone. Therefore I conclude that he cannot lift the stone.

God: lifts the stone

Observer A: Guess I was wrong, he was strong enough.

Or

Observer A: God appears strong enough to lift this stone. Therefore I conclude that, if he tries to lift the stone, he will fail.

God: Tries to lift the stone and fails

Observer A: Guess I was right.

Or

Observer A: God does not appear strong enough to lift this stone.

God: Lifts the stone

Observer A: Quit showing off God.

Or

Observer A: God appears strong enough to lift this stone.

God: Tries to lift it and fails

Observer A: Laughs at God's misfortune

Peter: Is lifting the stone Good or Evil?

[altonhare]

Again, you seem to demonstrate your inability to understand what a paradox is.

Is that like orthodocs and metadocs but spelled differently?

para-docs.jpg (1.47 KiB) Viewed 8511 times

ortho-docs.jpg (1.5 KiB) Viewed 8514 times

Or are you talking about concepts, not objects?

Orthodox: A set of objects Z specifying objects fulfilling criterion Z1.

Metadox: A set of objects Z specifying objects each fulfilling one criterion in the set of criteria ZX.

Paradox: A set of objects Z specifying objects each fulfilling any number of criteria in the set of criteria ZX, where the criteria in ZX may not be conceptual opposites (Z1 cannot state that the object it refers to is relatively long and Z2 state that the object it refers to is relatively short, for instance).

Lunidox (meaninglessdox): A set of objects Z containing objects each fulfilling any number of criteria in the set of criteria ZX, where the criteria in ZX may be conceptual opposites.

[altonhare]

So you understand that, if we define God can do anything, then he can do anything a priori.

Then you ask if God can do something without invoking a necessary contradiction. You are now not analyzing anything about God, but rather analyzing your own logic for internal consistency. If it is not internally consistent it is meaningless.

So all you're doing is defining the terms in your claim to see if they contradict each other. If they do, you need to define them another way until the statement is consistent (makes sense).

You state that God can create an incessantly growing stone, and can always lift this stone because it is always finite. You *define* the stone as always finite. You then say he cannot lift the infinite stone that he is in the process of creating but never actually creates. Let's analyze the possible contradictions:

A) God cannot create an infinitely large stone, contradicting the definition that God is omnipotent

B) A is wrong, God can (and does) create an infinitely large stone. However you state that God cannot lift an infinitely large stone, contradicting the definition that God is omnipotent

C) B is wrong. God can (and does) lift an infinitely large stone in accordance with his omnipotence. But does "infinite" contradict "stone"? If the stone is defined as infinite then the question is meaningless "Can God lift an infinite infinite?" On the other hand, is the definition of stone consistent with the description of it as "infinite", i.e. is "infinite stone" a self-contradiction?

D) An infinite stone is not a self-contradiction, whatever Antone's definition of "stone" is, does not demand that the stone have a border (that they are finite). God can (and does) create and lift the infinitely large stone, in accordance with his omnipotence.

A and B involve discarding the original premise/hypothesis (God is omnipotent) and thus throwing out the question altogether. C and D demand we define object in such a way that it may be infinite (not have a border).

Therefore if Antone insists the question is not meaningless (not A and B) then he will have to define stone such that it may be described as infinite without contradiction. So far he has defined "infinite stone" as an "incessantly growing stone" which is, at any time, finite. This is an explicit contradiction (trying to describe the stone as both infinite and finite). God can lift an incessantly growing stone, but asking if God can lift an "infinite stone" is meaningless and has nothing to do with God, but rather everything to do with the definition of "infinite stone".

My conclusion is that, if we define God as able to do anything, he can indeed do anything. Including picking up an incessantly growing stone.

I conclude that saying otherwise means you contradicted your own definition of God or your own definition of stone, which is a problem with your logic, not a problem with God's omnipotence.

Am I pointing out the logical flaws clearly enough now Antone?

[mague]

We have to do a bit bean counting. Omnipotence is comming from potencial. Omni potencial is not all-mighty, just all-possible.

Define the difference between "all mighty" and "all possible".

The omnipotent god has the potencial to do anything, but not neccessary the might to do it.

Sorry about my poor language skills. But i do hope you can sense this thin layer between all-mighty and all-possible.

You go see two doctors. The one tells you: I will heal you. The other one tells you: I ll try all possible to heal you.
Which one you like more ? The all-mighty or the all-possible ?

[altonhare]

We have to do a bit bean counting. Omnipotence is comming from potencial. Omni potencial is not all-mighty, just all-possible.

Define the difference between "all mighty" and "all possible".

The omnipotent god has the potencial to do anything, but not neccessary the might to do it.

Sorry about my poor language skills. But i do hope you can sense this thin layer between all-mighty and all-possible.

You go see two doctors. The one tells you: I will heal you. The other one tells you: I ll try all possible to heal you.
Which one you like more ? The all-mighty or the all-possible ?

As far as I can see, the difference between "almighty" and "all possible", is simply the fact that we cannot have God create an object that is a self-contradiction. Like, we can't define a circle as an object with 1 edge and a square as an object with 4 edges, then ask God to create a square circle. The problem is not with God, the problem is with our own logic. God is still omnipotent, by definition, it's our own idiocy if we try to talk about self-contradictions .

[Antone]

opps

[Antone]

Let's analyze the possible contradictions:

A) God cannot create an infinitely large stone, contradicting the definition that God is omnipotent.

Wrong.

God can (and is) engaged in the process of creating an infinitely large stone, as long as he continues to increase the size of the stone from time to time. Since the God that we have defined is immortal, he can do this if he so chooses. What God cannot do is finish creating the infinite stone. This does not not imply a limit to God's omnipotence--any more than the fact that God God cannot create a [blue shirt] that is [white]. This is a matter of the definition of [blue] and [white] not God's omnipotence. God could change the [definition of blue] so that what was [blue] in now [white]. But he would not have made [what is now blue] into [something that is now white].

The infinite argument is exactly the same. To be infinite, something must [go on forever] or [be without end]. To complete something we must [bring its creation to an end]. These are incompatible definitions. So it is impossible for God to [complete] that which must be [incomplete by definition].

Once again, as we have defined God, he most certainly can create the infinite stone, future tense. This is possible because God lives forever, so he will always be around to make the stone bigger. He cannot lift the [infinite stone] because such a thing cannot exist in the present or past tense. And it is not possible to [HAVE lifted] something in the future.

An interesting side question might be: God can promise to lift the infinite stone in the future, but since the stone will never be completed, is this promise a lie? I

B) A is wrong, God can (and does) create an infinitely large stone. However you state that God cannot lift an infinitely large stone, contradicting the definition that God is omnipotent

Wrong.

God can engage in the process of creating the infinite stone. Be he never does actually create it. God cannot lift what cannot exist. God can lift nothing... but that is only because we are giving [nothing] two distinctly different meanings. It is possible for God to [lift nothing]--meaning that he [doesn't lift anything]. But it is not possible for God to lift [nothing]--meaning that he would [lift that something which is nothing]. There is no [something that is nothing]. And even an omnipotent God cannot lift what cannot exist. He can raise his arms in a lifting motion, that this could be called [lifting nothing]. But it is lifting nothing in the first sense, not in the second sense.

C) B is wrong. God can (and does) lift an infinitely large stone in accordance with his omnipotence. But does "infinite" contradict "stone"? If the stone is defined as infinite then the question is meaningless "Can God lift an infinite infinite?" On the other hand, is the definition of stone consistent with the description of it as "infinite", i.e. is "infinite stone" a self-contradiction?

This is clearly nonsense.

God could lift the infinite stone if it were ever completed. But it cannot be completed by its very nature. The rest of you babbling here is meaningless.

D) An infinite stone is not a self-contradiction, whatever Antone's definition of "stone" is, does not demand that the stone have a border (that they are finite). God can (and does) create and lift the infinitely large stone, in accordance with his omnipotence.

You're right that the infinite stone is not a self-contradiction. But the rest of your commentary is virtually meaningless.

No, the [infinite stone] does not have a [single border]--any more than [walking] involves a [single pose]. It is a [collection of borders spread out over time], much as [walking] is a [collection of poses spread out over time]. The infinite stone is the [process spread out over time of creating a larger and larger stone]. This cannot be encapsulated in a single shape/border, just as [walking] is a process that cannot be [defined by a single snapshot]. When we look at a picture we recognize that the person in the photo was walking when the picture was taken, but we recognize this fact only because we've seen walking (and pictures of walking) enough to recognize most of the infinitely many [static poses] that comprise the [process of walking]. But a [static pose] is not the [fluid process of walking]. So what we are looking at on the surface of the picture is not walking. It is a frozen, immobile pose--and walking necessarily involves movement. Walking is the process of transitioning from one pose to another in a prescribed manner. The [static pose] and the [fluid walking] are incompatible opposites.

Again, even the omnipotent God cannot walk by holding a single unchanging pose.

In the same way, the [future tense--infinite stone] and the [past tense--created stone] are incompatible opposites. God can [create--future tense] the infinite stone, because he will always be around to engage in the process. But he cannot [create--present tense] the infinite stone. And since the infinite stone will never exist as a static/present tense object, the omnipotent God cannot lift what does not yet exist--and will never currently exist.

So far he has defined "infinite stone" as an "incessantly growing stone" which is, at any time, finite. This is an explicit contradiction (trying to describe the stone as both infinite and finite). God can lift an incessantly growing stone, but asking if God can lift an "infinite stone" is meaningless and has nothing to do with God, but rather everything to do with the definition of "infinite stone".

Wrong again.
Technically, saying that a stone is [incessantly growing] is not enough to make clear what we mean by an [infinite stone]. I suspect that incessantly growing was your terminology, not mine--but in either case, it may be worth explaining the distinction in greater detail.

It is possible for God to lift a [stone that is incessantly growing]--just as it is possible to lift a child who is continually growing the whole time that you are lifting them. But having lifted that child, does not mean that you've lifted the child who is as large as he will eventually be. You lifted a smaller, not-fully-grown version of the child.

In the same way, it is possible to lift [finite versions of the infinite stone]--but none of these [finite versions] ARE the [infinite stone]. The [infinite stone] is [all of these finite versions collectively]. This is exactly analogous to a number in an infinite sequence. Each individual number is finite. But the sequence of numbers is infinite--precisely because there will never be a final number. Now, we cannot write out such an infinite sequence, because we will not live forever. The closest we can come to actualizing an infinite set is to create a set that follows a predictable pattern and then say keep adding more numbers using that pattern. For instance:

{2, 4, 6, 8, 10, 12, 14...}

the ellipsis says [keep adding more numbers using the same pattern].

This is the [set of even numbers]. Conceptually, I have completed this set, because I know what it means. But I haven't actualized the set because I haven't actually written down each of the numbers that it must possess. Now, we can ask the question, does this set contain an infinitely large number. I would say "NO, there isn't a single number in this set that is infinite." What is infinite is the series itself, not the individual numbers that the series contains.

In exactly the same way, there are an [infinite series of specific boulders shapes] that will come into being as God increases the boulder without end. None of these boulder shapes is the actual [infinite boulder]. The [infinite boulder] is all of those shapes collectively. And that has no specific shape or border--any more than all of the numbers in an infinite sequence can have a specific magnitude.

Now, we can conceptualize what it might be like if there were indeed a last number. This [infinite number] would not have a specific magnitude. It's magnitude would literally be without end. Notice that this [Infinite number] has exactly the opposite characteristic that finite numbers possess--because all finite numbers have a specific magnitude.

In exactly the same way, the infinite boulder has the exact opposite characteristics of a finite boulder. It cannot be lifted--because it doesn't yet exist. Just as an infinite number doesn't have a magnitude because it doesn't yet exist--it is something that we can only bring into conceptual existence. It has no physical existence, because by definition it cannot exist physically. Therefore, we cannot attribute to it characteristics that are strictly physical in nature.

It is this inverting affect of logical opposites that prevents my arguments from being contradictory.

My conclusion is that, if we define God as able to do anything, he can indeed do anything.

There is a sense in which this is true, I suppose. But it would necessarily be a sense in which nothing had (or could have) any meaning.

If we define God as being able to make a [blue shirt] a [white shirt]... meaning not that he transformed the shirt from [one that was blue] to [one that was white], and not that he changed the definition of [blue] to [white]. But rather that he somehow made a [blue shirt] a [white shirt] without changing the definition of [blue] or [white]. Then (if this God existed) he would have to be able to do what we defined him as being able to do.

But what does that mean? There isn't any way to do what we have defined. Therefore, it would seem to be a priori knowledge that such a God cannot exist.

The problem with this assessment is that it isn't what being omnipotent means. Being all powerful means that [if there is something that by definition alone might be possible to do, you can do it]. No matter how heavy a stone is, by definitional limits alone, it is theoretically possible to lift it. So an omnipotent God must be able to lift any finite stone. But an infinite stone can't exist, by definition, and therefore it cannot be lifted, even by an omnipotent God. This is not a limit on the God's omnipotence. The fact that you cannot lift [something that does not exist] is not a limit on what [kind of something] you can lift--because [nothing] is [not something].

Just as saying "I am NOT going to the store" is the opposite of "I am going to the store," so too the [not] in [not something] inverts our expectations for God's ability to lift something. So, that [something] which is [not something] cannot be lifted, even by an omnipotent God. And this is not a contradiction in the [only sense of omnipotent that is capable of having meaning].

If you insist on keeping your discussion within the framework of a definition that is (by definition) meaningless, then there is no point in discussing anything, is there?

Am I pointing out the logical flaws clearly enough now Antone?

I'm afraid you were unsuccessful in both your attempts to point out flaws and in your attempts to be clear.

[Antone]

...we cannot have God create an object that is a self-contradiction. Like, we can't define a circle as an object with 1 edge and a square as an object with 4 edges, then ask God to create a square circle. The problem is not with God, the problem is with our own logic. God is still omnipotent, by definition, it's our own idiocy if we try to talk about self-contradictions .

With this I agree.

My point has been that there is a way to define infinity so that the apparent contradiction of the riddle ceases to be a true contradiction. When we define the nature of infinity accurately, there isn't any contradiction in the idea of God creating (future tense) a boulder that is so large that he can't lift it (present tense).

[junglelord]

Infinity, Fractal...simple, elegant, profound....mendelbot set baby.

[StevenJay]

Interesting how discussions involving the combined topics; infinity and Prime Creator (I avoid using the "God" handle in most circles, as it tends to be saddled with too much preconceived, socially conditioned baggage), invariably de-evolve into one manifested fragmented position debating with another manifested fragmented position about that which is non-manifest.

[allynh]

I love that picture. Where did you get it, are there more.