This is the famous "omnipotence paradox". If the answer is yes, He can, then His weightlifting-power is limited, if the answer is no, He can't, than His creating-power is limited. Either way, God is not omnipotent.
There are a few proposed answers from big thinkers. (just type "omnipotence paradox" in google, or wikipedia)
I would like to suggest the following answer:
The answer for this question is not yes, neither no. The answer is: it is a wrong question. Why?
Let's see first, how infinite works in mathematics (don't worry, it is not difficult maths, just a little logic). Infinite is not an exact number. If you add one to infinite, what is the result? Infinite. So, the second infinite is bigger than the first one, since we added one to it. The same way, if we subtract one from infinite, we get infinite. In this case the second infinite is smaller than the first one.
The same, using mathematical signs:
∞ + 1 = ∞
∞ - 1 = ∞
if these are true, than:
∞ < ∞
∞ > ∞
You can't really add/subtract a number to/from infinite. You will always get the same number, then the number which you added/subtracted doesn't exist. Let me demonstrate it with a very simple equation:
∞ + 1 = ∞ / - ∞
1 = 0
(or 1 = ∞)
But this is not true: 1 is not 0, neither infinite. One is one.
Therefore we can't use our known mathematical operations with infinite, because - as we've just seen - they will terminate in a false result. This happens with summation, subtraction, multiplication, division, and all the other known operations. We can't even use the smaller/bigger signs. Why is it so? Because all these mathematical operations are for the finite World. For real numbers, which are all finite. When we use infinite, all the finite operations and relation marks fail.
Now, let's go back to the "omnipotent paradox". Can God create a stone, which He cannot lift up? Let God's creating-power be "C", and his lifting-power "L". We assume, that both L and C are infinite (that is why the whole question is asked). The question is: which is bigger, L or C ? which of these statements is true?
C < L now the answer is: He can't, so He is not omnipotent, because His creation-power is limited.
C > L now the answer is: He can, so He is not omnipotent, because His lifting-power is limited.
C = L now the answer is again He can't, so He is not omnipotent, because His creating-power is limited.
But we've seen above, that we can't say C < L, or C > L, neither C = L, because both C and L are infinite, and relation marks don't work in the World of infinite.
Therefore the answer for the original question is:
The question is wrong, because it has a false assumption, that relation marks can be used in the World of infinite.
The question is wrong, because it has a false assumption, that relation marks can be used in the World of infinite.
First of all: Hi, it has been a long time!
ReplyDeleteSecond: Great post, keep it going! :)
Third: As far as I know (I'm no expert, just took one or two courses on the subject in college), you can use relation marks in the world of infinite: http://en.wikipedia.org/wiki/Cardinality_of_the_continuum
There are different cardinalities of infinites (the number of elements in the real numbers set is > than the number of elements in the natural set, and the number of elements in the real numbers set is = than the number of elements in the irrational numbers set, for example).
Regards,
Hi Andres, how is it going?
ReplyDeleteThanks, so I think (even though I am even less expert, since I am not a mathematician) in some of the abstract examples you can use relation marks, since it is obvious that all natural numbers are real numbers, but not all real numbers (f.e. 2.536) are natural numbers, so the real number set must be bigger, than the natural one.
But, in the omnipotence paradox we are using physical (finite!) qualities (how many kilograms/pounds is the limit for God in these two actions of creating and lifting up) which are not abstract. And here, we can't say, that "they have the same quantity, except that some elements are missing from one". We don't know anything about them before experience, or figuring out somehow one by one. We are comparing two qualities, which are independent from each other.
I hope it makes sense, it is very late here now...
Everything cool here in Chile ;)
ReplyDelete"since it is obvious that all natural numbers are real numbers, but not all real numbers (f.e. 2.536) are natural numbers, so the real number set must be bigger, than the natural one."
Not true. All irrational numbers are real numbers and not all real numbers are irrational numbers, but they have the same cardinality. The same happens with odd numbers and natural numbers, etc.
"in the omnipotence paradox we are using physical (finite!) qualities (how many kilograms/pounds is the limit for God in these two actions of creating and lifting up) which are not abstract."
That was not your original argument. If we are talking about physical (finite!) qualities, then are you saying that God's strenght and God's omnipotence are finite?
"All irrational numbers are real numbers and not all real numbers are irrational numbers, but they have the same cardinality. The same happens with odd numbers and natural numbers, etc."
ReplyDeleteSorry, I don't get, how this disproves my comparison of real numbers and natural numbers.
"That was not your original argument. If we are talking about physical (finite!) qualities, then are you saying that God's strenght and God's omnipotence are finite?"
No, the opposite (of course). Physics (unlike the very abstract mathematics) is the science of the measurable finite World. God is infinite. We can't use finite methods for describing the infinite. We can't ask about the infinite, using finite science. This is connected to my reason, and i think, strengthening it.
Glad to hear, that Chile is cool! Maybe I should visit one day... ;)
"I don't get, how this disproves my comparison of real numbers and natural numbers."
ReplyDeleteIt disproves it because the fact that "all natural numbers are real numbers, but not all real numbers (f.e. 2.536) are natural numbers" doesn't imply (as you say) that "the real number set must be bigger, than the natural one."
---
"We can't use finite methods for describing the infinite. We can't ask about the infinite, using finite science."
That's what you said in your post. In my first comment I answered: "you can use relation marks in the world of infinite", meaning that relation marks are NOT finite methods, they can be used both for finite and infinite science.
Of course, come and visit, I have a guest-bed waiting for you (and live really close from a kosher shil)
Sorry for not responding for a few days...
ReplyDeleteSo,
"It disproves it because the fact that "all natural numbers are real numbers, but not all real numbers (f.e. 2.536) are natural numbers" doesn't imply (as you say) that "the real number set must be bigger, than the natural one.""
If group A has all members of group B, but group B doesn't have all members of group A, then group A must be bigger than group B. It is simple.
And I still hold, that we can't use our known finite mathematical operations in the World of infinite, because if we add a number (besides 0) to another "number" (if we can call infinite a number) and the result is the same "number", means, that the operation didn't work, or we couldn't interpret it. Both lead to the conclusion, that we can't use these operations on infinite. If this is true, then we can't use relation marks either, since adding a positive number should lead to increase (bigger), and subtracting to decrease (smaller).
Is the kosher shil chossidish?
Hi! don't worry for the delay ;)
ReplyDelete"If group A has all members of group B, but group B doesn't have all members of group A, then group A must be bigger than group B. It is simple."
It's not that simple, when we're talking about infinites that rule doesn't work, just like you said in your post infinite+1=infinite (this means that a set containing one more element than the others is still the same size).
The thing is that, Georg Cantor discovered a difference between kinds of infinite, the Real numbers are bigger than the natural numbers, based on this difference he defined the Real numbers as bigger than the Natural numbers (http://en.wikipedia.org/wiki/Cardinality#Finite.2C_countable_and_uncountable_sets), and since then in mathematics the finite mathematical operations you mention are used between different infinite sets (check the link I left in my first comment, they are used in that article)
"if we can call infinite a number"
We can't call infinite a number. That's why the operation is defined again for infinites. If you add 2 countable infinites, you get a countable infinite. If you add two uncountable infinites you get an uncountable infinite. If you add one of each, the uncountable infinite "absorbs" the countable infinite, and you get an uncountable infinite. (The cool thing is that you have different levels of uncountable (and there are an infinite uncountable number of these uncountable infinite numbers....crazy)..
Example, in infinite world (Every infinite set is called Alpha_n (isn't it cool they choose The jewish nickname of God to represent this?): Alpha1+Alpha2=Alpha2, Alpha1+Alpha3=Alpha3, Alpha1+Alpha2+Alpha3=Alpha3....etc...
"Both lead to the conclusion, that we can't use these operations on infinite."
We can, only that they are defined differently because infinites are not numbers. Alpha1's cardinality is bigger than Alpha2's cardinality.
So, relation marks in their usual numeric meaning can't be used, but in the infinite's cardinality meaning can. And since here we're talking about 2 infinite attributes of God, it makes sense to use them that way, the same way mathematicians use them regarding infinite sets.
When, in your article, you say: "The question is: which is bigger, L or C ?", you mean: " The question is: which has a bigger cardinality, L or C ?"
It's interesting how, maybe (not sure at all), you can answer here: L=C, because both L and C can be Limit(Aleph_i) when i->infinity. This would mean God can't beat one of his attributes using other of them, because all of them have exactly the same power (super-mega-infinite, or something), meaning: the question is wrong because it requires God to limit one of his attributes, and by definition, God can't limit himself because this would mean changing, and God doesn't change at all.
Gone wild, sorry. And I drunk just one beer! hahaha
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