Discussion on what it means to say an 'infinite God'
I had a discussion on a forum on the idea that infinity = existence without distinctions (as opposed to with distinctions) and whether that's the kind of person that God is. I thought I'd collect the points together in case people are interested in some depth in one promising account of what 'infinite God' means (link to discussion). A summary of the other person's point is in [brackets]. My opening arguments:
1. Take a plain of grass that's infinitely wide and infinitely long. With respect to horizontal location, you cannot find your place on it because it goes on forever in every direction. That distinction has been lost. Maybe the infinite involves the loss of every distinction in a similar way?
2. We can imagine numbers going up and up forever to infinity, but not reaching infinity. For there to be an absolute infinity there must be some kind of radical 'break' with the potentially infinite. But where can we find such a break? Perhaps from an 'existence without distinctions', which contains every possible number 'distinction-lessly'.
3. It explains the infinity + infinity = infinity intuition that we have (you can only get one infinite). If infinity is distinction-less, then you cannot separate a part of infinity from another part, or make another infinity, because there are no distinctions between anything.
4. This theory of infinity could explain how an apparently complicated God is really simple. If God personifies a world without any distinctions, then God must be the simplest thing possible. A leap of faith can let you believe that this entails a conscious, three-in-one God.
5. Explains why there can only be one God - Deu 6:4 (from points 3 and 4).
Thoughts?
1. Take a plain of grass that's infinitely wide and infinitely long. With respect to horizontal location, you cannot find your place on it because it goes on forever in every direction. That distinction has been lost. Maybe the infinite involves the loss of every distinction in a similar way?
[Someone posted: what about Cartesian coordinate systems (wikilink). They could solve this problem.]
I think I know what you mean. Let's say you put a wooden pole into the grass at some random location, then you could tell where you were by looking over your shoulder (let's say) at the pole in the ground. But isn't it interesting that you can only locate yourself because you've created distinctions in the plain of grass, i.e. you've made your area of interest/concern a finite area. If you don't put down the wooden pole (e.g.) then you're lost and there's no way of distinguishing your position from any other. So I would submit that in terms of showing that infinity takes away distinctions it still works as an example, although maybe a better one can be found.
[But you could distinguish where you are from the different blades of grass. And also, this example doesn't work because no plane (of grass or anything else) can be infinite.]
Instead of saying a plain of grass imagine that it's an empty, grey plane, like in a computer program. You can have horizontal locating coordinates if you mark your location in the plane, which is essentially creating a finite space within the infinity. But if you deal with the whole infinity then you've lost SOME information compared to a finite plane. You've lost the ability to say something like 'This plane is 5x5 metres' which you could do if the plane was finite. So on the basis of the fact you've lost information I think that the example does show infinity tends to take away distinctions.
Here's a graphic I made on this (below, click to enlarge):
[Explain the graphic.]
I guess the way God created distinctions out of distinction-less existence is something like placing a pole down in an grey plane that goes on forever in every direction. When you place the pole you've created a finite area within an infinity, and you can then do all the stuff included in human ideas (which are finite). So let's say there's this distinction-less reality, and suddenly God says 'Hey I'm going to allow for the concept of differences between stuff', and then suddenly God has a mathematical toolbox to make the laws of the universe based on finite numbers.
[So what's my argument?]
If there's a tree that's ∞ metres high, then you have a tree but no specific information about what height, because there is no such distinction. But if you have a tree with a finite height, then you have a tree and specific information about the height, which is a distinction. So by analogy, if you carry this process on as the core aspect of infinity, then infinity is distinction-less existence which distinction-lessly contains every possible distinction.
A 30 metre high X has more distinctions as a concept than an ∞ metre high X, because an ∞ metre high X 'holds off' putting a distinction like a specific height as yet (to use anthropomorphic language) for the sake of distinction-lessly containing every possible distinction in that concept.
2. We can imagine numbers going up and up forever to infinity, but not reaching infinity. For there to be an absolute infinity there must be some kind of radical 'break' with the potentially infinite. But where can we find such a break? Perhaps from an 'existence without distinctions', which contains every possible number 'distinction-lessly'.
[What's the difference between potential and actual infinity in this view? There is no difference in contemporary mathematics. Infinity means that you never stop counting.]
This is from the wiki on potential and actual infinity:
Aristotle also distinguished between actual and potential infinities. An actual infinity is something which is completed and definite and consists of infinitely many elements, and according to Aristotle, a paradoxical idea, both in theory and in nature. In respect to addition, a potentially infinite sequence or a series is potentially endless; being a potentially endless series means that one element can always be added to the series after another, and this process of adding elements is never exhausted.
[But ideas have advanced since Aristotle. Actual and potential infinities are now regarded as the same thing.]
3. It explains the infinity + infinity = infinity intuition that we have (you can only get one infinite). If infinity is distinction-less, then you cannot separate a part of infinity from another part, or make another infinity, because there are no distinctions between anything.
[Comment about Cantor's multiple infinities. Cantor the mathematician basically showed that there are an infinite number of infinities. Wikilink.]
Maybe there's appearance and there's a reality behind the appearance that we can't get at. Because of finite reasoning, the appearance will be of multiple infinities, no matter what. But behind the appearance there is a reality of only one distinction-less infinity. You've probably seen this approach elsewhere, it's a Kantian way of answering questions. This argument is circular in terms of establishing the infinity is distinction-less to someone else but internally it would make sense of the multiple infinity thing.
[How do you know this?]
I guess one argument that there's really only one infinity if mathematics shows otherwise, is that when you ask the average person (I remember this from a podcast) almost everyone has an opinion of infinity even though most of them wouldn't know many concepts from 'finite' mathematics. And intuitively we feel that there can't be more than one infinity. I think it's possible that the concept of infinity in our minds is an unconscious concept of distinction-less existence, which everyone has without needing to define it. But then again, if you look at infinity mathematically it appears as though there are lots.
One reason I like it is that a person who 'personifies' distinction-less existence - if that's possible - is truly eternal. That person could be seen as infinitely old - the first and the last. You can't ask where He/She/It came from. He/She/It simply is. That's an attractive concept for God it seems to me.
[But intuition is often wrong; like in the Monty Hall problem. It seems this theory is just speculation.]
The main problem with the idea seems to be that modern mathematics supports the idea of multiple infinities. To get around that, one needs to adopt a Kantian way out, but that is ultimately not going to be convincing to someone who doesn't agree initially.
I guess at the end of the day this is an interesting idea of infinity, that MIGHT be true, and it certainly works well with ideas about God, but in the end is simply not provable. Considering how hard it is to define actual infinity in a philosophical sense, this may not be so bad for the idea, since it is a hard thing to get one's head around, but it can go no further than interesting conjecture.
[Then that's all it can be.]
[Another point: also, the idea of God being distinction-less existence is like saying that God is a square circle. It's logically impossible.]
How so? If you're referring to the difference between distinction-less existence and the concept of a person/consciousness, in the sense that 'Why would such an existence be a godlike person' then that has a decent answer.
The way humans think is in terms of distinctions, so we work out 1+1=2 through distinctions, and the difference between smart and dumb is how many distinctions someone can order in the best way. But if you try to use that kind of distinction-ful reasoning to understand the distinction-less (excepting what I've said above because it's so general) then that's like putting a piece of paper through paper shredder and then trying to read the resulting mess. Distinction-ful reasoning has almost no power to understand the distinction-less, which is why we can't see that a) distinction-less existence is conscious, b) love, and c) a three-in-one God.
That's why we need to relate to God as a person rather than as an intellectual idea.
[I mean in the sense of distinction-less existence being logically impossible.]
Well, maybe I would define it in the sense that e.g. Cantor seemed to believe in an absolute infinite that was God, that 'transcended the transfinite numbers'. However, since I don't know the details I can't really say in what sense this was held as an idea of God/infinity. Cantor did say that the absolute infinite was a distinction-less unity (link). Even to Cantor it was kind of a mystical idea that resolved the paradoxes of infinity in God.
Unfortunately, the fact there appears to be multiple infinities does present an obstacle to this - maybe the Kantian way out works for that...
[Where does Cantor say this?]
It's not directly referred to but I think it's implied in the first one: "it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding."
Also I think we're talking about two different meanings of the word illogical.
2+2=5 is illogical because according to the rules of 'finite existence', 2+2 has to equal 4 by definition.
The absolute infinite is illogical according to the rules of finite existence as well. But this is the difference: the absolute infinite is not in finite space in any way. It's in infinite space. So such illogical aspects do not count against its truth and existence, as it's not in 'finite space', like they do with 2+2=5, which does exist in 'finite space'.
I think the same way about the trinity. If the trinity was in finite space then 3 persons = 1 person would count against its truth. But because it's in infinite space - in the infinite reality of God - then 3 persons = 1 person doesn't count against its truth because stuff might work differently there.
A discussion on free will and the infinite - how does the infinite possess free will?
[What's the difference between saying God is infinite and indefinite?]
From my perspective, I guess one could call distinction-less existence an 'actual indefinite' in that it loses all manner of distinctions/differentiations between and within anything, which is very indefinite. Not sure whether 'indefinite' implies anything more/different though.
I think free will could also go with the idea of the 'indefinite'. The indefinite world is not determined, so free will begins with God and then is granted to humans in a way that finite reasoning can't understand (because the finite by definition is precisely defined and can only act within its predetermined boundaries).
[But does this imply that God = everything and everything = God, if God is indefinite?]
I think God contains all possible distinctions in His being, but I would say that this 'containing' is done 'distinction-lessly', as opposed to God holding lots of individual items in His being. An analogy might be that a container full of chocolates is a 'distinction-ful' containing in that there are lots of individual chocolates in the container. But I think that when God (the distinction-less) contains everything, it's not like the lots of individual chocolates (e.g.). God somehow contains everything in a way that makes it contain 'distinction-lessly', while also having the potential to become separate.
1. Take a plain of grass that's infinitely wide and infinitely long. With respect to horizontal location, you cannot find your place on it because it goes on forever in every direction. That distinction has been lost. Maybe the infinite involves the loss of every distinction in a similar way?
2. We can imagine numbers going up and up forever to infinity, but not reaching infinity. For there to be an absolute infinity there must be some kind of radical 'break' with the potentially infinite. But where can we find such a break? Perhaps from an 'existence without distinctions', which contains every possible number 'distinction-lessly'.
3. It explains the infinity + infinity = infinity intuition that we have (you can only get one infinite). If infinity is distinction-less, then you cannot separate a part of infinity from another part, or make another infinity, because there are no distinctions between anything.
4. This theory of infinity could explain how an apparently complicated God is really simple. If God personifies a world without any distinctions, then God must be the simplest thing possible. A leap of faith can let you believe that this entails a conscious, three-in-one God.
5. Explains why there can only be one God - Deu 6:4 (from points 3 and 4).
Thoughts?
1. Take a plain of grass that's infinitely wide and infinitely long. With respect to horizontal location, you cannot find your place on it because it goes on forever in every direction. That distinction has been lost. Maybe the infinite involves the loss of every distinction in a similar way?
[Someone posted: what about Cartesian coordinate systems (wikilink). They could solve this problem.]
I think I know what you mean. Let's say you put a wooden pole into the grass at some random location, then you could tell where you were by looking over your shoulder (let's say) at the pole in the ground. But isn't it interesting that you can only locate yourself because you've created distinctions in the plain of grass, i.e. you've made your area of interest/concern a finite area. If you don't put down the wooden pole (e.g.) then you're lost and there's no way of distinguishing your position from any other. So I would submit that in terms of showing that infinity takes away distinctions it still works as an example, although maybe a better one can be found.
[But you could distinguish where you are from the different blades of grass. And also, this example doesn't work because no plane (of grass or anything else) can be infinite.]
Instead of saying a plain of grass imagine that it's an empty, grey plane, like in a computer program. You can have horizontal locating coordinates if you mark your location in the plane, which is essentially creating a finite space within the infinity. But if you deal with the whole infinity then you've lost SOME information compared to a finite plane. You've lost the ability to say something like 'This plane is 5x5 metres' which you could do if the plane was finite. So on the basis of the fact you've lost information I think that the example does show infinity tends to take away distinctions.
Here's a graphic I made on this (below, click to enlarge):
[Explain the graphic.]
I guess the way God created distinctions out of distinction-less existence is something like placing a pole down in an grey plane that goes on forever in every direction. When you place the pole you've created a finite area within an infinity, and you can then do all the stuff included in human ideas (which are finite). So let's say there's this distinction-less reality, and suddenly God says 'Hey I'm going to allow for the concept of differences between stuff', and then suddenly God has a mathematical toolbox to make the laws of the universe based on finite numbers.
[So what's my argument?]
If there's a tree that's ∞ metres high, then you have a tree but no specific information about what height, because there is no such distinction. But if you have a tree with a finite height, then you have a tree and specific information about the height, which is a distinction. So by analogy, if you carry this process on as the core aspect of infinity, then infinity is distinction-less existence which distinction-lessly contains every possible distinction.
A 30 metre high X has more distinctions as a concept than an ∞ metre high X, because an ∞ metre high X 'holds off' putting a distinction like a specific height as yet (to use anthropomorphic language) for the sake of distinction-lessly containing every possible distinction in that concept.
2. We can imagine numbers going up and up forever to infinity, but not reaching infinity. For there to be an absolute infinity there must be some kind of radical 'break' with the potentially infinite. But where can we find such a break? Perhaps from an 'existence without distinctions', which contains every possible number 'distinction-lessly'.
[What's the difference between potential and actual infinity in this view? There is no difference in contemporary mathematics. Infinity means that you never stop counting.]
This is from the wiki on potential and actual infinity:
Aristotle also distinguished between actual and potential infinities. An actual infinity is something which is completed and definite and consists of infinitely many elements, and according to Aristotle, a paradoxical idea, both in theory and in nature. In respect to addition, a potentially infinite sequence or a series is potentially endless; being a potentially endless series means that one element can always be added to the series after another, and this process of adding elements is never exhausted.
[But ideas have advanced since Aristotle. Actual and potential infinities are now regarded as the same thing.]
3. It explains the infinity + infinity = infinity intuition that we have (you can only get one infinite). If infinity is distinction-less, then you cannot separate a part of infinity from another part, or make another infinity, because there are no distinctions between anything.
[Comment about Cantor's multiple infinities. Cantor the mathematician basically showed that there are an infinite number of infinities. Wikilink.]
Maybe there's appearance and there's a reality behind the appearance that we can't get at. Because of finite reasoning, the appearance will be of multiple infinities, no matter what. But behind the appearance there is a reality of only one distinction-less infinity. You've probably seen this approach elsewhere, it's a Kantian way of answering questions. This argument is circular in terms of establishing the infinity is distinction-less to someone else but internally it would make sense of the multiple infinity thing.
[How do you know this?]
I guess one argument that there's really only one infinity if mathematics shows otherwise, is that when you ask the average person (I remember this from a podcast) almost everyone has an opinion of infinity even though most of them wouldn't know many concepts from 'finite' mathematics. And intuitively we feel that there can't be more than one infinity. I think it's possible that the concept of infinity in our minds is an unconscious concept of distinction-less existence, which everyone has without needing to define it. But then again, if you look at infinity mathematically it appears as though there are lots.
One reason I like it is that a person who 'personifies' distinction-less existence - if that's possible - is truly eternal. That person could be seen as infinitely old - the first and the last. You can't ask where He/She/It came from. He/She/It simply is. That's an attractive concept for God it seems to me.
[But intuition is often wrong; like in the Monty Hall problem. It seems this theory is just speculation.]
The main problem with the idea seems to be that modern mathematics supports the idea of multiple infinities. To get around that, one needs to adopt a Kantian way out, but that is ultimately not going to be convincing to someone who doesn't agree initially.
I guess at the end of the day this is an interesting idea of infinity, that MIGHT be true, and it certainly works well with ideas about God, but in the end is simply not provable. Considering how hard it is to define actual infinity in a philosophical sense, this may not be so bad for the idea, since it is a hard thing to get one's head around, but it can go no further than interesting conjecture.
[Then that's all it can be.]
[Another point: also, the idea of God being distinction-less existence is like saying that God is a square circle. It's logically impossible.]
How so? If you're referring to the difference between distinction-less existence and the concept of a person/consciousness, in the sense that 'Why would such an existence be a godlike person' then that has a decent answer.
The way humans think is in terms of distinctions, so we work out 1+1=2 through distinctions, and the difference between smart and dumb is how many distinctions someone can order in the best way. But if you try to use that kind of distinction-ful reasoning to understand the distinction-less (excepting what I've said above because it's so general) then that's like putting a piece of paper through paper shredder and then trying to read the resulting mess. Distinction-ful reasoning has almost no power to understand the distinction-less, which is why we can't see that a) distinction-less existence is conscious, b) love, and c) a three-in-one God.
That's why we need to relate to God as a person rather than as an intellectual idea.
[I mean in the sense of distinction-less existence being logically impossible.]
Well, maybe I would define it in the sense that e.g. Cantor seemed to believe in an absolute infinite that was God, that 'transcended the transfinite numbers'. However, since I don't know the details I can't really say in what sense this was held as an idea of God/infinity. Cantor did say that the absolute infinite was a distinction-less unity (link). Even to Cantor it was kind of a mystical idea that resolved the paradoxes of infinity in God.
Unfortunately, the fact there appears to be multiple infinities does present an obstacle to this - maybe the Kantian way out works for that...
[Where does Cantor say this?]
It's not directly referred to but I think it's implied in the first one: "it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding."
Also I think we're talking about two different meanings of the word illogical.
2+2=5 is illogical because according to the rules of 'finite existence', 2+2 has to equal 4 by definition.
The absolute infinite is illogical according to the rules of finite existence as well. But this is the difference: the absolute infinite is not in finite space in any way. It's in infinite space. So such illogical aspects do not count against its truth and existence, as it's not in 'finite space', like they do with 2+2=5, which does exist in 'finite space'.
I think the same way about the trinity. If the trinity was in finite space then 3 persons = 1 person would count against its truth. But because it's in infinite space - in the infinite reality of God - then 3 persons = 1 person doesn't count against its truth because stuff might work differently there.
A discussion on free will and the infinite - how does the infinite possess free will?
[What's the difference between saying God is infinite and indefinite?]
From my perspective, I guess one could call distinction-less existence an 'actual indefinite' in that it loses all manner of distinctions/differentiations between and within anything, which is very indefinite. Not sure whether 'indefinite' implies anything more/different though.
I think free will could also go with the idea of the 'indefinite'. The indefinite world is not determined, so free will begins with God and then is granted to humans in a way that finite reasoning can't understand (because the finite by definition is precisely defined and can only act within its predetermined boundaries).
[But does this imply that God = everything and everything = God, if God is indefinite?]
I think God contains all possible distinctions in His being, but I would say that this 'containing' is done 'distinction-lessly', as opposed to God holding lots of individual items in His being. An analogy might be that a container full of chocolates is a 'distinction-ful' containing in that there are lots of individual chocolates in the container. But I think that when God (the distinction-less) contains everything, it's not like the lots of individual chocolates (e.g.). God somehow contains everything in a way that makes it contain 'distinction-lessly', while also having the potential to become separate.
Labels: infinity, nature of God
posted by Will G | Tuesday, August 25, 2009
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