Weblog of a Christian philosophy student

Weblog of a Christian philosophy student. Please feel free to comment. All of my posts are public domain. Subscribe to posts [Atom]. Email me at countaltair [at] yahoo.com.au. I also run a Chinese to English translation business at www.willfanyi.com.

Location: Melbourne, Victoria, Australia

Tuesday, August 25, 2009

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).


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: ,

Wednesday, August 19, 2009

The moral philosophy of Jesus

Jesus as a philosopher. What are some interesting philosophical insights that could be gained from looking at Jesus' statements? In this post, I will highlight a couple of things that Jesus said that could be interpreted as an interesting take on Aristotelian virtue ethics.

In virtue ethics, the most important thing regarding knowing what's good is what a really virtuous person says. If you want to know what the right thing is, ask the person you know who's the most upright, virtuous person you can find. You shouldn't ask an evildoer whether it is right to do X or Y. Morality is so complicated that this is the best way of figuring out moral issues. You can't hope to figure out morality like 2 + 2 = 4. Morality is a very complicated, tricky thing, and another approach won't really work.

When Jesus is tempted by Satan in the Gospel of Matthew, he gives a very interesting reply to the temptation that sort of goes along with Aristotelian virtue ethics:

Matthew 4:8-10 "Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their splendor. "All this I will give you," he said, "if you will bow down and worship me." Jesus said to him, "Away from me, Satan! For it is written: 'Worship the Lord your God, and serve him only.'"

Combine that with these verses:

John 5:30 "By myself I can do nothing; I judge only as I hear, and my judgment is just, for I seek not to please myself but him who sent me."

Matthew 19:16-17 "Now a man came up to Jesus and asked, "Teacher, what good thing must I do to get eternal life?" "Why do you ask me about what is good?" Jesus replied. "There is only One who is good. If you want to enter life, obey the commandments."

Jesus identifies God as a being who is so good, so wonderfully upright and loving, that in comparison with God, no one else even deserves to be called 'good'.

I think one can see a bit of a connection between these verses...

Think about it like this: suppose you lived in a town and there was someone in the town who was quite unusual. While everyone in the town is a pretty decent person, this person is something more. This person cannot be tempted to do the wrong thing. When this person thinks about moral dilemmas, you know that he/she will give the right answer, because this person always thinks about the right thing in a clear way. It is impossible to tempt this person with an evil thought.

If you wanted wisdom on any ethical decision, you would always go to this person if you lived in the town. Although we usually make pretty good ethical judgements, the only way you could be really sure, the only way you could be 100% positive whether something was the right thing to do, would be to ask the person who cannot give a morally flawed answer. Whereas you, I, and everyone else can be tempted to see things in a selfish way, this special person must by definition see things in the morally correct way.

If you wanted someone to be the ruler over a society, then if possible, you would pick that particular person. While other people might be good rulers out of the goodness of their own hearts, this 'un-temptable' person would be good out of necessity. Surely, picking that person as a ruler could not go very wrong.

If you think about it like this, then it's easy to see the logic of Jesus' answer to Satan in Matthew 4:10. God is someone who cannot be tempted to do the wrong thing (James 1:13; Titus 1:2). So in Jesus' view, if you're in any doubt as to whether you should do something, there is one person who's answer you can always trust (assuming you could actually talk to Him/Her/It). The answer of a God who cannot be tempted by evil is 100% trustworthy by definition, unlike the answer of someone not like that (although someone else's view might be right as well, it is not trustworthy by definition).

So we see that, if you assume that there is a God who is like the person in the town example, and like the God alleged in the Bible, then there is a certain logic to everyone deferring to this God. Everyone else in all of existence can be tempted to do the wrong thing - even the human part of Jesus (Heb 4:15). Even the angels were tempted at one point according to Thomas Aquinas' interpretation of the fall of Satan. But not God - for some reason God, and only God, is impossible to tempt. So assuming that this God existed and this situation was the case, then wouldn't it make sense if everyone listened to what He/She/It had to say? And not only listen, but act accordingly?

If God really cannot be tempted by evil, then serving God like Jesus ("serve Him only") would actually give us our freedom, it wouldn't take it away. A God who couldn't be tempted to do evil would be love. And part of loving people is giving them free will. So we can see that only serving God means being a) free and b) honouring other people's freedom through love.

So if you look at Jesus' views in a 'virtue ethics' way, Jesus essentially says that the person to ask when it comes to moral issues is the only person who can never be tempted. If you follow this person, then the result will never go wrong (assuming you actually knew what God was saying). Given the truth of such a situation, serving this person with 'all your heart, soul, strength and mind' guarantees that the right thing will always be done. Therefore, as Jesus says, you should "serve only" this God rather than yourself or someone else.

Labels: , ,

Thursday, August 13, 2009

God cannot do evil. Does this raise problems?

The Bible says that God cannot do wrong:

James 1:13 "When tempted, no one should say, "God is tempting me." For God cannot be tempted by evil, nor does he tempt anyone"

Titus 1:2 "in hope of eternal life which God, who cannot lie, promised before time began"

Does this raise problems?

Some argue this means that God doesn't have free will. If God cannot do wrong, then how is God free to do wrong?

One response to this argument is that there are actually two kinds of 'cannot':

Cannot 1
Cannot 2

For example:

"I cannot throw this rock into space from my backyard." Cannot 1.

"So you think I should make money by robbing banks? I could never do something like that!" Cannot 2.

I would say that 'cannot 1' applies to physical impossibility. 'Cannot 2' applies to the inability to be tempted by something.

'Cannot 1' applies to physical objects. I cannot throw a rock into space because my body is physically unable to do so.

'Cannot 2' applies to persons, and deals with an inability to find reasons for doing something. Without a reason for doing something, I can't do it. For me to rob banks, I would need to have a reason to rob banks. But robbing banks is evil. As long as I remember that robbing banks is evil, then it's impossible for me to find a reason to rob banks. So I literally cannot rob banks as long as I remember that it's evil.

'Cannot 1', when applied to persons, takes away free will. If someone is put in prison, then they cannot ('cannot 1') go outside. They are not 'free' to go outside.

This is OK when it comes to God. Because 'cannot 1' doesn't apply to God, 'cannot 2' does. Christians think that God, being all-powerful, is physically able to do evil. The issue with God is that God cannot be tempted to do evil.

So the question is: does 'cannot 2' take away free will?

I don't think so. Consider this: as long as someone remembers that it's evil to murder someone, then they cannot be tempted to murder someone. No one could be tempted to murder someone while they were thinking that it's an evil thing to do. Think about it. It's impossible. And yet would anyone say that this being the case takes away free will?

Of course not. Someone doesn't lose their free will because they can't be tempted to murder someone while they remember that it's an evil thing to do.

So 'cannot 2' seems fine for free will, at least in some situations (described above).

And so it seems that God's free will is fine. It doesn't seem to hurt God's free will that He cannot do evil as long as the 'cannot' is 'cannot 2' (note: this analysis might only work with regard to evil).

So why doesn't God make 'cannot 2' apply to humans as well as to Himself?

The reason why God can't do this is that creatures must be able to think in terms of self-interest. This is because finite creatures need something to think with, for finite creatures this means finite reasoning, and the nature of finite reasoning is such that it always thinks in terms of self-interest (e.g. game theory). God can protect us from this 'dark side' to being a creature (as in the Garden of Eden) but the allure to think in terms of self-interest is always going to be there.

So for humans (especially after a 'Fall' like in the Garden of Eden) free will requires the ability to be tempted by evil, because of our self-interested mode of reasoning. But this isn't the case for God, who has a mode of reasoning (not finite) such that He doesn't think in terms of self-interest. We can't even imagine what this is like (Isaiah 55:8).

Labels: ,

Tuesday, August 04, 2009

Answers to tough questions: suffering

When we see suffering going on in the world, often not connected to wrongdoing, it is hard to see how a loving God exists. Suffering is also pretty random. The traditional Christian answer is that because we live in a fallen world, therefore terrible suffering must happen.

I think there are some gaps in this explanation. Here is my attempt to fill them:

We are mental and physical beings. Mentally, we have a mind which is not the same as our brain. Physically, we have a brain and a body. The mind is based off the brain, but it is not the same thing as the brain.

I think that the mind lives in a mental world that follows different rules to the physical world around us.

I think that one of these 'mental' rules works kind of like gravity. Say you throw a rock up into the air. It will fall down due to gravity. In an analogous way, in the Christian view, a mind is naturally connected to its creator, God, in the mental world. God is the 'super-mind' from which all other minds come, creating this connection.

But in the Christian/Judaic view, if a mind sins then it gets pushed away from its creator, God (in the mental world). Sin pushes a mind away from God sort of like a rock suddenly flying out into space instead of falling to the ground (for some reason).

When a mind is connected to God it feels infinite happiness. It is enjoying what God feels all the time. But when a mind is 'pushed away' from God due to sin, the mind suffers, and loses ultimate happiness.

The stuff I just described only goes on in the mental world. It does not happen physically. So physically, everything can be fine. Someone can be in good health, be having a good time etc., but if our minds are cut off from God due to sin then we must suffer no matter what is going on physically.

God makes our mind getting cut off from God go along with physical suffering, like e.g. a disease. It doesn't have to go along with physical suffering like disease. But whether it does or not, the suffering we must all feel is roughly the same. So God should not be blamed for making this process go along with physical suffering, because the same suffering must happen regardless.

I think this is how saying 'We live in a fallen world' can make sense of suffering, and yet 'God is love' and all-powerful.

Two questions remain:

1) Why does our mind get cut off from God due to sin?
Answer: Because the mind is connected to God, and God simply cannot be connected to a soul that does wrong. It's impossible for such a connection to be maintained, because God is holy. Even though God is all-powerful, God cannot allow sin in His presence (for a reason we may not fully know).

2) Why do some people suffer much more than others?
Answer: I'm not sure, but this argument does explain why there must be horrible suffering... even if we can't explain why some people suffer more than others. This must simply be left unexplained, and so the argument is not complete. But this argument is at least something...

Labels: , , ,