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, February 10, 2009

What do I mean when I say that God is an 'actual infinity'? What does that mean?

Podcast of this article.

(Picture of the relationship between God and the finite above, click to enlarge)

One might think that infinity is special because it reaches the 'end' of all numbers, like reaching the 'end' of a circle. But this doesn't explain what an 'actually infinite object' (such as God) would be like...

What kind of qualities does an 'actually infinite' thing have compared to a finite thing?

The most important quality that an 'actually infinite thing' has is that it exists in a world that doesn't allow for the concept of 'distinctions'. Like between 1 and 2, or red and yellow.

How could I ever go about showing such a strange conjecture?

Well you can use a thought experiment to show that infinite things cannot have distinctions.

Take a plain of grass somewhere. If it's finite, then it has an edge and a centre. There are lots of different places on the grass.

What if it's infinite? If you have an infinitely wide and infinitely long plain of grass, then there is no edge and no centre! So if you were on such a plain, then looking around, you could not distinguish your position from any other position on the grass. There is no 'middle' anywhere, no edge, no possible locating coordinates. So being actually infinite, as you can see, starts taking away distinctions... at least when it comes to location and trying to be at the centre of an infinite plain of grass.

Imagine that the plain of grass is turned into a cube, infinitely high, infinitely wide and infinitely long. Suppose you're inside it. Where's the edge? Where's the centre? It goes on forever. You can't distinguish your position from any other position in it in any way. When it comes to location and size, there are no distinctions in any infinite sized objects.

So you can see that objects start to lose their complexity and sense of difference/distinction when they're made infinite.

There are more reasons for believing the 'no distinction' idea. For one thing, there needs to be some kind of 'break' with finite thinking to enable potential infinity (1, 2, 3, 4, 5, ad infinitum) to become actual infinity. Otherwise numbers would just keep going up forever without reaching infinity. Actual infinity being 'distinction-less', while 'distinction-lessly containing all possible distinctions', would be a good candidate for such a break.

Also, this idea of no distinctions works well in explaining the '∞ + ∞ = ∞' intuition that we have. Infinity times, plus, or minus infinity still equals infinity... no matter what you do, infinity is always infinity. If infinity doesn't support our ideas regarding distinctions, then you could explain why we don't like messing around with the value of infinity because we subconsciously pick up that there are no distinctions in infinity.

There's also a further theological reason for thinking that there are no distinctions in infinity. There are good reasons for thinking of God as an absolutely simple being, without parts or distinctions to make Him complex. If we think of actual infinity as involving no distinctions, then after a theological leap saying that distinction-less infinity is somehow conscious, we can explain how a complex God is actually simple.

This partly explains why there can only be one God (Isaiah 43:10). If infinity is a distinction-less unity of everything, then you can't make another God because there are no distinctions in infinity that will allow you to make another God. There's nothing there that would allow you to separate, split off, or make a distinction between God and another God.

This also explains why finite reasoning cannot understand the infinite very well. Because infinity has a distinction-less existence, you'd need a distinction-less form of reasoning - that also somehow encompasses everything - to understand God and the soul properly. Otherwise with every step you took, you'd just be creating more and more distinctions in God in your analysis, and that wouldn't reflect how the distinction-less really is.

This hopefully explains what an 'actually infinite object' (like God) is like compared to a 'finite object' (like a table). It's a difference of quality. The actually infinite object allows for no distinctions in any way, and exists in a reality that makes that possible. A finite object both allows for and includes distinctions, and exists in a reality that makes such a situation necessary.

Through this weird quality (no distinctions) God gets to have quantitatively infinite reasoning. All possible distinctions are ultimately contained with the distinction-less, the infinite. If that's true, then God can perceive every number at once by checking what the distinction-less summary of all numbers says, that is contained within Himself. So God can say 'Hm... it looks like every number follows a certain pattern' by simply checking the summary of all numbers contained within the distinction-less, and thus use an 'infinite shortcut' to answer every mathematical problem.

A few important clarifications on God being love, a person and a trinity

I want to point out that this seems like a strange idea of God, very far from the loving father of Christianity. The Bible says that God is love. How is the God that I've described love?

I think we need to remember that something being simple in finite terms is very different from the kind of judgements anyone can make about the infinite, the reasons for which I've partly covered. In finite terms, something is simple if there's just 'one' of them, so 'one' is a simple, easy to understand number. In finite terms, the idea of God I've just described is a very 'simple' idea of an ultimate reality, because there's just 'one', it's easily defined and so on.

Finite simplicity argues against the Christian God. But finite simplicity has no connection to the kind of judgements you can make about the infinite, because the infinite is an entirely different kind of thing. So actually, what's simple when it comes to the infinite may be complicated to the finite. I think that the trinity, God being a person, and love coming from God, are such issues.

Somehow, for some reason, the infinite is three persons in one person, which are both three and one at the same time. Finite reasoning has just been thrown out the window, but that's OK, because this is on a different 'level' of reality. Distinction-less existence in other words, is a person, a trinity, and love, in a way that seems really complicated to finite reasoning but which actually isn't. God is the simplest kind of thing you could imagine, but from an infinite perspective rather than a finite perspective, which pretty much makes no sense to finite reasoning but oh well. We shouldn't expect it to.

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