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

Wednesday, January 28, 2009

Infinity and divine simplicity

1, 2, 3 are different numbers, used to make distinctions between things. It's because we have a concept of '1' that we can distinguish one parrot from no parrots, and '3' that we can distinguish 'three' persons from 'one' person.

But what if you had a kind of number that didn't fit in with this pattern of distinctions (1, 2, 3 and so on)? That is basically what infinity is - a different *kind* of number compared to finite numbers because of its infinitude. You might think that ∞ is just a really high number, a number like e.g. '8', but infinitely higher. But infinity can't be something like '8' otherwise it couldn't be actually infinite. For example, try adding zeroes on to the end of the highest number you can think of and see whether it ever reaches infinity. The lack of distinctions is what enables infinity to 'reach' infinity, because as soon as you introduce '1, 2, 3...' then everything breaks down into finitude and you can never reach infinity.

To put it another way, there must be something about infinity that prevents you from taking away or adding to it (infinity + infinity = infinity in a manner of speaking). How so? The reason is that infinity doesn't allow for our ideas regarding distinctions, so you can't get e.g. lots of infinities by adding them to each other.

(Picture of infinity compared to the finite above, click to enlarge)

If God was like a human, then God couldn't be simple. I have two arms, so obviously I can't be absolutely simple. I have different thoughts, so mentally I can't be absolutely simple. But I'm a finite human, and finiteness always contains distinctions (1, 2, 3...)

But if God is an infinite kind of person, then He's a personification of a world where there aren't any distinctions. There can't be a '1' of anything in God, nor a '3', nor an '8', because distinctions belong to finite concepts. Ergo, God is absolutely simple.

This also refutes Richard Dawkins' complexity argument against a designer. If infinity is absolutely simple (without internal distinctions) then God - as a personification of infinity - can't be said to be complex in any way. Dawkins' argument then falls apart.

Link to a great lecture on the nature of infinity.

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