St Luke's Church Eccleshill - Articles from "The Link"

The infinite thoughts of God?

Dear John,

Last month you wrote "there are different sizes of infinity." What a wonderful piece of information! I never realised that infinity came in different sizes. I don't think it will change my life, but it's the sort of bizarre thing I love to know.

Here's a puzzle to go with the angels on a pinhead: the psalmist writes "How precious to me are your thoughts, O God! How vast is the sum of them! Were I to count them, they would outnumber the grains of sand." Is he implying that God's thoughts are very many but finite, or are they countably infinite?

Even if they are countably infinite, this is only the smallest size of infinity and I wonder if is somewhat heretical to suggest that God (who is "that than which nothing greater can be conceived") should have his thoughts limited to the smallest size of infinity?

Blessings,
Fiona Jenkins

Dear Fiona,

The number of grains of sands is finite, but large. The psalmist is saying is that God's thoughts are more numerous - but not whether they are finite or infinite, and if infinite of what cardinal number. The next line in Psalm 139:18 is a problem: does "were I to come to the end I would still be with you" imply that the psalmist might eventually finish counting God's thoughts, which would mean they were finite? Or does he mean that the counting process might enumerate them all, in which case they'd be countably infinite? Or does he really envisage that the infinity might be uncountable? It's difficult to know - he didn't think in those terms.

I tend to agree it might be heretical to suggest that God's thoughts might be only countably infinite.

However, I have a difficulty with your statement about God. To speak of God as "that than which nothing greater can be conceived" is fundamentally a negative statement, and just as Cantor sought a positive definition of infinity I think we need a positive idea of God. Otherwise we get a paradox: "If 'God' created everything, who created 'God'? It is possible to conceive of a being which would be the creator of 'God', and this being would be greater than 'God', which contradicts the premise that nothing greater than 'God' can be conceived. It therefore follows that 'God' doesn't exist." The ancient Greeks realized this problem: their gods needed to have "titans" who created them. But who created the titans? In no time you'd get an infinite sequence of beings each of which created its predecessor ... oops, infinite numbers again!

Yours ever,
John Hartley

	*St Luke's Church, Eccleshill - The Link* magazine** The Link is published monthly at 40p (Senior Citizens 35p), and we deliver free within the parish and post copies (at the reader's expense) to those who request it. Please contact us if you would like a free copy for a trial period. September 2004, Page 2.
Home Page. Index of articles: by subject, by date. In this issue: (September 2004) Alpha, Infinity (2), Jeremiah, Deanery Plan. Infinity (1). Other articles on logic etc.	The infinite thoughts of God? Dear John, Last month you wrote "there are different sizes of infinity." What a wonderful piece of information! I never realised that infinity came in different sizes. I don't think it will change my life, but it's the sort of bizarre thing I love to know. Here's a puzzle to go with the angels on a pinhead: the psalmist writes "How precious to me are your thoughts, O God! How vast is the sum of them! Were I to count them, they would outnumber the grains of sand." Is he implying that God's thoughts are very many but finite, or are they countably infinite? Even if they are countably infinite, this is only the smallest size of infinity and I wonder if is somewhat heretical to suggest that God (who is "that than which nothing greater can be conceived") should have his thoughts limited to the smallest size of infinity? Blessings, Fiona Jenkins Dear Fiona, The number of grains of sands is finite, but large. The psalmist is saying is that God's thoughts are more numerous - but not whether they are finite or infinite, and if infinite of what cardinal number. The next line in Psalm 139:18 is a problem: does "were I to come to the end I would still be with you" imply that the psalmist might eventually finish counting God's thoughts, which would mean they were finite? Or does he mean that the counting process might enumerate them all, in which case they'd be countably infinite? Or does he really envisage that the infinity might be uncountable? It's difficult to know - he didn't think in those terms. I tend to agree it might be heretical to suggest that God's thoughts might be only countably infinite. However, I have a difficulty with your statement about God. To speak of God as "that than which nothing greater can be conceived" is fundamentally a negative statement, and just as Cantor sought a positive definition of infinity I think we need a positive idea of God. Otherwise we get a paradox: "If 'God' created everything, who created 'God'? It is possible to conceive of a being which would be the creator of 'God', and this being would be greater than 'God', which contradicts the premise that nothing greater than 'God' can be conceived. It therefore follows that 'God' doesn't exist." The ancient Greeks realized this problem: their gods needed to have "titans" who created them. But who created the titans? In no time you'd get an infinite sequence of beings each of which created its predecessor ... oops, infinite numbers again! Yours ever, John Hartley
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