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I can't imagine how this can be retold briefly and clearly, so I'll give you links that will help you understand.
First, a quote from the novel:
Five Proofs – a reference to the famous work of Thomas Aquinas Summa of Theology in which he gives five proofs of the existence of God:
Here, on the wiki, is a summary of them.
I can offer a brief popular summary of Immanuel Kant's thoughts on this subject here, at Kuraev's.