An interesting quote from Dean L. Overman’s Evidence for the Existence of God (Rowman and Littlefield: 2009):

There are real limits to any formal reasoning system attempting something in the nature of a mathematical proof.  Science and faith share a common belief that what we see as normal reality is not actual reality; the observable has something more fundamental hidden behind it.  This may be part of the reason a compelling proof of God’s existence or non-existence may not be possible.  Certainty in this world may not only be unknowable (to use Chaitin’s term) but is also unavailable.  This does not mean that an argument cannot be rational and plausible, but perhaps it cannot compel one to choose in a certain direction.

The result of these deeply embedded undecidable fundamentals in mathematics and all formal reasoning systems is that everyone has to make Pascal’s Wager or Kierkegaard’s leap of faith.  There are no exemptions.  Because abstention is a vote, agnosticism is not a real option.  Everyone lives and dies with a faith, whether the faith is theistic or naturalistic.  This is the way our reality appears to be structured, and everyone ultimately makes a choice, whether that choice is passive or active. (p.183)

Overman bases a good chunk of his argument on concepts of mind and consciousness related to quantum mechanics, and to the ideas derived from Godel’s incompleteness theorem in mathematics.