The place of scientific experience
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In the Bible Paul says "in the wisdom of God the world by wisdom knew not God" (1 Corinthians 1:21 AV)
Does this mean that we cannot use scientific arguments to prove that a Creator exists? Is it a fair reading to extrapolate to "in the wisdom of God the world by wisdom [cannot know] God"?
This would mean that it's impossible to prove that God exists. I.e. we need faith too.
Would this have any implications for Intelligent Design ?
I don't think it has any negative implications for ID, I think its the other way around personally. Check Romans 1.
Romans 1:20 — For since the creation of the world God's invisible qualities – his eternal power and divine nature – have been clearly seen, being understood from what has been made, so that men are without excuse.
See The Design Argument in the Bible.
An attempted mathematical proof that God exists (by Kurt Goedel, a very good mathematician) is described in the Wikipedia at Goedel's ontological proof