Godel demonstrated that every logical scheme, including mathematics, is dependent upon axioms that it cannot prove and that cannot be reduced to the scheme itself.
Intelligent design itself does not have any content… Much of what I've written about has been in reaction to the materialist superstition, the belief that the universe is a purely material phenomenon that can be reduced to physical and chemical laws. It's a concept that's infected the social sciences as well.
Academic scientists of any sort expect to be struck by lightning if they celebrate real creation de novo in the world.