> For one, the uncertainty principle suggests there is no exact, fully determined reality.
Absolutely not! The uncertainty principle suggests that position and momentum are inappropriate descriptions of reality. The quantum mechanical wave function would be a complete description, if quantum mechanics was all there is to reality.
> Second, Goedel showed us that logical systems are either incomplete or inconsistent.
He didn't. He showed us that finite theories in sufficiently powerful logical systems, specifically number theory expressed in first order logic, admit multiple models. Turning this into "any theory of the universe will be incomplete" is playing fast and lose with the meaning of the word "incomplete".
Absolutely not! The uncertainty principle suggests that position and momentum are inappropriate descriptions of reality. The quantum mechanical wave function would be a complete description, if quantum mechanics was all there is to reality.
> Second, Goedel showed us that logical systems are either incomplete or inconsistent.
He didn't. He showed us that finite theories in sufficiently powerful logical systems, specifically number theory expressed in first order logic, admit multiple models. Turning this into "any theory of the universe will be incomplete" is playing fast and lose with the meaning of the word "incomplete".