My former advisor Leonard Adleman, the 'A' in the RSA encryption algorithm and the inventor of DNA-based computation, has written up an interesting article that he thinks may shed some light on the relationship between mathematical logic and quantum mechanics. You can read about it over at Clifford V. Johnson's blog Asymptotia. Here is the link.
The Quantum Pontiff pontificates on Adleman's article here. The comment section is full of interesting references and insights. I highly recommend reading it.