Abstract
Gödel appears to have believed strongly that the human mind cannot be explained in
terms of any kind of computational physics, but he remained cautious in formulating
this belief as a rigorous consequence of his incompleteness theorems. In this chapter,
I discuss a modification of standard Gödel-type logical arguments, these appearing to
strengthen Gödel’s conclusions, and attempt to provide a persuasive case in support of
his standpoint that the actions of the mind must transcend computation.
It appears that Gödel did not consider the possibility that the laws of physics might
themselves involve noncomputational procedures; accordingly, he found himself driven
to the conclusion that mentality must lie beyond the actions of the physical brain. My
own arguments, on the other hand, are from the scientific standpoint that the mind is
a product of the brain’s physical activity. Accordingly, there must be something in the
physical actions of the world that itself transcends computation.
We do not appear to find such noncomputational action in the known laws of
physics, however, so we must seek it in currently undiscovered laws going beyond
presently accepted physical theory. I argue that the only plausibly relevant gap in current
understanding lies in a fundamental incompleteness in quantum theory, which reveals
itself only with significant mass displacements between quantum states (“Schrödinger’s
cats”). I contend that the need for new physics enters when gravitational effects just
begin to play a role. In a scheme developed jointly with Stuart Hameroff, this has direct
relevance within neuronal microtubules, and I describe this (still speculative) scheme
in the following.