Are the Gödel incompleteness theorems limitative results for the neurosciences?
Jeff Buechner
Journal of Biological Physics January 2010 DOI: 10.1007/s10867-009-9160-1 (opens in new tab)
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AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that neuroscience and molecular, systems, and synthetic biology may well avoid mathematical limitative results derived from the Gödel incompleteness theorems, and that demonstrating the limits cannot be avoided is a computational task beyond the capacities of finitary minds. The author also reformulates three philosophical claims about consciousness using the incompleteness theorems and argues these reformulations can be disarmed. |
Abstract
There are many kinds of limitative results in the sciences, some of which are philosophical. I am interested in examining one kind of limitative result in the neurosciences that is mathematical-a result secured by the Gödel incompleteness theorems. I will view the incompleteness theorems as independence results, develop a connection with independence results in set theory, and then argue that work in the neurosciences (as well as in molecular, systems and synthetic biology) may well avoid these mathematical limitative results. In showing this, I argue that demonstrating that one cannot avoid them is a computational task that is beyond the computational capacities of finitary minds. Along the way, I reformulate three philosophical claims about the nature of consciousness in terms of the Gödel incompleteness theorems and argue that these precise reformulations of the claims can be disarmed.