| dc.description.abstract | In 1931, Kurt Gödel proved his revolutionary incompleteness theorems, which demonstrate that formal mathematical systems are fundamentally limited in regards to what they can prove. While they are strictly mathematical results, they are sometimes argued to imply that a computational model cannot exactly model the human mind. Such arguments, often called Gödelian arguments against mechanism, attempt to show that the human mind is not limited in the way formal systems are as demonstrated by the incompleteness theorems.
This thesis examines two influential Gödelian arguments which are both shown to be unsuccessful. The first is by J. R. Lucas, an argument appealing to intuition, yet it makes a severe mistake of unjustifiably assuming consistency of the mind. Lucas argues that we as human beings can ``grasp" that the Gödel sentence is true; however, there is serious reason to doubt this claim. The second Gödelian argument considered is by Storrs McCall. This is a more sophisticated argument based on the claim that while the truth value of the Gödel sentence is unknown to us, we can see that it diverges from its provability. Understanding this divergence, McCall argues, is a demonstration of a uniquely human ability. McCall makes several mistakes in his argumentation as well, which causes him to fail in refuting mechanism.
Finally, I cautiously present an argument for why mechanism may never be disproven by an argument from the incompleteness theorems. Since a Gödelian argument must contain a claim of the mind being able to prove or understand something a machine cannot, it must make precise claims about how the mind deduces and reasons. Our knowledge of the human mind, I argue, is extremely unlikely to ever be precise enough and the anti-mechanist may be wise to look beyond Gödel’s work for an argument in support of his claim. | |
