Philosophical Essay on Human Cognition and Gödel’s Theorem

206 Are the Androids Dreaming Yet? If humans used a formal system to think, they would be limited by the incompleteness theorem and unable to discover new theorems that required them to extend the formal rules. Humans do not appear to have such a limitation and regularly extend their appreciation of mathematics by expanding the rules, and seeing through to the truth. Many scientists dislike this argument and think it farfetched, saying there is no evidence to show people see past the limitation. Our brains could be following a formal system capable of discovering everything we have discovered to date or, indeed, might encounter in the future. Why should we assume human minds are constrained in the same way as the mathematical systems they discover? There is no evidence to suggest a human thinking about Peano arithmetic is running a Peano based model in their head. When Peano discovered his theorem he was certainly extending our mathematical knowledge, but this does not imply he was extending the capability of his brain. The critics of Lucas and Penrose have one big problem to deal with. The formal system in our head would need to be able to see the truth in everything we could ever encounter. But, our formal system appears to be small. As infants, it is almost nonexistent. Where does this enormous system come from? It can’t come from our parents because they have the same problem; they were once children. You might argue that the capability of the human brain is huge and we can learn from all the other humans on earth, but let me remind you what Godel said. However large Two Giants HOUSE_OVERSIGHT_015896