Penrose’s New Argument and Paradox
In this paper we take a closer look at Penrose’s New Argument for the claim that the human mind cannot be mechanized and investigate whether the argument can be formalized in a sound and coherent way using a theory of truth and absolute provability. Our findings are negative; we can show that there will be no consistent theory that allows for a formalization of Penrose’s argument in a straightforward way. In a second step we consider Penrose’s overall strategy for arguing for his view and provide a reasonable theory of truth and absolute provability in which this strategy leads to a sound argument for the claim that the human mind cannot be mechanized. However, we argue that the argument is intuitively implausible since it relies on a pathological feature of the proposed theory.
This work was supported by the European Commission through a Marie Sklodowska Curie Individual Fellowship (TREPISTEME, Grant No. 703529). I wish to thank Catrin Campbell-Moore, Martin Fischer, Leon Horsten, Peter Koellner, Carlo Nicolai, and an anonymous referee for helpful comments on the content of this paper. Earlier versions of the paper were presented at the FSB Seminar in Bristol, the Fourth New College Logic Meeting, the University of Malaga and the Third Leuven-Bristol Workshop. I thank the audiences of these talks for their feedback.
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