Truth, Existence and Explanation pp 17-38 | Cite as

# Penrose’s *New Argument* and Paradox

## Abstract

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.

## Notes

### Acknowledgements

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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