Abstract
This paper intervenes in an argument over the number of thoughts that could be thought. The argument has important implications for supervenience physicalism, the thesis that all is physical or supervenient on the physical. If, per quantum mechanics, the number of possible physical states is finite while the number of possible thoughts is infinite, then the latter exceeds the former in number, and supervenience phyicalsim fails. Abelson (1970) first argued that possible thoughts are infinite as we can think of any of the infinite natural numbers. Subsequently, physicist Max Tegmark (2009b) argued that we cannot think of all the numbers there are, that some are simultaneously too large and too nondescript to reference. Porpora (2013) offered a brief proof countering Tegmark. Curtis (2015) then countered Porpora, arguing that Porpora’s argument runs afoul of the Berry paradox. This paper shows that while Curtis does offer an analogous proof that does fall prey to the Berry paradox, Porpora’s does not. The result reinstates Porpora’s argument with all its implications for supervenience physicalism and offers a clearer lesson from the Berry Paradox.
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Abelson, R. (1970). A refutation of mind-body identity. Philosophical Studies, 21(6), 85–90.
Clatterbaugh, K. C. (1972). A reply to an attempted refutation of mind-body Identity. Philosophical Studies, 23(1–2), 111–112.
Curtis, B. L. (2015). On there being infinitely many thinkable thoughts: a reply to Porpora and a defence of Tegmark. Philosophia, 43(1), 35–42.
French, J. D. (1988). The false assumption underlying berry’s paradox. The Journal of Symbolic Logic, 53(4), 1220–1223.
Grünbaum, A. (1972). Abelson on Feigl’s mind-body identity thesis. Philosophical Studies, 23(1–2), 119–121.
Grover, D. (1983). Berry’s paradox. Analysis, 43(4), 170–176.
Michaelson, Eliot and Marga Reimer (2019) "Reference." The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.). https://plato.stanford.edu/archives/spr2019/entries/reference/. Accessed 23 Jan 2021.
Pinter, C. C. (1971). Set theory. Addison-Wesley.
Porpora, D. V. (2013). How many thoughts are there? Or why we likely have no Tegmark duplicates 1010^115 m away. Philosophical studies, 163(1), 133–149.
Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology. New York: Oxford.
Stoljar, D. (2015). Physicalism. The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), Edward N. Zalta (ed.). https://plato.stanford.edu/archives/win2017/entries/physicalism/. Accessed 23 Jan 2021.
Tegmark, M. (2003). Parallel universes. Scientific American (May) 41–53.
Tegmark, M. (2009a). The Inflationary Multiverse. In Carr (ed.) Universe or multiverse? Cambridge: Cambridge University Press.
Tegmark, M. (2009b) http://space.mit.edu/home/tegmark/crazy.html. Accessed 19 Aug 2011.
Tipler, F. J. (1995). The physics of immortality. New York: Anchor.
Wadia, P. S. (1972). On ‘A Refutation of Mind-Body Identity.’ Philosophical Studies, 23(1–2), 113–115.
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I wish to thank Michael Anderson, Andrew Knight, Paul Tappenden, and an anonymous reviewer for very helpful comments on a prior draft of this paper.
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Porpora, D.V. Supervenience Physicalism and the Berry Paradox. Philosophia 49, 1681–1693 (2021). https://doi.org/10.1007/s11406-021-00324-8
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DOI: https://doi.org/10.1007/s11406-021-00324-8