Supervenience Physicalism and the Berry Paradox

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.