Theodor Nenu

This article purports to establish the philosophical inappropriateness of using established theorems in mathematical logic, such as Gödel's (1931) first incompleteness theorem, in order to conclude that human minds have a non-algorithmic nature. First, I will argue that the ongoing debate in the philosophy of mathematics concerning absolute provability is fully independent of the question whether our brains are biologically instantiated computers or not. Second, through a combination of evolutionary considerations and the phenomenon of vagueness, I will demonstrate the fragility of the ill-defined notion of an idealized mathematical mind, which plays a key role in the anticomputationalist arguments. Third, I will make the case that all these arguments adopt a psychologically implausible conception of the nature of the high-level algorithms behind our mathematical abilities. Lastly, I look at the recent advances in artificial intelligence in order to illustrate the philosophical sleight of hand on which the anticomputationalist argument operates.

Hofstadter [1979, 2007] offered a novel Gödelian proposal which purported to reconcile the apparently contradictory theses that (1) we can talk, in a non-trivial way, of mental causation being a real phenomenon and that (2) mental activity is ultimately grounded in low-level rule-governed neural processes. In this paper, we critically investigate Hofstadter’s analogical appeals to Gödel’s [1931] First Incompleteness Theorem, whose “diagonal” proof supposedly contains the key ideas required for understanding both consciousness and mental causation. We maintain that bringing sophisticated results from Mathematical Logic into play cannot furnish insights which would otherwise be unavailable. Lastly, we conclude that there are simply too many weighty details left unfilled in Hofstadter’s proposal. These really need to be fleshed out before we can even hope to say that our understanding of classical mind-body problems has been advanced through metamathematical parallels with Gödel’s work.