Are We Paraconsistent? On the Luca-Penrose Argument and the Computational Theory of Mind

I argue that if we are Turing machines, as the Computational Theory of Mind (CTM) holds, then we are paraconsistent, i.e. we do not implement classical logic as canonical versions of the CTM generally hold (or assume). I then show that this claim presents a serious challenge to the Lucas-Penrose argument (Lucas 1961, Penrose 1989, 94), as it collapses Lucas-Penrose into a disjunction (in a manner reminiscent of Benacerraf's (1967) famous objection to LucasPenrose). Specifically, whereas Lucas-Penrose concludes that we are not Turing machines, I show that the most one can conclude from the argument is that either we are not Turing machines or we are Turing machines implementing a nonclassical logic. In 'Minds, Machines and Gödcl,' J.R. Lucas (1961) put forth an argument against any mechanistic theory of mind that attempts to equate the human brain with a Turing machine (TM). Roughly, Lucas reasoned: (1) no consistent formal system (or TM implementing a formal system) can decide the Gödcl sentence ('I am not provable'), (2) the human mind can decide the Gödel sentence (i.e. we can look and see the truth of the sentence), therefore (3) the human mind cannot be a TM. Lucas' argument remains relevant—and continues to generate debate—as: (1) it can be taken as an attack on the enormously influential Computational Theory of Mind (CTM), and (2) Lucas' argument has been revived, defended and expanded in two recent books by R. Penrose (1989,94). Here, I argue that if we are in fact TMs, we implement a paraconsistent logic, and not a classical logic (FOL), as canonical versions of the CTM generally hold (or implicitly assume). I show that simply raising this possibility is enough to defeat Lucas' attempt to respond to Putnam's (1960,95) devastating criticism of Auslegung, Vol. 27, No. 1