Ron Chrisley - Simulation and indexical function individuation

Simulation and indexical function individuation: Why the diagonal argument does not establish the impossibility of machine consciousness

Diagonal arguments against algorithmic accounts of consciousness date back to Lucas, Turing and Gödel. Penrose’s formulation, which is the focus of this talk, uses the notion of a "Turing Machine Non-Halting Question” to establish not only the impossibility of algorithmic consciousness, but the impossibility of a digital computer to even simulate the behaviour of, e.g., conscious human mathematicians. I show that Penrose’s negative conclusions do not follow from his formal results. In particular, I show that 1) x can perfectly simulate y even if x and y do not compute the same class of functions; and 2) x can be conscious even if there exist conscious agents y that x cannot simulate. I establish 1) by a) characterizing the class of (Turing) computational systems as members of a more general class of question-answering systems; b) showing that for every class of question-answering systems (even finite ones) there exists a question relatively isomorphic to the original Turing Non-Halting Question, and c) showing how two question-answering systems may compute different functions, extensionally construed and yet compute the same class of functions, indexically intentionally construed. These results thus make (mathematical) room for the algorithmic generation of conscious behaviour.