Lucas Against Mechanism II: A Rejoinder

Extract

David Lewis criticizes an argument I put forward against mechansim on the grounds that I fail to distinguish between O_L, Lucas's ordinary potential arithmetic output, and O^M_L, Lucas's arithmetical output when accused of being some particular machine M; and correspondingly, between O_M the ordinary potential arithmetic output of the machine M, and O^N_M, the arithmetic output of the machine M when accused of being a particular machine N. For any given machine, M, N, O, P, Q, R,... etc., I can in principle (my critics are often very charitable in speaking as though I could in practice, but let me revert to an ideal mind) calculate a Godel sentence for that machine - indeed infinitely many, depending on the Godel numbering scheme adopted. The Godel sentence of a particular machine can, I claim, be seen to be true, if that machine is adequate for Elementary Peano Arithmetic. Hence, if I were accused of being M, I can on that supposition see that the Godel sentence of M is true, since I am capable of Elementary Peano Arithmetic and the machine M is said to be an adequate characterization of me.