Dear Fis Colleagues, I received this comment on Lucas's argument that seems to me short and sweet, so I am posting it for our general edification.
Best wishes, Alex ---------- Forwarded message ---------- “Proving” that we are not machines is somewhat quixotic from my point of view, in that it should be obvious that we are not machines! But so many people imagine that we could be nothing more than mechanisms that the Lucas-Godelian argument is helpful. But let us look at this argument. We start by assuming that I am a consistent Turing machine (CTM) (consistency being needed to apply Godel’s Theorem.) If I am a CTM, then I can be completely specified by at text T which I put out on the table here in front of me. And I then apply the Godel argument to T, producing a Theorem G that T cannot prove, but that I can prove. But I am identical with T. SO this is a contradiction. We have contradicted that I am a CTM. Therefore I am not a CTM. I cannot be a Consistent Turing Machine. If I am consistent then I am not a Turing machine. Otherwise I might be an inconsistent Turing machine. The argument shows that I must be consistent in order to conclude that I am not a Turing machine. I believe that I am consistent. I conclude that I am not a consistent Turing machine. And being consistent, I am not an inconsistent Turing machine. Therefore, I am not a Turing machine. (P.S. Another champion of the Lucas viewpoint is Roger Penrose in his books “The Emperor’s New Mind” and “Shadows of the Mind”.) -- Alex Hankey M.A. (Cantab.) PhD (M.I.T.) Distinguished Professor of Yoga and Physical Science, SVYASA, Eknath Bhavan, 19 Gavipuram Circle Bangalore 560019, Karnataka, India Mobile (Intn'l): +44 7710 534195 Mobile (India) +91 900 800 8789 ____________________________________________________________ 2015 JPBMB Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy <http://www.sciencedirect.com/science/journal/00796107/119/3>
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