By the way, the argument below was sent to me by Lou Kauffman. On 4 May 2016 at 20:11, Alex Hankey <alexhan...@gmail.com> wrote:
> 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> > -- 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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