RE Bruno Marchal: Gödel's theorem implies that machines which are looking at themselves (in a precise technical sense) develop a series of distinct phenomenologies (arguably corresponding to justifiable, knowable, observable, sensible).
ME: I find this a fascinating observation in that you are making a phenomenological association with a self-referential kind of machine. However, from the perspective of my proposal, surely your classes of machine are not operating from a critical instability where the information states themselves have the self-referential property embedded within them. Or are they? Or some of them? The question then arises whether such a machine could exhibit a capacity to "reason about" a problem, which it had been posed, and so tackle the problem as one of a member of.a class of similar problems? It is certainly true in mathematics that the human mind possesses such abilities to an outstanding extent: not only the ability to comprehend a problem, and secondly the ability to see the problem as a member of (in the context of) a class of similar problems, but also the ability to *generalize *a problem, and so *create* a class of similar problems as a context within which more general reasoning processes can be applied to solve the problem in question. An example of such an approach is given by the Taniyama-Shimura conjecture, "Each Elliptical Function is equivalent to a particular Modular Form", one step of the path followed by Andrew Wiles to prove Fermat's last theorem between 1986 and 1994. Does this not also illustrate aspects of the discussion of Godel's theorem, where Maxine has extensively quoted semantic objections to Godel's statement on the grounds (as I understand her) that it could not be construed as a direct product of phenomenological experience. May I say that I would not regard my paraphrase of Maxine's reason as a valid objection because I do not expect statements in mathematics to conform to requirements for statements to be considered phenomenological. The sentential calculus is constructed within the category of sets, and Frege and Russell and Whitehead were operating within that framework, as was Godel. I personally do not regard the category of sets as a valid framework for phenomenology. My construction of a new information theory appropriate to describe phenomenological experience specifically denies it. The sentential calculus of Frege & co has no bite - it is superficial and not the enamel required to start up the mind's intellectual digestion and absorption processes. -- 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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