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
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
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