Dear Alex, Thank you for this very balanced viewpoint about this part of the debate.
You write "Although formal systems are designed to apply to concepts within the world of thought i.e. the world of (abstract) phenomenal experience, they are not intended to have semantic application, but only syntactical consistency. To judge their validity or invalidity from a semantic (or even semiotic) perspective of Husserlian phenomena - experience, therefore seems to me to be inappropriate. “ From the point of view of a practicing mathematician the matter is a bit more complex. For we certainly are interested in the semantics of our formalities. We do not regard what we do as purely syntactical. There are meanings involved. For example one interprets algebra (quite formal) in terms of geometry (often quite intuitive) and one may think philosophically about the meanings of the Goedelian limitations on formal systems. Furthermore the most basic mathematical concepts such as the number three are highly conceptual and are understood that way (through the appearance of triples in both the mental and physical realms). The point of having good formalisms is sthat the formalism should have the least possible necessary interpretation and this leads to the multiplicity of interpretations that makes mathematics so fruitful. Think of the number of ways to interpret a second order linear differential equation, from fluid flow, to electricity to the oscillations of a pendulum. The point of nearly uninterpreted formalisms is that they are PATTERNS that can occur in many situations and lead us into the unknown including the internal unknown of their self-application. Thank you again, Lou Kauffman > On May 11, 2016, at 1:44 PM, Alex Hankey <alexhan...@gmail.com> wrote: > > Dear Colleagues, > > This discussion is continuing to be very enlightening, I feel, > for those aware of, but not intimately familiar with, details of > both Husserl's approach and Gödel’s statements / theorems. > > I suspect that part of the problem lies in the fact that we are dealing with > a highly contrasting pair of intellectual discussions, about two entirely > different universes of analysis (if that is the right term). I suspect that > they may not be compatible, and that that is the real cause for the conflict > of perspectives. > > Husserl was concerned with formulating a philosophically rigorous discussion > of the world of experience, from within the world of experience, and set up > his criteria on that basis. > > Gödel on the other hand was operating within the world of formal systems, and > showed that if a set of axioms containing arithmetic was consistent, it had > to be incomplete - valid statements could be made that are not derivable > within the formal system. > > Although formal systems are designed to apply to concepts within the world of > thought i.e. the world of (abstract) phenomenal experience, they are not > intended to have semantic application, but only syntactical consistency. To > judge their validity or invalidity from a semantic (or even semiotic) > perspective of Husserlian phenomena - experience, therefore seems to me to be > inappropriate. > > They are categorically different (linguistic?) structures. > Or have I snafued? > > Alex > > > > > -- > 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>_______________________________________________ > Fis mailing list > Fis@listas.unizar.es > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
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