<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Dear Alex,<div class="">Thank you for this very balanced viewpoint about this part of the debate.</div><div class=""><br class=""></div><div class="">You write "<span style="font-size: 12.8px;" class="">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. </span><font size="2" class="">“</font></div><div class=""><font size="2" class=""><br class=""></font></div><div class=""><font size="2" class="">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.</font></div><div class=""><font size="2" class="">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</font></div><div class=""><font size="2" class="">(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).</font></div><div class=""><font size="2" class="">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. </font><span style="font-size: small;" class="">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 </span><font size="2" class="">unknown of their self-application.</font></div><div class=""><font size="2" class=""><br class=""></font></div><div class=""><font size="2" class="">Thank you again,</font></div><div class=""><font size="2" class="">Lou Kauffman</font></div><div class=""><font size="2" class=""><br class=""></font><div><blockquote type="cite" class=""><div class="">On May 11, 2016, at 1:44 PM, Alex Hankey <<a href="mailto:alexhankey@gmail.com" class="">alexhankey@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">Dear Colleagues, <div class=""><br class=""></div><div class="">This discussion is continuing to be very enlightening, I feel, </div><div class="">for those aware of, but not intimately familiar with, details of </div><div class="">both Husserl's approach and <span style="font-size:12.8px" class="">Gödel’s </span>statements / theorems. </div><div class=""><br class=""></div><div class="">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. </div><div class=""><br class=""></div><div class="">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. </div><div class=""><br class=""></div><div class=""><span style="font-size:12.8px" class="">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. </span><br class=""></div><div class=""><span style="font-size:12.8px" class=""><br class=""></span></div><div class=""><span style="font-size:12.8px" class="">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. </span></div><div class=""><span style="font-size:12.8px" class=""><br class=""></span></div><div class=""><span style="font-size:12.8px" class="">They are categorically different (linguistic?) structures.</span></div><div class=""><span style="font-size:12.8px" class="">Or have I snafued?</span></div><div class=""><br class=""></div><div class="">Alex</div><div class=""> </div><div class=""><br class=""></div><div class=""><br clear="all" class=""><div class=""><br class=""></div>-- <br class=""><div class="gmail_signature"><div dir="ltr" class=""><div class=""><span style="font-family:arial,sans-serif;font-size:13px;border-collapse:collapse" class="">Alex Hankey M.A. (Cantab.) PhD</span><span style="font-family:arial,sans-serif;font-size:13px;border-collapse:collapse" class=""> (M.I.T.)<br class="">Distinguished Professor of Yoga and Physical Science,<br class="">
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