<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"><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 Terrence,<div class="">Condsider the Russell paradox. </div><div class="">Russell set is R = { x a set | x is not a member of itself}.</div><div class=""><br class=""></div><div class="">If instead we define</div><div class=""><br class=""></div><div class="">R = { x a set | x is not a member of itself, and x is defined PRIOR TO THE APPLICATION OF THIS DEFINITION}</div><div class=""><br class=""></div><div class="">then R is not a member of itself since it occurs AFTER the definition. </div><div class=""><br class=""></div><div class="">The definition itself provides a definition of before and after like the mirror in the Barber resolution.</div><div class=""><br class=""></div><div class="">Of course for this temporal interpretation, a new NOW comes into play every time the definition is activated. </div><div class="">Activation can be done by any cognizer of the definition.</div><div class="">Or it can be formalized by R_{t+1} = {x| x is a set that has been defined by time t}.</div><div class="">Then we could have</div><div class="">R_{0} = { }</div><div class="">R_{1} = { R_{0} } = { { } }</div><div class="">R_{3} = {R_{0}}, R_{1}} = {{}, {{}} }</div><div class="">…</div><div class="">For mathematical purposes the … can continue transfinitely to as high an ordinal as one wants.</div><div class=""><br class=""></div><div class="">The analogy with the mirror is the cut between BEFORE and AFTER.</div><div class="">Note that the definition </div><div class=""> R = { x a set | x is not a member of itself, and x is defined PRIOR TO THE APPLICATION OF THIS DEFINITION}</div><div class="">is still self-referential. </div><div class="">It is the temporal unfolding of this self-reference that leads to the temporality in the sense of successive times.</div><div class=""><br class=""></div><div class="">Best,</div><div class="">Lou Kauffman</div><div class="">P.S. I think this uses up my quota of responses for this week.</div><div class=""><br class=""><div class=""><blockquote type="cite" class=""><div class="">On Oct 25, 2017, at 2:13 PM, Terrence W. DEACON <<a href="mailto:deacon@berkeley.edu" class="">deacon@berkeley.edu</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">Adding a temporal dimension has often been offered as a way out of paradox in quasi-physical terms. This is because interpreting paradoxical logical relations or calculating their values generally produces interminably iterating self-contradicting or self-undermining results. Writers from G. S. Brown to Gregory Bateson (among others) have pointed out that one can resolve this in *process* terms (rather than assuming undecidable values) by focusing on this incessant oscillation itself (i.e. a meta-analysis that recognizes that the process of operating on these relations cannot be neglected).Using this meta-analysis one can take advantage of the dynamic that calculation or intepretation entails. It is also, of course, the way we make use of so-called imaginary values in mathematics, whose iteratively calculated results incessantly reverse sign from negative to positive. By simply accepting this fact as given and marking it with a distinctive token (e.g. "<i class="">i</i>" ) effectively generates an additional dimension that is useful in a wide range of applications from fourier to quantum analyses. So my question is whether using this mirror metaphor can be seen as a variant on this general approach. It also resonates with efforts to understand the interpretation of information in related terms (e.g. using complex numbers).<div class=""><br class=""></div><div class="">— Terry</div><div class=""><br class=""></div><div class="">PS A bit of reflection (no pun intended) also suggests that it is also relevant to our discussions about agency (which like the concept of "information" must be understood at different levels that need to be distinguished because they can easily be confused). My earlier point about the normative aspect of agency (and consistent with the previously posted URL to the paper by Barandiaran et al.) is that this implies the need for incessant contrary work to negate perturbation away from some "preferred" value or state. Although there can be many levels of displaced agency in both natural and artificial agents (like cybernetic systems such as thermostats and many biological regulative subsystems), there cannot be interminable regress of this displacement to establish these norms. At some point normativity requires ontological grounding where the grounded normative relation is the preservation of the systemic physical properties that produce the norm-preserving dynamic. This is paradoxically circular—a "strang loop" in Hofstadter's lingo. This avoids vicious regress as well avoiding assuming a cryptic "observer perspective." But it therefore requires that we treat different levels and degrees of "normative displacement" differently from one another. This both echoes Loet's point that we should not expect a single concept of agency, but it alternatively suggest that we may be able to construct a nested hierarchy of agency concepts (as Stan might suggest). So I glimpse that a set of parallel and converging views may underlie these superficially different domains of debate.</div></div><div class="gmail_extra"><br class=""><div class="gmail_quote">On Wed, Oct 25, 2017 at 2:45 AM, Krassimir Markov <span dir="ltr" class=""><<a href="mailto:markov@foibg.com" target="_blank" class="">markov@foibg.com</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear Lou, Bruno, and FIS Colleagues,<br class="">
<br class="">
Thank you for nice and polite comments to my post about “Barber paradox”.<br class="">
<br class="">
First of all, the main idea of the post was not to solve any paradox but<br class="">
to point two very important operations of Infos:<br class="">
- Direct reflection;<br class="">
- Transitive (indirect) reflection.<br class="">
There are no other ways for Infos to collect data from environment.<br class="">
<br class="">
Second, the example with paradox had shown the well known creative<br class="">
approach in the modeling - adding new dimensions in the model could help<br class="">
to better understand the modeling object or process. For instance:<br class="">
<br class="">
If our linear model contains a “paradox” point “X”:<br class="">
<br class="">
//////X//////<br class="">
<br class="">
by adding a new second dimension it may be explained and the paradox would<br class="">
be solved:<br class="">
<br class="">
\<br class="">
/////////////<br class="">
-------------<br class="">
//////X//////<br class="">
<br class="">
<br class="">
Friendly greetings<br class="">
Krassimir<br class="">
<br class="">
<br class="">
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</blockquote></div><br class=""><br clear="all" class=""><div class=""><br class=""></div>-- <br class=""><div class="gmail_signature" data-smartmail="gmail_signature">Professor Terrence W. Deacon<br class="">University of California, Berkeley</div>
</div>
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