Dear Terrence, Condsider the Russell paradox. Russell set is R = { x a set | x is not a member of itself}.

If instead we define R = { x a set | x is not a member of itself, and x is defined PRIOR TO THE APPLICATION OF THIS DEFINITION} then R is not a member of itself since it occurs AFTER the definition. The definition itself provides a definition of before and after like the mirror in the Barber resolution. Of course for this temporal interpretation, a new NOW comes into play every time the definition is activated. Activation can be done by any cognizer of the definition. Or it can be formalized by R_{t+1} = {x| x is a set that has been defined by time t}. Then we could have R_{0} = { } R_{1} = { R_{0} } = { { } } R_{3} = {R_{0}}, R_{1}} = {{}, {{}} } … For mathematical purposes the … can continue transfinitely to as high an ordinal as one wants. The analogy with the mirror is the cut between BEFORE and AFTER. Note that the definition R = { x a set | x is not a member of itself, and x is defined PRIOR TO THE APPLICATION OF THIS DEFINITION} is still self-referential. It is the temporal unfolding of this self-reference that leads to the temporality in the sense of successive times. Best, Lou Kauffman P.S. I think this uses up my quota of responses for this week. > On Oct 25, 2017, at 2:13 PM, Terrence W. DEACON <dea...@berkeley.edu > <mailto:dea...@berkeley.edu>> wrote: > > 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" ) 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). > > — Terry > > 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. > > On Wed, Oct 25, 2017 at 2:45 AM, Krassimir Markov <mar...@foibg.com > <mailto:mar...@foibg.com>> wrote: > Dear Lou, Bruno, and FIS Colleagues, > > Thank you for nice and polite comments to my post about “Barber paradox”. > > First of all, the main idea of the post was not to solve any paradox but > to point two very important operations of Infos: > - Direct reflection; > - Transitive (indirect) reflection. > There are no other ways for Infos to collect data from environment. > > Second, the example with paradox had shown the well known creative > approach in the modeling - adding new dimensions in the model could help > to better understand the modeling object or process. For instance: > > If our linear model contains a “paradox” point “X”: > > //////X////// > > by adding a new second dimension it may be explained and the paradox would > be solved: > > \ > ///////////// > ------------- > //////X////// > > > Friendly greetings > Krassimir > > > _______________________________________________ > Fis mailing list > Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis > <http://listas.unizar.es/cgi-bin/mailman/listinfo/fis> > > > > -- > Professor Terrence W. Deacon > University of California, Berkeley > _______________________________________________ > Fis mailing list > Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis

_______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis