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
>
>
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>
>
> --
> Professor Terrence W. Deacon
> University of California, Berkeley
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