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 

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 
is still self-referential. 
It is the temporal unfolding of this self-reference that leads to the 
temporality in the sense of successive times.

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 < 
> <>> 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 < 
> <>> 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
> <>
> <>
> -- 
> Professor Terrence W. Deacon
> University of California, Berkeley
> _______________________________________________
> Fis mailing list
> <>

Fis mailing list

Reply via email to