Part 01: Seldon’s Insights Series -- ‘Total NON-Closure: A Dialectical Arithmetic of Continual OPENing.

Part 01:  Seldon’s Insights Series --

‘Total NON-Closure:  A Dialectical Arithmetic of Continual OPENing.

Dear Readers,

It is my pleasure, and my honor, as an Officer of the Foundation Encyclopedia Dialectica [F.E.D.] Office of Public Liaison, to share with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

The first such release in this new series is entered below [Some E.D. standard edits have been applied, in the version presented below, to the direct transcript of our co-founder’s discourse].

ENJOY!

Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],

Officer, F.E.D. Office of Public Liaison, F.E.D. Special Council for Public Liaison.

“... The generic dialectical arithmetic of the _WQ «aufheben» operators does not exhibit “closure” in the sense that is typical for other arithmetics.”

“The _WQ ‘arithmetic for dialectics’ is, instead, an arithmetic of continual ontological opening -- of the continual production of new analytical-geometrical dimensions, mirroring the continual opening of new ‘‘‘dimensions’’’ of being, of kind, of ontology that we encounter in our physical universe, as well as in our mental universe(s) of creative thought, in terms of the continual burgeoning of new human ‘ideo-ontology’, e.g., in mathematics, etc.”

“That is, the _WQ arithmetic is designed to map, ‘‘‘algebraically’’’, continuing ontological revolution -- the irruption of new ontology, sometimes accompanied by the extinction of some extant older ontology; the oft self-accelerating ontological self-expansion of our «kosmos»:  ‘ontological dynamicity’; ‘onto-dynamasis’.”

“Every arithmetical operation involving _WQ ‘meta-number’ «aufheben» operators leaps to beyond and outside of the set, and of the analytical-geometrical space, _WQ, of these ‘meta-numbers’,

_WQ  =  { q₀, q₁, q₂, q₃, . . . }, viz. --

q₁ + q₂  is not in   _WQ

-- and --

q₁ x q₂  is not in  _WQ .”

“In general, for any j, k in W  =  { 0, 1, 2, 3, . . . }, thus for any q_j,  q_k  in  _WQ, excluding q₀ --

q_j + q_k  is not in  _WQ

-- and --

q_j x q_k  is not in  _WQ .”

“In _WQ analytical-geometrical space, each of the elements of _WQ is represented as an independent axis and dimension of that space, perpendicular to all of the other elements of _WQ, and with all extant axes intersecting in q₀.”

“However, every such dialectical-arithmetical operation generates a diagonal, or a ‘hyper-diagonal’, relative to those axes.”

“Thus, every such _WQ-arithmetical operation transcends _WQ-arithmetical space by way of ‘diagonal transcendence’. ...”