Part 08: Seldon’s Message Series -- ‘The Set of All Sets Paradigm of Dialectic’.

Part 08:  Seldon’s Message Series --

‘The Finitary Set of All Sets Paradigm for Dialectic’.

Dear Reader,

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 eighth 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].

This instalment addresses ‘the finitary set of all sets’, an ‘idea-object’ which, by its nature [definition], refuses to ‘‘‘sit still’’’ -- as would any “good” Parmenidean posit -- in the human mind that forms it, and which was the original paradigm of dialectic, as of ‘meta-dynamics’, in Seldonian theory and in its [psycho]historical order of development.

For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --

www.dialectics.info

ENJOY!

Regards,

Miguel Detonacciones,

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

Participant, F.E.D. Special Council for Public Liaison,

Officer, F.E.D. Office of Public Liaison.

“...Set theory is often taken to constitute the “logical” ‘‘‘foundation without foundation’’’ of all of mathematics.”

“... From the point of view of the broad tradition of dialectics, especially as re-founded by Hegel, it is no  surprise at all that the fundamental object of this set theory, the idea-object that set-theoretically -- i.e., that “extensionally” -- defines the very set concept itself -- namely the “set of all sets” -- is immanently and radically problematic for that theory.”   

“The “set of all sets” is an idea-object which refuses to “stay still” in the human mind that forms it, any more than the Hegelian concept of “Being”, the «arché»-category and foundation of Hegel’s entire «Logik»/«Natur»/«Geist» System, “stays still” in the human mind that forms it.”

“In our immanently critical analysis of this set theory, we have recourse to a realistic, finitary ‘‘‘set of all sets’’’, rooted in the realistic, finite universal set for a given ‘‘‘Universe-of-discourse’’’, i.e., with the power set, 2^U, or set of all subsets, of that universal set, U, as the «arché»-set of the finitary ‘‘‘set of all sets’’’, its first try at constituting that ‘‘‘finitary set of all sets’’’ for the U ‘“Universe of discourse”’ set.” 

“That ‘‘‘set of all sets’’’ is no static, “eternal”, Parmenidean posit, but, instead, and on the contrary, “is” a ‘mental eventity’, a ‘‘‘becoming’’’ rather than a “being”; a ‘self-dynamical’ object by virtue of its own self, its own definition, its own, ever-self-incomplete nature.”

“As such, it gives rise to a potentially infinite series-progression of «aufheben»-related, ‘meta-element-ization’-related sets[-of-sets-of...], that is, a progression of ‘‘‘classes[-of-classes-of...]’’’, that is, a progression of ‘‘‘categories[-of-categories-of...]’’’ -- i.e., a progression of ‘“numbers”’[-of-sets-as-set-elements] in the ancient sense of “number”/“«arithmos»”; a progression of «arithmoi» of a special kind.”

“This dialectical [«aufheben»] categorial progression is potentially infinite, but never “actually infinite”.

“The ‘extensional predicates’ which are the set-elements -- indeed, which are the ‘set/«monads»’ -- of each ‘set/«arithmos»’ in this ‘predico-dynamical’ progression of ‘sets /«arithmoi» become, in their «aufheben» increments with each ‘self-involutional’, power-set advance of this progression, more and more subtle and rarefied and distilled.”

“Eventually -- if this ‘set of all sets progression’ is used as a model of advancing human knowledge of the qualities of human experience -- these increments eventually become indiscernible for the human mind of the typical social individual of any given human-[psycho]historical epoch.”

“This progression, then, at such a point, effectively terminates, for and relative to that [psycho]historical epoch, i.e., when its latest increment of “set of all subsets” set-elements becomes unsolvable, ‘de-semantified’, unintelligible as specifying distinguishable experiential qualities for that social individual.”

“However, in the next [psycho]historical epoch of humanity, the range of discernible qualities -- of ‘extensional predicates’ -- may become extended. ...”