Part 02:
Dialectics and Self-Reflexive
Functions Series.
‘Self-«Aufheben» Negation’ --
‘‘‘Conservation’’’ Moment.
Dear Reader,
The
«aufheben» function is the dialectical ‘‘‘self-reflexive
function’’’ par excellence.
«Aufheben»
‘‘‘negation’’’ – i.e., dialectical, determinate ‘‘‘negation’’’
– is conservative ‘‘‘negation’’’.
An
ontological «arithmos»/category of «monads» that «aufheben»
self-‘‘‘negates’’’ is, in fact, doubly self-conserved.
Part
of its pre-self-‘‘‘negation’’’ self, i.e., one portion of its «monads»,
is ‘‘‘evolutely’’’ conserved – is continued in its existence – outside
of the new «arithmos» of «monads» that that self’s self-«aufheben»
creates.
The
other part of its pre-self-‘‘‘negation’’’ self – some of the former «monads»
of that ‘self-«aufheben»-ating’ «arithmos»/-category, are conserved
inside each of the new kind of «monads» of
the new ontological category/-«arithmos» that the ‘self-«aufheben»-ation’ of the earlier category/«arithmos» creates, or posits, by means of its self-«aufheben»
self-negation/self-conservation/self-elevation.
This
whole process of self-«aufheben» self-reflexive self-action/«auto-kinesis»
is driven by the ‘meta-Darwinian’ success, due to the sustained, accelerating rate
of expanded self-reproduction of the «monads» of that earlier «arithmos»/ontological
category.
One
of several alternative product-rule axioms of the N_Q_
axioms-systems of the ‘generic first arithmetic for modeling ordinal-categorial
dialectics’, the one that we call ‘the double-conservation «aufheben»
evolute product rule axiom’, abstractly reflects, as per its name, this ‘double
conservation’ character of dialectical
negation, ‘~’, with ‘Ä’ denoting «aufheben» ontological multiplication,
with ‘Å’ denoting categorial, oppositional/non-amalgamative
addition, and ‘|-=’
denoting ‘equal to per axiom’, qn in NQ, and n in N –
qn Ä qn º qn2 º qn(qn) º ~qn
|-= qn Å qn+n – such that:
q2n is qualitatively, ordinally ¹ to q1n.
If
generic qn, for n in N, is
interpreted/-assigned to represent a specific kind-of-being/-ontological
category/-«arithmos»-of-«monads»,
name it a – e.g.,
represented by qa – then:
qa Ä qa º qa2 º qa(qa) º ~qa
|-= qa Å qaa ,
such that category qaa is categorially,
‘«monad»-ically’,
qualitatively
and
ontologically
¹ to ontological category qa.
For more
information regarding these
Seldonian insights, and to read and/or download, free
of charge, PDFs and/or JPGs of Foundation books, other texts, and images, please see:
www.dialectics.info
For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights – specimens of ‘dialectical art’ – as well as dialectically-illustrated books
published by
the F.E.D. Press, see:
https://www.etsy.com/shop/DialecticsMATH
¡ENJOY!
Regards,
Miguel
Detonacciones,
Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];
Elected Member, F.E.D. General Council;
Participant, F.E.D. Special Council for Public Liaison;
Officer, F.E.D. Office of Public Liaison.
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