Wednesday, September 20, 2017

Part 03: Seldon’s Insights Series -- ‘Dialectical Meta-Equations’ and ‘Dialectical Meta-Models’.







Part 03:  Seldon’s Insights Series --

Dialectical Meta-Equations and Dialectical Meta-Models.







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 third 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].

For more about these key concepts, see --

http://www.dialectics.org/dialectics/Glossary_files/Glossary,Equations_vs._Meta-Equations,19JUN2014.jpg

http://www.dialectics.org/dialectics/Glossary_files/Glossary,Models_vs._Meta-Models,19JUN2014.jpg

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.







...The ‘‘‘categorial progressions’’’ -- the qualitative, non-amalgamative’ ‘‘‘sums’’’ of increasingly thought-concrete, increasingly determinate category symbols -- that we express via equalities using the NQ arithmetic and its algebra:  these we refer to as ‘[dialectical] META-equations.”

We do so because each such unity-to-diversity equating expression is ‘made up out of’, and thus ‘‘‘«aufheben»-contains’’’, a heterogeneous multiplicity of qualitatively different, ontologically different mere equations.”

“Indeed, they ‘‘‘«aufheben»-contain’’’ one such mere equation for each distinct, consecutive, relevant value of that expressions independent variable -- e.g., s [step number] for a synchronic, presentational dialectic; t [epochal time count] for a diachronic, historical dialectic.”

“Moreover, when each such equation formulates a distinct -- in these cases, a qualitatively distinct, ontologically distinct -- dialectical-mathematical model, then their single meta-equation also formulates a META-model, ‘made up out of a heterogeneous multiplicity of internally-related mere models; ‘‘‘«aufheben»-containing’’’ a heterogeneous multiplicity of such related models.”

“Now, of course, meta-equations do not arise from the NQ arithmetic/algebra alone.”

“For example, the general planular linear equation algebraic equalityy  =  mx + b’, given that its two parameters, m and b, denote ‘‘‘known variables’’’ [relative to the unknowns /variablesx and y] both range over R, the “Real numbers, is a purely”-quantitative meta-equation, ‘made up out of’ a multiplicity of linear mere models.”

“Likewise, the ‘«arché»-ic nonlinear differential equation, ‘dx(t)/dt  =  ax(t)^2’, about which we have spoken before, and will again, is also a purely”-quantitative meta-equation, given that its single control-parameter, a, ‘‘‘modifying’’’ its ‘function-unknown’, x(t), is taken as denoting a ‘‘‘variable parameter’’’, or ‘‘‘parameter variable’’’, e.g., again ranging over R, the “Real numbers, and co-determining the location of its “movable pole” singularity.  This meta-equationis again ‘‘‘contains’’’ a different nonlinear differential equation for each distinct value of a.”

“A characteristic which distinguishes NQ arithmetic/algebra meta-equations from the other kinds of meta-equations noted above is this:  because of the ‘‘‘evolute’’’, «aufheben» nature of the NQ multiplication operation, the categorial progression of each successor equation in an NQ meta-equationcontains all of the category symbol term(s) of all of its predecessor equations, as well as, and non-amalgamatively added-to, the new category symbol term(s) that this successor equation introduces for the first time in this succession.






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