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 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 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.info/dialectics/Glossary_files/Glossary,Equations_vs._Meta-Equations,19JUN2014.jpg

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

http://www.dialectics.info/dialectics/Glossary.html
http://www.dialectics.info/dialectics/Welcome.html

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 expression’s 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 equality ‘y  =  mx + b’, given that its two parameters, m and b, denote ‘‘‘known variables’’’ [relative to the ‘unknowns /variables’ x 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-equation’ 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-equation’ contains 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.”