Friday, May 11, 2018

New Internet Dialogue Opens on the F.E.D. ‘Dialectical Mathematics’.







New Internet Dialogue Opens on the F.E.D. Dialectical Mathematics.







Dear Readers,


A reddit participant recently posted, and commented upon, an F.E.D. dialectogram, on one of our conjectures as to the opening triad of our version of the dialectic of Nature, at --



The dialectogramthere posted is a variant of the following --




This posters comments included the following --

“This is true art.  I am actually in awe of how much effort this person has put into this stuff.”



I responded, on behalf of F.E.D., as follows --


“The 9 axioms, grounding the arithmetic/algebra for dialectics applied in the diagram posted above, are stated, within the www.dialectics.org web site, at --





“That these 9 axioms incorporate a version of the first four, “first-order logic” axioms of the “[Dedekind/]Peano Postulates” for the system of arithmetic of the “Natural” Numbers, makes this arithmetic/algebra for dialectic a “non-standard model” of the Natural Numbers.  Such were foretold by the co-application, at the level of “first order” logic, of the Gödel Completeness and Incompleteness Theorems -- two of the deepest theorems of modern “mathematical logic”. An intuitive, dialectical derivation of the system of these “dialectical meta-Natural meta-numbers” from that of the standard “Natural Numbers” is available, within the www.dialectics.org web site, via --




“That these 9 axioms suffice to deductively derive, as a theorem, by a simple direct proof, a STRONG CONTRARY to what Boole called his “fundamental law of thought”, or “law of duality”, which is the core “axiom” of original Boolean algebra, makes this arithmetic/algebra of dialectic a “contra-Boolean algebra” -- an algebraic dialectical logic.  This simple direct proof is presented, within the www.dialectics.org web site, here --





“The resulting dialectical logic is a “supplementary opposite” to Boole’s algebra for formal logic, one that “aufheben”-contains/conserves Boole’s “fundamental law”, but which also “aufheben”-elevates and “aufheben”-negates Boole’s fundamental law for formal logic.  This new, “contra-Boolean” algebra expands Boole’s “law of [EXO-]duality” into a more universal, more general “law of ENDO-duality”.” 

“The www.dialectics.org site also recognizes a third axioms-system of dialectical- algebraic logic, one which reconciles the opposition between the Boolean and “contra-Boolean” algebras, in[to] a single ‘uni-system’ of dialectical algebra, incorporating and integrating both.” 

“For more about this third system of algebraic dialectical logic, and about the entire, systematic “dialectic/systems-progression of the systems of algebraic [dialectical] logic” -- of “algebras for [dialectical] logic(s)” -- see:








Sunday, April 29, 2018

The Generic Octadic Format for Dialectic as Applied to ‘‘‘HISTORICAL [DIAchronic] DIALECTICS-in-General’’’.







The Generic Octadic Format for Dialectic as Applied to ‘‘‘HISTORICAL [DIAchronic] DIALECTICS-in-General’’’.







Dear Readers,


The F.E.D. General Council has recently released an Octadic-Format dialectogramic summary/overview of our generic meta-equation meta-modelas applied for Diachronic, HISTORICAL DIALECTICS-in-General, for its epochs t = 0 to t = 3.

A JPG of this dialectogram is scheduled to be posted to the F.E.D. main web site’s Applications Page, to its section entitled Universal Algorithmic-Heuristic Dialectical Method [Octadics, JPG8] --



For your convenience, I have also posted this image below, together with its dual-modelimage, and an image about our Dialectical-Encyclopedic Principle of dual modeling.


Regards,

Miguel
























Saturday, April 14, 2018

The SYSTEMATIC Dialectic of the CONTEMPORARY human-social formation, to presentation step s = 3 -- New Summary ‘Dialectogram’ co-depicting ‘allo-hybrid’ & ‘auto-hybrid’ socio-ontological categories together.







The SYSTEMATIC Dialectic of the CONTEMPORARY human-social formation, to presentation step s = 3 -- New Summary Dialectogramco-depictingallo-hybrid&auto-hybridsocio-ontological categories together.







Dear Readers,


The F.E.D. General Council has just approved release of a new, summary dialectogram, to presentation step s = 3, for a ‘‘‘systematic, synchronic-dialectical method of presentation of our contemporary human-social formation’’’, a formation that is common across much of our planet today. 

The meta-equation meta-model for this method of presentation is the synchronic, systematic, presentational counter-part to the diachronic, [psycho]historical meta-equation meta-model presented here in an earlier blog-entry.  Further exposition of that [psycho]historical meta-equation meta-model counter-part is available in the PDF text reachable via the following URL --


This new summary dialectogramco-depicts both theallo-hybridand theauto-hybridsocio-ontological category-symbols generated by this meta-model, together, in a unified format.

This image is scheduled for later posting to the F.E.D. main web site Applications Page --



For your convenience, I have pasted-in the JPEG of this image, together with that for its diachronic counter-part, below.


Such pairs of dialectogramdiagrams, and the pairs of dialectical meta-equation meta-models that they attempt to depict, are central to one of the key principles of duality that characterize our concept of a Dialectical Encyclopedia[i.e., of an ‘«Aufheben»-icEncyclopedia].  For eachDomain to be extensively defined and described in such an encyclopedia, the first-presented dialectical meta-equation meta-model describes the known history of that ‘Domain, up to its present meta-state.  The second-presented dialectical meta-equation meta-model describes the present meta-state of that ‘Domain in detail.  The first-presented dialectical meta-equation meta-model may also then be iterated and solved further, to beyond the present meta-stateof that Domain, to provide a prediction/pre-construction of the encyclopedists’ expected future for that Domain.


Regards,

Miguel
























Monday, April 09, 2018

Evolutionary Theory Beyond “The Modern Synthesis”.










Evolutionary Theory Beyond The Modern Synthesis.







Dear Readers,



I recently posted a comment to an [old] blog-entry, entitled “Is the “Modern Synthesis” Effectively Dead”, at --


-- as follows:

I have become aware of a new tradition in ‘‘‘evolutionary theory’’’ -- and in ‘meta-evolutionary theory’ -- that is also critical of the fetters upon evolutionary theory that had been imposed by “The Modern Synthesis”.

This new tradition is even critical of the very term “natural selection”, because of its subliminal connotations of some human-like agent [as in the “artificial” selection involved in human domestication of plant and animal species], i.e., some [pseudo-]subject, even some “divine” agent, “choosing” genomes, whereas the scientific essence of the Darwinian paradigm is one of differential rates of self-reproduction of populations, such that the populations exhibiting the highest SUSTAINED rates of self-expansion/of self-reproduction are the “fittest”.

More central to this new tradition is an evolutionary paradigm that extends -- and rigorously so -- the category of “evolution” to trans-genomic processes, and, hence also, to ‘meta-dynamics’ of ‘self-developing process’ in our cosmos that arose both before and beyond “biological evolution” per se, via their concept of ‘self-meta-unit-ization’, or of ‘self-meta-holon-ization’.

This new evolutionary paradigm can be stated, in general form, as follows:  populations of individual units of a given kind arise, by an earlier process of ‘meta-unit-ization’, which then successfully self-reproduce in expanding quantities [quantitative change as “mere” evolution], to the point where local ‘physical-spatial concentrations’, or ‘self-densifications’, of those units become sufficient to trigger the next consecutive step in ‘meta-evolution’; the irruption [‘meta-evolution’ as qualitative, ontological change, via a kind of ‘metafinite singularity’] of a new kind of units’ populations, via combinations of some of these units into ‘meta-units’, each such ‘meta-unit’ being made up out of an organized, heterogeneous multiplicity of its predecessor units.

Specific cases of this general ‘meta-evolutionary meta-dynamic’ would include the irruption of eukaryotic living cells from ‘pre-eukaryotic’ or “prokaryotic” living cells, by “endosymbiosis”, or “symbiogenesis”.

But such specific cases would also include the irruption of “composite” bosons and fermions from their “non-composite” brethren/ancestors; of atomic nuclei from composite “particles” [protons and neutrons] in “cosmological nucleosynthesis”, and; of molecules from atoms, e.g., in primordial “atomic clouds”, self-becoming “molecular clouds” -- all pre-biological cosmological phenomena.

Such specific cases of ‘meta-evolution by population meta-unit-ization’ would also include the formation of humans-led ‘meta-societies’, wherein multiple “social animal” and ‘social plant’ species-populations, as units, unite to form a higher kind of unit, via ‘‘‘mutual domestication’’’. 

The latter constitutes a necessarily post-biological phenomenon, in that the ‘meta-evolutionary’ irruption of such ‘humans-led meta-societies’ presupposes the prior stages of biological ‘meta-evolution’:  ‘pre-eukaryotes’ --> ‘pre-eukaryotes’ + eukaryotes --> ‘pre-eukaryotes’ + eukaryotes + [asocial] multi-[eukaryotic-]cellular organisms [“metazoa” and “metaphyta”] + social organisms [“social animals” and ‘social plants’].

Writings about this new [meta-]evolutionary paradigm are available via:  www.dialectics.org .



Regards,

Miguel






















Sunday, March 18, 2018

The Psychohistorical Dialectic of Human-Social Formation(s) -- PDF of new presentation.







The Psychohistorical Dialectic of Human-Social Formation(s) -- PDF of new presentation.







Dear Readers,



FYI:  The F.E.D. General Council has just approved release of a new presentation on the ‘Seldonian psychohistorical-dialectical meta-equation known as The Meta-Equation of Human-Social Formations Meta-Evolution. 

An earlier, less-detailed presentation of this meta-model is available in the PDF text reachable via the following URL --



This new presentation is scheduled for later posting to the F.E.D. main web site’s Applications Page --




For your convenience, I have posted the content of this presentation, below, in the form of JPEG images.



Regards,

Miguel



















































Wednesday, March 14, 2018

The Historical Dialectic of Human-Social Formation(s) to Epoch 3 -- New Summary ‘Dialectogram’ depicting ‘allo-hybrid’ as well as ‘auto-hybrid’ socio-ontological categories for the first time for our depictions of [psycho]HISTORICAL dialectics.







The Historical Dialectic of Human-Social Formation(s) to Epoch 3 -- New Summary Dialectogramdepictingallo-hybridas well asauto-hybridsocio-ontological categories for the first time for our depictions of [psycho]HISTORICAL dialectics.







Dear Readers,


The F.E.D. General Council has just approved release of a new, summary dialectogram for the ‘Seldonian psychohistorical-dialectical meta-equation known as The Meta-Equation of Human-Social Formations Meta-Evolution.  Further exposition of this meta-model is available in the PDF text reachable via the following URL --


This new summary dialectogramdepicts, for the first time for our depictions of [psycho]HISTORICAL dialectics, both theallo-hybridandauto-hybridsocio-ontological category-symbols generated by this meta-model.

This image is scheduled for later posting to the F.E.D. main web site Applications Page --



For your convenience, I have pasted-in the JPEG of this image, below.


Regards,

Miguel