Part 06: Seldon on Dialectical Method Series. The ‘Additive Procedure’.

 

 

 

 

Part 06: Seldon on Dialectical Method Series.

 

The ‘Additive Procedure’.

 

 

 

 

 

 

 

Dear Reader,

 

 

 

It is my pleasure, and my honor, as an elected member of the Foundation Encyclopedia Dialectica [F.E.D.] General Council, and as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, Encyclopedia Dialectica insights into key concepts of Seldonian Theory.

 

 

 

 

 

 

 

The statement posted below describes the F.E.D. ‘additive procedure’ for the solution of the Domain-specific dialectical-algebraic, ontic categorial-progression equations – the easiest to learn such solution-procedure – that are at the heart of the Seldonian dialectical method.

 

 

 

 

 

 

 

Seldon –

 

“The ‘additive procedure’ for the solution of dialectical, categorial progression equations is the qualitative arithmetical analogue of the “purely”-quantitative, Peano successor-function procedure for generating the Peano “Natural” numbers space/set, N.  It is, thus, the ‘Peanic Procedure’ for advancing to, starting from just the “Natural” number “1” as ‘«arché»-number’, the expanding space/set, e.g., of the “first-order logic”, ordinal '“Natural”' numbers. 

 

In each step, this, ‘Peanic’, procedure applies the ultra-simple, but also ‘proto-«aufheben»-ic’, ‘proto-dialectical’ Peano successor function, s –

s(n) = n + 1

– moving, in its generic step, from n Î N, to

(n + 1) Î N, such that both are '''contained''' in double-underscored N_, the “first-order logic”, ordinal-numbers version of the “Natural” Numbers axioms-system, featuring the first four of the five “Peano-Dedekind Postulates” for the “Natural” numbers arithmetic.

 

The “purely”-qualitative analogue of the above-stated “purely”-quantitative procedure – what we call the ‘Qualo-Peanic Procedure’ for the solution/- ‘semantification’ of the successive, consecutive category-symbols generated in a dialectical, ‘«aufheben»-ic’ succession/progression of initially unknown, i.e., ‘‘‘algebraic’’’, ontological-category symbols, potentially comprehending a given subject-matter Domain, is nearly as simple as the ‘Quanto-Peanic Procedure’ described above.

 

“That is, the ‘Qualo-Peanic Procedure’ proceeds by simply and repeatedly “adding” – juxtaposing – the subscripted letter representing the user-determined «arché»-category of the Domain, next to and to the right of the category-representing subscript of the most recent, most-advanced-in-complexity category-symbol in the categorial progression so far solved.  That subscript “addition”/juxtaposition generates the next unsolved category-symbol, for the next more complex ontological category of the Domain.”

 

“To solve for that newly generated, consecutive-next-in-complexity category-symbol, which will be a ‘bi-vocal’ [two-subscript] category-symbol at least, consolidate that ‘multi-vocal’ subscript into a, "uni-vocal",  single subscripted letter, representing a user-known category of the Domain being analyzed, in consistency with the consolidations/solutions already, previously produced by this procedure and by the given method-user.”

 

“What this means becomes clear when exemplified for a specific Domain.”

 

“Let’s be ambitious, and chose, for our exemplification, the case of the ‘everything Domain’, that is, that of Nature as historical totality, i.e., that of known cosmological natural history to-date: that of ‘The Dialectic of Nature’.”

 

“Suppose we chose, as the historical-dialectical «arché»-category for our Cosmos, the category of ‘pre-atomic’ “particles”, symbolizing that category by ‘q_r’, standing for the qualit(y)(ies) represented and shared by all of the “particle” units -- by the total «arithmos» [‘‘‘number’’’] of such “particle” units.  Note that q_r corresponds, in the generic/uninterpreted _NQ arithmetic to q₁, with the Peanic «arché» “1” as its subscript.  We assert this correspondence ideographically as ‘q_r [--> q₁’.”   

 

“The ‘additive procedure’ would then have us construct the next, second category in this cosmo-ontological categorial progression as ‘q_rr’.  Per the _NQ arithmetic’s ‘canons of interpretation’, this category-symbol connotes the conversion of the ‘_r’ by the ‘_r’ themselves, into ‘meta-particle’ units, each such ‘meta-particle’ unit being made up out of a heterogeneous multiplicity of ‘_r’ units.  Suppose that, to our “ears”, that “sounds” like an «arithmos» of “atom” units, each typical atom being made up out of a multiplicity of, e.g., proton, neutron, and electron “particle” units.  So we assert [‘|-’], as our “univocal” solution/definition [‘º’] for the meaning of, the initially “bi-vocal”, “algebraic-unknown” category-symbol ‘q_rr’: q_rr |-º  q_a, in the sense of primordial "cosmological nucleosynthesis", e.g., of Hydrogen and Helium atomic nuclei, from the 'densified' mutual interactions of particle units, resulting as myriads of primordial atoms units assembled in primordial 'atomic clouds', and, later, in the first generation of stars.  Where do those stars come into our dialectical, 'cosmo-ontology' categorial-progression 'meta-model'?”

 

Well, next, we would construct the third category-symbol in our ‘cosmo-ontological’ categorial progression, by “adding” «arché» ‘_r’ again to ‘_a’, thus obtaining ‘q_ar’ .  By the _NQ arithmetic’s ‘canons of interpretation’, this category-symbol connotes the conversion of the ‘_r’, by the ‘_a’, into [more of the] ‘_a’.  Suppose that, to our mind, this category-symbol thus connotes the category of the primordial conversion of proton “particle” units – i.e., of H⁺ ion units – into [more] atom units, in the original generation of stars, with protonic cores, fusing proton units into the “di-proton” units that readily become Helium atom meta-units, via the process named “primordial stellar nucleosynthesis”.  We may then assert, as our solution, q_ar |-º  q_s, with q_s representing the category of the "first generation" of star units.”  

 

“Our categorial progression solution for the ontological content of the dialectic of nature so far is thus –

‘q_r + q_a+ q_s’

– or –

 ‘particles + atoms + first-generation stars’

– as representing the ontological content of our cosmos at this stage in its self-developing history.”

 

“If we apply the procedure again, we obtain, as the next ‘algebraic unknown category-symbol’ to be solved-for, q_sr.  Because ‘q_sr’ decomposes, per our previous decisions/solutions, to q_arr, and because we had previously solved ‘_rr’ as ‘_a’, consistency with our preceding solutions requires that this symbol transform to q_aa.  The latter connotes the self-conversion of atoms into ‘meta-atomic’ units, each typical such ‘meta-unit’ made up out of a heterogeneous multiplicity of atom units, as its sub-units.  Suppose that, to us, this signifies the transformation of atoms, in the primordial ‘atomic clouds’, into molecule units, thereby transforming those primordial ‘atomic clouds’ into “molecular clouds”: q_aa |-º q_m.  Our categorial progression for the ontology of the cosmos for this, fourth, step is now –

‘q_r + q_a+ q_s+ q_m’

– or –

 ‘particles + atoms + first-generation stars’ + molecular clouds’

– as representing the ontological content of our cosmos at this stage in its self-developing history.  Most likely, by this point, you get the point.”  

 

 

 

 

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, and for free-of-charge download of F.E.D. Press books and other texts, 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.

 

 

 

 

 

 

YOU are invited to post your comments on this blog-entry below!