Tuesday, August 09, 2011

Mapping Back from "Interpreted" to "UNinterpreted" Dialectical-Arithmetic Expressions

Here is a shortcut "rule of thumb" for mapping back from "interpreted", specifically "assigned" dialectical "meta-numbers", e.g., assigned as "ontological-categorial qualifiers", to "uninterpreted" dialectical "meta-numbers" [or, really, contra Hilbert, to "minimally-interpreted" "meta-numbers", interpreted only as "ordinality qualifiers"], expressed using the main example of the immediately previous post --

If C or q/C connotes the Marxian socio-ontological category, or <<arithmos>>-of-<<monads>> [assemblage-of-units], named "Commodities", "assigned" to the minimally-interpreted "ordinal qualifier" q/1, then the C in q/C has the ordinal value 1, and, given '( )' in ( )X = (X), as the ordinal-value extraction-function, then (C) = (q/C) = q/(C) = q/1;

If q/CC = q/M = M connotes the Marxian socio-ontological category of "Monies", then (q/CC) = q/(CC) = q/(1+1) = q/2 = (M) = (q/M) = q/(M) = q/2;

If q/MM = q/K = K connotes the Marxian socio-ontological category of "Kapitals", then (q/MM) = q/(MM) = q/(2+2) = q/4 = (K) = (q/K) = q/(K) = q/4;

If q/KK = q/S = S connotes the Marxian, predicted future social-relations-of-production, socio-ontological category of "ASsociations-of-Producers", then (q/KK) = q/(KK) = q/(4+4) = q/8 = (S) = (q/S) = q/(S) = q/8.

Therefore also --

For q/MC, connoting the Marxian socio-ontological sub-category of the subsumption of "Commodities" by "Monies", or of "Money-mediated Commodity-Circulations", (q/MC) = q/((M)+(C)) = q/(2+1) = q/3;

For q/KC, connoting the Marxian socio-ontological sub-category of "Commodity-Kapital", (q/KC) = q/(K+C) = q/(4+1) = q/5;

For q/KM, connoting the Marxian socio-ontological sub-category of "Money-Kapital", (q/KM) = q/(KM) = q/(4+2) = q/6;

For q/KMC, connoting the Marxian socio-ontological sub-category of the "Kapitals Circulations-Processes as a Whole", (q/KMC) = q/(KMC) = q/(4+2+1) = q/7.

Summary rule-of-thumb: Juxtaposition of denominator-located "connotograms", such as the C, M, K and S of this example, once they have been resolved into their ordinal-number pure-quantitative residues, such as 1, 2, 4, and 8, respectively, for the example used above, calls for, not the multiplication of these residue values, as per the syntax of typical modern algebras [e.g., aa = a x a = a squared], but calls for, instead, their addition, as per the syntax of typical ancient arithmetics [e.g., in the case of "Roman Numerals", XX = "X + X" = 20].

For example --

(CC) = (C) + (C) = 1 + 1;

(MC) = (M) + (C) = 2 + 1;

(MM) = (M) + (M) = 2 + 2;

(KC) = (K) + (C) = 4 + 1;

(KM) = (K) + (M) = 4 + 2;

(KMC) = (K) + (M) + (C) = 4 + 2 + 1;

(KK) = (K) + (K) = 4 + 4.

Regards,

Miguel

F.E.D. definitions of special terms applied in the narrative above --

associations of producers
no definition for this term is available as yet in the Archive, but see Section 5 in --
http://www.equitism.org/Equitism/AmendmentXXVIII/AmendmentXXVIII.pdf

<<arithmos>>
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmos/Arithmos.htm

<<aufheben>>
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Aufheben/Aufheben.htm

connotograms
no definition for this term is available as yet in the Archive

[dialectical] meta-numbers
no definition for this term is available as yet in the Archive, but see --
http://www.dialectics.org/dialectics/Dialectic_Ideography_files/6_Dialectics-Part1c-Briefing_OCR.pdf

minimally-interpreted [symbols] [contra Hilbert]
no definition for this term is available as yet in the Archive

ontological-categorial qualifiers
no definition for this term is available as yet in the Archive

ontological category
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Onto/Onto.htm

ordinality
no definition for this term is available as yet in the Archive

ordinal number
no definition for this term is available as yet in the Archive

ordinality qualifiers
no definition for this term is available as yet in the Archive

qualifiers
no definition for this term is available as yet in the Archive

socio-ontological category
no definition for this term is available as yet in the Archive

subsumption
no definition for this term is available as yet in the Archive

uninterpreted [symbols] [cf. Hilbert]
no definition for this term is available as yet in the Archive