Saturday, July 13, 2013

A Brief Introduction to the Mathematics of Dialectics for the Non-Mathematical.

 Dear Readers,

For those of you who are not familiar with -- or who are averse to -- the languages of mathematics, here is a brief, non-mathematical introduction to "the mathematics of dialectics" --

The F.E.D. "First Dialectical Algebra" is an algebra whose constants and variables represent qualitatively-different kind-categories -- categories of different kinds of things.

The "times" operation of this algebra can be interpreted as describing how new, unprecedented kinds of things [and hence also their kind-categories] come into existence, when some of the units of old categories coalesce to form the units of new categories -- when some of the things of an already existing kind coalesce into the first of a new thing, the first of a new kind, the first thing of a new kind of thing, and, thus, of a new kind-category of things.


physical example:   primordial atoms coalescing to form the first molecules.

psychohistorical example [history of philosophy]: The plural plenitude of the fluent objects of reality, per Heraclitus's philosophy of flux, coalescing into the singular thing of eternal, frozen stasis -- "Being" -- per Parmenides's counter-philosophy of imperishable, unitary stillness, wherein all of the multitudinous objects of experience are denied / coalesced into an 'inexperienceable' singleness.

Then, together, the "objects" of these two philosophies hybridized, yielding the early philosophy of Plato as the "complex unity" [or "dialectical synthesis"] of these two prior philosophies:

(3) eternal immutable existence "above", in the domain of the Platonian <<Arithmoi Eidetikoi>> -- of the "Assemblages of Idea-Units";

(1) impermanent, transitory flux "below", in the domain of the Platonian <<Arithmoi Aisthetoi>> -- of the "Assemblages of Sensuously-Perceivable Units",

and, mediating "between" the two;

(2) changeless but also multiplicitous and reproducible units, in the domain of the Platonian <<Arithmoi Mathematikoi>> -- of the "Assemblages of Arithmetical Units".


definition: ''' convolute '''


---> H + qHH = H + P ---> H + P + qPH = H + P + A



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