Part 5. Recent Internet Dialogue on Seldonian Dialectical Arithmetic: Edited Excerpt from Transcript.

Dear Reader,



Below I have posted an edited excerpt from the fifth part of a recent web forum thread dialogue on F.E.D. dialectics in which I participated.

 
I have once again notated my interlocutor's queries by 'Q#.:', and my responses by 'R#.:'.

 
Please feel free to join in this dialogue here, by posting a query or comment via the Comment function of this blog.



Regards,

Miguel

Q5.:   You wrote "atoms x atoms  =  atoms + molecules" ... .

           How exactly is the molecule the antithesis of the atom?

R5.:  Excellent query!!! -- A query whose answer will call upon us to unfold a major, core portion of this entire dialectical method, without which this method cannot be understood, but with which, this method becomes almost obvious!

“Short[er] Answer”.  Because each single molecule is a dialectical, [self-]«aufheben», determinate [self-] negation of a [plural] sub-population, or ‘sub-«arithmos»’, of atoms.

‘The «arithmos» of molecules’ is the category representing, ‘connotationally’, ‘‘‘the [indefinite] NUMBER of molecules’’’, or ‘‘‘the [indefinite] population of molecules’’’ -- all that have ever existed, all that presently exist, all that ever will exist. 

‘The «arithmos» of atoms’ is the category representing, ‘connotationally’, ‘‘‘the [indefinite] NUMBER of atoms’’’, or ‘‘‘the [indefinite] population of atoms’’’ -- all that have ever existed, all that presently exist, all that ever will exist.

Recall that the original form of Occidental Dialectic, so-named, was that of Plato’s «arithmoi eidetikoi» -- of his multitudes of fundamental, supposedly causal ‘‘‘idea-units’’’, or of ‘‘‘«eide»-units’’’, organized into ... ‘idea-«species»’ [i.e., into ‘idea-«hypo-gene»’], under ‘idea-«gene»’, under ‘idea-«hyper-gene»’, etc., etc.

Any typical individual molecule, as a unit, or as a ‘‘‘logical individual’’’, or as an ‘‘‘element’’’ of the category of “molecules” -- to use the ancient Greek term, as a «monad» or «henad», or, to use an even more apt, ultra-modern term, as a ‘‘‘holon’’’ [Arthur Koestler], of the category, or «arithmos», of molecules -- is a dialectical, [self-]«aufheben», ‘self-hybridizing’, determinate [self-]negation of multiple units, individuals, «monads», «henads», or holons of the category, or «arithmos», of “atoms”.

That is, a molecule unit is a ‘meta¹-unit’ relative to an atom as a unit [as ‘meta⁰-unit’].

Indeed, a typical individual, single molecule unit can be defined as a ‘meta-atom’, made up out of a -- usually heterogeneous -- multiplicity of two or more distinct atom units.

Thus, a molecule unit -- any typical unit of the “molecules” category -- is, all together, a negation, or annulment, or cancellation of a multiplicity of atom units as mere atoms units, and also a conservation of those atom units, ‘“inside’’’ the new, molecule unit that they compose, and also an elevation of those atom units [in]to, to form, to help constitute a new, higher, richer, more complex, more determinate, more massive / more ‘‘‘concrete’’’, more ‘‘‘substantial’’’ ‘‘‘layer of reality’’’, or ‘‘‘level of existence’’’, or ‘‘‘scale of being’’’.

«aufheben»  =  negation-cum-conservation-cum-elevation, which is a ‘thesis-antithesis-synthesis’ in itself!

A molecule unit is thus not an absolute, indeterminate, abstract “negation” of any multiplicity, that is, of any ‘sub-«arithmos»’, of atom units -- a kind of ‘contra-empirical’, fictive “negation”, which would supposedly turn them into abstract nothingness [in violation of the empirical conservation of mass-energy principle].

Also, a molecule unit is thus neither a ‘‘‘complement[ary]-opposite’’’ [like “female vs. male”, or like “yin vs. yang”] to an atom unit, nor is it an ‘‘‘annihilatory-opposite’’’ [like “matter vs. anti-matter”, or like a fatal disease vs. the living body that it attacks, or like “good vs. evil”] to an atom unit, but it is a ‘supplementary-opposite’  to an atom unit [like a ‘‘‘[political-economic-democratic-]communist society vs. a capitalist society’’’, or like ‘‘‘a money unit vs. a commodity unit’’’ in Marx’s theory], for more about which, see --

http://www.dialectics.info/dialectics/Vignettes_files/Aoristos_Dyosphainthos,F.E.D._Vignette_%236,The_Dialectic_of_Oppositions,first_posted_29NOV2012.pdf .

Now, of course, there are exceptional cases wherein the individual molecule in question is made up out of, not a heterogeneous multiplicity of atom units, but, instead, is made up out of a homogeneous multiplicity of [still distinct] atom units, e.g., H2, O2, O3, etc.

So, we say that the «arithmos» / category of molecules is a ‘meta¹-«arithmos»’ relative to the ‘[meta⁰-]«arithmos»’ / category of atoms, and thus a ‘meta¹-category’ of atoms, if not, in any immediately obvious way, also a ‘contra-category’ to the category of “atoms”.

If we symbolize the category / «arithmos» of “atoms” by ‘qa’, then the “molecules” category / «arithmos» is signified, per our interpretation, by the symbol ‘qaa   =   qm’, the double subscript, ‘aa’, here signifying that category  ‘qm’ is the result of a ‘self-combination’ of category ‘qa’, also signifying ‘self-hybridizations’ of the units of ‘qa’.

Similarly, [next] “prokaryotic” cells [e.g., bacteria] are ‘meta-molecules’, [next] eukaryotic cells [e.g., yeast cells] are ‘meta-prokaryotes’, [next] ‘‘‘multi-[eukaryotic-]cellular organisms’’’ [‘meta-biota’ -- “meta-zoa” [e.g., bears] and “meta-phyta” [e.g., trees]] are ‘meta-eukaryotes’, and proto-language-based “animal societies” [e.g., wolves, reindeer, horses, cattle, meerkats, etc., etc.] are ‘meta-multicellular organisms’, i.e., ‘meta-meta-biota’, or ‘meta²-biota’, etc.

Such ‘meta-«monad»-ization’, ‘meta-unit-ization’, ‘meta-«henad»-ization’, ‘meta-holon-ization’, ‘meta-element-ization’, or ‘meta-individual-ization’ is, as we have found in our research, the typical concrete, material form of the core-dialectical «aufheben» [self-]operation / [self-]process, although we have encountered some exceptional instances of [self-]«aufheben» dialectic that do not appear to involve its concretization as a [self-]‘meta-«monad»-ization’ operation/process, as of our present degree of discernment.

We call this core principle of dialectics ‘The Principle of «aufheben» Meta-Unitization’, or ‘The Principle of «aufheben» Meta-Monadization’, or ‘The Principle of «aufheben» Meta-Holonization’, or ‘The Principle of «aufheben» Meta-Elementization’, or ‘The Principle of «aufheben» Meta-Individualization’, etc.

This dialectical principle can also be articulated from a viewpoint of mathematical ‘categorial combinatorics’, or ‘class combinatorics’. 

From that perspective, we name it ‘The [Contra-Boolean] Principle of «aufheben» Self-Combinations’, and it can be stated as follows:   

‘Categorial «aufheben» Self-Combinations are the Sole Source of New Dialectical Antithesis Categories’.