Part 12: ‘Seldon’s Dialectics’ Series. Why Numbers [#] are [Self-]Contradictions [_#_], intuitively.

 

 

 

 

Part 12: ‘Seldon’s Dialectics’ Series.

 

Why Numbers [#] are [Self-]Contradictions  [_#_], intuitively.

 

 

 

 

 

 

 

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, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

 

This 12th release of this recent such series is posted below [Some E.D. standard edits have been applied, in the version presented below, by the editors of the F.E.D. Special Council for the Encyclopedia, to the direct transcript of our co-founder’s discourse].

 

 

 

Seldon –

 

“We use ‘#’ to denote the relation of ‘dialectical contradiction’ [a doubly-slashed – doubly-negated – equals sign].”

 

“Given that, we assert as follows -- 

‘Numbers # Numbers’

-- or just -- 

# # # 

-- with ‘#’ standing for “Natural”, “cardinal”, “numbers”.”

 

“That is, we assert that the category of [“natural”] numbers is self-contradictory.” 

 

“This assertion is a moment of the immanent critique that drives the transition ‘N_ --) N_ ~+~ _{N_} Q_’, 

via the self-critique of the first-order logic [double-underscored N], Peano-Dedekind axiomatization of the “natural” numbers, N_.  [The other moment of that immanent critique is the ‘intra-duality’ of the non-cardinal, “ordinal” aspect of the “natural” numbers -- the subtle inner tension between “ordinal quantity” and ‘ordinal quality’; between {1st, 2nd, 3rd, 4th, ...} and {1st-ness, 2nd-ness, 3rd-ness, 4th-ness, ...}]. 

 

“Why is it that we say that the ‘ideo-ontological’ category of the “natural” numbers, colloquially and collectively designated by ‘#’, are dialectical self-contradictions, and, therefore, are inherent in the set of all rules of ‘‘‘dialectical contradictions’’’ and of ‘‘‘dialectics’’’ as a whole, which we denote by ‘#_’ [double-underscored ‘#’]?”

 

“We do so by the following, dialectical, reasoning.” 

 

“Every “natural number”, Î#, is held to be an assemblage or plurality, treated as a unity, of one or more identical, abstract, unqualified units, each denoted by ‘1’.  E.g. --

1 º {1};

2 = 1 + 1, or {1  1};

3 = 1 + 1 + 1, or {1  1  1},

-- and so on.” 

 

“However, if all of these abstract units, each ‘1’, are identical, then there can really be only one of them, only 1 (one) 1.  Hence all of the other “natural” numbers – 2, 3, 4, etc. – collapse into just ‘1’, just as the set --

{1, 1, 1, …, 1} 

-- is really just {1}.  Thus, no actual “natural” numbers can actually exist, because even ‘1’ is not a “number of 1s”, but is only just 1 (one) 1.  Hence, no numbers exist.  Their composition by “multiple” identical units is even propositionally self-contradictory, hence impossible.” 

 

“This reductio ad absurdum fallacy is a consequence of the unacknowledged, unqualified abstractness of the formal “natural” numbers, which in fact are not “natural” in the ‘paleolithically’-human sense at all.  They are a latter-day ‘‘‘psychohistorical’’’ product of the emergence of ‘“the society based upon the exchange-value”’ [Marx], and of its corresponding human «mentalité», first emergent in [proto-]commodity barter, and, later, developing into monies-mediated exchange of commodities.  The most abstract form of “the exchange-value” is Marx’s category of “the elementary or accidental form of [commodity-]value”, abstracted from all money-mediation.  That Marxian category is the ‘«arché»-category’ of the entire, gigantic edifice of Marx’s immanent critique of the ideology-compromised science of capitalist political-economics.”

 

“For more-concrete, qualified, informal, really-natural numbers -- e.g., for numbers of apples – intuitively:

one apple plus one apple does equal two apples.  This is, in part, because no two actual apples are, or can ever be, exactly “identical”.  More than one apple – many, many more than one apple – can exist, have existed, and do exist now, and, ‘expectedly’, will exist, far into the future.  And no two apples can be exactly like one another.  Even if, somehow, two apples existed that were in all other ways indistinguishable, they could still not be identical, because they must occupy – to remain “apples” at all – two different, separate – physical-spatially separated – distinct volumes of physical space.”

 

“No such “space”, or “spacing”, or physical-spatial segregation is available for the abstract, mental – aphysical – unqualified unit(“s”), ‘1’, of the formal, so-called “natural”, number(“s”)!”

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, 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.

 

 

 

 

 

 

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