Part 09: Seldon’s Axioms Series. Re-Presentation of the nQ Axioms-System as a Whole.

 

 

 

Part 09: Seldon’s Axioms Series.

 

 

Re-Presentation of the _NQ Axioms-System as a Whole.

 

 

 

 

 

 

 

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 definitions of the key elements of Seldonian Theory.

 

The 9th text in this new such series is posted both above and 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 –

 

“In our presentations of the core axioms of the _NQ arithmetic for modeling dialectics, we should emphasize the character of that arithmetic as a “non-standard model of the Peano Natural Numbers” –    

“…The [E.D. – by Gödel] incompleteness theorems hold also for higher-order formalizations of number theory.  If only first-order formalizations are considered, then the [E.D. – also by Gödel] completeness theorem applies as well, and together they yield not a contradiction, but an interesting conclusion: Any sentence of [E.D. – “Natural”] arithmetic that is undecidable must be true in some models of Peano’s axioms (lest it be formally refutable) and false in others (lest it be formally provable).  In particular, there must be models of first-order Peano arithmetic whose elements do not “behave” the same as the [E.D. – “standard”] “natural numbers”.  Such nonstandard models were unforeseen and unintended, but they cannot be ignored, for their existence implies that no first-order axiomatization of number theory can be adequate to the task of deriving as theorems exactly those statements that are true of the [E.D. – “standard”] natural numbers.  [E.D. – emphases as in original].”

[J. W. Dawson, Jr., Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters, Ltd., 1997, pp. 67-68.].”

 

“To do so, it would be helpful to organize our nine core axioms in the following new format:

 

Section 1: ‘Peanic Axioms’ [axioms §1–§4; a non-standard version of the first 4, first-order-logic “Peano Postulates”];

Section 2: ‘Bridging Axiom’ [axiom §5; links _NQ to N]

Section 3: ‘Non-Peanic Non-Standard Axioms’ [axioms §6–§9; the axioms which define the major ‘ideo-ontological’ differences distinguishing _N  Q   from N   ].”

 

 

 

 

 

 

 

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.

 

 

 

 

 

 

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

 

 

 

 

 

 

Dialogue with a Reader: On ‘‘‘Self-INVOLUTION’’’ and the Dialectic of Nature.

 

 

 

 

 

 

 

 

Dialogue with a Reader:

On ‘‘‘Self-INVOLUTION’’’ and the Dialectic of Nature.

 

 

 

Reader: “…Could you explain how you are using the term “self-involution” —  what you mean by this, and how you are using this term in conjunction with the term “aufheben”?”

 

“I know what the latter means, but I am not clear about “self-involution” — and whether it is necessary or redundant when conjoined to “aufheben”.” 

“So you may be using this term in a technical sense with which I am not acquainted.” 

 

“Also I am wondering about how you are characterizing evolutionary processes, that is, what is the mechanism by which things (cells, plants, animals, etc.) evolve.”

 

“I am suspicious of the use of the terms “aufheben” and “self-involution” in this regard — note, I said suspicious, not rejecting.”

 

“I can explain my suspicions if and when you provide a little more detail.”

 

“So maybe along with defining “self-involution” you could explain how it applies to the examples you gave in our previous correspondence --

 

1.  “atoms are the neo-ontological product of our stipulated first self-«aufheben» self-involution, that of “particles”;”

2.  “molecules are the neo-ontological product of our modeled second self-«aufheben» self-involution, that of atoms;”

3.  “prokaryotic living cells are the neo-ontological product of our modeled 3rd self-«aufheben» self-involution, that of molecules [the leap from molecules to living cells is a big one, that could be sub-divided into mere ‘‘‘mers’’’, “poly-mers”; ‘poly-poly-mers’, etc., once more has been learned about pre-biological molecular evolution];”

4.  “eukaryotic living cells are the neo-ontological product of the 4th self-«aufheben» self-involution, that of the prokaryotes;”

5.  “asocial ‘multi-eukaryotic-cellular organisms’ are the neo-ontological product of the 5th self-«aufheben» self-involution, that of the eukaryotes;”

6.  “social organisms – ‘multi-eukaryotic-cellular’ “social animals” [social “meta-zoa”], and ‘multi-eukaryotic-cellular’ ‘social plants’ [social “meta-phyta”] are the neo-ontological products of the 6th self-«aufheben» self-involution, that of the asocial ‘meta-biota’;”

7.  “human, ‘meta-social’ societies are the neo-ontological product of the 7th self-«aufheben» self-involution, that of merely-social [meta^0-social] organisms – that of merely-social, proto-languages-based “meta-zoa” and “meta-phyta”.

 

If possible, please try to make your explanations understandable to an air-head like myself.”

 

 

 

My reply: First off, you are not an “air-head”, but someone who is concerned with, and who thinks about, the major issues facing Terran humanity as a whole – not someone who is totally and obsessively concerned with only the pettiest details of “personal” creature comforts, etc., etc.

That, of course, does not mean that you and I agree about the optimal resolution of those major issues.

 

I have formatted my reply to your query as a series of JPG image-pages, posted below, so that I can incorporate original illustrative images and ideographical symbols where needed.

 

¡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.

 

 

 

 

 

 

 

 

For more information regarding the 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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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