Tuesday, March 12, 2024

Part 07: ‘Seldon’s Ideographies’ Series. Radical Dualism Relation-Sign.

 


 

 

 

Part 07: ‘Seldon’s Ideographies Series.

 

Radical Dualism Relation-Sign.

 

 

 

 

 

 

 

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 7th release of this new 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 the sign ‘¬|®’ to describe a perceived relationship of radical dualism, or of antinomy -- Kantian or ‘Kantianesque’ -- between two categories, or between two propositions.

 

We use this sign to describe the views and persuasions of others, such as Kant’s opinions, rather than to describe our own views, because we do not expect to find actual antinomies, actual radical dualisms, in reality.

 

Consider Kant’s paired, opposed propositions regarding human opinions of universal physical space from his “Antinomy of Pure Reason”0 --

 

 

“…the world is not infinite, as regards extension in space, but enclosed in limits”.1

¬|®

“…the world is not limited with regard to space, that is, it is infinite in extension”.2

 

This “transcendental dialectic”, the apparently absolute antithesis of these two propositions, each seemingly true, but each apparently radically denying the other, and thus absolutely opposed, absolutely irresolvable -- forming an apparently absolute contradiction, an apparently eternal, radical duality -- represent a catastrophe of failure for Kant’s “pure reason”.

 

Kant purports to prove true each, both of these – mutually formally contradictory – propositions, thus in effect, proving a contradiction to be true.

 

Because of the resulting impasse of “pure reason”, which abhors formal propositional contradiction -- akin, perhaps, to a more extreme form of Zenoan «reductio ad absurdum» or of Socratean «elenchus» -- Kant asserts to have refuted, not just each of these propositions, and not just their mutual relationship or pairing, but to have refuted the competency of pure reason itself, when applied to objects, such as, here, to universal physical space, that “transcend” human experience.

 

Is such antinomy the price that human reason pays for speculating beyond direct human experience?

 

Apparently not!  Not in the mind of Albert Einstein, in his Theory of General Relativity, and not in the many minds of those who have grasped his, so-far empirically corroborated, work ever since its publication in 1915.

 

Apparently Einstein had something in store that would “transcend” the ken of Kant, something beyond anticipation in Kant’s time.

 

The ‘dialectogram’ posted above depicts Einstein’s – ‘unstatedly’-dialectical – resolution, and, thereby, Einstein’s dialectical refutation, via dialectical synthesis, of Kant’s antinomy of universal physical space.  In Einstein’s own words –

 

Can we picture to ourselves a three-dimensional universe which is finite, yet

unbounded? … Yes.3

 

The, “4-dimensional”, “space-time continuum” geometries which solve Einstein’s General Relativity Field Equations for Gravity – which solve, simultaneously, Einstein’s ten, nonlinear, partial differential equations for the “shape” of space[-time] -- the ‘curvations’ of which, induced by the presence of densifications of mass-energy, manifest to us as the “force” of gravity, exhibit solutions to Kant’s antinomy of physical space; geometries which are both finite and unbounded.

 

Of course, the antinomial, actually antithetical relation between Kant’s two propositions is also a relation of formal-logical, propositional contradiction.  Our symbol for that kind of relationship is described in –


F.E.D. Dialectics: Part 02: ‘Seldon’s Ideographies’ Series. The Seldonian Sign for Propositional Contradiction. (feddialectics-miguel.blogspot.com)

 

 

Moreover, if their antithesis is construed categorially, then their mutual relationship is one of dialectical, ontological-categorial contradiction

 

Finite physical spaces # Unbounded physical spaces,

 

or, in its ‘“well-formed”’ form –

 

uncritical space concepts # uncritical space concepts.

 

 

Our symbol for that kind of relationship is presented in –


F.E.D. Dialectics: Part 05: ‘Seldon’s Ideographies’ Series. Seldon’s Symbol for ‘‘‘Dialectical [Self-]Contradiction’’’. (feddialectics-miguel.blogspot.com)

 

 

Categorially, Einstein’s General-Relativistic, ‘‘‘complex unity’’’, determinations-rich, ‘multi-determinational’ solution to Kant’s antinomy, is the ‘uni-category’, modified for the involvement of Lambda “Dark Energy” anti-gravity, which is describable as the category of –

 

Finite, indefinitely-self-expanding, unbounded, negatively-curved, anti-gravity-involving physical space-times.

 

That is, Einstein’s solution to Kant’s antinomy applies not just to the, presently ruled-out, classic case of a “positively-curved supersphere” geometry that can also solve the General Relativity Field Equations, but a universe fore-doomed to catastrophically and apocalyptically recollapse, into a “singularity”.

 

Einstein’s solutions also include the present consensus view of our actual cosmological geometry, akin to the classic “negatively-curved”, saddle-like geometry-solution to the General Relativity Field Equations, but involving an anti-gravity”, expansive counter-tendency to the gravitic, contractive tendency, e.g., the self-expansive tendency of “Dark Energy”.

 

In that solution, as in the “supersphere” solution, e.g., one’s space vehicle would be able to travel a vast but still finite distance to bring one’s vehicle, and oneself, or one’s descendants, back to one’s physical-geometrical starting point, without ever encountering a “boundary” – without ever meeting an inextricable end to physical space – anywhere along that entire journey.

 

 

We do not expect to encounter true antinomies, but we must admit that the antithetical diremptions oft posited as if –

 

Discreteness  ¬|®  Continuousness,

 

and

 

Freedom  ¬|®  Necessity

 

-- still give us pause, as their full dialectical resolution, their fully-adequate uni-categories, or ‘‘‘complex unities’’’, still elude us.

 

___________________________________________________________________________________________________________

0[Immanuel Kant, Critique of Pure Reason, Anchor, NY: 1966Book II. …, Second Division. Transcendental Dialectic, Chapter II. The Antinomy of Pure Reason, Section 2. Antithetic of Pure Reason].

1[Immanuel Kant, Critique of Pure Reason, ibid., p. 308].

2[Immanuel Kant, Critique of Pure Reason, ibid., p. 307].

3[Albert Einstein, Geometry and Experience, address to Prussian Academy of Sciences, Berlin, 27 Jan. 1922].

 

 

 

 

 

 

 

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 artas 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!

 

 

 

 

 

 

 

 

 

 

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