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 –
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 –
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: 1966, Book 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 --
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!
No comments:
Post a Comment