Log24

Friday, October 13, 2023

Turn, Turn, Turn

Filed under: General — Tags: , , — m759 @ 3:06 am

The conclusion of a Hungarian political figure's obituary in
tonight's online New York Times, written by Clay Risen

"A quietly religious man, he spent his last years translating
works dealing with Roman Catholic canon law."

This  journal on the Hungarian's date of death, October 8,
a Sunday, dealt in part with the submission to Wikipedia of
the following brief article . . . and its prompt rejection.

The Cullinane diamond theorem is a theorem
about the Galois geometry underlying
the Miracle Octad Generator of R. T. Curtis.[1]

The theorem also explains symmetry properties of the
sort of chevron or diamond designs often found on quilts.

Reference

1. Cullinane diamond theorem at
the Encyclopedia of Mathematics

Some quotations I prefer to Catholic canon law —

Ludwig Wittgenstein,
Philosophical Investigations  (1953)

97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior  to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be
allowed to affect it ——It must rather be of
the purest crystal. But this crystal does not appear
as an abstraction; but as something concrete,
indeed, as the most concrete,
as it were the hardest  thing there is.

* See the post Wittgenstein's Diamond.

Related language in Łukasiewicz (1937)—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

See as well Diamond Theory in 1937.

Thursday, February 2, 2023

The Menand Lede

Filed under: General — Tags: — m759 @ 4:29 pm

"When the Washington Post  unveiled the slogan
'Democracy Dies in Darkness,' on February 17, 2017,
people in the news business made fun of it.
'Sounds like the next Batman movie,' the New York Times’ 
executive editor, Dean Baquet, said."

— Louis Menand in The New Yorker ,
"When Americans Lost Faith in the News," Jan. 30, 2023.

See also Darkness  in this  journal.

Not so dark:

A Log24 post from February 17, 2017
regarding that year's Groundhog Day — The dies natalis
(in the Catholic sense) of St. Bertram Kostant.

Friday, January 31, 2020

Notes for a Blue Guitar

Filed under: General — m759 @ 11:00 pm

Gravatar at the weblog of Peter J. Cameron

Same Gravatar in blue —

Synchronology check —

Click Lukasiewicz for further remarks.

Wednesday, October 3, 2018

Adamantine Meditation

Filed under: General,Geometry — Tags: — m759 @ 12:24 pm

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

A Catholic philosopher —

Related art —

Image result for mog miracle octad bricks

Saturday, July 1, 2017

Polish Logic

Filed under: General — m759 @ 11:55 pm

See Lukasiewicz in this journal.

Wednesday, November 9, 2011

Polish Logic–

Filed under: General — Tags: — m759 @ 11:23 am

The Big Lukasiewicz

“Lord Arglay had a suspicion that the Stone
would be purely logical.  Yes, he thought,
but what, in that sense, were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

See also Łukasiewicz in Wikipedia and Lukasiewicz in this journal.

The latter's Christian references seem preferable to yesterday's
link to a scene from the Coen brothers' film "The Big Lebowski."

For those who prefer  a Christ-for-Jews there is
also Harvard's version. See The Crimson Passion.

Sunday, July 10, 2011

Wittgenstein’s Diamond

Filed under: General,Geometry — Tags: , — m759 @ 9:29 am

Philosophical Investigations  (1953)

97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior  to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be allowed to affect it
——It must rather be of the purest crystal.
But this crystal does not appear as an abstraction;
but as something concrete, indeed, as the most concrete,
as it were the hardest  thing there is
(Tractatus Logico-Philosophicus  No. 5.5563).

— Translation by G.E.M. Anscombe

5.5563

All propositions of our colloquial language
are actually, just as they are, logically completely in order.
That simple thing which we ought to give here is not
a model of the truth but the complete truth itself.

(Our problems are not abstract but perhaps
the most concrete that there are.)

97. Das Denken ist mit einem Nimbus umgeben.
—Sein Wesen, die Logik, stellt eine Ordnung dar,
und zwar die Ordnung a priori der Welt,
d.i. die Ordnung der Möglichkeiten ,
die Welt und Denken gemeinsam sein muß.
Diese Ordnung aber, scheint es, muß
höchst einfach  sein. Sie ist vor  aller Erfahrung;
muß sich durch die ganze Erfahrung hindurchziehen;
ihr selbst darf keine erfahrungsmäßige Trübe oder Unsicherheit anhaften.
——Sie muß vielmehr vom reinsten Kristall sein.
Dieser Kristall aber erscheint nicht als eine Abstraktion;
sondern als etwas Konkretes, ja als das Konkreteste,
gleichsam Härteste . (Log. Phil. Abh.  No. 5.5563.)

See also

Related language in Łukasiewicz (1937)—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

* Updates of 9:29 PM ET July 10, 2011—

A  mnemonic  from a course titled “Galois Connections and Modal Logics“—

“Traditionally, there are two modalities, namely, possibility and necessity.
The basic modal operators are usually written box (square) for necessarily
and diamond (diamond) for possibly. Then, for example, diamondP  can be read as
‘it is possibly the case that P .'”

See also Intensional Semantics , lecture notes by Kai von Fintel and Irene Heim, MIT, Spring 2007 edition—

“The diamond symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬¬. The dual symbol was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich  ‘possible.’”

Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.

Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.

Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.

Saturday, November 27, 2010

Simplex Sigillum Veri

Filed under: General,Geometry — m759 @ 7:20 am

An Adamantine View of "The [Philosophers'] Stone"

The New York Times  column "The Stone" on Sunday, Nov. 21 had this—

"Wittgenstein was formally presenting his Tractatus Logico-Philosophicus , an already well-known work he had written in 1921, as his doctoral thesis. Russell and Moore were respectfully suggesting that they didn’t quite understand proposition 5.4541 when they were abruptly cut off by the irritable Wittgenstein. 'I don’t expect you to understand!' (I am relying on local legend here….)"

Proposition 5.4541*—

http://www.log24.com/log/pix10B/101127-WittgensteinSimplex.jpg

Related material, found during a further search—

A commentary on "simplex sigillum veri" leads to the phrase "adamantine crystalline structure of logic"—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

For related metaphors, see The Diamond Cube, Design Cube 2x2x2, and A Simple Reflection Group of Order 168.

Here Łukasiewicz's phrase "the hardest of materials" apparently suggested the commentators' adjective "adamantine." The word "diamond" in the links above refers of course not to a material, but to a geometric form, the equiangular rhombus. For a connection of this sort of geometry with logic, see The Diamond Theorem and The Geometry of Logic.

For more about God, a Stone, logic, and cubes, see Tale  (Nov. 23).

* 5.4541 in the German original—

  Die Lösungen der logischen Probleme müssen einfach sein,
  denn sie setzen den Standard der Einfachheit.
  Die Menschen haben immer geahnt, dass es
  ein Gebiet von Fragen geben müsse, deren Antworten—
  a priori—symmetrisch, und zu einem abgeschlossenen,
  regelmäßigen Gebilde vereint liegen.
  Ein Gebiet, in dem der Satz gilt: simplex sigillum veri.

  Here "einfach" means "simple," not "neat," and "Gebiet" means
  "area, region, field, realm," not (except metaphorically) "sphere."

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