“The bond with reality is cut.”
— Hans Freudenthal, 1962
Related screenshot of a book review
from the November AMS Notices —
Saturday, October 17, 2020
Modernist Cuts
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Saturday, September 5, 2020
Ikonologie des Zwischenraums
The title is from a Cornell page in the previous post.
Related material (click to enlarge) —
The above remarks on primitive mentality suggest
a review of Snakes on a Plane.
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Friday, June 26, 2020
Persons and Operators and Things
| Harvard University Press on a book, Persons and Things, it published on March 31, 2010 Moving effortlessly between symbolist poetry and Barbie dolls, artificial intelligence and Kleist, Kant, and Winnicott, Barbara Johnson not only clarifies psychological and social dynamics; she also re-dramatizes the work of important tropes—without ever losing sight of the ethical imperative with which she begins: the need to treat persons as persons. In Persons and Things , Johnson turns deconstruction around to make a fundamental contribution to the new aesthetics. She begins with the most elementary thing we know: and reveals that their claims upon us are fraudulent. Johnson revolutionizes the method by showing that the inanimate thing exposed as a delusion is central to fantasy life, that fantasy life, however deluded, should be taken seriously, and that although a work of art “is formed around something missing,” this “void is its vanishing point, not its essence.” She shows deftly and delicately that the void inside Keats’s urn, Heidegger’s jug, or Wallace Stevens’s jar forms the center around which we tend to organize our worlds. The new aesthetics should restore fluidities between persons and things. In pursuing it, Johnson calls upon Ovid, Keats, Poe, Plath, and others who have inhabited this in-between space. The entire process operates via a subtlety that only a critic of Johnson’s caliber could reveal to us. |
I prefer the more straightforward insanity of Operators and Things .
Barbara Johnson reportedly died on Aug. 27, 2009. See that date
in other posts now tagged Autistic Enchantment. (That phrase is
the sort of sneering tag one may expect from deplorable academics.)
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Friday, April 17, 2020
A Mechanism of Fission
The above title was suggested by the previous post, Explosive Remarks.
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Sunday, February 9, 2020
Hors d’Oeuvre
From the May Day 2016 link above, in “Sunday Appetizer from 1984” —
| The 2015 German edition of Beautiful Mathematics , a 2011 Mathematical Association of America (MAA) book, was retitled Mathematische Appetithäppchen — Mathematical Appetizers . The German edition mentions the author’s source, omitted in the original American edition, for his section 5.17, “A Group of Operations” (in German, 5.17, “Eine Gruppe von Operationen”) —
That source was a document that has been on the Web |
From the Gap Dance link above, in “Reading for Devil’s Night” —
“Das Nichts nichtet.” — Martin Heidegger.
And “Appropriation Appropriates.”
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Tuesday, February 4, 2020
Cleavage
From Martin Heidegger's
Contributions to Philosophy (From Enowning) ,
Translated by Parvis Emad and Kenneth Maly,
Indiana University Press, 1999 (first published in German
in 1989 as Beiträge zur Philosophie (Vom Ereignis) but
written in 1936-1938 —
"The 'between' [das Zwischen ] is the simple 'bursting open'
that enowns be-ing to a being, which up until then is held back
from what is ownmost to it and is not yet to be named a being.
This 'bursting open' is the clearing for the sheltered. But the
'bursting open' does not disperse. and the clearing is not a mere
emptiness.
The 'between' [das Zwischen ] which bursts open gathers
what it removes into the open of its strifing and refusing
belongingness, moves unto the ab-ground , out of which everything
(god, man, world, earth) recoils in swaying into itself and thus leaves
to be-ing the unique decidedness of en-ownment."
— 270, "The Essential Sway of Be-ing" (p. 341)
"Enownment and enstrifing, historical grounding and decision,
uniqueness and the onefold, what has the character of
the between [Zwischenhafte ] and the cleavage [Geklüft ] —
they never name the essential sway of be-ing as properties
but rather in each case the whole essential swaying* of its essential
sway."
— 270, "The Essential Sway of Be-ing" (p. 342)
* For "swaying" as "unfolding," see (for instance)
the Stanford Encyclopedia of Philosophy and
also George Kovacs, Thinking and Be-ing in Heidegger's
Beiträge zur Philosophie (Vom Ereignis) ,
Zeta Books, 2015.
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Thursday, January 23, 2020
The Demarcation of Nothing
"… nothing could be demarcated as 'hors d'oeuvre'…"
— Geoffrey Hartman in his Haskins Lecture for 2000
(quoted here on Columbus Day, 2004).
See also May Day 2016 and Gap Dance.
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Wednesday, January 22, 2020
Gap Dance
From Wallace Stevens, "The Man with the Blue Guitar":
IX
And the color, the overcast blue
Of the air, in which the blue guitar
Is a form, described but difficult,
And I am merely a shadow hunched
Above the arrowy, still strings,
The maker of a thing yet to be made . . . .
"Arrowy, still strings" from the diamond theorem
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Wednesday, January 15, 2020
Paradigm Shift
Illustration, from a search in this journal for “Symplectic” —
.
Some background: Rift-design in this journal and …
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Saturday, December 14, 2019
Colorful Tale
The above image is from
"A Four-Color Theorem:
Function Decomposition Over a Finite Field,"
http://finitegeometry.org/sc/gen/mapsys.html.
These partitions of an 8-set into four 2-sets
occur also in Wednesday night's post
Miracle Octad Generator Structure.
This post was suggested by a Daily News
story from August 8, 2011, and by a Log24
post from that same date, "Organizing the
Mine Workers" —
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Monday, December 2, 2019
Aesthetics at Harvard
"What the piece of art is about is the gray space in the middle."
— David Bowie, as quoted in the above Crimson piece.
Bowie's "gray space" is the space between the art and the beholder.
I prefer the gray space in the following figure —
Context: The Trinity Stone (Log24, June 4, 2018).
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Thursday, June 13, 2019
Seeing the Seing
The phrase "experimental metaphysics" appeared in Peter Woit's weblog on June 11.
Google reveals that . . .
"… 'experimental metaphysics' is a term coined by Abner Shimony …."
Shimony reportedly died on August 8, 2015. Also on that date —
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Tuesday, May 21, 2019
Monday, May 20, 2019
The Bond with Reality
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Tuesday, May 7, 2019
Breach
"Honored in the Breach:
Graham Bader on Absence as Memorial"
Artforum International , April 2012
|
. . . . "In the wake of a century marked by inconceivable atrocity, the use of emptiness as a commemorative trope has arguably become a standard tactic, a default style of public memory. The power of the voids at and around Ground Zero is generated by their origin in real historical circumstance rather than such purely commemorative intent: They are indices as well as icons of the losses they mark.
Nowhere is the negotiation between these two possibilities–on the one hand, the co-optation of absence as tasteful mnemonic trope; on the other, absence's disruptive potential as brute historical scar–more evident than in Berlin, a city whose history, as Andreas Huyssen has argued, can be seen as a 'narrative of voids.' Writing in 1997, Huyssen saw this tale culminating in Berlin's post-wall development, defined equally by an obsessive covering-over of the city's lacunae–above all in the elaborate commercial projects then proliferating in the miles-long stretch occupied until 1989 by the Berlin Wall–and a carefully orchestrated deployment of absence as memorial device, particularly in the 'voids' integrated by architect Daniel Libeskind into his addition to the Berlin Museum, now known as the Jewish Museum Berlin." |
See also Breach in this journal.
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Monday, May 6, 2019
One Stuff
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Saturday, May 4, 2019
Inside the White Cube
See also Espacement and The Thing and I.
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Wednesday, April 24, 2019
Critical Visibility
Correction — "Death has 'the whole spirit sparkling…'"
should be "Peace after death has 'the whole spirit sparkling….'"
The page number, 373, is a reference to Wallace Stevens:
Collected Poetry and Prose , Library of America, 1997.
See also the previous post, "Critical Invisibility."
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Tuesday, April 23, 2019
Critical Invisibility
From Gotay and Isenberg, "The Symplectization of Science,"
Gazette des Mathématiciens 54, 59-79 (1992):
"… what is the origin of the unusual name 'symplectic'? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure 'line complex group' the 'symplectic group.'
… the adjective 'symplectic' means 'plaited together' or 'woven.'
This is wonderfully apt…."
On "The Emperor's New Clothes" —
|
Andersen’s weavers, as one commentator points out, are merely insisting that “the value of their labor be recognized apart from its material embodiment.” The invisible cloth they weave may never manifest itself in material terms, but the description of its beauty (“as light as spiderwebs” and “exquisite”) turns it into one of the many wondrous objects found in Andersen’s fairy tales. It is that cloth that captivates us, making us do the imaginative work of seeing something beautiful even when it has no material reality. Deeply resonant with meaning and of rare aesthetic beauty—even if they never become real—the cloth and other wondrous objets d’art have attained a certain degree of critical invisibility. — Maria Tatar, The Annotated Hans Christian Andersen (W. W. Norton & Company, 2007). Kindle Edition. |
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A Certain Dramatic Artfulness
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Monday, March 25, 2019
Espacement
(Continued from the previous post.)
|
In-Between "Spacing" and the "Chôra " (Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.), Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010) "The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)." 1 Jacques Derrida, “La Différance,” in Marges – de la philosophie (Paris: Minuit, 1972), p. 14. Henceforth cited as D . 2 Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and Difference (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW . 3 Jacques Derrida, Le Toucher, Jean-Luc Nancy (Paris: Galilée, 2000), p. 207. . . . . "… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance that Derrida must, in a 'properly' apotropaic gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…." 16 Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger 2 (1990): 207-227. . . . . … "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.' |
For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements ) between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).
Espacements
For the Church of Synchronology —
See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.
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Sunday, March 24, 2019
Espacement: Geometry of the Interstice in Literary Theory
"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982
|
https://www.parrhesiajournal.org/ Parrhesia No. 3 • 2007 • 22–32
(Up) Against the (In) Between: Interstitial Spatiality by Clare Blackburne Blackburne — www.parrhesiajournal.org 24 — "The excessive notion of espacement as the resurgent spatiality of that which is supposedly ‘without space’ (most notably, writing), alerts us to the highly dynamic nature of the interstice – a movement whose discontinuous and ‘aberrant’ nature requires further analysis." Blackburne — www.parrhesiajournal.org 25 — "Espacement also evokes the ambiguous figure of the interstice, and is related to the equally complex derridean notions of chora , différance , the trace and the supplement. Derrida’s reading of the Platonic chora in Chora L Works (a series of discussions with the architect Peter Eisenman) as something which defies the logics of non-contradiction and binarity, implies the internal heterogeneity and instability of all structures, neither ‘sensible’ nor ‘intelligible’ but a third genus which escapes conceptual capture.25 Crucially, chora , spacing, dissemination and différance are highly dynamic concepts, involving hybridity, an ongoing ‘corruption’ of categories, and a ‘bastard reasoning.’26 Derrida identification of différance in Margins of Philosophy , as an ‘unappropriable excess’ that operates through spacing as ‘the becoming-space of time or the becoming-time of space,’27 chimes with his description of chora as an ‘unidentifiable excess’ that is ‘the spacing which is the condition for everything to take place,’ opening up the interval as the plurivocity of writing in defiance of ‘origin’ and ‘essence.’28 In this unfolding of différance , spacing ‘insinuates into presence an interval,’29 again alerting us to the crucial role of the interstice in deconstruction, and, as Derrida observes in Positions , its impact as ‘a movement, a displacement that indicates an irreducible alterity’: ‘Spacing is the impossibility for an identity to be closed on itself, on the inside of its proper interiority, or on its coincidence with itself. The irreducibility of spacing is the irreducibility of the other.’30"
25. Quoted in Jeffrey Kipnis and Thomas Leeser, eds., 26. Ibid, 25.
27. Derrida, Margins of Philosophy. 28. Derrida, Chora L Works , 19 and 10. 29. Ibid, 203. 30. Derrida, Positions , 94. |
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Saturday, March 23, 2019
Another Typology
"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982
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Thursday, March 21, 2019
Geometry of Interstices
Finite Galois geometry with the underlying field the simplest one possible —
namely, the two-element field GF(2) — is a geometry of interstices :
For some less precise remarks, see the tags Interstice and Interality.
The rationalist motto "sincerity, order, logic and clarity" was quoted
by Charles Jencks in the previous post.
This post was suggested by some remarks from Queensland that
seem to exemplify these qualities —
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Tuesday, March 5, 2019
The Eightfold Cube and PSL(2,7)
For PSL(2,7), this is ((49-1)(49-7))/((7-1)(2))=168.
The group GL(3,2), also of order 168, acts naturally
on the set of seven cube-slicings below —
Another way to picture the seven natural slicings —
Application of the above images to picturing the
isomorphism of PSL(2,7) with GL(3,2) —
.gif)
For a more detailed proof, see . . .
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Saturday, September 29, 2018
“Ikonologie des Zwischenraums”
The title is from Warburg. The Zwischenraum lines and shaded "cuts"
below are to be added together in characteristic two, i.e., via the
set-theoretic symmetric difference operator.
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Saturday, September 15, 2018
Eidetic Reduction in Geometry
|
"Husserl is not the greatest philosopher of all times. — Kurt Gödel as quoted by Gian-Carlo Rota Some results from a Google search — Eidetic reduction | philosophy | Britannica.com Eidetic reduction, in phenomenology, a method by which the philosopher moves from the consciousness of individual and concrete objects to the transempirical realm of pure essences and thus achieves an intuition of the eidos (Greek: “shape”) of a thing—i.e., of what it is in its invariable and essential structure, apart … Phenomenology Online » Eidetic Reduction
The eidetic reduction: eidos. Method: Bracket all incidental meaning and ask: what are some of the possible invariate aspects of this experience? The research Eidetic reduction – New World Encyclopedia Sep 19, 2017 – Eidetic reduction is a technique in Husserlian phenomenology, used to identify the essential components of the given phenomenon or experience. |
For example —
The reduction of two-colorings and four-colorings of a square or cubic
array of subsquares or subcubes to lines, sets of lines, cuts, or sets of
cuts between* the subsquares or subcubes.
See the diamond theorem and the eightfold cube.
* Cf. posts tagged Interality and Interstice.
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Thursday, September 13, 2018
Godard and Interality
The previous post, "One Plus One," suggests some further
art-historical remarks on interality —
|
From Third Text , 2013, Vol. 27, No. 6, pp. 774–785 — "Genealogy of the Image in Histoire(s) du Cinéma : Godard, Warburg and the Iconology of the Interstice" * * * * P. 775 — My discussion will focus on the significance of the concept of the ‘space in-between,’ its importance for Godard’s work and its role in a relational historiography of images more broadly. I hope to corroborate how Godard functions as a twenty-first century archaeologist of the moving image, constructing a meta-cinematic collage that, while consisting of an indexing of (almost exclusively) pre-existing filmic samples, ends up becoming a hybrid work of art in its own right. Godard, in the final analysis, expands the Warburgian programme of iconology into that of a cinematographic iconology of the interstice. * * * * P. 777 — Godard conceives of the image only in the plural, in the intermediate space between two images, be it a prolonged one (in Histoire(s) there are frequent instances of black screens) or a non-existent one (superimposition, co-presence of two images on screen). He comments: ‘[For me] it’s always two, begin by showing two images rather than one, that’s what I call image, the one made up of two’ [18] and elsewhere, ‘I perceived . . . cinema is that which is between things, not things [themselves] but between one and another.’ [19] 18. Jean-Luc Godard and Youssef Ishaghpour, "Archéologie du cinéma et mémoire du siècle," Farrago ,Tours, 2000, p. 27. The title of this work is reflective of the Godardian agenda that permeates Histoire(s) . 19. Jean-Luc Godard, "Introduction à une véritable histoire du cinéma," Albatros , Paris,1980, p. 145 * * * * P. 783 — If it is in ‘the in-between’ that thought is born, then for Godard cinematography as ‘a form that thinks . . . was born with the advent of modern painting.’ [62] 62. Godard and Ishaghpour, op. cit., pp 45–46. * * * * P. 785 — Warburg commented on the signification of the black spaces that he placed between images in his analysis of the network of intervals in Mnemosyne , by quoting Johann Wolfgang Goethe’s dictum ‘the truth inhabits the middle space.’ [68] This citation induces a feeling of déjà-vu for the viewer of Histoire(s). The link was not missed by Warburg himself, as one of his diary entries testifies: ‘We can compare this phenomenon [the iconology of the interval] to that of the cinematic montage, the domain of the interpretation is an intervallic one.’ [69] 68. Warburg, Mnemosyne , pp 135–146. 69. Warburg is quoted in Didi-Huberman, L’image survivante, p. 503. (Georges Didi-Huberman, L’image survivante. Histoire de l’art et temps des fantômes selon Aby Warburg , Minuit, Paris, 2002) |
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Saturday, September 8, 2018
Monday, July 23, 2018
Space 101
From the April 1st publication date of "Interality Shows Through,"
by Geling Shang —
See too yesterday's post Space.
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Sunday, July 22, 2018
Sunday, January 7, 2018
Saturday, January 6, 2018
Report from Red Mountain
Tom Wolfe in The Painted Word (1975):
“It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde understood, they
were not only theories but … hot news,
straight from the studios, from the scene.”
Harold Rosenberg in The New Yorker (click to enlarge)—
See also Interality and the Eightfold Cube .
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Friday, January 5, 2018
Types of Ambiguity
From "The Principle of Sufficient Reason," by George David Birkhoff,
in "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940 —
From the same lecture —
|
Up to the present point my aim has been to consider a variety of applications of the Principle of Sufficient Reason, without attempting any precise formulation of the Principle itself. With these applications in mind I will venture to formulate the Principle and a related Heuristic Conjecture in quasi-mathematical form as follows: PRINCIPLE OF SUFFICIENT REASON. If there appears in any theory T a set of ambiguously determined ( i e . symmetrically entering) variables, then these variables can themselves be determined only to the extent allowed by the corresponding group G. Consequently any problem concerning these variables which has a uniquely determined solution, must itself be formulated so as to be unchanged by the operations of the group G ( i e . must involve the variables symmetrically). HEURISTIC CONJECTURE. The final form of any scientific theory T is: (1) based on a few simple postulates; and (2) contains an extensive ambiguity, associated symmetry, and underlying group G, in such wise that, if the language and laws of the theory of groups be taken for granted, the whole theory T appears as nearly self-evident in virtue of the above Principle. The Principle of Sufficient Reason and the Heuristic Conjecture, as just formulated, have the advantage of not involving excessively subjective ideas, while at the same time retaining the essential kernel of the matter. In my opinion it is essentially this principle and this conjecture which are destined always to operate as the basic criteria for the scientist in extending our knowledge and understanding of the world. It is also my belief that, in so far as there is anything definite in the realm of Metaphysics, it will consist in further applications of the same general type. This general conclusion may be given the following suggestive symbolic form:
While the skillful metaphysical use of the Principle must always be regarded as of dubious logical status, nevertheless I believe it will remain the most important weapon of the philosopher. |
Related remarks by a founding member of the Metaphysical Club:
See also the previous post, "Seven Types of Interality."
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Seven Types of Interality*
* See the term interality in this journal.
For many synonyms, see
“The Human Seriousness of Interality,”
by Peter Zhang, Grand Valley State University,
China Media Research 11(2), 2015, 93-103.
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Thursday, January 4, 2018
Perspectives from a Chinese Jar
" . . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."
— T. S. Eliot, Four Quartets
"The Grand Valley spirit never dies."
— Adapted from the Tao Te Ching
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Monday, January 16, 2017
Interality Illustrated
For the "interality" of the title, click on the tag.
Click the above image for posts tagged "The Positive."
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Sunday, January 15, 2017
April First Interality
Data for an essay titled "Interality in Heidegger" —
See also Log24 posts
on that same date —
April 1, 2015.
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