Wednesday, January 30, 2013

Abstract Possibility

Filed under: General — m759 @ 1:01 PM

Today's NY Times  "Stone Links" to philosophy include
a link to a review of a collection of Hilary Putnam's papers.

Related material, from Putnam's "What is Mathematical
" (Historia Mathematica  2 (1975): 529-543)—

"In this paper I argue that mathematics should be interpreted realistically – that is, that mathematics makes assertions that are objectively true or false, independently of the human mind, and that something answers to such mathematical notions as ‘set’ and ‘function’. This is not to say that reality is somehow bifurcated – that there is one reality of material things, and then, over and above it, a second reality of ‘mathematical things’. A set of objects, for example, depends for its existence on those objects: if they are destroyed, then there is no longer such a set. (Of course, we may say that the set exists ‘tenselessly’, but we may also say the objects exist ‘tenselessly’: this is just to say that in pure mathematics we can sometimes ignore the important difference between ‘exists now’ and ‘did exist, exists now, or will exist’.) Not only are the ‘objects’ of pure mathematics conditional upon material objects; they are, in a sense, merely abstract possibilities. Studying how mathematical objects behave might better be described as studying what structures are abstractly possible and what structures are not abstractly possible."

See also Wittgenstein's Diamond and Plato's Diamond.

Saturday, June 9, 2012

Misquoting Nietzsche

Filed under: General — Tags: — m759 @ 11:01 AM

Jim Holt in tomorrow’s New York Times

“Allow me to quote Nietzsche
(although I know that will be considered
by some to be in bad taste):

‘As the circle of science grows larger,
it touches paradox at more places.'”

A possible source for this misquotation—
Harvard University Press

IMAGE- Hilary Putnam misquoting Nietzsche on 'the circle of science'

A more accurate quotation—

Anyone who has ever experienced the pleasure of Socratic insight and felt how, spreading in ever-widening circles, it seeks to embrace the whole world of appearances, will never again find any stimulus toward existence more violent than the craving to complete this conquest and to weave the net impenetrably tight. To one who feels that way, the Platonic Socrates will appear as the teacher of an altogether new form of “Greek cheerfulness” and blissful affirmation of existence that seeks to discharge itself in actions— most often in maieutic and educational influences on noble youths, with a view to eventually producing a genius.

But science, spurred by its powerful illusion, speeds irresistibly towards its limits where its optimism, concealed in the essence of logic, suffers shipwreck. For the periphery of the circle of science has an infinite number of points; and while there is no telling how this circle could ever be surveyed completely, noble and gifted men nevertheless reach, e’er half their time and inevitably, such boundary points on the periphery from which one gazes into what defies illumination. When they see to their horror how logic coils up at these boundaries and finally bites its own tail— suddenly the new form of insight breaks through, tragic insight  which, merely to be endured, needs art as a protection and remedy.

— Friedrich Nietzsche, The Birth of Tragedy , translated by Walter Kaufmann (Modern Library)

Tuesday, May 25, 2010


Filed under: General — Tags: , — m759 @ 9:57 AM

“Nuvoletta in her lightdress, spunn of sisteen shimmers,
was looking down on them, leaning over the bannistars….

Fuvver, that Skand, he was up in Norwood’s sokaparlour….”

Finnegans Wake

To counteract the darkness of today’s 2:01 AM entry—

Part I— Artist Josefine Lyche describes her methods

A “Internet and hard work”
B “Books, both fiction and theory”

Part II I, too, now rely mostly on the Internet for material. However, like Lyche, I have Plan B— books.

Where I happen to be now, there are piles of them. Here is the pile nearest to hand, from top to bottom.

(The books are in no particular order, and put in the same pile for no particular reason.)

  1. Philip Rieff— Sacred Order/Social Order, Vol. I: My Life Among the Deathworks
  2. Dennis L. Weeks— Steps Toward Salvation: An Examination of Coinherence and Substitution in the Seven Novels of Charles Williams
  3. Erwin Panofsky— Idea: A Concept in Art Theory
  4. Max Picard— The World of Silence
  5. Walter J. Ong, S. J.— Hopkins, the Self, and God
  6. Richard Robinson— Definition
  7. X. J. Kennedy and Dana Gioia, eds.— An Introduction to Poetry
  8. Richard J. Trudeau— The Non-Euclidean Revolution
  9. William T. Noon, S. J.— Joyce and Aquinas
  10. Munro Leaf— Four-and-Twenty Watchbirds
  11. Jane Scovell— Oona: Living in the Shadows
  12. Charles Williams— The Figure of Beatrice
  13. Francis L. Fennell, ed.— The Fine Delight: Centenary Essays on the Poetry of Gerard Manley Hopkins
  14. Hilary Putnam— Renewing Philosophy
  15. Paul Tillich— On the Boundary
  16. C. S. Lewis— George MacDonald

Lyche probably could easily make her own list of what Joyce might call “sisteen shimmers.”

Friday, May 2, 2003

Friday May 2, 2003

Filed under: General — m759 @ 4:15 PM


The following flashback to March 2002 seems a suitable entry for May, which is Mental Health Month.

Zen and Language Games

by Steven H. Cullinane
on March First, 2002

Two Experts Speak —

A Jew on Language Games

From On Certainty, by Ludwig Wittgenstein (Oxford, Basil Blackwell, 1969):

#508: What can I rely on?
#509: I really want to say that a language game is only possible if one trusts something. (I did not say “can trust something”).
— Quoted by Hilary Putnam in Renewing Philosophy, Chapter 8 (Harvard University Press, 1992)

An Arab on Deconstruction

From “Deconstructing Postmodernism,” by Ziauddin Sardar, at the website “The Free Arab Voice”:

Doubt, the perpetual and perennial condition of postmodernism, is best described by the motto of the cult television series The X-files: ‘Trust no One’….

Deconstruction – the methodology of discursive analysis – is the norm of postmodernism. Everything has to be deconstructed. But once deconstruction has reached its natural conclusion, we are left with a grand void: there is nothing, but nothing, that can remotely provide us with meaning, with a sense of direction, with a scale to distinguish good from evil.

Those who, having reviewed a thousand years of lies by Jews, Arabs, and Christians, are sick of language games, and who are also offended by the recent skillful deconstruction of the World Trade Center, may find some religious solace in the philosophy of Zen.

Though truth may be very hard to find in the pages of most books, the page numbers are generally reliable. This leads to the following Zen meditations.

From a review of the film “The Terminator”:

Some like to see Sarah as a sort of Mother of God, and her son as the saviour in a holy context. John Connor, J.C. , but these initials are also those of the director, so make up your own mind.
— http://www.geocities.com/

From a journal note on religion, science, and the meaning of life written in 1998 on the day after Sinatra died and the Pennsylvania lottery number came up “256”:

“What is 256 about?”
— S. H. Cullinane

From Michael Crichton’s Rising Sun (Ballantine paperback, 1993) —
John Connor (aka J. C.) offers the following metaphysical comment on the page number that appears above his words (256):

“It seems to be.”
“Is your investigation finished?”
“For all practical purposes, yes,” Connor said.

Connor is correct. The number 256 does indeed seem to be, and indeed it seemed to be again only yesterday evening, when the Pennsylvania lottery again made a metaphysical statement.

Our Zen meditation on the trustworthiness of page numbers concludes with another passage from Rising Sun, this time on page 373:

Connor sighed.
“The clock isn’t moving.”

Here J. C. offers another trenchant comment on his current page number.

The metaphysical significance of 373, “the eternal in the temporal,” is also discussed in the Buddhist classic A Flag for Sunrise, by Robert Stone (Knopf hardcover, 1981)… on, of course, page 373.

Tuesday, January 14, 2003

Tuesday January 14, 2003

Filed under: General — Tags: — m759 @ 5:55 PM

Remarks on Day 14 of
the Year of Our Lord 2003

On this date —

Alfred Tarski was born in 1902 in Warsaw, and

Kurt Friedrich Gödel died in 1978 in Princeton.

What is Truth?

“What is called ‘losing’ in chess may constitute winning in another game.”

Cited in “A Note on Wittgenstein’s ‘Notorious Paragraph’ about the Gödel Theorem,” by Juliet Floyd (Boston University) and Hilary Putnam (Harvard University), Journal of Philosophy (November 2000), 45 (11): 624-632.

See also

Juliet Floyd’s “Prose versus proof : Wittgenstein on Gödel, Tarski and truth,” Philosophia Mathematica  3, vol. 9 (2001): 901-928,


Juliet Floyd’s “The Rule of the Mathematical: Wittgenstein’s Later Discussions.” PhD Dissertation, Harvard University, 1990. Abstract in Dissertation Abstracts International (June 1991), 51 (12A): 4146-A:

“My thesis aims to defend Wittgenstein from the charges of benighted arrogance traditionally levelled against him.”

Romeo: O, she doth teach
the torches to burn bright!
 “Romeo and Juliet,” Act One, Scene V

  Ludwig Wittgenstein, Remarks on the Foundations of Mathematics (revised edition, Cambridge, Mass.: MIT Press, 1978)

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