Tag Archives: Richard Feynman

Mathematics and Logic

Large parts of this post are taken up with two subjects:

  1. The notion (due to Collingwood) of criteriological sciences, logic being one of them.

  2. Gödel’s theorems of completeness and incompleteness, as examples of results in the science of logic.

Like the most recent in the current spate of mathematics posts, the present one has arisen from material originally drafted for the first post in this series.

In that post, I defined mathematics as the science whose findings are proved by deduction. This definition does not say what mathematics is about. We can say however what logic is about: it is about mathematics quâ deduction, and more generally about reasoning as such. This makes logic a criteriological science, because logic seeks, examines, clarifies and limits the criteria whereby we can make deductions. As examples of this activity, Gödel’s theorems are, in a crude sense to be refined below, that

  • everything true in all possible mathematical worlds can be deduced;

  • some things true in the world of numbers can never be deduced;

  • the latter theorem is one of those things.

Continue reading

Be Sex Binary, We Are Not

Content warning: suicide.

The following sentence is bold in the last paragraph of an essay: “the science is clear and conclusive: sex is not binary, transgender people are real.” I don’t know what the writer means by this. As far as I can tell, as a biological concept used for explaining reproduction, sex has two kinds or parts or sides or aspects, and the essay tacitly affirms this; at the same time, obviously persons called transgender exist.

☾ ♂ ☿ ♃ ♀ ♄ ☉

The title of the essay is a command: “Stop Using Phony Science to Justify Transphobia.” I can support that. I don’t even need the qualifier “phony.” If transphobia is the kind of morbid fear suggested by the suffix “-phobia,” then science ought to help dispel this, not promote it.

One might also just say, Stop using phony science.

Continue reading

Poetry and Mathematics

This reviews some reading and thinking of recent weeks, pertaining more or less to the title subjects, of which it may be worth noting that

  • poetry is from ποιέω “make”;
  • mathematics is from μανθάνω “learn.”

Summary added August 23, 2020: Mathematics may bring out such emotions as poetry does; but in the ideal, a work of mathematics is correct or not, in a sense that everybody will agree on. Here I review work of

  1. Lisa Morrow, writing in Meanjin as an immigrant to Istanbul, like me;
  2. Wendell Berry, in “The Peace of Wild Things,” which things “do not tax their lives with forethought / of grief,” and include the stars;
  3. Randall Jarrell, in The Animal Family;
  4. Mary Midgley, in Evolution as a Religion, on how we see animals;
  5. James Beall, astronomer, poet of the stars, tutor at my college;
  6. Edith Södergran, in “God,” as translated by Nicholas Lawrence in Cordite;
  7. Lukas Moodysson, in Fucking Åmål, where Agnes’s father notices that his daughter is reading Edith Södergran;
  8. Thomas J.J. Altizer, in The Gospel of Christian Atheism, a book that I kept from my father’s collection;
  9. Özge Samancı, in Dare to Disappoint, where the character to be disappointed is the father of the artist, and where Özlem (the artist’s friend and mine) praises the poetry of mathematics;
  10. Fiona Hile, writing, quâ editor of an issue of Cordite featuring poetry of mathematics, about the set theory of Maryanthe Malliaris and Saharon Shelah;
  11. Anupama Pilbrow, a poet writing in Meanjin about studying mathematics;
  12. Robert Pirsig, about students who ask their teacher, “Is this what you want?”
  13. R. G. Collingwood, who in Speculum Mentis analyzes Art, Religion, Science, History, and Philosophy as modes of existence;
  14. Michael Oakeshott, supposedly influenced by Collingwood, but also considered a forefather of “postmodern conservatism,” and analyzing existence into different modes from Collingwood’s, the latter according to the article in the Stanford Encyclopedia of Philosophy by Terry Nardin, who reports, “to insist on the primacy of any single mode is not only boorish but barbaric”;
  15. Allan Bloom, who suggests, in The Closing of the American Mind, that for Ronald Reagan, for the Soviet Union to be “the evil empire” and to “have different values” from the United States is the same thing;
  16. Galen Strawson, who seems to belie the possibility of different modes of being by saying, “we know exactly what consciousness is,” and also, “The nature of physical stuff is mysterious except insofar as consciousness is itself a form of physical stuff,” when (according to me) consciousness is simply not physical, not in the sense of being studied by physics.

A Twitter friend living here in Istanbul announced (on June 16) her pleasure in having a memoir published in Meanjin.

Meanjin cover, Winter 2020: a bird crushed by a stone heart

Continue reading


Because Herman Wouk was going to put physicists in a novel, Richard Feynman advised him to learn calculus: “It’s the language God talks.” I think I know what Feynman meant. Calculus is the means by which we express the laws of the physical universe. This is the universe that, according to the mythology, God brought into existence with such commands as, “Let there be light.” Calculus has allowed us to refine those words of creation from the Biblical account. Credited as a discover of calculus, as well as of physical laws, Isaac Newton was given an epitaph (ultimately not used) by Alexander Pope:

Nature and Nature’s laws lay hid in night:
God said, Let Newton be! and all was light.

I don’t know, but maybe Steven Strogatz quotes Pope’s words in his 2019 book, Infinite Powers: How Calculus Reveals the Secrets of the Universe. This is where I found out about Wouk’s visit with Feynman. I saw the book recently (Saturday, February 22, 2020) in Pandora Kitabevi here in Istanbul. I looked in the book for a certain topic that was of interest to me, but did not find it; then I found a serious misunderstanding.

book cover: Steven Strogatz, Infinite Powers Continue reading

On Gödel’s Incompleteness Theorem

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

I shall review the mathematics of the theorem, first in outline, later in more detail. The mathematics is difficult. I have trouble reproducing it at will and even just confirming what I have already written about it below (for I am adding these words a year after the original publication of this essay).

The difficulty of Gödel’s mathematics is part of the point of this essay. A person who thinks Gödel’s Theorem is unsurprising is probably a person who does not understand it.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification.

Continue reading

Academic Freedom

(See also other articles in the Freedom category.)

Yesterday (March 24, 2016) was the first day of the sixth Models and Groups Istanbul meeting. There were participants from the Middle East, Europe, and America. Kıvanç Ersoy was to speak about his own mathematics. He could not speak, because he was in prison. He, Esra Mungan, and Muzaffer Kaya were in prison, because the three of them had publicly insisted that the government of Turkey make peace in the southeast of the country. Absurd, but true. Continue reading

Nicole at the Golden Horn

The setting was gorgeous. We were atop a hotel (and former convent) opposite the compound of the Italian Consulate—the Italian Embassy, in Ottoman times, before Mustafa Kemal founded the Turkish Republic and moved the capital to Ankara. We looked out over old trees. The street just below us was closed to cars; off to the right it became a stairway and a narrow passage up to İstiklâl Caddesi. Beyond the trees of the Consulate were the Golden Horn and Seraglio Point, with the Bosphorus and the Sea of Marmara beyond. As night fell, electric lights illuminated the Seraglio itself—Topkapı Palace—along with the Hagia Sophia.
Continue reading