Category Archives: question and answer

Concerning the logic of question and answer described in An Autobiography

Even More on Dialectic

At the beginning of the first post “On Dialectic,” I raised the question of why I put so much into such posts. I propose now a couple of answers.

  1. I want to collect all evidence for what I am investigating – currently dialectic in Plato’s Republic. As Arthur Conan Doyle (1859–1930) has Sherlock Holmes say in A Study in Scarlet (1887; Wordsworth Classics, 2004),

    It is a capital mistake to theorize before you have all the evidence. It biases the judgment.

    And yet in Religion and Philosophy (1916), Collingwood states “the fundamental axiom of all thinking,”

    namely that whatever exists stands in some definite relation to the other things that exist.

    Thus “all the evidence” is everything in the world.

  2. I am engaged in such self-defense as a certain Islamic philosopher is, by the account of Strauss in Persecution and the Art of Writing (1952):

    Fārābī avails himself then of the specific immunity of the commentator or of the historian in order to speak his mind concerning grave matters in his “historical” works, rather than in the works in which he speaks in his own name.

Cloud with several lobes above deciduous trees in leaf
View from our balcony
Sanatçılar Sitesi, Tarabya, Istanbul
Saturday, July 8, 2023

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Anthropology of Mathematics

This essay was long when originally published; now, on November 30, 2019, I have made it longer, in an attempt to clarify some points.

The essay begins with two brief quotations, from Collingwood and Pirsig respectively, about what it takes to know people.

  • The Pirsig quote is from Lila, which is somewhat interesting as a novel, but naive about metaphysics; it might have benefited from an understanding of Collingwood’s Essay on Metaphysics.

  • A recent article by Ray Monk in Prospect seems to justify my interest in Collingwood; eventually I have a look at the article.

Ideas that come up along the way include the following.

  1. For C. S. Lewis, the reality of moral truth shows there is something beyond the scope of natural science.

  2. I say the same for mathematical truth.

  3. Truths we learn as children are open to question. In their educational childhoods, mathematicians have often learned wrongly the techniques of induction and recursion.

  4. The philosophical thesis of physicalism is of doubtful value.

  5. Mathematicians and philosophers who ape them (as in a particular definition of physicalism) use “iff” needlessly.

  6. A pair of mathematicians who use “iff” needlessly seem also to misunderstand induction and recursion.

  7. Their work is nonetheless admirable, like the famous expression of universal equality by the slave-driving Thomas Jefferson.

  8. Mathematical truth is discovered and confirmed by thought.

  9. Truth is a product of every kind of science; it is not an object of natural science.

  10. The distinction between thinking and feeling is a theme of Collingwood.

  11. In particular, thought is self-critical: it judges whether itself is going well.

  12. Students of mathematics must learn their right to judge what is correct, along with their responsibility to reach agreement with others about what is correct. I say this.

  13. Students of English must learn not only to judge their own work, but even that they can judge it. Pirsig says this.

  14. For Monk, Collingwood’s demise has meant Ryle’s rise: unfortunately so since, for one thing, Ryle has no interest in the past.

  15. In a metaphor developed by Matthew Arnold, Collingwood and Pirsig are two of my touchstones.

  16. Thoreau is another. He affects indifference to the past, but his real views are more subtle.

  17. According to Monk, Collingwood could have been a professional violinist; Ryle had “no ear for tunes.”

  18. For Collingwood, Victoria’s memorial to Albert was hideous; for Pirsig, Victorian America was the same.

  19. Again according to Monk, some persons might mistake Collingwood for Wittgenstein.

  20. My method of gathering together ideas, as outlined above, resembles Pirsig’s method, described in Lila, of collecting ideas on index cards.

  21. Our problems are not vague, but precise.


When Donald Trump won the 2016 U.S. Presidential election, which opinion polls had said he would lose, I wrote a post here called “How To Learn about People.” I thought for example that just calling people up and asking whom they would vote for was not a great way to learn about them, even if all you wanted to know was whom they would vote for. Why should people tell you the truth?

Saturn eclipse mosaic from Cassini

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Writing, Typography, and Nature

Note added February 10, 2019: I return to this rambling essay, two years later in the Math Village. The main points are as follows.

  • Writing is of value, even if you never again read what you write.
  • There is also value to reading again, as in the present case.
  • A referee rejected a submitted article of mine in the history of mathematics because its order did not make sense – to that referee, though a fellow mathematician thought well of the article. A revision was eventually published as “On Commensurability and Symmetry.”
  • In the preface to The Elements of Typographical Style, Robert Bringhurst wonders how he can write a rulebook when we are all free to be different. He thus sets up an antithesis, such as I would investigate later in “Antitheses.”
  • From being simply a means of copying, typography has become a means of expression.
  • Yet typography should not draw attention to itself, just as, according to Fowler in A Dictionary of Modern English Usage, pronunciation (notably of foreign words) should not.
  • Through my own experience of typography with LaTeX [and HTML, as in this blog], I have developed some opinions differing from some others’.
  • Bringhurst samples Thoreau,
    • whose ridicule of letters sent by post applies today to electronic media, and
    • who rightly bemoans how enjoying the woods is thought idle; cutting them down, productive.
  • In Gödel, Escher, Bach, Douglas Hofstadter wonders how a message can be recognized by any intelligence. Bringhurst restricts the question to concern intelligences on this earth.
  • In my youth, Hofstadter introduced me to Zen Flesh, Zen Bones, (edited by Reps and Senzaki), whose influence on me I consider.
  • The Zen story about whether “this very mind is Buddha” suggests a further development of Collingwood’s “logic of question and answer.”
  • Through looking at another translation, I consider how Reps and Senzaki turned Chinese into English.
  • Rereading this blog led me back to Hofstadter.

Here are some meditations on some books read during a stay in the Nesin Mathematics Village, January, 2017. I originally posted this article from the Village; now, back in Istanbul, a few days into February, recovering from the flu that I started coming down with in the Village, I am correcting some errors and trying to clarify some obscurities.

From below, a wooded hill, with buildings near the crest
Nesin Mathematics Village from the east
Wednesday, January 18, 2017

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NL VI: “Language”

Index to this series

This is about the first section of Chapter VI, “Language,” of The New Leviathan. The whole chapter can be ana­lyzed into five sections, with §N consisting of those paragraphs numbered 6. N or 6. NX. I summarize the sections as follows:

  1. Language is an abstraction from discourse. Discourse is an activity together with what is meant by it. (¶¶6. 1–19)
  2. Through language, we become conscious of our feelings. Becoming conscious of our language is another step, which is taken by artists. (¶¶6. 2–29)
  3. A feeling is not “mediated” by the language we use for it. (¶¶6. 3–36)
  4. Hobbes discovered that language is prior to knowledge. (¶¶6. 4–47)
  5. Those who dispute this finding over­look that not all language is rational. (¶¶6. 5–59)

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Books hung out with

Here are some books that I have read more times than I can remember.

  1. R. G. Collingwood, The Principles of Art (1938);
  2. Somerset Maugham, The Razor’s Edge (1944);
  3. Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance (1974).

The years of my first readings were 1987, 1984, and 1982, respectively, as best I can remember; in any case, their order is opposite to the order of publication.

I want to say some things about the books and their writers. I intend especially to address the last book, which I shall call ZAMM. From Pirsig’s more recent book, Lila, I mention only the author’s description of keeping notes on slips of paper, then arranging and rearranging them, in hopes that he might finally produce a book out of them. The present article might be considered as a collection of such notes, not necessarily forming a coherent whole. There are more notes that I might add in future.


While I was in high school, I paid the price of three dollars and thirty-three cents (plus tax) for the peculiar purple book in square format called Be Here Now. I suppose the title can be taken as a summation of the spiritual advice contained in the book. This advice is apparently derived mainly from Hinduism, though given to us by an American once called Richard Alpert, who spent a lot of time taking LSD with Timothy Leary. After I had gone off to read Great Books at St John’s College in Annapolis in 1983, and transferred to Santa Fe after a year, I learned that the Director of Laboratories on the occidental campus had lived at a sort of monastery or commune, elsewhere in New Mexico, supported by sales of Be Here Now.

The book ends with lists of recommended reading, headed with the warning, “Painted cakes do not satisfy hunger.” There are three lists:

  1. Books to hang out with.
  2. Books to visit with now and then.
  3. Books it’s useful to have met.

The “books to hang out with” are thirty-five authors and teachers and scriptures. Those that I have on my own shelves are the Bhagavad Gita, the Holy Bible, the Tibetan Book of the Dead, the Tao Te Ching, the I Ching, and the poems of Hafiz. I have not really hung out with any of these, except maybe parts of the Bible and the Tao Te Ching (the latter in the 1972 translation of Gia-Fu Feng and Jane English, illustrated with Chinese calligraphy of the former on lovely spare nature photographs by the latter).

From Be Here Now’s longer list of “books to visit with now and then,” I have read only some of the poetry of Rumi and William Blake, along with Hesse’s Siddhartha, Merton’s Seven Story Mountain, Reps’s Zen Flesh, Zen Bones, Rilke’s Duino Elegies, and Thoreau’s Walden. From the final, longest section, of “books it’s useful to have met,” the works that I have read are a curious mix of mostly science fiction and St John’s College Program books, by Asimov, Bradbury, Castaneda, Dante, Descartes, Heinlein, Milton, Pascal, Plotinus, Plato, Saint-Exupéry, Salinger, and Tolkien.


The three books that I listed at the beginning are among the books that I have hung out with. Let me record here a flaw in my memory concerning one of them. Before checking the lists in Be Here Now, I thought I remembered that The Razor’s Edge was there somewhere, if only among the “books it’s useful to have met”. But it is not there. Since it seems to fit the theme of spiritual journeys, I wonder if its absence is due to ignorance or oversight. Possibly Maugham was judged to be a spiritual lightweight. However, because on a web page I said The Razor’s Edge was one of my favorite books, I received emails from a fellow, calling himself the Wanderling, who said that his mentor, and not a fellow called Guy Hague, was the person who had been the source for Maugham’s character Larry Darrell.


Some people never read a book more than once. Some people cannot even conceive of doing this. Jerry Seinfeld would appear to be one of those people. In an early episode of his television series, Jerry ridicules George for wanting to retrieve some already-read books from the girlfriend with whom he has just broken up.

Presumably Seinfeld could conceive of watching a television show more than once. It is only because I have watched Seinfeld episodes more than once that I am able to recall and mention Jerry’s foolishness about books in the first place.

Recently I increased by one the unknown number of my readings of ZAMM. Earlier in this month of June, 2013, above the Tyrrhenian Sea, in the gorgeous hilltop setting of Ravello, where I was attending a mathematics conference, in the early mornings I would rise, sit outside, and either work on mathematics or read ZAMM.

photo of terrace in Ravello
ZAMM in the morning in Ravello

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