Category Archives: question and answer

Concerning the logic of question and answer described in An Autobiography

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 use “iff” needlessly.

  6. One pair who do this 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

With other questions about people, even just understanding what it means to be the truth is a challenge. If you wanted to understand people whose occupation (like mine) was mathematics, you would need to learn what it meant to prove a theorem, that is, prove it true. Mere observation would not be enough; and on this point I cite two authors whom I often take up in this blog.

  • In the words of R. G. Collingwood in Religion and Philosophy (1916, page 42), quoted in An Autobiography (1940, page 93) as well as in the earlier post here, “The mind, regarded in this external way, really ceases to be a mind at all.”

  • In the words of English teacher and anthropologist Verne Dusenberry, quoted by Robert Pirsig in Lila (1991, page 35), “The trouble with the objective approach is that you don’t learn much that way.”

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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.

Nesin Mathematics Village from the east, Wednesday, January 18, 2017
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

The following are some books that I have read more times than I can remember. I list them in order of publication, though my first readings of them came in the opposite order:

  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).

I want to say some things about all of these books, and their writers. I intend especially to address the last book, which I shall call ZAMM. Continue reading