Author Archives: David Pierce

Mathematician & logician; amateur of philosophy; relation of journalists; alumnus of St John’s College (USA); living in Ankara & Istanbul since 2000

On the Odyssey, Book II

Having been put to bed by Eurycleia at the end of Book I of the Odyssey, Telemachus gets up in the morning and has the people summoned to council, at the beginning of Book II.

Three books with beads

There is no mention of a breakfast. Perhaps none is eaten. On the other hand, Telemachus probably relieves his bladder at least, and there is no mention of that either.

Telemachus straps on a ξίφος, but arrives at the assembly with a χάλκεον ἔγχος in hand. Wilson calls it a sword in either case; for Fitzgerald and Lattimore, the first weapon is a sword, but the second a spear and a bronze spear, respectively. Cunliffe’s lexicon supports the men; however, for Liddell and Scott, an ἔγχος can also be a sword, at least in Sophocles. For Beekes, ξίφος is Pre-Greek, and ἔγχος may be so. Continue reading

Ordinals

This is about the ordinal numbers, which (except for the finite ones) are less well known than the real numbers, although theoretically simpler.

The numbers of either kind compose a linear order: they can be arranged in a line, from less to greater. The orders have similarities and differences:

  • Of real numbers,

    • there is no greatest,

    • there is no least,

    • there is a countable dense set (namely the rational numbers),

    • every nonempty set with an upper bound has a least upper bound.

  • Of ordinal numbers,

    • there is no greatest,

    • every nonempty set has a least element,

    • those less than a given one compose a set,

    • every set has a least upper bound.

One can conclude in particular that the ordinals as a whole do not compose a set; they are a proper class. This is the Burali-Forti Paradox.

Diagram of reals as a solid line without endpoints; the ordinals as a sequence of dots, periodically coming to a limit Continue reading

On the Odyssey, Book I

  • In reading his rendition of the Iliad, having enjoyed hearing Chapman speak out loud and bold;

  • having enjoyed writing here about each book, particularly the last ten books in ten days on an Aegean beach in September of this year (2019);

  • having taken the name of this blog from the first line of the Odyssey;

  • having obtained, from Homer Books here in Istanbul, Emily Wilson’s recent translation (New York: Norton, 2018);

  • Book on table, Wilson's Odyssey Continue reading

Computer Recovery

I record here how I fixed my computer, because

  • I am pleased to have been able to do it, and

  • I may have to do it again.

Briefly, when Windows on my laptop failed, I installed Ubuntu, but this failed. Somebody else installed Ubuntu again, and this worked for a while before failing. I managed to fix that problem for myself; but later an upgrade failed. Now I have fixed that.

Computer on table by window at dawn

This post is some kind of laboratory notebook. Continue reading

On the Idea of History

Our environment may influence our feelings, but what we make of those feelings is up to us. Thus we are free; we are not constrained by some fixed “human nature”—or if we are, who is to say what its limits are?


Rembrandt van Rijn (and Workshop?), Dutch, 1606-1669,
The Apostle Paul, c. 1657, oil on canvas,
Widener Collection, National Gallery of Art

Insofar as we humans have come to recognize our freedom, we have done so after thinking that what we did depended on our class—our kind, our sort, even our “race.” We might distinguish three stages of thought about ourselves.

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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 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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On Translation

Achilles is found singing to a lyre, in a passage of Book IX of the Iliad. Homer sets the scene in five dactylic hexameters; George Chapman translates them into four couplets of fourteeners.

I wrote a post about each book of the Iliad, in Chapman’s version of 1611. As I said at the end, I look forward to reading Emily Wilson’s version. Meanwhile, here I examine the vignette of the lyre in several existing English translations, as well as in the original.

Three books mentioned in the text Continue reading

On Chapman’s Homer’s Iliad, Book XXIV

One man kills another, legally, according to the laws of war, such as they are. The two sides fight over the body, which might be ransomed, if taken by the killer’s side; however, the body is not so taken. The friend of the slain man kills the killer and takes his body to mutilate, though this be sacrilege.

The father of the newly slain man crosses enemy lines to ransom his son’s body. He puts his lips to the hand of the killer, who agrees to give up the body, even coming to admire the father, who in turn admires him.

Rembrandt van Rijn (Dutch, 1606-69), Lucretia, 1664, oil on canvas, Andrew W. Mellon Collection. National Gallery of Art, Washington

Such are the emotions of the Iliad. Homer depicts them as terrifically as Rembrandt does those of a woman, Lucretia, about to kill herself in shame for having been raped. One might consider these works as “emotion porn,” where the second element of this phrase denotes

written or visual material that emphasizes the sensuous or sensational aspects of a non-sexual subject, appealing to its audience in a manner likened to the titillating effect of pornography

—in the words of the third edition of the Oxford English Dictionary, as quoted by Arnold Zwicky in a blog article, “X porn.” Continue reading

On Chapman’s Homer’s Iliad, Book XXIII

Book XXII of the Iliad is rich in human emotion; Book XXIII, in anthropological detail. The books form a natural sequence:

  1. Defiance, flight, fight, and death of a man.
  2. Funeral and memorial games for a man.

That the man is different in either case creates tension, to be resolved in the next and final book (whose emotions I once took up in “Homer for the Civilian”).

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On Chapman’s Homer’s Iliad, Book XXII

Andromache draws a hot bath, for Hector to slip into when he comes home from the war. Actually she has her maids heat the water, while she herself weaves flowers into a tapestry.

Mouth of stream forming border between Balıkesir and İzmir

All the Trojans managed to slip into the safety of Troy, while Achilles was distracted in Book XXI of the Iliad. Only Hector and Deiphobus have stayed outside. Hector is really glad to have his brother along to confront Achilles.

Continue reading