Category Archives: Prose

Donne’s Undertaking

I was recently called on to recommend a poem. I chose “The Undertaking” of John Donne. I want to say here why.

  • The poem (quoted below) has a sound that impressed me when first I read it, more than thirty years ago.

  • The poem alludes to ideals:

    • of recognizing what is good for its own sake;

    • of climbing a rung or two on Diotima’s ladder or stairway of love, recounted by Socrates in Plato’s Symposium (211c):

      And the true order of going, or being led by another, to the things of love (τὰ ἐρωτικά), is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps (οἳ ἐπαναβαθμοί) only, and from one going on to two, and from two to all fair forms (τὰ καλὰ σώματα), and from fair forms to fair practices (τὰ καλὰ ἐπιτηδεύματα), and from fair practices to fair notions (τὰ καλὰ μαθήματα), until from fair notions he arrives at the notion of absolute beauty, and at last knows what the essence of beauty is (ὃ ἔστι καλόν).

  • The sound of Donne’s poem may seduce one into thinking the ideals worthy.

Analytic Geometry and Donne's complete poetry

Two books that were my mother’s

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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

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.

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Math, Maugham, and Man

A human being was once a man. A female of the species was a wife; a male, a were. The word “were” was used in werewolf, but also were-eld, which became our “world.” Our word "woman" comes from wife-man.

That is roughly the history, which I shall review later in a bit more detail. It would be a fallacy to think the history told us how we must use the words “woman” and “man” today. The history does suggest what may happen again: in a world dominated by men, a word like “person,” intended for any human being, may come to have its own meaning dominated by men. Yet again, this is no reason not to try to make our language better.

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On Causation

Causation seems commonly to be understood as a physical concept, like being a fossil. The paleontologist seeks the one right answer to the question of when a particular dinosaur bone became part of the fossil record; likewise readers of international news seem to think there is one right answer to the question of whether Donald Trump or Ali Khamenei caused the shooting down of Ukraine International Airlines Flight 752 on January 8, 2020.

There is not one right answer. If you are Trump, you caused 176 civilian deaths by attacking the Iranians and provoking their response. If you are Mitch McConnell, you caused the deaths by inhibiting the removal of Trump from office. If you are Khamenei, you did it by meeting Trump’s fire with fire.

Being a cause does not mean you deserve condemnation or praise: that is another matter.

Causation is relative. This is an observation by R. G. Collingwood in An Essay on Metaphysics (1940). Continue reading

Logic of Elliptic Curves

In my 1997 doctoral dissertation, the main idea came as I was lying in bed one Sunday morning. 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.

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NL XLII: The First Barbarism: The Saracens

Index to this series

Executive summary: The barbarians who overran the Western Roman Empire were not barbarists in Collingwood’s technical sense. However, “in the seventh century a movement inspired by hostility towards everything Roman … and everything Christian, flared up on the south-eastern frontier of the Roman world” (42. 22). This movement was therefore barbarist. Failing to conquer Europe, either from the east at Constantinople, or from the west at Tours, the movement settled down and ceased being barbarist—by the account in Chapter XLII, “The First Barbarism: The Saracens,” and later, in Collingwood’s New Leviathan. I check this account against more recent sources; it is barbarist to think that the “movement” in question, or indeed any movement, must always be barbarist; I look at the “civilization” of the British Empire as portrayed in a story of Maugham, and I compare a character of the story to Collingwood.


Collingwood’s historical account of barbarisms is a minefield, if one wishes not to sound like a barbarist oneself. The four examples will be

  1. the Saracens,
  2. the “Albigensian Heresy” (or the Bogomils),
  3. the Turks, and
  4. the Germans.

The very formula “the X”—definite article followed by national or quasi-national adjective—this has a barbaric use in branding a people with indelible features. A retort then is “not all X,” as in “not all men.” Collingwood issues such a proviso himself:

45. 68. Please observe, Reader, that I am not talking about all Germans. I do not say that all Germans are liars. I know of some who are not; those heroes, for example, who continue in spite of everything the Nazis can do to run their secret wireless station and keep on printing Das Wahre Deutschland.

Das wahre Deutschland, from a Swiss antiquarian bookshop, Antiquariat Peter Petrej

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NL XXVII: Force in Politics

Index to this series

Executive summary (added September 12, 2018): When persons cannot rule themselves, they are ruled by force, as a duty, by other persons, for the benefit and pleasure of all. Force includes fraud and deceit; but their use must be limited, if those persons who are being ruled by force now will one day join the ruling class themselves. If a liberal and a conservative party take up respectively the ideals of democracy and aristocracy discussed in the last chapter, the parties must understand that each needs the other, in order to engage in the dialectic that aims for the best society. If somebody thinks the two parties waste energy, either in pretending to be in opposition to one another, or in actually being opposed, then that person is effectively wishing for tyranny.


In my last post on the New Leviathan (which was my first for this year), I said Collingwood would discuss the British parliament in Chapter XXVII. That chapter is now my subject.

The ruling class must incorporate new members from time to time, whether anybody thinks about it or not (27. 75). Anybody who does think about it may take up one of two goals (27. 77).

27. 79. To hasten the percolation of liberty throughout every part of the body politic was the avowed aim of the Liberal party; to retard it was the avowed aim of the Conservative party.

27. 8. The relation between them was consciously dialectical. They were not fundamentally in disagreement. Both held it as an axiom that the process of percolation must go on. Both held that given certain circumstances, which might very well change from time to time, there was an optimum rate for it, discoverable within a reasonable margin of error by experiment.

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Writing and Inversion

Executive summary: The “voice” of a transitive verb may be active or passive. A piece of writing may be vigorous or torpid. There is not an exact correspondence between passive verbs and torpid writing. However, a passive verb is used to effect inversion of subject and object. One may also invert subject and auxiliary verb, subject and predicate, or two clauses, always adding new words. Each inversion may lead to torpid writing. This is what Strunk warned about in The Elements of Style, by issuing the command, “Use the active voice.” The command must be followed with discretion. Williams makes the same case, more elaborately, in Style: Towards Clarity and Grace. There is no foolproof executive summary of how to write well.


When E. B. White revised William Strunk’s original Elements of Style, he did not retain Strunk’s “Introductory,” whose first paragraph said of the book,

The experience of its writer has been that once past the essentials, students profit most by individual instruction based on the problems of their own work, and that each instructor has his own body of theory, which he may prefer to that offered by any textbook.

Perhaps many students today cannot receive individual instruction. They are just given textbooks that try to spell out everything. Continue reading