Category Archives: Collingwood

Concerning the philosopher R. G. Collingwood (1889–1943). Many if not most of my posts concern Collingwood somehow, so this category may not be of much use. See Articles on Collingwood for some articles by other persons

Thoreau and Anacreon

Gray clouds over blue sky over white clouds over buildings

At the beginning of Walden, the author says he wrote its pages, “or rather the bulk of them,” in the isolated house he had built by the pond of that name. He lived there, 1845–7. He wrote there also A Week on the Concord and Merrimack Rivers. He had spent the week of the title with his brother, who died of tetanus in January, 1842. Writes Laura Dassow Walls,

Into the narrative of his 1839 river trip with John, Henry had woven everything he ever felt, thought, and experienced …

This in Henry David Thoreau: A Life (University of Chicago Press, 2017). Weaving is Thoreau’s metaphor, used in Walden in a consideration of what is worth doing in life.

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Doing and Suffering

Edited March 30, 2020

To do injustice is worse than to suffer it. Socrates proves this to Polus and Callicles in the dialogue of Plato called the Gorgias.

I wish to review the proofs, because I think they are correct, and their result is worth knowing.

Loeb Plato III cover

Or is the result already clear to everybody?

Whom would you rather be: a Muslim in India, under attack by a Hindu mob, or a member of that mob?

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Evolution of Reality

I enjoy and recommend Robert Wright’s Nonzero Newsletter, which presents thought on both American politics and thought itself.

Tiny green plants on red tile roof, cloudy day

In a 2017 post of this blog, I quoted Wright’s 1988 article in The Atlantic Monthly about Edward Fredkin. Somewhat differently from Fredkin, I spelled out my title, “What Philosophy Is,” without actually being a professional philosopher. I touched on a theme that I shall take up now: that thinkers today could benefit from knowing the thought of R. G. Collingwood.

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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

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.

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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 XVIII

I analyze Book XVIII of the Iliad into seven scenes.

Branches against sky

  1. Achilles receives from Antilochus the news of Patroclus’s death, and Thetis receives the news from Achilles. She tells him not to fight till she has brought new arms from Mulciber (Chapman’s lines 1–136).

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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.

There is bitter debate, even within feminism, over whether you can be a woman, just by declaring yourself to be one, regardless of your history and anatomy. As an outsider in either case, I would propose to compare womanhood and Judaism. There are ways to become Jewish. They may not be easy, since being Jewish is a big responsibility. If you are going to take it on, your understanding should be clear, and your motives good.

Regarding the question of who is a woman, both sides would seem to think there is a meaningful distinction between women and men; they just disagree over where to make it. I just want to point out that the distinction need not be made with pronouns. In Turkish, for example, you cannot choose your personal pronoun, since the language has only one of them on offer.

Returning to the noun “man” and derivatives, I do declare a certain affinity for the adjective “freshman,” as being descriptive and as beginning the series that continues with “sophomore, junior, senior.” The series is more interesting than “first-year, second-year,” and so forth. It is likewise interesting that our fingers are not named with ordinal numbers, but in order are pinkie, ring-finger, middle finger, and index finger. A passage in the Republic (523c–d) refers simply to

three fingers, the little finger, the second, and the middle (τρεῖς … δάκτυλοι, ὅ τε σμικρότατος καὶ ὁ δεύτερος καὶ ὁ μέσος) … Each one of them appears to be equally a finger (δάκτυλος μέν που αὐτῶν φαίνεται ὁμοίως ἕκαστος) …

None of this is any reason not to beware using “man” for women.

I did some of the etymological research here while keeping notes on the progress of an upper-level course in the fall of 2015. In that course, I had my students reading Pappus of Alexandria about the “Hexagon Theorem” named for him. In my notes, I recalled how my students had read Euclid in the first semester of their freshman year.

I had developed the idea of the course of reading Pappus after finding that the Wikipedia article on Pappus’s Hexagon Theorem had no discussion of Pappus’s original work. Now the article has a section called “Origins,” because I added it.

The Hexagon Theorem solves a problem that has interested me since I began reading Euclid with first-year students here in Istanbul in 2011. The general problem is to develop a theory of proportion from Book i alone of the Elements. The specific problem is to prove that, if AD, BE, and CF have a common point, and AB and AC are parallel to DE and DF respectively, then BC is parallel to EF. This is Desargues’s Theorem, in what I would call the “pyramidal” case. If, like Euclid in Books v and vi, you have a theory of proportion that yields Thales’s Theorem, whereby a line cuts two sides of a triangle proportionally if and only if the line is parallel to the base of the triangle,—if you have this theorem, then Desargues’s Theorem follows immediately; conversely, Desargues’s Theorem implies that the statement of Thales’s Theorem will serve as a definition of proportion.

Euclid’s theory of proportion relies the “Archimedean” hypothesis that of two lengths, some multiple of the less exceeds the greater. In The Foundations of Geometry (based on lectures of 1898–9), David Hilbert shows that the hypothesis is not needed. Robin Hartshorne provides an exposition in Euclid and Beyond (2000). The key is a “segment arithmetic”: a theory of taking sums and products of pairs of lengths. I propose the alternative of a “polygon arithmetic.” This involves only sums, not products; but it allows us to prove Desargues’s Theorem in stages, once we have Pappus’s Hexagon Theorem in the “parallel” case: if AB and AC are parallel to DE and DF respectively, and D and A lie on BC and EF respectively, then BF is parallel to CE. The hexagon here is ABFDEC. The theorem follows, as Pappus shows, from a theorem in Book I of the Elements, that triangles on the same base are equal if and only if the line joining their apices is parallel to the common base.

Apollonius uses polygon arithmetic in the proof I wrote about in “Elliptical Affinity” last spring. Since then, I have talked about these matters in Prague and elsewhere.

Again, when keeping a record for myself about a course of reading Pappus, I noted the results of some research in the etymology of “woman” and “man.” I return to that research now, because I have had reason to think of my own first year at college. I think of it as the freshman year of myself and all of my classmates, female and male, even though, in my last post here, I expressed the intention of avoiding “man” in an epicene sense.

I am thinking of my freshman year, because I read Herodotus then, and Somerset Maugham mentions Herodotus in the first section of The Razor’s Edge:

I have taken the liberty that historians have taken from the time of Herodotus to put into the mouths of the persons of my narrative speeches that I did not myself hear and could not possibly have heard. I have done this for the same reasons as the historians have, to give liveliness and verisimilitude to scenes that would have been ineffective if they had been merely recounted. I want to be read and I think I am justified in doing what I can to make my book readable.

I first read The Razor’s Edge, for my own pleasure, while I was a student, probably after reading Herodotus on assignment. I have lost count of how many times I have read Maugham’s novel since then. Now I have read it once more, since writing in my last post, “To read a composition properly is to compose it again for ourselves.”

A passage of Maugham’s composition is relevant to the question of whether we ought to use “he” when the referent may be a woman:

… she looked at me reflectively. “Do you think any the worse of me for what I did?”

“Would you care?”

“Strange as it may seem to you, I would. I want you to think well of me.”

I grinned.

“My dear, I’m a very immoral person,” I answered. “When I’m really fond of anyone, though I deplore his wrongdoing it doesn’t make me less fond of him. You’re not a bad woman in your way and you have every grace and every charm. I don’t enjoy your beauty any the less because I know how much it owes to the happy combination of perfect taste and ruthless determination. You only lack one thing to make you completely enchanting.”

She smiled and waited.


The smile died on her lips and she gave me a glance that was totally lacking in amenity …

Maugham is addressing a woman of whom he has told us,

… from the pretty girl whose glowing health, high spirits and brilliant colour had given her attractiveness she was become a beautiful woman. That she owed her beauty in some degree to art, discipline and mortification of the flesh did not seem to matter.

Isabel’s beauty is unnatural. I questioned the possibility of writing naturally, in an essay “On Knowing Ourselves.” Maugham appears to write naturally; but how much of this is due to art, discipline, and mortification of the flesh? As we have seen, he admits to “doing what I can to make my book readable.” He says of Isabel’s uncle,

He was still unwilling to accept such painters as Picasso and Braque—“horrors, my dear fellow, horrors”—whom certain misguided enthusiasts were making such a fuss about, but felt himself at long last justified in extending his patronage to the Impressionists and so adorned his walls with some very pretty pictures. I remember a Monet of people rowing on a river, a Pissarro of a quay and a bridge on the Seine, a Tahitian landscape by Gauguin and a charming Renoir of a young girl in profile with long yellow hair hanging down her back. His house when finished was fresh and gay, unusual, and simple with that simplicity that you knew could only have been achieved at great expense.

At what expense is the simplicity of Maugham’s writing achieved? It may come naturally to him to refer to an unspecified person with masculine pronouns, even though the intended example is the woman whom he is addressing.

Mathematics, Maugham, and “man” are all connected here, at least by me, who never considered myself as warranting a label like ADHD, though I fancy I understand the point of a recent tweet, which at this writing has received more than 39 thousand Likes, one by me:

I am concerned not with the etymology of “squirrel” (which comes to us via French and Latin from the Greek σκίουρος, which Liddell and Scott take as a compound of σκιά “shadow” and οὐρά “tail,” although Skeat thinks this may be “popular etymology”); I am concerned with the etymology of “man,” in connection with current concerns about pronoun use and sexism in language.

The Etymological Fallacy is indeed a fallacy. There is no reason to think a word does or even should continue to mean what it once meant. Collingwood had some comments about this in Chapter XXXIV, “What Civilization Means Generically,” of The New Leviathan:

34. 26. Etymology, in fact, is a good servant to the historical study of language; but a bad master.

34. 27. It is a good servant when it helps to explain why words mean what in fact they do mean.

The traditional English term for a first-year student was “freshman.” It was also a tradition that these students would be male. Today, at Mimar Sinan Güzel Sanatlar Üniversitesi, not only are some of our mathematics students female: most of them are. In principle, any one of our first-year students may still be called a freshman, provided the second component of this term is understood to mean simply a human being. Whether “man” can be understood simply in this general way is not clear, even though the generic sense is the “prominent sense” of the word man in Old English (Hoad, “man,” p. 279), this being the language spoken in England before the Norman Invasion of 1066.

In Old English, male and female specimens of the human species were wer and wīf  respectively. Strictly, the latter word was wif ; modern scholars now mark the vowel with a macron, to show length (Smith, §6, page 4). The marking may be useful for distinguishing between words originally spelled the same, such as gōd “good” and god “god.”

The word wīf  became “wife” in Modern English. Meanwhile, wīf  also became part of the compound wīfman, which was first masculine in gender, then feminine (Hoad, “woman,” p. 544). The compound became wimman in the tenth century, with the plural wimmen. We have retained the pronunciation of the plural for today’s “women”; in the twelfth century, the singular wimman became wumman, giving us today’s pronunciation of “woman” (Skeat, “woman,” p. 614).

The Old English wer is cognate with “virile” and is seen in “werewolf.” The word “world” can be understood as compounded from wer and “eld”; the latter is an archaic noun meaning “age” in various senses, derived from the original form of the adjective “old.” The James Brown song “It’s a Man’s Man’s Man’s World” (credited also to Brown’s girlfriend Betty Jean Newsome) is wilfully redundant; but even to say “man’s world” is redundant, etymologically speaking.

I pick up the information about the James Brown song from the Web, especially Wikipedia. Information about etymologies might be considered as common knowledge, obtainable from many dictionaries; I have indicated the actual books that I used by citing the sources of specific points not found (or perhaps not found as prominently) in other sources. I have also looked at the Oxford English Dictionary (Murray), in the “compact” form that, as a freshman at St John’s College, I acquired from a graduating senior who was looking to lighten their load of personal possessions. That book remains in my physical possession in Istanbul, as do all of the other books that I list below.


T. F. Hoad, editor. The Concise Oxford Dictionary of English Etymology. Oxford University Press, Oxford and New York, 1986. Reissued in new covers, 1996.
Liddell and Scott
Henry George Liddell and Robert Scott. A Greek-English Lexicon. Clarendon Press, Oxford, 1996. “Revised and augmented throughout by Sir Henry Stuart Jones, with the assistance of Roderick McKenzie and with the cooperation of many scholars. With a revised supplement.” First edition 1843; ninth edition 1940.
W. Somerset Maugham. The Razor’s Edge. The Blakiston Company, Philadelphia, 1944.
James A. H. Murray et al., editors. The Compact Edition of the Oxford English Dictionary. Oxford University Press, 1971. Complete text reproduced micrographically. Two volumes. Original publication, 1884–1928.
Walter W. Skeat. A Concise Etymological Dictionary of the English Language. Perigee Books, New York, 1980. Original date of this edition not given. First edition 1882.
C. Alphonso Smith. An Old English Grammar and Exercise Book. Allyn and Bacon, Boston and Chicago, 1898. With inflections, syntax, selections for reading, and glossary. New edition, revised and enlarged. First edition 1896.

On Being Given to Know

  1. What if we could upload books to our brains?
  2. What if a machine could tell us what was true?

We may speculate, and it is interesting that we do speculate, because I think the questions do not ultimately make sense—not the sense that seems to be intended anyway, whereby something can be got for nothing.

View from Şavşat

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