Category Archives: Persons

Courage

Below is my essay on courage, first drafted in April of last year (2024). A reason to think of it now is a recent pair of essays, coming from the United States:

The latter takes up all of the virtues that Socrates does.

Plato didn’t get everything right, but he remains one of the most widely studied philosophers in western history for a reason. In Book IV of The Republic, he discusses the four cardinal virtues. Hope didn’t make the list.

Here they are:

  • Wisdom (or prudence)
  • Self-control (or temperance)
  • Fairness (or justice)
  • Fortitude (or courage)

These four virtues feed a healthy society. We’re supposed to teach them to our young and practice them every day. Hope stems from an insufficient knowledge about the world, but fortitude grows out of wisdom.

We’re long on hope, but short on fortitude.

It would be good if we had more fortitude. As Wildfire writes more recently, in “Fighting Fascism at The End of The World: What nobody wants to say” (August 20, 2025),

It’s gotten popular to tell people to physically throw themselves in front of ICE agents to stop arrests. Allow me to pose a rude question: If someone won’t even wear a piece of cloth on their face for a few hours a day, are they going to get thrown in jail to protect someone they don’t even know?

For Aristotle at least, there is a distinction between the two qualities that could be meant by fortitude and courage respectively. The distinction is a theme of my own essay below.

Aristotle, Nichomachean Ethics, Crisp translation; behind it calm water, with wooded bluffs dotted with houses beyond

Aristotle, Nicomachean Ethics
Tuesday, July 11, 2023
I usually read Rackham’s translation in the Loeb edition
sometimes along the Bosphorus, as here

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Astronomy Anomaly

Aristotle was the subject of the last three posts on this blog:

Perception Deception
The Philosopher asserts in De Anima that the eyes cannot be in error about color; Josef Albers contradicts this.
Imitation Limitation
In the Poetics, Aristotle seems to use mimêsis as a differentia of poiêsis among the technai. Arts not poetry are nonetheless imitative, but perhaps artists are to be distinguished for imitating themselves.
Purity Obscurity
Does catharsis clean the emotions, or wash them away?

Two more posts might have taken up the latter half of the Poetics, but they never materialized.

I turn now to the work held under the arm of Aristotle’s teacher, at the center of Raphael’s School of Athens.


Small book atop a pile of rubble on a beach, sea beyond

Altınova, Balıkesir, Monday, June 16, 2025

I was able to start reading Plato’s Timaeus at the beach during the Feast of the Sacrifice. In the dialogue, Critias describes Timaeus as being “our best astronomer” (ὄντα ἀστρονομικώτατον ἡμῶν, 27a).

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Purity Obscurity

The covers of the books named just below, showing a stern bearded face (Aristotle), a wrench like a flower on a stem among leaves (Pirsig), a dirt road lined with brick buildings (Eliot)
Books taken up in this post:

Aristotle’s Poetics,
George Eliot’s Middlemarch,
Robert Pirsig’s Zen and the Art of Motorcycle Maintenance

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Imitation Limitation

I alluded to this post in my last one, “Perception Deception.” There I questioned the gnomic assertion of its title.

The questioning then consisted of little more than quoting De Anima, where Aristotle points out that a sense cannot be deceived by its proper object. In particular, sight detects color infallibly.


Can of Coca-Cola held in a hand
I do not recall the source of this particular image, which I saved on March 29, 2024. The concept, at least, is apparently due to Akiyoshi Kitaoka.


If you see red in the image above, you are not mistaken, even if none of the pixels is of a kind called red.

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Perception Deception


John Donne, Holy Sonnet XIX
(on the last line, “make” should be “ſhake”)

This post involves:

  • “the” philosopher –
    • Aristotle;
  • two mathematicians –
    • Euclid,
    • David Hilbert;
  • three persons associated with Black Mountain College –
    • Josef Albers,
    • Dorothea Rockburne,
    • Max Dehn;
  • one person (in addition to myself and Dehn) associated with St John’s College –
    • David Bolotin.

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Removal

This is about metaphor.


Handwritten sign in shop window: ΜΕΤΑΦΕΡΘΗΚΑΜΕ …
Shop window in Athens, Monday, July 10, 2017:
ΜΕΤΑΦΕΡΘΗΚΑΜΕ
ΔΙΠΛΑ ΣΤΟ 46Α

ΤΑΚΗΣ
Μεταφερθήκαμε is the first-person plural passive aorist of μεταφέρω. I guess the meaning of the sign is, “We moved next door to 46A – Takis.” I took the photo, just so I could use it at a time like this. I didn’t try to talk with Takis.

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Subjective and Objective

The use of a distinction between the subjective and the objective has sometimes made me suspicious. The suggestion is made here that Gödel’s Incompleteness Theorem relies on the distinction. I shall look at this more in “Gödel and AI.” Meanwhile, the major sources for the present post are the following.

  1. William James, Psychology: Briefer Course (1892), on “the stream of thought, of consciousness, or of subjective life” – also on
    • nerves as telephone lines;
    • emotions as resulting from “a physical effect on the nerves.”
  2. C. F. von Weizsäcker, The Relevance of Science (1964), on how “Cosmogony … is, objectively speaking, the way in which the world came into being, or it is, subjectively speaking, the teaching about this way.”
  3. Robert Pirsig, Zen and the Art of Motorcycle Maintenance (1974), on whether quality is objective or subjective (the answer is no) – also on the distinction between the classical and the romantic.
  4. R. G. Collingwood, Speculum Mentis (1924), on
    • his usage whereby
      • what pertains to a consciousness is called subjective;
      • what the consciousness is of is called objective;
    • atoning for the Fall, that is, the separation of subject from object

    – also (in response to James) on how emotions don’t need a physical source.

  5. James Mumford, “Therapy Beyond Good and Evil: A nonjudgmental psychology is failing patients who need to hear hard truths” (perhaps the hard truths of the title are objective truths, and what the patients need to hear is that their own subjective evaluations of themselves may be wrong).
  6. William Egginton, “Why Kant Wouldn’t Fear ChatGPT-4” (for a computer, there is nothing beyond what it “knows” – all is subjective).
  7. Kurt Gödel, “On formally undecidable propositions of Principia mathematica and related systems I” (the Incompleteness Theorem relies on a distinction between a [subjective] statement and its [objective] meaning).
  8. Shannon Vallor, “The Thoughts The Civilized Keep” (they require labor, with a history).

Minor sources include the following.

  1. James Joyce, Ulysses, as presenting streams of consciousness.
  2. Sigrid Undset, Kristin Lavransdatter, as being more readable.
  3. Aristotle, Nicomachean Ethics and Physics, on how there is not deliberation about the cosmos, or the irrationality of √2, or how to build a ship.
  4. Jared Henderson, “How to read Aristotle’s Nicomachean Ethics.”
  5. C. S. Lewis, The Magician’s Nephew, where an iron bar grows into a lamp-post the way Aristotle imagines a log’s growing into a ship.
  6. a letter to Analog magazine on how religion is false science.
  7. Robert Pirsig, Lila, on the distinction between the static and the dynamic.
  8. Elle Hunt, “Octopus farming turns my stomach – but are some species really more worthy than others?”
  9. the Hebrew Bible (Psalms and Ezekiel) on eating words.
  10. Alexander Bevilacqua, “Saints for Supper” (a review of Jérémie Koering, Iconophages: A History of Ingesting Images).
  11. Jack A. Goldstone and Peter Turchin, “Welcome To The ‘Turbulent Twenties’.”
  12. David Allen Green, “‘Twelfth Night Till Candlemas’ – the story of a forty-year book-quest and of its remarkable ending.”

Having started last spring, my wife and I recently completed a project to read Ulysses together. I was glad to be able to put the book back on the shelf. It sits there, next to another of comparable length, Kristin Lavransdatter; this is because I order my books according to the birth of the writer (or subject), and James Joyce was born February 2, 1882; Sigrid Undset, May 5.

I read her book on my own, for and with pleasure, and it entered into my thoughts on the Nicomachean Ethics of Aristotle, expressed for example in “Impermanence” (on Book IX, chapters i–iii; the common theme was how children might forget their mothers, but not conversely; Maya Angelou recalled how many black women had nursed white children in America).


Three haloed figures in front of a fourth with spread arms and wings; faces are mostly scratched out
Karanlık Kilise (Dark Church), Göreme Open Air Museum
Cappadocia, January 11, 2009

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Free Groups and Topology

My title alludes to some notes for the layperson that I rediscovered recently. I have reviewed and edited them, and they are below, in the following sections (linked to by the titles after the three main bullets; other links are to Wikipedia).

  • Quasicrystals,” based on an email of mine sent to a group of alumni of St John’s College on October 8, 2011. This was my contribution to a thread in which somebody said that
    • Dan Schechtman (whom she called Danny) was a worthy recipient of that year’s Nobel Prize in Chemistry for the discovery of quasicrystals, but
    • John Cahn deserved credit, even the prize itself, as the real discoverer.

    My wife and I had recently moved to Istanbul, and the Istanbul Model Theory Seminar had just got going. The Nobel Prize and quasicrystals had been mentioned there too.

  • Free Groups,” based on an email of October 10, 2011. I tried to describe free groups to somebody who expressed interest, but who also called himself the world’s worst mathematician.
  • Topology” – a draft of an attempt to describe that subject. In graduate school, I got excited about the definition of a topological space when I first encountered it. Here I try to motivate the definition by abstracting from the properties of the Cartesian plane as a metric space. I give the example of the Zariski topology on the same plane. I start to talk about the topology derived from the Gromov–Hausdorff metric on the space of groups with n generators, but then I stop.

A green landscape
Vegetable plot in Yeniköy (where Cavafy lived a while), Istanbul, Saturday, September 28, 2024

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Tests

This post concerns different kinds of knowledge, as for example of Achilles, or Cyrus the Great, or even oneself.

According to the last sentence of the “Findings” column in Harper’s for June, 2023,

Researchers developed a blood test for anxiety, which was found to underlie the joy of missing out.

Those researchers need a weatherman to tell which way the wind blows.

Similar research is reported in the Guardian Weekly for 9 September, 2022. The article is called “‘I’m glowing’: How an app is helping us measure the joy of trees.” The app in question does not detect your joy in the woods; it gives you a way to record your own self-assessment for later study. However, writes Patrick Barkham,

several studies suggest that more biodiversity has a bigger boost on people’s mental health, while the recording of brain activity in response to forest density found a more relaxed state and reduced tension and fatigue in forests with a lower density of trees.

Are you going to need a brain scan to tell if you are chilling out? Other people may relax among a few trees; does that mean you will?

My grandfather Kenneth Crawford described his own grandparents’ house in Wisconsin as being

innocent of plumbing, central heat or telephone. But the proportions were good and it was set in a grove of assorted trees.

I wish he had named some of the trees in the assortment. Right now I’ve got doves cooing in the umbrella pines overhead. Beneath these are oleanders and laurels and pomegranate trees.

Pine trunk next to leaves and needles of other trees; white wall below

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Rethinking

Last week, a student wrote me, “Is there going to be a proof question on the number theory exam?”

I answered,

As far as I’m concerned, the answer to every mathematical question is a proof, because everybody can check whether the answer is right.

I meant that the answer should provide the means for the reader to re-enact the answerer’s thought.

A bay seen from a hill across trees and houses, with green hills beyond (and heavier development at the top)
View from Büyükdere, Sarıyer, Istanbul
We live near the big building at Hacıosman
just over the horizon on the right
Sunday, June 30, 2024

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