Monthly Archives: August 2025

Ethics of Mathematics

The 12 blue edges of a cube and the 12 green edges of an octahedron respectively bisect one another at right angles

Zometool construction, Ankara, November 20, 2010

The main point of this post is to share a passage from an essay by the late William Thurston:

1 What is it that mathematicians accomplish?

… We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.

Therefore, we need to ask ourselves:

2 How do people understand mathematics?

This is a very hard question. Understanding is an individual and internal matter that is hard to be fully aware of, hard to understand and often hard to communicate …

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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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Just World

In “Biological History,” I talk about some stories by Somerset Maugham. The theme is a confusion between biological (or generally physical) facts and historical (or personal) facts.

I originally made the post on January 9, 2023. I have returned to it a few times since. I did this most recently when a friend told me of purchasing, in Toronto, Ontario, a two-volume edition of Maugham’s complete short stories. Probably this was the same edition that I had bought in Hamilton, Ontario, a quarter-century earlier.

Working again through “Biological History,” I wanted to spell out a remark about what is either the just-world hypothesis or the just-world fallacy. I am going to do that here, using verses of Parmenides of Elea. Parmenides will lead me in turn to Dr Seuss and the fallacy of artificial intelligence.

Book and paraphernalia on a picnic table below a pine tree with crows on the bare lower branches

Where I read Parmenides
Erguvantepe, Sarıyer, Istanbul
July 19, 2025

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