Tag Archives: Kant

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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On Kant’s Groundwork

Below are some notes (by me) on Immanuel Kant’s 1785 treatise, Grundlegung zur Metaphysik der Sitten. This is the work that introduces the categorical imperative. My notes are in sections corresponding to Kant’s, but with my own titles (after the preface):

  1. That there appears to be a moral law.
  2. What the moral law must be.
  3. Whether there can be a moral law.

The English title of the treatise is Groundwork for the Metaphysics of Morals. Apparently the first word can also be Grounding or Foundation or even Fundamental Principles, and the ensuing preposition can be of. Also, in imitation of the German, Metaphysics can be made singular in form.


Book, bottle, &c. on picnic table; through the trees beyond, water with a passage to open sea

One place I have been reading Kant is Çamlık Parkı, Erguvantepe, Kireçburnu, Sarıyer, İstanbul, here on Wednesday, July 2, 2025. Çamlık = pine grove; erguvan = Judas tree: tepe = peak; kireç burnu = lime point (source for the construction of Rumeli Hisarı, a fortress used in the Ottoman siege of Constantinople, which led to the conquest of the city in 1453); sarı yer = yellow place, perhaps so named for the soil in some part of today’s borough.

The view is of the Bosphorus as it opens to the Black Sea. Jason would have passed through the opening with the Argonauts, and Xenophon with the Ten Thousand. Now the third Bosphorus Bridge crosses it


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Motivated Reasoning in the Cyropaedia of Xenophon

The son of the king of Persia wants to press the advantage, after the combined forces of Media, Persia, Armenia, and Chaldaea have

  • killed the Assyrian king, along with most of his best men, and
  • driven the rest of the Assyrian army from their fortifications.

The king of Media is of another mind: he would rather quit while he is ahead. He has an argument for standing pat, by the account of Xenophon in the Cyropaedia (IV.i.11–18).

One may consider the argument of Cyaxares as an example of “motivated reasoning.” I think it is a specious argument: attractive, but ultimately unsound. Perhaps I say that, only because the king’s nephew Cyrus rejects the argument, but is nonetheless successful in what he goes on to do. With his Persian troops and as many Medians as wish to join them, along with the Hyrcanians, who have defected from Assyria, Cyrus pursues and defeats again the Assyrian army. He kills the kings of Cappadocia and Arabia, and he puts to flight both the king of Phrygia and Croesus, king of Lydia (IV.ii.28–31). Of course, this is not the end of the story; history never ends.

I have been reading and discussing the eight books of the Cyropaedia with a Catherine Project group, at the rate of half a book a week, since July 8 of this year (2024). Thus we shall have completed the sixth book (called “On the Eve of the Great Battle” in the Loeb edition) on September 23. It has astonished me that some of my fellow readers think well of the argument for taking it easy, even as they acknowledge that the man who makes it may be a fool. The argument does not seem to me like one that a king such as Cyaxares can afford to make.

Possibly Xenophon has an esoteric message, as Plato is thought to have. However, although these two writers had a common teacher in Socrates, he never went far from Athens. Xenophon helped lead a stranded army of ten thousand Greek mercenaries, from Babylon north to the Black Sea, after the failure of the coup for which they had been hired by Cyrus the Younger. Xenophon admires a practical man who can actually get things done. This being what Cyrus the Elder is, he is the hero of the Cyropaedia. I shall review my textual reasons for saying this. First I shall look at “motivated reasoning” today, along with the idea that we could have “evolved” to use it. (In short, the rest of this post has the three parts just linked to.)

Pine bough above; bushes below; blue sky, sparkling water, and sand in between

Photo taken September 17, 2024, of Lesbos over the sea, from a beach in Lydia. Of this country, Chrysantas says to Cyrus, after the latter has pursued the Assyrians over the objections of his uncle Cyaxares (Cyropaedia VI.ii.21),

since it now appears that Syria is not to be the only prize – though there is much to be got in Syria, flocks and herds and corn and palm-trees yielding fruit – but Lydia as well, Lydia the land of wine and oil and fig-trees, Lydia, to whose shores the sea brings more good things than eyes can feast on, I say that once we realise this we can mope no longer, our spirits will rise apace, and we shall hasten to lay our hands on the Lydian wealth without delay.

This is in response to the suggestion of Cyrus that his army are intimidated by the alliance that Assyria has formed with Lydia.

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Sweetness

Our subject is pleasure as such. The Greek word is ἡδονή, which is both

  • the source of hedonism and
  • the cousin of sweetness.

The shared Indo-European root of the adjectives ἡδύς and sweet is *su̯ād-, and its existence is a symbol for a lot of what Aristotle has to say, here in the final chapters, xi–xiv, of Book VII of the Nicomachean Ethics.

Birds over a marina, above them clouds lit by a rising sun
Somebody was feeding the gulls
Thursday morning, February 1, 2024
Tarabya

Things taste good because they are good. At least sweet things can be good, if used properly; but this qualification causes a lot of difficulty.

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Freeness

I write this now while many are suffering. Unfortunately that is always true.

What I am supposed to be focused on is virtue in the use of money. I shall get to this.

Toilet facility covered with the image of a forest sits in a real forest

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NL XI: “Desire”

Index to this series

The four parts of Collingwood’s New Leviathan (1942) are Man, Society, Civilization, and Barbarism. From the first part, we are considering Chapter XI, “Desire.”

Pablo Picasso, The Lovers (1923; National Gallery of Art, Washington)
Pablo Picasso, “The Lovers,” 1923
National Gallery of Art, Washington

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The Tradition of Western Philosophy

Note added October 16, 2018: Here I compare two projects of re-examining the philosophical tradition named in my title. The projects are those of

  • R. G. Collingwood in An Essay on Philosophical Method (Oxford, 1933);

  • Stringfellow Barr and Scott Buchanan at St John’s College in Annapolis, Maryland, beginning in 1937.

I review

  • how I ended up as a student at St John’s;

  • how Collingwood has been read (or not read) by myself and others, notably Simon Blackburn;

  • how Collingwood’s Essay is based on the hypothesis of the “overlap of classes.”

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