Category Archives: Aristotle


One day during the Trojan War, Apollo and Athena decide to give the combatants a break. The general conflict is to be replaced with a one-on-one. The Olympians induce Helenus to tell his brother Hector to take on whichever of the Greeks is up for it.

Only Menelaus will accept the challenge at first. His brother Agamemnon makes him withdraw. When none of the other Greeks comes forward, Nestor chides them. After a story of his former prowess, he utters the words that Chapman renders as two couplets:

O that my youth were now as fresh, and all my powers as sound;
Soone should bold Hector be impugn’d: yet you that most are crownd
With fortitude, of all our hoast; euen you, me thinkes are slow,
Not free, and set on fire with lust, t’encounter such a foe.

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Mathematics and Logic

Here is another in the recent spate of mathematics posts. I take up now, as I did in my last post, some material that I had originally drafted for the first post in this series.

Whenever it has been designated for its own post, material can grow, as has the material of this post in the drafting. Large parts of this post are taken up with

  1. the notion (due to Collingwood) of criteriological sciences, logic being one of them;

  2. Gödel’s logical theorems of completeness and incompleteness.

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Map of Art

The bulk of this post is a summary of the chapter on art in Collingwood’s Speculum Mentis: or The Map of Knowledge (1924). The motto of the book is the first clause of I Corinthians 13:12:

Βλέπομεν γὰρ ἄρτι δι’ ἐσόπτρου ἐν αἰνίγματι

For now we see through a glass, darkly

The chapter “Art” has eight sections:

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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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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

NL XXVI: Democracy and Aristocracy

Index to this series

Executive summary (added September 12, 2018, edited January 26, 2019).

  1. Aristocracy and democracy are abstractions (§§26. 1[0]–28). Inseparable from one another, they are properly understood as correlative rules for the ruling class:

    1. Don’t let in anybody who is unqualified.
    2. Don’t keep out anybody who is.
  2. By what Collingwood will call, in Chapter XXXI of the New Leviathan, the Principle of the Limited Objective, (which was recognized by the Early Church Fathers,) the ruling class should be prepared to solve, not every problem (as Plato wanted), but those problems that are expected to come up (§§26. 3[0]–34).

  3. The democratic and aristocratic principles have been at work throughout the history of Europe: in Greece, in Rome, under the feudalism of the Middle Ages. The French Revolution was not only democratic, but also aristocratic, for aiming to give power to the bourgeoisie, not the entire population (§§26. 4[0]–66).

  4. Adapted from the literary concept of peripety, the concept of revolution actually has no place in history, where there are no heroes or villains, just human beings, partly good and partly bad (§§26. 7[0]–82).

  5. The concept of a revolution in history is even dangerous, if it leads you to think a political problem can have been solved once for all (§§26. 9[0]–96).

There can be no pure democracy, not for a length of time, not if we understand a democracy to be a society whose ruling class is the whole of it. Even the most extreme democrat of ancient Greece never contemplated citizenship for women, slaves, or resident foreigners. We may be more liberal today, at least regarding women and slavery. Still we do not open the ruling class to foreigners, such as myself where I am; nor do we open it to children. We could do so, in the sense of extending the franchise to all human residents. Both possibilities were discussed favorably in the early 1990s in The Nation, as I recall, in one case by a legal minor. However, perhaps most children could not be given such adminstrative duties as used to be assigned by lot to Athenian citizens. Even if they could, what of the animals that live among us—shall they be citizens?

Edward Hicks (American, 1780-1849),
The Cornell Farm, 1848, oil on canvas,
Gift of Edgar William and Bernice Chrysler Garbisch,
National Gallery of Art Continue reading

What It Takes

This essay ends up considering arguments that natural science—especially mathematical physics—is based on absolute presup­positions whose mythological expression is found in Christianity—especially the doctrine of Incarnation.

I take note along the way of continuing censorship of Wikipedia by the Turkish state.

The post falls into sections as follows.

  • Where to start. To the thesis that everybody can be a philosopher, an antithesis is that persons with the professional title of philosopher ought to know the history of their subject.

  • Ontology. Disdain for this history may lead to misunderstanding of Anselm’s supposed proof of the existence of God.

  • Presupposition. To prove anything, you need a pou sto, or what Collingwood calls an absolute presupposition.

  • Progression. Newton rejected antiquated presuppositions.

  • Reaction. Coal-burners and racists reject new presuppositions.

  • Universality. From the 47th chapter of the Tao Te Ching (in the translation of Gia-fu Feng and Jane English):

    Without going outside, you may know the whole world.
    Without looking through the window, you may see the ways of heaven.
    The farther you go, the less you know.

    Thus the wise know without traveling;
    See without looking;
    Work without doing.

  • Religion. To say that we can know the laws governing the entire universe is like saying a human can be God.

  • Censorship. Thus everybody who believes in mathematical physics is a Christian, if only in the way that, by the Sun Language Theory, everybody in the world already speaks Turkish.

  • Trinity. That the university has several departments, all studying the same world—this is supposed to correspond to the triune conception of divinity.

This post began as a parenthesis in another post, yet to be completed, about passion and reason. To anchor that post in an established text, I thought back to David Hume, according to whom,

Reason is, and ought only to be[,] the slave of the passions, and can never pretend to any other office than to serve and obey them.

This might express something I said in my previous post: “Reason is the power of testing what we want.” However, I had not really read Hume since college. I thought more about things that had not ended up in the previous post—which was called “Effectiveness” and concerned the article of Eugene Wigner with that word in its title. As I thought and wrote, it seemed I was putting so much into a parenthesis that it could be another post. True, the same might be said of many things in this blog. In any case, the parenthesis in question became the present post.

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War and Talk

This is a foray into the mystery of how things happen, based the 164th of the 361 chapters of War and Peace. This chapter contains, in a one-sentence paragraph, a summary of Tolstoy’s theory of history:

Each man lives for himself, using his freedom to attain his personal aims, and feels with his whole being that he can now do or abstain from doing this or that action; but as soon as he has done it, that action performed at a certain moment in time becomes irrevocable and belongs to history, in which it has not a free but a predestined significance.

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Freedom to Listen

“It’s a free country, so shut up!”

On Thursday, February 16 of this year (2017), at Bosphorus University, a talk on the subject of freedom of speech was given by a Guardian columnist who was a history professor at Oxford. This was Timothy Garton Ash, who observed that freedom of speech and of the press had been severely curtailed in Turkey. For a defender of the regime, the accusation might be belied by the speaker’s freedom to make it. Academics can still come from abroad and give their critical talks. However, as Professor Garton Ash detailed, many Turkish academics have been fired from their positions; many journalists have been imprisoned; other journalists cannot get their articles published. Continue reading