Category Archives: Aristotle

Charles Bell’s Axiomatic Drama

Here is an annotated transcription of a 1981 manuscript by Charles Greenleaf Bell (1916–2010) called “The Axiomatic Drama of Classical Physics.” A theme is what Heraclitus observed, as in fragment B49a of Diels, LXXXI of Bywater, and D65a of Laks and Most:

We step and we do not step into the same rivers, we are and we are not.
ποταμοῖς τοῖς αὐτοῖς ἐμβαίνομέν τε καὶ οὐκ ἐμβαίνομεν, εἶμέν τε καὶ οὐκ εἶμεν.

Bell reviews the mathematics, and the thought behind it, of

  1. free fall,
  2. the pendulum,
  3. the Carnot heat engine.

In a postlude called “The Uses of Paradox,” Bell notes:

Forty-five years ago I decided that when reason drives a sheer impasse into an activity which in fact goes on, we have to think of the polar cleavage as both real and unreal.

I like that reference to “an activity which in fact goes on.” In youth it may be hard to recognize that there are activities that do go on. We do things then, but that they will get anywhere may be no more than a dream. In any case, Bell himself goes on:

… that is a job as huge and demanding as Aristotle’s, and for me at 70, just begun.

“Look,” my friends say, “Bell’s been doing the same thing since he was 25. About that time he had a vision of Paradox as paradise, and he’s been stuck there ever since.”

Bell’s picture next to Aristotle’s Physics
The back of Bell’s Five Chambered Heart with
the front of the OCT of Aristotle’s Physics

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On Plato’s Republic, 14

Index to this series

In the tenth and final book of Plato’s Republic (Stephanus 595–621), with the help of Glaucon, Socrates does three things:

  1. Confirm and strengthen the ban on imitative poetry carried out in Book III.
  2. Prove the immortality of the soul.
  3. Tell the Myth of Er about how best to make use of that immortality.


Bernard Picart
Glaucus Turned into a Sea-God, 1731
“Just as those who catch sight of the sea Glaucus would no longer easily see his original nature because some of the old parts of his body have been broken off and the others have been ground down and thoroughly maimed by the waves at the same time as other things have grown on him – shells, seaweed, and rocks – so that he resembles any beast rather than what he was by nature, so, too, we see the soul in such a condition because of countless evils” – Republic 611d

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Nature

Index to this series

Can Socrates really “find a natural support for justice,” as Allan Bloom says he must? It is strictly impossible, I say in “Bloom, Badiou, Ryle, Shorey.” Inevitably there is more that can be said, and I shall try to get some of it said here.

Sand, sea, mountains, sky
Anatolian sand, Aegean sea, Lesbian mountains
Uranus over all
Profesörler Sitesi, Altınova, Balıkesir, Turkey
September 24, 2021

There’s a lot in this post. I drafted the final part first, while I was still at the beach; I’m not there now, and I have to move on. Here in Istanbul, I have added the initial part (and brought pieces of the early draft forward), largely to look at the relations between the thoughts of

  • Leo Strauss, Bloom’s teacher;
  • R. G. Collingwood, my teacher, through his books (he died twenty-two years before my birth), and the subject of some of Strauss’s criticism.

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On Plato’s Republic, 5

Index to this series

Our fifth scheduled reading in the Republic is Book IV (Stephanus pages 419–45). Socrates speaks

  • with Adeimantus, through the completion of the construction of the city in speech;
  • with Glaucon, after he insists (427d) that Socrates join in the search for justice in the city; they find it and map it back to the individual.

Three dogs sit in the shade of a beach umbrella
Intellect, spirit, and appetite
Profesörler Sitesi, Altınova, Balıkesir, Turkey
September 13, 2021

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Automatia

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

Large parts of this post are taken up with two subjects:

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

  2. Gödel’s theorems of completeness and incompleteness, as examples of results in the science of logic.

Like the most recent in the current spate of mathematics posts, the present one has arisen from material originally drafted for the first post in this series.

In that post, I defined mathematics as the science whose findings are proved by deduction. This definition does not say what mathematics is about. We can say however what logic is about: it is about mathematics quâ deduction, and more generally about reasoning as such. This makes logic a criteriological science, because logic seeks, examines, clarifies and limits the criteria whereby we can make deductions. As examples of this activity, Gödel’s theorems are, in a crude sense to be refined below, that

  • everything true in all possible mathematical worlds can be deduced;

  • some things true in the world of numbers can never be deduced;

  • the latter theorem is one of those things.

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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.

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Logic of Elliptic Curves

In my 1997 doctoral dissertation, the main idea came as I was lying in bed one Sunday morning. Continue reading