Category Archives: Principles of Art

On Chapman’s Homer’s Iliad, Book XVIII

I analyze Book XVIII of the Iliad into seven scenes.

Branches against sky

  1. Achilles receives from Antilochus the news of Patroclus’s death, and Thetis receives the news from Achilles. She tells him not to fight till she has brought new arms from Mulciber (Chapman’s lines 1–136).

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NL XXXIV: What Civilization Means Generically

Index to this series

Turning now to Part III of Collingwood’s New Leviathan (1942), we take up civilization, a topic of utmost importance, featuring as it does, for example, in the controversial hypothesis of the “Clash of Civilizations,” and generally being something that reactionaries say they want to defend.

Civilization is something that happens to a community (34. 4). We studied communities as such in Part II, and their members individually in Part I.

Civilization is a “process of approximation to an ideal state” (34. 5). That is the gist of Chapter XXXIV, “What ‘Civilization’ Means: Generically.” There will be a lot to spell out.


We have returned to Istanbul. Below are
sunset photos from our last night on the Aegean coast

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NL XXXI: Classical Physics and Classical Politics

Index to this series

As my beach holiday winds down, so perhaps does the current spate of blog posts. Here is one more. Setting aside Homer, I continue immediately with Collingwood, in part because, in the 2000 paperback impression of the 1992 Revised Edition of the New Leviathan that I take to the shore, I have now also read the Editor’s Introduction by David Boucher. (Back at the cottage, I have to type out the quotes from this that I make below; for quotes of Collingwood himself, I cut and paste from a scan of the 1947 corrected reprint of the 1942 First Edition.)

As I could infer from my pencil-marks, I had read Boucher’s introduction some time before; but I could remember little of it. I think it is aimed at professional philosophers, rather than at anybody who would admire Collingwood for saying, as he does in An Autobiography (page 6), when he describes getting prepared to go to Rugby School,

The ghost of a silly seventeenth-century squabble still haunts our classrooms, infecting teachers and pupils with the lunatic idea that studies must be either ‘classical’ or ‘modern’. I was equally well fitted to specialize in Greek and Latin, or in modern history and languages (I spoke and read French and German almost as easily as English), or in the natural sciences; and nothing would have afforded my mind its proper nourishment except to study equally all three.

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NL XXX: War As the Breakdown of Policy

Index to this series

Humans have not always made war (30. 1); why do we make it now? War is said to be a continuation of policy (30. 14); but as Collingwood cleverly points out (30. 15), the saying due to Clausewitz (30. 69) is ambiguous: a continuation could be an extension or a breakdown (30. 16–17).

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A New Kind of Science

Executive summary. Some sciences are called descriptive, empirical, or natural; others, prescriptive or normative. We should recognize a third kind of science, which studies the criteria as such that a thinking being imposes on itself as it tries to achieve success. I propose linguistics as an example. Collingwood introduced the term criteriological for the third kind of science. This was in The Principles of Art (1938), though I find the germ of the concept in earlier work, even in Collingwood’s first book, Religion and Philosophy (1916), in the passage on psychology that the author would recall in An Autobiography (1939).

Collingwood’s examples of criteriological sciences are logic, ethics, aesthetics, and economics. Pirsig effectively (and independently) works out rhetoric as an example in Zen and the Art of Motorcycle Maintenance (1974). We may benefit from clarity here, given how people can have a strong reaction to being lectured by experts. For Collingwood, such a reaction is found in Nazi Germany; see the last chapter of The New Leviathan (1942). Reactions to grammar are the subject of my own two ensuing articles, “Writing and Inversion” and “Writing Rules.”


Some sciences are not recognized for what they are. The sciences themselves are not new, but a proper understanding of them may be new to some of us, including myself.

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Re-enactment

Executive summary (added October 6, 2018). Historian Niall Ferguson praises Collingwood as a philosopher of history, while showing no sign of understanding Collingwood’s actual philosophy. This provokes me. My comments are in the following sections.

Presupposition
By Collingwood’s account, there is a science of our absolute presuppositions, be these in natural science or in politics. The science of absolute presuppositions is metaphysics, and it is an historical science, because absolute presuppositions do change with time.
Thinking
The historian’s job is to know the thoughts of the past. Leo Strauss disagrees with Collingwood over how one goes about this; but he would seem to agree with Collingwood that what is to be known is thought, as distinct from feeling.
Failures
I know of three examples of failures to understand Collingwood (Niall Ferguson provides a fourth).
History
Ferguson reviews a book in which twenty historians try to recover the feeling of certain historical events. By saying that for Collingwood, “the historian was limited to reconstructing recorded thoughts,” Ferguson errs in two ways.

  1. Those thoughts need not be “recorded,” but anything can be used as evidence for a thought, if one knows how to use it.
  2. Feelings from the past can come down to us, only if they have been converted to thoughts.

See also “The Ambiguity of Feeling.”

Experiment
To know whether “an individual act altered the course of history,” Ferguson does recognize that we need to know more than past feelings. For him, “We need to imagine what would’ve happened if the act in question had not happened.” However, we cannot say where any particular thought is going to go, until we see where it does go, by thinking it. In this sense, every thought alters the course of history. Neither then can we say where a thought would have gone. In this way, history is different from natural science.

Presupposition

A theme of my last two articles here (namely “What It Takes” and, before that, “Effectiveness”) is the value of metaphysics, as being concerned with such problems as the following:

  • Physics has not been able to reconcile its theories of the infinitesimally small and the infinitely large.
  • America has not been able, in the words of Martin Luther King, to live out the true meaning of its creed, that all of us are created equal.

In a technical sense, these problems may not belong to natural science or political science as such. Considered as diseases, whether of the body politic or of the “body scientific,” the problems may not be curable, either by the body’s own immune system, or by remedies from outside. What is needed may be something resembling psychoanalysis, so to speak, or what Collingwood actually calls metaphysical analysis. This is an examination of absolute presuppositions, or the fundamental assumptions that have heretofore been left unquestioned. The analyst—the metaphysician—may suspect what those assumptions are; but the patient must confirm the suspicion, or else discover the assumptions independently. In any case, the patient will not be cured without agreeing that there is a disease.

Cures do happen, because absolute presuppositions change. Continue reading

Effectiveness

Preface

First published May 17, 2018, this essay concerns Eugene Wigner’s 1960 article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I wrote a lot, which I now propose to summarize by section. (The meditations also continue in the next article.)

  • Some things are miraculous. Among Wigner’s examples are
    • that mathematics is possible at all, and
    • that “regularities” in the physical world can be discovered, as by Galileo and Newton.

    For Wigner, we should be grateful for the undeserved gift of a mathematial formulation of the laws of physics. This makes no sense theologically—and here I agree with the character Larry Darrell in Somerset Maugham’s novel The Razor’s Edge. Wigner’s idea that our mathematical reasoning power has been brought to perfection makes no sense to me either.

  • Everything is miraculous. Here I agree with Collingwood in Religion and Philosophy. A miracle cannot be the breaking of a natural law, since such a thing cannot be broken. A great artist like Beethoven follows no rules in the first place, or makes them up as he goes along; and he is like God in this way.
  • Natural law. That it cannot be broken is part of the very concept of natural law. Quantum phenomena and the theory of relativity have not in fact been brought under a single law; for Wigner, it may not be possible.
  • Mystery. Not only can we not define miracles, but (as we should have observed in the first place) we cannot even say when they happen. If like Wigner we call something miraculous, this means it cleanses our own doors of perception, in the sense of William Blake.
  • Definitions. In his treatment of miracle in Religion and Philosophy, Collingwood shows the futility of trying to define a term when you are not sure how to use it. He makes this futility explicit in The Principles of Art. If we are going to think about the use of mathematics in natural science, this means we ought to be mathematician, natural scientist, and philosopher; and not just “natural scientist,” but physicist and biologist, since if mathematics is effective in physics, it would seem to be ineffective in biology.
  • Being a philosopher. We are all philosophers, in the sense that Maugham describes in the story “Appearance and Reality,” if only we think. All thought is for the sake of action. This does not mean that thought occurs separately from an action and is to be judged by the action. We may value “pure” thought, such as doing mathematics or making music or living the contemplative life of a monk. This however moves me to a give a thought to the disaster of contemporary politics.
  • Philosophizing about science. For present purposes, compart­ment­al­ization of knowledge is a problem. So is the dominance of analytic philosophy, for suggesting (as one cited person seems to think) that big problems can be broken into little ones and solved independently. In mathematics, students should learn their right to question somebody else’s solutions to problems. In philosophy, the problems themselves will be our own. Philosophy as such cannot decide what the problems of physics or biology are, though it may help to understand the “absolute presuppositions” that underlie the problems. Philosophers quâ metaphysicians cannot determine once for all what the general structure of the universe is. This does not mean they should do “experimental philosophy,” taking opinion polls about supposedly philosophical questions. What matters is not what people say, but what they mean and are trying to mean. As Collingwood observes, metaphysics is an historical science.

For more on the last points, see a more recent article, “Re-enactment.” (This Preface added June 3, 2018.)


I am writing from the Math Village, and here I happen to have read that Abraham Lincoln kept no known diary as such, but noted his thoughts on loose slips of paper. Admired because he “could simply sit down and write another of his eloquent public letters,”

Lincoln demurred. “I had it nearly all in there,” he said, pointing to an open desk drawer. “It was in disconnected thoughts, which I had jotted down from time to time on separate scraps of paper.” This was how he worked, the president explained. It was on such scraps of paper, accumulating over the years into a diaristic density, that Lincoln saved and assembled what he described to the visitor as his “best thoughts on the subject.”

Thus Ronald C. White, “Notes to Self,” Harper’s, February 2018. My own notes to self are normally in bound notebooks, and perhaps later in blog articles such as the present one, which is inspired by the 1960 article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” by Eugene Wigner.
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Boolean Arithmetic

Mathematics can be highly abstract, even when it remains applicable to daily life. I want to show this with the mathematics behind logic puzzles, such as how to derive a conclusion using all of the following premisses:

  1. Babies are illogical.
  2. Nobody is despised who can manage a crocodile.
  3. Illogical persons are despised.

The example, from Terence Tao’s blog, is attributed to Lewis Carroll. By the first and third premisses, babies are despised; by the second premiss then, babies cannot manage crocodiles.

George Boole, The Laws of Thought (1854), Open Court, 1940

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On Knowing Ourselves

In a 2012 post in this blog, I criticized a 2009 essay called “50 Years of Stupid Grammar Advice.” The putative advice was that of Strunk and White; but their advice was not in fact grammatical. They wrote not the elements of grammar, but The Elements of Style. They gave style advice by precept and example. The advice is good, if well understood. The critic should recognize that, as I wrote, “Rules of style are supposed to induce thinking, not obedience.”

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The Tree of Life

My two recent courses at the Nesin Mathematics Village had a common theme. I want to describe the theme here, as simply as I can—I mean, by using as little technical knowledge of mathematics as I can. But I shall talk also about related poetry and philosophy, of T. S. Eliot and R. G. Collingwood respectively.


An elaborate binary tree, with spirals

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