Category Archives: Science

Writing and Inversion

Executive summary: The “voice” of a transitive verb may be active or passive. A piece of writing may be vigorous or torpid. There is not an exact correspondence between passive verbs and torpid writing. However, a passive verb is used to effect inversion of subject and object. One may also invert subject and auxiliary verb, subject and predicate, or two clauses, always adding new words. Each inversion may lead to torpid writing. This is what Strunk warned about in The Elements of Style, by issuing the command, “Use the active voice.” The command must be followed with discretion. Williams makes the same case, more elaborately, in Style: Towards Clarity and Grace. There is no foolproof executive summary of how to write well.


When E. B. White revised William Strunk’s original Elements of Style, he did not retain Strunk’s “Introductory,” whose first paragraph said of the book,

The experience of its writer has been that once past the essentials, students profit most by individual instruction based on the problems of their own work, and that each instructor has his own body of theory, which he may prefer to that offered by any textbook.

Perhaps many students today cannot receive individual instruction. They are just given textbooks that try to spell out everything. I have sensed this in mathematics, where new calculus books seem a lot bigger than those of 1950 and earlier. Continue reading

A New Kind of Science

Executive summary: There are sciences called descriptive, empirical, or natural; and there are sciences called prescriptive or normative. A third kind of science studies the criteria as such that a thinking being, such as one of us, imposes on itself as it tries to achieve success. Collingwood developed the concept and coined the term criteriological for such a science. Logic, ethics, aesthetics, and economics are Collingwood’s examples; I propose also linguistics as an example. Pirsig effectively works out rhetoric as an example. Getting these things straight may be of political use.


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.

Here I supplement and update “Strunk and White,” a post in which I took issue with a professional linguist’s attacks on The Elements of Style. This book was William Strunk’s “little book” (53 pages), made slightly less little (71 pages) by E. B. White. In an essay called “50 Years of Stupid Grammar Advice,” Geoffrey Pullum suggests that Strunk and White give a prescriptive account of English grammar, though they fail to understand it; in The Cambridge Grammar of the English Language (1842 pages), Pullum and Rodney Huddleston claim to present the same subject descriptively. 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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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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NL XIX: Two Senses of the Word “Society”

Executive summary (below) | Index to this series

After a break of half a year, I return to reading Collingwood’s New Leviathan. Being on holiday at an Aegean beach gives me the opportunity. While here, I may also return to Chapman’s Homer’s Iliad. Last winter I finished Part I of the New Leviathan, the part called “Man.” Here I continue with the first chapter of “Society.” I have reason to look at what Mary Midgley and Albert Einstein say about science. Collingwood’s investigation suggests a way of thinking about prejudice and discrimination.

Part II of the New Leviathan is “Society,” and the first two chapters of this, XIX and XX, concern the distinction between society proper and two more general notions. In Chapter XX, the more general notion will be community. In Chapter XIX, the more general notion has not got its own proper name, and so Collingwood denotes it by writing “society,” in quotation marks.

A “society” of chairs at the beach (Altınova 2017.08.31)

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Duty to Nature

Index to this series

Summary and update (added October 14, 2018): When we do something, or propose to do something, we may explain it or justify it—give a reason for it—as being useful, right, or dutiful. Such is the theory of Collingwood, analyzed here, especially with regard to a question that has increasing urgency: have we a duty, not only to one another, but to nature?

When I originally composed this post, I had recently analyzed several relevant chapters of Collingwood’s New Leviathan:

Those chapters are the last in Part I, “Man.” Part II, “Society,” returns to the same ideas in Chapter XXVIII, “The Forms of Political Action.” I would analyze this, 18 months later; it has an example of abuse of the concept of duty, by the German political theorist Treitschke.

By one interpretation of a passage in Herodotus, the ancient Persians perceived a duty to nature, by a teaching now attributed to Zoroaster. His teachings influenced Manichaeism, and thus in turn the “Albigensian heresy,” the subject of Chapter XLIII of the New Leviathan.

We tend to explain what happens in the world the way we explain what we ourselves do. If our ethics are utilitarian, then, like the ancient Greeks, we may see things in nature too as serving purposes. If we govern, or aim to govern, our own behavior by laws, then we may also seek laws of nature, as physicists do now.

Being general in form, utility and law provide incomplete accounts of exactly what we do. Though we may not always use the word this way, duty is to be conceived as providing a complete account of what we do. Conscience tells us that we have a duty; then we have to reason out what it is. The corresponding science of the world is history, which studies us as free agents. Collingwood does not describe a corresponding science of nature as such, at least not in the New Leviathan; but at the end of his first book, Religion and Philosophy, he concluded that everything that happened must be an act of will. This was in the chapter called “Miracle,” which I looked at especially in “Effectiveness.”

It may be hard to distinguish lawful action from dutiful action. Here I look at the examples of

  • paying off a student loan;
  • smoking cigarettes, when rules restrict it;
  • collecting armaments, because, at the Last Supper, by the account in Luke, Jesus recommended buying swords;
  • Islam, as a rule-bound religion;
  • Christian denigrators of Islam, who find in it rules that they think believers must be bound by, even as some Muslims find inspiration in the teachings of Prophet Jesus.

I conclude with an Episcopal priest called Stephen Blackmer, for whom nature is a church and a member of his congregation.


This is a synthesis of some ideas from a recent spate of posts in this blog. A theme is the question of why we do what we do, and whether what we do to Nature in particular—how we think of Nature—can change.

Farhang Mehr, The Zoroastrian Tradition, cover with image of Zarathustra Continue reading

NL XVIII: “Theoretical Reason”

Index to this series

Reason is primarily practical: it explains why we do what we do. Secondarily, reason explains why others do what they do (18. 1): this makes reason theoretical, though not entirely so, since questions about others arise from, and are answered by, our relations with those others (18. 11). The experimental method involves such relations: we do something to the world, to see how it will respond (18. 12). Continue reading

NL XIII: “Choice”

Index to this series

Adolph Gottlieb, “Centrifugal,” gouache on paperboard, 1961 (National Gallery of Art, Washington; gift of the Woodward Foundation)

Adolph Gottlieb, “Centrifugal,” 1961 (National Gallery of Art, Washington; gift of the Woodward Foundation)

The key idea of Chapter XIII of New Leviathan is the correct statement of the “problem of free will”: Continue reading

Happiness

If only tangentially sometimes, this is about living in Turkey, especially under the ongoing official state of emergency.

Aristotle, Marx & Engels, and Collingwood

Aristotle, Marx & Engels, and Collingwood

A blog article on Medium recently struck me for its treatment of science. Dated October 3, the article is called The Purpose Of Life Is Not Happiness: It’s Usefulness, and its opening section is as follows.

For the longest time, I believed that there’s only purpose of life: And that is to be happy. Continue reading

Beykoz, Istanbul

After five years in Istanbul, we continue to learn how much there is still to discover here. Now we have been to the Asian borough of Beykoz. Much of what we saw there was rural, and the topography and flora reminded me of Appalachia. I have nothing to say about the poverty and ignorance that might be suggested by this term; for me, Appalachia was always a locus for holidays, mostly at my late uncle’s place in West Virginia, but also in the form of bicycle tours. Travelling now to Beykoz, Country roads, I could think, take me home, to the place I belong! We got there by public bus from our European borough of Şişli.

Polonezköy, Beykoz, 2016.08.14

Polonezköy, Beykoz, 2016.08.14

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