Category Archives: Science

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. 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

Continue reading

Be Sex Binary, We Are Not

Content warning: suicide.

The following sentence is bold in the last paragraph of an essay: “the science is clear and conclusive: sex is not binary, transgender people are real.” I don’t know what the writer means by this. As far as I can tell, as a biological concept used for explaining reproduction, sex has two kinds or parts or sides or aspects, and the essay tacitly affirms this; at the same time, obviously persons called transgender exist.

☾ ♂ ☿ ♃ ♀ ♄ ☉

The title of the essay is a command: “Stop Using Phony Science to Justify Transphobia.” I can support that. I don’t even need the qualifier “phony.” If transphobia is the kind of morbid fear suggested by the suffix “-phobia,” then science ought to help dispel this, not promote it.

One might also just say, Stop using phony science.

Continue reading

On Gödel’s Incompleteness Theorem

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

I shall review the mathematics of the theorem, first in outline, later in more detail. The mathematics is difficult. I have trouble reproducing it at will and even just confirming what I have already written about it below (for I am adding these words a year after the original publication of this essay).

The difficulty of Gödel’s mathematics is part of the point of this essay. A person who thinks Gödel’s Theorem is unsurprising is probably a person who does not understand it.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification.

Continue reading

Antitheses

This is an attempt at a dialectical understanding of freedom and responsibility, punishment and forgiveness, things like that. My text is a part of the Gospel, though I attribute no special supernatural power to this. I shall refer also to the Dialogues of Plato.

The Antitheses are the six parallel teachings, delivered by Jesus of Nazareth in the Sermon on the Mount, as recounted in Chapter 5 of the Gospel According to St Matthew, starting at verse 21. I summarize:

  1. Do not kill people; do not even get angry with them.

  2. Do not commit adultery; do not even fantasize about it.

  3. In divorce, follow the established procedure; do not even divorce.

  4. Do not forswear yourself; do not even swear.

  5. Keep retribution commensurate with the crime; do not even seek retribution.

  6. Love your neighbor; love even your enemy.

Continue reading

NL XLII: The First Barbarism: The Saracens

Index to this series

Executive summary: The barbarians who overran the Western Roman Empire were not barbarists in Collingwood’s technical sense. However, “in the seventh century a movement inspired by hostility towards everything Roman … and everything Christian, flared up on the south-eastern frontier of the Roman world” (42. 22). This movement was therefore barbarist. Failing to conquer Europe, either from the east at Constantinople, or from the west at Tours, the movement settled down and ceased being barbarist—by the account in Chapter XLII, “The First Barbarism: The Saracens,” and later, in Collingwood’s New Leviathan. I check this account against more recent sources; it is barbarist to think that the “movement” in question, or indeed any movement, must always be barbarist; I look at the “civilization” of the British Empire as portrayed in a story of Maugham, and I compare a character of the story to Collingwood.


Collingwood’s historical account of barbarisms is a minefield, if one wishes not to sound like a barbarist oneself. The four examples will be

  1. the Saracens,
  2. the “Albigensian Heresy” (or the Bogomils),
  3. the Turks, and
  4. the Germans.

The very formula “the X”—definite article followed by national or quasi-national adjective—this has a barbaric use in branding a people with indelible features. A retort then is “not all X,” as in “not all men.” Collingwood issues such a proviso himself:

45. 68. Please observe, Reader, that I am not talking about all Germans. I do not say that all Germans are liars. I know of some who are not; those heroes, for example, who continue in spite of everything the Nazis can do to run their secret wireless station and keep on printing Das Wahre Deutschland.

Das wahre Deutschland, from a Swiss antiquarian bookshop, Antiquariat Peter Petrej

Continue reading

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.

Continue reading

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.

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.

Continue reading

Effectiveness

Preface

First posted 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.)

Continue reading

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)

Continue reading