Category Archives: New Leviathan



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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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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NL XXV: The Three Laws of Politics

Index to this series

A pervading theme of the New Leviathan is freedom of will. Whether we actually have it is only a pseudo-problem (13. 17). Some persons have been fooled into thinking it a problem, perhaps by the misleading myth that free will is a divine gift, like life itself, breathed into our nostrils when, in Genesis 2:7, God forms us of the dust of the ground. As Collingwood observes at the end of Chapter XXIII, “The Family As a Society,” we are born neither free nor in chains. We have to grow up. Growing up is becoming free.

The Book of Genesis Illustrated by Robert Crumb (New York: Norton, 2009)

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On Chapman’s Homer’s Iliad, Book IX

Index to this series | Text of Chapman’s Homer’s Iliad

Book IX of the Iliad is easily summarized. Chapman does it in four lines.

TO Agamemnon (vrging hopelesse flight)
Stand Diomed, and Nestor opposite:
By Nestors counsell, Legats are dismist,
To Thetis sonne, who still denies t’assist.

These lines hide a wealth of thought. To suggest some of the gems of the book, I expand the summary.

Dog and seaweed on shore opposite Lesbos, 2017.09.14

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NL XXIV: The Body Politic, Social and Non-Social

Index to this series

Dialectic is the way to come to terms with a world of constant change. On the internet in particular, too many persons engage in eristic, staking out a position like the Greeks at Troy, who built a wall around their ships on the shore and tried to defend it against all comers.

Dogs stake out their positions in the shade,

In the argument of the New Leviathan, we pass from the family to the state, which Collingwood calls the body politic. This is what political theory must give a scientific account of (24.1). We consider three phases of political theory:

  1. ancient,
  2. medieval, and
  3. modern.

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NL XXIII: The Family As a Society

Index to this series

The last chapter was called “The Family As a Mixed Community,” because the family consists of both a society and a non-social part, called the nursery. Now we are looking at “The Family As a Society.” We are not in contradiction, but are in the flux that Heraclitus observed in all existence (24. 62). The inmates of the nursery normally grow and join the society of their parents: the family as a whole is a society in this sense.

Altınova bazaar, Wednesday, September 13, 2017

If the child is to join the society of its parents, an act of will on both sides is required. This is a key idea of the chapter, one to be carried on to considerations of the state. Collingwood talks a lot about the implications of contraception for the family. He seems to find the practice distasteful; but the possibility of the practice is a boon to freedom, for making us think about things.

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NL XXII: The Family As a Mixed Community

Index to this series

This chapter and the next concern the family, which like most communities is a mixed community (22.11): part of it is a non-social community, but some part of it is a society proper (22.1), this being, again, as in Chapter XX especially, a community constituted as an act of will on the part of its members.

Thus some members of the family are wilfully so, and some are not. The latter are children, who constitute the nursery (22.12). This is self-emptying, in the sense that children grow up and leave it; it is not self-filling, since children themselves cannot have children (22.21). The nursery is rather replenished by parents (22.17).

The family being a politically sensitive topic, we want to know where Collingwood is going with his account of it. In the present short chapter, he will mention some qualifications and modifications of the basic set-up just described. The next chapter will mention how contraception changed the understanding of the family in Collingwood’s lifetime (he had been born in 1889).

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NL XXI: Society as Joint Will

Index to this series

A society is an act of will. To form a society is to say, or rather to mean, that we, the intended members of the society, will do something, and not just that we shall do something.

We ask how it is possible to say, “We will.” We ask, as readers, either of Collingwood’s New Leviathan, or at least of what I am writing about this book. I ask, while on holiday at the beach with, for the last few days, my nephew and niece, ages eight and three respectively. When I was a little older than they, I was incensed to think, as an American, that Ronald Reagan might destroy us all in a nuclear war with the Soviet Union. Later I read the words of Christopher Hitchens, from an older generation, who could remember where he was when John F. Kennedy almost killed him—along with everybody else, during the Cuban Missile Crisis. Such worries now return under an American President who seems to embody the worst ruler that Plato could imagine.

Writing in England the early 1940s, Collingwood contended with Fascism and Nazism. He tried to articulate why they must be fought, and what was worth defending. Though generals are accused of always fighting the last war, I read Collingwood with the notion that his thoughts, like Plato’s, are still of value.

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NL XX: Society and Community

Index to this series

A society is an act of will: it emerges and persists because its members will that it do so. We said this in the previous chapter; we say it now in more detail. In particular, we impose on a society no such further requirement of economic interest as Roman lawyers (apparently) did.

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NL XIX: Two Senses of the Word “Society”

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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