Category Archives: New Leviathan

Anthropology of Mathematics

This essay was long when originally published; now, on November 30, 2019, I have made it longer, in an attempt to clarify some points.

The essay begins with two brief quotations, from Collingwood and Pirsig respectively, about what it takes to know people. The Pirsig quote is from Lila, which is somewhat interesting as a novel, but naive about metaphysics; it might have benefited from an understanding of Collingwood’s Essay on Metaphysics. A recent article by Ray Monk in Prospect seems to justify my interest in Collingwood; eventually I have a look at the article. Ideas that come up along the way include the following.

  1. For C. S. Lewis, the reality of moral truth shows there is something beyond the scope of natural science.

  2. I say the same for mathematical truth.

  3. Truths we learn as children are open to question. In their educational childhoods, mathematicians have often learned wrongly the techniques of induction and recursion.

  4. The philosophical thesis of physicalism is of doubtful value.

  5. Mathematicians and philosophers who ape them use “iff” needlessly.

  6. One pair who do this seem also to misunderstand induction and recursion.

  7. Their work is nonetheless admirable, like the famous expression of universal equality by the slave-driving Thomas Jefferson.

  8. Mathematical truth is discovered and confirmed by thought.

  9. Truth is a product of every kind of science; it is not an object of natural science.

  10. The distinction between thinking and feeling is a theme of Collingwood.

  11. In particular, thought is self-critical: it judges whether itself is going well.

  12. Students of mathematics must learn their right to judge what is correct, along with their responsibility to reach agreement with others about what is correct. I say this.

  13. Students of English must learn not only to judge their own work, but even that they can judge it. Pirsig says this.

  14. For Monk, Collingwood’s demise has meant Ryle’s rise: unfortunately so since, for one thing, Ryle has no interest in the past.

  15. In a metaphor developed by Matthew Arnold, Collingwood and Pirsig are two of my touchstones.

  16. Thoreau is another. He affects indifference to the past, but his real views are more subtle.

  17. According to Monk, Collingwood could have been a professional violinist; Ryle had “no ear for tunes.”

  18. For Collingwood, Victoria’s memorial to Albert was hideous; for Pirsig, Victorian America was the same.

  19. Again according to Monk, some persons might mistake Collingwood for Wittgenstein.

  20. My method of gathering together ideas, as outlined above, resembles Pirsig’s method, described in Lila, of collecting ideas on index cards.

  21. Our problems are not vague, but precise.


When Donald Trump won the 2016 U.S. Presidential election, which opinion polls had said he would lose, I wrote a post here called “How To Learn about People.” I thought for example that just calling people up and asking whom they would vote for was not a great way to learn about them, even if all you wanted to know was whom they would vote for. Why should people tell you the truth?

Saturn eclipse mosaic from Cassini

With other questions about people, even just understanding what it means to be the truth is a challenge. If you wanted to understand people whose occupation (like mine) was mathematics, you would need to learn what it meant to prove a theorem, that is, prove it true. Mere observation would not be enough; and on this point I cite two authors whom I often take up in this blog.

  • In the words of R. G. Collingwood in Religion and Philosophy (1916, page 42), quoted in An Autobiography (1940, page 93) as well as in the earlier post here, “The mind, regarded in this external way, really ceases to be a mind at all.”

  • In the words of English teacher and anthropologist Verne Dusenberry, quoted by Robert Pirsig in Lila (1991, page 35), “The trouble with the objective approach is that you don’t learn much that way.”

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NL I: “Body and Mind” Again

Index to this series

“We are beginning an inquiry into civilization,” writes Collingwood, “and the revolt against it which is the most conspicuous thing going on at the present time.” The time is the early 1940s.

Human tourists photographing sculptured supine blue ape with chrome testicles outside the Intercontinental Hotel, Prague Continue reading

Piety

The post below is a way to record a passage in the Euthyphro where Socrates say something true and important about mathematics. The passage is on a list of Platonic passages that I recently found, having written it in a notebook on May 23, 2018. The other passages are in the Republic; Continue reading

NL XLV: The Germans

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At the end of Collingwood’s New Leviathan (1942), we reach a chapter whose theme is that of my more recent articles on grammar.

By August Macke – The Yorck Project (2002) 10.000 Meisterwerke der Malerei (DVD-ROM), distributed by DIRECTMEDIA Publishing GmbH. ISBN: 3936122202., Public Domain, Link

As history, Collingwood’s last chapter is difficult, for the reasons that trouble Herbert Read at the beginning of his Concise History of Modern Painting (revised 1968, augmented 1974). Read opens his first chapter with a passage from Collingwood’s Speculum Mentis (1924):

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NL XLIV: The Turks

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The last part of Collingwood’s New Leviathan (Oxford, 1942) is “Barbarism.” The first chapter of the part is “What Barbarism Is”; the remaining chapters describe examples of barbarism in turn. The fourth and last example is the one that Britain is fighting as Collingwood writes.

Sun behind mosque on cover of The Ottoman Centuries (Lord Kinross, a.k.a. Patrick Balfour) 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 as I shall say, 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.

For better or worse, these are part of the cultural heritage of many of us; they are at least a commentary on the cultural heritage (the Mosaic Law) of more of us.

I write now specifically, because I think the Antitheses can illustrate or illuminate some contemporary philosophical concerns, Continue reading

NL XLIII: The Second Barbarism: The ‘Albigensian Heresy’

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Summary. Suppose your society has certain rites and customs, perceived as essential to its functioning. When some persons among you reject those rites and customs, what are you going to do? Persecution would be the normal response of a society that aimed to preserve itself. In the example to be considered here, the society is medieval Christendom, where

  • buildings called churches were customarily the abode of friendly spirits, and
  • the rite of swearing an oath was a sign of special commitment.

Oaths and churches were rejected by persons called Paulicians, or Bogomils, or Albigensians. Their beliefs were Manichaean. These persons were persecuted so successfully that we do not understand them very well. Therefore we must leave open the question of whether they were barbarists.

Here I am going to review, among other things,

  • what it means to fight barbarism;
  • the response to German bombardment described in Goodbye, Mr. Chips;
  • what Jesus Christ says about swearing;
  • how the United States accommodates various beliefs (as by allowing affirming instead of swearing, or allowing Muslims to swear on a Quran);
  • the threat of a lying President;
  • the threat of ignoring climate change;
  • the etymology of heresy;
  • the discussion of mythos and logos in Pirsig.

Fire temple, Yazd, Iran, September 2012. See “Duty to Nature

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NL XLII: The First Barbarism: The Saracens

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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

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NL XLI: What Barbarism Is

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Civilization being agreement, barbarism has no chance in the long run (41. 67):

41. 76. For barbarism implies not only a quarrel between any barbarist and any civilized man; it also implies a quarrel between anyone barbarist and any other; and that any state of harmony between them is merely this quarrel suspended.

The barbarist is somebody “who imitates the conditions of an uncivilized world” (41. 53); but an actual attempt to bring about those conditions will need cooperation, and this will be a step towards civility. Here perhaps we should distinguish cooperation from the kind of coerced organization seen in a fascist state. Specific examples will be considered in the later chapters of Part IV of the New Leviathan. We are now considering “What Barbarism Is,” in general terms.

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NL XL: Peace and Plenty

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With “Peace and Plenty,” we reach the end of the account of civilization in Collingwood’s New Leviathan. What remains is the account of barbarism. Strictly speaking, we little need it. Civilization quâ ideal of civility is the positive end of civilization quâ process, and as was pointed out on Chapter XXXII, “Society and Nature in the Classical Politics,” the positive end is the primary thing to know in conducting a process (32. 35–6).

“May Day, 1929,” V. V. Kuptsov

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