Tag Archives: 2018

On Gödel’s Incompleteness Theorem

December 15, 2018 – 8:43 am

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.

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By David Pierce | Posted in Archimedes, Categorical Thinking, Descartes, Euclid, Exposition, Hitchens, Mathematics, Philosophy, Philosophy of Mathematics, Science | Also tagged , , , , , , , , , , , , , , , , , , , , | Comments (13)

Antitheses

December 13, 2018 – 10:18 am

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.

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By David Pierce | Posted in Collingwood, dialectic, Freedom, Galileo, New Leviathan, overlap of classes, Philosophy, Plato, Science, Stoicism | Also tagged , , , , , , | Comments (30)

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

October 13, 2018 – 7:01 am

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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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By David Pierce | Posted in Collingwood, dialectic, Language, New Leviathan, Pacifism, Philosophy, Pirsig, Plato | Also tagged , , , , , , , , , | Comments (6)

NL XLII: The First Barbarism: The Saracens

October 1, 2018 – 5:49 am

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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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By David Pierce | Posted in Collingwood, dialectic, Galileo, History, Maugham, New Leviathan, Philosophy, Philosophy of History, Plato | Also tagged , , , , , , , , | Comments (4)

NL XLI: What Barbarism Is

September 27, 2018 – 6:22 pm

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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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By David Pierce | Posted in Causation, Collingwood, dialectic, New Leviathan, Philosophy, Plato | Also tagged , , , , , | Comments (3)

NL XL: Peace and Plenty

September 25, 2018 – 8:46 am

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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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By David Pierce | Posted in Collingwood, dialectic, New Leviathan, Pacifism, Philosophy, Plato | Also tagged , , , , , | Comments (2)

NL XXXIX: Law and Order

September 23, 2018 – 10:10 am

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In the New Leviathan, three chapters ago, the essence of civilization was found in not using force against one another. Two chapters ago, civilization was found to be achieved, or at least perpetuated, through education by amateurs, especially within families.

Samuel F. B. Morse (American, 1791-1872), The House of Representatives, 1822, probably reworked 1823, oil on canvas, Corcoran Collection (Museum Purchase, Gallery Fund), National Gallery of Art

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By David Pierce | Posted in Collingwood, dialectic, New Leviathan, Philosophy, Plato | Comments (4)

NL XXXVIII: Civilization and Wealth

September 21, 2018 – 6:08 pm

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To be richer than another person is to have economic power over that person (38. 61). The rich can force the poor to sell their labor for a lower price (38. 64) than if the poor were free (38. 65) of the emotional strain of poverty (38. 66).

Rembrandt, Esau Selling His Birthright, c. 1640–1, British Museum

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By David Pierce | Posted in Collingwood, Fowler, New Leviathan, Philosophy | Comments (1)

NL XXXVII: Civilization As Education

September 20, 2018 – 7:47 am

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Knowing, from the previous chapter, what civilization is, we ask: How do we bring it about? Collingwood’s answer is to homeschool our children.

This is the New Leviathan’s first detailed piece of positive advice, and it may sound crazy. Rather than list reasons why, I want to see what sense can be made of the ideas.

Civility is respect (37. 15). To respect another person is to recognize their freedom (37. 14). To do this, one needs self-respect (37. 13).

Instead of respect, we may approach another person with servility, namely “the demeanour of a man lacking self-respect towards one whom he fears” (37. 17). The will to barbarism is just the will to servility (37. 19).


Mary Cassatt (American, 1844-1926)
The Boating Party, 1893/1894, oil on canvas
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By David Pierce | Posted in Collingwood, Education, New Leviathan, Pacifism, Philosophy, Plato | Also tagged , , , , , , | Comments (12)

NL XXXVI: The Essence of Civilization

September 18, 2018 – 8:56 am

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After thirty-five earlier chapters, we reach the point of the New Leviathan. The essence of civilization is being civil to one another (36. 5).

Henri Rousseau (French, 1844 – 1910), The Equatorial Jungle, 1909, oil on canvas, Chester Dale Collection, National Gallery of Art

That may sound trivial or tautologous. It’s not. We are talking about being civil, in the ancient sense discussed in the previous chapter:

35. 41. Behaving ‘civilly’ to a man means respecting his feelings: abstaining from shocking him, annoying him, frightening him, or (briefly) arousing in him any passion or desire which might diminish his self-respect (13. 31); that is, threaten his consciousness of freedom by making him feel that his power of choice is in danger of breaking down and the passion or desire likely to take charge (13. 67).

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By David Pierce | Posted in Collingwood, dialectic, New Leviathan, Philosophy, Plato | Also tagged | Comments (6)