This attempt at exposition of Gödel’s Incompleteness Theorem was inspired or provoked by somebody else’s attempt at the same thing, in a blog post that a friend directed me to (by means of a Twitter message on November 17, 2020). I wanted in response to set the theorem in the context of mathematics rather than computer science.
Executive summary. The English grammatical moods—indicative, imperative, subjunctive—were not understood till the nineteenth century, according to an 1882 doctoral dissertation, On the Use of the Subjunctive Mood in Anglo-Saxon. Considering illustrative passages that happen to be from Plato, Alfred Douglas, Evelyn Waugh, and especially John Donne; looking ultimately at John McWhorter’s 2015 essay, “English is not normal”; I review the subjunctive mood, grammar in general, and my own lack of understanding till I was in college.
Achilles is found singing to a lyre, in a passage of Book IX of the Iliad. Homer sets the scene in five dactylic hexameters; George Chapman translates them into four couplets of fourteeners.
I wrote a post about each book of the Iliad, in Chapman’s version of 1611. As I said at the end, I look forward to reading Emily Wilson’s version. Meanwhile, here I examine the vignette of the lyre in several existing English translations, as well as in the original.
I analyze Book XVIII of the Iliad into seven scenes.
Achilles receives from Antilochus the news of Patroclus’s death, and Thetis receives the news from Achilles. She tells him not to fight till she has brought new arms from Mulciber (Chapman’s lines 1–136).
A human being was once a man. A female of the species was a wife; a male, a were. The word “were” was used in werewolf, but also were-eld, which became our “world.” Our word "woman" comes from wife-man.
That is roughly the history, which I shall review later in a bit more detail. It would be a fallacy to think the history told us how we must use the words “woman” and “man” today. The history does suggest what may happen again: in a world dominated by men, a word like “person,” intended for any human being, may come to have its own meaning dominated by men. Yet again, this is no reason not to try to make our language better.
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
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):
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
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,
Fire temple, Yazd, Iran, September 2012. See “Duty to Nature”
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
Polytropy 