A certain thesis is reasonable to me, and yet it would seem to anger persons whom I wish to respect. I am trying to understand why it does.
The hypothesis of the homunculus in the sperm
by Nicolaas Hartsoeker, 1695
Perhaps the manner of expression of the thesis is the problem. Thus one person tweets:
Having been put to bed by Eurycleia at the end of Book I of the Odyssey, Telemachus gets up in the morning and has the people summoned to council, at the beginning of Book II.
There is no mention of a breakfast. Perhaps none is eaten. On the other hand, Telemachus probably relieves his bladder at least, and there is no mention of that either.
Telemachus straps on a ξίφος, but arrives at the assembly with a χάλκεον ἔγχος in hand. Wilson calls it a sword in either case; for Fitzgerald and Lattimore, the first weapon is a sword, but the second a spear and a bronze spear, respectively. Cunliffe’s lexicon supports the men; however, for Liddell and Scott, an ἔγχος can also be a sword, at least in Sophocles. For Beekes, ξίφος is Pre-Greek, and ἔγχος may be so. Continue reading
This is about the ordinal numbers, which (except for the finite ones) are less well known than the real numbers, although theoretically simpler.
The numbers of either kind compose a linear order: they can be arranged in a line, from less to greater. The orders have similarities and differences:
Note. Would it be helpful to write that more verbosely?
One can conclude in particular that the ordinals as a whole do not compose a set; they are a proper class. This is the Burali-Forti Paradox.
In reading his rendition of the Iliad, having enjoyed hearing Chapman speak out loud and bold;
having enjoyed writing here about each book, particularly the last ten books in ten days on an Aegean beach in September of this year (2019);
having taken the name of this blog from the first line of the Odyssey;
having obtained, from Homer Books here in Istanbul, Emily Wilson’s recent translation (New York: Norton, 2018);
Part of this post is a laboratory notebook. I record how I fixed my computer, because
I am pleased to have been able to do it, and
I may have to do it again.
Briefly, when Windows on my laptop failed, I installed Ubuntu, but this failed. Somebody else installed Ubuntu again, and this worked for a while before failing. I managed to fix that problem for myself; but later an upgrade failed. Now I have fixed that. 
I am recording further issues in an addendum.
Note added, March 10–11, 2021. The bulk of this post concerns race in the theory of history, particularly the theory attributed to Johann Gottfried Herder (1744–1803). Not having read Herder for myself, I rely on the accounts of
Somebody like Herder may introduce race as an hypothesis to explain history, but ultimately the hypothesis fails, by denying us the freedom that is essential to history as such. Nonetheless, Forster defends Herder as having
an impartial concern for all human beings … Herder does also insist on respecting, preserving, and advancing national groupings. However, this is entirely unalarming,
because, for one thing, “The ‘nation’ in question is not racial but linguistic and cultural.”
Change Collingwood’s word “race” to “linguistic and cultural grouping” then. I think his conclusion remains sound: “Once Herder’s theory of race is accepted, there is no escaping the Nazi marriage laws.”
More detail is in the post below. I go on to review the philosophy of history that Collingwood presents in the Introduction of The Idea of History. This book provided me with a title for the post.
I wrote a lot in this post, as I often do. Growing self-conscious for being opinionated about the theory of history, I listed the published evidence of my actually being an historian (an historian of ancient Greek mathematics in particular).
I originally wrote that my research had been inspired by a tweet. The author of that tweet also wrote the nice long comment on this post. However, although the tweet can be found on the Internet Archive, the author later deleted his Twitter account, and so the tweet appears on Twitter today as a gap in the thread above my own tweet in response to the other tweet.
That missing tweet referred to another tweet of the author, but the Internet Archive seems not to have saved it. It did save the present post; so if one were curious, one could see the changes that I have made since initial publication, or rather since September 29, 2020, when the Archive took the first snapshot.
The changes are for style and local clarity. Any large-scale changes would need me to recover the spirit that possessed me when I originally wrote.
I return to this post now, simply because a friend mentioned reading Middlemarch, and I remembered quoting George Eliot’s novel in a blog post, and that post turned out to be this one.
Had somebody mentioned reading Herder, I might have recalled writing about him in a blog post; that would be this post too.
Our environment may influence our feelings, but what we make of those feelings is up to us. Thus we are free; we are not constrained by some fixed “human nature”—or if we are, who is to say what its limits are?
Rembrandt van Rijn (and Workshop?), Dutch, 1606–1669,
The Apostle Paul, c. 1657, oil on canvas,
Widener Collection, National Gallery of Art
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.
For C. S. Lewis, the reality of moral truth shows there is something beyond the scope of natural science.
I say the same for mathematical truth.
Truths we learn as children are open to question. In their educational childhoods, mathematicians have often learned wrongly the techniques of induction and recursion.
The philosophical thesis of physicalism is of doubtful value.
Mathematicians and philosophers who ape them (as in a particular definition of physicalism) use “iff” needlessly.
A pair of mathematicians who use “iff” needlessly seem also to misunderstand induction and recursion.
Their work is nonetheless admirable, like the famous expression of universal equality by the slave-driving Thomas Jefferson.
Mathematical truth is discovered and confirmed by thought.
Truth is a product of every kind of science; it is not an object of natural science.
The distinction between thinking and feeling is a theme of Collingwood.
In particular, thought is self-critical: it judges whether itself is going well.
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.
Students of English must learn not only to judge their own work, but even that they can judge it. Pirsig says this.
For Monk, Collingwood’s demise has meant Ryle’s rise: unfortunately so since, for one thing, Ryle has no interest in the past.
In a metaphor developed by Matthew Arnold, Collingwood and Pirsig are two of my touchstones.
Thoreau is another. He affects indifference to the past, but his real views are more subtle.
According to Monk, Collingwood could have been a professional violinist; Ryle had “no ear for tunes.”
For Collingwood, Victoria’s memorial to Albert was hideous; for Pirsig, Victorian America was the same.
Again according to Monk, some persons might mistake Collingwood for Wittgenstein.
My method of gathering together ideas, as outlined above, resembles Pirsig’s method, described in Lila, of collecting ideas on index cards.
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?
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.
One man kills another, legally, according to the laws of war, such as they are. The two sides fight over the body, which might be ransomed, if taken by the killer’s side; however, the body is not so taken. The friend of the slain man kills the killer and takes his body to mutilate, though this be sacrilege.
The father of the newly slain man crosses enemy lines to ransom his son’s body. He puts his lips to the hand of the killer, who agrees to give up the body, even coming to admire the father, who in turn admires him.
Rembrandt van Rijn (Dutch, 1606-69)
Lucretia, 1664, oil on canvas
Andrew W. Mellon Collection
National Gallery of Art, Washington
Book XXII of the Iliad is rich in human emotion; Book XXIII, in anthropological detail. The books form a natural sequence:
That the man is different in either case creates tension, to be resolved in the next and final book (whose emotions I once took up in “Homer for the Civilian”).
Polytropy 