Our fifth scheduled reading in the Republic is Book IV (Stephanus pages 419–45). Socrates speaks
Intellect, spirit, and appetite
Profesörler Sitesi, Altınova, Balıkesir, Turkey
September 13, 2021
This is mostly about avoiding things. An early theme of Plato’s Republic is avoiding the deprivations of solitary life through politics. Some of us would rather just avoid politics. Such persons include Henry David Thoreau, Gilbert Ryle, and the inventor of the h-index (he is a physicist called Jorge E. Hirsch, but I know nothing else about him). I mentioned these persons in my last Plato post, “Badiou, Bloom, Ryle, Shorey.” I have some more to say about them here. In “Civil Disobedience” (1848), for example, Thoreau writes, “it is, after all, with men and not with parchment that I quarrel”; but measures like the h-index are used to hide the human factor in the equations used to judge us.
All photos are from Profesörler Sitesi, Altınova, Balıkesir, Turkey
September 21–3, 2021
In this reading:
The Friar tells a tale about a summoner, who becomes sworn brother to another man. The man turns out to be a devil, but it hardly matters to the summoner, he being more lawless than the devil, who himself takes only what is rightfully his, including the summoner.
We are skipping the Summoner’s own tale.
The Clerk tells a tale of a common woman with a preternatural patience for the abuse of her noble husband, who (she thinks) has her children put to death and will take another wife. Chaucer makes disclaimers, both as the Clerk and as himself. The Clerk refers explicitly to the Epistle of James, who writes in Chapter 1,
2 My brethren, count it all joy when ye fall into divers temptations;
3 Knowing this, that the trying of your faith worketh patience.
4 But let patience have her perfect work, that ye may be perfect and entire, wanting nothing.
Griselda follows, as it were, the teachings of Epictetus, here in Chapter XI of the Encheiridion (translation of George Long):
Never say about any thing, I have lost it, but say I have restored it. Is your child dead ? It has been restored. Is your wife dead ? She has been restored. Has your estate been taken from you ? Has not then this also been restored? But he who has taken it from me is a bad man. But what is it to you, by whose hands the giver demanded it back ? So long as he may allow you, take care of it as a thing which belongs to another, as travellers do with their inn.
Large parts of this post are taken up with two subjects:
The notion (due to Collingwood) of criteriological sciences, logic being one of them.
Gödel’s theorems of completeness and incompleteness, as examples of results in the science of logic.
Like the most recent in the current spate of mathematics posts, the present one has arisen from material originally drafted for the first post in this series.
In that post, I defined mathematics as the science whose findings are proved by deduction. This definition does not say what mathematics is about. We can say however what logic is about: it is about mathematics quâ deduction, and more generally about reasoning as such. This makes logic a criteriological science, because logic seeks, examines, clarifies and limits the criteria whereby we can make deductions. As examples of this activity, Gödel’s theorems are, in a crude sense to be refined below, that
everything true in all possible mathematical worlds can be deduced;
some things true in the world of numbers can never be deduced;
the latter theorem is one of those things.
Note added February 10, 2019: I return to this rambling essay, two years later in the Math Village. The main points are as follows.
Here are some meditations on some books read during a stay in the Nesin Mathematics Village, January, 2017. I originally posted this article from the Village; now, back in Istanbul, a few days into February, recovering from the flu that I started coming down with in the Village, I am correcting some errors and trying to clarify some obscurities.
Nesin Mathematics Village from the east
Wednesday, January 18, 2017
This essay – these notes for an essay, this draft of an essay – is inspired by Robert Pirsig’s first book. I have made sectional divisions where they seemed to occur naturally.
While we who work at universities may be employed by the state, our true work is to serve not the state as such, but what may be called knowledge, or science, or reason. This is a theme of Pirsig, which I take up here.
Note added January 13, 2019. This essay concerns a letter I once wrote about
the infinitely large and small, as contemplated by Pascal in that one of the Pensées headed Disproportion de l’homme;
Zen Buddhism.
Since the ideas of Collingwood often dominate this blog, one may ask why they influence me. My old letter provides some evidence, since I wrote it before I had read anything by Collingwood but The Principles of Art.
The present essay has the first of this blog’s several mentions of the slogan
verba volant scripta manent,
which may not mean what we tend to think today.
The indicated pensée happens to allude to the definition of God as
une sphère infinie dont le centre est partout, la circonférence nulle part;
I have taken up this definition not here, but in later posts, apparently without recollection of its use by Pascal.
When do our thoughts progress, and when do they only confirm what we have always thought?
In December of 1987, I was between college and graduate school. I was living with my mother in Virginia, doing some tutoring at my old high school, waiting for inspiration about what to do next. Inspiration did come in the course of the following year, when I was working at an organic farm in West Virginia. I was going to apply to graduate schools in mathematics or philosophy (earlier I had considered also physics); then, in a dream, I understood that I had to do mathematics.
Meanwhile, among other things, I exchanged letters with college classmates. I am going to quote and examine a letter written by me whose precise date is 13 December 1987. I am able to transcribe my handwritten words, because I kept a photocopy of them. The photocopy sat in a folder in my mother’s house, in my old room in the attic, for more than twenty-six years. Now that I read again what I wrote, I find ideas such as I have found (and agreed with) more recently in Collingwood, especially in his early books Religion and Philosophy (1916) and Speculum Mentis (1924).
Polytropy 