Category Archives: Education

Şirince 2014

July 19, 2014 – 7:01 am

This is about our second visit to the Nesin Mathematical Village in Şirince this year. The first visit was to attend the Summer School Around Valuation Theory, May 22–26. Now we have come back to teach, as usual, in the Turkish Mathematical Society Undergraduate and Graduate Summer School. This time we are teaching not just one week, but two: July 14–27. My own course, as several times in the past, is on nonstandard analysis. Each course meets every day but Thursday, two hours a day.

The Math Village only increases in beauty every year, as I mean to suggest by posting a few photographs below.

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By David Pierce | Also posted in Mathematics, Nesin Mathematics Village, Turkey | Tagged , , , , , | Comments (10)

Interconnectedness

June 30, 2014 – 1:19 pm

Note added January 13, 2019. This essay concerns a letter I once wrote about

  • teaching;
  • 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.

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By David Pierce | Also posted in “God is a circle …”, Collingwood, Contradiction, overlap of classes, Philosophy, Principles of Art, West Virginia | Tagged , , , , , , , , , , | Comments (7)

NL VI: “Language”

February 27, 2014 – 3:37 pm

Index to this series

This is about the first section of Chapter VI, “Language,” of The New Leviathan. The whole chapter can be ana­lyzed into five sections, with §N consisting of those paragraphs numbered 6. N or 6. NX. I summarize the sections as follows:

  1. Language is an abstraction from discourse. Discourse is an activity together with what is meant by it. (¶¶6. 1–19)
  2. Through language, we become conscious of our feelings. Becoming conscious of our language is another step, which is taken by artists. (¶¶6. 2–29)
  3. A feeling is not “mediated” by the language we use for it. (¶¶6. 3–36)
  4. Hobbes discovered that language is prior to knowledge. (¶¶6. 4–47)
  5. Those who dispute this finding over­look that not all language is rational. (¶¶6. 5–59)

Continue reading →

By David Pierce | Also posted in Collingwood, Istanbul, Language, New Leviathan, Philosophy, Plato, Principles of Art, question and answer | Tagged , | Comments (4)

NL III: “Body As Mind”

January 25, 2014 – 7:17 am

Index to this series

In Chapter I of The New Leviathan, we stipulated that natural science, the “science of body,” must be free to pursue its own aims. But we ourselves are doing science of mind, and:

1. 85. The sciences of mind, unless they preach error or confuse the issue by dishonest or involuntary obscurity, can tell us nothing but what each can verify for himself by reflecting on his own mind.

All of us can be scientists of mind, if only we are capable of reflection: Continue reading →

By David Pierce | Also posted in Collingwood, Conic Sections, Descartes, Euclid, History, Mathematics, New Leviathan, overlap of classes, Philosophy, Philosophy of History, Plato, Principles of Art, Psychology, Science | Tagged , , , , , , , | Comments (7)

NL II: “The Relation Between Body and Mind”

January 20, 2014 – 11:39 am

Index to this series

I continue making notes on The New Leviathan of R. G. Collingwood (1889–1943). Now my main concern is with the second chapter, “The Relation Between Body and Mind”; but I shall range widely, as I did for the first chapter.

Preliminaries

Some writers begin with an outline, which they proceed to fill out with words. At least, they do this if they do what they are taught in school, according to Robert Pirsig:

He showed how the aspect of Quality called unity, the hanging-togetherness of a story, could be improved with a technique called an outline. The authority of an argument could be jacked up with a technique called footnotes, which gives authoritative reference. Outlines and footnotes are standard things taught in all freshman composition classes, but now as devices for improving Quality they had a purpose.

That is from Zen and the Art of Motorcycle Maintenance, chapter 17.

Does anybody strictly follow the textbook method of writing? Continue reading →

By David Pierce | Also posted in absolute presuppositions, Categorical Thinking, Collingwood, Descartes, History, Logic, Mathematics, New Leviathan, Ontological Proof, overlap of classes, Philosophy, Philosophy of History, Pirsig, Plato, Science | Tagged , , , , , , , , , | Comments (13)

Give childhood back to children

January 15, 2014 – 9:55 am

Give childhood back to children.

via Give childhood back to children.

I created this article by pressing a button beneath the friend’s article that is linked to above. That article links in turn to an article by Peter Gray in The Independent with the headline “Give childhood back to children: if we want our offspring to have happy, productive and moral lives, we must allow more time for play, not less”. Gray writes,

I’m lucky. I grew up in the United States in the 1950s, at the tail end of what the historian Howard Chudacoff refers to as the “golden age” of children’s free play. The need for child labour had declined greatly, decades earlier, and adults had not yet begun to take away the freedom that children had gained.

I don’t think Gray quite says this, but it seems to me that making young people study in school for the sake of their future remunerative employment is just another form of child labor, even if it is supposed to be for their own good. As angry children are supposedly wont to say, they didn’t ask to be born in the first place.

By David Pierce | Tagged | Comments (1)

NL I: “Body and Mind”

January 13, 2014 – 2:35 pm

Index to this series. See also a later, shorter article on this chapter

The Chapter in Isolation

“Body and Mind” is the opening chapter of Collingwood’s New Leviathan. The chapter is a fine work of rhetoric that could stand on its own, though it invites further reading. In these respects it resembles the first of the ten traditional books of Plato’s Republic, or even the first of the thirteen books of Euclid’s Elements. The analogy with Euclid becomes a bit tighter when we consider that each chapter of The New Leviathan is divided into short paragraphs, which are numbered sequentially for ease of reference.

Continue reading →

By David Pierce | Also posted in absolute presuppositions, Collingwood, Criteriological Science, Descartes, dialectic, Euclid, Logic, New Leviathan, Philosophy, Plato, Principles of Art, Psychology, Science | Tagged , , , , , , , , , | Comments (19)

The Tradition of Western Philosophy

September 10, 2013 – 1:41 pm

Note added October 16, 2018: Here I compare two projects of re-examining the philosophical tradition named in my title. The projects are those of

  • R. G. Collingwood in An Essay on Philosophical Method (Oxford, 1933);

  • Stringfellow Barr and Scott Buchanan at St John’s College in Annapolis, Maryland, beginning in 1937.

I review

  • how I ended up as a student at St John’s;

  • how Collingwood has been read (or not read) by myself and others, notably Simon Blackburn;

  • how Collingwood’s Essay is based on the hypothesis of the “overlap of classes.”

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By David Pierce | Also posted in absolute presuppositions, Collingwood, Descartes, dialectic, Euclid, History, Logic, Mathematics, overlap of classes, Philosophy, Philosophy of History, Pirsig, Plato, Principles of Art, Science, T. S. Eliot | Tagged , , , , , , , , , , , , , , , | Comments (11)

Learning mathematics

May 14, 2013 – 11:23 am

This is mostly reminiscences about high school. I also give some opinions about how mathematics ought to be learned. The post originally formed one piece with my last article, “Limits.”

I learned calculus, and the epsilon-delta definition of limit, in Washington D.C., in my last two years at St Albans School, in a course taught by a peculiar fellow named Donald J. Brown. The first of these two years was officially called Precalculus Honors, but some time in that year, we started in on calculus proper.

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By David Pierce | Also posted in Archimedes, Calculus, Euclid, G. H. Hardy, Logic, Mathematics, Philosophy of Mathematics, Strunk and White | Tagged , , , , , , , , , , , | Comments (5)

Limits

May 4, 2013 – 12:54 pm

This is about limits in mathematics: both the technical notion that arises in calculus, and the barriers to comprehension that one might reach in one’s own studies. I am going to say a few technical things about the technical notion, but there is no reason why this should be a barrier to your reading: you can just skip the paragraphs that have special symbols in them.

Looking up something else in the online magazine called Slate, I noted a reprint of an article called “What It Feels Like to Be Bad at Math” from a blog called Math With Bad Drawings by Ben Orlin. Now teaching high-school mathematics, Mr Orlin recalls his difficulties in an undergraduate topology course. His memories help him understand the difficulties of his own students. When students do not study, why is this? It is because studying makes them conscious of how much they do not understand. They feel stupid, and they do not like this feeling. Continue reading →

By David Pierce | Also posted in Archimedes, Calculus, Mathematics, Philosophy of Mathematics, Plato | Tagged , , , , | Comments (6)