Category Archives: Mathematicians

The Peace of Liberal Education

January 13, 2015 – 1:33 pm
The wall of Dolmabahçe Sarayı, January 11, 2015

The wall of Dolmabahçe Sarayı, January 11, 2015

The occasion of this article is my discovery of a published Turkish translation of Collingwood’s Speculum Mentis or The Map of Knowledge (Oxford, 1924). Published as Speculum Mentis ya da Bilginin Haritası (Ankara: Doğu Batı, 2014), the translation is by Kubilay Aysevenler and Zerrin Eren. Near the end of the book, Collingwood writes the following paragraph about education, or what I would call more precisely liberal education. The main purpose of this article then is to offer the paragraph to any reader who happens to stop by.

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By David Pierce | Also posted in Collingwood, Education, Euclid, History, Homer, Istanbul, Language, Mathematics, Philosophy, Philosophy of History, Principles of Art, Turkish | Tagged , , , , , , , , , | Comments (3)

Bosphorus Sky

December 19, 2014 – 4:14 pm

This is about the morning of Thursday, December 18, 2014, a morning I spent by the Bosphorus, thinking mostly about poetry, and photographing the sky.

Seagulls against clouds and a brighter sea

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By David Pierce | Also posted in Archimedes, Bosphorus, Collingwood, Descartes, Education, History, Istanbul, Language, Mathematics, Nature, Nesin Mathematics Village, Philosophy, Poetry, Principles of Art, Psychology, Tourism, Turkey, Turkish | Tagged , , , , , , , | Comments (7)

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, Education, Euclid, History, Mathematics, New Leviathan, overlap of classes, Philosophy, Philosophy of History, Plato, Principles of Art, Psychology, Science | Tagged , , , , , , , | Comments (7)

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.

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

Psychology

August 28, 2013 – 9:40 am

Preface (January 17–18, 2019). This essay is built around two extended quotations from Collingwood:

  1. From the posthumous Idea of History (1946) with the core idea, “people do not know what they are doing until they have done it.”
  2. From An Essay on Philosophical Method (1933), about how logic is neither a purely descriptive nor a purely normative science.

The quotations pertain to the title subject of psychology for the following reasons.

  1. Psychological experiments show that we may not know what we are doing until we have done it.
  2. Psychology is a descriptive science.

Psychological experiments can tell us about what we do, only when we presuppose the general applicability of their findings. This is true for any descriptive science. Philosophy demands more. A philosophical science like logic is categorical, in the sense of the second listed quotation, because it is what Collingwood will later call criteriological. I go on to discuss criteriological sciences as such in “A New Kind of Science,” but not here.

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By David Pierce | Also posted in Categorical Thinking, Collingwood, Criteriological Science, Euclid, Galileo, Logic, Ontological Proof, Philosophy, Principles of Art, Psychology, Science | 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, Education, 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, Education, Mathematics, Philosophy of Mathematics, Plato | Tagged , , , , | Comments (6)