Tag Archives: Ruth Fuller Sasaki

Mathematics and Logic

Here is another in the recent spate of mathematics posts. I take up now, as I did in my last post, some material that I had originally drafted for the first post in this series.

Whenever it has been designated for its own post, material can grow, as has the material of this post in the drafting. Large parts of this post are taken up with

  1. the notion (due to Collingwood) of criteriological sciences, logic being one of them;

  2. Gödel’s logical theorems of completeness and incompleteness.

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Interconnectedness

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.

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).

books

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