Tag Archives: Ruth Fuller Sasaki

Mathematics and Logic

I continue with the mathematics posts, taking up, as I did in the last, material originally drafted for the first.

Designated for its own post, material can grow, as has the material of this post in the drafting. Large parts of it 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.

I have 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. This makes logic a criteriological science, since it seeks, examines, clarifies and limits the criteria whereby we can make deductions. As examples of this activity, Gödel’s theorems are 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.

Continue reading

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; this definition is not taken up here, but it is 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. Continue reading