## Tag Archives: Taoism

### Mathematics and Logic

Large parts of this post are taken up with two subjects:

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

2. 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.

### Donne’s Undertaking

I was recently called on to recommend a poem. I chose “The Undertaking” of John Donne. I want to say here why.

• The poem (quoted below) has a sound that impressed me when first I read it, more than thirty years ago.

• The poem alludes to ideals:

• of recognizing what is good for its own sake;

• of climbing a rung or two on Diotima’s ladder or stairway of love, recounted by Socrates in Plato’s Symposium (211c):

And the true order of going, or being led by another, to the things of love (τὰ ἐρωτικά), is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps (οἳ ἐπαναβαθμοί) only, and from one going on to two, and from two to all fair forms (τὰ καλὰ σώματα), and from fair forms to fair practices (τὰ καλὰ ἐπιτηδεύματα), and from fair practices to fair notions (τὰ καλὰ μαθήματα), until from fair notions he arrives at the notion of absolute beauty, and at last knows what the essence of beauty is (ὃ ἔστι καλόν).

• The sound of Donne’s poem may seduce one into thinking the ideals worthy.

Two books that were my mother’s

### Anthropology of Mathematics

This essay was long when originally published; now, on November 30, 2019, I have made it longer, in an attempt to clarify some points.

The essay begins with two brief quotations, from Collingwood and Pirsig respectively, about what it takes to know people.

• The Pirsig quote is from Lila, which is somewhat interesting as a novel, but naive about metaphysics; it might have benefited from an understanding of Collingwood’s Essay on Metaphysics.

• A recent article by Ray Monk in Prospect seems to justify my interest in Collingwood; eventually I have a look at the article.

Ideas that come up along the way include the following.

### On Chapman’s Homer’s Iliad, Book X

Index to this series | Text of Chapman’s Homer’s Iliad

In Book X of the Iliad, Diomedes and Ulysses go to spy on the Trojan camp at night. When they return to the Greek camp,

1. Then entred they the meere maine sea, to cleanse their honord sweate
2. From off their feet, their thighes and neckes…

I can enter the same sea now. After more than ten months, I return to my reading of Homer, and Chapman’s Homer, as I have returned to the place where I was doing it last year, on the Aegean coast opposite Lesbos, after the sweat-soaked struggle of—teaching in the Nesin Mathematics Village, south of here, in the hills above Ephesus.

### What It Takes

This essay ends up considering arguments that natural science—especially mathematical physics—is based on absolute presup­positions whose mythological expression is found in Christianity—especially the doctrine of Incarnation.

I take note along the way of continuing censorship of Wikipedia by the Turkish state.

The post falls into sections as follows.

• Where to start. To the thesis that everybody can be a philosopher, an antithesis is that persons with the professional title of philosopher ought to know the history of their subject.

• Ontology. Disdain for this history may lead to misunderstanding of Anselm’s supposed proof of the existence of God.

• Presupposition. To prove anything, you need a pou sto, or what Collingwood calls an absolute presupposition.

• Progression. Newton rejected antiquated presuppositions.

• Reaction. Coal-burners and racists reject new presuppositions.

• Universality. From the 47th chapter of the Tao Te Ching (in the translation of Gia-fu Feng and Jane English):

Without going outside, you may know the whole world.
Without looking through the window, you may see the ways of heaven.
The farther you go, the less you know.

Thus the wise know without traveling;
See without looking;
Work without doing.

• Religion. To say that we can know the laws governing the entire universe is like saying a human can be God.

• Censorship. Thus everybody who believes in mathematical physics is a Christian, if only in the way that, by the Sun Language Theory, everybody in the world already speaks Turkish.

• Trinity. That the university has several departments, all studying the same world—this is supposed to correspond to the triune conception of divinity.

This post began as a parenthesis in another post, yet to be completed, about passion and reason. To anchor that post in an established text, I thought back to David Hume, according to whom,

Reason is, and ought only to be[,] the slave of the passions, and can never pretend to any other office than to serve and obey them.

This might express something I said in my previous post: “Reason is the power of testing what we want.” However, I had not really read Hume since college. I thought more about things that had not ended up in the previous post—which was called “Effectiveness” and concerned the article of Eugene Wigner with that word in its title. As I thought and wrote, it seemed I was putting so much into a parenthesis that it could be another post. True, the same might be said of many things in this blog. In any case, the parenthesis in question became the present post.

### 0

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.

### The Peace of Liberal Education

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.

### Books hung out with

The following are some books that I have read more times than I can remember. I list them in order of publication, though my first readings of them came in the opposite order:

1. R. G. Collingwood, The Principles of Art (1938);
2. Somerset Maugham, The Razor’s Edge (1944);
3. Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance (1974).

I want to say some things about all of these books, and their writers. I intend especially to address the last book, which I shall call ZAMM. Continue reading