Tag Archives: Donald Trump

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.

  1. For C. S. Lewis, the reality of moral truth shows there is something beyond the scope of natural science.

  2. I say the same for mathematical truth.

  3. Truths we learn as children are open to question. In their educational childhoods, mathematicians have often learned wrongly the techniques of induction and recursion.

  4. The philosophical thesis of physicalism is of doubtful value.

  5. Mathematicians and philosophers who ape them (as in a particular definition of physicalism) use “iff” needlessly.

  6. A pair of mathematicians who use “iff” needlessly seem also to misunderstand induction and recursion.

  7. Their work is nonetheless admirable, like the famous expression of universal equality by the slave-driving Thomas Jefferson.

  8. Mathematical truth is discovered and confirmed by thought.

  9. Truth is a product of every kind of science; it is not an object of natural science.

  10. The distinction between thinking and feeling is a theme of Collingwood.

  11. In particular, thought is self-critical: it judges whether itself is going well.

  12. Students of mathematics must learn their right to judge what is correct, along with their responsibility to reach agreement with others about what is correct. I say this.

  13. Students of English must learn not only to judge their own work, but even that they can judge it. Pirsig says this.

  14. For Monk, Collingwood’s demise has meant Ryle’s rise: unfortunately so since, for one thing, Ryle has no interest in the past.

  15. In a metaphor developed by Matthew Arnold, Collingwood and Pirsig are two of my touchstones.

  16. Thoreau is another. He affects indifference to the past, but his real views are more subtle.

  17. According to Monk, Collingwood could have been a professional violinist; Ryle had “no ear for tunes.”

  18. For Collingwood, Victoria’s memorial to Albert was hideous; for Pirsig, Victorian America was the same.

  19. Again according to Monk, some persons might mistake Collingwood for Wittgenstein.

  20. My method of gathering together ideas, as outlined above, resembles Pirsig’s method, described in Lila, of collecting ideas on index cards.

  21. Our problems are not vague, but precise.


When Donald Trump won the 2016 U.S. Presidential election, which opinion polls had said he would lose, I wrote a post here called “How To Learn about People.” I thought for example that just calling people up and asking whom they would vote for was not a great way to learn about them, even if all you wanted to know was whom they would vote for. Why should people tell you the truth?

Saturn eclipse mosaic from Cassini

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NL XLI: What Barbarism Is

Index to this series

Civilization being agreement, barbarism has no chance in the long run (41. 67):

41. 76. For barbarism implies not only a quarrel between any barbarist and any civilized man; it also implies a quarrel between anyone barbarist and any other; and that any state of harmony between them is merely this quarrel suspended.

The barbarist is somebody “who imitates the conditions of an uncivilized world” (41. 53); but an actual attempt to bring about those conditions will need cooperation, and this will be a step towards civility. Here perhaps we should distinguish cooperation from the kind of coerced organization seen in a fascist state. Specific examples will be considered in the later chapters of Part IV of the New Leviathan. We are now considering “What Barbarism Is,” in general terms.

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A New Kind of Science

Executive summary. Some sciences are called descriptive, empirical, or natural; others, prescriptive or normative. We should recognize a third kind of science, which studies the criteria as such that a thinking being imposes on itself as it tries to achieve success. I propose linguistics as an example. Collingwood introduced the term criteriological for the third kind of science. This was in The Principles of Art (1938), though I find the germ of the concept in earlier work, even in Collingwood’s first book, Religion and Philosophy (1916), in the passage on psychology that the author would recall in An Autobiography (1939).

Collingwood’s examples of criteriological sciences are logic, ethics, aesthetics, and economics. Pirsig effectively (and independently) works out rhetoric as an example in Zen and the Art of Motorcycle Maintenance (1974). We may benefit from clarity here, given how people can have a strong reaction to being lectured by experts. For Collingwood, such a reaction is found in Nazi Germany; see the last chapter of The New Leviathan (1942). Reactions to grammar are the subject of my own two ensuing articles, “Writing and Inversion” and “Writing Rules.”


Some sciences are not recognized for what they are. The sciences themselves are not new, but a proper understanding of them may be new to some of us, including myself.

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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.

David Hume, A Treatise of Human Nature

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NL XXI: Society as Joint Will

Index to this series

Executive summary (added September 10, 2018):

1.
I cannot say “I will” without recognizing the possibility of joining with others to say “we will.”
2.
A social consciousness consists of (1) a precise idea of one’s place in a society and (2) a vague sense of the society as a whole. The latter sense may be incorrect, having been foolishly accepted on the word of an authority.
3.
Properly understood, ruling, of itself and perhaps of a non-social community, may be all that a society does. It is the responsibility of the members alone.
4.
To form a society means (1) to form social relations and (2) to do this for some purpose. To focus on (1) yields the idea of a universal society—which cannot actually exist, despite foolish hopes for the League of Nations.
5.
The universal society cannot exist, because we produce a society by transforming an earlier community, and some trace of this must remain.
6.
Members of a society are equal, (1) in having the freedom to join and (2) in just being members. A society may create an inequality, as by delegating authority. There may be natural inequalities, not produced by the society itself; society may compensate for them, turn them into assets, or even depend on them, as in the case of initiative.
7.
Rule by force (in a non-social community) may be by rewards and punishments, that is, objects of desire and fear. These may be promised or threatened fraudulently. One who grows too accustomed to exerting force may lose freedom of will.
8.
Societies institute criminal law to mitigate members’ losses of freedom of will.
9.
Societies can be temporary or permanent.

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How to Learn about People

A chance encounter with a Medieval definition of God, used as the title of a sculpture, leads to an ancient plane tree and to more consideration of what can go wrong with public opinion polls.

Ancient plane tree of Bayır, Marmaris Peninsula, September 9, 2010

Ancient plane tree of Bayır, Marmaris Peninsula, September 9, 2010

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