Tag Archives: Wittgenstein

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 use “iff” needlessly.

  6. One pair who do this 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

With other questions about people, even just understanding what it means to be the truth is a challenge. If you wanted to understand people whose occupation (like mine) was mathematics, you would need to learn what it meant to prove a theorem, that is, prove it true. Mere observation would not be enough; and on this point I cite two authors whom I often take up in this blog.

  • In the words of R. G. Collingwood in Religion and Philosophy (1916, page 42), quoted in An Autobiography (1940, page 93) as well as in the earlier post here, “The mind, regarded in this external way, really ceases to be a mind at all.”

  • In the words of English teacher and anthropologist Verne Dusenberry, quoted by Robert Pirsig in Lila (1991, page 35), “The trouble with the objective approach is that you don’t learn much that way.”

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Nature and Death

Thoughts on mortality and the evolution of the universe, occasioned by a funeral and by Collingwood’s Idea of Nature and Plato’s Phaedo

Cebeci, Ankara, 2016.05.17

When the husband of my second-grade teacher died, I wanted to pay my respects. My father took me to the funeral home, where I hid behind him as he greeted the family of the deceased. My teacher was not among them. When invited to view the body, I looked over and saw it, lying off to the side in an open casket. I had never seen the man when he was alive. I declined the opportunity to gaze at his lifeless form. Until I came to Turkey, this was my closest approach to the materiality of death—except for a visit to the medical school of the University of New Mexico in Albuquerque. There, as part of the laboratory program at St John’s College in Santa Fe, students viewed dissected human cadavers.

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NL XIV: “Reason”

Index to this series

Summary added January 29, 2019, revised May 8, 2019. Practical reason is the support of one intention by another; theoretical, one proposition by another. Reasoning is thus always “motivated reasoning”: we engage in it to relieve the distress of uncertainty. Reason is primarily practical, only secondarily theoretical; and the reason for saying this is the persistence of anthropomorphism in theoretical reasoning: by the Law of Primitive Survivals in Chapter IX, we tend to think even of inanimate objects as forming intentions the way we do.

Reasons for adding this summary of Chapter XIV of Collingwood’s New Leviathan include

  • the tortuousness of the following post on the chapter,
  • the provocation of a Guardian column by Oliver Burkeman on motivated reasoning.

Says Burkeman, whose “problem” is apparently motivated reasoning itself,

One of the sneakier forms of the problem, highlighted in a recent essay by the American ethicist Jennifer Zamzow, is “solution aversion”: people judge the seriousness of a social problem, it’s been found, partly based on how appetising or displeasing they find the proposed solution. Obviously, that’s illogical …

On the contrary, how we reason cannot be “illogical,” any more than how we speak can be “ungrammatical.” Logic is an account, or an analysis, of how we do actually reason; grammar, of how we speak. Of course we may make errors, by our own standards.

Rogier van der Weyden (Netherlandish, 1399/1400-1464), Portrait of a Lady, c. 1460, oil on panel, Andrew W. Mellon Collection
Rogier van der Weyden (Netherlandish, 1399/1400–1464),
Portrait of a Lady, c. 1460, oil on panel
National Gallery of Art, Washington; Andrew W. Mellon Collection


There was a rumor that Collingwood had become a communist. According to David Boucher, editor of the revised (1992) edition of The New Leviathan, the rumor was one of the “many reasons why [that book] failed to attract the acclaim which had been afforded Collingwood’s other major works.” Continue reading

Thales of Miletus

This is about Thales of Miletus and what it means to study him. I am moved to ask what history is in the first place. It is a study of the freedom in which we face our conditions. Thales had his way of understanding the world, and we may benefit from trying to learn it.

“The Thaleses of the future are meeting in Didim, September 24,  2016”

“The Thaleses of the future are meeting in Didim, September 24, 2016”

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