Category Archives: Categorical Thinking

On Gödel’s Incompleteness Theorem

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification. Continue reading

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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The Private, Unskilled One

I went into Istanbul’s Pandora Bookshop a month ago, looking for an English translation of War and Peace, since the Garnett translation I had read at college was falling apart. I was told the Oxford World’s Classics edition (with the Maude translation) was coming the next week, and it did come.

Elif Batuman, The Idiot, in Nesin Matematik Köyü, Kayser Dağı Mevkii, Şirince, Selçuk, İzmir, Turkey, 2017.05.18

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Facts (NL IX, ‘Retrospect,’ first 6 paragraphs)

Index to this series

A certain person says,

I am not better than you or more virtuous than you. If you see me on the right path, help me. If you see me on the wrong path, advise me and halt me. And obey me as far as I obey God.

How should one hear these words: as an eminently reasonable expression of benevolent humility such as any of us might honorably make? Well, no matter how qualified, the command obey me might be a warning sign. The words are in fact from a recently published video, as quoted in the Guardian Weekly (Vol 190 No 5, 11–17 July 2014, p. 4). The speaker is the man whose nom de guerre is Abu Bakr al-Baghdadi, on whose head the Department of State of the United States of America placed a ten-million-dollar bounty in 2011. He now styles himself Ibrahim, Caliph of the Islamic State, a new entity that is supposed to restore the lost Muslim glory of past centuries. This restoration is to be achieved through war. War requires military discipline, with punishments meted out for infractions like insubordination, not to mention the slaughter of those perceived as enemies. So al-Baghdadi’s request to be advised and halted if seen to be in the wrong must be interpreted rather carefully.

It is difficult to know how to interpret somebody’s words. With that I pass to the transitional chapter in the first part, “Man,” of Collingwood’s New Leviathan.

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NL II: “The Relation Between Body and Mind”

Index to this series

I continue making notes on The New Leviathan of R. G. Collingwood (1889–1943). Now my main concern is with the second chapter, “The Relation Between Body and Mind”; but I shall range widely, as I did for the first chapter.

Preliminaries

Some writers begin with an outline, which they proceed to fill out with words. At least, they do this if they do what they are taught in school, according to Robert Pirsig:

He showed how the aspect of Quality called unity, the hanging-togetherness of a story, could be improved with a technique called an outline. The authority of an argument could be jacked up with a technique called footnotes, which gives authoritative reference. Outlines and footnotes are standard things taught in all freshman composition classes, but now as devices for improving Quality they had a purpose.

That is from Zen and the Art of Motorcycle Maintenance, chapter 17.

Does anybody strictly follow the textbook method of writing? Continue reading

Psychology

Preface (January 17–18, 2019). This essay is built around two extended quotations from Collingwood.

  1. One is from the posthumous Idea of History (1946) with the core idea, “people do not know what they are doing until they have done it.”
  2. The other is from An Essay on Philosophical Method (1933), about how logic is neither a purely descriptive nor a purely normative science.

The quotations pertain to the title subject of psychology for the following reasons.

  1. Psychological experiments show that we may not know what we are doing until we have done it.
  2. Psychology is a descriptive science.

Psychological experiments can tell us about what we do, only when we presuppose the general applicability of their findings. This is true for any descriptive science. Philosophy demands more. A philosophical science like logic is categorical, in the sense of the second listed quotation, because it is what Collingwood will later call criteriological. I go on to discuss criteriological sciences as such in “A New Kind of Science,” but not here.

Here I suggest examples of not knowing where one’s life is going. A simpler example would be making art. By the account of The Principles of Art (1938), this is something we do all the time, as for example when we utter a new sentence. We do not know what the sentence is going to be, until it is said. On the other hand, we do somehow guide its utterance. See the quotation about painting at the end of “Freedom.

Collingwood discusses categorical thinking for the sake of explaining the Ontological Proof, which I go on to analyze myself in later articles. Meanwhile, the present essay ends with a look at Graham Priest’s dismissive treatment of the Proof.


The original purpose of this article is to record a passage in The Idea of History of R.G. Collingwood (1889–1943). I bought and read this book in 2001. I was looking back at it recently, because I was reading Herodotus, and I wanted to see again what Collingwood had to say about him and other ancient historians.

The passage that I want to talk about reminded me of some psychological experiments whose conclusions can be overblown. Writing before those experiments, Collingwood shows that the similar conclusions can be drawn, in more useful form, without the pretence of a scientific experiment.

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