Category Archives: Criteriological Science

Unfortunately I am not aware that anybody since Collingwood has tried to develop the idea of a criteriological science. My first big attempt to explicate the idea is “A New Kind of Science.” That post is linked to by every post in this category, and more. Any of those posts may give some idea of criteriological science; “Mathematics and Logic” is probably the most thorough supplement to “A New Kind of Science”

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.

Continue reading

On Chapman’s Homer’s Iliad, Book XV

After a year, I return to reading the Iliad on the Asian mainland of Turkey. I am opposite Lesbos, south of Mount Ida, where in the last episode, Juno seduced Jove, so that he would not see Neptune’s interference on behalf of the Greeks, in the war down at Troy.

We were here in Altınova (in the province of Balıkesir) in July, but my mind then was on mathematics, including mathematics coming out of my April post here, “Elliptical Affinity.” I went on to speak of this mathematics in two other countries, one of these the homeland of Medea. In the other country, I was moved to write a post concerning the book I had already blogged a lot about. Now Ayşe and other Peace Academics are being cleared of charges, our fall semester does not begin till October, and we can spend time at the beach.

Twelve Apostles, a former Armenian church, now a mosque, in Kars

Continue reading

NL XXXII: Society and Nature in the Classical Politics

Index to this series

In the last chapter, we described classical politics by analogy with classical physics. Now we turn entirely to politics. The nature of “Society and Nature in the Classical Politics,” Chapter XXXII of the New Leviathan, is not the nature studied by physics; it is the nature of the “state of nature” (32. 32), which is our theoretical political origin.

The “problem of the classical politics” (32. 1) is “to give an account of the social element” of political life (32. 19). The non-social element of political life is nature (32. 19).

Continue reading

NL XXXI: Classical Physics and Classical Politics

Index to this series

As my beach holiday winds down, so perhaps does the current spate of blog posts. Here is one more. Setting aside Homer, I continue immediately with Collingwood, in part because, in the 2000 paperback impression of the 1992 Revised Edition of the New Leviathan that I take to the shore, I have now also read the Editor’s Introduction by David Boucher. (Back at the cottage, I have to type out the quotes from this that I make below; for quotes of Collingwood himself, I cut and paste from a scan of the 1947 corrected reprint of the 1942 First Edition.)

As I could infer from my pencil-marks, I had read Boucher’s introduction some time before; but I could remember little of it. I think it is aimed at professional philosophers, rather than at anybody who would admire Collingwood for saying, as he does in An Autobiography (page 6), when he describes getting prepared to go to Rugby School,

The ghost of a silly seventeenth-century squabble still haunts our classrooms, infecting teachers and pupils with the lunatic idea that studies must be either ‘classical’ or ‘modern’. I was equally well fitted to specialize in Greek and Latin, or in modern history and languages (I spoke and read French and German almost as easily as English), or in the natural sciences; and nothing would have afforded my mind its proper nourishment except to study equally all three.

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.

Continue reading

War and Talk

This is a foray into the mystery of how things happen, based the 164th of the 361 chapters of War and Peace. This chapter contains, in a one-sentence paragraph, a summary of Tolstoy’s theory of history:

Each man lives for himself, using his freedom to attain his personal aims, and feels with his whole being that he can now do or abstain from doing this or that action; but as soon as he has done it, that action performed at a certain moment in time becomes irrevocable and belongs to history, in which it has not a free but a predestined significance.

Continue reading

NL I: “Body and Mind”

Index to this series. See also a later, shorter article on this chapter

The Chapter in Isolation

“Body and Mind” is the opening chapter of Collingwood’s New Leviathan. The chapter is a fine work of rhetoric that could stand on its own, though it invites further reading. In these respects it resembles the first of the ten traditional books of Plato’s Republic, or even the first of the thirteen books of Euclid’s Elements. The analogy with Euclid becomes a bit tighter when we consider that each chapter of The New Leviathan is divided into short paragraphs, which are numbered sequentially for ease of reference.

Continue reading


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.

Continue reading