Polytropy

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.

Since his father had given him more Greek and Latin than most boys knew, Collingwood became a classical scholar. Decades later, he regretted not having been a novelist. In 1939, just before turning 50, he wrote his wife Ethel from what is now Jogyakarta,

I don’t think I ever realized before, how fatally I missed my bus when I took a job at Oxford instead of becoming a professional writer. I know why I did it, it was because I was angry with my father for being that sort of person and not being able to bring up his family in consequence …

My source here is page 537 of Collingwood’s Autobiography and Other Writings, edited with an introduction by David Boucher and Teresa Smith (Oxford 2013, paperback edition 2017, photographs at rgcollingwood.uk), a book with eleven useful essays by different scholars on different aspects of Collingwood. The “Other Writings” of the title refers mainly to the log of Collingwood’s voyage to what is now Indonesia. The trip had been prescribed by a doctor as a rest cure from the ills brought on by overwork. However, on the way east, Collingwood spent his time on shipboard writing An Essay on Metaphysics, when he wasn’t revising the proofs of An Autobiography. In the latter book, he observes that a good writer writes for his or her own time:

Whether a given proposition is true or false, significant or meaningless, depends on what question it was meant to answer …

Now, the question ‘To what question did So-and-so intend this proposition for an answer?’ is an historical question, and therefore cannot be settled except by historical methods. When So-and-so wrote in a distant past, it is generally a very difficult one, because writers (at any rate good writers) always write for their contemporaries, and in particular for those who are ‘likely to be interested’, which means those who are already asking the question to which an answer is being offered; and consequently a writer very seldom explains what the question is that he is trying to answer.

Thucydides wrote for all time; but then he apparently thought there was an unchanging human nature, and in this sense we might all be considered his contemporaries. In any case, Collingwood writes for his time; and in the New Leviathan, this means a time when Germany is trying to conquer and rule Europe. After reviewing various opinions about Collingwood’s views of the relation of philosophy and history, and in particular the use of the historical method of re-enactment in metaphysics, Boucher concludes in his introduction (page xl),

It was only by means of a union of philosophy and history, Collingwood believed, that the principles and values of European civilization could be retrieved. The union of philosophy and history was therefore imperative, and this is why in a letter to E. R. Hughes, Collingwood could say that ‘I am quite clear that this idea could save Europe, and believe nothing else can’ [the letter is in the Bodleian Library, Oxford]. The New Leviathan is the result of this union, and Collingwood’s personal contribution to the war effort to save Europe against the barbarians.

One may well ask what writing a long difficult book like the New Leviathan can contribute to fighting a war; but then what else can a dying man more than fifty years old do? We have seen Collingwood’s criticism of pacifism starting in Chapter XXIX:

29. 98. ‘Pacifism’ is war-mongery complicated by defeatism. The ‘pacifist’ is not interested in politics. He is interested only in his own ‘clear conscience’. Let the world be given over to the sword, his conscience is clear so long as he was not the first to draw it. That he forced others to draw it is nothing to him.

One may well say that writing the New Leviathan is Collingwood’s way of clearing his conscience. This is not bad in itself.

Why and how does a novelist write? It may be useful to keep this question in mind while reading Collingwood. Boucher argues (pages xxxvi–ii),

If we mean by the term historicism that philosophy becomes resolved into history, and that all knowledge is historical knowledge, then the evidence obliges us to believe that Collingwood certainly became a historicist towards the end of his life.

I suppose this is the kind of thing that professional philosophers have to think about. I myself would ask whether, for example, I do history, or should do history, and what insights Collingwood can offer in this pursuit. I shall give an example below.

I started reading and writing about the New Leviathan in this blog before the institution of a presidential system in the country where I live, and before the rise of Donald Trump as a politician in my country of origin.

In reviewing Chapter XXX, I did not take up Collingwood’s description of a Yahoo herd, whose mental development has not reached the stage of free will (30. 52). For such a herd, war might well be called not a breakdown, but an extension of policy (30. 5), since within itself the herd can only exert force eristically, with no notion of reaching agreements dialectically (30. 69). The Yahoo herd does not exist and never existed (30. 71); it is an abstraction of what we are trying to get away from (30. 75). However, “The Yahoo is always with us” (30. 8):

30. 86. The neurotic or terrified wars of the twentieth century differ in kind from the democratic, hopeful, expansive wars of the nineteenth, and those from the mercenary dynastic wars of the eighteenth, fought under sporting rules like the royal sport they were. The world is always breeding new types of Yahoo.

30. 87. In order to deal with them as they appear, the political consciousness of mankind must be infinitely adaptable.

How then do we adapt the New Leviathan to our life?

Chapter XXXI develops an analogy between two sciences. These sciences are now classical, in the sense that Homer and Virgil are classical: they are not the last word on their subject, but everybody interested in the subject should know them (31. 22).

The two sciences are physics (as we now call it), as developed by Galileo and Newton (31. 1), and politics as developed by Hobbes, Locke, and Rousseau (31. 2). Physics was natural or experimental philosophy to those who did it (31. 18). For politics as a science, Collingwood does not use the term “political science.”

In Bacon’s metaphor, the scientist is a bee, collecting nectar and converting it to honey (31. 27) by mixing in the acid that she herself secretes (31. 32). The scientist collects facts and converts them into laws (31. 28) by applying abstractions (31. 33).

The abstractions of physics are those of pure mathematics (31. 51). The mathematics is both “elementary,” in the sense of being “inherited from the ancients” (31. 53), and advanced, in the sense of being “invented by mathematicians in modern times” (31. 54). Advanced mathematics includes the analytic geometry of Descartes and the fluxions or calculus of Newton and Leibniz.

The abstractions of politics are those of law, namely Roman law and its revisions in medieval and modern Europe. We have already said that law is what the scientist aims to produce. There is an ambiguity in the term law, though Collingwood does not remark on it.

31. 59. The abstractions which the classical politics brought to the work of interpreting its facts were the abstractions of law. As mathematics is the logic of physics, so law is the logic of politics.

The allusion in the last quoted sentence is to an earlier description of classical science as being founded on a “double principle”: “that inquiries of this kind must be based on an empirically accurate study of facts, and on a logically accurate study of implications” (31. 15).

Collingwood disparages a certain contemporary school of philosophy of mathematics, after saying of Galileo and Newton,

31. 19. Neither (need I say?) fell into the error of identifying logic in general with mathematics. That error has been preached of late, but it has no warrant in the classical physics.

As a mathematical logician, I agree that logic and mathematics are not identical. I like what was suggested to me once by a colleague whose pioneering work I had studied in graduate school: Logic is like physics in having an object. Physics and logic are about something; mathematics, like Seinfeld, is about nothing. (The Seinfeld reference is my addition. I do not name the mathematical logician I cite, since I am not sure how seriously he took what he was saying.)

Physics studies the natural world; logic studies reason. This is in accord with Collingwood’s notion, stated first in The Principles of Art, that logic is a criteriological science. The research that I do professionally is mathematics, but mathematics that comes out of the criteriological study of mathematics: mathematics done self-consciously.

It is important that logic is not mathematics. Otherwise, in having a logic, politics would have to be mathematical. In my last post, I shared (in both senses) what I understood as Collingwood’s objection to the imposition in philosophy of the logic of mathematics.

The logic of physics is mathematics, in the sense that physical laws can be used like mathematical axioms and can sometimes be proved like mathematical theorems. Here I have in mind Newton’s second law of motion and law of universal gravitation, which can be used to prove Kepler’s laws of planetary motion.

Concerning gravity, Collingwood makes an interesting remark. There are really two ways of understanding the scientific process. One way is as interpreting facts, as described above (31. 32).

31. 33. The other is applying abstractions: starting with pure abstractions and converting these into laws by bringing them into relation with the facts whose laws they henceforth are. ‘Are’, I say, not ‘are thought to be’; the Newtonian law of gravitation is (not ‘is thought to be’) the law of direct variation as the product of the masses and inverse variation as the square of the distance between the centres. In formulating this law Newton was applying ideas in pure mathematics that had long been familiar.

There is not a law out there, waiting to be discovered, though we may get it wrong. The world is out there, in all of its particularity, waiting to be organized (perhaps only in thought) by us.

Such a point is made by Pirsig in Zen and the Art of Motorcycle Maintenance. One evening around the camp fire, during the motorcycle trip that is the armature of the novel, as mathematics is the armature of physics (31. 26), Pirsig’s son Chris tells ghost stories. Pirsig denies believing in ghosts. A boy at Chris’s YMCA camp believes in ghosts, and Pirsig says the boy must be spoofing. Then Pirsig learns that the boy is an American Indian, and he changes tack.

“My own opinion is that the intellect of modern man isn’t that superior. IQs aren’t that much different. Those Indians and medieval men were just as intelligent as we are, but the context in which they thought was completely different. Within that context of thought, ghosts and spirits are quite as real as atoms, particles, photons and quanta are to a modern man. In that sense I believe in ghosts. Modern man has his ghosts and spirits too, you know.”

“What?”

“Oh, the laws of physics and of logic—the number system—the principle of algebraic substitution. These are ghosts. We just believe in them so thoroughly they seem real.”

“They seem real to me,” John says.

“I don’t get it,” says Chris.

So I go on. “For example, it seems completely natural to presume that gravitation and the law of gravitation existed before Isaac Newton. It would sound nutty to think that until the seventeenth century there was no gravity.”

“Of course.”

“So when did this law start? Has it always existed?”

John is frowning, wondering what I am getting at.

“What I’m driving at,” I say, “is the notion that before the beginning of the earth, before the sun and the stars were formed, before the primal generation of anything, the law of gravity existed.”

“Sure.”

“Sitting there, having no mass of its own, no energy of its own, not in anyone’s mind because there wasn’t anyone, not in space because there was no space either, not anywhere … this law of gravity still existed?”

Now John seems not so sure.

“If that law of gravity existed,” I say, “I honestly don’t know what a thing has to do to be nonexistent. It seems to me that law of gravity has passed every test of nonexistence there is. You cannot think of a single attribute of nonexistence that that law of gravity didn’t have. Or a single scientific attribute of existence it did have. And yet it is still ‘common sense’ to believe that it existed.”

John says, “I guess I’d have to think about it.”

“Well, I predict that if you think about it long enough you will find yourself going round and round and round and round until you finally reach only one possible, rational, intelligent conclusion. The law of gravity and gravity itself did not exist before Isaac Newton. No other conclusion makes sense.

“And what that means,” I say before he can interrupt, “and what that means is that that law of gravity exists nowhere except in people’s heads! It’s a ghost! We are all of us very arrogant and conceited about running down other people’s ghosts but just as ignorant and barbaric and superstitious about our own.”

“Why does everybody believe in the law of gravity then?”

“Mass hypnosis. In a very orthodox form known as ‘education.’ ”

I appreciate that Pirsig had to go his own way. I am sympathetic to what he says in Lila, that most professional philosophers are really “philosophologists,” talking about philosophy rather than doing it; they put

a philosophological cart before the philosophical horse. Philosophologists not only start by putting the cart first; they usually forget the horse entirely. They say first you should read what all the great philosophers of history have said and then you should decide what you want to say. The catch here is that by the time you’ve read what all the great philosophers of history have said you’ll be at least two hundred years old.

Still, Pirsig might have learned from Collingwood.

Along such lines as Pirsig sketches, I argue that physics cannot be studied by the methods of physics. As a science, but a natural or empirical science, physics itself must be studied by a criteriological science. The same person can do both natural and criteriological science. She or he may need to, as Collingwood argues in An Essay on Metaphysics. When the professional metaphysicians do not do their job properly, the professional natural scientists have to do it. Then they are doing “progressive anti-metaphysics,” which is really metaphysics; I discussed this in “What It Takes.”

Returning to the New Leviathan, I note that, except for the reference to the law of gravitation, Collingwood is not too specific about how mathematics is used in physics. He has said that the scientist is like a bee—and therefore not like an ant, who stores just what she finds outside; or a spider, whose web comes just from herself. The main point then, about mathematics as the logic of physics, is the following.

31. 29. A law is neither a crude fact nor (as some ant-logicians pretend) a collection of crude facts. It cannot be established by an observation or an experiment, or many of them. Nor is it a theorem in pure mathematics, to be established by a mathematical operation. It is midway between the two: a hybrid. It is what the scientist can breed from facts by crossing them with pure abstractions, which is another way of saying what Bacon said. It is what he can breed from pure abstractions by crossing them with facts. If any reader knows too little of scientific work to understand the metaphor, I willingly apologize for its obscurity.

For the moment treating mathematics as a natural science, a part of physics, I suggest that, for the “ant-logician,” the fraction 2⁄3 is a certain collection, namely the collection of ordered pairs (x, y) of counting numbers such that 3x = 2y. This is good enough for modern mathematical work, because we have proved that the collection just described is an equivalence-class, determined by a relation that we have proved to be an equivalence-relation. The relation is the one that Euclid calls being proportional or having the same ratio. However, modern mathematicians misread Euclid’s definition, because we think any old definition will do, as long as it gives the desired result; but Euclid’s definition is the “right” or “natural” one, the one that makes having the same ratio obviously an equivalence-relation.

That is the bit of history that I referred to earlier. It is relevant to a key point of Collingwood’s chapter.

31. 61. All modern science recognizes what I will call the principle of the limited objective. That is the most fundamental difference between the modern sciences and the sciences of ancient Greece.

In asking what x is, the Greek wants to know its “essence,” namely “everything you need know about x in order to work out a complete science of it” (31. 64). What is unchanged in science today is that x is, as the Greeks discovered (31. 65), not a material body. Today, however, we want to know only those facts about x that we think we can interpret (31. 68).

In physics, what we think we can interpret is what we can consider mathematically.

31. 7. The classical physics obeyed the principle of the limited objective, limiting its explanatory efforts to such facts as admitted of mathematical treatment. The unlimited objective, the hope of understanding Nature at large, was abandoned. In its place was put the limited objective, understanding so much of Nature as could be measured, weighed, or in some other way treated mathematically.

In politics, what corresponds to mathematics in this sense is society (31. 81).

If physics is going to study the world mathematically, there has to be a belief that this is possible, even if not everything in the world will be explained in this way. This seems to be an absolute presupposition, in the sense of An Essay on Metaphysics, though Collingwood does not call it that. There is a corresponding presupposition in politics:

31. 83. No one doubted that some elements in that admittedly complex thing we call political life were homogeneous with the facts of social life or partnership; and that the project of limiting our objective to the study of these elements in political life would give results; limited, but worth having.

Since ancient Greek mathematics lived on into medieval and modern times (31. 53), it could be used in classical physics. I would add another condition for its being used. Despite what I said above about mathematics in general, Greek mathematics was about the world that would be studied by physics, even though Euclid’s systematic development of geometry had nothing to do with the actual needs of land-surveying, and this is what the word geometry meant.

Politics can look at partnerships, and the logic of politics can be Roman law and its derivatives, because Roman law governed partnerships. Collingwood’s full account of the “abstractions of law” in this sense is interesting.

31. 6. These again were of two kinds, elementary and advanced. Elementary law, for the authors of the classical politics, was Roman law; which they knew as well as the classical physicists knew Euclid and the multiplication table, and for the same reason. Advanced law meant the revision, partly expansive and partly corrective, which Roman law had received in the legal institutions of medieval and modern Europe; and not only in the countries which ‘received’ Roman law: on the contrary, especially in those which did not; whose lawyers by no means neglected the study of Roman law, and owed a great deal to it in the formulation of their own. This revision of Roman law was as important for the classical politics as the revision of Greek mathematics by the invention of analytical geometry and the differential calculus for the classical physics.

According to Collingwood, the principle of limited objective predates classical physics itself:

31. 71. The principle of limited objective, applied to physics with memorable results by Galileo, was not first laid down by Galileo. It was first expounded by those too little known writers (if they were better known the main lines of European history would be better understood) whom we call the Christian Fathers. The sciences with unlimited objectives went bankrupt with what is called the collapse of ancient paganism. The Christian sciences (nostra philosophia, one of the Fathers calls them) are sciences with limited objectives.

Collingwood says a lot more about the contribution of the Christian Fathers to modern physics in “The Existence of God” in An Essay on Metaphysics. (See “What It Takes.”) I should like to see other scholarship on these matters, especially since a friend has pointed me to a recent book about how Christianity went downhill, once it became the official religion of the Roman Empire; scholarly sources quoted on Wikipedia suggest that the book’s own scholarship is bad.

Collingwood closes his chapter by suggesting that he is doing original history: “It is by correcting the ideas of the Roman civilians in the light of this long medieval and modern experience of partnership in many different forms that I have been able (20. 6 seqq.) so to modify those ideas as to bring the central notion they express into harmony with the modern European use of words” (31. 93).