Effectiveness

Preface

First published May 17, 2018, this essay concerns Eugene Wigner’s 1960 article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I wrote a lot, which I now propose to summarize by section. (The meditations also continue in the next article.)

  • Some things are miraculous. Among Wigner’s examples are
    • that mathematics is possible at all, and
    • that “regularities” in the physical world can be discovered, as by Galileo and Newton.

    For Wigner, we should be grateful for the undeserved gift of a mathematial formulation of the laws of physics. This makes no sense theologically—and here I agree with the character Larry Darrell in Somerset Maugham’s novel The Razor’s Edge. Wigner’s idea that our mathematical reasoning power has been brought to perfection makes no sense to me either.

  • Everything is miraculous. Here I agree with Collingwood in Religion and Philosophy. A miracle cannot be the breaking of a natural law, since such a thing cannot be broken. A great artist like Beethoven follows no rules in the first place, or makes them up as he goes along; and he is like God in this way.
  • Natural law. That it cannot be broken is part of the very concept of natural law. Quantum phenomena and the theory of relativity have not in fact been brought under a single law; for Wigner, it may not be possible.
  • Mystery. Not only can we not define miracles, but (as we should have observed in the first place) we cannot even say when they happen. If like Wigner we call something miraculous, this means it cleanses our own doors of perception, in the sense of William Blake.
  • Definitions. In his treatment of miracle in Religion and Philosophy, Collingwood shows the futility of trying to define a term when you are not sure how to use it. He makes this futility explicit in The Principles of Art. If we are going to think about the use of mathematics in natural science, this means we ought to be mathematician, natural scientist, and philosopher; and not just “natural scientist,” but physicist and biologist, since if mathematics is effective in physics, it would seem to be ineffective in biology.
  • Being a philosopher. We are all philosophers, in the sense that Maugham describes in the story “Appearance and Reality,” if only we think. All thought is for the sake of action. This does not mean that thought occurs separately from an action and is to be judged by the action. We may value “pure” thought, such as doing mathematics or making music or living the contemplative life of a monk. This however moves me to a give a thought to the disaster of contemporary politics.
  • Philosophizing about science. For present purposes, compart­ment­al­ization of knowledge is a problem. So is the dominance of analytic philosophy, for suggesting (as one cited person seems to think) that big problems can be broken into little ones and solved independently. In mathematics, students should learn their right to question somebody else’s solutions to problems. In philosophy, the problems themselves will be our own. Philosophy as such cannot decide what the problems of physics or biology are, though it may help to understand the “absolute presuppositions” that underlie the problems. Philosophers quâ metaphysicians cannot determine once for all what the general structure of the universe is. This does not mean they should do “experimental philosophy,” taking opinion polls about supposedly philosophical questions. What matters is not what people say, but what they mean and are trying to mean. As Collingwood observes, metaphysics is an historical science.

For more on the last points, see a more recent article, “Re-enactment.” (This Preface added June 3, 2018.)


I am writing from the Math Village, and here I happen to have read that Abraham Lincoln kept no known diary as such, but noted his thoughts on loose slips of paper. Admired because he “could simply sit down and write another of his eloquent public letters,”

Lincoln demurred. “I had it nearly all in there,” he said, pointing to an open desk drawer. “It was in disconnected thoughts, which I had jotted down from time to time on separate scraps of paper.” This was how he worked, the president explained. It was on such scraps of paper, accumulating over the years into a diaristic density, that Lincoln saved and assembled what he described to the visitor as his “best thoughts on the subject.”

Thus Ronald C. White, “Notes to Self,” Harper’s, February 2018. My own notes to self are normally in bound notebooks, and perhaps later in blog articles such as the present one, which is inspired by the 1960 article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” by Eugene Wigner.

Some things are miraculous

Wigner makes frequent reference to miracles. First mathematics itself is a miracle:

The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.

I am not sure it even makes sense to speak of perfection of reason. Some persons may do mathematics better than others, in the sense of more readily finding theorems and proofs that all of us can appreciate; this does not mean that any of us is close to perfection, any more than climbing a stairway at noon puts us close to the sun.

Reason is the power of testing what we want. In order to prove a theorem, I have to want it to be true. Desire is not enough; the theorem might be false. In this case, to find a counter-example, I have to want to find one. I may simply want to know whether the theorem is true. Reason is then like a machine to tell me the answer. The sooner the answer comes, the more perfect the machine, perhaps; but then it is not clear to me that perfection is really instant gratification.

Wigner’s essay is our main subject, and mathematical reason is not its main subject. Even though, for Wigner, “aesthetic sense” alone gives us mathematical concepts such as the so-called complex numbers, and “nothing in our experience suggests the introduction of these quantities,” their use in physics is

not a calculational trick of applied mathematics, but comes close to being a necessity in the formulation of the laws of quantum mechanics.

The possibility of such laws at all is Wigner’s second miracle:

It is, as Schrödinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.

Is it really a miracle that we can discover such laws? It may be no more a miracle than that Columbus could discover the New World in 1492.

Miracles would seem to be connected with religion. I recall a religious bumper sticker on a car on the street where I grew up. According to the sticker, “The Bible has the answer.” There was something funny about this. As was said by the car-owner’s younger brother, who was seven years older than I: the Bible might have the answer, but what was the question?

I am proud never to have owned a car; but if I had somewhere to put a bumper sticker, it might read, “Collingwood has the answer.” If we ask how the miracle can occur whereby, as Wigner says,

the law of gravitation as formulated by Newton…based on very scanty observations…which he could verify with an accuracy of about 4% has proved to be accurate to less than a ten thousandth of a per cent,

—if we ask how the miracle of Newton’s discovery can happen, then I propose to find in Collingwood, not an answer perhaps, but clarification, and relief from the pessimism that strangely suffuses Wigner’s paper.

Wigner himself acknowledges his pessimism in his closing paragraph, which begins, “Let me end on a more cheerful note.” The note is not that cheerful:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it…

Why should we be grateful? I agree with Larry Darrell in The Razor’s Edge (1944), who recalls to Somerset Maugham a stay in a monastery in Alsace in the 1920s:

“I used to listen to the monks repeating the Lord’s Prayer; I wondered how they could continue to pray without misgiving to their heavenly father to give them their daily bread. Do children beseech their earthly father to give them sustenance? They expect him to do it, they neither feel nor need to feel gratitude to him for doing it, and we have only blame for a man who brings children into the world that he can’t or won’t provide for. It seemed to me that if an omnipotent creator was not prepared to provide his creatures with the necessities of existence, material and spiritual, he’d have done better not to create them.”

One may respond that what Larry says is fine, if one wishes to remain a child; part of growing up is learning to give credit where it is due. I would then cite Larry’s further exchange with Maugham:

“You’ve had a great deal of success,” he went on. “Do you want to be praised to your face?”

“It only embarrasses me.”

“That’s what I should have thought. I couldn’t believe that God wanted it either…”

Everything is miraculous

Wigner proposes that we should be grateful for the miracle of mathematics in physics. Why this miracle in particular? In Collingwood’s first book, Religion and Philosophy (1916), the ultimate chapter is called “Miracle,” and the conclusion is, “nothing exists that is not miraculous”:

We are not in a position to say that while a headache cured by prayer is a mystery and therefore presumably miraculous, a headache cured by drugs is scientifically understood and therefore not mysterious nor miraculous… Every cure is equally a miracle, and every doctor (like every other active and creative mind) a miracle-worker, in the only sense which can reasonably be attached to the word.

Collingwood’s rhetorical strategy in the chapter has been to start by trying to define miracles:

We shall offer no opinion on the historicity of any particular miracle, or on the motive which may have underlain it; we shall confine ourselves strictly to the problem of defining the conception of miracle as such.

Three possible solutions fail.

  1. If a miracle is the interference of God in the course of nature, this violates the notions of both
    • God, as the source of all being, and
    • nature, as being governed by law.
  2. If there is no god, but only nature, still its laws cannot be broken, even by some supposedly higher law. Unlike legal statutes, laws of nature are unbreakable by definition.
  3. If there is only God, then there is no distinguishing this deity’s non-miraculous activities from the miraculous. For example, the deity does not act
    • sometimes normally, other times abnormally;
    • sometimes mediately, other times immediately.

On the last point, Collingwood seems to disagree with Michael Attaleiates, Byzantine historian of the Battle of Manzikert in 1071, whereby the first Turkish peoples migrated to Anatolia. I quoted Michael in “Early Tulips” on the subject of an earthquake in Constantinople, eight years earlier; as a result of the earthquake, which did not utterly destroy the city,

one theory of those who investigate earthquakes as natural phenomena was overturned, namely that the tremors are caused at random… For if the motion was caused, as they claim, solely by the violence of those elements as they twist around in the hollows of the earth and create flows of compressed air, then the tremors would not have any order to them and their vast and irrepressible force would not cease at the point of collapse, lest the entire world be subsequently destroyed. On this occasion the tremor was revealed as a sign sent from God, given that the turbulent motion was both large and also orderly, and its purpose was to restrain and control human urges.

Thus Michael seems to think that some extraordinary events represent the direct interference of God with nature. On the other hand, he does go on to suggest, perhaps, that every event can be so understood:

That earthquakes are caused by air flows or the motion of the waters is not out of place considering the interconnected structure of nature, and it is even likely to be true to a certain extent. However, the shaking does not happen randomly—this is what is being refuted by us—rather, it is caused by divine will, given that God does not govern the things of this world in an unmediated way. Thus, the immediate cause of rain appears to be the gathering of clouds and the cause of thunder and lightning their crashing together, but everything, according to those who think in a pious way, depends on divine will.

For Collingwood, it may make sense to say that some of our activities are normal, some abnormal; however, as the great artist, in a strict sense, respects no norm, neither does God:

What then are Beethoven’s rules of composition? Here is the secret: they are recast for every new work. The “rule” is nothing but another name for the ground-plan of the new work itself. He simply invents new rules as he goes along, to meet his requirements. And that means that in the sense of the word with which we started he has no rules at all.

In The Razor’s Edge, Larry raises the question from a different angle:

“Like Rolla, I’ve come too late into a world too old. I should have been born in the Middle Ages when faith was a matter of course; then my way would have been clear to me and I’d have sought to enter the order. I couldn’t believe. I wanted to believe, but I couldn’t believe in a God who wasn’t better than the ordinary decent man. The monks told me that God had created the world for his glorification. That didn’t seem to me a very worthy object. Did Beethoven create his symphonies for his glorification? I don’t believe it. I believe he created them because the music in his soul demanded expression and then all he tried to do was to make them as perfect as he knew how.

Natural law

The most relevant point for us in Collingwood’s argument, and perhaps the most difficult and controversial, is that natural laws cannot be broken. If you think you know a natural law, and yet you encounter an exception, this means not that a miracle has occurred, but that you did not fully understand the law in the first place, or perhaps you simply didn’t have a law. This is an historical statement about the modern practice of natural science.

Or perhaps it is a normative statement about how people ought to understand natural law. For as Collingwood says,

There is a great deal of loose talking and vague thinking on this point. People speak of laws exactly as if they were individual persons; we hear of the reign of law, the compulsion of law, the decree of law, or even sometimes of disobedience and defiance of the laws of nature. Such wild mythology obscures the true conception of law so hopelessly in the popular mind, that people can entertain the idea of two laws conflicting…

Eugene Wigner does entertain the idea of two laws conflicting:

We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity… So far, the two theories could not be united, that is, no mathematical formulation exists to which both of these theories are approximations. All physicists believe that a union of the two theories is inherently possible and that we shall find it. Nevertheless, it is possible also to imagine that no union of the two theories can be found. This example illustrates the two possibilities, of union and of conflict, mentioned before, both of which are conceivable.

In thinking of what his business really is, can a physicist like Wigner use the help of a metaphysician like Collingwood? This is the latter’s suggestion in Essay on Metaphysics (1940), though that book is more of a warning to the philosophers: their business is to understand what the physicists are really doing, not tell them what they ought to be doing.

Mystery

Meanwhile, in Religion and Philosophy, having shown to his own satisfaction (and mine) that a definition of miracle is impossible, Collingwood now steps back to observe that, regardless of formal definitions, we cannot even distinguish between what is miraculous and what is not. Everything is a miracle, as was said above, though we do not always see it.

This is the function of those events which we call, par excellence, Miracles; they force themselves upon our eyes as a standing testimony to the deadness and falsity of our materialistic dogmas, and compel us to face reality as it is, free, infinite, self-creative in unpredicted ways.

I hear the echo of William Blake, from the passage in The Marriage of Heaven and Hell that inspired Aldous Huxley and (through his mediation) The Doors:

But first the notion that man has a body distinct from his soul, is to be expunged; this I shall do, by printing in the infernal method, by corrosives, which in Hell are salutary and medicinal, melting apparent surfaces away, and displaying the infinite which was hid.

If the doors of perception were cleansed every thing would appear to man as it is, infinite.

For man has closed himself up, til he sees all things thro’ narrow chinks of his cavern.

Collingwood himself quotes not Blake, but a later mystic poet, Francis Thompson, in The Mistress of Vision:

All things by immortal power,
Near or far,
Hiddenly
To each other linkèd are,
That thou canst not stir a flower
Without troubling of a star.

In a review, T. S. Eliot had some criticism of Collingwood’s book, but concluded:

The philosophical interpretation of the Incarnation, of the Atonement and of Miracle, are extremely well handled.

This is from “Shorter Notices,” International Journal of Ethics, vol. 27, no. 4, 1917, pp. 534–544; I took the text from JSTOR. Five months older than Collingwood, Eliot attended his lectures at Oxford on Aristotle’s De Anima.

Definitions

Having been a university lecturer for some two decades, I am proud to have seen some of my students go on to become lecturers themselves. (One of them is an organizer of the conference now at the Math Village; another is an invited speaker.) Collingwood may be proud when, at the end of The Principles of Art (1938), he praises his student and critic Eliot for having taken artistic competence

forwards into a new path where the ‘artist’, laying aside his individualistic pretensions, walks as the spokesman of his audience.

…[Eliot] has set the example by taking as his theme in a long series of poems a subject that interests every one, the decay of our civilization. Apart from one or two trifles, Mr. Eliot has never published a line of ‘pure literature’. Looking back, one sees the whole of his early verse as a succession of sketches and studies for The Waste Land.

At the beginning of the book, Collingwood observes that we cannot define a term without understanding how we actually use it:

A question of this kind [“What is art?”] has to be answered in two stages. First, we must make sure that the key word (in this case ‘art’) is a word which we know how to apply where it ought to be applied and refuse where it ought to be refused…

Secondly, we must proceed to a definition of the term ‘art’. This comes second, and not first, because no one can even try to define a term until he has settled in his own mind a definite usage of it: no one can define a term in common use until he has satisfied himself that his personal usage of it harmonizes with the common usage.

In that spirit, to criticize Wigner’s essay properly, we ought to be mathematician, natural scientist, and philosopher. Wigner himself seems to treat physics as the archetype of a natural science; but we ought not to forget biology, given the remark of Israel Gelfand,

There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.

The quotation is from my friend Alexandre Borovik, whose recollection of Gelfand’s words now serves as a cited source for two Wikipedia articles:

  1. on Wigner’s original article and
  2. on Gelfand’s phrase “Unreasonable ineffectiveness of mathe­matics,” or the concept named by it.

For my own reading, I took the text of Wigner’s essay from a page at Dartmouth. Because of unlinked text in French at the end of that page, I infer that the (uncited) origin of the text is a page of the website of somebody called Patrick Peccatte, though he does not make his name prominent.

Being a philosopher

If we would be critics, then the requirement that we be philosophers is in some sense automatically satisfied. Here again is Somerset Maugham:

Though Lisette was a philosopher only in the sense in which we are all philosophers, that she exercised thought in dealing with the problems of existence, her feeling for reality was so strong and her sympathy for appearance so genuine that she might almost claim to have established that reconciliation of irreconcilables at which the philosophers have for so many centuries been aiming.

We are all philosophers. The quotation is from a story that was first published in November, 1934, though it appeared in the collection called Creatures of Circumstance only in 1947. (My source here is the thorough “Repères bibliographiques” in Maugham’s Nouvelles complètes, Paris: Omnibus, 1992.) The passage alludes to the story’s title, “Appearance and Reality,” taken from a book of the same name, of whose author Collingwood writes in his own Autobiography (1939),

Bradley, though he lived in Oxford down to his death in 1924, never taught there and never sought in any way to propagate his philosophy by personal contacts. He lived a very retired life; although I lived within a few hundred yards of him for sixteen years, I never to my knowledge set eyes on him.

From Maugham’s description of a woman who was, in the language of the day, a mannequin, I would remove the apologetic words “though” and “only”:

Lisette was a philosopher in the sense in which we are all philosophers, that she exercised thought in dealing with the problems of existence.

This is remarkably generous, especially from a writer who might easily (though mistakenly) be called cynical. We are all potentially philosophers. This supplements what I opined at the end of my article “What Philosophy Is” in this blog: “There is only one philosophical question: ‘What are we going to do now?’ ” If this is a question for us, the answer must be to think.

I do agree with Collingwood at the beginning of the Prologue of his second book, Speculum Mentis (1924):

All thought exists for the sake of action. We try to understand ourselves and our world only in order that we may learn how to live. The end of our self-knowledge is not the contemplation by enlightened intellects of their own mysterious nature, but the freer and more effectual self-revelation of that nature in a vigorous practical life.

One can disagree with this. One of my former tutors from St John’s College did, in an email exchange two years ago. A student of Leo Strauss, he argued that for Plato and Aristotle, the wisest among us have already learned how best to live, and this is to live the life of thought.

I am not sure that this is a real disagreement with Collingwood. I would disagree with Collingwood myself, if he meant for example that education was good only for the sake of getting a job. I addressed this point in “Şirince 2014,” saying that the Nesin Mathematics Village ought to receive government support, not because of any technological benefits that mathematical education may help to produce, but simply because thinking (about mathematics, in this case) is good in itself.

I think Collingwood in Speculum Mentis is objecting to the notion that we can justify ourselves merely by thinking, because thought (he also says “knowledge”) satisfies a human need as surely as food and clothing. The philosopher

knows very well that his [sic] thoughts are not quoted on the Stock Exchange along with corn and rubber, and that when he offers them to the world, the world is frankly uninterested. Except by professed students, his lectures are unattended and his books unread.

Think we must. The error is to think that there is something that is only thinking. Collingwood argues this in Religion and Philosophy:

In the theory of the religious life offered by religion itself, there is no dualism at all between knowing and acting. The two things are united, for instance by the author of the fourth Gospel, in such a way that they are absolutely indistinguishable. The term used to express their unity is “love,” an activity which in its perfect manifestation is represented as the perfection of the religious life. The whole of the great final discourse in John is an exposition of this conception; nothing can be clearer than the way in which the spirit of love is identified on the one hand with that of truth, and on the other with that of morality or obedience.

I suppose the “great final discourse of John” is the last chapter of that gospel, wherein we are told,

15 So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my lambs.

More than two decades after writing about these things, Collingwood visited the monastery of the island of Santorini, on the sailing trip recorded in The First Mate’s Log (1940). I discussed the travellers’ visit to Delphi in “On Knowing Ourselves.” At Santorini, though charmed by the monks in person, Collingwood’s companions—students from Oxford—had a utilitarian prejudice against monasticism. Collingwood pointed out to them that the monks had the admiration and respect of the other islanders. Mathematicians might have such respect, even in Britain:

The social justification of pure mathematics as a career in any given society, then, is the fact that the society in question thinks pure mathematics worth studying: decides that the work of studying pure mathematics is one of the things which it wants to go on, and delegates this function, as somehow necessary for its own intellectual welfare, to a man or group of men [sic] who will undertake it.

Publication of one’s mathematical results is irrelevant:

Unless there is value in being a pure mathematician, there is no value in publishing works on pure mathematics; for the only positive result these works could have is to make more people into pure mathematicians; and a society which does not think it a good thing to have one pure mathematician among its members will hardly think it a good thing to have many.

Thus speaks a Collingwood who has done many years of thinking and living since writing that all thought exists for the sake of action. I don’t think he has changed his mind. When he wrote in 1924, he understood us to live in

a world full of desperate evils and among men [sic] crushed beneath the burden of daily tasks too hard for their solitary strength.

Collingwood may not have been ready then to blame the ruling class for the state of the world. However, when he came back from his Mediterranean cruise with a beard, his colleagues at Oxford thought he had gone Communist.

I recall from the 1990s the story of a retired man towing a recreational vehicle through Idaho with his wife. A tire blew out, the rubber wore away, the rim dragged along the asphalt, and sparks set fires in the dry grass on the roadside. The current President of the United States is like that driver, with one exception. Unlike Fred Howard, Donald Trump will never pull over, look back, and feel any regret for what he has done. If he does, it will be a miracle.

If what we humans can do in mathematics and physics is to be judged as miraculous, what about our failures of governance?

For the record, I thought I had read the fire story in one of the Readings in Harper’s; but I could not find it in the online archive. I found instead a Google group archive, which pointed me to an article in People dated June 14, 1993.

Philosophizing about science

In considering the question of the effectiveness of mathematics in science, Sasha Borovik suggests that philosophers are asking the wrong questions. They may do so, if philosophers are the people holding positions in philosophy departments. Compartmentalizing knowledge can be a problem. I wish therefore that I had a better-documented source on this than Fifty Thinkers Who Shaped the Modern World (London: Atlantic Books, 2012). In the chapter on F. H. Bradley, discussed above, Stephen Trombley describes the advent of professional philosophy:

In the period between 1850 and 1903 there wasn’t a school of British idealism, there was simply British philosophy, the general tendency of which was idealist. ‘British idealism’ is better regarded as a pejorative term created by early analytic philosophers to identify the status quo they wished to supplant with their own brand of thinking. The strange death of idealism in British philosophy goes hand in hand with philosophy’s transformation from a gentleman’s pastime into a profession… [T. H.] Green’s career is a milestone in the history of philosophy because, according to the utilitarian Henry Sidgwick (1838–1900), he was the first professional philosopher in the English-speaking world.

The early analytic philosophers’ war on British idealism can be seen to involve much more than the desire to supplant neo-Hegelian idealism and metaphysics in its entirety with logicism: they also wanted the idealists’ jobs. The analytic side won both battles. The professionalization of philosophy in Britain and the United States resulted in the death of idealism and the erection of analytic philosophy as the official way of thinking; in this way a generation of teachers led by Russell, Moore and Wittgenstein spawned a new generation of followers, who in turn kept the analytic torch burning brightly in the English-speaking world throughout the twentieth century as their students and their students’ students took up university teaching jobs. (There are notable exceptions…)

In its very name, analytic philosophy suggests the breaking up of big problems into little ones, so as to solve them independently. This seems to be the idea of a person whose page about Wigner came up in a search. He says of himself,

He has likely read more works of philosophers and scientists than any other modern thinker, and has critically analyzed and written about the ideas of hundreds of them on these I-Phi web pages, as seen in the left navigation.

None of those philosophers is Collingwood.

When I was in high school in Washington, D. C., a fellow on a public bus started talking to me, and he told me how many hundreds of pages of Einstein he had read. Then he asked if I could tell him what a partial derivative was. “I think it’s the derivative when you hold all but one of the variables constant,” he said, or something like that. If he wasn’t sure, what could he have understood of physics? For Eugene Wigner, a remarkable feature of natural law, at least in classical mechanics, is that it tells us not positions or their first derivatives, but their second derivatives.

Bob Doyle must know what a partial derivative is. As he tells us, still in the third person,

Bob earned a Ph.D in Astrophysics from Harvard in 1968 and is now an Associate in the Harvard Astronomy Department.

This information is also found in a 2012 Harvard Magazine article. The tagline of Doyle’s own website is “solving philosophical problems with the new information philosophy.” I congratulate him, but I would point out that one’s own philosophical problems cannot be solved by anybody else.

In mathematics, what I want my students to learn is not this or that theorem, but their right to see to proof of any theorem, before they will accept it. In practice, we are willing to accept our colleagues’ judgment of the correctness of theorems that we want to use in our own work. In philosophy though, again I go back to my article “What Philosophy Is,” now for the idea that, as Collingwood observes in the Introduction to An Essay on Philosophical Method (1933),

in a philosophical inquiry what we are trying to do is not to discover something of which until now we have been ignorant, but to know better something which in some sense we knew already.

One might ask how I can find my own answers if I keep referring to Collingwood. One might just as well ask what physics can have to do with philosophy. Physics is something that all of us have a sense of, and some of us actively engage in. If people in philosophy departments try to tell physicists what to do, this is a problem. Collingwood addresses this problem rather severely in the first chapter of The New Leviathan (1942):

1. 57. At one blow, by enunciating the apparently harmless proposition that physics or chemistry is the science of matter, physiology the science of life, or the like, we have evoked the whole apparatus of scientific persecution; I mean the persecution of scientists for daring to be scientists.

1. 58. In whose interest is such a persecution carried on? Who stands to gain by it? The nominal beneficiary differs from time to time: sometimes it is religion, sometimes statecraft, and so on. None of these has ever in fact gained a ha’porth of advantage. The actual beneficiary has always been obsolete science.

Without quoting this particular passage, I elaborated on the idea elsewhere, considering also Collingwood’s Essay on Metaphysics. Having more recently read the ten new essays by contemporary scholars in Collingwood’s Autobiography and Other Writings (2013), presuming that those scholars have reported on any significant criticism of Collingwood, I agree more than ever with Simon Blackburn’s review of an earlier book,

in most respects the neglect of Collingwood’s thought may be our tragedy rather than his.

In “Nature and Death” I took some issue with Blackburn’s style of personal criticism, which I thought an unpleasant product of academic competition. Mary Beard is able to write more serenely, in her own review,

it is surely crucial that [Collingwood] was a product of the old Oxford ‘Greats’ (that is, classics) course, which focused the last two and a half years of a student’s work on the parallel study of ancient history on the one hand, and ancient and modern philosophy on the other. Most students were much better at one side than the other, and most stories tell of the desperate attempts by would-be ancient historians to cram enough Plato, Descartes and Hume to get their high-flying pass in the final exams (or alternatively of desperate attempts by would-be philosophers to remember enough of the Peloponnesian War or Agricola’s campaigns in Britain to do the same). In the context of Greats, Collingwood was not a maverick with two incompatible interests. Given the educational aims of the course, he was a rare success, even if something of a quirky overachiever; his combination of interests was exactly what Greats was designed to promote.

Writing in An Autobiography of going off to preparatory school, Collingwood describes a different split, not between history and philosophy:

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.

I take him not to be boasting, but to be uttering the plain facts, like Beard.

Blackburn writes also of Collingwood,

I doubt if he is more than a ghost in the footnotes to syllabi across the Western world.

I know of one case in which Collingwood has been thus reduced. He appears only in an endnote for the introductory chapter of Metaphysics: A contemporary introduction (London: Routledge, 1998). Michael J. Loux tells us that he will not use the conception—attributed to Kant, Collingwood, and others—of metaphysics as a study of our “conceptual scheme.” He will rather

focus on the issues that arise when we attempt to provide a general account of the structure of all that there is.

If giving “a general account of the structure of all that there is” is different from doing natural science, then I think it is what Collingwood does in metaphysics. For him this is the science of absolute presuppositions. An important one of these is that the universe operates according to laws of such a kind that Wigner mentions: Newton’s law of gravitation, with the corollary found earlier by Galileo.

An important point for Collingwood, and one that Loux errs in overlooking, is that metaphysics is an historical science. If suppositions are absolute, it is not in the sense that they never change. They are unquestioned, perhaps only for a time. See Collingwood’s Idea of Nature (1945), discussed in “Nature and Death,” for a review of how the idea of nature has changed. Wigner’s conception of the universe as governed by law would seem to be modern.

Not to recognize the possibility of historical change in absolute presuppositions is to be open to allowing the scientific persecution mentioned above, and also other kinds of persecution. Thus Loux says, seemingly innocuously, in a chapter on universals,

few will deny that many of our ways of sorting things are fixed by the objects themselves. It is not as if we just arbitrarily choose to call some things triangular, others circular, and still others square; they are triangular, circular, and square. Likewise, it is not a mere consequence of human thought or language that there are elephants, oak trees, and paramecia. They come that way, and our language and thought reflect these antecently given facts about them.

Thinking like Loux, some persons say the Bible is telling a plain fact when it says in Genesis,

So God created man in his own image, in the image of God created he him; male and female created he them.

We are all born male or female, and there is nothing we can do to change that. This a doctrine though, defensively declaimed by persons whose absolute presuppositions are being brought into question. If those persons are upset by the idea of one’s choosing one’s own pronouns, I would only point out that in Turkish there is no choice, because there is no gender: every person and every thing is just o. You can still be as sexist as you want to be, in Turkish as in any other language.

I can agree with Loux, if he just wants to say that opinion polls cannot tell us the nature of the universe. This is why I am incredulous that there is actually a line of inquiry called experimental philosophy, and it is not physics.

Apparently some Western researchers discovered in the late 1990s that “people of East Asian and of Indian descent” have different notions of what knowledge is from Westerners.

Stich and colleagues argued that this kind of variation in intuitions should cause a big shift in the way that analytic philosophy is practised. Until this point, most philosophers had traditionally thought it was fine to sit in their armchairs and consider their own intuitions. It was the way that philosophy was done. But experimental evidence, they claimed, undermined this traditional practice. If such differences of intuition existed, they wrote: ‘Why should we privilege our intuitions rather than the intuitions of some other group?’ If different groups had different intuitions, it wasn’t enough to say that ‘our’ intuition about justice or knowledge or free will is such-and-such. Rather, the philosopher must at the very least specify whose intuition is relevant, and why that intuition should matter rather than another one.

This is from an essay by Stephanie Wykstra in Aeon dated 01 May 2018; I learned of it from a tweet. It’s great to learn that there are different ways of thinking. It’s essential to getting along in life. However, as I asserted earlier, your own philosophical problems cannot be solved by anybody else. Obviously others can help you. If you seek this help, you can call it an experiment if you like; but you must not think it’s like climbing the Tower of Pisa and dropping weights. In philosophy, you will not learn from your “experimental” subject unless you recognize that they are engaged in the same enquiry as you.

The quoted passages by Beard and Blackburn are from reviews of the biography of Collingwood by Fred Inglis called History Man (Princeton, 2010). Inglis connects Collingwood’s metaphysics to later thinkers:

Scanning the intellectual landscape for signs and wonders that do not so much declare Collingwood’s influence as give a glimpse of his aliveness to changes in the winds and tides of thought, one’s eye is caught in 1962 by Thomas Kuhn’s amazing book, The Structure of Scientific Revolutions.

…It is noteworthy, moreover, that Kuhn pays tribute to the help and friendship of Stanley Cavell who…is surely the American philosopher closest to Collingwood in taste, manner, and heresy.

Neither in Cavell’s work nor in Kuhn’s can I find reference to Collingwood, but Kuhn provided a definitive account not only of certain absolute presuppositions that, in his idiom, constituted the “paradigms” of “normal science,” but also caught those paradigms in the process of changing. It is perhaps worthy of note also that a prominent Collingwoodian, Stephen Toulmin, spotted the similarity in ideas but haughtily and wrongly described them as a “crude” “popularisation.” Kuhn wasn’t “crude,” he was bold…

I have yet to learn for myself whether Toulmin or Inglis (or somebody else) has the right attitude towards Kuhn; I shall still call it a tragedy that Collingwood is not better known, especially if one wants to think about what mathematics is doing in science.

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