Polytropy

A recent theme of this blog has been juxtapositions, especially of paintings, as in the articles “Pairing of paintings” and “More pairings” (both from July, 2013).

In this article I juxtapose two texts, from the 1930s. Both of them decry current intellectual troubles. Both find a solution in a return to the intellectual tradition.

1. One of the texts is American: the “Bulletin of St. John’s College in Annapolis 1937–38”. This is currently was available in a pdf image of a 2004 reprint. (The link died, but the Internet Archive saved the content, most recently from June 22, 2013.)

2. The other text is British, from 1933: R. G. Collingwood’s Essay on Philosophical Method, especially its final section, which I quote at the end of this article.

St John’s College is my alma mater, and I use that term seriously, for its meaning of “foster mother.” R. G. Collingwood is my favorite philosopher. The College lately has difficulty attracting enough students. Collingwood does not attract many readers. I think both of these situations are unfortunate. I cannot propose that bringing together Collingwood and the College will help either one to become more popular. But it may help interested persons to understand what St John’s College is all about. Not that the College is about one thing, and Collingwood is about the same thing. By one account that I have heard, the College was changed in the 1950s, and not for the better, under the leadership of the author of Greek Mathematical Thought and the Origin of Algebra.

The 1937 “Bulletin” of the College announced the New Program. Because of this Program, I chose to attend the College in 1983. Looking back from thirty years later, I would articulate my reason for attending the College as follows. I was living in a tradition, whether I liked it or not, and I wanted to know what it meant. I wanted to know what it really was. I thought the tradition needed questioning: here I was fired up by Robert Pirsig’s philosophical travel book, Zen and the Art of Motorcycle Main­tenance. (I recently wrote about this book and others in another blog article, “Books hung out with.”)

Before the Pirsig influence though, in my tenth-grade geometry class, I was dissatisfied with our textbook. I wished we would just read Euclid. This is what I ended up doing at St. John’s, although by that time I knew a lot more mathematics, perhaps too much. My article “Learning Mathematics” concerns my last two years of high school. Before that, in tenth-grade geometry, I don’t think I had a clear reason for disliking our textbook; I was mainly offended by the condescending tone, the sense that the text was written for children. I did find Euclid in the library, and I read some of him. Having spent a lot more time with him now, I have clearer reasons for disliking the tenth-grade geometry text; but that is a matter for another article, not yet written. (The text was Weeks and Adkins, A Course in Geometry: Plane and Solid, Ginn and Company, Lexington MA, 1970; I refer to it in “On Commensurability and Symmetry,” Journal of Humanistic Mathematics, Volume 7, Issue 2, July 2017, pages 90–148.)

I never heard of Collingwood at St. John’s. This is not because he was too young. My senior language tutorial at the College spent some time with Collingwood’s slightly younger contemporary, Wittgenstein. We read from his Philosophical Investigations. Even in the freshman language tutorial, after reading my first essay, my tutor recommended the Philosophical Investigations, because of a similarity of style as well as general theme. Both Wittgenstein and I gave our readers little clue about where we were going.

Where I am going now is, as I said, the last section of Collingwood’s Essay on Philosophical Method. But I shall go there a bit slowly. You can skip ahead if you want, to the long block of quoted text at the end of this article.

Collingwood’s words are inspiring in their defense of the sixty generations of continuous philosophical thought that we are the beneficiaries of. At least, Collingwood’s words are inspiring, if you are already open to something like the New Program of St John’s College.

Collingwood writes well. At least I think so. It is a reason why I call him my favorite philosopher. Perhaps it is a non-philosophical reason; I am not sure. But I have twelve books on my shelf published under Collingwood’s name (some posthumously). I have read them all, in some cases several times. I did get bogged down in The Philosophy of Enchantment, which consists of manuscripts not properly edited for publication by Collingwood himself. For some reason I have not finished The Idea of Nature. This book, however, in its 1960 paperback edition, like the 1958 paperback edition of The Principles of Art, has never gone out of print. Other Collingwood books have been brought back into print with long editorial introductions, and appendices from the Collingwood archive.

There is even a recent biography of Collingwood: History Man by Fred Inglis. This is favorably reviewed by Simon Blackburn, who also favorably reviews Collingwood himself. By the way, I think Blackburn is mistaken to say that, for Collingwood, our “absolute presuppositions” are knowable by future generations, but not by ourselves. These absolute presuppositions are the proper subject of metaphysics, and as I read Collingwood’s Essay on Metaphysics, we can know our presuppositions; it is just difficult. (See “What It Takes,” May, 2018.)

“If Collingwood is as acute and interesting as I have suggested,” writes Blackburn, “how does it happen that he is largely a minority interest?” Blackburn thinks Collingwood boasts about his abilities, and this puts readers off. I don’t see it, myself. Maybe you have to be part of the British scholarly elite to see it. Collingwood wrote an autobiography, and perhaps such an endeavor needs an author who thinks highly of himself. In the autobiography, Collingwood tells how he has had to part intellectual company with all of his Oxford colleagues. It takes nerve to go out on your own; therefore Collingwood is implicitly telling us he has this nerve.

It also took nerve on the part of Stringfellow Barr and Scott Buchanan to create the New Program of St. John’s College. One of Collingwood’s complaints about his philosophical colleagues is that they do not properly read their predecessors. At best they select isolated passages in order to refute them. I don’t think this is exactly Barr and Buchanan’s issue with American education of their time. But their recommendation is the same as Collingwood’s: to go back to the sources, neither disputatiously nor worshipfully, but critically in the best sense.

In the Introduction to his Essay on Philosophical Method, Collingwood sets his work in a line that includes Socrates, Plato, Descartes, and Kant. I attempt a brief summary of Collingwood’s introductory summary of the contributions of these four.

1. Socrates recognizes that philosophical knowledge is already in us; the proper method for bringing it out is not observing, but questioning. In this way, philosophical knowledge resembles mathematical knowledge, as the character of Socrates shows in Plato’s Meno. Here, by being questioned, a person raised as a slave in Meno’s house is led to discover that, to double a given square, he needs to construct a square on the given square’s diagonal.

2. Mathematics and philosophy are nonetheless different. Plato understands this. Collingwood observes,

   Mathematics and dialectic are so far alike that each begins with an hypothesis: “Let so-and-so be assumed.” But in mathematics the hypothesis forms a barrier to all further thought in that direction: the rules of mathematical method do not allow us to ask “Is this assumption true? Let us see what would follow if it were not.” Hence mathematics, although intellectual, is not intellectual à outrance; it is a way of thinking, but it is also a way of refusing to think.

   The meaning of “hypothesis” here is not clear, be it according to Collingwood or Plato. I think Plato has not seen the possibility of a systematic development of mathematics such as is found in Euclid. Collingwood has seen it, but the understanding of it has changed over the generations. I do like Collingwood’s saying that mathematics is a way of refusing to think. Learning mathematics does mean learning not to think about some things. A student of mine once could not learn linear algebra properly, because he thought that no more than three spatial dimensions were possible.

   In any case, philosophy allows and indeed requires the questioning of hypotheses. This is Plato’s contribution to method: “the conception of philosophy as the one sphere in which thought moves with perfect freedom.” But this still does not distinguish philosophy from mathematics; it seems only to broaden the scope of the same kind of thinking.

3. Whatever method Descartes uses in his own thinking, the method he tells us about is again excessively mathematical.

4. Kant sees this, but his answer is to distinguish methodology from philosophy itself. First work out your method, and then do your philosophy with it. Such a separation is untenable.

What then is Collingwood’s contribution? Formally, his Essay on Philosophical Method is built up on the hypothesis of an overlap of classes. There is no such overlap in mathematics. A straight line is not curved. You may say that it is curved, because a straight line is a circle of infinite radius, and all circles are curved; but in this case, the difference between straight and curved has become the difference between finite and infinite.

Neither do the classes of empirical science overlap. An animal is not a plant. Collingwood acknowledges that there are borderline cases. I am not sure, but I think the biologist’s response to such cases is to improve the classification system so that such cases can be accommodated. The ideal remains the same: to divide the world of living things into classes, so that every living thing belongs unambiguously to one and only one of those classes.

Philosophy goes astray when it tries to classify the world in this way. Collingwood himself went astray in his first book, Religion and Philosophy. Recognizing there that religion, theology, and philosophy had something in common, he concluded that they were the same thing. But they are not the same, as he understands later; they are overlapping classes.

All philosophical classes overlap with others. The notion sometimes sounds absurd. Maybe it is a rhetorical trick; but it has good results. The class of what you agree with must overlap with the class of what you disagree with. If you are a philosopher, you cannot simply explain what is wrong with somebody else’s work; you have to do the same work better. This is similar to the point of a Friday-night lecture given by the Dean of St John’s College, Santa Fe campus, in the fall of 1985.

What I remember most clearly from Robert Neidorf’s lecture is that if on page Y of a book you find a sentence contradicting a sentence on page X, it doesn’t mean the book is wrong. A new student did not like this. He objected to Mr Neidorf’s criticisms of formal logic. I think the student may have been an Objectivist. He missed the irony in Mr Neidorf’s having been the author of a textbook called Deductive Forms: An Elementary Logic.

Collingwood has a lot more to say in his essay, all resting on the hypothesis of the overlap of classes. He checks his conclusions against the thoughts of the great philosophers, who are read at St John’s. (One exception is Spinoza, who was not read in my day.) This checking is the kind of hypothesis-questioning enjoined by Plato. But it seems circular. How can philosophy advance, if it needs to be confirmed by what has already been done?

Collingwood suggests that there is even a double circularity. If I understand him, he means roughly that using the tradition to confirm the philosophy erected on it is one circle; but appealing to the tradition at all is another circle, since it requires the assumption that there is a tradition. This objection is in the next-to-last section of Collingwood’s book. The last section is Collingwood’s “oblique” response; I end with this:

Assumption for assumption, which are we to prefer? That in sixty generations of continuous thought philosophers have been exerting themselves wholly in vain, and have waited for the first word of good sense until we came on the scene? Or that this labour has been on the whole profitable, and its history the history of an effort neither contemptible nor unrewarded? There is no one who does not prefer the second; and those who seem to have abandoned it in favour of the first have done so not from conceit but from disappointment. They have tried to see the history of thought as a history of achievement and progress; they have failed; and they have deserted their original assumption for another which no one, unless smarting under that experience, could contemplate without ridicule and disgust.

Yet it is surely in such a crisis as this that we should be most careful in choosing our path. The natural scientist, beginning with the assumption that nature is rational, has not allowed himself to be turned from that assumption by any of the difficulties into which it has led him; and it is because he has regarded that assumption as not only legitimate but obligatory that he has won the respect of the whole world. If the scientist is obliged to assume that nature is rational, and that any failure to make sense of it is a failure to understand it, the corresponding assumption is obligatory for the historian, and this not least when he is the historian of thought.

So far from apologizing, therefore, for assuming that there is such a thing as the tradition of philosophy, to be discovered by historical study, and that this tradition has been going on sound lines, to be appreciated by philosophical criticism, I would maintain that this is the only assumption which can be legitimately made. Let it, for the moment, be called a mere assumption; at least I think it may be claimed that on this assumption the history of philosophy, properly studied and analysed, confirms the hope which I expressed in the first chapter: that by reconsidering the problem of method and adopting some such principles as are outlined in this essay, philosophy may find an issue from its present state of perplexity, and set its feet once more on the path of progress.