Polytropy

Our environment may influence our feelings, but what we make of those feelings is up to us. Thus we are free; we are not constrained by some fixed “human nature”—or if we are, who is to say what its limits are?

Insofar as we humans have come to recognize our freedom, we have apparently done so after thinking that what we did depended on our class—our kind, our sort, even our “race.” We might distinguish three stages of thought about ourselves.

Universal:

We are all the same.

Classificatory:

We are the same within classes, which differ from one another.

Individual:

We all differ from one another.

One might pass through these stages in either order. The classificatory stage is but a way station. This does seem to mean that racism can be progress, just as nationalism may be progress over petty local rivalries, or rising up against injustice may be progress, even though you attack the wrong targets. But the progress then is incomplete. For one thing, how can any particular classification of humanity be definitive, once for all?

Being itself an exercise in individual freedom, this blog has taken up freedom as a subject more than once, notably in “Thales of Miletus.”

R. G. Collingwood spells out the meaning of freedom in “The Principles of History,” published posthumously in The Principles of History and Other Writings in Philosophy of History (1999). Dated February 20, 1939, the following is from § 4, called “Nature as Environment,” of Chapter 3, “Nature and Action”; the bold emphasis, here and later, is mine, to help the reader avoid reading all of my lengthy quotations in their entirety.

I do not doubt, again, that the purely physical effects produced in man’s organism by its physical environment are accompanied by corresponding effects in his emotions and appetites; although this is a subject on which information is very difficult to procure, because what has been written about it has mostly been written by men who did not understand the difference between feelings and thoughts, or were doing their best, consciously or unconsciously, to obscure that difference …

It is not nature as such and in itself (where nature means the natural environment) that turns man’s energies here in one direction, there in another: it is what man makes of nature by his enterprise, his dexterity, his ingenuity, or his lack of these things …

That historically we have come to recognize our freedom through racism is an argument of Collingwood’s Idea of History (1946). The key figure is Herder, subject of § 2 of Part III, “The Threshold of Scientific History,” of The Idea of History. I shall be quoting that section several times, using pilcrows to indicate Collingwood’s new paragraphs:

¶ Herder, so far as I know, was the first thinker to recognize in a systematic way that there are differences between different kinds of men [sic], and that human nature is not uniform but diversified. He pointed out that what makes Chinese civilization, for example, what it is cannot be the geography and climate of China but only the peculiar nature of the Chinese. If different kinds of men are placed in the same environment, they will exploit the resources of that environment in different ways and thus create different kinds of civilization.

To say that different persons may exploit their environments differently is not objectionable; different kinds of persons, is objectionable. Collingwood continues his summary of Herder’s ideas, introducing anthropology (a theme of my last post):

The determining fact in history, therefore, is the special peculiarities not of man in general but of this or that kind of man. These special peculiarities Herder regarded as racial peculiarities: that is, the inherited psychological characteristics of the varieties of the human species. Herder is thus the father of anthropology, meaning by that the science which (a) distinguishes various physical types of human beings, and (b) studies the manners and customs of these various types as expressions of psychological peculiarities going with physical ones.

To be precise, anthropology in this sense has two “absolute presupposions”:

1. That we come in various physical types, hence psychological types.

2. That our manners and customs are expressions of these types.

Absolute presuppositions as such are the subject of An Essay on Metaphysics (1940); but the lectures that became Parts I–IV of The Idea of History were first written and delivered as lectures in 1936 (revised and repeated in 1940). I understand that there are also different schools of anthropology; the differences may then be traced to absolute presuppositions.

Collingwood gives credit where it is due:

¶ This was an important new step in the conception of human nature, because it recognized that human nature was not a datum but a problem: not something everywhere uniform, whose fundamental characteristics could be discovered once for all, but something variable, whose special characteristics called for separate investigation in special cases.

He avoids giving more credit than is due:

But even so, the conception was not a genuinely historical one. The psychological characteristics of each race were regarded as fixed and uniform, so that instead of the Enlightenment’s conception of a single fixed human nature we now have the conception of several fixed human natures. Each of these is regarded not as an historical product but as a presupposition of history. There is still no conception of a people’s character as having been made what it is by that people’s historical experience; on the contrary, its historical experience is regarded as a mere result of its fixed character.

¶ At the present time, we have seen enough of the evil consequences of this theory to be on our guard against it. The racial theory of civilization has ceased to be scientifically respectable. To-day we only know it as a sophistical excuse for national pride and national hatred …

I have not read Herder for myself. The article on him by Michael Forster in the Stanford Encyclopedia of Philosophy has an elaborate defense. As above, so below, bold emphasis in the quotation is mine, except for the bibliographical reference HPW to J.G. Herder: Philosophical Writings (Cambridge University Press, 2002), edited and translated by Forster himself. In his SEP article, he formulates a kind of conservatism:

Concerning international politics, Herder has often been classified as a “nationalist” or (perhaps even worse) a “German nationalist” (for example, by R. R. Ergang in Herder and the Foundations of German Nationalism [1931] and K. R. Popper in The Open Society and its Enemies [1945]). Some other philosophers from the period deserve such a characterization (for instance, Fichte). But where Herder is concerned it is deeply misleading and unjust. On the contrary, like Kant’s, his fundamental position in international politics is a committed cosmopolitanism, an impartial concern for all human beings. This is a large part of the force of his ideal of “humanity”. Hence, for example, in the Letters for the Advancement he approvingly quotes Fénelon’s remark, “I love my family more than myself; more than my family my fatherland; more than my fatherland humankind” (HPW 389). Moreover, Herder’s cosmopolitanism is arguably purer than Kant’s. Kant’s is undermined by various prejudices that he harbors—in particular, racism, antisemitism, and misogyny (Kleingeld 2013). By contrast, Herder’s is free of such prejudices, which he indeed worked tirelessly to combat.

Herder does also insist on respecting, preserving, and advancing national groupings. However, this is entirely unalarming, for the following reasons: (1) For Herder, this is emphatically something that must be done for all national groupings equally—not just or especially Germany! (In the Letters for the Advancement he emphatically rejects any such notion of a “favorite people [Favoritvolk]”, as he puts it [HPW 394].) (2) The “nation” in question is not racial but linguistic and cultural (in the Ideas and elsewhere Herder indeed criticizes and rejects the very concept of race). (3) Herder does not seek to seal off nations from each other’s influence or to keep them static; he regards inter-linguistic and -cultural exchange and linguistic-cultural development as normal and welcomes them. (4) Nor does his commitment to national groupings involve a centralized, militarized state (in the Ideas and elsewhere he strongly advocates the disappearance of such a state and its replacement by loosely federated local governments with minimal instruments of force). (5) In addition, his insistence on respecting national groupings is accompanied by the strongest denunciations of military conflict, colonial exploitation, and all other forms of harm between nations; a demand that nations instead peacefully cooperate and compete in trade and intellectual endeavors for their mutual benefit; and a plea that they should indeed actively work to help each other.

Moreover, Herder has compelling reasons for this insistence on respecting national groupings: (1) The deep diversity of values between nations entails that homogenization is only a fantasy: non-existent and impracticable. (2) Such diversity also entails that, to the extent that it is practicable, it cannot occur voluntarily but only through external coercion. (3) In practice, attempts to achieve it, for example, by European colonialism, are moreover coercive from, and subserve, ulterior motives of domination and exploitation. (4) Furthermore, real national variety is positively valuable, both as affording individuals a vital sense of local belonging and in itself.

Indeed, Herder’s pluralist cosmopolitanism is an important and attractive alternative to the homogenizing forms of cosmopolitanism, based on delusions concerning either the fact or the prospect of universally shared values, that have predominated since the Enlightenment and are still popular today, both among philosophers (especially in the Anglophone world) and in international political organizations such as the United Nations.

Compare a recent tweet from The American Conservative (linked to a 2003 article):

“The belief that democratic institutions, behavior, and ways of thought can be exported and transplanted to societies that have no traditions of them is a profoundly unconservative, indeed a radical, belief.”

—The American Conservative (@amconmag) October 19, 2019

The position that Forster ascribes to Herder may be defensible; but it cannot logically be Herder’s, by Collingwood’s account in The Idea of History, III.2:

¶ It would be possible to defend [Herder] by arguing that his theory of racial differences does not in itself give any ground for believing in the superiority of one race over another …

¶ But this would not be a legitimate interpretation of Herder’s thought. It is essential to his whole point of view that the differences between the social and political institutions of different races are derived not from the historical experience of each race but from its innate psychological peculiarities, and this is fatal to a true understanding of history … Once Herder’s theory of race is accepted, there is no escaping the Nazi marriage laws.

If Forster would have a counterargument, I’m not sure it could be based on his article, according to which:

Herder’s theories of interpretation and translation both rest on a certain epoch-making insight of his: Whereas such eminent Enlightenment philosopher-historians as Hume and Voltaire had normally still held that, as Hume put it, “mankind are so much the same in all times and places that history informs us of nothing new or strange” (1748: section VIII, part I, 65), Herder discovered, or at least saw more clearly than anyone before him, that this was false, that peoples from different historical periods and cultures vary tremendously in their concepts, beliefs, values, (perceptual and affective) sensations, and so forth. He also recognized that similar, albeit usually less dramatic, variations occur even between individuals within a single period and culture. These positions are prominent in many of Herder’s works (see, e.g., On the Change of Taste [1766], This Too a Philosophy of History, and On the Cognition and Sensation). Let us call them together his principle of radical mental difference.

… Herder also refers to the second half of his doctrine of radical mental difference—individual variations in mode of thought even within a single period and culture—as a source of the need for psychological interpretation …

None of this contradicts Collingwood’s contention that, for Herder, our natures are fixed; Forster indeed seems to confirm it and to agree with Herder:

Finally, Herder’s ethical theory is important not only for what it includes but also for what it omits. In particular, he shows little interest in the issue of free will, hardly ever if at all implying that such a thing exists or that it is a precondition of moral responsibility … This position contrasts sharply with that of most modern moral philosophers, including Hume and Kant, for example. However, it looks much less idiosyncratic if one takes a broader perspective and notices, for instance, that neither the earlier Greeks (e.g., Homer) nor the Chinese ethical tradition have [sic] had any conception of free will or any inclination to think that such a thing is required for moral responsibility. Moreover, I would argue that Herder’s position here, like that of these other traditions, turns out to be a great virtue, since the very conception of free will and of morality’s dependence on it, which has dominated western philosophy and religion since late antiquity, turns out to be thoroughly misbegotten.

Thus ends Forster’s account of Herder’s moral philosophy. I don’t know what to make of the parenthesis represented above by the dots of ellipsis:

(Freedom in the sense of a sort of autonomy, or flexibility, that exists within the limits of laws of nature and merely amounts to a certain liberty from constraint by narrow instincts and political freedom are another matter; he is interested in these.)

That there is no such “flexibility” is a presupposition of natural science. At least before the twentieth-century advent of probabilistic laws, what scientist would call off the search for laws of nature, before they were found to determine everything to the last detail? History is in fundamental conflict with natural science, because man is distinct from nature. We shall come back to this.

Maybe Herder was too early to know the deterministic dream of science. His dates are 1744–1803, and Laplace describes only in 1814 an intellect (“Laplace’s demon”) that can compute the future of the universe from its present state; however, Roger Joseph Boscovich seems to have formulated a similar determinism in 1758.

In the main passage, I don’t know how Forster thinks Herder separates freedom from responsibility. In “Antitheses,” I argue that responsibility without freedom is incoherent, though Sabine Hossenfelder says we have it. Am I supposed to explain this apparently agreement of Herder and Hossenfelder by observing that both are German? Forster himself is cosmopolitan in background, having studied in the UK, Germany, and the US; holding American, UK, and Irish citizenship; and now being based in Germany, though still visiting the US annually.)

Collingwood concludes his own account of Herder thus (I am adding the bullets along with the pilcrow):

¶ The problem which Herder bequeathed to his successors, therefore, was the problem of thinking out clearly the distinction between nature and man:

• nature as a process or sum of processes governed by laws which are blindly obeyed,

• man as a process or sum of processes governed (as Kant was to put it) not by law simply but by consciousness of law.

It had to be shown that history is a process of this second type: that is to say, that the life of man is an historical life because it is a mental or spiritual life.

“It had to be shown that history is [such] a process”; that is, this had to be discovered as an absolute presupposition of doing history as a science.

I am left with the question of whether to read Herder himself. The Idea of History provokes such questions, since the book is Collingwood’s review of how historians since Herodotus have done history, and I have read few of those historians. This may be why The Idea of History is the book of Collingwood’s that I have spent the least time with, though it did move me in 2013 to write a post called “Psychology,” during a reading of Herodotus.

The Idea of History is “undoubtedly Collingwood’s best known book,” according to Jan van der Dussen in his Preface to the Revised Edition (1994).

Though formally trained in graduate school only as a mathematician, I declare that I have become also an historian of ancient Greek mathematics. What I have to show of my work includes:

1. “Abscissas and Ordinates,” Journal of Humanistic Mathematics 5 (2015), no. 1, pages 233–264.

2. “Thales and the Nine-point Conic,” The De Morgan Gazette 8 (2016), no. 4, 27–78.

3. “The Geometry of Numbers in Euclid,” this blog, January 2, 2017, reposted in The De Morgan Forum.

4. “On Commensurability and Symmetry,” Journal of Humanistic Mathematics, Volume 7, Issue 2 (July 2017), pages 90–148.

5. “Euclid Mathematically and Historically,” colloquium talk in the Department of Mathematics, Bilkent University, Ankara, Wednesday, March 7, 2018, 3:40–4:30 p.m.

6. “Elliptical Affinity,” this blog, April 17, 2019.

7. “Ratio Then and Now,” invited talk at Model Theory and Mathematical Logic: Conference in honor of Chris Laskowski’s 60th birthday, University of Maryland, College Park, June 21–3, 2019.

I include the Bilkent talk in my list, because ideas that I talked about (which are seen also in “The Geometry of Numbers in Euclid”) seem to have ended up in the introduction of the Turkish translation of Euclid by the person who had invited me to Bilkent.

My historical work has been addressed mainly to mathematicians, and it has been published (when it has been) in journals edited by mathematicians. Nonetheless, by studying Euclid’s theory of numbers, I have come to believe that mathematicians working today do not understand it, because of our habit of immediately translating what we read into our own terms. Historians have trouble for a different reason, namely not being mathematicians.

Mathematicians turn history into a story, a myth, useful for our mathematics, as Michael Spivak confesses in beginning A Comprehensive Introduction to Differential Geometry (Houston: Publish or Perish, 1979; numeration and formatting mine):

There are two main premises on which these notes are based …

1. it is absurdly inefficient to eschew the modern language of manifolds, bundles, forms, etc., which was developed precisely in order to rigorize the concepts of classical differential geometry …

2. in order for an introduction to differential geometry to expose the geometric aspect of the subject, an historical approach is necessary …

Of course, I do not think that one should follow all the intricacies of the historical process, with its inevitable duplications and false leads. What is intended, rather, is a presentation of the subject along the lines which its development might have followed; as Bernard Morin said to me, there is no reason, in mathematics any more than in biology, why ontogeny must recapitulate phylogeny. When modern terminology finally is introduced, it should be as an outgrowth of this (mythical) historical development.

Spivak’s aim is the understanding of mathematics; the historian’s, of ourselves, at least by Collingwood’s account. Mathematics taught as a liberal art may then be history; but history in which one will learn, as much as one can, the meaning of truth in mathematics, as discussed in the previous post.

I am not trained as an historian; but I am trained in the liberal arts, so to speak, by having spent four years at a college where everybody reads the same great books, by choice, out of conviction or faith that they are worth reading. Classes are discussions around a table, possibly concerning the mathematical argument that a student has made at the blackboard.

According to the Editor’s Introduction to The Idea of History, Collingwood planned, and partially completed, three series of books:

1. Philosophical Essays:

   • An Essay on Philosophical Method (1933),

   • An Essay on Metaphysics (1940);

2. Philosophical Principles:

   • The Principles of Art (1938),

   • The Principles of History;

3. Studies in the History of Ideas:

   • The Idea of Nature,

   • The Idea of History.

On the manuscript of The Principles of History, Collingwood left a note to his wife, authorizing her to publish it

with a preface by yourself explaining that it is a fragment of what I had, for 25 years at least, looked forward to writing as my chief work.

He had looked forward to writing it; but then came the war with Germany, and it was more urgent to respond directly to fascism and nazism with the New Leviathan.

I recall Casaubon’s “Synoptical Tabulation for the use of Mrs Casaubon” in Chapter XLIX of George Eliot’s Middlemarch. Mrs Casaubon was supposed to complete her late husband’s life work, the “Key to All Mythologies.” She wrote a response in Chapter LIV:

I could not use it. Do you not see now that I could not submit my soul to yours, by working hopelessly at what I have no belief in—Dorothea?

Collingwood’s widow left publication of her late husband’s remaining work to Oxford University Press, which chose Collingwood’s former student T. M. Knox to make a selection. He edited Collingwood’s drafts and notes into the last two books on the list above. Parts of what Collingwood had intended for The Principles of History ended up in The Idea of History. The remaining parts were thought lost when van der Dussen edited the 1994 Revised Edition, but were discovered in 1995 in the archives of the Oxford University Press. They were published in The Principles of History and other Writings in the Philosophy of History, edited by van der Dussen and W. H. Dray, in 1999.

I have gone mainly to that 1999 publication (if not to An Autobiography) when I want to think about history. Now, as I said, I am reminded of the value of The Idea of History.

The book started out as lectures. The Introduction lends itself to summary, and I engage in this now.

By the philosophy of history,

• Voltaire meant critical or scientific history, in which the historian makes up their own mind about things;

• Hegel meant universal or world history;

• positivists meant discovering laws of history.

Collingwood will work out what he means. Philosophy is thought about thought.

• The historian thinks about the past.

• The psychologist thinks about the historian.

• The philosopher thinks about the relation between the historian and the past.

For example, the psychologist may

argue that historians are people who build up a fantasy-world, like artists, because they are too neurotic to live effectively in the actual world, but, unlike artists, project this fantasy-world into the past because they connect the origin of their neuroses with past events in their own childhood and always go back and back to the past in a vain attempt to disentangle these neuroses. This analysis might go into further detail, and show how the historian’s interest in a commanding figure such as Julius Caesar expresses his childish attitude to his father, and so on.

Collingwood does not dismiss such analysis of the historian’s thought, but notes the lack of any concern for the object of the thought.

Thought in its relation to its object is not mere thought but knowledge; thus, what is for psychology the theory of mere thought, of mental events in abstraction from any object, is for philosophy the theory of knowledge. Where the psychologist asks himself: How do historians think? the philosopher asks himself: How do historians know?

The distinction here between thought and knowledge, and the idea of an object of thought, will give way in An Essay on Metaphysics to the distinction between feeling and thought, and the idea of criteria for thinking well.

Philosophy has historically had foci:

• In ancient Greece, the foundations of mathematics;

• in the Middle Ages, relations of God and humanity;

• from the sixteenth to the nineteenth centuries, the foundations of natural science.

However,

in the eighteenth century people began thinking critically about history, as they had already learnt to think critically about the external world, because history began to be regarded as a special form of thought, not quite like mathematics or theology or science.

A special technique of history was not worked out till the nineteenth century. The inquiry into this technique is the philosophy of history, in the sense of The Idea of History. The inquiry will have two stages, working

1. first with history in isolation,

2. then to relate the results to others (as natural science led the way from syllogistic logic to the methods of Descartes and Bacon, and from medieval theology to that of Descartes and Spinoza).

The Idea of History will remain at the first stage. We have to investigate, of history, its

1. nature,

2. object,

3. method, and

4. value.

To do this, we have to be both

• historians and

• philosophers.

Being the former is more important. Everybody may learn some history in school; however, this history is

• superficial,

• out of date, and

• possessed of an illusory finality.

Such concerns lead to the notion of scientific persecution in Chapter I of the New Leviathan. As for the four questions about history:

1. History is an attempt to answer questions that we ourselves raise: thus, a science.

2. The object of history is “res gestae: actions of human beings that have been done in the past.”

3. History interprets evidence, particularly documents.

4. History is for self-knowledge. “Knowing yourself means knowing what you can do; and since nobody knows what he can do until he tries, the only clue to what man can do is what man has done.”

I said Collingwood started with Herotodus. Actually he starts with a Sumerian inscription from the third millenium bce:

A dispute arises between the kings of Lagash and of Umma about the boundaries of their respective territories. The dispute is submitted to the arbitration of Mesilim, king of Kish, and is settled by the gods, of whom the kings of Kish, Lagash, and Umma are merely the agents or ministers:

Upon the truthful word of the god Enlil, king of the territories, the god Ningirsu and the god Shara deliberated. Mesilim, king of Kish, at the behest of his god, Gu-Silim, … erected in [this] place a stela. Ush, isag of Umma, acted in accordance with his ambitious designs. He removed Mesilim’s stela and came to the plain of Lagash. At the righteous word of the god Ningirsu, warrior of the god Enlil, a combat with Umma took place. At the word of the god Enlil, the great divine net laid low the enemies, and funerary tells were placed in their stead in the plain.

Collingwood quotes the passage as transcribed by Monsieur Charles F. Jean in European Civilization (1935), edited by Edward Eyre. He quotes also Jean’s observation, “Historiography is represented by official inscriptions” such as this.

“I take him to mean that this kind of thing is not really history,” says Collingwood, “but is something in certain ways resembling history”; and he agrees.