Unity and Antinomy
This piece was originally published on 03/08/20
Classification conceals as much as it reveals — differences between classes are brought into relief, while differences within classes are concealed. Indeed, minimising differences within classes is how mathematical techniques like k-means clustering work. Thus any classification will have strengths and weaknesses; the question is whether those strengths and weaknesses complement our other methods of analysis.
K-means clustering seeks to minimise the distances between points in a cluster and the mean of that cluster, for a given number of clusters
To some extent, we have to classify; we have to find a way to give structure to our information in order to make sense of it. As historians, we divide the past up into centuries and nations; we think about British imperial policy in the 19th century, or Italian art in the quattrocento. Yet while we use these framings of the past, we simultaneously rebel against them; we talk about the long 19th century, or remember how the century as a unit of historical measurement was more or less invented by the Lutheran ‘Centuriators of Magdeburg’ in the 1620s, or remind ourselves of the complex connections between the ‘Italian’ and ‘Dutch’ ‘Renaissances’. Perhaps a classification is only as useful as the disagreements it provokes.
“The fox”, according to the Greek poet Archilocus, “knows many things, but the hedgehog knows one big thing.” Isaiah Berlin saw in this parable a means of classifying all thinkers:
“For there exists a great chasm between those, on one side, who relate everything to a single central vision, one system, less or more coherent or articulate, in terms of which they understand, think and feel — a single, universal, organising principle in terms of which alone all that they are and say has significance — and, on the other side, those who pursue many ends, often unrelated and even contradictory, connected, if at all, only in some de facto way, for some psychological or physiological cause, related to no moral or aesthetic principle.”
Berlin, as was his custom, took this opportunity to display his breadth of reading:
“in this sense, Dante belongs to the first category [hedgehogs], Shakespeare to the second; Plato, Lucretius, Pascal, Hegel, Dostoevsky, Nietzsche, Ibsen, Proust are, in varying degrees, hedgehogs; Herodotus, Aristotle, Montaigne, Erasmus, Molière, Goethe, Pushkin, Balzac, Joyce are foxes.”
The point of making this classification, I think, is twofold:
It gives us a shorthand, a heuristic, for understanding the work of these thinkers. If they are a hedgehog, then we can find a common thread in their work which can represent the whole; if they are a fox, then we can use any individual contrasts within that work to demonstrate the non-existence of such a thread.
It groups thinkers together, inviting comparison between them. Once we know that Proust and Dante are both hedgehogs, we might ask what else they have in common.
If we had used a supervised learning algorithm rather than a Greek fable to do the classification, then we might also wonder what the classes had in common; might this combination of factors speak of some deeper structure in the dataset? No individual pixel can tell us whether a picture is a cat or a dog; but a neural network can identify the combinations of edges which can be used to classify the images. In the same way, an analysis of consumer behaviour might identify groups of customers who may not seem to have much in common, but turn out to be more or less likely to buy a product.
Another way, inspired by Berlin, of classifying thinkers (or even individual works) would be to think about antinomies: contradictory laws. Is it the case that at the heart of some works there is a unity, and at others, an antinomy? Some books seek to draw connections; others, contrasts. The third book of Cicero’s On Duties argues that what is expedient is also just, and vice versa; that is, the best possible outcome is achieved by acting in accordance with law and morality. There is a fundamental unity between the two concepts. Richard Cobden believed that a single principle, free trade, could unite and solve not just the world’s economic problems, but also its moral conflicts:
“I see in the Free-trade principle that which shall act on the moral world as the principle of gravitation in the universe, — drawing men together, thrusting aside the antagonism of race, and creed, and language, and uniting us in the bonds of eternal peace… I believe that the speculative philosopher of a thousand years hence will date the greatest revolution that ever happened in the world’s history from the triumph of the principle which we have met here to advocate.”
The benefits of Free Trade, from LSE British Political Posters 1905–1910
Cobden was a hedgehog too — but the same judgment might be made of his protectionist opponents. Both were in some sense extremists. The difference was that Joseph Chamberlain and the other Tariff Reformers perceived an opposition between the interests of imperial powers, whereas in free trade Cobden saw a chance for convergence.
Early scholastic philosophy sought to resolve disagreements between authorities in order to find a basic truth: non adversa, sed diversa (not opposite, but different); the title of the greatest work of the twelfth century, Gratian’s Concordia discordantium canonum (the Concordance of Discordant Canons), tells you everything you need to know.
In contrast, William of Ockham’s use of the Augustinian concepts of divine and human law, ius poli and ius fori, demonstrates that the two can be in opposition: it is possible for a cheat to lawfully own property according to human law, and yet for him to have it unjustly in the eyes of God. The difference between divine and human law lies at the heart of Ockham’s political thought. Reading Machiavelli’s il Principe and Discorsi presses the reader to accept the incompatibility of the classical and Christian ideals. Machiavelli’s work is characterised by conflict in another sense. Most classical thinkers, including Cicero, would have agreed with Sallust that nam concordia parvae res crescunt, discordia maxumae dilabuntur (while small things grow from harmony, even the greatest will be destroyed by discord.); yet Machiavelli wrote in the Discorsi that “all the laws made in favour of liberty are born of the disunity between [the leading men and the ordinary citizens]”. Machiavelli, then, saw disagreement as the root of civic flourishing: non concordia, sed adversa.
Brother Ockham, from a 1341 manuscript
This approach produces a different partition to that of the hedgehog and the fox. One can use a contradiction to explain a wide range of phenomena, and thus be an antinomian hedgehog. Perhaps you divide the world into the spiritual and the temporal, or understand things using taqlid or ijtihad, but never both. Marx, that supreme hedgehog, saw the history of the world as the history of class conflict.
Such a division shouldn’t be the first way we come to understand thinkers; but if it is a valid division at all, and cuts thinkers in a novel way, then it may prompt us to reassess what we think we know about the giants of the past — and our own thinking.
A surprising consequence of being an antinomian (until I come across my own ancient parable!) fox is that one has to reject, or at least qualify, some commonly held truths. Is consistency really key? As mantras go, only ‘hard work pays off’ is more incontestable; but perhaps we shouldn’t be consistent all the time (and thus perhaps be consistent none of the time). If solving problems requires a range of approaches and greatness comes from conflict, then change should be embraced and planned for. As Sir Humphrey Appleby loved to remind us, tempora mutantur et nos mutamur in illis - times change, and we change with them.