The excluded middle

The law of the excluded middle may be succinctly stated as

A v -A

that is, either A or not A, where ‘A’ stands for some proposition such as ‘Socrates is mortal’. That should be in a nice chunky font with the correct symbols. The devil is in the ‘or’, and the one logicians usually mean is the exclusive or: you can’t have it both ways. Socrates took the hemlock, and died. QED.

Beginning students of logic commonly find this hard to digest. It is a poor representation of the way we usually think and argue. When it comes to mortal questions (to borrow from Thomas Nagel’s title), we tend to see in black and white. Either something is wrong or it is right; a person is a man or a woman; a person is black or white. Our world is made up of structural oppositions: the raw and the cooked. The black that excludes every shade of grey doesn’t even exist. It doesn’t help to say that it emits no photons. For the Chinese, this is a calligraphic axiom, or aphorism: black writing on white paper.

I have recently encountered my own philistine impatience with the dry preoccupations of analytic philosophy anew in Oswald Wiener, whose vituperative and obscene novel, with an English translation in the works, takes aim at Wittgenstein, both early and late. Perhaps the nub of the frustration is the sense that philosophy has become scholastic, turning away from all important problems. I’m no philosopher, but the other way to see this is that philosophy north of the English Channel, starting with Kant, is deflationary. That’s a term with a specific epistemological Sitz im Leben, but I take it as emblematic of a certain humility, expressed in Kant’s metaphor of the Wohnhaus, reason’s homely abode (I can’t remember whether this comes in the Preface or the Introduction to the first Critique). It’s no good answering those large questions if the foundations are unsound. That being recognised, there is an obligation to avoid pronouncing on them. There was nothing humble, though, about the tone of voice in which that was first asserted at Oxford a century ago.

Much of the basis on which we lead our lives is false, but we require those fictions to live at all, just as Hume said he needed faith to drink a glass of water. How, for example, can we ever trust another person? To do so relies on a presumption of good faith, or perhaps simply goodness, that invites refutation by experience, and calls for the blind eye. The world is grey, but we must pretend it is black and white to make it intelligible.

The origin of the idea of structural oppositions lies with Saussure: phonology is the logic of the sounds in a language according to the distinctions it deems to be salient, in order that man may speak intelligibly. This is especially clear when it comes to vowels, which are formed by positioning tongue and jaw across a continuum of available space. A is not A in proportion as it matches certain criteria (for example, if the tongue is a certain number of millimetres from the palate) but by virtue of not being E. The line between them is an indistinct border region that is in fact unfenced. The native speaker (barring interference from surrounding consonants, always present, but we must avert our gaze from it) aims for the middle of the correct region, but achieves idiomatic fluency not by hitting one spot, but by staying as far away from the edges as may be. This is different from playing the violin, but it feels the same: it’s very hard as a foreigner to get it right, but effortless for those born to it. The temptation (to take a different example) is to fudge the distinction between long and short by aiming at the border, but you must articulate it with conviction (as in Italian, or Finnish, or for that matter, Latin); this is hidden from English speakers because distinctions of length generally coexist with differences of quality.

Language spoken idiomatically gives an impression of well-tempered rightness, with everything in its place, like a familiar domestic setting. Moving to the higher level of (I suppose) syntax shows how much fiction is woven into that sense. If one attempts to accurately transcribe recorded speech, it disintegrates into a concatenation of false starts and mumbles. There is no single level of accurate transcription, as opposed to the tidied up version. When linguists make such transcriptions, the level of detail will depend on their purpose. Anyone who has tried it with a tape recorder knows just how hard that is.

A squirrel just raced across my lawn, and probably up a tree, a perfect sine wave rippling through it as its mode of locomotion in the horizontal plane. That is its nature, one thing visible to us that it knows superlatively well; as the spider weaves her web, and as we do the sort of thing I have been trying to write about. Dogs can see it too, and it commonly enrages them: that sinuosity cries out to be expunged, if only it could be caught before the tree. Sometimes when I am cycling I almost run over a squirrel, transfixed by frisky indecision.

But the world is not structured like a language; we are. There is blindness in that, and it cannot be cured by philosophy averting its gaze.

Medicine (doesn’t work)

Early on, my doctoral supervisor returned a draft to me with a red line through an entire section, headed “Methodological considerations”. We didn’t discuss it, but I took him to mean: just do it, and cut out the huffing and puffing. In another institution I won’t name, I experienced the opposite, more usual approach. There is meant to be an Aristotelian inevitability to the marriage of theory, method and matter, rigorously demonstrated. The result is generally uncontroversial and pedestrian. Jim did give us his thoughts on creative method, though — a slightly different question. Some plan in outline, others write “generatively”, that is, they just start writing and knock it into shape as they go.

I have what should probably be called a journal, with its origins in the diary I kept as a young man. At some point I lost the sense that what I wrote about my own life was sufficiently honest or penetrating to be worth the trouble, but I have sporadically continued to write about things of the kind that also appear here. My only readers are accidental ones, but nonetheless, these thoughts are more lucidly expressed, and mean to be more engaging, than what I put down for my own eyes alone, which are losing their acuity. Certain preoccupations return, indeed, with roots in my own unremarkable life. An intellectual focus itself tends towards objectivity, or generality. If medicine “doesn’t work”, that isn’t a complaint about my own doctor.

But these posts are like light that catches one face of a crystal; they fall short of making up a whole. Recently I dipped into Leopardi’s notebook, the Zibaldone, meant for his own use alone, which is still quite discursive; and interesting for its detail. He believed, following Locke, that the mind’s capacity for talent is a unitary quality, no different in the mathematician or the poet; so one could with application become the other, and might just as well have turned out a musician. The key is the capacity to form habits. This may not be a fair account of his theory; but you don’t have to agree with it to delight in the fine observation and psychological persuasiveness of the examples he gives. Then on the next page, he is talking about Horace’s style, or the derivation of Italian dialect words.

What struck me is the examples are meant to support the theory, and yet they don’t have any power to unsettle it; it just sits on top, like a cut glass chandelier illuminating the furniture below. But Leopardi isn’t dogmatic, on the contrary, his mind sparkles with freshness and independence. This is both an example of my own theory, and perhaps of the dangers of theories. Our rational justifications for things such as social practices (slavery, democracy, witchcraft trials) just sit on top. It’s a commonplace that modern medicine works because of its sound empirical basis. We have thrown out leeches along with the four humours. Smoking, like masturbation, is bad for you (doctors used to recommend it, less than a century ago). I hardly need to spell it out.

The trouble is that I can’t. All this, put together into an argument, is not even original; though I dare say it puts me in company I wouldn’t gladly choose. All that remains is misanthropy: we are such stupid, cruel creatures. To put it another way, though hardly with more optimism: rationality may be rare to vanishing, but it is still our cardinal moral obligation.

Memnosyne

Memory is the mother of the Muses. The ancient world bequeathed to the Middle Ages the legacy of mnemotechnic. These methods seem arid and laborious to us; it must have been the printing press that did for them. When you learn something by heart, you make it your own. But there are vestiges: times tables, amo amas amat. Music would be quite inconceivable without impregnating the fingers with memory. The Chinese must still learn characters by their thousands. On that base stands literature and civilisation.

The Person from Porlock interrupted — was it Coleridge? I can’t remember — writing about Kubla Khan, and by the time his tedious business was done, inspiration was banished. I think there’s a poem by Browning about it. Porlock is the evil twin of serendipity. The muse will not come out when bidden, but can be tamed with regularity, like a cat with saucers of milk. You must give her good store.

The Person from Porlock yesterday was a meteorogical interruption to regularity. Because of the rain yesterday afternoon, I did not go to the library and my books; therefore, I put off posting here till after lunch. And it was gone. It would have been good, I promise.

There is a silver lining, perhaps. If I can work those rough thoughts up into something, it may be more substantial. They are intriguing, like the fragments of Stesichorus. For example: “medicine — doesn’t work”. Indeed not, but I don’t think that was what I meant.

Showing my working: the spur of this post was in the notes on this bit of Theocritus:

... αἴ κά μοι τὺ φίλος τὸν ἐφίμερον ὕμνον ἀείσῃς.
κοὔτί τυ κερτομέω. πόταγ᾽ ὦγαθέ: τὰν γὰρ ἀοιδὰν
οὔτί πη εἰς ᾿Αίδαν γε τὸν ἐκλελάθοντα φυλαξεῖς.

The shepherd will give Thyrsis the fine cup he has just described, if (ai ka) he sings his fine song about Daphnis. Don’t mess me about, come on; you can’t take the song with you to Hades, who drives out memory. The loss of memory would be a particularly apt, or cruel, punishment for a singer or poet.