If anything at all comes to your mind when you think of analytic philosophy, it’s probably not the word ‘beauty’. Yet analytic philosophy has its own kind of beauty, akin to the beauty one finds in some poetry. Or so I shall attempt to argue.
Philosophy has always trafficked in beauty. The Platonic vision of the third realm of forms and the memorable cave analogy used to illustrate it; Spinoza’s austere deterministic God-cum-Nature and Hegel’s ever striving onward Geist are, among other things, aesthetically attractive pictures of the world. They capture our imagination; we behold them with the wonder Socrates said was the foundation of philosophy.
You would be forgiven for thinking that philosophy has abandoned the aim of appealing to our sense of beauty. If you’ve tried to read some recent analytic work, and you don’t have the appropriate academic background, you probably came away disappointed, thinking that dryness and technical hair-splitting has replaced the sweeping visions of the great thinkers of the past. More than likely though, you just haven’t tried; analytic philosophy isn’t a vital cultural force today. It’s not the sort of thing that non-specialists read.
While perhaps understandable, this is a shame. The very best contemporary work in philosophy ranks, in its imaginative sweep, with the very best work of all time. We have philosophers today who have the systematic and original visions of reality of the sort we associate with Plato, or with Spinoza, or with Hegel. My goal is to give a couple of examples of such visions, as well as to provide an explanation of wherein their aesthetic value lies.
You probably haven’t heard of Oxford philosopher Timothy Williamson. The holder of the most prestigious philosophy professorship in the UK, he would come near the top of most working philosophers’ lists of greatest living philosopher. He has written books on language, metaphysics, and epistemology, as well as hundreds of articles in the best journals. He is famous for being sharp as well as generous in discussion. His work abounds with formal logic and is written with great precision in a sombre, austere (OK, dull) prose style. And the vision of reality that emerges from his work is, I’ll argue, aesthetically on a par with the all-time greats.
He argues for extremely surprising conclusions. For example, consider his views on vagueness. Obama is 56. Is he old? What do you think? It seems kind of unclear. His 16 year old daughter Sasha is definitely not old. And his companion in the former presidents’ club George H.W. Bush, at 93, is definitely old. But Obama? We don’t want to say either that he’s old or that he’s not. And we don’t want to say it because we don’t think it’s true that he’s either old or not.
Examples of this sort abound. How many hairs must one have on one’s head to be bald? How many kilograms must I weight to be thin? There just don’t seem to be answers to these questions; language is vague in the sense sometimes it’s neither true nor false that something is a certain way.
But Williamson denies this: he thinks there are answers to these questions. Obama is either old or not old. There’s a certain number n of hairs such that if you have n+1 hairs you are not bald, but if you have n, you are bald. Ditto kilograms and weight.
It’s worth just pausing to think how weird this is. Oldness, baldness, and thinness seem to be gradual phenomena. They’re not things that just happens to a person. It seems absurd to ask exactly when Obama got old. It seems absurd to say he went to bed one night not old and woke up old. It’s equally absurd to ask at exactly what precise time Homer Simpson became bald, or what sad microsecond it was I ceased to be thin. But for Williamson these questions have precise answers.
Here’s another weird feature of Williamson’s theory of reality. Gandhi and Marilyn Monroe could have had a child together. That’s possible: unlikely, certainly, but it definitely possible. But that putative kid doesn’t exist, surely. No such child is to be found: if we make a list of all existing things, we’ll put me, this table, the sun, and so on, but no child. Williamson disagrees. An object exists which is possibly the child of that unlikely couple. If you tot up all the world’s furniture, you have to count it.
Why does Williamson think these weird things? He does so, at least in part, because his preferred theories of formal logic enjoin him to think them. I’ll explain what I mean by logic in a second, but we can think of it, preliminarily, as a formal mathematical theory. So he thinks formal mathematical theories underlie our all too human concerns about our age, or our weight, or what-could-have-been.
This, I’ll claim, is a poetic way of viewing the world. A school of poetry, as I’ll show (the so- and aptly- called ‘metaphysical’ poets and those whom they influenced) relied on yoking together ideas violently to achieve its effects. Thus T.S. Eliot, famously, began a poem by comparing surgery and the night sky:
Let us go then, you and I,
When the evening is spread out against the sky
Like a patient etherised upon a table
(T.S. Eliot, 'The Love Song Of J. Alfred Prufcock')
We should understand analytic philosophy in the same way. It also yokes together ideas of different sorts — the precise world of mathematical logic on the one hand, and the messily human realm of language use and what-could-have-beens that guide how we speak and think about the world — and it has, when seen this way, the same sort of beauty.
Analytic philosophy was born, more or less, with the development of new tools for logical analysis. Let me try to briefly explain what that means. We use language for many different purposes: to gossip, to persuade, to offend, to impress. And different languages are more or less good for different purposes. For example, English is a very good language for poetry, because it has a large vocabulary that permits a great deal of playfulness. It has a richness which, to use some stock examples, lets Shakespeare’s Macbeth, at that point guilt-laden from having murdered Malcolm, express the thought that he couldn’t wash the blood from his hands in the sea. Instead, his hands would turn the sea red:
My hands will rather…
The multitudinous seas incarnadine
(Macbeth Act 2, Scene 2, 58–60)
Where ‘incarnadine’ is a word which Shakespeare verbed from an Italian adjective meaning flesh-coloured, and the bumpy latinate ‘multitudinous’ suggests crashing waves. Or again:
Light thickens
And the crow makes wing to the rooky wood
(Macbeth, Act 3, Scene 2, 52–53)
Where ‘rooky’ is just plain old Anglo-Saxon ‘rook’ with a plain old Anglo-Saxon ‘y’ chucked on the end of it. Later writers, such as James Joyce, would exploit English’s poetic richness to and perhaps beyond breaking point in Ulysses and then Finnegans Wake.
But we don’t always want such expressive power. Joyce’s fellow Irish writer Samuel Beckett, for example, struggled with English. He wanted a simpler, less rich language, in which it would be easier to write, as he said, ‘without style’. French, he thought, was perfect for that, and that’s why Waiting For Godot was originally En Attendant Godot.
At the turn of the century, philosophers turned their minds to the development of a language good neither for expansive verbal fireworks, or the cramped dialogues of tramps, but for reasoning. Gottlob Frege and Bertrand Russell wanted to make a language apt for talking about and pursuing research in maths and science.
Natural languages, like English and French, aren’t perfect for this. The expressive richness that Shakespeare exploited holds them back. While being able to say the same thing in a bunch of ways is good for the poet, it’s confusing for the logician. Consider:
Obama is married
The former president is a married man
He (pointing at Obama) married.
All these sentences say pretty much the same thing, but they do so in such a variety of ways that it takes time to recognise this fact. The variety of English hinders our ability to discern when two sentences say the same thing, and this is a disadvantage for a precise scientific language.
But if English is sometimes too rich, it’s also sometimes too poor. Sometimes, a sentence has more than one meaning. Consider:
Every girl in the bar asked a guy to dance
This has two readings. On one, there’s one very popular guy who is the object of all the girls’ affections. On the other, there can be more than one guy: Alexandra can ask Zebediah to dance, Beth can ask Yuri to dance, and so on. Things can get confusing if we don’t attend to these ambiguities.
In light of these deficiencies, Frege and his followers tried to make an ideal language apt for reasoning, without the flaws of English or other natural languages. As we just saw, English has a bewildering array of expressions you can use to talk about objects like Obama, the differences between which are irrelevant. So in our ideal language, we abstract from that difference, and just have one type of expression that stand for objects, namely single roman letters. In our language, for example, we might have the following assignment of meaning to expressions, which is essentially (a part of) its dictionary:
‘a’ stands for Obama
‘b’ stands for Bush
‘c’ stands for Carter
Similarly, in English there’s a bewildering array of expressions you can use to say that an object is a certain way (married, in the above example). Again, these differences are irrelevant for scientific purposes, so again let’s get rid of them, and have just one type of expression that stands for ways things can be:
‘F’ picks out the things that are married
‘G’ picks out the things from Georgia
‘H’ picks out the things from Hawaii
So now note that all of the English ways of saying ‘Obama is married’ (‘the former president got married’, ‘He is a married man’ ‘Obama married someone’ and so on) now receive the nice clean translation ‘Fa’. Similarly, ‘Carter is from Georgia’ is simply ‘Gc’. Isn’t that much neater?
We can do the same thing for other parts of language. Take conjunctions like ‘and’ and ‘or’, modifiers like ‘not’, and conditionals (‘If blah then bloop’). We can introduce new symbols for them whose meaning you can work out from the below examples:
AND: Fa ∧ Gc = Obama is married and Carter is from Georgia
OR: Fa ∨ Gc = Obama is married or Carter is from Georgia
NOT: ¬Fa = Obama is not married
IF-THEN: Fa →Gc = If Obama is married, then Carter is from Georgia
We can introduce, moreover, ways to talk generally: not only about what Obama or Carter does, but about what everybody does, or some indefinite person does, as so:
SOME: ∃xFx= Someone is married
ALL: ∀xFx= Everyone is married
(Strictly speaking, these mean respectively some thing is married and every thing is married, but we can ignore that subtlety.) With this in mind, we can disambiguate our sentence about the possibly popular guy into these two different sentences (not bothering, strictly speaking, to translate ‘Girl’, ‘Boy’, and ‘Ask’ all the way down to a single letter, as would be proper):
∀x∃y Girl(x)→ Boy(y)∧ Ask(x,y)
∃x∀y Girl(x)∧ Boy(y)∧ Ask(x,y)
That’s helpful. We now have, more or less, the language known as the predicate calculus or logic, a clear, unambiguous language which can, as should be evident from the above, say quite a lot of things.
That’s not the end of the story, though. We’re concerned with reasoning — with getting new knowledge from stuff we already know. Now, putting your newly won knowledge to use, let’s introduce a new predicate ‘I’ which stands for the things which are from America, and consider these two arguments. On the left of ‘so’ we have the premise, and on the right, the conclusion:
Ha∧Gc so Ha
Gc so Ic
If you do the simple translation you should see the following: the sentence after ‘so’ follows from the sentences before the dot. Given the former, you can conclude the latter. But you might notice they do so in different ways. No matter what meaning we assign to H, G, a, and c, Gc will follow from Ha∧Gc. This doesn’t hold for the lower example. If we reassigned ‘I’ to stand for the things from Ireland, for example, it would no longer follow.
The mere form of the top inference guarantees its truth; not so for the latter. We can collect up all those inferences that are allowable merely in virtue of their form and from them figure out a series of rules of reasoning. Our first rule is that from an ‘and’ sentence like Ha∧Gc, one may conclude the left conjunct, and there are a series of other well understood rules governing the other expressions.
Now, as it so happens, from a very plausible looking set of such rules, which we can call classical logic, we can deduce the following, for any sentence p:
p∨¬p
Known as the law of excluded middle, it says that either Obama is tall or Obama is not tall, and Nairobi is in Kenya or Nairobi is not in Keyna, and …well, hopefully you see the pattern. Whatever you plug in for p, you get a truth, according to this law.
But now think about Obama and his age. While George HW Bush is old, Obama isn’t old. But nor Obama is not old, unlike, say, his daughter Sasha. So it seems we have to deny
Obama is old or Obama is not old
But that means that vagueness and our set of logical rules, classical logic, clash. The imprecision of the use of language and the precision of the logical realm are out of sync. Something has to give. Classical logic is simple, well-studied, and powerful. Our use of language, that there are vague terms, that seems hard to deny: it seems just like an obvious fact that there’s no fact of the matter about Obama’s oldness or not. What to do?
Williamson’s audacious move is to side with logic. No matter how weird it may seem, we should stick with classical logic. We should maintain Obama is old or Obama is not old is true. Either he is or he isn’t.
Again, take a moment to realise how counterintuitive this is. When we say of a person that he’s old, there is, for Williamson, some precise number of years that person must be. It might be 71 or it might be 80 or, maybe, it might be 65. But there is some number: before you’re that age you’re not old, and as soon as the clock rolls round suddenly you’re old.
And the reason he thinks this is because if we didn’t think it, we would be forced to give up classical logic. Classical logic, an imposing abstract mathematical structure, towers over and determines what we say when we reassure our father awk sure you’re not too old to run a marathon.
Or take his argument for the existence of the possible child of Monroe and Gandhi. It goes, roughly, the same way. In order to have a language apt for talking about possibility, we need to add some expressions to our language that perform this function. Without going into the details, we introduce some new symbols whose meanings you can infer from the below. For any p:
◇p=it is possibly the case that p
□p = it is necessarily the case that p
And then we need to add some rules. And as it so happens, the simplest set of rules yields the following. For any F:
◇∃xFx→∃x◇Fx
In English, if possibly something is F (say, the child of Gandhi and Monroe) then there is something which is possibly an F. Now, it’s definitely possible that something is a child of Gandhi and Monroe; so, the above tells us, there is something that is possibly that child. Among the world’s furniture we may find a being that possesses that property.
Although the details would take us too far afield, one of the reason for holding this, known as the Barcan formula, is just that it gives us a simple logic. Again, Williamson boldly opts for simple logic, damn the counterintuitive consequences.
Before going on I should say that in each case, Williamson bolsters his case in great detail, with many other arguments for his position and against his opponents’. But a taste for simple logic is undeniably a central motivator for him.
Here’s the way to see the Williamsonian view. On the one hand, we have the mathematical, precise languages of formal logic, and on the other we have the messy imprecision of the world we as humans inhabit, with its vagueness and impermanence. Most don’t think they’re connected. He does. And that’s what makes him a poet.
Keats famously said that truth is beauty and beauty truth. That may be, but for the purposes of this essay I want to separate them. I don’t care so much about the truth of Williamson’s world-view; I want to talk about its beauty. I will argue that we should view his philosophy in the same way as we view poetry.
Ben Johnson spoke of poets known, by a happy coincidence, as ‘metaphysical’ that in their work ‘the most heterogeneous ideas are yoked together by force’. Consider thus the following. John Donne, the courtier-cum-poet-cum-cleric, is writing about his and his girlfriend’s souls:
If they be two, they are two so
As stiff twin compasses are two;
Thy soul, the fix’d foot, makes no show
To move, but doth, if th’ other do.
And though it in the centre sit,
Yet, when the other far doth roam,
It leans, and hearkens after it,
And grows erect, as that comes home
(from 'A Valediction: Forbidding Mourning')
There are three ideas here tightly bound up: first, there’s the souls of the lovers. From that, we move to the figure of the compass, which conveys how in sync the souls are: just as the foot of a compass may rotate around and around without ever moving any distance from the other centred foot, so no matter where his girlfriend moves, he is there with her. But this closeness of soul is itself then linked up to the body (‘erect’ is not an accident) and so we come to have this very vivid, strange, geometrical image of stiff linked souls. Or think about:
Our hands were firmly cemented
With a fast balme, which thence did spring,
Our eye-beames twisted, and did thred
Our eyes, upon one double string
(from 'The Ecstasy')
How odd this is! Literally petrifying; think of the warmth of a hand and then think of cement (moreover, there’s apparently some allusions to alchemy here, which wasn’t quite as discredited when Donne was writing). And as for the last two lines — if you think they are completely bizarre, and almost horrible-comical, you’re right. But it works — it really breathes fresh, if ambiguous, light into this old romantic set piece.
T.S. Eliot, famously, was much taken with these metaphysical poets, and it shows in his own work, such as the line from Prufrock I quoted at the beginning. He proposed an explanation for what the metaphysical poets were up to, and what was unique about them:
Tennyson and Browning are poets, and they think; but they do not feel their thought as immediately as the odour of a rose. A thought to Donne was an experience; it modified his sensibility. When a poet’s mind is perfectly well equipped for its work, it is constantly amalgamating disparate experience; the ordinary man’s experience is chaotic, irregular, fragmentary. The latter falls in love, or read Spinoza, and these two experiences have nothing to do with each other, or with the noise of the typewriter or the smell of cooking; in the mind of the poet these experiences are always forming new wholes
(from 'The Metaphysical Poets')
So our poets: when Donne falls in love, he sees it via alchemy and trigonometry and weird body horror avant la lettre; when Eliot looks at a sky, he thinks of surgery.
And so, and here is my claim, our analytic philosophers. When Williamson thinks of the many possibilities neglected (of which a Gandhi Marilyn affair is admittedly an outré example), or the chaotic mess of language use, and again when he thinks of classical and modal logic, these don’t, as for most of us, have “nothing to do with each other”, but rather form a new whole. He sees our day to day affairs through the prism of logic, and it’s this weird vantage point which yields for us his bizarre but wonder-inspiring world of possible beings and precise moments at which one ages. He’s a poet even if he doesn’t know it (it’s amusing to note that his recent book Modal Logic As Metaphysics even has a simile for a title).
Similarly, I think, for the range of contemporary analytic philosophers. In trying to understand the vagaries of language use or of morals or of reality itself, analytic philosophers frequently produce these sort of creative juxtapositions of ideas the mere contemplation of which should appeal to anyone with a taste for bold visions of reality. So next time you have a yen for philosophy, but are put off by turgid prose and numbered premises, think about persevering, in the hope that you might find, with Keats, both truth and beauty.
(forthcoming in Think, originally posted on medium on February 9th (https://medium.com/@mittmattmutt/the-beauty-of-analytic-philosophy-6acf106a6a3e)
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