The Ramsey Effect

Picture,​ if you can, a single person with the talents of Keats, Schubert and Seurat: an inspired poet, a prodigious composer, a revolutionary painter, a figure of unlimited promise who died, like them, in his youthful prime. If you replace poetry, music and painting with mathematics, economics and philosophy, the person you end up with is Frank Plumpton Ramsey. A fellow of King’s College, Cambridge, Ramsey was born in 1903 and died before he turned 27, having done extraordinary work in all three fields. He is revered by academics, his influence evinced by the almost comical range of ideas named after him. In mathematics: Ramsey theory, Ramsey’s theorem and Ramsey numbers. In economics: Ramsey pricing, Ramsey problems and two rules, one Ramsey’s, one shared with Keynes. In philosophy: Ramsey sentences, the Ramsey test, the Ramsey-Lewis theory of reference, and the Mill-Ramsey-Lewis account of natural laws. Many of his ideas were so groundbreaking that they were taken up in earnest only decades later. This phenomenon has also been named after him: the Ramsey effect is what happens when you find your apparently novel insight anticipated, more elegantly, by Frank Ramsey.

Yet Ramsey’s name isn’t widely known. His work is often inaccessible, a fact of which he was dispassionately aware: philosophy, he noted in a talk given in 1925, ‘has become too technical for the layman’. Then there’s his personality, modest and genial. Unlike Ludwig Wittgenstein, with whom his career was entwined, Ramsey didn’t fit the stereotype of the tortured genius. After his early death, he was eclipsed by Wittgenstein, whose influence dominated Cambridge philosophy for decades. Ramsey’s admirers have ventured to project what would have happened in philosophy had he lived. But, as he knew, the counterfactual is idle: there is no fact of the matter. What we do know is that if Wittgenstein had died at 26, he would have left little more than the notes on logic he compiled before beginning to write the Tractatus Logico-Philosophicus in 1916. The loss would be unfathomable.

In Frank Ramsey: A Sheer Excess of Powers, Cheryl Misak shows us how much Ramsey achieved in the little time he had. Her book is not the first to tell the story of his life: an unfinished memoir by his younger sister, Margaret Paul, was published in 2012, but it was missing a crucial chapter – about Wittgenstein’s return to Cambridge in 1929 – and wasn’t especially good on the philosophy. Misak, a philosopher at the University of Toronto, draws on extensive archival research, unpublished interviews with Ramsey’s widow, siblings, friends and colleagues, and on experts who contribute ‘guest boxes’ on Ramsey’s more esoteric ideas. Her book is unlikely to be bettered.

Ramsey’s impact on philosophy is difficult to grasp without a sense of the intellectual ferment in the discipline at the turn of the 20th century. Cambridge philosophers were beginning to absorb the profound advances in logic and the philosophy of language made by the German logician and philosopher Gottlob Frege. It seemed rational to hope that the new logic would chart the structure and limits of what could possibly be true, and help explain how language can express such truths. In 1911, Frege sent Wittgenstein to Cambridge to work with Bertrand Russell. Together with the less technically minded G.E. Moore, they would be seen as the architects of ‘analytic philosophy’.

That phrase creates some difficulties, partly as a result of the fractious conflict that developed between analytic and Continental philosophy, the latter epitomised by the likes of Martin Heidegger and Jacques Derrida. But the taxonomy is bizarre, as Bernard Williams once complained, since it contrasts a method or approach to philosophy with a geographical region, ‘rather as though one divided cars into front-wheel drive and Japanese’. Even the term ‘analytic philosophy’ is misleading. When it came into common usage in the 1950s, it mashed together Russell, Moore and Wittgenstein with the logical positivism of the Vienna Circle and the ‘ordinary language philosophy’ then current in Oxford. The effect was to associate analytic philosophy with the idea that philosophers should model themselves on and defer to scientists, and with a taste for pedantic linguistic analysis. None of this applied to the Cambridge in which Ramsey arrived as an undergraduate. The philosophical analysis of Russell, Moore and Wittgenstein didn’t particularly engage with science and was directed not at words but rather at the truths they can express. When the journal Analysis was founded in 1933, aiming to build on the work of the ‘Cambridge school’, its remit was ‘the elucidation or explanation of facts, or groups of facts, the general nature of which is, by common consent, already known’.

The pinnacle of the Cambridge school, and the impetus for Ramsey’s intervention, was Wittgenstein’s Tractatus, a work of skyscraping ambition. Wittgenstein wanted to make sense of the peculiar necessity of logic. When you let go of an apple, it’s bound to fall: the law of gravitation means that apples can’t just float in the air. But this necessity is relative, since the laws of nature could have been quite different. Logic’s necessity is more profound. It’s impossible for a contradiction like ‘Snow is white and snow is not white’ to be true, and this necessity seems absolute. ‘Laws of logic’ don’t function like laws of nature, keeping reality in line, since if they did we could ask why those laws could not be otherwise. What then prevents a contradiction from being true? Or if that seems a silly question, what makes it silly? Wittgenstein’s answer was that logic is built into the very form of thought. By this he meant not the form or character of human cognition but the form of what can be thought, or what can be true.

Wittgenstein posits a multiplicity of ‘elementary propositions’, each of them logically simple. Their simplicity makes it possible for any of them to be true in any combination; logic can’t prevent it. To elementary propositions, Wittgenstein applies his ‘picture theory’: these propositions correspond to ‘propositional signs’ – roughly, sentences – that are isomorphic with them, containing terms that correspond to ‘symbols’ in the proposition, which correspond in turn to simple elements of the world. Wittgenstein builds every other proposition out of elementary propositions by a single logical operation, repeated indefinitely, to yield an inventory of possible truths. Sentences that do not correspond to propositions in the inventory are declared nonsensical. The breathtaking claim of the Tractatus is to have mapped the absolute limits of sense.

The Tractatus is formidably difficult, as this lightning summary attests. Matters aren’t made easier by its style: the book consists of a series of numbered aphorisms with little connecting argument. Wittgenstein wrote the book in German while serving in the Austrian army during the First World War. Astonishingly, the task of translating it was given to an 18-year-old undergraduate in mathematics. Who was this prodigy and how had he come to be entrusted with an enterprise so vital to analytic philosophy?

Frank Ramsey’s​ father was a journeyman mathematician at Magdalene College, Cambridge, known for writing successful textbooks. Ramsey’s mother read history at St Hugh’s College, Oxford, and was a political activist whose convictions had a deep influence on Frank, her oldest son. He had three siblings, Michael, Bridget and Margaret; Michael went on to become a notably progressive archbishop of Canterbury. Frank’s brilliance was evident from the start. He taught himself to read almost as soon as he could talk and won a scholarship to Winchester, where he was miserable but excelled in mathematics and won a prize for German. By his final year of school, he was reading Adam Smith, Marx, Alfred Marshall and Keynes in economics; in philosophy, Hume, Kant, Mach, Brentano, Moore and Russell. He won a scholarship to study mathematics at Trinity College. Despite spending much of his time on economics and philosophy, he came first in the Tripos exams for both Part I and Part II.

Misak provides by far the most complete picture we have of Ramsey’s personality and personal life. Moore ‘had soon come to feel of him, as of Wittgenstein, that he was “very much cleverer than I was”’. In his obituary of Ramsey, Keynes describes his ‘bulky Johnsonian frame, his spontaneous gurgling laugh, the simplicity of his feelings and reactions, half-alarming sometimes and occasionally almost cruel in their directness and literalness, his honesty of mind and heart, his modesty, and the amazing, easy efficiency of the intellectual machine which ground away behind his wide temples and broad, smiling face’.

Ramsey’s social circle overlapped with the Bloomsbury Group and he shared their ideology of intimate friendship and free love. This didn’t always work out well. At one point, he became obsessed with a friend’s wife, asking her bluntly: ‘Margaret, will you fuck with me?’ She turned him down and he was distraught. Partly on the advice of the woman’s husband, given via Ramsey’s mother, Ramsey went to Vienna to be psychoanalysed. By all accounts, his six-month treatment was effective. When he returned to Cambridge in 1924, he began seeing Lettice Baker and they got married the following year. They had an open relationship and, apart from one rough patch, seem to have been very happy. They had two daughters, Jane and Sarah.

In the midst of this, Ramsey was doing philosophy. He translated the Tractatus in the winter of 1921-22, though the credit was given to one of his mentors, C.K. Ogden. The translation appeared in 1922 and was reviewed in the journal Mind – by Frank Ramsey. The book was ‘important’, he wrote, but ‘very difficult to understand’. He raised a series of objections that changed the course of Cambridge philosophy.

One was anticipated by Wittgenstein: if sentences that don’t correspond to propositions in the Tractatus inventory are nonsense, what about the sentences that make up the Tractatus itself? When Wittgenstein purports to define the nature of propositions, he is not stating facts that could be otherwise, but nor are his claims logical truths. By the standards of the Tractatus, he is talking nonsense. Wittgenstein embraced this result, directing his readers to throw away the ladder once they have climbed it: those who understand the Tractatus will come to recognise that much of it makes no sense. The same goes for ethics and aesthetics: nonsense too. The most important things, for Wittgenstein, can’t be said – hence the strain of mysticism in his work. Ramsey was having none of it. If ‘the chief proposition of philosophy is that philosophy is nonsense,’ he later wrote, ‘we must then take seriously that it is nonsense, and not pretend, as Wittgenstein does, that it is important nonsense.’ Spurning the austerity of the Tractatus, Ramsey hoped to make sense of language that goes beyond its limits.

A second objection persuaded Wittgenstein that the project of the Tractatus must fail. Known as the colour incompatibility problem, it’s deceptively simple. According to Wittgenstein, the only absolute necessity is logical necessity, explained by the form of thought, which is what determines that ‘Snow is white and snow is not white’ can’t be true. The problem is that not everything impossible looks like a logical contradiction. ‘Snow is white and snow is black’ is necessarily false: it couldn’t possibly be true, at least if it means black and white all over. But logically it seems to have the same form as ‘Snow is white and snow is cold,’ which states a possible truth. In the Tractatus, Wittgenstein addressed this problem by contending that the surface form of sentences deceives us. Despite appearances, colour terms are logically complex, to be analysed in terms of the physics of colour and ultimately in terms of elementary propositions about the movements of particles. Ramsey pointed out that this merely defers the problem:

[Even] supposing that the physicist thus provides an analysis of what we mean by ‘red’, Mr Wittgenstein is only reducing the difficulty to that of the necessary properties of space, time and matter, or the ether. He explicitly makes it depend on the impossibility of a particle being in two places at the same time.

Wittgenstein wrestled with the colour incompatibility problem on his return to Cambridge in 1929 and eventually gave up. Ironically, it’s not entirely clear that Ramsey followed suit. In his first published paper in philosophy, ‘Universals’, Ramsey argued that ‘we know and can know nothing whatever about the forms of [elementary] propositions.’ Perhaps there is some suitable analysis of ‘black’ and ‘white’ and we are simply ignorant of it. As the American philosopher Sarah Moss showed in 2012, we can solve the colour incompatibility problem if we place weak enough constraints on what the elementary propositions are like. Ramsey would not have objected. He believed that the basic structure of reality is utterly unlike the structure we infer from words. Even the least dogmatic thinker might assume that the contrast between nouns like ‘Frosty the Snowman’ and predicates like ‘is white’ corresponds to a distinction in reality between particular things and the properties they instantiate. We know at least that much about the structure of what there is. The argument of ‘Universals’ was that we don’t: ‘the whole theory of particulars and universals,’ Ramsey held, ‘is due to mistaking for a fundamental characteristic of reality what is merely a characteristic of language.’

Ramsey combined a sturdy resolution to follow the argument wherever it led, even into alien territory, with a sober refusal to make things more mysterious than they are. Like the later Wittgenstein, he thought philosophers had been bewitched by language; unlike Wittgenstein, he still saw room for constructive theorising. Among his most influential views – one that laid the foundation for the edifice on which he worked, at pace, in his last four years – was that ‘there is really no separate problem of truth but merely a linguistic muddle.’ Some uses of ‘true’ were simply redundant: ‘“It is true that Caesar was murdered” means no more than that Caesar was murdered.’ And it is only an accident of grammar that prevents us from dispensing with the rest. ‘Everything Ramsey said is true’ means that for every proposition p, if Ramsey said p then p, which is ungrammatical because the final ‘p’ needs a verb; hence ‘p is true.’ But we’d make no mistake if we spoke a language that broke this rule and had no word for ‘true’. For Ramsey, the real question was not about truth, but about what it is to believe or assert that Caesar was murdered and so to believe or assert what can be true or false. Ramsey’s idea was that a given belief is to be understood in terms of its causes and effects, the ways in which it’s formed and the role it plays in behaviour, in conjunction with other beliefs, desires and mental states. This idea, now called functionalism in the philosophy of mind, is considered by many the most promising way to make sense of mental representation.

Ramsey went on to extend this functionalism – he called it pragmatism – to degrees of confidence or ‘partial beliefs’, which he interpreted as probabilities. He measured degrees of belief by considering betting behaviour. If you are neutral about the truth of a given proposition, p, and you are indifferent between a bet that gives you an n per cent chance of winning a prize and a bet in which you win the prize if p is true, your degree of belief in p is n. Ramsey showed how to generalise this point and make it more precise. In doing so, he invented the decision theory that underlies huge swathes of contemporary economics and social science, and the ‘subjective’ interpretation of probability that is central to so-called Bayesian statistics along with the allied field of formal epistemology, which applies mathematical tools to the philosophy of knowledge and belief.

Before his death, Ramsey began to make good on the promise of explaining what Wittgenstein’s Tractatus could not, exploring uses of language that elude the picture theory. He devised a method for interpreting theoretical claims in science by way of observable facts, treating hypotheses as useful fictions: ‘“There is such a quality as mass” is nonsense,’ he wrote, ‘unless it means merely to affirm the consequences of a mechanical theory.’ Ramsey’s approach predicts the incommensurability of sufficiently divergent outlooks, anticipating Thomas Kuhn on the structure of scientific revolutions by more than thirty years. He went on to interpret causal laws and conditional statements not in terms of causal or conditional facts but by appeal to rules for judgment. To hold that if A happens B will happen too is to accept a rule of believing that B will happen when you believe that A has occurred. In each case, Ramsey explains the sense of the ‘secondary system’ – of scientific theories, or causal and conditional statements – in terms of its relationship with the ‘primary system’ of factual language to which the Tractatus was confined. And in each case, he appeals to the practical significance of language. Drawing on the American pragmatist C.S. Peirce, he applies to the secondary system ‘Peirce’s notion of truth as what everyone will believe in the end’. Scientific theories can’t be true, for Ramsey, in the sense of picturing facts, but they can be called ‘true’ when they serve their purpose indefinitely, in light of all future evidence.

Ramsey​ was a pragmatist not just in theory but in practice. As an undergraduate he worked for a socialist group researching employment conditions in Cambridge. In a talk in 1924, Misak records, he gave ‘an early, perhaps the earliest, analysis of the economics of marriage, child-bearing and child-rearing’. And he went on to write two of the most influential papers in 20th-century economics, one on optimal taxation, the other on optimal savings.

The second paper, in particular, is worth revisiting. Its question was how much a society should save, and how much it should consume, so as to maximise aggregate wellbeing for the indefinite future. Ramsey’s apparatus is now central to discussions of the long-term economics of climate change. How much should we invest in abating carbon emissions, consuming less for the sake of future generations? A key variable in the mathematics is the ‘social discount rate’: the rate at which we discount the wellbeing of future generations, giving their lives less weight in our calculations as time goes on. For instance, if we discount wellbeing at an annual rate of 1 per cent, the significance of human suffering, as reflected in the numbers, decreases by about two thirds for every hundred years. Because they compound over time, differences in the social discount rate have an enormous impact on policy. They are responsible for the wildly disparate recommendations of economists such as William Nordhaus and Nicholas Stern. Nordhaus proposed modest but meaningful steps to mitigate global warming. The 2006 Stern Review was more radical, advocating a carbon tax ten times higher than Nordhaus had advised and an investment in mitigation of seven times the global aid budget: the difference stemmed largely from Stern’s refusal to discount the wellbeing of future people, as Nordhaus had done. Although his paper explored the mathematics of temporal discounting, Ramsey agreed with Stern: the idea that future generations count for less ‘is ethically indefensible and arises merely from a weakness of the imagination’. Ramsey would have been a climate hawk.

In a different context, he was more open to attitudes that discount the future. Misak returns more than once to his most lovable essay, given as a talk to the Cambridge Apostles. Framed as a discussion of the fact that there’s no subject to discuss – the kind of joke philosophers enjoy – it ends with the meaning of life. It’s addressed to those who feel that human life is meaningless in an immense and endless cosmos:

Where I seem to differ from some of my friends is in attaching little importance to physical size. I don’t feel the least humble before the vastness of the heavens. The stars may be large but they cannot think or love; and these are qualities that impress me far more than size does. I take no credit for weighing nearly 17 stone … In time the world will cool and everything will die; but that is a long time off still, and its present value at compound discount is almost nothing. Nor is the present less valuable because the future will be blank.

While a social discount rate is ethically indefensible, it makes sense for us, as individuals, to focus on the here and now. Ramsey concludes with a pragmatic argument for optimism:

I find, just now at least, the world a pleasant and exciting place. You may find it depressing; I am sorry for you, and you despise me. But I have reason and you have none; you would only have a reason for despising me if your feeling corresponded to the fact in a way mine didn’t. But neither can correspond to the fact. The fact is not in itself good or bad; it is just that it thrills me but depresses you. On the other hand, I pity you with reason, because it is pleasanter to be thrilled than to be depressed, and not merely pleasanter but better for all one’s activities.

Misak finds in these remarks a nascent theory of ethical language, the vindication of another secondary system: ‘Our fundamental attitudes toward life can be debated, justified and criticised according to whether they promote or hinder human flourishing … We can ask, for instance: does the focus on the human rather than the astronomical angle result in a better life?’ I understand the urge to read into Ramsey’s words, but he doesn’t point here to a theory of ethics and it would be an implausible theory if he had. You can’t assess the truth of someone’s ethical beliefs – for instance, the belief that it’s ethically indefensible to discount the wellbeing of future people – by the effects on them of holding that belief. There are inconvenient truths.

If he had lived long enough, Ramsey might have furnished a theory of ethics that found a place for ethical truth in the natural world. But we have no way of knowing what that theory would have been. In November 1929, he was laid up in bed with a chill, quickly followed by jaundice. He hadn’t recovered by the beginning of January, at which point Lettice’s uncle, a surgeon, had him admitted to Guy’s Hospital in London. An operation found his gall bladder inflamed but no diagnosis could be made. He died on 19 January 1930. The cause of death remains uncertain.

Although he has few professed disciples, Ramsey’s ideas are pervasive in philosophy today: you can’t open a copy of Mind without finding an allusion to them. Wittgenstein is more famous, but the architecture of the discipline now is closer to Ramsey’s design. Philosophers could be depressed about his early death or thrilled that he lived at all. The facts don’t tell us how to feel; but it’s pleasanter to be thrilled than to be depressed, and not merely pleasanter but better for all one’s activities.