In Plato's Apology, Socrates declares:

First-order knowledge is important, but second-order knowledge of what one does or does not know is even more important: That is, it is essential to have what we might call “epistemic self-knowledge.” Scientists are knowledge-driven. That is why inductive methods are so popular in science. Knowledge is a good thing, but there are situations in which we require more – in which we require wisdom and thus epistemic self-knowledge. For example, when our theories fail to deliver results, when we are forced to find new theories or create new hypotheses, it is vital to know what one does not know.

Indirectly, Socrates tells us something about rational decision making. When everything is propitious, when we can represent our knowledge and our values with unique probability distributions and precise utility functions, we can simply maximize expected utility. We can use one of the classical theories – for example, Ramsey's, or Savage's, or Jeffrey's theory. But when we are uncertain about the extent of our knowledge, when things are indeterminate, or when we are uncertain about our preferences, we know that the traditional theories will be of little or no use to us.

In his essay entitled ‘Mathematical Logic’ written in 1926, Ramsey gives his opinion of the evolution of mathematical logic after the publication of Principia Mathematica. The essay is largely a defence of the ideas of logicism against the attacks by Hilbert's formalism and Brouwer's intuitionism. Ramsey had already criticized Hilbert and Brouwer in ‘The Foundation of Mathematics’, and ‘Mathematical Logic’ is only a popular version of this criticism.

Hilbert's view of mathematics as a game with marks is in Ramsey's eyes an impossible theory for an analysis of mathematical concepts.

During the first decades of this century the intellectual atmosphere at Cambridge was exceptionally lively and creative. Thinkers such as the philosophers C. D. Broad, W. E. Johnson, G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and the economist J. M. Keynes have had a decisive impact on modern research and social debate. Their ideas have become generally known from numbers of scholarly essays, books and biographies. But the greatest of them all is scarcely known outside a small circle of specialists. Frank Plumpton Ramsey, who died in 1930 at the age of only 26, in a series of brilliant essays laid the foundations of several new and flourishing theories in philosophy, mathematics and economics. However, not until recently, decades after Ramsey's death, have we gradually realized what unprecedented originality his work contains. When intellectual vigour began to ebb away from Cambridge in the years following his death, his genius did not show to full advantage.

My aim in this book is to give a comprehensive picture of Frank Ramsey's philosophical and scientific research. I have tried to present and discuss as straightforwardly as possible his often difficult ideas and theories, put them into a historical context and demonstrate their importance for modern research. My hope is that the reader who does not have any previous knowledge of the subjects discussed will be able to profit from the book, and that the specialist will also enjoy it.

For a generation of philosophers Ramsey is probably best known as ‘the one who revised the theory of types suggested in Principia Mathematica’. At least this is the impression one gets looking up what is said about him in philosophical dictionaries or works on the history of philosophy (more often than not, he is not even mentioned). But it should be clear by now that Ramsey has made significant contributions to various other areas of research. There are several reasons for emphasizing his contributions to formal logic and mathematics. In the 1920s and 1930s, many philosophers were occupied with digesting the new theses of Principia Mathematica and Tractatus. Ramsey's profound and important criticism of these two works of philosophy has, of course, contributed to his reputation. Another reason Ramsey is primarily known for his works on logic and mathematics might be the somewhat misleading title of the first edition of his collected papers. Braithwaite obviously thought it would be a good idea to let the first essay of the volume, ‘The Foundations of Mathematics’, give its name to the book. But a book with this title hardly entices a larger audience. And this is true regardless of how many other brilliant (non-formal) papers the book contains. The most likely reason for Ramsey's reputation as a logician is, however, the simple fact that his contributions to formal logic and mathematics are of a remarkable power.

Sometimes it can be pleasant and stimulating to turn to fresh fields of research – to try to apply one's knowledge to other areas. The philosopher who has grown weary of his own subject may look upon the experimental elements of psychology as tempting. Now and then such escapades turn out to be extremely successful. But more often than not the attempts evoke no more than an appreciative word from friendly colleagues in other disciplines.

Under the influence of the Cambridge economists J. M. Keynes and A. Pigou, Ramsey decided to test his mathematical and philosophical knowledge in the field of economics at the end of the 1920s. What Ramsey achieved were two essays of the highest class. Both ‘A Contribution to the Theory of Taxation’ (1927) and ‘A Mathematical Theory of Saving’ (1928) have given rise to new and flourishing schools of economic theory. The former essay is the point of departure for the theory of optimal taxation and the latter lays the foundations for the theory of optimal saving.

But it is perhaps primarily the essay on saving that has been noticed and discussed in the literature of economics. According to Keynes, who must be considered a competent judge, this essay is:

The title of this chapter indicates that this is not intended to be a complete biographical portrait of Frank Ramsey. Such a task would be difficult to carry out for various reasons. There is hardly anything written about him and what there is gives a sketchy outline. Moreover, for obvious reasons, there are few people now living who knew Ramsey and who would be able to straighten out the many queries we have. I have instead preferred to put together parts of the biographical fragments to be found in the literature. I hope that these glimpses will give some impression of the whole person.

In writing this chapter I have drawn greatly on D. H. Mellor's excellent radio programme ‘Better than the Stars’, which was broadcast by BBC Radio 3 on 27 February 1978 on the occasion of the seventy-fifth anniversary of Ramsey's birth.

BIOGRAPHICAL DATA

Frank Plumpton Ramsey was born on 22 February 1903 and died at the age of 26 on 19 January 1930. Ramsey suffered from a chronic and increasingly serious liver complaint, contracted jaundice after an operation and died at Guy's Hospital in London. He left a wife, Lettice Ramsey and two daughters. Frank Ramsey came from a distinctly academic background, his brother became Archbishop of Canterbury and his two sisters also received a solid university education. Ramsey's mother was active in politics and he inherited from her a very profound social awareness.

Frank Ramsey's bibliography contains 18 published works. Eight of these are fairly extensive philosophical and scientific essays; the rest are reviews, short notes and articles for the Encyclopædia Britannica. The bibliography would, however, be incomplete if one did not add the articles published posthumously in 1931 and 1978 in The Foundations of Mathematics and Other Logical Essays (edited by R. B. Braithwaite) and Foundations: Essays in Philosophy, Logic, Mathematics and Economics (edited by D. H. Mellor). Thus the core of Ramsey's philosophical and scientific work consists of no more than, say, 15 papers. But they are 15 remarkable papers, profound and full of originality. Today most of them are recognized as the foundation of flourishing theories in logic, mathematics, philosophy of mathematics, statistics, probability theory, decision theory, semantics, scientific method, cognitive science, metaphysics and economics. But they are more than 15 brilliant essays on 15 disparate subjects. They all contain the same view of philosophy – a method of analysis – merging a sound portion of realism (or, as Moore preferred to put it, ‘the soundest common sense’) with Ramsey's kind of pragmatist philosophy.

In 1922, when he was only 19 years old, Ramsey published three short articles, two of them in the Cambridge Magazine. One of these, ‘Mr Keynes on Probability’, is a review of Keynes's A Treatise on Probability.

We now turn to one of the central problems of metaphysics, namely, the classical problem of universals. Ramsey writes on the subject in his first essay of some length, ‘Universals’, which was published in Mind in 1925, and he returns to the problem in an essay written for a symposium with H. W. B. Joseph and Richard Braithwaite, entitled ‘Universals and the “Method of Analysis”’.

Ramsey was interested in the problem of universals because his investigations of the foundations of mathematics more or less forced him to take this metaphysical problem seriously – which is more than one can say about most philosophers today, who try to escape it by not discussing it. However, one does not need to be dealing with the foundations of mathematics to see how central the problem of universals is. It can be approached in various ways.

If I lift my eyes for a moment from the yellow screen of the word-processor and look around my office, I will find a number of things which are yellow, too. On the bookshelves there are a number of yellow books; true, the shade of yellow varies, but nonetheless they are all yellow, and on the desk there are a couple of typical government-owned yellow pencils. These books, pencils and the yellow screen differ in a number of ways; yet they have a common characteristic – yellowness. The property these particulars all share is a universal.

What does it mean to say that we know something? Do we know anything at all? What is there to say that we are not brains floating in a glass tank in a laboratory? Flapping our ears – which have been left to us – we sail along in the glass tank. With our eyes which we have also been allowed to retain, we peer through the glass sides of the tank. The tank is placed in an even bigger tank on the inside of which is a screen. Onto this screen the laboratory staff project our reality. Smells and other sense perceptions are produced by electrodes inserted into our brains. At the same time as new slides are projected onto the white screen, a computer activates the electrodes in predetermined sequences. Would there be any noticeable difference between our actual life and life in such a tank? If the experiment were properly conducted, the brain would become just as hungry as we do and just as exhausted; it would fall in love now and again with one or other of the people projected on the screen; and so on. How then can we know that our life is not lived in such a tank? It is difficult to answer this sceptical question in a totally satisfactory way. Just as we have difficulty in convincing the solipsist of our existence, we have difficulty in convincing the sceptic that knowledge about a factual world is possible.

Ramsey abandoned logicism in 1929 for a finitistic view of mathematics (see Chapter 6). Behind this conversion lay his dissatisfaction with the axiom of infinity of set theory. However, it was not only Ramsey's view of mathematics that evolved during the period between 1926 and 1929 but his whole philosophical outlook. The advances in logic led the majority of British philosophers into fresh fields of research. The inter-war years were characterized by a more pragmatically biased philosophy. Ramsey was not unaffected by these currents. He read Peirce, was influenced by Johnson and turned increasingly toward pragmatism. The first sign of this change in Ramsey's philosophy is to be seen in ‘Truth and Probability’ (1926). This essay is imbued with the pragmatism of Peirce, although Wittgenstein's strong impact is still very noticeable and the mathematical elegance is there as always.

In this section we discuss some of the problems Ramsey was pondering during the period 1926–9. In some cases he presented complete solutions to a philosophical problem, but very often he only sketched a proposal for a solution. Things would have turned out quite differently had Ramsey lived longer than he did. Some of the ideas which Ramsey had and which proved extremely rewarding were only mentioned by him in passing.