A compilation of all previously published writings on philosophy and the foundations of mathematics from the greatest of the generation of Cambridge scholars that included G.E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes.

This article rebuts Ramsey's earlier theory, in 'Universals of Law and of Fact', of how laws of nature differ from other true generalisations. It argues that our laws are rules we use in judging 'if I meet an F I shall regard it as a G'. This temporal asymmetry is derived from that of cause and effect and used to distinguish what's past as what we can know about without knowing our present intentions.

The present publication forms part of a projected book that F. P. Ramsey drafted but never completed. It survived among his papers and ultimately came into the possession of the University of Pittsburgh in the circumstances detailed in the Editor's Introduction. Our hope in issuing this work at this stage - some sixty years after Ramsey's premature death at the age of 26 - is both to provide yet another token of his amazing philosophical creativity, and also to make available (...) an important datum for the still to be written history of the development of philosophical analysis. This is a book whose appearance will, we hope and expect, be appreciated both by those interested in linguistic philosophy itself and by those concerned for its historical development in the present century. EDITORS'INTRODUCTION 1. THE RAMSEY COLLECTION Frank Plump ton Ramsey was an extra ordinary scholarly phenomenon. Son of a distinguished mathematician and President of Magdalene College, Cambridge and brother of Arthur Michael, eventual Archbishop of Canterbury, Ramsey was closely connected with Cambridge throughout his life, ultimately becoming lecturer in Mathematics in the University. Notwithstanding his great mathematical talent, it was primarily logic and philosophy that engaged his interests, and he wrote original and important contributions to logic, semantics, epistomology, probability theory, philosophy of science, and economics, in addition to seminal work in the foundations of mathematics. (shrink)

Haack, S. Is truth flat or bumpy?--Chihara, C. S. Ramsey 's theory of types.--Loar, B. Ramsey 's theory of belief and truth.--Skorupski, J. Ramsey on Belief.--Hookway, C. Inference, partial belief, and psychological laws.--Skyrms, B. Higher order degrees of belief.--Mellor, D. H. Consciousness and degrees of belief.--Blackburn, S. Opinions and chances.--Grandy, R. E. Ramsey, reliability, and knowledge.--Cohen, L. J. The problem of natural laws.--Giedymin, J. Hamilton's method in geometrical optics and Ramsey 's view of theories.

F. D. Maurice was a distinguished Christian theologian, much respected by academics and artists of his day and afterwards. This volume, originally published in 1951, contains the text of seven lectures delivered in his honour in 1942 by Arthur Ramsey, later Archbishop of Canterbury, and covers Maurice's career and his impact on later students of theology. This book will be of value to anyone with an interest in Christian socialism or in Maurice's wider work.

The Rainbow Ramsey Theorem is essentially an "anti-Ramsey" theorem which states that certain types of colorings must be injective on a large subset (rather than constant on a large subset). Surprisingly, this version follows easily from Ramsey's Theorem, even in the weak system RCA₀ of reverse mathematics. We answer the question of the converse implication for pairs, showing that the Rainbow Ramsey Theorem for pairs is in fact strictly weaker than Ramsey's Theorem for pairs over RCA₀. The separation involves techniques (...) from the theory of randomness by showing that every 2-random bounds an ω-model of the Rainbow Ramsey Theorem for pairs. These results also provide as a corollary a new proof of Martin's theorem that the hyperimmune degrees have measure one. (shrink)

This is a transcript of a conversation between P F Strawson and Gareth Evans in 1973, filmed for The Open University. Under the title 'Truth', Strawson and Evans discuss the question as to whether the distinction between genuinely fact-stating uses of language and other uses can be grounded on a theory of truth, especially a 'thin' notion of truth in the tradition of F P Ramsey.

Bill McKibben’s book, Enough, is about cloning, genetic enhancement, and nanotechnology. His thesis is that these things are bad—nay, they are downright evil. In vivid and readable prose, McKibben explains what will soon be possible with these technologies and provides a dystopian portrait of the future. His alarmist tone is effective. Despite having read several similar works and remaining unmoved, McKibben’s images struck home with me. I began to feel, in my gut, anxiety about the genetically engineered future. McKibben is (...) no stranger to raising the dangers of new technology. His The End of Nature is widely acclaimed to have alerted an unsuspecting public about the danger of global warming. Alarmism was appropriate for The End of Nature, since little was written on global warming prior to 1989. But despite McKibben’s effective writing, his alarmism seems out of place for his current topic, since the potential harms of cloning and genetic engineering have been discussed in the academic and popular press for some time. Remember, it has been 34 years since the appearance of Paul Ramsey’s Fabricated Man, and 72 years since Huxley’s Brave New World.McKibben’s most prominent argument against human genetic engineering is that it will cause psychological harm to the people produced from the use of the technology. McKibben claims that people with the knowledge that they resulted from engineered embryos will undergo a crisis in personal responsibility. So, he argues, engineered people will not know whether to take credit for their achievements, . Likewise, engineered …. (shrink)

The first part of this book contains essays on Dostoevski's Christian insights, Marxism compared to Christianity as a religion, and the Christian significance of Sartre's "ontological" interpretation of sexuality. A second group of essays develops the author's concern with Christian social ethics and modern interpretations of the concept of natural law, in the writings of Brunner, Cahn, Maritain, Tillich, H. R. Niebuhr, and Reinhold Niebuhr. Ramsey's treatment of these writers is generally sympathetic and sensitive.--P. F. L.

It seems to make perfectly good sense to distinguish between what is expressed and the way in which it is expressed. There is little doubt that there are many different ways of saying the same thing open to us. If I denied this, I would certainly be wrong. And yet a word of caution may not be amiss. Among logicians a tendency has grown up to concentrate their attention on those properties of a statement which make it true or false, (...) what they call a “proposition”, and to neglect the form in which it is expressed. I think it is a dangerous tendency as it may lead to overlooking all sorts of differences which are due to the form. Let me give an example taken from F. P. Ramsey. (shrink)

In the Tractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, (...) we identify three ways in which the first notational convention can be implemented, show that two of these are compatible with the text of the Tractatus, and argue on systematic and historical grounds, adducing posthumous work of Ramsey’s, for one of these as Wittgenstein’s envisaged method. With respect to the second Tractarian proposal, we discuss how Wittgenstein distinguished between general and non-general propositions and argue that, claims to the contrary notwithstanding, an expressively adequate N-operator notation is implicit in the Tractatus when taken in its intellectual environment. We finally introduce a variety of sound and complete tableau calculi for first-order logics formulated in a Wittgensteinian notation. The first of these is based on the contemporary notion of logical truth as truth in all structures. The others take into account the Tractarian notion of logical truth as truth in all structures over one fixed universe of objects. Here the appropriate tableau rules depend on whether this universe is infinite or finite in size, and in the latter case on its exact finite cardinality. As it is obviously easy to express how propositions can be constructed by means of this operation and how propositions are not to be constructed by means of it, this must be capable of exact expression. 5.503. (shrink)

It is widely assumed that there exist certain objects which can in no way be distinguished from each other, unless by their location in space or other reference-system. Some of these are, in a broad sense, 'empirical objects', such as electrons. Their case would seem to be similar to that of certain mathematical 'objects', such as the minimum set of manifolds defining the dimensionality of an R -space. It is therefore at first sight surprising that there exists no branch of (...) mathematics, in which a third parity-relation, besides equality and inequality, is admitted; for this would seem to furnish an appropriate model for application to such instances as these. I hope, in this work, to show that such a mathematics in feasible, and could have useful applications if only in a limited field. The concept of what I here call 'indistinguishability' is not unknown in logic, albeit much neglected. It is mentioned, for example, by F. P. Ramsey [1] who criticizes Whitehead and Russell [2] for defining 'identity' in such a way as to make indistinguishables identical. But, so far as I can discover, no one has made any systematic attempt to open up the territory which lies behind these ideas. What we find, on doing so, is a body of mathematics, offering only a limited prospect of practical usefulness, but which on the theoretical side presents a strong challenge to conventional ideas. (shrink)

After a chapter which is an introduction to and summary of the rest of the book, chapter 2 begins by criticizing various attempts to do away with theories, such as the Reichenbach-Salmon conception of theoretical truth in terms of observational consequences, and the Ramsey strategy of replacing first-order theoretical sentences by second-order nontheoretical ones; it then argues against hypothetico-deductivist theories of confirmation on the grounds that they are unable to handle the relevance of evidence to theory, whether or not other (...) formal constraints or even nonformal ones such as simplicity and explanatory power are added to those theories; it ends with an exposition of the Reichenbach-Carnap conventionalist thesis that the confirmation of hypotheses with evidence presupposes analytic principles connecting hypothetical and empirical concepts. Chapter 3 criticizes Bayesian theories of confirmation on such grounds as that the a priori arguments for Bayesian restrictions on beliefs are insufficient; that the Bayesian explanations of notions like variety of evidence, ad hocness, and simplicity are inadequate; and that they cannot account, without drastic revisions, for the relevance of evidence to theory, especially old evidence to new theory. Chapter 4 is an unsympathetic account of historically oriented philosophies of science; Lakatos’s notion of progressive research programs and Laudan’s theory of problem-solving effectiveness are found to be insufficiently precise and dubbed examples of "new fuzziness", while the Sneed-Stegmüller dynamics of theories is regarded as "a paradigm of misplaced rigor" ; and all three are criticized as unable to explicate the concept of evidential relevance. Chapter 5 is a formal and informal elaboration of the basic idea in Glymour’s account of theory and evidence, namely that confirmation or support is a three-term relation among evidence, hypothesis, and theory, so that evidence confirms an hypothesis only relative to a theory, and such that evidence e confirms hypothesis h relative to T if T with e implies, but T without e does not imply, an instance of h, and T with e does not imply a comparable hypothesis h’ different from h; the most interesting part of this chapter is a series of discussions showing how such an idea makes sense of the "methodological truisms" that it is possible selectively to test certain parts of a theory but not others, that a theory is supported better by a greater variety of evidence, that redundant or physically meaningless quantities are an undesirable feature of theories, that there are no inviolable rules, that a "white shoe" does not confirm "all ravens are black," that a theory is more useful and better supported than the set of its observational consequences, and that the hypothetico-deductive method often works. Since Glymour claims no originality for the conception of this general account, but only for its description, he plausibly thinks it necessary to apply it to some important historical cases of actual science; he does so in the next chapter by discussing at some length the structure and merits of Ptolemaic and Copernican astronomy, of Newton’s universal gravitation, of nineteenth century atomism, of Freud’s Rat Man, and of general relativity. For example, he argues convincingly that Copernicanism was better supported by the evidence available even before the telescope because it alone, and not the Ptolemaic theory, can determine some planetary properties which are presupposed by both theories, can test and confirm some common hypotheses, and can be confirmed in an essential rather than incidental manner; and though Glymour admits that the Copernicans tended to argue in terms of explanatory rather than confirmatory superiority, he sketches an interesting account of the relation between explanation and confirmation which strengthens his case. He also analyzes the text at the beginning of book 3 of Newton’s Principia and compiles a reconstruction of the intricate details of the inferential structure of the argument to universal gravitation; his impressive reconstruction clearly shows that Newton’s method is neither the inductivist one he himself thought he was following, nor the one attributed to him by Pierre Duhem, but rather one in accordance with Glymour’s so-called "bootstrap strategy" of repeatedly using the evidence from Kepler’s second and third laws, from lunar data, and from falling bodies, together with the theory consisting of the second and third laws of motion, to arrive at increasingly general instances of the principle of universal gravitation. Glymour’s account of arguments for and against the atomic theory from Thomson to Cannizzaro is his longest historical example, but he himself admits that this illustration of the bootstrap strategy is "certainly not the neatest", and rather "diffuse, and perhaps disconnected". Chapter 7 is a detailed application of the same principles to the technique known among social scientists as "causal modeling"; since such "causal models" are essentially systems of algebraic equations, Glymour’s account shows indirectly that the bootstrap strategy is applicable to any scientific theory presented as a set of algebraic equations; this, of course is not surprising, since the formal considerations with which Glymour begins the exposition of his theory in chapter 5 involve systems of algebraic equations. Chapter 8 is an attempt to apply Glymour’s theory of evidence to the very common scientific practice of curve-fitting, where one measures values of two or more quantities and then infers a functional relationship; Glymour argues that simpler polynomials are preferred because they are tested more frequently and more severely by the data and because they are more informative; but then he criticizes his own explanation and concludes that "the bootstrap procedures of chapter 5 do not seem to help the problem much more than a whit" ; this is admirably honest, but if one wants an additional logical or methodological rationale, then one would perhaps have to go to the meta-level and say that Glymour is here testing his own theory, and he is more interested in a further illustration of the bootstrap methodology even with a failed test, than he is to claim universal or exclusive validity for it. In chapter 9 Glymour uses his bootstrap theory of confirmation to criticize geometrical conventionalism; he considers the alternative theories of space or space-time proposed by conventionalists to show the radical undetermination of geometries by evidence, for example, a non-Euclidean geometry with no universal force instead of Newtonian gravitation with Euclidean geometry; he argues that such alternatives are simply not as well tested as the originals and that their equivalence to the originals is questionable. The last chapter is a brief discussion of further problems worthy of future investigation. (shrink)