Online research in philosophy

F. P. Ramsey pointed out in Theories that the observational content of a theory expressed partly in non-observational terms is retained in the sentence resulting from existentially generalizing the conjunction of all sentences of the theory with respect to all nonobservational terms. Such terms are thus avoidable in principle, but only at the cost of forming a single "monolithic" sentence. This paper suggests that communication may be thought of as occurring not only by sentence but by clause, a sentential formula closed except for a special kind of variable. Understanding such clauses requires incorporating them within the scope of one's own Ramsey sentence. Many concepts of deductive and inductive logic carry over without great change. But the concepts of truth and designation are extendible to clauses only in the sense that assertions involving them must, to be understood, in turn be construed as clauses and incorporated into the Ramsey sentence. The behavior of these extended concepts of truth and designation suggests an explication of coherence truth within a correspondence-truth framework.

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.

In her preface to this collection of 11 new essays on Ramsey, Frápolli clarifies the nonhistorical orientation of the volume: ‘Our way of honoring Ramsey has been to think with him and, wherever possible, to go beyond that, putting his ideas to work and seeing how far they can reach’ (ix). This certainly makes sense for the topics of many of these essays, building as they do on Ramsey’s rich contributions to economics and reliabilist epistemology as well as on his suggestive proposals about truth, pragmatism and the content of scientific theories. Unfortunately, such an orientation leads to mixed results for the four essays that squarely focus on Ramsey’s philosophy of logic and mathematics. Here Ramsey’s contemporary significance is more debatable and the most fertile mathematical innovation that Ramsey offered, namely ‘Ramsey theory’, is not noted by the contributors to this volume.

In his late paper ‘General Propositions and Causality’, Ramsey argues that unrestricted universal generalisations such as ‘All men are mortal’ are not genuine propositions.1 About this, as about much else in that paper, Ramsey had recently changed his mind. A few years earlier, both in ‘Facts and Propositions’ and in ‘Mathematical Logic’, he had argued that such generalisations are equivalent to infinite conjunctions.2 But by 1929 his ideas about infinity had changed, and it was concerns about the infinite character of unrestricted generalisations which led him to his new view.

The method of Ramsey sentences has been proposed for handling theoretical constructs within a scientific system. Essentially it consists of constructing a certain "monolithic" sentence for an entire theory. In this present paper several improvements are suggested which help to overcome some of the awkward features of the method. In particular we have here many Ramsey sentences rather than just one, each erstwhile primitive theoretical term giving rise to a Ramsey sentence. Such a sentence in effect defines what we call a Ramsey constant. Using Ramsey constants, we attempt to improve the method in important logical and semantical respects. It is suggested also that such constants are of interest for the philosophy of mathematics.

Of the three views of theoretical knowledge which form the focus of this article, the first has its source in the work of Russell, the second in Ramsey, and the third in Carnap. Although very different, all three views subscribe to a principle I formulate as ‘the structuralist thesis’; they are also naturally expressed using the concept of a Ramsey sentence. I distinguish the framework of assumptions which give rise to the structuralist thesis from an unproblematic emphasis on the importance of ‘structural’ differences for the analysis and interpretation of theories belonging to the exact sciences, and I review a number of logical properties of Ramsey sentences using very simple arithmetical theories and their models. I then develop a reconstruction of the views of Russell, Ramsey, and Carnap that clarifies the interrelationships among them by appealing to aspects of the arithmetical examples that inform my discussion of Ramsey sentences. I conclude with an account of the philosophical basis of the structuralist thesis and the fundamental difficulty to which it leads.

It is often thought that questions of reference are crucial in assessing scientific realism, construed as the view that successful theories are at least approximately true descriptions of the unobservable; realism is justified only if terms in empirically successful theories generally refer to genuinely existing entities or properties. In this paper this view is questioned. First, it is argued that there are good reasons to think that questions of realism are largely decided by convention and carry no epistemic significance. An alternative conception of realism is then proposed, which focuses on the Ramsey sentences of scientific theories, constructed in the manner of David Lewis's 'How to define theoretical terms'. It is argued that because the Ramsey sentence of a theory preserves the epistemically significant part of the theory's content without generating commitments to any particular conclusions about reference, the realism issue is better addressed by asking whether Ramsey sentences of theories, rather than the theories themselves, are approximately true.

In the present paper I want to do two things. First, I want to discuss Ramsey’s own views of Ramsey-sentences. This, it seems to me, is an important issue not just (or mainly) because of its historical interest. It has a deep philosophical significance. Addressing it will enable us to see what Ramsey’s lasting contribution in the philosophy of science was as well as what its relevance to today’s problems is. Since the 1950s, where the interest in Ramsey’s views has mushroomed, there have been a number of different ways to read Ramsey’s views and to reconstruct Ramsey’s project. The second aim of the present paper is to discuss the most significant and controversial of this reconstruction, viz., structuralism. After some discussion of the problems of structuralism in the philosophy of science, as this was exemplified in Bertrand Russell’s and Grover Maxwell’s views and has re-appeared in Elie Zahar’s and John Worrall’s thought, I will argue that, for good reasons, Ramsey did not see his Ramsey-sentences as part of some sort of structuralist programme. I will close with an image of scientific theories that Ramsey might have found congenial. I will call it Ramseyan humility.

Solovay has shown that if F: [ω] ω → 2 is a clopen partition with recursive code, then there is an infinite homogeneous hyperarithmetic set for the partition (a basis result). Simpson has shown that for every 0 α , where α is a recursive ordinal, there is a clopen partition F: [ω] ω → 2 such that every infinite homogeneous set is Turing above 0 α (an anti-basis result). Here we refine these results, by associating the "order type" of a clopen set with the Turing complexity of the infinite homogeneous sets. We also consider the Nash-Williams barrier theorem and its relation to the clopen Ramsey theorem.