*An Objective Theory of Probability*, Methuen, 1973, pp. 250 + x

This book develops an objective, but non-frequency, theory of probability. The frequency theory of probability is based on an operationalist philosophy, which is criticized by considering the concept of mass in mechanics. It is suggested that probability should be introduced as an undefined term satisfying the Kolmogorov axioms, and that this mathematical calculus should be connected to experience not by a definition of probability in terms of frequency, but by adopting a falsifying rule for probability statements, designed to underpin the statistical tests which are used in practice.

2. *Frege, Dedekind, and Peano on the Foundations of Arithmetic*, Van Gorcum, 1982, pp. 103 + ix

In contrast to most books about Frege, this one treats Frege not as an isolated figure, but in the context of his contemporaries Dedekind and Peano. It is argued that Frege was primarily a philosopher of mathematics. His contributions to logic and the philosophy of language arose from his attempt to provide arithmetic with a logicist foundation.

3. *Revolutions in Mathematics*, Oxford University Press, 1992, pp. 353 + xi

This is a collection, which I edited, on the question of whether revolutions occur in mathematics. The 12 contributors consider a considerable variety of examples from the history of mathematics, and express a considerable variety of opinions regarding the underlying question. Some think that revolutions do occur in mathematics, while other think they don’t. My own contribution builds on my earlier work on Frege by arguing that Frege initiated a revolution in logic (the Fregean revolution) which is quite analogous to the Copernican revolution in astronomy and physics.

4. *Philosophy of Science in the Twentieth Century: Four Central Themes*, Blackwell, 1993, pp. 251 + xv

This book traces the development in the twentieth century of four central themes in the philosophy of science: inductivism, conventionalism, the nature of observation, and the demarcation between science and metaphysics. The movement of ideas is placed against the background of the lives of the philosophers and of the contemporary developments in science. As in my 1982 book on Frege, the emphasis is on the social. Philosophers are not treated as isolated figures but as part of a community of other philosophers with whom they interacted.

5. *Artificial Intelligence and Scientific Method*, Oxford University Press, 1996, pp. 176 + xv

As I show in my 1993 book, the revolution in physics in the first three decades of the twentieth century encouraged the criticism of inductivism which we find in Duhem and Popper. In the present book, I show that the development of artificial intelligence (AI) from about 1980 has had the opposite effect, and has led to a revival of inductivism. This is hardly surprising since a central technique of AI is machine learning, which consists of induction from data. The book analyses the nature of this machine induction and discusses how it challenges current views about scientific method. The book also shows how the use of logic in AI can lead to a new framework for logic and make possible an inductive logic. The book concludes with a discussion of the hotly contested question of whether computers might become intellectually superior to human beings.

6. *Philosophical Theories of Probability*, Routledge, 2000, pp. 223 + xiv

This book gives an exposition of the main philosophical theories of probability, which are: the classical, logical, subjective, frequency and propensity. It also expounds a new theory the *intersubjective* which is a development of the subjective view, and gives a distinctive version of the propensity theory. The book argues for a pluralist view, where there can be more than one valid interpretation of probability, each appropriate in a different context.

7. C. Cellucci & D. Gillies (Eds.) *Mathematical Reasoning and Heuristics*, 2005, King’s College Publications, pp. 212 +xxx

This is a collection edited by Carlo Cellucci and myself. Many of the contributors are interested in issues to do with the development of mathematics. My own paper suggests three heuristics, namely (a) the Use of Philosophical Ideas, (b) New Practical Problems, and (c) Domain Interaction. They are illustrated by the example of the Discovery of Bayesian networks. Carlo Cellucci’s paper gives a good short account of his controversial views on the philosophy of mathematics, namely his criticism of the axiomatic method as the method of mathematics, and suggestion that the real method of mathematics is the analytic method.

8. *How Should Research be Organised? *College Publications, 2008, pp. 137 + xii

This book applies results from history and philosophy of science to the question of research organisation. It begins by criticizing the research assessment exercise (RAE) which was introduced in the UK in 1986 by Margaret Thatcher and continued until 2008. The problem with the RAE and similar systems is that it is not possible immediately to give a valid assessment of the value of a piece of research. This is shown by numerous examples from the history of science where research, which we now judge to have been a major advance, was initially condemned as valueless and only after twenty or thirty years recognised to have been a breakthrough. Ideas from the philosophy of science explain why this phenomenon of ‘delayed recognition’ occurs, and show that it is particularly likely to happen to major advances. So basing research funding on assessments carried out after a few years is likely to reduce the overall quality of research by stifling the most valuable research programmes. As well as criticizing the RAE approach to research organisation, the book suggests an alternative approach which is likely to be both cheaper and more successful. This is based on the way research was organised at Cambridge, UK in the period 1897 to 1953. This period was one of the most remarkably productive of good research in the history of Cambridge, and indeed of any university.

9. *Causality, Probability, and Medicine*, Routledge, pp. 300 + xvi

This book is the result of about two decades of research in philosophy of science for medicine. It presents a theory of generic (or type) causality for theoretical medicine, an area in which causality is the central concept. Part I of the book considers those theories which relate causality to action, intervention, and manipulation. A particular theory of this type (the action-related theory of causality) is developed for the deterministic case, and illustrated by the example of Koch’s work on cholera. Part II of the book considers causality and mechanisms. The mechanistic theory of causality is rejected in favour of a causal theory of mechanisms, where causality is explicated by the action-related theory. However, it is argued that mechanisms and evidence of mechanism are very important for medicine, and this leads to a criticism of evidence-based medicine (EBM). Again this part is illustrated by a variety of examples including research into coronary heart disease, and the first use in medicine of randomized controlled trials (RCTs). This was to examine the efficacy of streptomycin as a cure for tuberculosis. Part III considers causality and probability. Causality often needs to be connected to probability, but it is not clear how this should be done, and paradoxes have arisen in many attempted solutions to the problem. The approach developed here uses causal networks in which the probabilities are interpreted as propensities. This approach is compared to the rather different one put forward by Pearl.