The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

This paper suggests a new principle for confirmation theory which is called the principle of explanatory surplus. This principle is shown to be non-Bayesian in character, and to lead to a treatment of simplicity in science. Two cases of the principle of explanatory surplus are considered. The first (number of parameters) is illustrated by curve-fitting examples, while the second (number of theoretical assumptions) is illustrated by the examples of Newton's Laws and Adler's Theory of the Inferiority Complex.

Evidence-based medicine (EBM) makes use of explicit procedures for grading evidence for causal claims. Normally, these procedures categorise evidence of correlation produced by statistical trials as better evidence for a causal claim than evidence of mechanisms produced by other methods. We argue, in contrast, that evidence of mechanisms needs to be viewed as complementary to, rather than inferior to, evidence of correlation. In this paper we first set out the case for treating evidence of mechanisms alongside evidence of correlation in (...) explicit protocols for evaluating evidence. Next we provide case studies which exemplify the ways in which evidence of mechanisms complements evidence of correlation in practice. Finally, we put forward some general considerations as to how the two sorts of evidence can be more closely integrated by EBM. (shrink)

Social revolutions--that is critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. But can the idea of revolutionary upheaval be extended to the world of ideas and theoretical debate? The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences. A fascinating, but little known, off-shoot of this was a debate which began in the United States in the mid-1970's as to whether the concept of revolution could (...) be applied to mathematics as well as science. Michael Grove declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave some examples. This book is the first comprehensive examination of the question. It reprints the original papers of Grove, Dauben, and Mehrtens, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics, who each discuss an important episode and consider whether it was a revolution. The whole question of mathematical revolutions is thus examined comprehensively and from a variety of perspectives. This thought-provoking volume will interest mathematicians, philosophers, and historians alike. (shrink)

According to current hierarchies of evidence for EBM, evidence of correlation is always more important than evidence of mechanisms when evaluating and establishing causal claims. We argue that evidence of mechanisms needs to be treated alongside evidence of correlation. This is for three reasons. First, correlation is always a fallible indicator of causation, subject in particular to the problem of confounding; evidence of mechanisms can in some cases be more important than evidence of correlation when assessing a causal claim. Second, (...) evidence of mechanisms is often required in order to obtain evidence of correlation. Third, evidence of mechanisms is often required in order to generalise and apply causal claims. While the EBM movement has been enormously successful in making explicit and critically examining one aspect of our evidential practice, i.e., evidence of correlation, we wish to extend this line of work to make explicit and critically examine a second aspect of our evidential practices: evidence of mechanisms. (shrink)

Why is understanding causation so important in philosophy and the sciences? Should causation be defined in terms of probability? Whilst causation plays a major role in theories and concepts of medicine, little attempt has been made to connect causation and probability with medicine itself. Causality, Probability, and Medicine is one of the first books to apply philosophical reasoning about causality to important topics and debates in medicine. Donald Gillies provides a thorough introduction to and assessment of competing theories (...) of causality in philosophy, including action-related theories, causality and mechanisms, and causality and probability. Throughout the book he applies them to important discoveries and theories within medicine, such as germ theory; tuberculosis and cholera; smoking and heart disease; the first ever randomized controlled trial designed to test the treatment of tuberculosis; the growing area of philosophy of evidence-based medicine; and philosophy of epidemiology. This book will be of great interest to students and researchers in philosophy of science and philosophy of medicine, as well as those working in medicine, nursing and related health disciplines where a working knowledge of causality and probability is required. (shrink)

Artificial Intelligence and Scientific Method examines the remarkable advances made in the field of AI over the past twenty years, discussing their profound implications for philosophy. Taking a clear, non-technical approach, Donald Gillies shows how current views on scientific method are challenged by this recent research, and suggests a new framework for the study of logic. Finally, he draws on work by such seminal thinkers as Bacon, Gdel, Popper, Penrose, and Lucas, to address the hotly-contested question of whether (...) computers might become intellectually superior to human beings. (shrink)

The propensity interpretation of probability was introduced by Popper ([1957]), but has subsequently been developed in different ways by quite a number of philosophers of science. This paper does not attempt a complete survey, but discusses a number of different versions of the theory, thereby giving some idea of the varieties of propensity. Propensity theories are classified into (i) long-run and (ii) single-case. The paper argues for a long-run version of the propensity theory, but this is contrasted with two single-case (...) propensity theories, one due to Miller and the later Popper, and the other to Fetzer. The three approaches are compared by examining how they deal with a key problem for the propensity approach, namely the relationship between propensity and causality and Humphreys' paradox. (shrink)

This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of limiting frequency and claims that (...) probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the ‘actual world of experiments’. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper’s concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics. (shrink)

Semmelweis’s investigations of puerperal fever are some of the most interesting in the history of medicine. This paper considers Hempel’s analysis of the Semmelweis case. It argues that this analysis is inadequate and needs to be supplemented by some Kuhnian ideas. Kuhn’s notion of paradigm needs to be modified to apply to medicine in order to take account of the classification schemes involved in medical theorising. However with a suitable modification it provides an explanation of Semmelweis’s failure which is argued (...) to be superior to some of the external reasons often given. Despite this success in applying Kuhn’s ideas to medicine, it is argued that these ideas must be further modified to take account of the fact that medicine is not a natural science but primarily a practice designed to prevent and cure diseases. (shrink)

The paper begins with a discussion of Russell's view that the notion of cause is unnecessary for science and can therefore be eliminated. It is argued that this is true for theoretical physics but untrue for medicine, where the notion of cause plays a central role. Medical theories are closely connected with practical action (attempts to cure and prevent disease), whereas theoretical physics is more remote from applications. This suggests the view that causal laws are appropriate in a context where (...) there is a close connection to action. This leads to a development of an action-related theory of causality which is similar to the agency theory of Menzies and Price, but differs from it in a number of respects, one of which is the following. Menzies and Price connect ‘A causes B’ with an action to produce B by instantiating A, but, particularly in the case of medicine, the law can also be linked to the action of trying to avoid B by ensuring that A is not instantiated. The action-related theory has in common with the agency theory of Menzies and Price the ability to explain causal asymmetry in a simple fashion, but the introduction of avoidance actions together with some ideas taken from Russell enable some of the objections to agency accounts of causality to be met. Introduction Russell on causality Preliminary exposition of the action-related theory Differences between the action-related theory and the agency theory of Menzies and Price Explanation of causal asymmetry Objections to the action-related theory Extension of the theory to the indeterminate case. (shrink)

Semmelweis’s investigations of puerperal fever are some of the most interesting in the history of medicine. This paper considers Hempel’s analysis of the Semmelweis case. It argues that this analysis is inadequate and needs to be supplemented by some Kuhnian ideas. Kuhn’s notion of paradigm needs to be modified to apply to medicine in order to take account of the classification schemes involved in medical theorising. However with a suitable modification it provides an explanation of Semmelweis’s failure which is argued (...) to be superior to some of the external reasons often given. Despite this success in applying Kuhn’s ideas to medicine, it is argued that these ideas must be further modified to take account of the fact that medicine is not a natural science but primarily a practice designed to prevent and cure diseases. (shrink)

This paper introduces what is called the intersubjective interpretation of the probability calculus. Intersubjective probabilities are related to subjective probabilities, and the paper begins with a particular formulation of the familiar Dutch Book argument. This argument is then extended, in Section 3, to social groups, and this enables the concept of intersubjective probability to be introduced in Section 4. It is then argued that the intersubjective interpretation is the appropriate one for the probabilities which appear in confirmation theory whether of (...) a Bayesian or a Popperian variety. The final section of the paper states and tries to answer an objection due to Putnam. (shrink)

Hume bases his argument against miracles on an informal principle. This paper gives a formal explication of this principle of Hume’s, and then shows that this explication can be rigorously proved in a Bayesian framework.

The paper begins with an exposition of Aristotle’s own philosophy of mathematics. It is claimed that this is based on two postulates. The first is the embodiment postulate, which states that mathematical objects exist not in a separate world, but embodied in the material world. The second is that infinity is always potential and never actual. It is argued that Aristotle’s philosophy gave an adequate account of ancient Greek mathematics; but that his second postulate does not apply to modern mathematics, (...) which assumes the existence of the actual infinite. However, it is claimed that the embodiment postulate does still hold in contemporary mathematics, and this is argued in detail by considering the natural numbers and the sets of ZFC. (shrink)

This paper seeks to analyse the effects on Economics of Research Assessment Systems, such as the Research Assessment Exercise (or RAE) which was carried out in the UK between 1986 and 2008. The paper begins by pointing out that, in the 2008 RAE, economics turned out to be the research area which was accorded the highest valuation of any subject in the UK, even though economists were then under attack for failing to predict the global financial crash which had occurred (...) a few months earlier. One aim of the paper is to explain this economics anomaly in research assessment. The paper goes on to point out a key difference between economics and the natural sciences. Most areas of the natural sciences are dominated for most of the time by a single, generally accepted, paradigm, whereas there are always in economics different schools of thought which have different and highly conflicting paradigms. Given this situation, it is argued that the effect of research assessment systems in economics is to strengthen the majority school in the subject (whatever that is), and weaken the minority schools. This conclusion is supported by empirical data collected by Frederic Lee for the UK. It is then shown that the greater the dominance of the majority school, the higher the overall valuation of the subject is likely to be, and this is used to explain the anomaly noted earlier. It is argued that research in economics flourishes better in a situation in which there are a number of different schools treated equally, than in one in which a single school dominates. The conclusion is that research assessment systems have a negative effect on research in economics and give misleading results. Instead of such systems, an attempt should be made to encourage pluralism in the subject. (shrink)

This paper takes up a suggestion made by Floridi that the digital revolution is bringing about a profound change in our metaphysics. The paper aims to bring some older views from philosophy of mathematics to bear on this problem. The older views are concerned principally with mathematical realism—that is the claim that mathematical entities such as numbers exist. The new context for the discussion is informational realism, where the problem shifts to the question of the reality of information. Mathematical realism (...) is perhaps a special case of informational realism. The older views concerned with mathematical realism are the various theories of World 3. The concept of World 3 was introduced by Frege, whose position was close to Plato’s original views. Popper developed the theory of World 3 in a different direction which is characterised as ‘constructive Platonism’. But how is World 3 constructed? This is explored by means of two analogies: the analogy with money, and the analogy with meaning, as explicated by the later Wittgenstein. This leads to the development of an account of informational realism as constructive Aristoteliansim. Finally, this version of informational realism is compared with the informational structural realism which Floridi develops in his 2008 and 2009 papers in Synthese. Similarities and differences between the two positions are noted. (shrink)

This paper begins by developing a causal theory of mechanisms in medicine, and illustrates the theory with the example of the mechanism of the disease anthrax as elucidated by Koch. The causal approach to mechanisms is then compared to the Machamer, Darden, Craver approach. At first sight the two approaches appear to be very different, but it is argued that the divergence is less than it initially seems. There are some differences, however, and it is argued that, where these differences (...) occur, the causal approach to mechanisms is superior. (shrink)

This paper considers whether philosophy of mathematics could benefit by the introduction of some sociology. It begins by considering Lakatos's arguments that philosophy of science should be kept free of any sociology. An attempt is made to criticize these arguments, and then a positive argument is given for introducing a sociological dimension into the philosophy of mathematics. This argument is illustrated by considering Brouwer's account of numbers as mental constructions. The paper concludes with a critical discussion of Azzouni's view that (...) mathematics differs fundamentally from other social practices. (shrink)

The aim of this paper is to consider whether critical rationalism has any ideas which could usefully be applied to the internet. Today we tend to take the internet for granted and it is easy to forget that it was only about two decades ago that it began to be used to any significant extent. Accordingly in section 1 of the paper, there is a brief consideration of the history of the internet. At first sight this makes it looks implausible (...) that any of Popper’s ideas could be applicable to the internet, since Popper died before the internet came into general use. However, section 2 argues that Popper’s theory of World 3 does apply very well to the internet. This application is significant because, as shown in section 3, it leads to the problem of misinformation, which is one of the most significant problems generated by the internet. In section 4 there is an attempt to solve this problem using ideas taken from Popper’s epistemology. It is argued that there should be changes in education designed to prepare students for the internet age. Teaching in the internet age should focus on presenting to the students not just the accepted theories but also the evidence on which they are based. An illustration of how this might be done is given by considering an example from science teaching, namely the teaching of Newtonian mechanics in the last years of school or first years of university. (shrink)

This volume is a collection of papers on philosophy of mathematics which deal with a series of questions quite different from those which occupied the minds of the proponents of the three classic schools: logicism, formalism, and intuitionism. The questions of the volume are not to do with justification in the traditional sense, but with a variety of other topics. Some are concerned with discovery and the growth of mathematics. How does the semantics of mathematics change as the subject develops? (...) What heuristics are involved in mathematical discovery, and do such heuristics constitute a logic of mathematical discovery? What new problems have been introduced by the development of mathematics since the 1930s? Other questions are concerned with the applications of mathematics both to physics and to the new field of computer science. Then there is the new question of whether the axiomatic method is really so essential to mathematics as is often supposed, and the question, which goes back to Wittgenstein, of the sense in which mathematical proofs are compelling. Taking these questions together they give part of an emerging agenda which is likely to carry philosophy of mathematics forward into the twenty first century. (shrink)

The development of causal modelling since the 1950s has been accompanied by a number of controversies, the most striking of which concerns the Markov condition. Reichenbach's conjunctive forks did satisfy the Markov condition, while Salmon's interactive forks did not. Subsequently some experts in the field have argued that adequate causal models should always satisfy the Markov condition, while others have claimed that non-Markovian causal models are needed in some cases. This paper argues for the second position by considering the multi-causal (...) forks, which are widespread in contemporary medicine (Section 2). A non-Markovian causal model for such forks is introduced and shown to be mathematically tractable (Sections 6, 7, and 8). The paper also gives a general discussion of the controversy about the Markov condition (Section 1), and of the related controversy about probabilistic causality (Sections 3, 4, and 5). (shrink)

The Einsteinian revolution, which began around 1905, was one of the most remarkable in the history of physics. It replaced Newtonian mechanics, which had been accepted as completely correct for nearly 200 years, by the special and general theories of relativity. It also eliminated the aether, which had dominated physics throughout the nineteenth century. This paper poses the question of why this momentous scientific revolution began. The suggested answer is in terms of the remarkable series of discoveries and inventions which (...) occurred in the preceding decade and which were the result of technological developments in instrumentation. The paper gives a survey of these inventions and discoveries, which include X-rays, radioactivity, the electron, wireless transmissions across the Atlantic and the patenting of the first thermionic valve. An attempt is then made to show that it was these developments, which gave rise to special relativity. (shrink)

Dynamic interaction is said to occur when two significanrly different fields A and B come into relation, and their interaction is dynamic in the sense that at first the flow of ideas is principally from A to B, but later ideas from B come to influence A. Two examples are given of dynamic interactions with the philosophy of mathematics. The first is with philosophy of scicnce, and thc sccond with computer science. Theanalysis cnables Lakatos to be charactcrised as thc first (...) to devclop the philosophy of mathematics using ideas taken from thc philosophy of science. (shrink)

This paper argues for a claim made by Maria Carla Galavotti that the use of indeterministic causality involves one in Simpson's paradox. It is shown specifically that a consideration of Hesslow's well-known counter-example leads to Simpson's paradox.

Outlines the key concepts in the work of Foucault, showing how his concepts of discourse, of power/knowledge, and of governmentality offer a way to understand how ideas of educational leadership and management have emerged, how they serve to establish a discipline, and how they construct individuals in particular ideological ways.

The main thesis of this paper is that the empirical success of Keynesianism shows it to be scientific. Keynesianism here refers not to a specific theory, but to a paradigm. It is argued that Kuhn's notion of paradigm can be applied to economics, but, in contrast to the natural sciences, in economics there are always competing paradigms. The principal ones in contemporary economics are the Neoclassical, Keynesian and Marxist. To investigate whether the Keynesian paradigm is scientific we need a criterion (...) for the scientificity of a paradigm. The paper first considers one approach to this problem due to Kant, but this is rejected as incorrect and called 'the Kantian fallacy'. Another approach is then put forward: 'the empirical confirmation principle', and reasons are given for accepting this as correct. Using this principle, it is then argued that that Keynesianism is indeed scientific. (shrink)

Traditionally logic was considered as having two branches deductive and inductive. However the development of the subject from Frege up to about 1970 brought about a divergence between deductive and inductive logic. It is argued in this paper that developments in artificial intelligence in the last twenty or so years have created a new framework for logic in which deductive and inductive logic can, once again, be treated as similar branches of the same discipline.

This paper investigates the relations between causality and propensity. Aparticular version of the propensity theory of probability is introduced, and it is argued that propensities in this sense are not causes. Some conclusions regarding propensities can, however, be inferred from causal statements, but these hold only under restrictive conditions which prevent cause being defined in terms of propensity. The notion of a Bayesian propensity network is introduced, and the relations between such networks and causal networks is investigated. It is argued (...) that causal networks cannot be identified with Bayesian propensity networks, but that causal networks can be a valuable heuristic guide for the construction of Bayesian propensity networks. (shrink)

Popper's writings cover a remarkably wide range of subjects. The spectrum runs from Plato's theory of politics to the foundations of quantum mechanics. Yet even amidst this variety the philosophy of probability occupies a prominent place. David Miller once pointed out to me that more than half of Popper's The Logic of Scientific Discovery is taken up with discussions of probability. I checked this claim using the 1972 6th revised impression of The Logic of Scientific Discovery , and found that (...) of the approximately 450 pages of text, approximately 250 are to do with probability. Thus Miller's claim is amply justified. It seems indeed that the philosophy of probability was one of Popper's favourite subjects, and, as we shall see, Popper certainly enriched the field with several striking innovations. In this area, as in others, Popper held very definite views, and criticized his opponents in no uncertain terms. Popper was an objectivist and anti-Bayesian, and his criticisms were directed against subjectivism and Bayesianism. (shrink)

Suppose we were to ask some students of philosophy to imagine a typical book of classical German philosophy and describe its general style and character, how might they reply? I suspect that they would answer somewhat as follows. The book would be long and heavy, it would be written in a complicated style which employed only very abstract terms, and it would be extremely difficult to understand. At all events a description of this kind does indeed fit many famous works (...) of German philosophy. Let us take for example Hegel's Phenomenology of Spirit of 1807. The 1977 English translation published by Oxford has 591 pages, and as for style here is a typical passage: Self-consciousness found the Thing to be like itself, and itself to be like a Thing; i.e., it is aware that it is in itself the objectively real world. It is no longer the immediate certainty of being all reality, but a certainty for which the immediate in general has the form of something superseded, so that the objectivity of the immediate still has only the value of something superficial, its inner being and essence being self-consciousness itself. The object, to which it is positively related, is therefore a self-consciousness. It is in the form of thinghood, i.e. it is independent ; but it is certain that this independent object is for it not something alien, and thus it knows that it is in principle recognized by the object. It is Spirit which, in the duplication of its self-consciousness and in the independence of both, has the certainty of its unity with itself. This certainty has now to be raised to the level of truth; what holds good for it in principle , and in its inner certainty, has to enter into its consciousness and become explicit fork. (shrink)

This paper is divided into two parts. In the first part , I will describe briefly how advances in artificial intelligence in the 1970s led to the crucial problem of handling uncertainty, and how attempts to solve this problem led in turn to the emergence of the new theory of Bayesian networks. I will try to focus in this historical account on the key ideas and will not give a full account of the technical details. Then, in the second part (...) , I will consider the implications of these new results for the long-standing controversy between Bayesians and non-Bayesians. (shrink)

This paper is divided into two parts. In the first part, I will describe briefly how advances in artificial intelligence in the 1970s led to the crucial problem of handling uncertainty, and how attempts to solve this problem led in turn to the emergence of the new theory of Bayesian networks. I will try to focus in this historical account on the key ideas and will not give a full account of the technical details. Then, in the second part, I (...) will consider the implications of these new results for the long-standing controversy between Bayesians and non-Bayesians. (shrink)

The aim of this article is to explore what the concept of interdisciplinarity can bring to our developing understanding of education as a field of enquiry. We shall draw upon some recent writing on the disciplines of education in order to explore the potentially negative consequences of the way in which the disciplines are institutionalised and territorialised. We also assign some prominence to a personal account of an eminent anthropologist's perambulations through a disciplinary landscape in order to put forward an (...) initial, tentative view of interdisciplinary endeavour. Nietzsche's essay 'Schopenhauer as educator' and the distinction between measurable time (chronos) and lived time (kairos) are the vehicles through which the authors explore the nature of intellectual inquiry. They also consider the implications of the prevalence of spatial and cartographic metaphors in scholarship in this area of enquiry, and reflect on the contrasting notions of habitation and occupation. They put forward the view that the key to understanding the role of the disciplines of education is in exploring the reciprocal relations between the lives of academics and the institutions of the disciplines (books, articles, reports, societies, journals, conferences, networks), between personal narrative and grand narrative, and in attempting to reconcile full-bodied being and the ghostly life of 'pure knowledge'. (shrink)