Much of scientific inference involves fitting numerical data with a curve, or functional relation. The received view is that the fittest curve is the curve which best balances the conflicting demands of simplicity and accuracy, where simplicity is measured by the number ofparameters in the curve. The problem with this view is that there is no commonly accepted justification for desiring simplicity. This paper presents a measure of the stability of equations. It is argued that the fittest curve is the (...) curve which best balances stability and accuracy. The received view is defended with a proof that simplicity corresponds to stability, for linear regression equations. 1This paper is based on part of my doctoral dissertation. My thanks go to my thesis supervisor Professor Alasdair Urquhart for his encouragement, constructive criticism, and for directing me to several relevant articles: to my advisor Professor Ian Hacking for reminding me to concentrate on results that might have some application in the real world; and to my friend Wendy Brandts for sharing her ideas on a closely related problem. My thanks also to an anonymous referee of The British Journal of the Philosophy of Science for several helpful comments, to my friends and family for unfailing support, and to the Social Sciences and Humanities Research Council (awards 452-86-5885 and 453-87-0513) and the University of Toronto for financial assistance. (shrink)

The controversy surrounding Popper's proposed solution to the problem of induction is beginning to display many of the symptoms of being interminable. For decades the discussion has continued, apparently without any progress being made. Again and again, Popperians and their critics have accused each other of ‘missing the point’. The essay attempts to explain what exactly is ‘the point’ of the problem of induction, and asks whether Popper does indeed miss it. An answer is proposed, and on this basis an (...) explanation for the puzzling interminability and emptiness of the above dialogue is put forward. (shrink)

In this paper a new conception of foundation-oriented epistemology is developed. The major challenge for foundation-oriented justifications consists in the problem of stopping the justificational regress without taking recourse to dogmatic assumptions or circular reasoning. Two alternative accounts that attempt to circumvent this problem, coherentism and externalism, are critically discussed and rejected as unsatisfactory. It is argued that optimality arguments are a new type of foundation-oriented justification that can stop the justificational regress. This is demonstrated on the basis of a (...) novel result in the area of induction: the optimality of meta-induction. In the final section the method of optimality justification is generalized to deductive and abductive inferences. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

Deductive and inductive logic confront this skeptical challenge: we can justify any logical principle only by means of an argument but we can acquire justification by means of an argument only if we are already justified in believing some logical principle. We could solve this problem if probative arguments do not require justified belief in their corresponding conditionals. For if not, then inferential justification would not require justified belief in any logical principle. So even arguments whose corresponding conditionals are epistemically (...) dependent upon their conclusions--epistemically self-supporting arguments--need not be viciously circular. R. B. Braithwaite and James Van Cleve use internalist and externalist versions of this strategy in their proposed solutions to the problem of induction. Unfortunately, their arguments for self-support are unsound and any theory of inferential justification that does not require justified belief in the corresponding conditionals of justification-affording arguments is unacceptably arbitrary. So self-supporting arguments cannot be justification-creating. (shrink)

Karl Popper is famous for having proposed that science advances by a process of conjecture and refutation. He is also famous for defending the open society against what he saw as its arch enemies – Plato and Marx. Popper’s contributions to thought are of profound importance, but they are not the last word on the subject. They need to be improved. My concern in this book is to spell out what is of greatest importance in Popper’s work, what its failings (...) are, how it needs to be improved to overcome these failings, and what implications emerge as a result. The book consists of a collection of essays which dramatically develop Karl Popper’s views about natural and social science, and how we should go about trying to solve social problems. Criticism of Popper’s falsificationist philosophy of natural science leads to a conception of science that I call aim-oriented empiricism. This makes explicit metaphysical theses concerning the comprehensibility and knowability of the universe that are an implicit part of scientific knowledge – implicit in the way science excludes all theories that are not explanatory, even those that are more successful empirically than accepted theories. Aim-oriented empiricism has major implications, not just for the academic discipline of philosophy of science, but for science itself. Popper generalized his philosophy of science of falsificationism to arrive at a new conception of rationality – critical rationalism – the key methodological idea of Popper’s profound critical exploration of political and social issues in his The Open Society and Its Enemies, and The Poverty of Historicism. This path of Popper, from scientific method to rationality and social and political issues is followed here, but the starting point is aim-oriented empiricism rather than falsificationism. Aim-oriented empiricism is generalized to form a conception of rationality I call aim-oriented rationalism. This has far-reaching implications for political and social issues, for the nature of social inquiry and the humanities, and indeed for academic inquiry as a whole. The strategies for tackling social problems that arise from aim-oriented rationalism improve on Popper’s recommended strategies of piecemeal social engineering and critical rationalism, associated with Popper’s conception of the open society. This book thus sets out to develop Popper’s philosophy in new and fruitful directions. The theme of the book, in short, is to discover what can be learned from scientific progress about how to achieve social progress towards a better world. (shrink)

The aim of this contribution is to provide a rather general answer to Hume's problem, the well-known problem of induction. To this end, it is very useful to apply his differentiation between ``relations of ideas'' and ``matters of fact'', and to reconsider earlier approaches. In so doing, we consider the problem formally, as well as empirically. Next, received attempts to solve the problem are discussed. The basic structure of inductive problems is exposed in chap. 6. Our final conclusions are to (...) the positive, i.e., Hume's problem can be dealt with - solved - in a constructive way. More specifically, bounded generalisations can be justified, and the key to the solution is the concept of information. (shrink)

I begin by making some distinctions between kinds of response to a skeptical claim, the purpose of which is to explain what I mean by a "dissolution" of the problem of induction, and to focus on one of the ways it can be implemented. I then argue that previous attempts to dissolve the problem in this way fail, present mine, and defend it. Finally, I show that the dissolution of the problem doesn't improve our normative situation and may even worsen (...) it. (shrink)