In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. But physical theory routinely predicts the values of observable magnitudes within very small ranges of error. The chance of this sort of predictive success without a true theory suggests that Hume's argument is flawed. However, Colin Howson argues that there is no flaw and examines the implications of this disturbing conclusion; he also offers a solution to one of the central (...) problems of Western philosophy, the problem of induction. (shrink)

In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.

in Handbook of the Philosophy of Information, J. van Behthem and P. Adriaans, eds., to appear.

This book is devoted to a different proposal--that the logical structure of the scientist's method should guarantee eventual arrival at the truth given the scientist's background assumptions.

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Introduction 1 1 Inductive Inference: A New Approach 19 2 Luck, License, and Lingo 31 3 Natural Kinds 41 4 Concerning a Fiction about How Facts Are Forecast 57 5 Grue 79 6 Concepts of Projectibility and the Problems of Induction 97 7 Induction, Conceptual Spaces, and AI 117 8 The Projectibility Constraint 135 9 Simplicity as a Pragmatic Criterion for Deciding What Hypotheses to Take Seriously 153 10 A Grue Thought in a Bleen Shade: ’Grue’ as a Disjunctive Predicate (...) 173 11 Entrenchment 193 12 No Model, No Inference: A Bayesian Primer on the Grue Problem 225 13 Bayesian Projectibility 241 14 Learning and Projectibility 263 15 Selecting Variables and Getting to the Truth 273 Annotated Bibliography 281 Index 459. (shrink)

This paper studies the use of hypotheses schemes in generatinginductive predictions. After discussing Carnap–Hintikka inductive logic,hypotheses schemes are defined and illustrated with two partitions. Onepartition results in the Carnapian continuum of inductive methods, the otherresults in predictions typical for hasty generalization. Following theseexamples I argue that choosing a partition comes down to making inductiveassumptions on patterns in the data, and that by choosing appropriately anyinductive assumption can be made. Further considerations on partitions makeclear that they do not suggest any solution (...) to the problem of induction.Hypotheses schemes provide the tools for making inductive assumptions, but theyalso reveal the need for such assumptions. (shrink)

This article suggests a ‘best alternative' justification of induction (in the sense of Reichenbach) which is based on meta-induction . The meta-inductivist applies the principle of induction to all competing prediction methods which are accessible to her. It is demonstrated, and illustrated by computer simulations, that there exist meta-inductivistic prediction strategies whose success is approximately optimal among all accessible prediction methods in arbitrary possible worlds, and which dominate the success of every noninductive prediction strategy. The proposed justification of meta-induction is (...) mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. *Received November 2005; revised March 2008. †To contact the author, please write to: Department of Philosophy, University of Duesseldorf, Universitaetsstrasse 1, Geb. 23.21, Duesseldorf, Germany D-40225; e-mail: [email protected]. (shrink)

Among the various meanings in which the word ‘probability’ is used in everyday language, in the discussion of scientists, and in the theories of probability, there are especially two which must be clearly distinguished. We shall use for them the terms ‘probability1’ and ‘probability2'. Probability1 is a logical concept, a certain logical relation between two sentences ; it is the same as the concept of degree of confirmation. I shall write briefly “c” for “degree of confirmation,” and “c” for “the (...) degree of confirmation of the hypothesis h on the evidence e“; the evidence is usually a report on the results of our observations. On the other hand, probability2 is an empirical concept; it is the relative frequency in the long run of one property with respect to another. The controversy between the so-called logical conception of probability, as represented e.g. by Keynes, and Jeffreys, and others, and the frequency conception, maintained e.g. by v. Mises and Reichenbach, seems to me futile. These two theories deal with two different probability concepts which are both of great importance for science. Therefore, the theories are not incompatible, but rather supplement each other. (shrink)

This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...) I argue that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analog of Mathematical CT. The correct physical analog of Mathematical CT is Modest Physical CT. I propose to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function. Finally, I suggest that proposed counterexamples to Physical CT are still far from falsifying it because they have not been shown to satisfy the usability constraint. (shrink)

In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but more on the philosophical (...) and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction. (shrink)