Arguably, Hume's greatest single contribution to contemporary philosophy of science has been the problem of induction (1739). Before attempting its statement, we need to spend a few words identifying the subject matter of this corner of epistemology. At a first pass, induction concerns ampliative inferences drawn on the basis of evidence (presumably, evidence acquired more or less directly from experience)—that is, inferences whose conclusions are not (validly) entailed by the premises. Philosophers have historically drawn further distinctions, often appropriating the term (...) “induction” to mark them; since we will not be concerned with the philosophical issues for which these distinctions are relevant, we will use the word “inductive” in a catch-all sense synonymous with “ampliative”. But we will follow the usual practice of choosing, as our paradigm example of inductive inferences, inferences about the future based on evidence drawn from the past and present. A further refinement is more important. Opinion typically comes in degrees, and this fact makes a great deal of difference to how we understand inductive inferences. For while it is often harmless to talk about the conclusions that can be rationally believed on the basis of some.. (shrink)

Oxford Philosophical Texts Series Editor: John Cottingham The Oxford Philosophical Texts series consists of authoritative teaching editions of canonical texts in the history of philosophy from the ancient world down to modern times. Each volume provides a clear, well laid out text together with a comprehensive introduction by a leading specialist, giving the student detailed critical guidance on the intellectual context of the work and the structure and philosophical importance of the main arguments. Endnotes are supplied which provide further commentary (...) on the arguments and explain unfamiliar references and terminology, and a full bibliography and index are also included. The series aims to build up a definitive corpus of key texts in the Western philosophical tradition, which will form a reliable and enduring resource for students and teachers alike. David Hume's aim in writing An Enquiry concerning Human Understanding was to introduce his philosophy to a European culture in which many educated people read original works of philosophy. He gives an elegant and accessible presentation of strikingly original and challenging views about the limited powers of human understanding, the attractions of scepticism, the compatibility of free will and determinism, and weaknesses in the foundations of religion. Hume's philosophy was highly controversial in the eighteenth century and remains so today. The text printed in this edition is that of the Clarendon critical edition of Hume's works. A substantial introduction by the editor explains the intellectual background to the work and surveys its main themes. The volume also includes detailed explanatory notes on the text, a glossary of terms, a full list of references, and a section of supplementary readings. (shrink)

David Hume's Enquiry concerning Human Understanding is the definitive statement of the greatest philosopher in the English language. His arguments in support of reasoning from experience, and against the "sophistry and illusion"of religiously inspired philosophical fantasies, caused controversy in the eighteenth century and are strikingly relevant today, when faith and science continue to clash. The Enquiry considers the origin and processes of human thought, reaching the stark conclusion that we can have no ultimate understanding of the physical world, or indeed (...) our own minds. In either sphere we must depend on instinctive learning from experience, recognizing our animal nature and the limits of reason. Hume's calm and open-minded skepticism thus aims to provide a new basis for science, liberating us from the "superstition" of false metaphysics and religion. His Enquiry remains one of the best introductions to the study of philosophy, and his edition places it in its historical and philosophical context. (shrink)

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)

Knowledge in a Social World offers a philosophy for the information age. Alvin Goldman explores new frontiers by creating a thoroughgoing social epistemology, moving beyond the traditional focus on solitary knowers. Against the tides of postmodernism and social constructionism Goldman defends the integrity of truth and shows how to promote it by well-designed forms of social interaction. From science to education, from law to democracy, he shows why and how public institutions should seek knowledge-enhancing practices. The result is a bold, (...) timely, and systematic treatment of the philosophical foundations of an information society. (shrink)

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

Explaining the connection, if any, between simplicity and truth is among the deepest problems facing the philosophy of science, statistics, and machine learning. Say that an efficient truth finding method minimizes worst case costs en route to converging to the true answer to a theory choice problem. Let the costs considered include the number of times a false answer is selected, the number of times opinion is reversed, and the times at which the reversals occur. It is demonstrated that (1) (...) always choosing the simplest theory compatible with experience, and (2) hanging onto it while it remains simplest, is both necessary and sufficient for efficiency. †To contact the author, please write to: Department of Philosophy, Carnegie Mellon University, Baker Hall 135, Pittsburgh, PA 15213-3890; e-mail: [email protected]. (shrink)

In his commentary on my paper, “Means-Ends Epistemology”, David Chart constructs a Riddle of Induction with the following feature: Means-ends analysis, as I formulated it in the paper, selects “all emeralds are grue” as the optimal conjecture after observing a sample of all green emeralds. Chart’s construction is rigorous and correct. If we disagree, it is in the philosophical morals to be drawn from his example. Such morals are best discussed by elucidating some of the larger epistemological issues involved. “Means-ends (...) Epistemology” sought a normative theory of hypothesis selection. I defined what it means for an inductive method to reliably and efficiently find a correct hypothesis from a set of alternative hypotheses. (In fact, I investigated a number of standards of empirical success for inductive methods.) Call such methods optimal. We may take optimal inferences to be those made by optimal methods. This defines a relation Optimal-Inference(h,e,H): “given the set of alternative hypotheses H, and evidence e, hypothesis h is an optimal inference”. One fundamental difference between the means-ends approach and traditional confirmation theory is that the latter has sought a two-place relation between theory and evidence alone, something like “hypothesis h is highly confirmed given evidence e”. From my point of view, posing the problem of induction as discerning the right relation between theory and evidence is elliptical because it leaves unspecified the set of alternative hypotheses under investigation (as well as other relevant factors, such as the scientist’s background knowledge, observational means, cognitive capacities and epistemic values). Chart’s Riddle highlights the fact that depending on the space of alternative hypotheses, means-ends analysis may select a different hypothesis on the same evidence: “all emeralds are green” in my Goodmanian Riddle, and “all emeralds are grue” in his. To my mind, his example.. (shrink)

Marc Lange has criticized my assertion that relative to a Bayesian conception of inductive reasoning, Hume's argument for inductive scepticism cannot be run. I reply that the way in which Lange suggests one should run the Humean argument in a Bayesian framework ignores the fact that in Bayesian models of learning from experience, the domain of an agent's probability measure is exogenously determined. I also show that Lange is incorrect to equate probability distributions which 'support inductive inferences' with probability distributions (...) which assign probability to contingent propositions/events. (shrink)

This paper pursues a thorough-going instrumentalist, or means-ends, approach to the theory of inductive inference. I consider three epistemic aims: convergence to a correct theory, fast convergence to a correct theory and steady convergence to a correct theory (avoiding retractions). For each of these, two questions arise: (1) What is the structure of inductive problems in which these aims are feasible? (2) When feasible, what are the inference methods that attain them? Formal learning theory provides the tools for a complete (...) set of answers to these questions. As an illustration of the results, I apply means-ends analysis to various versions of Goodman's Riddle of Induction. (shrink)

Many philosophers agree that Hume was not simply objecting to inductive inferences on the grounds of their logical invalidity and that his description of our inductive behaviour was inadequate, but none the less regard his argument against induction as irrefutable. I argue that this constellation of opinions contains a serious tension. In the light of the tension, I re-examine Hume’s actual sceptical argument and show that the argument as it stands is valid but unsound. I argue that it can only (...) be converted into a sound one if our inductive behaviour can be characterized as a process of rule-governed ampliation. Drawing on some Bayesian ideas, I argue that our inductive behaviour probably cannot be characterized in that way, so our immunity from Hume is secure. Finally, I compare my response to Hume’s argument with some other well known responses. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

In a recent paper replying to the inductive sceptic, Samir Okasha says that the Humean argument for inductive scepticism depends on mistakenly construing inductive reasoning as based on a principle of the uniformity of nature. I dispute Okasha's argument that we are entitled to the background beliefs on which (he says) inductive reasoning depends. Furthermore, I argue that the sorts of theoretically impoverished contexts to which a uniformity-of-nature principle has traditionally been restricted are exactly the contexts relevant to the inductive (...) sceptic's argument, and (pace Okasha) are not at all remote from actual scientific practice. I discuss several scientific examples involving such contexts. (shrink)

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.

It is widely agreed that Hume’s description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume’s argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume’s sceptical argument goes wrong, due to Elliott Sober. Sober argues that Hume committed a (...) quantifier-shift fallacy, i.e. inferred a statement of ∃∀ form from one of V∀∃ form. The implications of this diagnosis for the traditional problem of induction are briefly examined. The author suggests that, were his philosophy received, we must alter from the foundation the greatest part of the sciences. Hume 1740. (shrink)

Not since Ernest Nagel’s 1939 monograph on the theory of probability has there been a comprehensive elementary survey of the philosophical problems of probablity and induction. This is an authoritative and up-to-date treatment of the subject, and yet it is relatively brief and nontechnical. Hume’s skeptical arguments regarding the justification of induction are taken as a point of departure, and a variety of traditional and contemporary ways of dealing with this problem are considered. The author then sets forth his own (...) criteria of adequacy for interpretations of probability. Utilizing these criteria he analyzes contemporary theories of probability, as well as the older classical and subjective interpretations. (shrink)

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

It is widely agreed that Hume's description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume's argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume's sceptical argument goes wrong, due to Elliott Sober. Sober argues that Hume committed a (...) quantifier-shift fallacy, i.e. inferred a statement of ?? form from one of ?? form. The implications of this diagnosis for the traditional problem of induction are briefly examined. (shrink)

This comprehensive anthology of Bertrand Russell's writings brings together his definitive essays from the period 1903 to 1959. It covers the most fertile and the most lasting work on every significant area he published in.

Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper's notion of degrees of testability is linked to (...) minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham's razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman's riddle is just one example. (shrink)

Few can imagine a world without telephones or televisions; many depend on computers and the Internet as part of daily life. Without scientific theory, these developments would not have been possible. In this exceptionally clear and engaging introduction to philosophy of science, James Ladyman explores the philosophical questions that arise when we reflect on the nature of the scientific method and the knowledge it produces. He discusses whether fundamental philosophical questions about knowledge and reality might be answered by science, and (...) considers in detail the debate between realists and antirealists about the extent of scientific knowledge. Along the way, central topics in philosophy of science, such as the demarcation of science from non-science, induction, confirmation and falsification, the relationship between theory and observation and relativism are all addressed. Important and complex current debates over underdetermination, inference to the best explaination and the implications of radical theory change are clarified and clearly explained for those new to the subject. (shrink)

Co-published with the University of Queensland Press. HPC holds rights in North America and U. S. Dependencies. Since its first publication in 1976, Alan Chalmers's highly regarded and widely read work--translated into eighteen languages--has become a classic introduction to the scientific method, known for its accessibility to beginners and its value as a resource for advanced students and scholars. In addition to overall improvements and updates inspired by Chalmers's experience as a teacher, comments from his readers, and recent developments in (...) the field, this fourth edition features an extensive chapter-long postscript that draws on his research into the history of atomism to illustrate important themes in the philosophy of science. Identifying the qualitative difference between knowledge of atoms as it figures in contemporary science and metaphysical speculations about atoms common in philosophy since the time of Democritus offers a revealing and instructive way to address the question at the heart of this groundbreaking work: What is this thing called science? (shrink)

Eric Martin and Daniel N. Osherson present a theory of inductive logic built on model theory. Their aim is to extend the mathematics of Formal Learning Theory to a more general setting and to provide a more accurate image of empirical inquiry. The formal results of their study illuminate aspects of scientific inquiry that are not covered by the commonly applied Bayesian approach.

We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ...

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)

This paper describes the corner-stones of a means-ends approach to the philosophy of inductive inference. I begin with a fallibilist ideal of convergence to the truth in the long run, or in the 'limit of inquiry'. I determine which methods are optimal for attaining additional epistemic aims (notably fast and steady convergence to the truth). Means-ends vindications of (a version of) Occam's Razor and the natural generalizations in a Goodmanian Riddle of Induction illustrate the power of this approach. The paper (...) establishes a hierarchy of means-ends notions of empirical success, and discusses a number of issues, results and applications of means-ends epistemology. (shrink)

I have applied a fairly general, learning theoretic perspective to some questions raised by Reichenbach's positions on induction and discovery. This is appropriate in an examination of the significance of Reichenbach's work, since the learning-theoretic perspective is to some degree part of Reichenbach's reliabilist legacy. I have argued that Reichenbach's positivism and his infatuation with probabilities are both irrelevant to his views on induction, which are principally grounded in the notion of limiting reliability. I have suggested that limiting reliability is (...) still a formidable basis for the formulation of methodological norms, particularly when reliability cannot possibly be had in the short run, so that refined judgments about evidential support must depend upon measure-theoretic choices having nothing to do in the short run with the truth of the hypothesis under investigation. To illustrate the generality of Reichenbach's program, I showed how it can be applied to methods that aim to solve arbitrary assessment and discovery problems in various senses. In this generalized Reichenbachian setting, we can characterize the intrinsic complexity of reliable inductive inference in terms of topological complexity. Finally, I let Reichenbach's theory of induction have the last say about hypothetico-deductive method. (shrink)

Hans Reichenbach made a bold and original attempt to ‘vindicate’ induction. He proposed a rule, the ‘straight rule’ of induction, which would guarantee inductive success if any rule of induction would. A central problem facing his attempt to vindicate the straight rule is that too many other rules are just as good as the straight rule if our only constraint on what counts as ‘success’ for an inductive rule is that it is ‘asymptotic’, i.e. that it converges in the limit (...) to the true limiting frequency (of some type of outcome O in a sequence of events) whenever such a limiting frequency exists. In this paper I consider the consequences of requiring speed-optimality of asymptotic methods, that is, requiring that inductive methods must get to the truth as quickly as possible. Two main results are proved: (1) the straight rule is speed-optimal; (2) there are (uncountably) many non-speed-optimal asymptotic methods. A further result gives a sufficient but not necessary condition for speed-optimality among asymptotic methods. Some consequences and open questions are then discussed. (shrink)

After Hume, attempts to forge an empiricist epistemology have taken three forms, which I shall call the First, Middle, and Third Way. The First still attempts an a priori demonstration that our cognitive methods satisfy some criterion of adequacy. The Middle Way is pursued under the banners of naturalism and scientific realism, and aims at the same conclusion on non-apriori grounds. After arguing that both fail, I shall describe the general characteristics of the Third Way, an alternative epistemology suitable for (...) empiricism. (shrink)