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Switch to: References
Citations of:
Inference, Method and Decision
British Journal for the Philosophy of Science 29 (3):301-304 (1978)
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The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...) |
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Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief ½ to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used (...) |
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According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) |
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This paper refutes two important and influential views in one fell stroke. The first is G.E. Moore’s view that assertions of the form ‘Q but I don’t believe that Q’ are inherently “absurd.” The second is Gareth Evans’s view that justification to assert Q entails justification to assert that you believe Q. Both views run aground the possibility of being justified in accepting eliminativism about belief. A corollary is that a principle recently defended by John Williams is also false, namely, (...) |
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Why did Copernicus's research programme supersede Ptolemy's?’, Lakatos and Zahar argued that, on Zahar's criterion for ‘novel fact’, Copernican theory was objectively scientifically superior to Ptolemaic theory. They are mistaken, Lakatos and Zahar applied Zahar's criterion to ‘a historical thought-experiment’—fictional rather than real history. Further, in their fictional history, they compared Copernicus to Eudoxus rather than Ptolemy, ignored Tycho Brahe, and did not consider facts that would be novel for geostatic theories. When Zahar's criterion is applied to real history, the (...) |
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The Raven and the Bayesian. As an essential benefit of their probabilistic account of confirmation, Bayesians state that it provides a twofold solution to the ravens paradox. It is supposed to show that (i) the paradox’s conclusion is tenable because a white shoe only negligibly confirms the hypothesis that all ravens are black, and (ii) the paradox’s first premise is false anyway because a black raven can speak against the hypothesis. I argue that both proposals are not only unable to (...) |
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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 (...) |
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Van Fraassen argues that explanatory power cannot be a conformational virtue. In this paper I will show that informational features of scientific theories can be positively relevant to their levels of conformation. Thus, in the cases where the explanatory power of a theory is tied to an informational feature of the theory, it can still be the case that the explanatory power of the theory is positively relevant to its level of confirmation. |
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Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities (...) |
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Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is (...) |
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I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics (NPT). I argue that NPT principles arose not out of behavioral aims, where the concern is solely with behaving correctly sufficiently often in some long run, but out of the epistemological aim of learning about causes of experimental results (e.g., distinguishing genuine from spurious effects). The view Pearson did hold gives a (...) |
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While orthodox (Neyman-Pearson) statistical tests enjoy widespread use in science, the philosophical controversy over their appropriateness for obtaining scientific knowledge remains unresolved. I shall suggest an explanation and a resolution of this controversy. The source of the controversy, I argue, is that orthodox tests are typically interpreted as rules for making optimal decisions as to how to behave--where optimality is measured by the frequency of errors the test would commit in a long series of trials. Most philosophers of statistics, however, (...) |
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Theories of statistical testing may be seen as attempts to provide systematic means for evaluating scientific conjectures on the basis of incomplete or inaccurate observational data. The Neyman-Pearson Theory of Testing (NPT) has purported to provide an objective means for testing statistical hypotheses corresponding to scientific claims. Despite their widespread use in science, methods of NPT have themselves been accused of failing to be objective; and the purported objectivity of scientific claims based upon NPT has been called into question. The (...) |
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Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...) |
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This paper rejects a traditional epistemic interpretation of conditional probability. Suppose some chance process produces outcomes X, Y,..., with probabilities P(X), P(Y),... If later observation reveals that outcome Y has in fact been achieved, then the probability of outcome X cannot normally be revised to P(X|Y) ['P&Y)/P(Y)]. This can only be done in exceptional circumstances - when more than just knowledge of Y-ness has been attained. The primary reason for this is that the weight of a piece of evidence varies (...) |
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Parsimony is a virtue of empirical theories. Is it also a virtue of philosophical theories? I review four contemporary accounts of the virtue of parsimony in empirical theorizing, and consider how each might apply to two prominent appeals to parsimony in the philosophical literature, those made on behalf of physicalism and on behalf of nominalism. None of the accounts of the virtue of parsimony extends naturally to either of these philosophical cases. This suggests that in typical philosophical contexts, ontological simplicity (...) |
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My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...) |
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Two of the most influential theories about scientific inference are inference to the best explanation and Bayesianism. How are they related? Bas van Fraassen has claimed that IBE and Bayesianism are incompatible rival theories, as any probabilistic version of IBE would violate Bayesian conditionalization. In response, several authors have defended the view that IBE is compatible with Bayesian updating. They claim that the explanatory considerations in IBE are taken into account by the Bayesian because the Bayesian either does or should (...) |
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It is argued that we need a richer version of Bayesian decision theory, admitting both subjective and objective probabilities and providing rational criteria for choice of our prior probabilities. We also need a theory of tentative acceptance of empirical hypotheses. There is a discussion of subjective and of objective probabilities and of the relationship between them, as well as a discussion of the criteria used in choosing our prior probabilities, such as the principles of indifference and of maximum entropy, and (...) |
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Frequentism and Bayesianism represent very different approaches to hypothesis testing, and this presents a skeptical challenge for Bayesians. Given that most empirical research uses frequentist methods, why (if at all) should we rely on it? While it is well known that there are conditions under which Bayesian and frequentist methods agree, without some reason to think these conditions are typically met, the Bayesian hasn’t shown why we are usually safe in relying on results reported by significance testers. In this article, (...) |
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Drawing substantive conclusions from linear causal models that perform acceptably on statistical tests is unreasonable if it is not known how alternatives fare on these same tests. We describe a computer program, TETRAD, that helps to search rapidly for plausible alternatives to a given causal structure. The program is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence. We describe these principles, discuss how TETRAD employs them, and argue that these principles make TETRAD an effective tool. (...) |
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In recent years philosophers of science have turned away from positivist programs for explicating scientific rationality through detailed accounts of scientific procedure and turned toward large-scale accounts of scientific change. One important motivation for this was better fit with the history of science. Paying particular attention to the large-scale theories of Lakatos and Laudan I argue that the history of science is no better accommodated by the new large-scale theories than it was by the earlier positivist philosophies of science; both (...) |
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What has science actually achieved? A theory of achievement should define what has been achieved, describe the means or methods used in science, and explain how such methods lead to such achievements. Predictive accuracy is one truth‐related achievement of science, and there is an explanation of why common scientific practices tend to increase predictive accuracy. Akaike’s explanation for the success of AIC is limited to interpolative predictive accuracy. But therein lies the strength of the general framework, for it also provides (...) |
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The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox (...) |
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The idea that the changing entropy of a system is relevant to explaining why we know more about the system's past than about its future has been criticized on several fronts. This paper assesses the criticisms and clarifies the epistemology of the inference problem. It deploys a Markov process model to investigate the relationship between entropy and temporally asymmetric inference. |
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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 (...) |
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The idea that simplicity matters in science is as old as science itself, with the much cited example of Ockham's Razor, 'entia non sunt multiplicanda praeter necessitatem': entities are not to be multiplied beyond necessity. A problem with Ockham's razor is that nearly everybody seems to accept it, but few are able to define its exact meaning and to make it operational in a non-arbitrary way. Using a multidisciplinary perspective including philosophers, mathematicians, econometricians and economists, this 2002 monograph examines simplicity (...) |
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Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) |
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