Ockham's razor, the principle of parsimony, states that simpler theories are better than theories that are more complex. It has a history dating back to Aristotle and it plays an important role in current physics, biology, and psychology. The razor also gets used outside of science - in everyday life and in philosophy. This book evaluates the principle and discusses its many applications. Fascinating examples from different domains provide a rich basis for contemplating the principle's promises and perils. It is (...) obvious that simpler theories are beautiful and easy to understand; the hard problem is to figure out why the simplicity of a theory should be relevant to saying what the world is like. In this book, the ABCs of probability theory are succinctly developed and put to work to describe two 'parsimony paradigms' within which this problem can be solved. (shrink)

Popper formulates and explains his non-justificationist theory of knowledge. Science--empirical science--aims at true explanatory theories, yet it can never prove, finally establish, or justify any of its theories as true, not even if it is in fact a true theory. Science must continue to question and criticize all its theories, even those which happen to be true.

Sherrilyn Roush defends a new theory of knowledge and evidence, based on the idea of "tracking" the truth, as the best approach to a wide range of questions about knowledge-related phenomena. The theory explains, for example, why scepticism is frustrating, why knowledge is power, and why better evidence makes you more likely to have knowledge. Tracking Truth provides a unification of the concepts of knowledge and evidence, and argues against traditional epistemological realist and anti-realist positions about scientific theories and for (...) a piecemeal approach based on a criterion of evidence, a position Roush calls "real anti-realism." Epistemologists and philosophers of science will recognize this as a significant original contribution. (shrink)

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...) Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

_Popper’s Critical Rationalism_ presents Popper’s views on science, knowledge, and inquiry, and examines the significance and tenability of these in light of recent developments in philosophy of science, philosophy of probability, and epistemology. It develops a fresh and novel philosophical position on science, which employs key insights from Popper while rejecting other elements of his philosophy. Central theses include: Crucial questions about scientific method arise at the level of the group, rather than that of the individual. Although criticism is vital (...) for science, dogmatism is important too. Belief in scientific theories is permissible even in the absence of evidence in their favour. The aim of science is to eliminate false theories. Critical rationalism can be understood as a form of virtue epistemology. (shrink)

Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...) Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe = 0. If P = P then Cb = Cb. (shrink)

It is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2. In this paper we distinguish four senses of confirmation and examine additional conditions under which confirmation in different senses becomes transitive. We conduct this examination both in the general case where H1 confirms H2 and in the special case where H1 also logically entails H2. Based on these analyses, we argue that (...) the Screening-Off Condition is the most important condition for transitivity in confirmation because of its generality and ease of application. We illustrate our point with the example of Moore’s “proof” of the existence of a material world, where H1 logically entails H2, the Screening-Off Condition holds, and confirmation in all four senses turns out to be transitive. (shrink)

Surprisingly, modified versions of the confirmation theory (Carnap and Hempel) and truth approximation theory (Popper) turn out to be smoothly sythesizable. The glue between the two appears to be the instrumentalist methodology, rather than that of the falsificationalist. The instrumentalist methodology, used in the separate, comparative evaluation of theories in terms of their successes and problems (hence, even if already falsified), provides in theory and practice the straight road to short-term empirical progress in science ( à la Laudan). It is (...) also argued that such progress is also functional for all kinds of truth approximation: observational, referential, and theoretical. This sheds new light on the long-term dynamics of science and hence on the relation between the main epistemological positions, viz., instrumentalism (Toulmin, Laudan), constructive empiricism (Van Fraassen), referential realism (Hacking, Cartwright), and theory realism of a non-essentialist nature (constructive realism à la Popper). Readership: Open minded philosophers and scientists. The book explains and justifies the scientist's intuition that the debate among philosophers about instrumentalism and realism has almost no practical consequences. (shrink)

(new version: 10/30/07). Click here to download the companion Mathematica 6 notebook that goes along with this paper.

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, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

Igor Douven establishes several new intransitivity results concerning evidential support. I add to Douven’s very instructive discussion by establishing two further intransitivity results and a transitivity result.

Confirmation of a hypothesis by evidence can be measured by one of the so far known incremental measures of confirmation. As we show, incremental measures can be formally defined as the measures of confirmation satisfying a certain small set of basic conditions. Moreover, several kinds of incremental measure may be characterized on the basis of appropriate structural properties. In particular, we focus on the so-called Matthew properties: we introduce a family of six Matthew properties including the reverse Matthew effect; we (...) further prove that incremental measures endowed with reverse Matthew effect are possible; finally, we shortly consider the problem of the plausibility of Matthew properties. (shrink)

It is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2. In this paper we distinguish four senses of confirmation and examine additional conditions under which confirmation in different senses becomes transitive. We conduct this examination both in the general case where H1 confirms H2 and in the special case where H1 also logically entails H2. Based on these analyses, we argue that (...) the Screening-Off Condition is the most important condition for transitivity in confirmation because of its generality and ease of application. We illustrate our point with the example of Moore’s ‘‘proof’’ of the existence of a material world, where H1 logically entails H2, the Screening-Off Condition holds, and confirmation in all four senses turns out to be transitive. (shrink)

We explore the grammar of Bayesian confirmation by focusing on some likelihood principles, including the Weak Law of Likelihood. We show that none of the likelihood principles proposed so far is satisfied by all incremental measures of confirmation, and we argue that some of these measures indeed obey new, prima facie strange, antilikelihood principles. To prove this, we introduce a new measure that violates the Weak Law of Likelihood while satisfying a strong antilikelihood condition. We conclude by hinting at some (...) relevant links between the likelihood principles considered here and other properties of Bayesian confirmation recently explored in the literature. (shrink)

It is known that evidential support, on the Bayesian definition of this notion, is intransitive. According to some, however, the Bayesian definition is too weak to be materially adequate. This paper investigates whether evidential support is transitive on some plausible probabilistic strengthening of that definition. It is shown that the answer is negative. In fact, it will appear that even under conditions under which the Bayesian notion of evidential support is transitive, the most plausible candidate strengthenings are not.

Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.

There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and LR. (...) The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation. (shrink)

Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...) set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories. (shrink)

According to influential accounts of scientific method, such as critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in statistical inference and science in general, their philosophical foundations remain shaky. In particular, the interpretation of non-significant results—those that do not reject the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis, or provide a reason to accept it? Popper sought for measures of corroboration that could (...) adequately answer this question. According to Popper, corroboration is different from probability-raising, and grounded in the predictive success and testability of a hypothesis. As such, corroboration becomes an indicator of the scientific value of a hypothesis and guides our practical preferences over hypotheses that have been subjected to severe tests. This article proves two impossibility results for corroboration measures based on statistical relevance. The generality of these results shows that Popper’s qualitative characterization of corroboration must be misguided. I explore what a more promising and scientifically useful concept of corroboration could look like. (shrink)

This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

It is generally accepted that Popper‘s degree of corroboration, though “inductivist” in a very general and weak sense, is not inductivist in a strong sense, i.e. when by ‘inductivism’ we mean the thesis that the right measure of evidential support has a probabilistic character. The aim of this paper is to challenge this common view by arguing that Popper can be regarded as an inductivist, not only in the weak broad sense but also in a narrower, probabilistic sense. In section (...) 2, first, I begin by briefly characterizing the relevant notion of inductivism that is at stake here; second, I present and discuss the main Popperian argument against it and show that in the only reading in which the argument is formally it is restricted to cases of predicted evidence, and that even if restricted in this way the argument is formally valid it is nevertheless materially unsound. In section 3, I analyze the desiderata that, according to Popper, any acceptable measure for evidential support must satisfy, I clean away its ad-hoc components and show that all the remaining desiderata are satisfied by inductuvist-in-strict-sense measures. In section 4 I demonstrate that two of these desiderata, accepted by Popper, imply that in cases of predicted evidence any measure that satisfies them is qualitatively indistinguishable from conditional probability. Finally I defend that this amounts to a kind of strong inductivism that enters into conflict with Popper’s anti-inductivist argument and declarations, and that this conflict does not depend on the incremental versus non-incremental distinction for evidential-support measures, making Popper’s position inconsistent in any reading.Keywords: Popper; Inductivism; Confirmation; Corroboration. (shrink)