Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which (...) demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results. (shrink)

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside _The Open Society and Its Enemies_ as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

Models are a principle instrument of modern science. They are built, applied, tested, compared, revised and interpreted in an expansive scientific literature. Throughout this paper, I will argue that models are also a valuable tool for the philosopher of science. In particular, I will discuss how the methodology of Bayesian Networks can elucidate two central problems in the philosophy of science. The first thesis I will explore is the variety-of-evidence thesis, which argues that the more varied the supporting evidence, the (...) greater the degree of confirmation for a given hypothesis. However, when investigated using Bayesian methodology, this thesis turns out not to be sacrosanct. In fact, under certain conditions, a hypothesis receives more confirmation from evidence that is obtained from one rather than more instruments, and from evidence that confirms one rather than more testable consequences of the hypothesis. The second challenge that I will investigate is scientific theory change. This application highlights a different virtue of modeling methodology. In particular, I will argue that Bayesian modeling illustrates how two seemingly unrelated aspects of theory change, namely the (Kuhnian) stability of (normal) science and the ability of anomalies to over turn that stability and lead to theory change, are in fact united by a single underlying principle, in this case, coherence. In the end, I will argue that these two examples bring out some metatheoretical reflections regarding the following questions: What are the differences between modeling in science and modeling in philosophy? What is the scope of the modeling method in philosophy? And what does this imply for our understanding of Bayesianism? (shrink)

With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the (...) book deserves to become a classic....There is a great deal of interest in the book besides these basic matters [forumlating rules of acceptance]. Some of the most interesting chapters are those that examine the implications of such rules. The discussions of probability, generalization, and various forms of inference are brilliant and enlightening. Indeed, the problems and methods elaborated by Professor Levi in his book serve as a new foundation for the study of inductive inference."--Keith Lehrer, Nous"Levi's book is an extremely interesting report on 'tentative and speculative first steps' toward a decision-theoretic approach to inductive inference....Professor Levi is to be congratulated on his ingenious development and application of this approach...."--Richard C. Jeffrey, The Journal of Philosophy. (shrink)

In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions play within the witness testimony model Olsson uses to establish his result. Olsson (...) maintains that his witness model yields charitable ceteris paribus conditions for any theory of probabilistic coherence. Not so. In fact, Olsson's model, like Bayesian witness models in general, selects a peculiar class of models that are in no way representative of the range of options available to coherence theorists. Recent positive results suggest that there is a way to develop a formal theory of coherence after all. Further, although Bayesian witness models are not conducive to the truth, they are conducive to reliability. (shrink)

This essay presents results about a deviation from independence measure called focused correlation . This measure explicates the formal relationship between probabilistic dependence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield's ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson's claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology (...) that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. Introduction Correlation Measures 2.1 Standard covariance and correlation measures 2.2 The Wayne–Shogenji measure 2.3 Interpreting correlation measures 2.4 Correlation and evidential independence Focused Correlation Conclusion Appendix CiteULike Connotea Del.icio.us What's this? (shrink)

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

Over the past years, a number of probabilistic measures of coherence have been proposed. As shown in the paper, however, many of them do not conform to the intuitition that equivalent testimonies are highly coherent, regardless of their prior probability.

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if P(B)=P(C). But (...) such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability. (shrink)

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that (...) any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy. (shrink)

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but (...) in agreement . We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6). (shrink)

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in (...) agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic versus semantic formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence. (shrink)

One of the integral parts of Bayesian coherentism is the view that the relation of ‘being no less coherent than’ is fully determined by the probabilistic features of the sets of propositions to be ordered. In the last one and a half decades, a variety of probabilistic measures of coherence have been put forward. However, there is large disagreement as to which of these measures best captures the pre-theoretic notion of coherence. This paper contributes to the debate on coherence measures (...) by considering three classes of adequacy constraints. Various independence and dependence relations between the members of each class will be taken into account in order to reveal the ‘grammar’ of probabilistic coherence measures. Afterwards, existing proposals are examined with respect to this list of desiderata. Given that for purely mathematical reasons there can be no measure that satisfies all constraints, the grammar allows the coherentist to articulate an informed pluralist stance as regards probabilistic measures of coherence. (shrink)

The debate on probabilistic measures of coherence flourishes for about 15 years now. Initiated by papers that have been published around the turn of the millennium, many different proposals have since then been put forward. This contribution is partly devoted to a reassessment of extant coherence measures. Focusing on a small number of reasonable adequacy constraints I show that (i) there can be no coherence measure that satisfies all constraints, and that (ii) subsets of these adequacy constraints motivate two different (...) classes of coherence measures. These classes do not coincide with the common distinction between coherence as mutual support and coherence as relative set-theoretic overlap. Finally, I put forward arguments to the effect that for each such class of coherence measures there is an outstanding measure that outperforms all other extant proposals. One of these measures has recently been put forward in the literature, while the other one is based on a novel probabilistic measure of confirmation. (shrink)

The success of Bovens and Hartmann’s recent “impossibility result” against Bayesian Coherentism relies upon the adoption of a specific set of ceteris paribus conditions. In this paper, I argue that these conditions are not clearly appropriate; certain proposed coherence measures motivate different such conditions and also call for the rejection of at least one of Bovens and Hartmann’s conditions. I show that there exist sets of intuitively plausible ceteris paribus conditions that allow one to sidestep the impossibility result. This shifts (...) the debate from the merits of the impossibility result itself to the underlying choice of ceteris paribus conditions. (shrink)

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (asmeasured) of a set of testimonies implies a higher probability that the witnesses are reliable. Recently, it has been proved that the Shogenji measure of coherence is reliability conducive in restricted scenarios (e.g., Olsson and Schubert, Synthese, 157:297–308, 2007). In this article, I investigate whether the Shogenji measure, or any other coherence measure, is reliability conducive in general. An impossibility theorem is (...) proved to the effect that this is not the case. I conclude that coherence is not reliability conducive. (shrink)

Striving for a probabilistic explication of coherence, scholars proposed a distinction between agreement and striking agreement. In this paper I argue that only the former should be considered a genuine concept of coherence. In a second step the relation between coherence and reliability is assessed. I show that it is possible to concur with common intuitions regarding the impact of coherence on reliability in various types of witness scenarios by means of an agreement measure of coherence. Highlighting the need to (...) separate the impact of coherence and specificity on reliability it is finally shown that a recently proposed vindication of the Shogenji measure qua measure of coherence vanishes. (shrink)

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood that the witnesses are reliable. Recently, it has been proved that several coherence measures proposed in the literature are reliability conducive in a restricted scenario (Olsson and Schubert 2007, Synthese 157:297–308). My aim is to investigate which coherence measures turn out to be reliability conducive in the more general scenario where it is any finite (...) number of witnesses that give equivalent reports. It is shown that only the so-called Shogenji measure is reliability conducive in this scenario. I take that to be an argument for the Shogenji measure being a fruitful explication of coherence. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

There is an emerging consensus in the literature on probabilistic coherence that such coherence cannot be truth conducive unless the information sources providing the cohering information are individually credible and collectively independent. Furthermore, coherence can at best be truth conducive in a ceteris paribus sense. Bovens and Hartmann have argued that there cannot be any measure of coherence that is truth conducive even in this very weak sense. In this paper, I give an alternative impossibility proof. I provide a relatively (...) detailed comparison of the two results, which turn out to be logically unrelated, and argue that my result answers a question raised by Bovens and Hartmann’s study. Finally, I discuss the epistemological ramifications of these findings and try to make plausible that a shift to an explanatory framework such as Thagard’s is unlikely to turn the impossibility into a possibility. (shrink)

A measure of coherence is said to be truth conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood of truth. Recent impossibility results strongly indicate that there are no (non-trivial) probabilistic coherence measures that are truth conducive. Indeed, this holds even if truth conduciveness is understood in a weak ceteris paribus sense (Bovens & Hartmann, 2003, Bayesian epistemology. New York, Oxford: Oxford University Press; Olsson, 2005, Against coherence: Truth probability and justification. Oxford: (...) Oxford University Press). This raises the problem of how coherence could nonetheless be an epistemically important property. Our proposal is that coherence may be linked in a certain way to reliability. We define a measure of coherence to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher probability that the information sources are reliable. Restricting ourselves to the most basic case, we investigate which coherence measures in the literature are reliability conducive. It turns out that, while a number of measures fail to be reliability conducive, except possibly in a trivial and uninteresting sense, Shogenji’s measure and several measures generated by Douven and Meijs’s recipe are notable exceptions to this rule. (shrink)

What does it take for one proposition to be closer to the truth than another. In this, the first published monograph on the topic, Oddie develops a comprehensive theory that takes the likeness in truthlikeness seriously.

I show that the two most devastating objections to Shogenji's formal account of coherence necessarily involve information sets of cardinality . Given this, I surmise that the problem with Shogenji's measure has more to do with his means of generalizing the measure than with the measure itself. I defend this claim by offering an alternative generalization of Shogenji's measure. This alternative retains the intuitive merits of the original measure while avoiding both of the relevant problems that befall it. In the (...) light of all of this, I suggest that there is new hope for Shogenji's analysis: Shogenji's early and influential attempt at measuring coherence, when generalized in a subset-sensitive way, is able to clear its most troubling objections. (shrink)

If coherence is to have justificatory status, as some analytical philosophers think it has, it must be truth-conducive, if perhaps only under certain specific conditions. This paper is a critical discussion of some recent arguments that seek to show that under no reasonable conditions can coherence be truth-conducive. More specifically, it considers Bovens and Hartmann’s and Olsson’s “impossibility results,” which attempt to show that coherence cannot possibly be a truth-conducive property. We point to various ways in which the advocates of (...) a coherence theory of justification may attempt to divert the threat of these results. (shrink)

In this paper I consider whether there is a measure of coherence that could be rightly claimed to generalize the notion of logical equivalence. I show that Fitelson’s (2003) proposal to that effect encounters some serious difficulties. Furthermore, there is reason to believe that no mutual-support measure could ever be suitable for the formalization of coherence as generalized logical equivalence. Instead, it appears that the only plausible candidate for such a measure is one of relative overlap. The measure I propose (...) in this paper is quite similar to Olsson’s (2002) proposal but differs from it by not being susceptible to the type of counterexample that Bovens and Hartmann (2003) have devised against it. (shrink)

Bovens and Hartmann (Bayesian Epistemology, Oxford: Oxford University Press, 2003) propose to analyze coherence as a confidence-boosting property. On the basis of this idea, they construct a new probabilistic theory of coherence. In this paper, I will attempt to show that the resulting measure of coherence clashes with some of the intuitions that motivate it. Also, I will try to show that this clash is not due to the view on coherence as a confidence-boosting property or to the general features (...) of the model that Bovens and Hartmann use to analyze coherence. It will turn out that there is at least one other measure that is similarly based on the concept of a confidence-boosting property, but does not have the same counterintuitive results. (shrink)

Bovens and Hartmann propose to analyze coherence as a confidence-boosting property. On the basis of this idea, they construct a new probabilistic theory of coherence. In this paper, I will attempt to show that the resulting measure of coherence clashes with some of the intuitions that motivate it. Also, I will try to show that this clash is not due to the view on coherence as a confidence-boosting property or to the general features of the model that Bovens and Hartmann (...) use to analyze coherence. It will turn out that there is at least one other measure that is similarly based on the concept of a confidence-boosting property, but does not have the same counterintuitive results. (shrink)

In this article I give a naturalistic-cum-formal analysis of the relation between beauty, empirical success, and truth. The analysis is based on the one hand on a hypothetical variant of the so-called 'mere-exposure effect' which has been more or less established in experimental psychology regarding exposure-affect relationships in general and aesthetic appreciation in particular (Zajonc 1968; Temme 1983; Bornstein 1989; (Ye 2000). On the other hand it is based on the formal theory of truthlikeness and truth approximation as presented in (...) my From Instrumentalism to Constructive Realism (2000). The analysis supports the findings of James McAllister in his beautiful Beauty and Revolutiorl in Science (1996), by explaining and justifying them. First, scientists are essentially right in regarding aesthetic criteria useful for empirical progress and even for truth approximation, provided they conceive of them as less hard than empirical criteria. Second, the aesthetic criteria of the time, the 'aesthetic canon', may well be based on 'aesthetic induction' regarding nonempirical features of paradigms of successful theories which scientists have come to appreciate as beautiful. Third, aesthetic criteria can play a crucial, schismatic role in scientific revolutions. Since they may well be wrong, they may, in the hands of aesthetic conservatives, retard empirical progress and hence truth approximation, but this does not happen in the hands of aesthetically flexible, 'revolutionary' scientists. (shrink)

How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change this. Using a (...) custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures. (shrink)

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

Two of the probabilistic measures of coherence discussed in this paper take probabilistic dependence into account and so depend on prior probabilities in a fundamental way. An example is given which suggests that this prior-dependence can lead to potential problems. Another coherence measure is shown to be independent of prior probabilities in a clearly defined sense and consequently is able to avoid such problems. The issue of prior-dependence is linked to the fact that the first two measures can be understood (...) as measures of coherence as striking agreement, while the third measure represents coherence as agreement. Thus, prior (in)dependence can be used to distinguish different conceptions of coherence. (shrink)

Popper’s original definition of verisimilitude in terms of comparisons of truth content and falsity content has known counter-examples. More complicated approaches have met with mixed success. This paper uses a new account of logical content to develop a definition of verisimilitude that is close to Popper’s original account. It is claimed that Popper’s mistake was to couch his account of truth and falsity content in terms of true and false consequences. Comparison to a similar approach by Schurz and Wiengartner show (...) certain advantages of this new approach. (shrink)

Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..