Stanley Stevens draws a useful distinction among ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this article, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an interval measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus, I conclude that the log-likelihood measure is the only good candidate interval measure.

An overview of the German philosophy of science community is given for the years 1992–2012, based on a survey in which 159 philosophers of science in Germany participated. To this end, the institutional background of the German philosophy of science community is examined in terms of journals, centers, and associations. Furthermore, a qualitative description and a quantitative analysis of our survey results are presented. Quantitative estimates are given for: (a) academic positions, (b) research foci, (c) philosophers’ of science most important (...) publications, and (d) externally funded projects, where for (c) all survey participants had indicated their five most important publications in philosophy of science. In addition, the survey results for (a)–(c) are also qualitatively described, as they are interesting in their own right. With respect to (a), we estimated the gender distribution among academic positions. Concerning (c), we quantified philosophers’ of science preference for (i) journals and publishers, (ii) publication format, (iii) language, and (iv) coauthorship for their most important publications. With regard to research projects, we determined their (i) prevalence, (ii) length, and (iii) trend (an increase in number?) as well as their most frequent (iv) research foci and (v) funding organizations. We also distinguished between German-based and non-German-based journals, publishers, and funding institutions, making it thereby possible to evaluate the involvement of the German philosophy of science community in the international research landscape. Finally, we discuss some implications of our findings. (shrink)

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than (...) probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability. (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 paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of plausible (...) adequacy conditions. The paper concludes by sketching future research avenues. (shrink)

In “What price coherence?”, Klein and Warfield put forward a simple argument that triggered an extensive debate on the epistemic virtues of coherence. As is well-known, this debate yielded far-reaching impossibility results to the effect that coherence is not conducive to truth, even if construed in a ceteris paribus sense. A large part of the present paper is devoted to a re-evaluation of these results. As is argued, all explications of truth-conduciveness leave out an important aspect: while it might not (...) be the case that coherence is truth-conducive, it might be conducive to verisimilitude or epistemic utility. Unfortunately, it is shown that the answer for both these issues must be in the negative, again. Furthermore, we shift the focus from sets of beliefs to particular beliefs: as is shown, neither is any of the extant probabilistic measures of coherence truth-conducive on the level of particular beliefs, nor does weakening these measures to quasi-orderings establish the link between coherence and truth for an important amount of measures. All in all, the results in this paper cast a serious doubt on the approach of establishing a link between coherence and truth. Finally, recent arguments that shift the focus from the relationship between coherence and truth to the one between coherence and confirmation are assessed. (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)

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)

Proposals for rigorously explicating the concept of confirmation in probabilistic terms abound. To foster discussions on the formal properties of the proposed measures, recent years have seen the upshot of a number of representation theorems that uniquely determine a confirmation measure based on a number of desiderata. However, the results that have been presented so far focus exclusively on the concept of incremental confirmation. This leaves open the question whether similar results can be obtained for the concept of absolute confirmation. (...) This article closes the gap by providing a representation theorem for absolute confirmation measures. (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)

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, but (...) none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, but (...) none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

Philosophical discussions on causal inference in medicine are stuck in dyadic camps, each defending one kind of evidence or method rather than another as best support for causal hypotheses. Whereas Evidence Based Medicine advocates the use of Randomised Controlled Trials and systematic reviews of RCTs as gold standard, philosophers of science emphasise the importance of mechanisms and their distinctive informational contribution to causal inference and assessment. Some have suggested the adoption of a pluralistic approach to causal inference, and an inductive (...) rather than hypothetico-deductive inferential paradigm. However, these proposals deliver no clear guidelines about how such plurality of evidence sources should jointly justify hypotheses of causal associations. We here develop such guidelines by first giving a philosophical analysis of the underpinnings of Hill’s viewpoints on causality. We then put forward an evidence-amalgamation framework adopting a Bayesian net approach to model causal inference in pharmacology for the assessment of harms. Our framework accommodates a number of intuitions already expressed in the literature concerning the EBM vs. pluralist debate on causal inference, evidence hierarchies, causal holism, relevance, and reliability. (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)

The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...) antiquated” .What seems not to have lost any of its currency is the problem which inductive logic is meant to address. Inference from limited ascertained information to uncertain hypotheses is ubiquitous in learning, prediction and discovery. The logical insight that such kind of inference is fallible m .. (shrink)

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the (...) reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information-theoretic formalism. (shrink)

Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” (“halfers”) and those endorsing the “1/3 view” (“thirders”). The disagreement concerns the evidential relevance of self-locating information. Unlike halfers, thirders regard self-locating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations of the Sleeping Beauty Problem do (...) not fit either the “1/2 view” or the “1/3 view.” Human reasoners tend to acknowledge self-locating evidence as relevant, but discount its weight significantly. Accordingly, self-locating information may trigger more cautious judgments of confirmation than familiar kinds of statistical evidence. We also discuss how these results can advance the debate by providing a more nuanced and empirically grounded account or explication of the evidential impact of self-locating information. (shrink)

Jonah N. Schupbach and Jan Sprenger and Vincenzo Crupi and Katya Tentori have recently proposed measures of explanatory power and have shown that they are characterized by certain arguably desirable conditions or axioms. I further examine the properties of these two measures, and a third measure considered by I. J. Good and Timothy McGrew . This third measure also has an axiomatic representation. I consider a simple coin-tossing example in which only the Crupi–Tentori measure does not perform well. The Schupbach–Sprenger (...) and Good–McGrew measures are based on different notions of explanatory power, but both are tenable. 1 Introduction2 Measures of Explanatory Power3 The Schupbach–Sprenger Measure4 The Crupi–Tentori Measure5 The Good–McGrew Measure6 Affirmative versus Comprehensive Explanatory Power7 Coin-Flipping Examples8 Decomposition9 Conclusion. (shrink)