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)

A major open question in the borderlands between epistemology and philosophy of science concerns whether Bayesian updating and abductive inference are compatible. Some philosophers—most influentially Bas van Fraassen—have argued that they are not. Others have disagreed, arguing that abduction, properly understood, is indeed compatible with Bayesianism. Here we present two formal results that allow us to tackle this question from a new angle. We start by formulating what we take to be a minimal version of the claim that abduction is (...) a rational pattern of reasoning. We then show that this minimal abductivist principle, when combined with Bayesian updating by conditionalization, places surprisingly strong and controversial constraints on how we must measure explanatory power. The lesson is not that Bayesianism is definitely incompatible with abduction, but that both compatibilism and incompatibilism have hitherto unrecognized consequences. We end the paper by formulating these consequences in the form of a trilemma. (shrink)

We discuss two influential views of unification: mutual information unification (MIU) and common origin unification (COU). We propose a simple probabilistic measure for COU and compare it with Myrvold’s (2003, 2017) probabilistic measure for MIU. We then explore how well these two measures perform in simple causal settings. After highlighting several deficiencies, we propose causal constraints for both measures. A comparison with explanatory power shows that the causal version of COU is one step ahead in simple causal settings. However, slightly (...) increasing the complexity of the underlying causal structure shows that both measures can easily disagree with explanatory power. The upshot of this is that even sophisticated causally constrained measures for unification ultimately fail to track explanatory relevance. This shows that unification and explanation are not as closely related as many philosophers thought. (shrink)

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s interventionist conception of causation. The viability of these responses has been challenged by Gebharter, who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs (...) for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s anti-reductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an anti-reductionist interventionist account of causation.1. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

This paper provides a new approach to inference to the best explanation based on a new coherence measure for comparing how well hypotheses explain the evidence. It addresses a number of criticisms of the use of probabilistic measures in this context by Clark Glymour, including limitations of earlier work on IBE. Computer experiments are used to show that the new approach finds the truth with a high degree of accuracy in hypothesis selection tasks and that in some cases its accuracy (...) is greater than hypothesis selection based on maximizing posterior probability. Hence, by overcoming some of the problems with the previous approach, this work provides a more adequate defence of IBE and suggests that IBE not only tracks truth but also has practical advantages over the previous approach. Applications of the new approach to parameter estimation and model selection are also explored. (shrink)

The idea that good explanations come with strong changes in probabilities has been very common. This criterion is called probabilistic difference-making. Since it is an intuitive criterion and has a long tradition in the literature on scientific explanation, it comes as a surprise that probabilistic difference-making is rarely discussed in the context of interventionist causal explanation. Specificity, proportionality, and stability are usually employed to measure explanatory power instead. This paper is a first step into the larger project of connecting difference-making (...) to the interventionist debate, and it starts by investigating whether probabilistic difference-making is contained in the notion of specificity. The choice of specificity is motivated by the observation that both probabilistic difference-making and specificity build on similar underlying intuitions. When comparing measures for both specificity and probabilistic difference-making, it turns out that the measures are not strictly correlated, and so the thesis that probabilistic difference-making is encoded within specificity has to be rejected. Some consequences of this result are discussed as well. (shrink)

Several philosophers propose probabilistic measures of how well a potential scientific explanation would explain the given evidence. These measures could elaborate “best” in “inference to the best explanation”. This paper argues that none of these measures succeeds. The paper considers the various rival explanations that scientists proposed for the parallelogram of forces. Scientists regarded various features of these proposals as making them more or less “lovely”. None of these probabilistic measures of loveliness can reflect these features. The paper concludes by (...) considering the kinds of probabilities that could reflect these features. (shrink)