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 <em>degrees of belief</em>. 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. <em>Bayesian Philosophy of Science</em> 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.<br>
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