The hospital industry in many countries is characterized by right-skewed distributions of hospitals’ sizes and varied ownership types, raising numerous questions about the performance of hospitals of different sizes and ownership types. In an era of aging populations and increasing healthcare costs, evaluating and understanding the consumption of resources to produce healthcare outcomes is increasingly important for policy discussions. This chapter discusses recent developments in the statistical and econometric literature on DEA and FDH estimators that can be used to examine hospitals’ technical efficiency and productivity. Use of these new results and methods is illustrated by revisiting the Burgess and Wilson hospital studies of the 1990s to estimate and make inference about the technical efficiency of US hospitals, make inferences about returns to scale and other model features, and test for differences among US hospitals across ownership types and size groups in the context of a rigorous, statistical paradigm that was unavailable to researchers until recently.

Students are introduced the logic, foundation, and basics of statistical inference. The need for samples is first discussed and then how samples can be used to make inferences about the larger population. The normal distribution is then discussed, along with Z-scores to illustrate basic probability and the logic of statistical significance.

Experience is the cornerstone of Epicurean philosophy and nowhere is this more apparent than in the Epicurean views about the nature, formation, and application of concepts. ‘The Epicureans on Preconceptions and Other Concepts’ by Gábor Betegh and Voula Tsouna aims to piece together the approach to concepts suggested by Epicurus and his early associates, trace its historical development over a period of approximately five centuries, compare it with competing views, and highlight the philosophical value of the Epicurean account on that subject. It is not clear whether, properly speaking, the Epicureans can be claimed to have a theory about concepts. However, an in-depth discussion of the relevant questions will show that the Epicureans advance a coherent if elliptical explanation of the nature and formation of concepts and of their epistemological and ethical role. Also, the chapter establishes that, although the core of the Epicurean account remains fundamentally unaffected, there are shifts of emphasis and new developments marking the passage from one generation of Epicureans to another and from one era to the next.

The Victorian era is often seen as solidifying modern law’s idealization of number, rule, and definition. Yet Wilkie Collins thwarts the trend toward “trial by mathematics” and “actuarial justice” by adopting an antinumerical example as the basis for a literary experiment. The bizarre third verdict (“not proven”) of Scots law, which falls between “guilty” and “not guilty” and acts as an acquittal that nonetheless imputes a lack of evidence for conviction, structures his detective novel The Law and the Lady (1875). Revealing Collins’s sources in trial reports and legal treatises, this chapter shows how uncertainty inflects judicial reasoning and models of reading. The verdict of “not proven” undercuts the truth claims of binary judgment at law, subverts normative categories, and allows for more flexible visions of social judgment. Collins makes visible a counter-trend to certainty and closure in legal institutions and Victorian novels about the law. The chapter briefly treats Anthony Trollope’s Orley Farm (1862) and Mary Braddon’s An Open Verdict (1878), which also promote types of inference and models of critical judgment that value the tentative, hesitant, and processual, evading the calculative pressures of nineteenth-century law and life.

In his treatment of the Wittgensteinian paradox about rule-following, Saul Kripke represents the non-reductionist approach, according to which meaning something by an expression is a sui generis state that cannot be elucidated in more basic terms, as brushing philosophical questions under the rug. This representation of non-reductionism aligns with the conception of some of its proponents. Meaning is viewed by these philosophers as an explanatory primitive that provides the basic materials for philosophical inquiry, and whose nature cannot serve as an object for that inquiry. There is, however, an alternative way of conceiving of non-reductionism, which makes it possible to tackle philosophical questions about the nature of meaning head-on, and thus to respond to Kripke’s challenge in an illuminating manner.

If some of our knowledge cannot be articulated, how does it make itself manifest? It will not surprise anyone who has followed the argument of this book up to now that there are things that we can do with knowledge besides talking about it. Millikan, as we saw, used his knowledge of experimentation and of professional discourse to guide his exemplary investigations of the charge of the electron. Neither was something he made explicit; I doubt that he (or anyone) could have. No practitioner who looked at Millikan’s work found any basis for these accusations, because their training endowed them with a knowledge only available to practitioners. They all made effective use of this knowledge, despite not being able to articulate its content. That kind of knowledge manifests itself not in the form of beliefs, but rather in the scholar’s sense of how things seem.

Chapter 3 focuses on lexical semantics–pragmatics. Drawing on the views adopted in Construction Grammar and Relevance Theory, it provides an in-depth analysis aimed at exploring the nature of conceptual content and its use in context. It is argued that lexical concepts are best characterized by means of rich networks of encyclopedic knowledge, an approach that enables Relevance Theory to resolve a number of conflicting assumptions (including the presumed paradox discussed in Leclercq, 2022). At the same time, the case is made that this knowledge constitutes an intrinsically context-sensitive semantic potential that serves as the foundation of an inferential process guided by strong pragmatic principles. This process is addressed in terms of lexically regulated saturation, which forms the cornerstone of the integrated model outlined in this book.

This chapter details the practical, theoretical, and philosophical aspects of experimental science. It discusses how one chooses a project, performs experiments, interprets the resulting data, makes inferences, and develops and tests theories. It then asks the question, "are our theories accurate representations of the natural world, that is, do they reflect reality?" Surprisingly, this is not an easy question to answer. Scientists assume so, but are they warranted in this assumption? Realists say "yes," but anti-realists argue that realism is simply a mental representation of the world as we perceive it, that is, metaphysical in nature. Regardless of one's sense of reality, the fact remains that science has been and continues to be of tremendous practical value. It would have to be a miracle if our knowledge and manipulation of the nature were not real. Even if they were, how do we know they are true in an absolute sense, not just relative to our own experience? This is a thorny philosophical question, the answer to which depends on the context in which it is asked. The take-home message for the practicing scientist is "never assume your results are true."

This chapter outlines a theory of moral perception, describes a structural analogy between perception and action, and indicates how perception can provide an objective basis for moral knowledge. It is shown to have a basis in the kinds of grounds that underlie the moral properties to which moral perception responds, such as the violence of a face-slapping. With this outline of a theory of moral perception in view, the chapter describes the presentational phenomenal character of moral perception. Prominent in this presentationality is the phenomenological integration between our moral sensibility and our non-moral perception of the various kinds of natural properties that ground moral properties. Moral perception is possible without moral judgment but commonly yields it. It is also possible without moral emotion but may arise from it in some cases and evoke it in others. Many perceptually grounded judgments are justified; many also express empirical moral knowledge.

Inductive reasoning involves generalizing from samples of evidence to novel cases. Previous work in this field has focused on how sample contents guide the inductive process. This chapter reviews a more recent and complementary line of research that emphasizes the role of the sampling process in induction. In line with a Bayesian model of induction, beliefs about how a sample was generated are shown to have a profound effect on the inferences that people draw. This is first illustrated in research on beliefs about sampling intentions: was the sample generated to illustrate a concept or was it generated randomly? A related body of work examines the effects of sampling frames: beliefs about selection mechanisms that cause some instances to appear in a sample and others to be excluded. The chapter describes key empirical findings from these research programs and highlights emerging issues such as the effect of timing of information about sample generation (i.e., whether it comes before or after the observed sample) and individual differences in inductive reasoning. The concluding section examines how this work can be extended to more complex reasoning problems where observed data are subject to selection biases.

Before venturing into the study of choreographies, we introduce the formalism of inference systems. Inference systems are widely used in the fields of formal logic and programming languages and they were later applied to theory of choreographies as well.

Many of the problems that human minds need to solve – including learning concepts, causal relationships, and languages – require making informed inferences from limited data. Bayesian models of cognition consider how an ideal agent should solve these problems, drawing on ideas from probability theory, statistics, machine learning, and artificial intelligence.  The resulting models can then be used to understand human behavior, identifying in formal terms the knowledge that human minds draw on when solving these problems and identifying potential mechanisms by which their solutions might be implemented. This chapter provides an introduction to Bayesian models of cognition, starting with the basic principles of probability theory and then considering more advanced topics such as graphical models, causal learning, hierarchical Bayesian models, and Markov chain Monte Carlo. The chapter ends with a brief review of recent theoretical developments.