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Much of the evidence for quantum mechanics is statistical in nature. Relative frequency data summarizing the results of repeated experiments is compared to probabilities calculated from the theory; close agreement between the observed relative frequencies and calculated probabilities is taken as evidence in favour of the theory. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to this sort of reasoning. Since, on the Everett interpretation, all outcomes with non-zero amplitude are actualized on different branches, it is not obvious that sense can be made of ascribing probabilities to outcomes of experiments, and this poses a prima facie problem for statistical inference. It is incumbent on the Everettian either to make sense of ascribing probabilities to outcomes of experiments in the Everett interpretation, or to find a substitute on which the usual statistical analysis of experimental results continues to count as evidence for quantum mechanics, and, since it is the very evidence for quantum mechanics that is at stake, this must be done in a way that does not presuppose the correctness of Everettian quantum mechanics. This requires an account of theory confirmation that applies to branching-universe theories but does not presuppose the correctness of any such theory. This chapter supplies and defends such an account. The account has the consequence that statistical evidence can confirm a branching-universe theory such as Everettian quantum mechanics in the same way in which it can confirm a non-branching probabilistic theory.

In this chapter we will take stock and consider some questions and applications that merit future attention. In §10.1 we will encounter some questions arising from the topics covered in this book. Sect. 10.2, 10.3, 10.4 will advertise the application of objective Bayesian erastemology to statistics, confirmation theoryand metaphysics respectively. As we see, there is plenty on the agenda for those wishing to contribute to the objective Bayesian research programme.

This chapter clarifies two notions which are central to the book: the content of a scientific representation and how we can think of the confirmation of these representations. When mathematics is central to a representation a number of complications arise which are explored in this chapter. Pincock argues that the accuracy conditions of a representation can be understood in terms of the existence of a structural relation between a mathematical structure and a physical target system. This helps to clarify the process of confirming such representations. The second half of the chapter considers the prospects for applying confirmation theory to help with these questions and argues that there are systematic problems in dealing with how mathematics helps with confirmation.

This chapter argues that logical subtraction has a role to play in confirmation theory via the notion of surplus content. Subject matter does, too, via the notion of content-part. Content-part lets us define a new type of evidential relation; E pervasively probabilifies H if it probabilifies “all of it,” meaning H and its parts. This helps with the tacking and raven paradoxes. Equivalent generalizations can be about different things, which affect their evidential relations. Inductive skeptics do not care about confirmation, but they derive some benefit too, for they care about verisimilitude—one theory having more truth in it than another—and the truth in a theory is made up of its wholly true parts.

In “Scientific Knowledge,” Philip Kitcher challenges arguments that deny the truth of the theoretical claims of science, and he attempts to discover reasons for endorsing the truth of such claims. He suggests that the discovery of such reasons might succeed if we ask why anyone thinks that the theoretical claims we accept are true and then look for answers that reconstruct actual belief‐generating processes. To this end, Kitcher presents the “homely argument” for scientific truth, which claims that when a field of science is continually applied to yield precise predictions, then it is at least approximately true. He defends this approach and offers a supplementary account that gives more attention to detail. This account includes a historical aspect (a dependence on the previous conclusions of scientists) that must answer to skeptical challenges and a social aspect (the coordination of individuals in pursuit of specific knowledge‐related goals).

This chapter reviews and criticizes various strategies for making sense of quantum-mechanical probability-talk in the context of Everett Picture, with particular attention to recent such strategies involving decision theory.

While situating the contribution of the volume within the recent trajectory of philosophy of religion, this chapter highlights the formative role that the notion of probability has exercised on the philosophy of religion in recent times. Tracing a number of key debates from their formulation in the work of David Hume, it looks at the assimilation of probability and confirmation theory within philosophy of religion with reference to five topical areas of the discipline: testimony and miracles; design arguments; the problem of evil; Pascal’s wager; and faith and reason. In doing so, it provides short summaries of each chapter, explaining how they contribute to certain key debates. It concludes with the prediction that probability theory will continue to enjoy a profound influence on the philosophy of religion for some time to come.

Confirmation of scientific theories by empirical evidence is an important element of scientific reasoning and a central topic in philosophy of science. Bayesian Confirmation Theory—the analysis of confirmation in terms of degree of belief—is the most popular model of inductive reasoning. It comes in two varieties: confirmation as firmness (of belief), and confirmation as increase in firmness. We show why increase in firmness is a particularly fruitful explication of degree of confirmation, and how it resolves longstanding paradoxes of inductive inference (e.g., the paradox of the ravens, the tacking paradoxes and the grue paradox). Finally, we give an axiomatic characterization of various confirmation measures and we discuss the question of whether there is a single adequate measure of confirmation or whether a pluralist position is more promising

Chapter 4 focuses on Bayesian confirmation theory, a formal theory of reasoning based on probability theory. It deals with important, and related, general ideas, such as rationality, confirmation, and inductive inference, including statistical inference. The chapter also provides a selective discussion of Bayesian statistics. The chapter traces some of the broad contours of Bayesian confirmation theory and then presents an evaluation of a philosophy of Bayesian statistical practice. Psychology’s attitudes to Bayesianism are briefly discussed. Considered is the question of whether Bayesianism provides an illuminating account of the approach to theory evaluation known as inference to the best explanation. The chapter offers some broad recommendations for research practice.

In science, phenomena are often unexplained by the available scientific theories. At some point, it may be discovered that a novel theory accounts for this phenomenon—and this seems to confirm the theory because a persistent anomaly is resolved. However, Bayesian confirmation theory—primarily a theory for updating beliefs in the light of learning new information—struggles to describe confirmation by such cases of “old evidence”. We discuss the two main varieties of the Problem of Old Evidence (POE)—the static and the dynamic POE—, criticize existing solutions and develop two novel Bayesian models. They show how the discovery of explanatory and deductive relationships, or the absence of alternative explanations for the phenomenon in question, can confirm a theory. Finally, we assess the overall prospects of Bayesian Confirmation Theory in the light of the POE.

There are situations where people have multiple reasons to do a certain action, a, that are individually worse than a reason to do another incompatible act. But in some of these cases, the reasons to do a taken together (which can be called the accrual of the reasons to do a) make it so that you ought to do a. This chapter explores how the weight of individual reasons determines how strongly an accrual of reasons supports an act. It argues that a key to understanding how individual reasons determine how strongly an accrual supports an act is to distinguish sharply between derivative and non-derivative reasons.

The chapter proposes that, contrary intuitions notwithstanding, dogmatists accept a variety of Moorean arguments as legitimate ways to acquire a justification for their conclusions. The chapter counters an ensuing objection from Bayesian confirmation theory, arguing by way of example that acquisition of justification is compatible with the probability lowering that Bayesian confirmation theory predicts to take place in many Moorean arguments. Appealing to considerations concerning defeat, it then shows that a minimal strengthening of dogmatism is incompatible with the classical, additive theory of the very structure of probabilities, and it consequently investigates a more dogmatist-friendly non-classical, super-additive theory of both the structure and dynamics of probabilities, in which the probability of the conclusion of a Moorean argument rises no less than the probability of its premise, and in which perception can play this epistemic role without either presupposing or directly contributing justification for a principle linking appearances with reality.

Long before skeptical theism was called “skeptical theism,” Stephen Wykstra defended a version of it based on an epistemological principle he called CORNEA. In this chapter, elementary confirmation theory is used to analyze CORNEA’s core. This allows one to see precisely what is right about Wykstra’s very influential defense of skeptical theism and precisely what is wrong with it. A key premise of Wykstra’s defense is that, on the assumption that God exists, one wouldn’t expect to know God’s reasons for allowing certain evils. This chapter shows that, while that premise together with CORNEA’s core shows that a general inability to adequately explain the existence of those evils in terms of theism is not strong evidence against theism, it fails to show that the evils themselves are not strong evidence against theism.

Community psychology can potentially illustrate the dynamic interplay between the qualities of people and the attributes of smaller social settings and larger social environments. This requires research methods that attempt to illustrate environmental complexity. Thinking psychologically and ecologically are interdependent approaches. The process of theory confirmation is adapted to informed insights from the community as well as current knowledge from the literature. An educated view of a particular place creates a dynamic interplay between prior knowledge and informed insights. The views of the place can be related to the concepts in the literature, and the concepts from the literature can be assessed based on their salience in this particular community. The use of ecological concepts affirms that there is need for a real interdependence between the wishes and aspirations of the community participants and the project staff.

Convincing scientific theories are often hard to find, especially when empirical evidence is scarce (e.g., in particle physics). Once scientists have found a theory, they often believe that there are not many distinct alternatives to it. Is this belief justified? We model how the failure to find a feasible alternative can increase the degree of belief in a scientific theory—in other words, we establish the validity of the No Alternatives Argument and the possibility of non-empirical theory confirmation from a Bayesian point of view. Then we evaluate scope and limits of this argument (e.g., by calculating the degree of confirmation it provides) and relate it to other argument forms such as Inference to the Best Explanation (IBE) or “There is No Alternative” (TINA).

This chapter motivates why, and under which circumstances, the explanatory power of a scientific hypothesis with respect to a body of evidence can be explicated by means of statistical relevance. This account is traced back to its historic roots in Peirce and Hempel and defended against its critics (e.g., contrasting statistical relevance to purely causal accounts of explanation). Then we derive various Bayesian explications of explanatory power using the method of representation theorems and we compare their properties from a normative point of view. Finally we evaluate how such measures of explanatory power can ground a theory of Inference to the Best Explanation (IBE).