David H. Glass

This chapter develops and defends a formal epistemology of conjunctive explanation by determining the conditions under which multiple distinct explanations are better than one. The general approach is to identify an appropriate measure of explanatory goodness that can then be applied to conjunctive explanations. If a conjunctive explanation is to be preferred it needs to have greater explanatory virtue (e.g., power or scope) with respect to the evidence, but this explanatory gain is insufficient on its own. Given a conjunctive explanation’s greater complexity, it also has a cost associated with it and so a balance needs to be struck between the gain and the cost. This is achieved by employing a Bayesian measure proposed by I. J. Good. This chapter explores some properties of this measure and its application to the epistemology of conjunctive explanation. In so doing, it addresses the general question of whether it is desirable to have more informative, less probable hypotheses when seeking good explanations.

Competition between scientific hypotheses is not always a matter of mutual exclusivity. Consistent hypotheses can compete to varying degrees either directly or indirectly via a body of evidence. We motivate and defend a particular account of hypothesis competition by showing how it captures these features. Computer simulations of Bayesian inference are used to highlight the limitations of adopting mutual exclusivity as a simplifying assumption to model scientific reasoning, particularly due to the exclusion of hypotheses that may be true. We end with a case study demonstrating the subtleties involved in hypothesis competition in scientific practice.

When is it _explanatorily_ better to adopt a conjunction of explanatory hypotheses as opposed to committing to only some of them? Although conjunctive explanations are inevitably less probable than less committed alternatives, we argue that the answer is not ‘never’. This paper provides an account of the conditions under which explanatory considerations warrant a preference for less probable, conjunctive explanations. After setting out four formal conditions that must be met by such an account, we consider the shortcomings of several approaches. We develop an account that avoids these shortcomings and then defend it by applying it to a well-known example of explanatory reasoning in contemporary science.

Philosophers and psychologists are increasingly investigating the conditions under which multiple explanations are better in conjunction than they are individually. This book brings together leading scholars to provide an interdisciplinary and unified discussion of such "conjunctive explanations." The book starts with an introductory chapter expounding the notion of conjunctive explanation and motivating a multifaceted approach to its study. The remaining chapters are divided into three parts. Part I includes chapters on "The Nature of Conjunctive Explanations." Each chapter illustrates distinct ways in which explanatory multiplicity is motivated by a careful study of the nature and concept of explanation. The second part ("Reasoning about Conjunctive Explanations") includes chapters on the epistemology and logic of conjunctive explanations. Here the contributors propose and evaluate various norms for reasoning correctly about and to conjunctive explanations. Part III concerns "The Psychology of Conjunctive Explanations," with contributions discussing conditions under which humans entertain and hold multiple explanations of single explananda simultaneously and the cognitive limitations and capacities for doing so. Conjunctive Explanations will be of interest to researchers and advanced students working on explanation in philosophy of science, epistemology, philosophical logic, and cognitive psychology.

Richard Dawkins has a dilemma when it comes to design arguments. On the one hand, he maintains that it was Darwin who killed off design and so implies that his rejection of design depends upon the findings of modern science. On the other hand, he follows Hume when he claims that appealing to a designer does not explain anything and so implies that rejection of design need not be based on the findings of modern science. These contrasting approaches lead to the following dilemma: if he claims that Darwinism is necessary for rejecting design, he has no satisfactory response to design arguments based on the order in the laws of physics or the fine-tuning of the physical constants; alternatively, if Humean arguments are doing most of the work, this would undermine one of his main contentions, that atheism is justified by science and especially by evolution. In any case, his Humean arguments do not provide a more secure basis for his atheism because they are seriously flawed. A particular problem is that his argument for the improbability of theism rests on a highly questionable application of probability theory since, even if it were sound, it would only establish that the prior probability of God’s existence is low, a conclusion which is compatible with the posterior probability of God’s existence being high

Rope Kojonen has presented a novel argument for design in biology by drawing on insights from evolutionary science. Without objecting to the explanatory role of evolution, he argues that there is further explanatory work to be done and that this is best achieved by an appeal to design. Here, I interpret his argument, and attempt to evaluate it, as a conjunctive explanation since he appeals to two explanations to account for the purposeful order and complexity of living organisms. Understood in this way, I argue that he makes a very plausible case that two explanations (evolution and design) are better than one (evolution). I also explore the role that direct guidance by God might play in such an argument.

Two models are developed for updating opinions in social networks under situations where certain beliefs might be considered to be competing. These two models represent different attitudes of people towards the perceived conflict between beliefs. In both models agents have a degree of tolerance, which represents the extent to which the agent takes into account the differing beliefs of other agents, and a degree of conflict, which represents the extent to which two beliefs are considered to be competing. Computer simulations are used to determine how the opinion dynamics are affected by the inclusion of conflict. Results show that conflict can enhance the formation of consensus within the network in certain circumstances according to one of the models.

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.

Two of the probabilistic measures of coherence discussed in this paper take probabilistic dependence into account and so depend on prior probabilities in a fundamental way. An example is given which suggests that this prior-dependence can lead to potential problems. Another coherence measure is shown to be independent of prior probabilities in a clearly defined sense and consequently is able to avoid such problems. The issue of prior-dependence is linked to the fact that the first two measures can be understood as measures of coherence as striking agreement, while the third measure represents coherence as agreement. Thus, prior (in)dependence can be used to distinguish different conceptions of coherence.

In discussions about the existence of God, it is sometimes claimed that the progress of science has removed the need for God. This paper uses a Bayesian analysis of Ockham’s razor to formulate and evaluate this argument, which is referred to as the science explains away God argument. Four different strategies for responding to this argument are presented and evaluated. It is argued that one of these strategies highlights how difficult it is to show that the conditions for applying Ockham’s razor are satisfied and hence why SEAGA is very unlikely to succeed.

This paper considers an application of work on probabilistic measures of coherence to inference to the best explanation. Rather than considering information reported from different sources, as is usually the case when discussing coherence measures, the approach adopted here is to use a coherence measure to rank competing explanations in terms of their coherence with a piece of evidence. By adopting such an approach IBE can be made more precise and so a major objection to this mode of reasoning can be addressed. Advantages of the coherence - based approach are pointed out by comparing it with several other ways to characterize ‘ best explanation ’ and showing that it takes into account their insights while overcoming some of their problems. The consequences of adopting this approach for IBE are discussed in the context of recent discussions about the relationship between IBE and Bayesianism

In the form of inference known as inference to the best explanation there are various ways to characterise what is meant by the best explanation. This paper considers a number of such characterisations including several based on confirmation measures and several based on coherence measures. The goal is to find a measure which adequately captures what is meant by 'best' and which also yields the truth with a high degree of probability. Computer simulations are used to show that the overlap coherence measure achieves this goal, enabling the true explanation to be identified almost as often as an approach which simply selects the most probable explanation. Further advantages to this approach are also considered in the case where there is uncertainty in the prior probability distribution