This chapter surveys some of the many types of models used in science, and some of the many ways scientists use models. Of particular interest for our purposes are the relationships between models and other aspects of scientific inquiry, such as data, experiments, and theories. Our discussion shows important ways in which modeling can be thought of as a distinct and autonomous scientific activity, but always models can be crucial for making use of data and theories and for performing experiments. The growing reliance on simulation models has raised new and important questions about the kind of knowledge gained by simulations and the relationship between simulation and experimentation. Is it important to distinguish between simulation and experimentation, and if so, why?

The concepts of inductive and deductive inference are introduced and contrasted. An artificial example is used to emphasize the logical structure of the problem of induction. To see how the problem of induction relates (and also does not relate) to a real episode of experimental inquiry, this chapter considers the case of Isaac Newton’s optical experiments using prisms to investigate the refraction of light. Although Newton did not concern himself with the problem of induction as philosophers now understand it, he used experimental strategies designed to address possible errors in the conclusions about light that he drew from his observations.

This chapter surveys influential ideas about scientific explanation. The idea that scientific explanation is a matter of logical deduction from scientific laws has played an important role both as the basis for positive accounts of scientific explanation and as a target of critical arguments spurring the investigation of alternative views. The chapter reviews some of the reasons in favor holding such a covering-law view of explanation and then turn to some alternatives. The chapter also considers a pragmatically oriented account of the act of explaining. Another alternative focuses on the idea that explanations unify phenomena, showing how seemingly different things are manifestations of a single truth about nature. Several approaches emphasize the way explanations indicate what causes something to happen, whether by reference to a process, a possible manipulation, or a mechanism.

The chapter reviews an approach to the development of a ‘scientific philosophy’ that developed in the early decades of the twentieth century in Central Europe. Logical empiricists combined an interest in using the resources of formal logic and an empiricist orientation to propose ways of distinguishing meaningful scientific discourse from what they regarded as cognitively meaningless metaphysical statements. In so doing, they articulated important and influential ideas about how to characterize the relationship between observations serving as evidence and the theories for which they are relevant. The chapter also examines their assumptions about the nature and structure of physical theories and how those shaped efforts such as Rudolf Carnap’s development of a theory purporting to quantify how much a particular body of evidence confirms a particular theory.

One philosophical approach that directly responds to the problem of induction is falsificationism, first proposed by Karl Popper. This chapter examines how falsificationists propose to account for the growth of scientific knowledge without appealing to inductive reasoning. Their approach relies on attempts to falsify general hypotheses through experiments and observations. Additional logical concepts are introduced in this chapter to facilitate the logical analysis of such falsification. The concept of corroboration, central to the falsificationist view, is introduced. The apparatus of falsificationism is applied to the example of Newton’s optical experiments introduced in Chapter 1. Finally, falsificationism is discussed in relation to conventionalism, a philosophical idea that in some ways falsificationism attacks and in other ways exemplifies.

In practice, much of statistical reasoning in science relies on probabilities subject to interpretation as relative frequencies. This chapter explains how probability can be understood in terms of relative frequencies and the uses scientists and philosophers have devised for frequentist probabilities. Particularly prominent in those uses are error probabilities associated with particular approaches to hypothesis testing. The approaches pioneered by Ronald Fisher and by Jerzy Neyman and Egon Pearson are outlined and explained through examples. The chapter then explores the error-statistical philosophy advocated by Deborah Mayo as a general framework for thinking about how we learn from empirical data. The error-statistical approach utilizes a frequentist framework for probabilities to articulate a view of severe testingof hypotheses as the means by which scientists increase experimental knowledge. Error statistics represents an important alternative to Bayesian approaches to scientific inquiry, and this chapter considers its prospects and challenges.

According to the value-free ideal of science, scientists should draw their conclusions in a manner free of influence from value judgments. This ideal lends itself to a variety of interpretations and specifications. The ideal also faces numerous challenges that call into question not only whether it can be achieved but whether it really constitutes an ideal scientists ought to use to guide their actions. The chapter considers whether and in what conditions the value judgments of scientists might prevent or facilitate the achievement of scientific objectivity. From the role of value judgments in science the chapter turns to the closely related question of the appropriate role of scientists in the formulation of public policies. In many situations, the consideration of scientific evidence and scientific research bears importantly on questions of policy. The chapter then considers the complicated relationship between the reliance of policymakers on scientific expertise and the goals of democratic accountability and the public good.

Science is part of society, and scientific culture is part of a broader culture from which it gets much of its character. Sexism and patriarchy have been pervasive influences throughout the historical process that leads to our present scientific culture, with significant effects on science and scientists. Feminist thinkers have grappled with the problem of sexism in science and have developed a variety of philosophical responses to it. This chapter surveys some of those responses, with a focus on the ideas of feminist empiricism and feminist standpoint theory. Both approaches argue that incorporating feminist ideas will enable scientific communities to better achieve scientific aims of knowledge and objectivity, although they disagree on which feminist ideas are best suited to achieve this. The chapter also considers ways in which the two approaches have become more alike as they developed over the past several decades, hinting at a possible synthesis of the two approaches.