6 Epistemology, Probability, and Science
Jonathan Lopez
Chapter Learning Outcomes
Upon completion of this chapter, readers will be able to:
- Distinguish between formal and traditional epistemology, including their main characteristics, motivations, and assumptions.
- Cultivate an intuitive sense of how basic formal methods apply to everyday thinking and decision-making.
- Employ Bayesianism in scientific contexts, specifically for hypothesis testing.
- Evaluate the strengths and limitations of Bayesianism.
Preamble
Epistemologists have traditionally approached questions about the nature of knowledge and epistemic justification using informal methods, such as intuition, introspection, everyday concepts, and ordinary language. [1] Whether in addition to or in place of these methods, formal epistemology utilizes formal tools, such as logic, set theory, and mathematical probability. The upshot is greater precision, increased rigor, and an expanded range of applications. This chapter focuses on the formal approach in its most prominent manifestation: Bayesianism, which begins by discarding the traditional view of belief as an all-or-nothing affair (either you believe a proposition or you don’t) and instead treats belief as admitting of degrees. These degrees are governed by how strongly a proposition is supported by the evidence. Evidential support is measured by probability, especially with the help of a famous result in probability theory, Bayes’s theorem (hence the term, “Bayesian”). Our aim here is to understand the basics of Bayesianism, its pros and cons, and an extended application to the epistemology of science. As we’ll see, the Bayesian framework is a natural fit for the scientific context. Very seldom does a single experiment change the opinion of the scientific community; the quest for scientific truth is hard fought over many experiments and research programs as hypotheses gradually gain or lose favor in light of a changing body of evidence. Bayesianism allows us to model this process, come to a more robust understanding of scientific knowledge, and use this understanding to settle some controversies over theory choice.
Degrees of Belief
You are probably more confident in some beliefs than others. You’ve probably said things like “I’m [latex]100\%[/latex] sure I turned the oven off,” which is to say your confidence is high, or “I have a hunch he might not be telling the truth,” which is to say your confidence is low. When you closely scrutinize your beliefs, you’ll find that they fall along various points in a spectrum—a hierarchy which can’t be captured simply by saying that you either believe or you don’t. Such all-or-nothing terms lump beliefs together into broad categories, masking important differences among their locations in the hierarchy.
Suppose instead you understand belief as “admitting of degrees.” This allows you to distinguish beliefs in which you have varying degrees of confidence: your degree of belief in a proposition is