Adrià Segarra

In this thesis I motivate and develop a Hybrid Theory of Induction (HTI), and I explore some of its virtues and implications. The HTI is a hybrid second-order model of inductive support. It is a "hybrid" model of inductive support because it holds that two ingredients play a necessary role in understanding inductive support: rules and facts. It is a "second-order" model of inductive support because it is a model within which first-order models of inductive support (i.e. logics of induction) can fit. In chapter 1 I argue that we need both rules and facts to play a role in a successful account of inductive support. Rules of induction accurately describe relations of inductive support when they are warranted; facts do the warranting work. I call this type of warrant "factual warrant". The resulting account is both functional and accurate, it helps us make sense of how different rules of induction can coexist and it allows us to resolve some current debates in induction. For the purposes of chapter 1 I adopt an existing binary account of factual warrant. In chapter 2 I develop a Graded account of Factual Warrant (GFW), according to which factual warrant comes in degrees. I integrate the GFW in the HTI. I then show that the GFW illuminates the connection between factual warrant and inductive support, and it can successfully account for the role of idealisations and theory in our understanding of inductive support. In chapter 3 I argue that the HTI is also useful for agents, since it can provide methodological guidance to ensure strong inferences and conceptual guidance to assess the strength of our inferences. Finally, in chapter 4, I explore Bayesian inductive logics from the perspective of the HTI. This analysis brings to light the central role that probability models play in Bayesian inductive logics, offering a logical underpinning for some recent suggestions in Bayesian epistemology. Furthermore, throughout this thesis I analyse in detail three rules of induction from the perspective of the HTI: enumerative induction in chapter 2, causal inference in chapter 3 and Bayesian inductive logics in chapter 4. These analyses illustrate how the HTI can help us think more clearly about rules of induction, offering new tools to tackle existing challenges.

There are two important traditions in the philosophy of induction. According to one tradition, which has dominated for the last couple of centuries, inductive arguments are warranted by rules. Bayesianism is the most popular view within this tradition. Rules of induction provide functional accounts of inductive support, but no rule is universal; hence, no rule is by itself an accurate model of inductive support. According to another tradition, inductive arguments are not warranted by rules but by matters of fact. Norton’s material theory of induction (MTI) is an influential view within this tradition. Norton’s MTI fails to provide an account of inductive support, but it provides a good account of inductive warrant that can help us define the domain of validity of each rule of induction. Despite their limitations, both approaches to induction are illuminating important aspects of how relations of inductive support work. In this article I present a hybrid theory of induction (HTI), in which I acknowledge and articulate the role of both rules and matters of fact in our understanding of inductive support. According to the HTI, rules of induction accurately describe relations of inductive support when they are warranted, and a rule of induction is warranted if the right facts about the matter of the induction obtain. Crucially, the HTI allows us to address the main challenges that each tradition faces while retaining their strengths, thus obtaining a functional and accurate account of inductive support. The HTI also provides a useful general framework to examine and understand induction, to make sense of how different rules of induction can coexist and to tackle some problems in epistemology. Moreover, the HTI allows us to clarify and resolve some current debates on induction, like the apparent divide between Norton and rule-based theorists.