Online research in philosophy

A simple indeterministic system is displayed and it is urged that we cannot responsibly infer inductively over it if we presume that the probability calculus is the appropriate logic of induction. The example illustrates the general thesis of a material theory of induction, that the logic appropriate to a particular domain is determined by the facts that prevail there.

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. This approach explains why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts.

In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to some universal schema. An inductive inference problem concerning indeterministic, non-probabilistic systems in physics is posed and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction.

History of science and the material theory of induction: Einstein’s quanta, mercury’s perihelion Content Type Journal Article Pages 3-27 DOI 10.1007/s13194-010-0001-7 Authors John D. Norton, Center for Philosophy of Science, University of Pittsburgh, Pittsburgh, PA USA Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 1.

In this essay, I take the role as friendly commentator and call attention to three potential worries for John D. Norton’s material theory of induction (Norton, 2003). I attempt to show (1) that his “principle argument” is based on a false dichotomy, (2) that the idea that facts ultimately derive their license from matters of fact is debatable, and (3) that one of the core implications of his theory is untenable for historical and fundamental reasons.

In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that Hume’s celebrated “problem of induction” can no longer be set up and is thereby dissolved.

My purpose in this chapter is to survey some of the principal approaches to inductive inference in the philosophy of science literature. My first concern will be the general principles that underlie the many accounts of induction in this literature. When these accounts are considered in isolation, as is more commonly the case, it is easy to overlook that virtually all accounts depend on one of very few basic principles and that the proliferation of accounts can be understood as efforts to ameliorate the weaknesses of those few principles. In the earlier sections, I will lay out three inductive principles and the families of accounts of induction they engender. In later sections I will review standard problems in the philosophical literature that have supported some pessimism about induction and suggest that their import has been greatly overrated. In the final sections I will return to the proliferation of accounts of induction that frustrates efforts at a final codification. I will suggest that this proliferation appears troublesome only as long as we expect inductive inference to be subsumed under a single formal theory. If we adopt a material theory of induction in which individual inductions are licensed by particular facts that prevail only in local domains, then the proliferation is expected and not problematic.

For several years, through the “material theory of induction,” I have urged that inductive inferences are not licensed by universal schemas, but by material facts that hold only locally (Norton, 2003, 2005). My goal has been to defend inductive inference against inductive skeptics by demonstrating when and how inductive inferences are properly made. Since I have always admired Peter Achinstein as a staunch defender of induction, it was a surprise when Peter..

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction.