Recapitulation

Abstract

The purpose of this book is to clarify probability concepts and analyze the structure of probabilistic reasoning. The intent is to give an account that is precise enough to actually be useful in philosophy, decision theory, and statistics. An ultimate objective will be to implement the theory of probabilistic reasoning in a computer program that models human probabilistic reasoning. The result will be an AI system that is capable of doing sophisticated scientific reasoning. However, that takes us beyond the scope of the present book. The purpose of this chapter is to give a brief restatement of the main points of the theory of nomic probability and provide an assessment of its accomplishments. The theory of nomic probability has a parsimonious basis. This consists of two sets of principles. First, there are the epistemic principles (A3) and (D3):(A3) If F is projectible with respect to G and r > .5, then ┌prob(F/G) > r┐ is a prima facie reason for the conditional ┌Gc ⊃ Fc┐, the strength of the reason depending upon the value of r. (D3) If F is projectible with respect to H then ┌Hc & prob(F/G&H) < prob(F/G) ┐ is an undercutting defeater for rprob(F/G) > r┐ as a prima facie reason for ┌Gc ⊃ Fc┐. Second, there are some computational principles that generate a calculus of nomic probabilities. These principles jointly constitute the conceptual role of the concept of nomic probability and are the basic principles from which the entire theory of nomic probability follows. The epistemic principles presuppose a prior epistemological framework governing the interaction of prima facie reasons and defeaters. Certain aspects of that framework play an important role in the theory of nomic probability. For example, the principle of collective defeat is used recurrently throughout the book. The details of the epistemological framework are complicated, but they are not specific to the theory of probability. They are part of general epistemology. The computational principles are formulated in terms of what some will regard as an extravagant ontology of sets of possible objects and possible worlds. It is important to realize that this ontology need not be taken seriously.