Abstract

Bayesianism as an intellectual movement promises much, if the views of some statisticians and some philosophers are to be believed. But increasingly, the pat answers to the problems raised by the critics cannot stand up to philosophical scrutiny. While the formalism of Bayesianism is easy to understand, its interpretation is less clear. I take Professor Isaac Levi's work The Enterprise of Knowledge to be the most philosophically satisfactory defense of Bayesianism which remains faithful to an objective view of scientific practice. ;My work is in part a defense of Levi's approach to Bayesianism and in part a criticism of Levi's defense. ;My first chapter defends Levi's decision-theoretic approach to Bayesianism and it presents a rejection of a variety of Bayesian possibilities such as Bayesian probabilism and Bayesian probabilistic acceptance theories. This leads to a critical appraisal of Levi's inductive system as a putative complete inductive logic. I criticize some of the limitations of his system, such as its inability to show how generalizations can be accepted into a corpus of beliefs and how large scale contractions of knowledge can rationally take place. I characterize in various ways Levi's Bayesian theory. The most important characterization of his theory is its relationship to what Levi describes as strict Bayesianism. I focus attention on the chance-based Direct Inference schema of Levi's Bayesian systems. I explain how the problem of direct inference is the key problem of statistical inference, and the problems involved in Levi's 'solution' to it. In the fourth chapter I compare Levi's approach to the problem of direct inference with the direct inference theory advanced by H. E. Kyburg. ;This is a complex comparison, and leads to a direct confrontation between Bayesianism, and an important version of Frequentist statistical inference, in the spirit of R. A. Fisher, which Kyburg's position represents. ;Levi claims that the issue between these two schools of inductive logic is settled in favor of his Bayesian theory by reference to the 'conditionalization' axiom. I show that that conclusion is premature after an examination of the arguments. I conclude that the question of whether in the end a Bayesian or Frequentist inductive logic is fully adequate is still an open one.