Investigations in the Theory of Confirmation and Inductive Inference

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This project comprises a series of studies into confirmation theory and the nature of inductive inference. The first part is designed to deepen our understanding of a scheme of inference known as demonstrative inference. In it, an inductive inference from evidence to hypothesis is rendered deductive (demonstrative) by the addition of suitable general assumptions to the premises. This turns out to be a strategy used quite frequently in the history of science as a way of controlling inductive risk. The principal investigator will seek further examples of these inferences and also attempt to understand how it is possible for a special class of these inferences to be self-validating in the sense that the success of the inference also supplies support for the general assumptions. In the second part, the principal investigator will seek to understand the weaknesses and strengths of the Bayesian treatment of confirmation theory by developing an axiom system for probability theory. The axiom system will not be designed to be as parsimonious as possible, but rather to be based on intuitively distinct commitments concerning the nature of confirmation. This will enable various of the appealing properties of the Bayesian scheme to be distinguished from others. Finally the principal investigator will briefly explore several heresies pertaining to inductive inference.