Abstract

The thesis of the dissertation is that relations between statements of a formal language, which are suitably constrained to mirror the non-quantitative probability relation 'is not more probable than', can serve as a semantics for that language and that this absolute, comparative, probabilistic semantics is a generalization of absolute, quantitative, probabilistic semantics, that is, the semantics for a formal language that employs one-place functions that obey the laws of the probability calculus. ;Chapter one provides an historical sketch of the area to which the dissertation is a contribution. It traces the development of what came to be known as probabilistic semantics from the work of Sir Karl Popper through Robert Stalnaker, William Harper, Hartry Field, Kent Bendall, and Hugues Leblanc. It also provides a brief history of probability as a non-quantitative concept by discussing the work of Bruno De Finetti, Bernard Koopman, and Charles Morgan. It concludes by explaining the thesis of the dissertation in light of the just-sketched tradition and spells out the program for the rest of the work. ;Chapter two presents the syntax of a propositional language PL and provides an absolute comparative probabilistic semantics for it. It then shows that the language is sound and complete with respect to that semantics. The last section gives an account of generalization and argues that this semantics is a generalization of the absolute comparative probabilistic semantics for PL. This amounts to claiming that for every probability function there is a corresponding probability relation and for every member of a proper subset of probability relations, namely, that set which contains only comparable relations, there is at least one probability function corresponding to it. ;Chapter three offers the same kind of results obtained in chapter two for a first order language FL. ;The final chapter offers a summation of the results and highlights some of the features of absolute comparative probabilistic semantics such as the intensionality of the logical operators and the existence of what are termed 'assumption sets'. It also suggests possible avenues of application and research involving the new semantics