Compositional Anomalies in the Semantics of Evidence

Abstract

Publisher Summary This chapter explores that semantic theory plays a central role in the normative and descriptive theory of deductive inference, but its role in the study of inductive inference has been much less prominent. The disparity is both odd and understandable. It is odd because deductive and inductive reasoning both rely heavily on linguistic representations and semantic theory is the natural tool for investigating inference within propositional structures. The axiomatic theory of subjective probability specifies further properties of belief strength that characterize so-called coherent beliefs; if strength of belief is coherent in this sense, then there exist numerical probabilities that represent the belief strength ordering and satisfy the mathematical laws of probability. A theory of semantics relates three aspects of language: (1) the syntactic structure of propositions, that is, a specification of how complex propositions are built from simpler parts, (2) the semantic structure of propositions, that is, a specification of the relation between propositional structure, reference, and truth values, and (3) inference rules that define inferential relations in terms of syntactic and semantic structure. The chapter considers variety of empirical results that illustrate concretely the relationship between strength of belief, propositional structure, and the structure of evidence. Many of the phenomena discussed in the chapter are characterized as compositional anomalies-they are cases in which observed relations in belief strength conflict with the semantic structure of propositions, or at least with well-established theories of this semantic structure.