A Mathematical Model of Meaning

This book offers a mathematical model of meaning, and thereby provides answers to the following kinds of questions: What is meaning? What is the relation between meaning, information, value, and purpose? What ingredients are necessary for a system to exhibit meaning? What behaviors, and capacities for behavior, are particular to meaning-oriented agents? Is there a relatively simple mathematical model that can adequately capture the dynamics -- and diversity -- of meaning-oriented agents? How do we best bridge the divide between interpretive paradigms that are qualitative and context-rich and formal methods that are quantitative and domain-general?

While the model incorporates core ideas from a pragmatist tradition, it weaves together a range of powerful ideas from other paradigms, including Bayesian inference, statistical mechanics, decision theory, mathematical biology, evolutionary game theory, possible world semantics, and linguistic anthropology. Its analytic framework thereby allows for a relatively seamless integration of distinct methods and theories.

After introducing the model, and reviewing its core assumptions, six short chapters explore the entailments of the model, and assay its merits, by using it to analyze a variety of increasingly complex scenarios. As will be seen, the math is done in a complete, but conversational way. And the formalism begins simply and ramps up slowly, such that a wide range of readers will be able to understand the concepts, follow the arguments, and assess the claims.