# Description

The book is a research monograph on the notions of truth and assertibility as they relate to the foundations of mathematics. It is aimed at a general mathematical and philosophical audience. The central novelty is an axiomatic treatment of the concept of assertibility. This provides us with a device that can be used to handle difficulties that have plagued philosophical logic for over a century. Two examples relate to Frege's formulation of second-order logic and Tarski's characterization of truth predicates for formal languages. Both are widely recognized as fundamental advances, but both are also seen as being seriously flawed: Frege's system, as Russell showed, is inconsistent, and Tarski's definition fails to capture the compositionality of truth. A formal assertibility predicate can be used to repair both problems. The repairs are technically interesting and conceptually compelling. The approach in this book will be of interest not only for the uses the author has put it to, but also as a flexible tool that may have many more applications in logic and the foundations of mathematics.

**Contents:**TruthConceptsDeductionAssertibilitySystemsSurveyability**Readership:**Undergraduates, graduates and researchers in mathematics, logic and philosophy.**Key Features:**Although this is a research monograph, the material is presented at an elementary level that will be accessible to readers with minimal background. Undergraduates in mathematics or philosophy will have no trouble reading all but a handful of the more advanced sections. Because it deals with topics in the foundations of mathematics, it will appeal to readers with a variety of interests ranging from mathematics to logic to philosophyWhile it draws on a variety of sources such as classical proof theory and intuitionistic logic, the approach of the book is highly novel. The material presented here cannot be found anywhere elseKeywords:Truth;Assertibility;Philosophical Logic;Philosophy of Mathematics;Philosophy of Language;Intuitionism;Constructivism;Liar Paradox;Russell's Paradox;Semantic Paradoxes, Second Order Logic