Essays in Logical Semantics

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge.

This volume collects 22 essays on the history of logic written by outstanding specialists in the field. The book was originally prompted by the 2018-2019 celebrations in honor of Massimo Mugnai, a world-renowned historian of logic, whose contributions on Medieval and Modern logic, and to the understanding of the logical writings of Leibniz in particular, have shaped the field in the last four decades. Given the large number of recent contributions in the history of logic that have some connections or debts with Mugnai’s work, the editors have attempted to produce a volume showing the vastness of the development of logic throughout the centuries.

This book is a collection of essays that offer original logical and philosophical investigations into the century-long endeavor to understand paradoxes. It bridges the gap between the two most prominent traditions in the analysis of paradoxes: the truth-theoretic and proof-theoretic approaches. The truth-theoretic tradition stems from Alfred Tarski's solution to the semantic paradoxes, while the proof-theoretic tradition dates back to Dag Prawitz's analysis of set-theoretic paradoxes in terms of structural proof theory. Rather than viewing these traditions as competing perspectives, this volume advocates for the idea that a deeper understanding of paradoxes requires insights from both truth-theoretic and proof-theoretic conceptions of language and meaning. Although the collection does not aim to be exhaustive, it seeks to highlight the vast scope of the subject and its deep connections to various fields of inquiry. The essays are organized into four sections: the first focuses on methodology, the second and third examine paradoxes through the conventional lenses of logical investigation—semantics and syntax—, and the fourth presents a selection of paradoxes that extend beyond the interplay between syntax and semantics, exploring other dimensions of human rationality.