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.
1. Introduction (Mattia Petrolo and Giorgio Venturi).- Part I.
Methodological Considerations.
2. Paradoxes: between revision and
accommodation (Jonas R. Becker Arenhart and Ederson Safra Melo).- 3.
Reference Fixing and the Paradoxes (Mario Gómez-Torrente).-
4. Transcending
the Theory of Types (Simone Picenni and Thomas Schindler).- Part II. Semantic
Approaches to Paradoxes.
5. Paradoxes, Contradictions and Circularity
(Eduardo Barrio, Bruno Da Ré and Miguel Álvarez Lisboa).-
6. Impossible
Truths: a non-dialetheist paraconsistent approach to paradoxes (Guilherme
Cardoso).-
7. Paradoxes, Hypodoxes, and More (Camila Gallovich and Lucas
Rosenblatt).- Part III. Syntactic Approaches to Paradoxes.
8. Substructural
Solutions to the Semantic Paradoxes: a Dialetheic Perspective (Graham
Priest).-
9. A substructural solution to the Lottery and Preface Paradoxes
(Pilar Terrés Villalonga).- Part IV. Paradoxes of Epistemology and Vagueness.
10. Tolerance and degrees of truth (Pablo Cobreros, Paul Égré, David Ripley,
Robert van Rooij).-
11. Self-Referential Gettier Sentences (Volker Halbach
and Leon Horsten).-
12. Solovays Theorem and The Unexpected Examination
(Graham Leach-Krouse).-
13. Verdict Exclusion, Higher-Order Vagueness,
Cross-Order Vagueness and Borderlineness: Reflections on Footnote 41 of
CrispinWrights On Being in a Quandary (Elia Zardini).
Mattia Petrolo is FCT Research Fellow at the Centre for Philosophy of Science at the University of Lisbon (CFCUL). He earned his PhD from the University of Paris 7 Paris Diderot and held a postdoctoral fellowship at the French National Centre for Scientific Research (CNRS) in Paris, where he also served as a fixed-term lecturer at the University of Paris 1 Panthéon-Sorbonne. In 2018, he accepted a tenured assistant professorship at the Federal University of ABC in Brazil. He is also an associated member of the Institute for the History and Philosophy of Science and Technology (IHPST) in Paris. His research interests include computational logic, structural proof theory, philosophy of logic, and formal epistemology.
Giorgio Venturi is a tenure-track Associate Professor at the University of Pisa (Italy). In 2014 he obtained a doctorate in mathematics at the Université Paris 7 and a doctorate in philosophy at the Scuola Normale Superiore. Between 2017 and 2022 he was Assistant Professor at the University of Campinas. He is an associated member of the University of Brasilia and of the Konstanz Center for Philosophy of Mathematics. He is currently Secretary of the European Society for the Philosophy of Mathematics (ESPM) and a board member of the Associazione Italiana di Logica e Sue Applicazioni (AILA). He regularly publishes in the main specialist journals of logic. His works focus on set theory, modal logic and philosophy of mathematics.
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