The Architecture and Archaeology of Modern Logic
Description
This book honors the original and influential work by Göran Sundholm in the fields of the philosophy and history of logic and mathematics. Borne from two conferences held in Paris and Leiden on the occasion of Göran Sundholm's retirement in 2019, the contributions collected in this volume represent work from leading logicians and philosophers. Reflecting Sundholm's contributions to the history and philosophy of logic, this book is divided into two parts: the architecture and archaeology of logic.
The essays collected in the 'architecture' section cover primarily the systematic approach to basic logical concepts taken by Sundholm, including type theory, epistemic assumptions, and notions of consequence. The 'archaeology' section includes contributions focused on Sundholm's contributions to the history of philosophy and logic. Enclosing these two sections are, on the one end, autobiographical remarks of Sundholm's and, on the other, a paper on cooking and philosophy, reflectinganother of Sundholm's passions in life. This book is of interest to logicians, philosophers, mathematicians, and computer scientists.
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Ansten Klev is a researcher in the Institute of Philosophy at the Czech Academy of Sciences in Prague, where has been since 2015. Before moving to Prague, he obtained a PhD in philosophy under Göran Sundholm at Leiden University. Most of his work concerns philosophical aspects of Per Martin-Löf's constructive type theory. A topic of special interest, on which he has published a number of articles, has been the treatment of identity within this type theory. His other research interests include the philosophies of logic and mathematics more broadly, as well as the words and works of Rudolf Carnap, Richard Dedekind, Gottlob Frege, and Edmund Husserl.
Content
Chapter 1: A brief summary of Göran Sundholm's philosophical work.- Chapter 2: Formative experiences.- Chapter 3: Bibliography.- Chapter 4: Epistemic assumptions: Are they assumed to be backwards vindicated or forwards vindicable?.- Chapter 5: Dialogical logic and constructive type theory: New explorations.- Chapter 6: Are proofs objects or acts? A comparison of Prawitz's and Sundholm's semantics.- Chapter 7: How to classify varieties of consequence.- Chapter 8: Informal classical and intuitionistic proofs together.- Chapter 9: Judgmental and definitional equality from a Fregean perspective.- Chapter 10: "Sind die Zahlformeln beweisbar?".- Chapter 11: Handling mobility failures by modal types.- Chapter 12: The ideal of unity of science tested against the Liar.- Chapter 13: Vindicating the future: A dialogical stance on Belnap's approach to tomorrow's sea battle.- Chapter 14: Goodbye Oxhead. Prolegomena to the philosophy of the letter.- Chapter 15: Logical deducibility and logicality in 1837.- Chapter 16: Frege on knowing the fundamental laws of logic.- Chapter 17: Sundholm on Wittgenstein and Realism.- Chapter 18: Becker's rule is not Becker's rule.- Chapter 19: Judgment and commitment.- Chapter 20: Natural constructive proofs of A via A B, proof paradoxes, and impredicativity.- Chapter 21: Gastronomical Platonism.