Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium (Publications of the Austrian Ludwig ... Ludwig Wittgenstein Society, New, 26)

This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach. Contents 5 Preface 9 Part I: Philosophy of Logic 15 Link’s Revenge: A Case Study in Natural Language Mereology 15 Universal Translatability: An Optimality- Based Justification of (Classical) Logic 49 Invariance and Necessity 67 Translations Between Logics: A Survey 83 On the Relation of Logic to Metalogic 103 Free Logic and the Quantified Argument Calculus 117 Dependencies Between Quantifiers Vs. Dependencies Between Variables 129 Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic 145 Truth, Paradox, and the Procedural Conception of Fregean Sense 165 Wittgenstein and Frege on Assertion 181 Assertions and Their Justification: Demonstration and Self-Evidence 195 Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality 209 Part II: Philosophy of Mathematics 227 Neologicist Foundations: Inconsistent Abstraction Principles and Part-Whole 227 What Hilbert and Bernays Meant by “Finitism” 261 Wittgenstein and Turing 275 Remarks on Two Papers of Paul Bernays 309 The Significance of the Curry-Howard Isomorphism 325 Reductions of Mathematics: Foundation or Horizon? 339 What Are the Axioms for Numbers and Who Invented Them? 355 Part III: Wittgenstein 371 Following a Rule: Waismann’s Variation 371 Propositions in Wittgenstein and Ramsey 387 An Unexpected Feature of Classical Propositional Logic in the Tractatus 397 Ontology in Tractatus Logico-Philosophicus: A Topological Approach 409 Adding 4.0241 to TLP 427 Understanding Wittgenstein’s Wood Sellers 441 On the Infinite, In-Potentia: Discovery of the Hidden Revision of Philosophical Investigations and Its Relation to TS 209 Through the Eyes of Wittgensteinian Mathematics 453 Incomplete Pictures and Specific Forms: Wittgenstein Around 1930 469 „Man kann die Menschen nicht zum Guten führen“ – Zur Logik des moralischen Urteils bei Wittgenstein und Hegel 485 Der Status mathematischer und religiöser Sätze bei Wittgenstein 497 Gutes Sehen 511 Wittgenstein’s Conjecture 527 Index of Names 547 Index of Subjects 551 Publications of the series include the official proceedings of the ALWS-conferences and of their special workshops. The series is open also for other high-quality publications, especially on the philosophy of Ludwig Wittgenstein and its influence on contemporary analytic philosophy.