Philosophy of Logic and Mathematics. Proceedings of the 41st International Ludwig Wittgenstein Symposium
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.
This paper addresses Ludwig Wittgenstein’s claim that “there can never be surprises in logic” (Tractatus 6.1251) from a perspective of the distinction between substantial and dynamic models of formality. It attempts to provide an interpretation of this claim as stressing the dynamic formality of logic. Focusing on interactive interpretation of compositionality as dynamic formality, it argues for the advantages of dynamic, i.e., gametheoretical approach to some binary semantical phenomena. Firstly, model-theoretical and game-theoretical interpretations of binary quantifiers are compared. Secondly, the paper offers an analysis of Wittgenstein’s idea that binary colours (e.g., bluish green, reddish green, etc.) possess logical structures. To answer some experimental challenges, it provides a game-theoretical interpretation of the colours opponency in Payoff Independence (PI) logic. Comparing Nikolay Vasiliev’s logical principles and Wittgenstein’s internal properties and relations, Wittgenstein’s approach is argued for as an attempt of modelling a balance between logic and the empirical.