Philosophy of Logic and Mathematics
Description
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 Wolenski and Richard Zach.
More details
Other editions
Additional editions
Persons
Gabriele Mras
, WU Vienna, Austria;
Bernhard Ritter
, AAU Klagenfurt, Austria;
Paul Weingartner
, University Salzburg, Austria.
Content
- Intro
- Contents
- Preface
- Part I: Philosophy of Logic
- Link's Revenge: A Case Study in Natural Language Mereology
- Universal Translatability: An Optimality- Based Justification of (Classical) Logic
- Invariance and Necessity
- Translations Between Logics: A Survey
- On the Relation of Logic to Metalogic
- Free Logic and the Quantified Argument Calculus
- Dependencies Between Quantifiers Vs. Dependencies Between Variables
- Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic
- Truth, Paradox, and the Procedural Conception of Fregean Sense
- Wittgenstein and Frege on Assertion
- Assertions and Their Justification: Demonstration and Self-Evidence
- Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality
- Part II: Philosophy of Mathematics
- Neologicist Foundations: Inconsistent Abstraction Principles and Part-Whole
- What Hilbert and Bernays Meant by "Finitism"
- Wittgenstein and Turing
- Remarks on Two Papers of Paul Bernays
- The Significance of the Curry-Howard Isomorphism
- Reductions of Mathematics: Foundation or Horizon?
- What Are the Axioms for Numbers and Who Invented Them?
- Part III: Wittgenstein
- Following a Rule: Waismann's Variation
- Propositions in Wittgenstein and Ramsey
- An Unexpected Feature of Classical Propositional Logic in the Tractatus
- Ontology in Tractatus Logico-Philosophicus: A Topological Approach
- Adding 4.0241 to TLP
- Understanding Wittgenstein's Wood Sellers
- 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
- Incomplete Pictures and Specific Forms: Wittgenstein Around 1930
- "Man kann die Menschen nicht zum Guten führen" - Zur Logik des moralischen Urteils bei Wittgenstein und Hegel
- Der Status mathematischer und religiöser Sätze bei Wittgenstein
- Gutes Sehen
- Wittgenstein's Conjecture
- Index of Names
- Index of Subjects
