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.

• 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