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Аннотация
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.
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Оглавление
- 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
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