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Essays on Mathematical and Philosophical Logic


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Table of Contents

I Proof Theory.- Some Facts from the Theory of Proofs and Some Fictions from General Proof Theory.- Proofs and the Meaning and Completeness of the Logical Constants.- Theory of Quantification and ‰-calculi.- Two Kinds of Extensions of Primitive Recursive Arithmetic.- Equality in the Presence of Apartness.- II Infinitary Languages.- Game-Theoretical Semantics and Back-and-Forth.- Infinitary Languages N?? and Generalized Partial Isomorphisms.- III Set Theory and Model Theory.- Generalizing Set-Theoretical Model Theory and an Analogue Theory on Admissible Sets.- Hierarchies of Model Theoretic Definability — An Approach to Second Order Logics.- Open Problems in the Theory of Ultrafilters.- IV Generalized Quantifiers.- The Reals Cannot Be Characterized Topologically with Strictly Local Properties and Countability Axioms.- On the Expressive Power of the Language Using the Henkin Quantifier.- Remarks on Free Quantifier Variables.- V Recursion Theory.- Recursion in 3E and a Splitting Theorem.- Retracts of Post’s Numbering and Effectivization of Quantifiers.- VI Logic and Natural Language.- Quantifiers in Natural Languages: Some Logical Problems, I.- Models for Natural Languages.- Backwards-Looking Operators in Tense Logic and in Natural Language.- VII Philosophical Logic.- Paradoxes in a Semantic Perspective.- Hintikka’s Possible Worlds and Rigid Designators.- On the Content Analysis of Two Normative Notions.- Singular Terms, Existence and Truth: Some Remarks on a First Order Logic of Existence.- VIII Truthlikeness.- On Distance From the Truth as a True Distance.- Truthlikeness in First-Order Languages.- Index of Names.

About the Author

Jaakko Hintikka is the author or co-author of thirty volumes and of some 300 scholarly articles in mathematical and philosophical logic, epistemology, language theory, philosophy of science, history of ideas and history of philosophy, including Aristotle, Descartes, Leibniz, Kant, Peirce, The Bloomsbury Group, Husserl and Wittgenstein. He has also been active in international scholarly organizations, most recently as the First Vice-President of FISP, Vice-President of IIP and Co-Chair of the American Organizing Committee of the Twentieth World Congress of Philosophy. He has been Editor-in-Chief of the International Journal Synthese and the Managing Editor of Synthese Library since 1965.

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