Synopses & Reviews
The foundations of mathematics are examined by reference to such crucial concepts as the informational independence of quantifiers, the standard-nonstandard distinction, completeness, computability, parallel processing and the extremality of models.
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.
Table of Contents
1. What Is Elementary Logic? Independence-Friendly Logic as the True Core Area of Logic.
2. A Revolution in Logic?
3. A Revolution in the Foundations of Mathematics?
4. Is There Completeness in Mathematics After Gödel?
5. Hilbert Vindicated?
6. Standard vs. Nonstandard Logic: A Watershed in the Foundations of Mathematics.
7. Standard vs. Nonstandard Logic: Higher-Order, Modal and First-Order Logics.
8. (with
Gabriel Sandu.) The Skeleton in Frege's Cupboard: The Standard vs. Nonstandard Distinction.
9. (with
Arto Mutanen.) An Alternative Concept of Computability.
10. (with
Gabriel Sandu.) What is the Logic of Parallel Processing?
11. Model Minimization - An Alternative to Circumscription.
12. New Foundations for Mathematical Theories.