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Principles of Mathematics Revisited
Author(s): Hintikka (Author)
- Publisher: Cambridge University Press
- Publication Date: 12 Jan. 2008
- Edition: Revised ed.
- Language: English
- Print length: 304 pages
- ISBN-10: 0521624983
- ISBN-13: 9780521624985
Book Description
This book, written by one of philosophy’s pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.
Editorial Reviews
Review
‘Hintikka’s new logic is highly original and will prove appealing to logicians, philosophers of mathematics, and mathematicians concerned with the foundations of the discipline.’ Studia Logica
Book Description
Hintikka proposes a new logic and uses it to explore the foundations of mathematics.
