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  3. The Principles of Mathematics Revisited
  • Cited by 185
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1996
Online ISBN:
9780511624919
DOI:
https://doi.org/10.1017/CBO9780511624919
Subjects:
Mathematics, Logic, Categories and Sets, Philosophy of Science, Philosophy
Information

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.

Reviews

‘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.’

Source: Studia Logica

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