The Principles of Mathematics Revisited

Cambridge University Press (1996)
Abstract
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.
Keywords Mathematics Philosophy  First-order logic
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Call number QA8.4.H56 1996
ISBN(s) 0521624983   9780521624985  
DOI 10.1093/bjps/49.2.309
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Juha Kontinen & Jouko Väänänen (2009). On Definability in Dependence Logic. Journal of Logic, Language and Information 18 (3):317-332.

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