David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Cambridge University Press (1996)
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|
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Citations of this work BETA
Jaakko Hintikka (2011). What is the Axiomatic Method? Synthese 183 (1):69-85.
Alessandro Torza (2013). How to Lewis a Kripke-Hintikka. Synthese 190 (4):743-779.
Jaakko Hintikka (2011). Method of Analysis: A Paradigm of Mathematical Reasoning? History and Philosophy of Logic 33 (1):49 - 67.
Jaakko Hintikka (2012). If Logic, Definitions and the Vicious Circle Principle. Journal of Philosophical Logic 41 (2):505-517.
Marc Pauly (2008). On the Role of Language in Social Choice Theory. Synthese 163 (2):227 - 243.
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