David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
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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|Buy the book||$5.65 used (91% off) $39.03 new (35% off) $59.99 direct from Amazon Amazon page|
|Call number||QA8.4.H56 1996|
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Citations of this work BETA
Juha Kontinen & Jouko Väänänen (2009). On Definability in Dependence Logic. Journal of Logic, Language and Information 18 (3):317-332.
André Bazzoni (2015). Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts. Journal of Philosophical Logic 44 (5):507-516.
Samson Abramsky & Jouko Väänänen (2009). From If to Bi. Synthese 167 (2):207 - 230.
Jakub Szymanik (2010). Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language. Linguistics and Philosophy 33 (3):215-250.
Ahti-Veikko Pietarinen (2005). Compositionality, Relevance, and Peirce's Logic of Existential Graphs. Axiomathes 15 (4):513-540.
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