David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
|Buy the book||$13.89 used (77% off) $42.41 new (30% off) $59.99 direct from Amazon Amazon page|
|Call number||QA8.4.H56 1996|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
André Bazzoni (2015). Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts. Journal of Philosophical Logic 44 (5):507-516.
Juha Kontinen & Jouko Väänänen (2009). On Definability in Dependence Logic. Journal of Logic, Language and Information 18 (3):317-332.
Jakub Szymanik (2010). Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language. Linguistics and Philosophy 33 (3):215-250.
Samson Abramsky & Jouko Väänänen (2009). From If to Bi. Synthese 167 (2):207 - 230.
Ahti-Veikko Pietarinen (2005). Compositionality, Relevance, and Peirce's Logic of Existential Graphs. Axiomathes 15 (4):513-540.
Similar books and articles
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP
Wilfrid Hodges (1997). Jaakko Hintikka, the Principles of Mathematics Revisited. Journal of Logic, Language and Information 6 (4):457-460.
Harold T. Hodes (1998). Book Review. The Principles of Mathematics Revisited. Jaakko Hintikka. [REVIEW] Journal of Symbolic Logic 63 (4):1615-23.
S. Shapiro (2012). Higher-Order Logic or Set Theory: A False Dilemma. Philosophia Mathematica 20 (3):305-323.
Jouko Vaananen (2001). Second-Order Logic and Foundations of Mathematics. Bulletin of Symbolic Logic 7 (4):504-520.
Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
Jaakko Hintikka (2009). A Proof of Nominalism: An Exercise in Successful Reduction in Logic. In A. Hieke & H. Leitgeb (eds.), Reduction - Abstraction - Analysis. Ontos
Added to index2009-01-28
Total downloads25 ( #147,105 of 1,790,061 )
Recent downloads (6 months)3 ( #264,810 of 1,790,061 )
How can I increase my downloads?