Both the constructive and predicative approaches to mathematics arose during the period of what was felt to be a foundational crisis in the early part of this century. Each critiqued an essential logical aspect of classical mathematics, namely concerning the unrestricted use of the law of excluded middle on the one hand, and of apparently circular \impredicative" de nitions on the other. But the positive redevelopment of mathematics along constructive, resp. predicative grounds did not emerge as really viable alternatives to classical, set-theoretically based mathematics until the 1960s. Now we have a massive amount of information, to which this lecture will constitute an introduction, about what can be done by what means, and about the theoretical interrelationships between various formal systems for constructive, predicative and classical analysis.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.Karin Katz & Mikhail Katz - 2012 - Foundations of Science 17 (1):51-89.
The Metamathematics of Ergodic Theory.Jeremy Avigad - 2009 - Annals of Pure and Applied Logic 157 (2):64-76.
Proofs and Retributions, Or: Why Sarah Can’T Take Limits.Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz & Mary Schaps - 2015 - Foundations of Science 20 (1):1-25.
Similar books and articles
On the Scope and Force of Indispensability Arguments.Geoffrey Hellman - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456-464.
On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions.Frank Waaldijk - 2004 - Foundations of Science 10 (3):249-324.
Russell's Theory of Descriptions Vs. The Predicative Analysis: A Reply to Graff.Berit Brogaard - unknown
Questioning Constructive Reverse Mathematics.I. Loeb - 2012 - Constructivist Foundations 7 (2):131-140.
From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics.Laura Crosilla & Peter Schuster (eds.) - 2005 - Oxford University Press.
Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'.H. Billinge - 2000 - British Journal for the Philosophy of Science 51 (2):299-318.
Added to index2009-01-28
Total downloads51 ( #101,246 of 2,158,890 )
Recent downloads (6 months)3 ( #132,304 of 2,158,890 )
How can I increase my downloads?