David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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
Karin Katz & Mikhail Katz (2012). A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science 17 (1):51-89.
Jeremy Avigad (2009). The Metamathematics of Ergodic Theory. Annals of Pure and Applied Logic 157 (2):64-76.
Similar books and articles
Geoffrey Hellman (1992). On the Scope and Force of Indispensability Arguments. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456 - 464.
Frank Waaldijk (2005). On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10 (3):249-324.
I. Loeb (2012). Questioning Constructive Reverse Mathematics. Constructivist Foundations 7 (2):131-140.
D. E. Over (1982). Predicative and Constructive Knowledge. Analysis 42 (3):140 - 146.
Laura Crosilla & Peter Schuster (eds.) (2005). From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics. Oxford University Press.
D. S. Bridges (1987). Varieties of Constructive Mathematics. Cambridge University Press.
H. Billinge (2000). Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'. British Journal for the Philosophy of Science 51 (2):299-318.
Added to index2009-01-28
Total downloads31 ( #65,217 of 1,410,065 )
Recent downloads (6 months)4 ( #57,890 of 1,410,065 )
How can I increase my downloads?