David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):349-373 (2006)
In the article the problem of independence in mathematics is discussed. The status of the continuum hypothesis, large cardinal axioms and the axiom of constructablility is presented in some detail. The problem whether incompleteness is really relevant for ordinary mathematics and for empirical science is investigated. Another aim of the article is to give some arguments for the thesis that the problem of reliability and justification of new axioms is well-posed and worthy of attention. In my opinion, investigations concerning the status of independent sentences give insight into our understanding of mathematical concepts, of mathematical knowledge and of the role of mathematics in empirical science.
|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
No citations found.
Similar books and articles
Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
Kenny Easwaran (2008). The Role of Axioms in Mathematics. Erkenntnis 68 (3):381 - 391.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Thomas Tymoczko (1991). Mathematics, Science and Ontology. Synthese 88 (2):201 - 228.
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.
Stewart Shapiro (1983). Mathematics and Reality. Philosophy of Science 50 (4):523-548.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4):351-360.
Leon Horsten, Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.
Added to index2009-01-28
Total downloads9 ( #150,574 of 1,096,547 )
Recent downloads (6 months)5 ( #49,071 of 1,096,547 )
How can I increase my downloads?