David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
In Christer Svennerlind (ed.), Ursus Philosophicus. Essays dedicated to Björn Haglund on his sixtieth birthday. Philosophical Communications (2004)
It is not unreasonable to think that the dispute between classical and intuitionistic mathematics might be unresolvable or 'faultless', in the sense of there being no objective way to settle it. If so, we would have a pretty case of relativism. In this note I argue, however, that there is in fact not even disagreement in any interesting sense, let alone a faultless one, in spite of appearances and claims to the contrary. A position I call classical pluralism is sketched, intended to provide a coherent methodological stance towards the issue. Some reasons to recommend this stance are given, as well as some speculations as to why not everyone might want to follow the recommendation.
|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
Stewart Shapiro (2014). Structures and Logics: A Case for (a) Relativism. Erkenntnis 79 (2):309-329.
Neil Tennant (1994). Intuitionistic Mathematics Does Not Needex Falso Quodlibet. Topoi 13 (2):127-133.
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.
A. S. Troelstra (1975). Axioms for Intuitionistic Mathematics Incompatible with Classical Logic. Mathematisch Instituut.
Stewart Shapiro (ed.) (1985). Intentional Mathematics. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
Stephen Cole Kleene (1965). The Foundations of Intuitionistic Mathematics. Amsterdam, North-Holland Pub. Co..
Daniel Dzierzgowski (1995). Models of Intuitionistic TT and N. Journal of Symbolic Logic 60 (2):640-653.
Victor N. Krivtsov (2000). A Negationless Interpretation of Intuitionistic Theories. I. Erkenntnis 64 (1-2):323-344.
Stefano Berardi (1999). Intuitionistic Completeness for First Order Classical Logic. Journal of Symbolic Logic 64 (1):304-312.
Michael A. E. Dummett (2000). Elements of Intuitionism. Oxford University Press.
Greg Restall (1997). Combining Possibilities and Negations. Studia Logica 59 (1):121-141.
H. Billinge (2000). Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'. British Journal for the Philosophy of Science 51 (2):299-318.
Michael A. E. Dummett (1974). Intuitionistic Mathematics and Logic. Mathematical Institute.
Wenceslao J. Gonzalez (1991). Intuitionistic Mathematics and Wittgenstein. History and Philosophy of Logic 12 (2):167-183.
Added to index2012-11-25
Total downloads14 ( #255,981 of 1,907,401 )
Recent downloads (6 months)1 ( #466,442 of 1,907,401 )
How can I increase my downloads?