David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 15 (2):149-172 (1994)
After the 1930s, the research into the foundations of mathematics changed.None of its main directions (logicism, formalism and intuitionism) had any longer the pretension to be the only true mathematics.Usually, the determining factor in the change is considered to be Gödel?s work, while Heyting?s role is neglected.In contrast, in this paper I first describe how Heyting directly suggested the abandonment of the big foundational questions and the putting forward of a new kind of foundational research consisting in the isolation of formal, intuitive, logical and platonistic elements within classical mathematics.Furthermore, I describe how Heyting indirectly influenced the abandon?ment of the old directions of foundational research by making out some lists of degrees of evidence that exist within intuitionism
|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
Arend Heyting (1948). Formal Logic and Mathematics. Synthese 6 (7-8):275 - 282.
Valeria Castaño & Marcela Muñoz Santis (2011). Subalgebras of Heyting and De Morgan Heyting Algebras. Studia Logica 98 (1-2):123-139.
Erich H. Reck (2009). Dedekind, Structural Reasoning, and Mathematical Understanding. In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. World Scientific. 150--173.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
A. Heyting (1956). Intuitionism. Amsterdam, North-Holland Pub. Co..
A. Heyting (1971). Intuitionism. Amsterdam,North-Holland Pub. Co..
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Miriam Franchella (1995). Like a Bee on a Windowpane: Heyting's Reflections on Solipsism. Synthese 105 (2):207 - 251.
Added to index2010-08-10
Total downloads14 ( #163,935 of 1,696,615 )
Recent downloads (6 months)2 ( #250,163 of 1,696,615 )
How can I increase my downloads?