David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program.
|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
Antonio Montalbán (2011). Open Questions in Reverse Mathematics. Bulletin of Symbolic Logic 17 (3):431-454.
Panu Raatikainen (2001). Exploring Randomness. Notices of the AMS 48 (9):992-6.
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
Uri Pincas (2011). Program Verification and Functioning of Operative Computing Revisited: How About Mathematics Engineering? [REVIEW] Minds and Machines 21 (2):337-359.
Richard Zach (2006). Hilbert's Program Then and Now. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 5--411.
Richard A. Shore (2010). Reverse Mathematics: The Playground of Logic. Bulletin of Symbolic Logic 16 (3):378-402.
Added to index2009-01-28
Total downloads13 ( #119,415 of 1,098,967 )
Recent downloads (6 months)2 ( #175,054 of 1,098,967 )
How can I increase my downloads?