David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
British Journal for the Philosophy of Science 55 (4):731-737 (2004)
Granted that truth is valuable we must recognize that certifiable truth is hard to come by, for example in the natural and social sciences. This paper examines the case of mathematics. As a result of the work of Gödel and Tarski we know that truth does not equate with proof. This has been used by Lucas and Penrose to argue that human minds can do things which digital computers can't, viz to know the truth of unprovable arithmetical statements. The argument is given a simple formulation in the context of sorites (Robinson) arithmetic, avoiding the complexities of formulating the Gödel sentence. The pros and cons of the argument are considered in relation to the conception of mathematical truth.
|Keywords||Arithmetic Logic Mathematics Mind Truth|
|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
Philip Hugly & Charles Sayward (1989). Can There Be a Proof That an Unprovable Sentence of Arithmetic is True? Dialectica 43 (43):289-292.
Jeffrey Ketland (1999). Deflationism and Tarski's Paradise. Mind 108 (429):69-94.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Otavio Bueno & Steven French (2005). A Coherence Theory of Truth. Manuscrito 28 (2):263-290.
Michael Gabbay (2010). A Formalist Philosophy of Mathematics Part I: Arithmetic. Studia Logica 96 (2):219-238.
Charles Sayward (2001). On Some Much Maligned Remarks of Wittgenstein on Gödel. Philosophical Investigations 24 (3):262–270.
Janet Folina (1994). Poincaré's Conception of the Objectivity of Mathematics. Philosophia Mathematica 2 (3):202-227.
Added to index2009-01-28
Total downloads30 ( #90,983 of 1,699,829 )
Recent downloads (6 months)1 ( #362,609 of 1,699,829 )
How can I increase my downloads?