David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 30 (3):241-250 (2001)
It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive
|Keywords||Gödel's proof formal system human mathematical reasoning|
|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
Jouko Väänänen & Dag Westerståhl (2010). In memoriam: Per Lindström. Theoria 76 (2):100-107.
Martin Kaså (2012). Experimental Logics, Mechanism and Knowable Consistency. Theoria 78 (3):213-224.
Similar books and articles
Rick Grush & Patricia Smith Churchland (1995). Gaps in Penroses Toiling. Journal of Consciousness Studies 2 (1):10-29.
Rick Grush & P. Churchland (1995). Gaps in Penrose's Toiling. In Thomas Metzinger (ed.), Journal of Consciousness Studies. Ferdinand Schoningh. 10-29.
William S. Robinson (1992). Penrose and Mathematical Ability. Analysis 52 (2):80-88.
John Lucas (2003). The Gödelian Argument: Turn Over the Page. Etica E Politica 5 (1):1.
Stewart Shapiro (2003). Mechanism, Truth, and Penrose's New Argument. Journal of Philosophical Logic 32 (1):19-42.
David J. Chalmers (1996). Minds, Machines, and Mathematics. Psyche 2:11-20.
William Seager (2003). Yesterday's Algorithm. Croatian Journal of Philosophy 3 (3):265-273.
Per Lindstrom (2006). Remarks on Penrose's New Argument. Journal of Philosophical Logic 35 (3):231-237.
William E. Seager (2003). Yesterday's Algorithm: Penrose and the Godel Argument. Croatian Journal of Philosophy 3 (9):265-273.
Added to index2009-01-28
Total downloads32 ( #65,270 of 1,692,449 )
Recent downloads (6 months)1 ( #184,284 of 1,692,449 )
How can I increase my downloads?