Journal of Philosophical Logic 30 (3):241-250 (2001)
|Abstract||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)|
|Through your library||Configure|
Similar books and articles
Per Lindstrom (2006). Remarks on Penrose's New Argument. Journal of Philosophical Logic 35 (3):231-237.
William Seager (2003). Yesterday's Algorithm. Croatian Journal of Philosophy 3 (3):265-273.
David J. Chalmers (1996). Minds, Machines, and Mathematics. Psyche 2:11-20.
Stewart Shapiro (2003). Mechanism, Truth, and Penrose's New Argument. Journal of Philosophical Logic 32 (1):19-42.
William S. Robinson (1992). Penrose and Mathematical Ability. Analysis 52 (2):80-88.
Rick Grush & P. Churchland (1995). Gaps in Penrose's Toiling. In Thomas Metzinger (ed.), Conscious Experience. Ferdinand Schoningh.
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 downloads29 ( #48,084 of 722,856 )
Recent downloads (6 months)1 ( #60,917 of 722,856 )
How can I increase my downloads?