"It was like fooling a kid into eating his vegetables," Professor Rosenhouse said in a telephone interview, adding, "Raymond took something like Godel's incompleteness theorems
and used a string of logic puzzles as a device for presenting them."
Once students have mastered Hardy's version of the proof (Hardy, 1941; Padula, 2006) together with Arianrhod's (2003) highly explanatory version, and perhaps, the proof of the existence of an infinity of prime numbers (Padula, 2003), Hardy's (1941) other example of an 'elegant' proof, they can progress to more difficult proofs such as: Godel's incompleteness theorems
(Padula, 2011) and the story of the solving of Fermat's last theorem (Singh, 2005).
Could it be that Godel's incompleteness theorems
go beyond mere analogy and are a sign of the limitations of even our theological (conceptual) beliefs about God?
--, 1992, Godel's Incompleteness Theorems
, Oxford University Press, Nueva York.
(13) In particular, Godel's incompleteness theorems
stated that formal languages defining natural numbers have inherent limitations as their own proof systems.
Further, from a technical perspective, by appealing to infinitary formal systems to which Godel's incompleteness theorems
do not apply, neo-formalists clearly overcome Godelian worries.
Let us now turn to Godel's incompleteness Theorems
. These, of course, have been held to have all kinds of problematic or unpalatable consequences.
programs which recognize theorems) in that the former do not seem to be limited by Godel's incompleteness theorems
whereas the latter do seem to be thus limited.
(24) We may point out that in Niebergall and Schirn 2002 we argue that a weak version of Hilbert's finitist metamathematics of the 1920s is compatible with Godel's Incompleteness Theorems
by using only what are clearly natural provability predicates.