[FOM] Is Godel's Theorem surprising?
=?ISO-5589-2?Q?Ser=E9ny_Gy=F6rgy?=
sereny at math.bme.hu
Sat Dec 9 18:03:25 EST 2006
Responding to Charlie Silver's remark:
>> I'm just wondering what accounts for the shock so to
>> speak of Godel's Theorem,
Laureano Luna Cabanero wrote:
> As for this second question, I can only refer to my
> own case; I would say we now know much better the
> possibilities and the logic of diagonalization in a
> broad sense. This helps me to see why logical and
> mathematical truth is inexhaustible by means of finite
> resources.
> I should add that diagonalization is itself
> surprising, so Godel's theorem still retains a bit of
> its mystery.
It is perhaps worth noting that Boolos's proof of
incompleteness (G. Boolos, A new proof of the
Godel incompleteness theorem. Notices
Amer. Math. Soc., 388-390 (1989)) based on the
formalization of the Berry paradox shows that
diagonalization does not play an essential
role in the incompleteness phenomenon.
(By the way, Boolos's method can be used to
show that the same is true for the
undefinability of truth and the undecidability
of provability as well
(cf. G. Sereny, Boolos-style proofs of limitative
theorems, Mathematical Logic Quarterly,
50 (2004), No.2, pp. 211-216).)
Gyorgy Sereny
More information about the FOM
mailing list