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r ide Are There AbsollJtelr Unsolvab le Problems? Godel's D ichotomy{d~QQer}
Author/C reator Feferrnen , Solomon
Pub lishe r O'l'ford uni ver sit y Pre ss
Yea r 2006· 01-09 0S:3tl:S1.0
Resource Type TEXT
Resource f orma t texVhtm l
language EnQlish
Note This is a critice l .analYSISof the first part of G6de l's 1951 Gibbs lectu re on ce rtain philosophical
consequ enc es of the incompl et eness theore ms . Godel's discussion is fremed in te rms of I'l distinction
bet wee n obje ctive rnethemetics and subjecti ve ma th em at ics, ecco rdinc to which the for me r consists of
the tru ths of mathematics in an ebsclute sense, and the latter consists of all hum an ly de monstrable
tru ths . The Clu es tion is wheth er' the se coincide; if the y do. no forma l axiomatic s ystem (or Tu rinq
mecbtne) cen compreh end th e met he rnetuinq pote ntia lities of hurnen tho ught, and , if not, ther e are
ebsctuteh un s o lv~b le rnethernetica l problems of diophantine form . Elther ... the hum an mind ...
infinitely su rp,u ses the powe rs of an y finite mach ine. or else there e ~ lst absolute ly unsolvable
diopha ntine problems .
Subject G&oumljde l on MathematiCs an d logic Special Issue Artid e
UFlL http :/ / ohllmat.o: