byron
Posts:
865
Registered:
3/3/09


Re: ZFC is inconsistent
Posted:
Mar 14, 2013 12:42 AM


On Thursday, March 14, 2013 4:40:18 AM UTC+11, Frederick Williams wrote: > spermatozon@yahoo.com wrote: > > > > > > > > Now we have paradoxes like > > > Russells paradox > > > BanachTarskin paradox > > > > Though Russell's paradox and the BanachTarski paradox (note the > > spelling in each case) are reasonably called paradoxes, they are > > paradoxes in two very different senses. > > > > In the Russell case, a contradiction arises from a few very reasonable > > (or at least reasonableseeming) assumptions. Therefore one or more of > > those assumptions must be rejected. > > > > In the BanachTarski case, assuming the axiom of choice leads not to a > > contradiction, but to something unexpected. If you find that unexpected > > thing actually repugnant, then reject the axiom of choice. Otherwise > > accept that the unexpected happens. Some mathematicians do reject the > > axiom of choice, but I do not know if any have done so because of > > BanachTarski. > > > > I suspect that a good many, on first hearing of the BanachTarski > > paradox, thought 'Wow! How about that! Isn't mathematics fun?' And > > perhaps: 'So what happens if Choice is false? Do any loopy things happen > > in that case?' Meanwhile, note that if set theory is consistent, one > > may safely assume either Choice or its negation. > > > >  > > When a true genius appears in the world, you may know him by > > this sign, that the dunces are all in confederacy against him. > > Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
yes
but zfc is inconsistent zfc bans impredicatice statements but is impredicative itsels so it bans itself thus zfc is inconsistent

