On Jun 8, 4:37 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Jun 9, 1:07 am, Peter Percival <peterxperci...@hotmail.com> wrote: > > > Charlie-Boo wrote: > > > On Jun 7, 2:24 am, Zeit Geist <tucsond...@me.com> wrote: > > > >> It was actually a desire to assure the consistency of the Calculus > > >> that eventually lead to the creation of ZFC. > > > > You mean avoid Russell's Paradox? > > Just use ALL(F):WFF F<->F > > E(S)A(X) XeS<->X~eX > <-> > E(S)A(X) XeS<->X~eX > > E(S)A(X) XeS<->X~eX > <-> > E(S)E(S) SeS<->S~eS > > E(S)A(X) XeS<->X~eX > <-> > FALSE > > CONTRADICTION CONTAINED IN A SUB-FORMULA! > > ~EXIST(RUSSELSET) > > THAT SIMPLE! > > > > > Zermelo created his set theory in order to prove that every set could we > > well-ordered. > > PROOF: 0;.44444444544444454444444454454444444544444... > > Herc
Very good - for starters. Now list as many theorems as you can that use the same proof but with different constants, in this case, instead of set and membership. Then identify a theorem that is proven with just one additional step beyond one of these, and apply it to the rest of the theorems. Here's a first step: The set of Turing Machines that do not halt yes on themselves is not recursively enumerable.