
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 7, 2012 7:38 PM


On Oct 5, 8:47 am, Frederick Williams <freddywilli...@btinternet.com> wrote: > Graham Cooper wrote: > > > Formal Theory means all sentences in the Theory are systematically > > enumerated. > > > ZFC is NOT a formal Theory! > > > There is no method given to distinguish between theorems and predicate > > calculus formulas. > > > [...] > > > You have NO WAY of enumerating Theorems! > > What is enumerated is G\"odel numbers of theorems. So which theorem > comes first depends on the enumerator and the G\"odel numbering.
Give them the Godel number consisting of the number of the first symbol times 100 plus the number of the second symbol etc. so the order of the numbers and of the wffs coincide. Then the first one is the theorem that is alphabetically first. Which one is that?
Or better yout, just start enumerating theorems and stop after the first one and tell us what it is ok?
What is theorem 1? Excellent question. A question that one could easily answer for any genuine axiomatic system!!!!!
CB
>  > Where are the songs of Summer?With the sun, > Oping the dusky eyelids of the south, > Till shade and silence waken up as one, > And morning sings with a warm odorous mouth.

