
If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 5, 2012 3:59 AM


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.
X=X is a formula. !(X=X) is a formula. E(X) !(X=X) is a formula.
XeX is a formula !(XeX) is a formula XeY is a formula XeY <> !(XeX) is a formula A(X) XeY <> !(XeX) is a formula E(Y)A(X) XeY <> !(XeX) is a formula
there are many, many wrong formulas in Predicate Calculus.
Predicate Calculus is just the SYNTAX CHECKER.
10 prnt "hello"
SYNTAX ERROR
10 print "hello" 20 goto 10
does not guarantee a WFF. (program)
You have NO WAY of enumerating Theorems!
Herc

