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Topic: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Replies: 39   Last Post: Oct 14, 2012 11:56 PM

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 Graham Cooper Posts: 4,495 Registered: 5/20/10
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

Date Subject Author
10/5/12 Graham Cooper
10/5/12 Frederick Williams
10/7/12 Charlie-Boo
10/5/12 Graham Cooper
10/5/12 Frederick Williams
10/5/12 Graham Cooper
10/7/12 Graham Cooper
10/8/12 Graham Cooper
10/9/12 Graham Cooper
10/11/12 Graham Cooper
10/12/12 Graham Cooper
10/12/12 Graham Cooper
10/12/12 camgirls@hush.com
10/12/12 Richard Tobin
10/12/12 camgirls@hush.com
10/13/12 george
10/13/12 Graham Cooper
10/14/12 george
10/13/12 Graham Cooper
10/13/12 george
10/13/12 george
10/13/12 Graham Cooper
10/14/12 Graham Cooper
10/14/12 Graham Cooper
10/14/12 Graham Cooper
10/5/12 Scott Berg
10/5/12 Curt Welch
10/6/12 Mike Terry
10/6/12 Graham Cooper