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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: 4,237
Registered: 5/20/10
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted: Oct 9, 2012 6:01 PM
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[1]
> a proof that Er[ xer <--> ~xex ].  IF THAT HAPPENS, THEN YOUR THEORY
> IS INCONSISTENT and SOME part of it MUST be abandoned.


So the AXIOMS are a *CONSTRAINT* what formula are allowed.


[2]
> (P->Q)->((P^R)->Q)  IS A TAUTOLOGY -- and there are MANY SIMPLE
> "algorithms" that PROVE THAT THAT IS A TAUTOLOGY!


only in FOL.

Axioms (R here) are 2OL or 3OL (Regularity)

so they range over all expressions within their own theory
(including P and Q)
and LIMIT the usage/range of certain symbols.



[3]
>You need ZFC to tell you what sets DO exist! -- This validity ONLY
>tells you that a certain kind of set canNOT exist!



ALL(set) mem e set IFF p(mem,set)
AND EXIST(anotherset) mem e anotherset


This is what ZFC does, limits the relation 'e'.


[4]
> The way this paradox can thwart your set theory
> IS IF your set theory, in proving that many sets exist,
> HAPPENS TO STUMBLE ACROSS
> a proof that Er[ xer <--> ~xex ].
> IF THAT HAPPENS, THEN YOUR THEORY IS
> INCONSISTENT and SOME part of it MUST be abandoned.
> In naive set theory, THIS DOES happen
> (this set r MUST exist), so naive set
> theory is inconsistent (and therefore worthless).



What's the difference between Predicate Calculus
and Naive Set Theory.

They are both ZERO-AXIOM logic systems.

If NST is inconsistent, what rules in Predicate Calculus
are you using to ensure ZFC does not inherit NST inconsistency?


Herc


Date Subject Author
10/5/12
Read If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Frederick Williams
10/7/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Charlie-Boo
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Frederick Williams
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/7/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/8/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/9/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/11/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
camgirls@hush.com
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Richard Tobin
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
camgirls@hush.com
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Scott Berg
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Curt Welch
10/6/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Mike Terry
10/6/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper

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