Re: If (P & ~P) -> Q is not derivable then Goedel's formula is not derivable


Newberry wrote:
Confutus wrote:

It's not a question of what you are or aren't happy with.
It's a question of whether you know a truth-table when you see one.

A truth table? A truth table?

A: P
B: ~P
C: P & ~P
D Q
E (P & ~P) -> Q

A | B | C | D | E
T F F T T
T F F U T
T F F F T
U U U T T
U U U U T
U U U F U
F T F T T
F T F U T
F T F F T

The sixth line is why I am unhappy with (P & ~P) --> Q.

Do these tables come from Lukasiewicz? What does your extension cosists
of?

They do. My extension consists of defining a strict Lukasiewicz
conditional,
P=> Q := [] (P -> Q), and exploring its properties. Mathematically,
this is an insignificant addition. because -> and [] are already
primitive or defined, but in practice, the difference it makes is
beyond belief.

P Q P -> Q P => Q
T T T T
T U U F
T F F F
U T T T
U U T T
U F U F
F T T T
F U T T
F F T T

.