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


Peter_Smith wrote:
Newberry wrote:

Therefore whenever

~(Ey)Fy (5)

then

~(Ey)(Fy & Gy) (6)

ought not to be derivable.

Really??? So the inference from "nobody agrees with Newberry" to
"nobody agrees with Newberry and defends his position" is invalid???
Very odd .....

As to the original claim, you can easily check that establishing
Gödel's Theorem in fact does not depend on using ex falso quodlibet
(e.g. the argument can be regimented in Tennant's version of relevant
logic).

Well, I simplified the argument to keep it brief. I should have said:

Therefore whenever

|- ~(Ey)Fy (5)

then

~(Ey)(Fy & Gy) (6)

ought not to be derivable. ~(Ey)Fy must be necessarily true for (6)
not to be derivable.

.

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