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.

.

Relevant Pages

  • Re: If (P & ~P) -> Q is not derivable then Goedels formula is not derivable
    ... So the inference from "nobody agrees with Newberry" to ... "nobody agrees with Newberry and defends his position" is invalid??? ...
    (sci.logic)
  • Re: Lift up that pointy white hat ... find a pinhead.
    ... Interesting that nobody has seen fit to post the CMA nominations that ... >I think we all ought to get in here, post as much country as we can ...
    (rec.music.country.western)
  • Re: Yogi Berra Grammar
    ... Bob Cunningham wrote: ... 640K ought to be enough for anybody. ... Nobody will ever need more than 640K of memory. ... In my defence, we were still in the very early days of the PC; I was using an Atari ST at home, and a floppy disc/k held more than enough stuff to keep one happy when it was a free gift. ...
    (alt.usage.english)
  • Re: It is a small world ........
    ... Jim you really ought to be more careful how you drive your car;-) ... nobody about that time of night you can go up one way streets the wrong ...
    (uk.radio.amateur)
  • Re: Orphan Drug
    ... volunteers, but ought we really to be exploiting them? ... given that the alternative is that nobody can ever ...
    (uk.legal)