Re: did Godel prove Incompleteness or did he disprove Excluded Middle?
From: William Elliot (marsh_at_privacy.net)
Date: 06/24/04
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Date: Wed, 23 Jun 2004 23:10:13 -0700
On Wed, 23 Jun 2004, Adam Megacz wrote:
> > What are the axioms for a second order language?
>
> You can look it up on google if you don't know.
> http://www.google.com/search?q=second.order.logic&ie=UTF-8&oe=UTF-8
>
> >> > It's also true in ZF, FOL and PL, however
> >> > |- p v ~p
> >> How do you get to that without the axiom of choice? BTW, I forgot to
> >> prefix this with a quantifier, so it should be
> >> |- \forall p . (p \/ ~p)
>
> Now please answer my question. I don't believe you.
>
If you had answered my question instead of sending me on a wild goose
chase, an answer would already be apparent. So when you know the axioms,
let me know and if you can't show a proof of
(Ap) p v ~p
I'll provide one for you if you're willing to describe what version
of 2nd order language you are using.
BTW, how are you expressing the axiom of choice in 2nd order language?
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