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Topic: A formal counter-example of Ax Ey P(x,y) -> Ey Ax P(x,y)
Replies: 4   Last Post: Dec 9, 2012 12:39 AM

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 Dan Christensen Posts: 6,557 Registered: 7/9/08
Re: A formal counter-example of Ax Ey P(x,y) -> Ey Ax P(x,y)
Posted: Dec 9, 2012 12:39 AM

On Dec 8, 6:30 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Dec 9, 9:05 am, Dan Christensen <Dan_Christen...@sympatico.ca>
> wrote:
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> > On Dec 8, 1:58 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > On Dec 8, 6:14 am, Dan Christensen <d...@dcproof.com> wrote:
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> > > > Let the domain of quantification be U = {x, y} for distinct x and y.
>
> > > > Let P be the "is equal to" relation on U.
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> > > > Then Ax Ey P(x,y) would be true since x=x and y=y
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> > > > And Ey Ax P(x,y) would be false since no element of U would be equal
> > > > to every element of U.

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> > > > See formal proof (in DC Proof 2.0 format) athttp://dcproof.com/PopSci.htm
>
> > > This is a classic Skolem Function example.
>
> > This problem is central to predicate calculus. Like Russell's Paradox,
> > it has spurred various "solutions," Skolem functions being one of
> > them. My own DC Proof system is another, more natural one (IMHO).

>
> > Dan

>
> a fine grain solution, but I think relational models, set at a time
> reasoning, although there is an intuitive understanding step required,
> will be more amenable to formal proofs being so much shorter and in
> the range of brute force proof search.  65 steps === n^65 is too big
> for a computer to ever come across, and that was a simple quantifier
> example.
>

You have to give a computer the rules. It's a bit much to expect it to
justify them. It takes a brain that have been evolving for billions of
years to do that.

Dan

Date Subject Author
12/8/12 Graham Cooper
12/8/12 Dan Christensen
12/8/12 Graham Cooper
12/9/12 Dan Christensen