Date: Dec 9, 2012 12:39 AM
Author: Dan Christensen
Subject: Re: A formal counter-example of Ax Ey P(x,y) -> Ey Ax P(x,y)
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.

>

> > > > 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

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> > > This is a classic Skolem Function example.

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> > 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

> > Download my DC Proof 2.0 software athttp://www.dcproof.com

>

> 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

Download my DC Proof 2.0 software at http://www.dcproof.com