```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:>>>>>>>>>> > On Dec 8, 1:58 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:>> > > On Dec 8, 6:14 am, Dan Christensen <d...@dcproof.com> wrote:>> > > > 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>> > > > And Ey Ax P(x,y) would be false since no element of U would be equal> > > > to every element of U.>> > > > 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> > 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 tojustify them. It takes a brain that have been evolving for billions ofyears to do that.DanDownload my DC Proof 2.0 software at http://www.dcproof.com
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