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tech / sci.logic / Re: Smullyan's Proof of the Drinkers Principle V3

Re: Smullyan's Proof of the Drinkers Principle V3

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https://www.novabbs.com/tech/article-flat.php?id=782&group=sci.logic#782

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Subject: Re: Smullyan's Proof of the Drinkers Principle V3
From: burse...@gmail.com (Mild Shock)
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by: Mild Shock - Mon, 29 May 2023 16:39 UTC

Similarly you can prove these two now:

EXIST(x):[x in d => p=d]

EXIST(x):[x in d => ~p=d]

Again indicating some over-generalization error somewhere.

Mild Shock schrieb am Montag, 29. Mai 2023 um 18:38:39 UTC+2:
> Garbage in, Garbage out as usual. Your nonsense here:
> http://www.dcproof.com/STGeneralizedDrinkersThm.htm" rel="nofollow" target="_blank">http://www.dcproof.com/STGeneralizedDrinkersThm.htm
>
> Allows to prove:
> EXIST(x):[x e s => ALL(x):x e s]]
>
> And you can also prove:
> EXIST(x):[x e s => ~ALL(x):x e s]]
>
> Why is this a blooper? Why are you subject to some
> errors of over generalization? You can try yourself, the
> FOL formulation doesn't have this defect:
>
> ∃x(Dx → ∀yDy) is valid.
> https://www.umsu.de/trees/#~7x(Dx~5~6yDy)
>
> ∃x(Dx → ¬∀yDy) is invalid.
> https://www.umsu.de/trees/#~7x(Dx~5~3~6yDy)
> Dan Christensen schrieb am Montag, 29. Mai 2023 um 18:34:03 UTC+2:
> > On Monday, May 29, 2023 at 12:03:11 PM UTC-4, Mild Shock (aka Mr. Collapse) wrote:
> > > If your intention was to remove x e U, to make it general.
> > > Then you commited an error in my opinion. FOL indicates
> > > that the FOL reading of EXIST(x):[...] amounts to
> > > EXIST(x):[U(x) & ...] when we start designating the universe
> > to some predicate U(_).
> >
> > [snip]
> >
> > Makes no sense. For a set-theoretic variation of DP that includes explicit mention of a pub set p (unlike Smullyan's original version), see the thread, "Yet another set-theoretic variation of the Drinkers' Paradox." There, using ordinary set theory and basic logic, I prove:
> >
> > ALL(d):ALL(p):[Set(d) & Set(p) => EXIST(x):[x in d => p=d]]
> >
> > Where d could be thought of as the set of people drinking in given pub, and p as the set of all people in that pub. Note that d and p are arbitrary, possibly empty sets. Since these are arbitrary sets, this results holds whether or not d is a subset of p.
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

Subject	Author
Re: Smullyan's Proof of the Drinkers Principle V3	Mild Shock