On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> >
> > The "Drinking Principle" is a purely logical theorem.
> >
> > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> >
> I have presented a new, purely set-theoretic version that <bla>

No, you haven't.

Your "set-theoretic version" has nothing to do with the "The Drinking Principle."

Hint (again): The "Drinking Principle" is a purely logical theorem.

When will you learn, Dan? *sigh*

On Tuesday, October 25, 2022 at 8:28:58 PM UTC+2, Dan Christensen wrote:

> Given only that "drinkers" and "pub" are arbitrary sets, we have <bla>

Hint: Smullyan's "Drinker Principle" does neither refer to sets, nor does it refer to a "pub".

You are completely "off track".

On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > >
> > > The "Drinking Principle" is a purely logical theorem.
> > >
> > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > >
> > I have presented a new, purely set-theoretic version that <bla>
>
> No, you haven't.
>
> Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
>

Oh, really? Compare and contrast:

Smullyan:

"[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
Smullyan, "What is the name of this book?" p. 210

DC Proof:

EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]

In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.

Close enough, don't you think, Fritz? Admit it. Or would you rather pout?

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On 10/25/2022 4:23 PM, Dan Christensen wrote:
> On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
>> On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
>>>>
>>>> The "Drinking Principle" is a purely logical theorem.
>>>>
>>>> Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
>>>>
>>> I have presented a new, purely set-theoretic version that <bla>
>>
>> No, you haven't.
>>
>> Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
>>
>
> Oh, really? Compare and contrast:
>
> Smullyan:
>
> "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> Smullyan, "What is the name of this book?" p. 210

Is there a hard core mormon in the pub when this someone drinks?

Why can your x be outside of the pub?

The correct translation (in the pub) would be:

EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]]

Can you prove that from Russells Paradox?

Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > >
> > > > The "Drinking Principle" is a purely logical theorem.
> > > >
> > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > >
> > > I have presented a new, purely set-theoretic version that <bla>
> >
> > No, you haven't.
> >
> > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> >
> Oh, really? Compare and contrast:
>
> Smullyan:
>
> "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> Smullyan, "What is the name of this book?" p. 210
>
> DC Proof:
> EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
> In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
>
> Close enough, don't you think, Fritz? Admit it. Or would you rather pout?
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, October 26, 2022 at 1:23:55 AM UTC+2, Dan Christensen wrote:
> On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > >
> > > I have presented a new, purely set-theoretic version that <bla>
> > >
> > No, you haven't.
> >
> Actually, your "set-theoretic version" has nothing to do with the "The Drinking Principle."

Hint: The "Drinker Principle" is a purely logical theorem.

=> "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)

> Smullyan:
>
> "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> Smullyan, "What is the name of this book?" p. 210

Ex(Dx -> AyDy).

(Note that in Smullyan's "interpretation" we assume that the universe of discourse consists of persons.)

If we really feel the need to mention a "pub" which "represents the universe of discourse", the "Drinker Principle" reads:

Ex(Px & (Dx -> Ay(Py -> Dy)).

See: https://en.wikipedia.org/wiki/Drinker_paradox

> DC Proof:
> EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
>
> In words:

There exists something such that when it is an element in the set /drinkers/, then the set /pub/ is a subset of the set /drinkers/.

Note that your formula is an instance of your "Crank Principle":

EXIST(x):[x in cranks => Phi] ,

where Phi may be any wff.

Now the latter relies on the "subset axiom". (And additional axioms?)

Hence your "Crank Principle" actually reads:

<subset axiom> => EXIST(x):[x in cranks => Phi].

Hint: This theorem has NOTHING to do with Smullyan's "Drinker Principle".

(The "Drinker Principle" does NOT have the form of a conditional. Hence it does not have an antecedents - it does not rely on a certain axiom of set theory. It is not formulated in set language, but in the laguage of pure predicate logic. It is NOT an instance of Ex(Dx -> Phi), etc. etc.)

Hint: It's an important "part" of the "Drinker Principle" that AxDx is possible. (!)

You really don't get it, moron.

==========
Sidenote:

With the axiom

EXIST(x):[x = x]

you should be able to prove:

EXIST(x):[x in drinkers => ALL(a):[a in drinkers]]

in DC Proof. (Right?)

This can be reformulated in the language of "pure predicate logic":

EXIST(x):[R(x, drinkers) => ALL(a):[R(a, drinkers)]].

Though I'd prefer the simpler version mentioned my Smullyan:

Ex(Dx -> AyDy).

On Wednesday, 26 October 2022 at 02:49:55 UTC+2, Fritz Feldhase wrote:
> On Wednesday, October 26, 2022 at 1:23:55 AM UTC+2, Dan Christensen wrote:
> > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > >
> > > > I have presented a new, purely set-theoretic version that <bla>
> > > >
> > > No, you haven't.
> > >
> > Actually, your "set-theoretic version" has nothing to do with the "The Drinking Principle."
>
> Hint: The "Drinker Principle" is a purely logical theorem.

Yes, indeed it is just another little illustration of how material
implication is not logical consequence.

> If we really feel the need to mention a "pub" which "represents the universe of discourse", the "Drinker Principle" reads:
>
> Ex(Px & (Dx -> Ay(Py -> Dy)).

All of that has been explained to him already several
times, even by me already a couple of wees ago...

Why do you still think this lying nazi moron is going to
be reasonable or even just honest any time soon??

You bunch of spamming idiot and polluters of all ponds...

*Plonk*

Julio

On Tuesday, October 25, 2022 at 8:14:25 PM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > > >
> > > > > The "Drinking Principle" is a purely logical theorem.
> > > > >
> > > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > > >
> > > > I have presented a new, purely set-theoretic version that <bla>
> > >
> > > No, you haven't.
> > >
> > > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> > >
> > Oh, really? Compare and contrast:
> >
> > Smullyan:
> >
> > "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> > Smullyan, "What is the name of this book?" p. 210
> >
> > DC Proof:
> > EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]

> > In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
> >
> > Close enough, don't you think, Fritz? Admit it. Or would you rather pout?

> Why can your x be outside of the pub?
>
> The correct translation (in the pub) would be:
>
> EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]]
>

There is actually no mention of a pub in the quote from Smullyan here or in his subsequent paragraphs. A more direct translation might be:

EXIST(x):[x in drinkers => ALL(a):a in drinkers]

But this makes no difference to the method of proof I used. The consequent could be ANY proposition whatsoever, be it true or false. It could be ALL(a): a in drinkers, or even be ~x in drinkers, thus contradicting the antecedent! See line 7 in

http://www.dcproof.com/DrinkersThm1.htm

where the consequent is introduced.

> Can you prove that from Russells Paradox?

Yes. See the link on line 1.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, 26 October 2022 at 03:10:13 UTC+2, Dan Christensen wrote:
> On Tuesday, October 25, 2022 at 8:14:25 PM UTC-4, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> > > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > > > >
> > > > > > The "Drinking Principle" is a purely logical theorem.
> > > > > >
> > > > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > > > >
> > > > > I have presented a new, purely set-theoretic version that <bla>
> > > >
> > > > No, you haven't.
> > > >
> > > > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> > > >
> > > Oh, really? Compare and contrast:
> > >
> > > Smullyan:
> > >
> > > "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> > > Smullyan, "What is the name of this book?" p. 210
> > >
> > > DC Proof:
> > > EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
>
> > > In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
> > >
> > > Close enough, don't you think, Fritz? Admit it. Or would you rather pout?
> > Why can your x be outside of the pub?
> >
> > The correct translation (in the pub) would be:
> >
> > EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]]
> >
> There is actually no mention of a pub in the quote from Smullyan here or in his subsequent paragraphs. A more direct translation might be:
>
> EXIST(x):[x in drinkers => ALL(a):a in drinkers]

Which is exactly what *he* has just written, and not a correction
of the mistake *you* have been making for weeks and still are
making.

> But this makes no difference to the method of proof I used.

Yes, it does but you again just snip it, you insane piece of nazi
crap: that the universe of discourse there becomes just a set here,
hence the restriction on the consequent that you keep missing.

You piece of lying shit...

*Spammer alert*

Julio

On Tuesday, October 25, 2022 at 9:21:41 PM UTC-4, ju...@diegidio.name wrote:
> On Wednesday, 26 October 2022 at 03:10:13 UTC+2, Dan Christensen wrote:
> > On Tuesday, October 25, 2022 at 8:14:25 PM UTC-4, Mostowski Collapse wrote:
> >
> > > Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> > > > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > > > > >
> > > > > > > The "Drinking Principle" is a purely logical theorem.
> > > > > > >
> > > > > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > > > > >
> > > > > > I have presented a new, purely set-theoretic version that <bla>
> > > > >
> > > > > No, you haven't.
> > > > >
> > > > > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> > > > >
> > > > Oh, really? Compare and contrast:
> > > >
> > > > Smullyan:
> > > >
> > > > "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> > > > Smullyan, "What is the name of this book?" p. 210
> > > >
> > > > DC Proof:
> > > > EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
> >
> > > > In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
> > > >
> > > > Close enough, don't you think, Fritz? Admit it. Or would you rather pout?
> > > Why can your x be outside of the pub?
> > >
> > > The correct translation (in the pub) would be:
> > >
> > > EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]] <------- "pub" mentioned twice here
> > >
> > There is actually no mention of a pub in the quote from Smullyan here or in his subsequent paragraphs. A more direct translation might be:
> >
> > EXIST(x):[x in drinkers => ALL(a):a in drinkers]

> Which is exactly what *he* has just written, and not a correction
> of the mistake *you* have been making for weeks and still are
> making.

[snip]

Look harder! Jan Burse (aka Mr. Collapse) mentions a pub twice in his "translation." (See above.) As it turns out, there is no need to mention it at all.

Now take a pill and calm down, Julio.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, 26 October 2022 at 03:39:46 UTC+2, Dan Christensen wrote:
> On Tuesday, October 25, 2022 at 9:21:41 PM UTC-4, ju...@diegidio.name wrote:
> > On Wednesday, 26 October 2022 at 03:10:13 UTC+2, Dan Christensen wrote:
> > > On Tuesday, October 25, 2022 at 8:14:25 PM UTC-4, Mostowski Collapse wrote:
> > >
> > > > Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> > > > > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > > > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > > > > > >
> > > > > > > > The "Drinking Principle" is a purely logical theorem.
> > > > > > > >
> > > > > > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > > > > > >
> > > > > > > I have presented a new, purely set-theoretic version that <bla>
> > > > > >
> > > > > > No, you haven't.
> > > > > >
> > > > > > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> > > > > >
> > > > > Oh, really? Compare and contrast:
> > > > >
> > > > > Smullyan:
> > > > >
> > > > > "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> > > > > Smullyan, "What is the name of this book?" p. 210
> > > > >
> > > > > DC Proof:
> > > > > EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
> > >
> > > > > In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
> > > > >
> > > > > Close enough, don't you think, Fritz? Admit it. Or would you rather pout?
> > > > Why can your x be outside of the pub?
> > > >
> > > > The correct translation (in the pub) would be:
> > > >
> > > > EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]] <------- "pub" mentioned twice here
> > > >
> > > There is actually no mention of a pub in the quote from Smullyan here or in his subsequent paragraphs. A more direct translation might be:
> > >
> > > EXIST(x):[x in drinkers => ALL(a):a in drinkers]
>
> > Which is exactly what *he* has just written, and not a correction
> > of the mistake *you* have been making for weeks and still are
> > making.
> [snip]
>
> Look harder! Jan Burse (aka Mr. Collapse) mentions a pub twice in his "translation." (See above.) As it turns out, there is no need to mention it at all.

I was talking about you your retarded mistakes and your
systematic lies, you still-snipping-and-lying piece of retarded shit.

> Now take a pill and calm down, Julio.

ESAD, you and the whole insane nazi-retarded bandwagon.

*Polluter of ponds alert*

Julio

On Tuesday, October 25, 2022 at 9:54:44 PM UTC-4, ju...@diegidio.name wrote:
> On Wednesday, 26 October 2022 at 03:39:46 UTC+2, Dan Christensen wrote:
> > On Tuesday, October 25, 2022 at 9:21:41 PM UTC-4, ju...@diegidio.name wrote:
> > > On Wednesday, 26 October 2022 at 03:10:13 UTC+2, Dan Christensen wrote:
> > > > On Tuesday, October 25, 2022 at 8:14:25 PM UTC-4, Mostowski Collapse wrote:
> > > >
> > > > > Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> > > > > > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > > > > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > > > > > > >
> > > > > > > > > The "Drinking Principle" is a purely logical theorem.
> > > > > > > > >
> > > > > > > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > > > > > > >
> > > > > > > > I have presented a new, purely set-theoretic version that <bla>
> > > > > > >
> > > > > > > No, you haven't.
> > > > > > >
> > > > > > > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> > > > > > >
> > > > > > Oh, really? Compare and contrast:
> > > > > >
> > > > > > Smullyan:
> > > > > >
> > > > > > "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> > > > > > Smullyan, "What is the name of this book?" p. 210
> > > > > >
> > > > > > DC Proof:
> > > > > > EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
> > > >
> > > > > > In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
> > > > > >
> > > > > > Close enough, don't you think, Fritz? Admit it. Or would you rather pout?
> > > > > Why can your x be outside of the pub?
> > > > >
> > > > > The correct translation (in the pub) would be:
> > > > >
> > > > > EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]] <------- "pub" mentioned twice here
> > > > >
> > > > There is actually no mention of a pub in the quote from Smullyan here or in his subsequent paragraphs. A more direct translation might be:
> > > >
> > > > EXIST(x):[x in drinkers => ALL(a):a in drinkers]
> >
> > > Which is exactly what *he* has just written, and not a correction
> > > of the mistake *you* have been making for weeks and still are
> > > making.
> > [snip]
> >
> > Look harder! Jan Burse (aka Mr. Collapse) mentions a pub twice in his "translation." (See above.) As it turns out, there is no need to mention it at all.

[snip childish abuse]

> > Now take a pill and calm down, Julio.

[snip more childish abuse]

That time of the month, Julio? Maybe another day...

On Wednesday, 26 October 2022 at 04:18:35 UTC+2, Dan Christensen wrote:
> On Tuesday, October 25, 2022 at 9:54:44 PM UTC-4, ju...@diegidio.name wrote:
> > On Wednesday, 26 October 2022 at 03:39:46 UTC+2, Dan Christensen wrote:
> > > On Tuesday, October 25, 2022 at 9:21:41 PM UTC-4, ju...@diegidio.name wrote:
> > > > On Wednesday, 26 October 2022 at 03:10:13 UTC+2, Dan Christensen wrote:
> > > > > On Tuesday, October 25, 2022 at 8:14:25 PM UTC-4, Mostowski Collapse wrote:
> > > > > > Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 01:23:55 UTC+2:
> > > > > > > On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
> > > > > > > > On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
> > > > > > > > > >
> > > > > > > > > > The "Drinking Principle" is a purely logical theorem.
> > > > > > > > > >
> > > > > > > > > > Hint: "There is a certain principle which plays an important role in modern logic and which some of my graduate students have affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
> > > > > > > > > >
> > > > > > > > > I have presented a new, purely set-theoretic version that <bla>
> > > > > > > >
> > > > > > > > No, you haven't.
> > > > > > > >
> > > > > > > > Your "set-theoretic version" has nothing to do with the "The Drinking Principle."
> > > > > > > >
> > > > > > > Oh, really? Compare and contrast:
> > > > > > >
> > > > > > > Smullyan:
> > > > > > >
> > > > > > > "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
> > > > > > > Smullyan, "What is the name of this book?" p. 210
> > > > > > >
> > > > > > > DC Proof:
> > > > > > > EXIST(x):[x in drinkers => ALL(a):[a in pub => a in drinkers]]
> > > > >
> > > > > > > In words: There exists x such that whenever x drinks, everyone (in the pub) drinks.
> > > > > > >
> > > > > > > Close enough, don't you think, Fritz? Admit it. Or would you rather pout?
> > > > > > Why can your x be outside of the pub?
> > > > > >
> > > > > > The correct translation (in the pub) would be:
> > > > > >
> > > > > > EXIST(x):[x in pub & [x in drinkers => ALL(a):[a in pub => a in drinkers]]] <------- "pub" mentioned twice here
> > > > > >
> > > > > There is actually no mention of a pub in the quote from Smullyan here or in his subsequent paragraphs. A more direct translation might be:
> > > > >
> > > > > EXIST(x):[x in drinkers => ALL(a):a in drinkers]
> > >
> > > > Which is exactly what *he* has just written, and not a correction
> > > > of the mistake *you* have been making for weeks and still are
> > > > making.
> > > [snip]
> > >
> > > Look harder! Jan Burse (aka Mr. Collapse) mentions a pub twice in his "translation." (See above.) As it turns out, there is no need to mention it at all.
> [snip childish abuse]
> > > Now take a pill and calm down, Julio.
> [snip more childish abuse]
>
> That time of the month, Julio? Maybe another day...

But it's *you* who should change, you nazi retarded
lying piece of shit: and indeed you just won't...

*Nazi-retarded polluter of ponds alert*

Julio

And why does your link not prove it, it shows this nonsense:

10 EXIST(x):[x e drinkers => ALL(a):[a e pub => a e drinkers]]
E Gen, 9

> There is actually no mention of a pub in the quote from Smullyan
> here or in his subsequent paragraphs. A more direct translation might be:
> EXIST(x):[x in drinkers => ALL(a):a in drinkers]

Chris M. Thomasson explained on 10/25/2022 :
> On 10/25/2022 4:23 PM, Dan Christensen wrote:
>> On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
>>> On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen wrote:
>>>>>
>>>>> The "Drinking Principle" is a purely logical theorem.
>>>>>
>>>>> Hint: "There is a certain principle which plays an important role in
>>>>> modern logic and which some of my graduate students have affectionately
>>>>> dubbed "The Drinking Principle." (Raymond Smullyan)
>>>>>
>>>> I have presented a new, purely set-theoretic version that <bla>
>>>
>>> No, you haven't.
>>>
>>> Your "set-theoretic version" has nothing to do with the "The Drinking
>>> Principle."
>>>
>>
>> Oh, really? Compare and contrast:
>>
>> Smullyan:
>>
>> "[T]here exists someone such that whenever he (or she) drinks, everybody
>> drinks."
>> Smullyan, "What is the name of this book?" p. 210
>
> Is there a hard core mormon in the pub when this someone drinks?

Do the drinks contain alcohol?

It's not about alcohol and pubs. Math is about abstractions.

There exists an object and an action such that when this object
undergoes this action, all such objects undergo such action.

On Wednesday, October 26, 2022 at 2:45:34 AM UTC-4, Mostowski Collapse wrote:

> > There is actually no mention of a pub in the quote from Smullyan
> > here or in his subsequent paragraphs. A more direct translation might be:
> > EXIST(x):[x in drinkers => ALL(a):a in drinkers]

> And why does your link not prove it, it shows this nonsense:
>
> 10 EXIST(x):[x e drinkers => ALL(a):[a e pub => a e drinkers]]
> E Gen, 9

"drinkers" is a set. And "ALL(a):[a in pub => a in drinkers]]" is proposition. (We could as easily have used the proposition, "ALL(a):a in drinkers.")

Like I said, for any set S and ANY proposition Q, we can infer that EXIST(x):[x in S => Q]

http://www.dcproof.com/STGeneralizedDrinkersThm.htm

A very counter-intuitive result, though it doesn't lead to any known internal contradictions. For good reason, however, we do not usually apply an existential quantifier to an implication (as here). In mathematics, universal quantifiers are applied to implications, and existential quantifiers are applied to conjunctions.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, October 26, 2022 at 4:30:19 PM UTC+2, Dan Christensen wrote:

> Like I said, for any set S and ANY proposition Q, we can infer that EXIST(x):[x in S => Q]

Yeah, your claim is nonsense. In the context of NF(U), say, there is a set s such that Ax(x e s).

Hence if V is that set, we would have: Ax(x e V).

Then we could derive, say,

~EXIST(x):[x in V => ~[P -> P]]

On the other hand, if you presuppose your "subset axiom", you

> can infer that EXIST(x):[x in S => Q] .

> A very counter-intuitive result,

Yeah, since it is an "artifact" of your "subset axiom" (originally introduced by Zermelo).

> though it doesn't lead to any known internal contradictions.

Indeed! :-)

Hint: The same is true for NF(U)'s "comprehension axiom".

> [...] In mathematics, universal quantifiers are applied to implications, and existential quantifiers are applied to conjunctions.

Common cases, but no law, dumbo.

On Wednesday, October 26, 2022 at 1:33:07 PM UTC-4, Fritz Feldhase wrote:
> On Wednesday, October 26, 2022 at 4:30:19 PM UTC+2, Dan Christensen wrote:
>
> > Like I said, for any set S and ANY proposition Q, we can infer that EXIST(x):[x in S => Q]

> Yeah, your claim is nonsense. In the context of NF(U), say, there is a set s such that Ax(x e s).
>
[snip]

Thanks anyway, but I will stick to the more conventional axioms and rules.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

Ever heard of Occams Razor?
If in the Drinker Paradox here:

EXIST(x):[D(x) => ALL(a):D(y)]

The right hand side of the implication could be
anything, your general Q, would we then go on, and
call the theorem with more specialized formula

ALL(a):D(y) the Drinker Paradox? Smullyan would
have made a story about such a Drinker Paradox,
but he didn't:

EXIST(x):[D(x) => Q]

This pretty much sums up your insanity.

"entities should not be multiplied beyond necessity"
https://en.wikipedia.org/wiki/Occam's_razor

Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 16:30:19 UTC+2:
> On Wednesday, October 26, 2022 at 2:45:34 AM UTC-4, Mostowski Collapse wrote:
>
> > > There is actually no mention of a pub in the quote from Smullyan
> > > here or in his subsequent paragraphs. A more direct translation might be:
> > > EXIST(x):[x in drinkers => ALL(a):a in drinkers]
>
> > And why does your link not prove it, it shows this nonsense:
> >
> > 10 EXIST(x):[x e drinkers => ALL(a):[a e pub => a e drinkers]]
> > E Gen, 9
> "drinkers" is a set. And "ALL(a):[a in pub => a in drinkers]]" is proposition. (We could as easily have used the proposition, "ALL(a):a in drinkers.")
>
> Like I said, for any set S and ANY proposition Q, we can infer that EXIST(x):[x in S => Q]
>
> http://www.dcproof.com/STGeneralizedDrinkersThm.htm" rel="nofollow" target="_blank">http://www.dcproof.com/STGeneralizedDrinkersThm.htm
>
> A very counter-intuitive result, though it doesn't lead to any known internal contradictions. For good reason, however, we do not usually apply an existential quantifier to an implication (as here). In mathematics, universal quantifiers are applied to implications, and existential quantifiers are applied to conjunctions.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, October 26, 2022 at 7:59:46 PM UTC+2, Dan Christensen wrote:
> On Wednesday, October 26, 2022 at 1:33:07 PM UTC-4, Fritz Feldhase wrote:
> > On Wednesday, October 26, 2022 at 4:30:19 PM UTC+2, Dan Christensen wrote:
> > >
> > > Like I said, for any set S and ANY proposition Q, we can infer that EXIST(x):[x in S => Q]
> > >
> > Yeah, your claim is nonsense. In the context of NF(U), say, there is a set s such that Ax(x e s).
> >
> [snip]
>
> Thanks anyway, but I will stick to the more conventional axioms and rules.

Look, dumbo, I'm just correcting your false/incorrect/nonsensical claims.

I really don't expect a crank changing his views.

Also we cannot replace D(x) by x e drinkers.
Because ALL(x):[x e drinkers] is never possible
for sets. So Q=ALL(a):D(a) in the case we move

from Predicates to Sets makes anyway no sense,
it would be anyway always false. And therefore the
proof that Smullyan gave wouldn't have two cases,

it would have only one case. But nevertheless
Dan Christensen insists to replace D(x) by x e drinkers.
Yes Dan can do that, LoL. Its at the core of his

Drinker Paradox that he cannot do it.

Go to here, it mentions a previous result:
http://www.dcproof.com/DrinkersThm1.htm

Follow his previous result into here:
http://www.dcproof.com/UniversalSet.htm

Still he talks as if he never proved Russels Paradox.
This pretty much sums up his insanity.

Mostowski Collapse schrieb am Mittwoch, 26. Oktober 2022 um 20:17:57 UTC+2:
> Ever heard of Occams Razor?
> If in the Drinker Paradox here:
>
> EXIST(x):[D(x) => ALL(a):D(a)]
>
> The right hand side of the implication could be
> anything, your general Q, would we then go on, and
> call the theorem with more specialized formula
>
> ALL(a):D(y) the Drinker Paradox? Smullyan would
> have made a story about such a Drinker Paradox,
> but he didn't:
>
> EXIST(x):[D(x) => Q]
>
> This pretty much sums up your insanity.
>
> "entities should not be multiplied beyond necessity"
> https://en.wikipedia.org/wiki/Occam's_razor
> Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 16:30:19 UTC+2:
> > On Wednesday, October 26, 2022 at 2:45:34 AM UTC-4, Mostowski Collapse wrote:
> >
> > > > There is actually no mention of a pub in the quote from Smullyan
> > > > here or in his subsequent paragraphs. A more direct translation might be:
> > > > EXIST(x):[x in drinkers => ALL(a):a in drinkers]
> >
> > > And why does your link not prove it, it shows this nonsense:
> > >
> > > 10 EXIST(x):[x e drinkers => ALL(a):[a e pub => a e drinkers]]
> > > E Gen, 9
> > "drinkers" is a set. And "ALL(a):[a in pub => a in drinkers]]" is proposition. (We could as easily have used the proposition, "ALL(a):a in drinkers.")
> >
> > Like I said, for any set S and ANY proposition Q, we can infer that EXIST(x):[x in S => Q]
> >
> > http://www.dcproof.com/STGeneralizedDrinkersThm.htm" rel="nofollow" target="_blank">http://www.dcproof.com/STGeneralizedDrinkersThm.htm
> >
> > A very counter-intuitive result, though it doesn't lead to any known internal contradictions. For good reason, however, we do not usually apply an existential quantifier to an implication (as here). In mathematics, universal quantifiers are applied to implications, and existential quantifiers are applied to conjunctions.
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, October 26, 2022 at 2:27:05 PM UTC-4, Mostowski Collapse wrote:
> Also we cannot replace D(x) by x e drinkers.

Of course you can. What is your problem, Jan Burse?

> Because ALL(x):[x e drinkers] is never possible
> for sets.

Exactly so.

> So Q=ALL(a):D(a) in the case we move
>
> from Predicates to Sets makes anyway no sense,

[snip]

It makes perfect sense from a pedagogical perspective: Students can use the familiar notations of set and subsets that they have used in math since childhood, or they could use the unfamiliar predicate notation. It is interesting that comparable results can be obtained:

[>
> Go to here, it mentions a previous result:
> http://www.dcproof.com/DrinkersThm1.htm
>
> Follow his previous result into here:
> http://www.dcproof.com/UniversalSet.htm
>

Yes.

> Still he talks as if he never proved Russels Paradox.

[snip childish abuse]

Maybe you didn't know, but you don't actually "prove" paradoxes, Jan Burse. Russell's Paradox was RESOLVED by modifying the axioms of set theory of the day (from Frege in the early 20th century). Using what was then the new Subset Axiom, we are able to prove the non-existence of the a universal set (see link).

I hope this helps.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

Is Autism your speciality Wonky Man aka Dan Cristensen.
It gets trivial if you replace D(x) by x e drinkers,
its not what Smullyan intended. I wrote alreay:

> And therefore the proof that Smullyan gave wouldn't
> have two cases, it would have only one case.

Because for a set you cannot have:

ALL(x):x e drinkers

It gets trivial in this part of the formula:

EXIST(x):[x e drinkers => ALL(y):y e drinkers]
^^^^^^^^^^^^^^^^^^^^^^ look here my darling

So Smullyans proof gets degenerate. Did you read and
understand Smullyans proof? Or does your brain work
like Archimedes Plutonium, who suffers from sever Alzheimer?

Dan Christensen schrieb am Mittwoch, 26. Oktober 2022 um 21:27:24 UTC+2:
> On Wednesday, October 26, 2022 at 2:27:05 PM UTC-4, Mostowski Collapse wrote:
> > Also we cannot replace D(x) by x e drinkers.
> Of course you can. What is your problem, Jan Burse?
> > Because ALL(x):[x e drinkers] is never possible
> > for sets.
> Exactly so.
> > So Q=ALL(a):D(a) in the case we move
> >
> > from Predicates to Sets makes anyway no sense,
> [snip]
>
> It makes perfect sense from a pedagogical perspective: Students can use the familiar notations of set and subsets that they have used in math since childhood, or they could use the unfamiliar predicate notation. It is interesting that comparable results can be obtained:
>
> [>
> > Go to here, it mentions a previous result:
> > http://www.dcproof.com/DrinkersThm1.htm" rel="nofollow" target="_blank">http://www.dcproof.com/DrinkersThm1.htm
> >
> > Follow his previous result into here:
> > http://www.dcproof.com/UniversalSet.htm
> >
> Yes.
> > Still he talks as if he never proved Russels Paradox.
> [snip childish abuse]
>
> Maybe you didn't know, but you don't actually "prove" paradoxes, Jan Burse. Russell's Paradox was RESOLVED by modifying the axioms of set theory of the day (from Frege in the early 20th century). Using what was then the new Subset Axiom, we are able to prove the non-existence of the a universal set (see link).
>
> I hope this helps.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On 10/26/2022 5:21 AM, FromTheRafters wrote:
> Chris M. Thomasson explained on 10/25/2022 :
>> On 10/25/2022 4:23 PM, Dan Christensen wrote:
>>> On Tuesday, October 25, 2022 at 5:35:28 PM UTC-4, Fritz Feldhase wrote:
>>>> On Tuesday, October 25, 2022 at 7:44:59 PM UTC+2, Dan Christensen
>>>> wrote:
>>>>>>
>>>>>> The "Drinking Principle" is a purely logical theorem.
>>>>>>
>>>>>> Hint: "There is a certain principle which plays an important role
>>>>>> in modern logic and which some of my graduate students have
>>>>>> affectionately dubbed "The Drinking Principle." (Raymond Smullyan)
>>>>>>
>>>>> I have presented a new, purely set-theoretic version that <bla>
>>>>
>>>> No, you haven't.
>>>>
>>>> Your "set-theoretic version" has nothing to do with the "The
>>>> Drinking Principle."
>>>>
>>>
>>> Oh, really? Compare and contrast:
>>>
>>> Smullyan:
>>>
>>> "[T]here exists someone such that whenever he (or she) drinks,
>>> everybody drinks."
>>> Smullyan, "What is the name of this book?" p. 210
>>
>> Is there a hard core mormon in the pub when this someone drinks?
>
> Do the drinks contain alcohol?

Ohhh. Good question! Well... The Mormon orders a virgin scotch and
water... ;^)

> It's not about alcohol and pubs. Math is about abstractions.
>
> There exists an object and an action such that when this object
> undergoes this action, all such objects undergo such action.

Touche!

On Wednesday, October 26, 2022 at 6:18:17 PM UTC-4, Mostowski Collapse wrote:
> Is Autism your speciality Wonky Man aka Dan Cristensen.
> It gets trivial if you replace D(x) by x e drinkers,

Too easy to prove??? I like to think of it as more accessible. Not a consideration for you, I know. Quite the contrary, right, Jan Burse?

> its not what Smullyan intended.

Oh, really???

He wrote: "[T]here exists someone such that whenever he (or she) drinks, everybody drinks."
--Smullyan, "What is the name of this book?" p. 210

Compare:

EXIST(x):[D(x) => ALL(y):D(y)] <------JB's translation

EXIST(x):[x in D => ALL(y): y in D] <----- DC's translation

The latter being, umm.... too easy to prove for your liking, Jan Burse???? Get a life!

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com