Update to DC Proof 2.0 now available

[Dan Christensen]

Minor bug fix. Release date: today.

Dan

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

[Archimedes Plutonium]

Linda Hasenfratz, Dan is a failure of logic and math, why not move him over to sci.logic where no-one cares what the failure says.

Linda Hasenfratz,Univ Western Ontario, when is Dan Christensen ever going to learn that Boole was wrong with his Logic truth tables, that he unfortunately switched around AND for OR, for the true AND truth table is TTTF not TFFF, for Boole's mistake leads to 2 OR 1 = 3 with AND as subtraction, yet your Dan Christensen is too sexed up or too dumb to teach our young students the truth of science.
> DAN AND HIS LOVER JAN NEEDS TO GO OVER TO SCI.LOGIC, NO-ONE WILL BOTHER THEM THERE, instead they have this stupid game of filling up sci.math with their ignorant insane 2 OR 1 = 3 with AND as subtraction.

On Sunday, October 16, 2022 at 11:07:10 PM UTC-5, Dan Christensen wrote:
> On Sunday, October 16, 2022 at 10:39:13 PM UTC-4, Mostowski Collapse wrote:
> Pay attention, Jan Burse.

> On Monday, October 21, 2019 at 1:29:49 PM UTC-5, Dan Christensen wrote:
> >
> > Are you ready, kids??? Bend over, er...
> >
> > Dan
>

So, is this how you teach students, Dan, the bend over....


> Univ Toronto, physics, Gordon F. West, Michael B. Walker, Henry M. Van Driel, David J. Rowe, John W. Moffat, John F. Martin, Robert K. Logan, Albert E. Litherland, Roland List, Philipp Kronberg, James King, Anthony W. Key, Bob Holdom, Ron M. Farquhar, R. Nigel Edwards, David J. Dunlop, James Drummond, Tom E. Drake, R.Fraser Code, Richard C. Bailey, Robin Armstrong
>
> Chancellor Rose M. Patten
> Pres. Meric Gertler
>
> Univ Toronto math dept
> Mustafa Akcoglu, Spyros Alexakis, Edward Barbeau, Thomas Bloom, Man-Duen Choi, Stephen Cook, Chandler Davis, Nicholas Derzko, Eric Ellers, Ilya Gekhtman, Ian Graham, Steve Halpern, Wahidul Haque, Abe Igelfeld, Velimir Jurdjevic, Ivan Kupka, Anthony Lam, Michael Lorimer, James McCool, Eric Mendelsohn, Kunio Murasugi, Jeremy Quastel, Peter Rosenthal, Paul Selick, Dipak Sen, Rick Sharpe, Stuart Smith, Frank Tall, Steve Tanny
> Univ Western Ontario math dept
> Janusz Adamus, Tatyana Barron, Dan Christensen, Graham Denham, Ajneet Dhillon, Matthias Franz, John Jardine, Massoud Khalkhali, Nicole Lemire, Jan Mináč, Victoria Olds, Martin Pinsonnault, Lex Renner, David Riley, Rasul Shafikov, Gordon Sinnamon
>
> Chancellor Linda Hasenfratz
> President Alan Shepard
> Amit Chakma (chem engr)
>
> Univ. Western Ontario physics dept
> Pauline Barmby, Shantanu Basu, Peter Brown, Alex Buchel, Jan Cami, Margret Campbell-Brown, Blaine Chronik, Robert Cockcroft, John R. de Bruyn, Colin Denniston, Giovanni Fanchini, Sarah Gallagher, Lyudmila Goncharova, Wayne Hocking, Martin Houde, Jeffrey L. Hutter, Carol Jones, Stan Metchev, Silvia Mittler, Els Peeters, Robert Sica, Aaron Sigut, Peter Simpson, Mahi Singh, Paul Wiegert, Eugene Wong, Martin Zinke-Allmang
>
>
> 
> On Monday, October 21, 2019 at 1:29:49 PM UTC-5, Dan Christensen wrote:
> >
> > Are you ready, kids??? Bend over, er...
> >
> > Dan
>
>
> Re: 81,045-Student victims of Rose M. Patten Univ Toronto from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Univ Toronto, physics, Gordon F. West, Michael B. Walker
> by Frank Cassa 12Apr2021 7:00 AM
>
>
>
> Re: 7,744-Student victims of Linda Hasenfratz Univ Western Ontario from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Chancellor Linda Hasenfratz President Alan Shepard
> 11:53 AM 10Apr2021
> by Wayne Decarlo
>
> Re: 102,852-Student victims of Dominic Barton, Univ Waterloo from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Dominic Barton, President Feridun Hamdullahpur physics
> by konyberg Apr 15, 2021, 3:09:41 PM
>
> Re: 176,232-Student Victims of Michael Meighen McGill Univ by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus... 0.5MeV electron when in truth it is the muon as the real electron
> by Dan Christensen Jul 2, 2021, 9:47:42 AM
>
>
> Re: 135,568 Student victims Queen's Univ. James Leech, Arthur B. McDonald by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus-- his mindless electron =0.5MeV when real electron of
> May 10, 2021
> by Professor Wordsmith
>
> Re: 135,566 Student victims Queen's Univ. James Leech, Arthur B. McDonald by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus-- his mindless electron =0.5MeV when real electron o
> May 10, 2021
> by Michael Moroney

[Mostowski Collapse]

It would be maybe more wise to make your tool
open source and available through some Git.

And your change doesn't affect this proof,
this proof doesn't use Arb Or Rule:

56 EXIST(x):[P(x) & [D(x) => ALL(y):[P(y) => D(y)]]]
Cases, 54, 55
https://groups.google.com/g/sci.logic/c/a7zRnh2NUdw/m/7EM0G94WAgAJ

The above proof shows, that the Russell Paradox and/or
related Set Theory are not needed.

[Mostowski Collapse]

There is also a further bug in DC Proof.

When I enter this here:

[A => B] => C

It shows this here:

A => B => C

But this is wrong, the later is usually read as:

A => [B => C]

Wrong associativity of (=>)/2 operator.

[Dan Christensen]

On Tuesday, October 18, 2022 at 5:49:05 PM UTC-4, Mostowski Collapse wrote:

> Mostowski Collapse schrieb am Dienstag, 18. Oktober 2022 um 23:30:44 UTC+2:
> > It would be maybe more wise to make your tool
> > open source and available through some Git.
> >
> > And your change doesn't affect this proof,
> > this proof doesn't use Arb Or Rule:
> >
> > 56 EXIST(x):[P(x) & [D(x) => ALL(y):[P(y) => D(y)]]]
> > Cases, 54, 55
> > https://groups.google.com/g/sci.logic/c/a7zRnh2NUdw/m/7EM0G94WAgAJ
> >
> > The above proof shows, that the Russell Paradox and/or
> > related Set Theory are not needed.
> > Dan Christensen schrieb am Dienstag, 18. Oktober 2022 um 23:12:55 UTC+2:
> > > Minor bug fix. Release date: today.

> There is also a further bug in DC Proof.
>
> When I enter this here:
>
> [A => B] => C
>
> It shows this here:
>
> A => B => C
>

As it should. In DC Proof, for consistency, all binary operators are left associative (read from left to right). Deal with it, Jan Burse.

[Dan Christensen]

STUDENTS BEWARE: Don't be a victim of AP's fake math and science

On Tuesday, October 18, 2022 at 5:28:52 PM UTC-4, Archimedes Plutonium wrote:
> ... Dan Christensen ...

[snip]

There you go again, Archie Poo! When will you learn? Once again...

From his antics here at sci.math, it is obvious that AP has abandoned all hope being recognized as a credible personality. He is a malicious internet troll who now wants only to mislead and confuse students. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives. Is it revenge for his endless string of personal failures in life? Who knows.

In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:

“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020

“The last and largest finite number is 10^604.”
--June 3, 2015

“0 appears to be the last and largest finite number”
--June 9, 2015

“0/0 must be equal to 1.”
-- June 9, 2015

“0 is an infinite irrational number.”
--June 28, 2015

“No negative numbers exist.”
--December 22, 2018

“Rationals are not numbers.”
--May 18, 2019

According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019

Which could explain...

“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019

AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:

“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019

AP seeks aid of Russian agents to promote failure in schools:

"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--November 9, 2017


And if that wasn't weird enough...

“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994

“The Universe itself is one gigantic big atom.”
--November 14, 2019

AP's sinister Atom God Cult of Failure???

“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)

[Fritz Feldhase]

On Tuesday, October 18, 2022 at 11:49:05 PM UTC+2, Mostowski Collapse wrote:

> A => B => C
>

> [this] is usually read as:

>
> A => [B => C]

For example:

"Implication is right associative, i.e. we read P -> Q -> R as P -> (Q -> R)."

Source: https://www.cs.nott.ac.uk/~psztxa/g52ifr/html/Prop.html

[Fritz Feldhase]

On Wednesday, October 19, 2022 at 12:26:53 AM UTC+2, Dan Christensen wrote:
> On Tuesday, October 18, 2022 at 5:49:05 PM UTC-4, Mostowski Collapse wrote:
> >
> > When I enter this here:
> >
> > [A => B] => C
> >
> > It shows this here:
> >
> > A => B => C
> >

> As it should. In <bla>

No, IT SHOULDN'T, you silly crank.

HINT: "When you enter p⇒q⇒r in Mathematica (with p \[Implies] q \[Implies] r), it displays p⇒(q⇒r)."

[Dan Christensen]

Thanks for the info, but I prefer the more natural left associativity. One less bizarre exception to explain to students.

[Fritz Feldhase]

On Wednesday, October 19, 2022 at 12:38:05 AM UTC+2, Dan Christensen wrote:

> Thanks for the info, but I prefer

to stay a crank.

Yeah, we know that already, Dan.

Actually, you are the prototyp of a crank.

[Mostowski Collapse]

No you need to change it. Its wrong.
Nothing to do with consistency.

[Dan Christensen]

On Tuesday, October 18, 2022 at 6:48:02 PM UTC-4, Fritz Feldhase wrote:
> On Wednesday, October 19, 2022 at 12:38:05 AM UTC+2, Dan Christensen wrote:
>

[snip childish abuse]

>
> Yeah, we know that already, Dan.
>

K.I.S.S.

[Mostowski Collapse]

I can still prove it, case a, in the case a and case b proof,
i was using one axiom from the natural numbers axioms
that one can call from the menu of DC Proof,

was using the brand new dcproof19.exe:

/* case a of case a and case b */
7 ALL(y):D(y) => EXIST(x):[D(x) => ALL(y):D(y)]
Conclusion, 2

The rest would then work like here:

27 EXIST(x):[D(x) => ALL(y):D(y)]
Cases, 25, 26
https://groups.google.com/g/sci.logic/c/a7zRnh2NUdw/m/1mnsYfgaAgAJ

---------------------------------- begin proof -------------------------------------

1 1 ε n
Axiom

2 ALL(y):D(y)
Premise

3 ~D(1) | ALL(y):D(y)
Arb Or, 2

4 ~~D(1) => ALL(y):D(y)
Imply-Or, 3

5 D(1) => ALL(y):D(y)
Rem DNeg, 4

6 EXIST(x):[D(x) => ALL(y):D(y)]
E Gen, 5

7 ALL(y):D(y) => EXIST(x):[D(x) => ALL(y):D(y)]
Conclusion, 2

----------------------------- end proof ----------------------------------------------------------------------

[Chris M. Thomasson]

Are you going to release your source code? Is it in VB 6?

[Dan Christensen]

No.

Is it in VB 6?

Yes.

Dan

[Dan Christensen]

Sorry, Jan Burse, but your proof is STILL a monstrosity -- even more so with your new axiom.

Dan

[Mostowski Collapse]

Dan Christensen doesn't open source is tool, since everybody
would see that he didn't write it on his own. If he would have
written on his own, he would understand DC Proof to the

extend that he can follow this line of argument which is
based on the Smullyan Book, and fabricate a proof. But
he cannot do so, he doesn't understand:

"Let us look at it this way: Either it is true that everybody
drinks or it isn't. Suppose it is true that everybody drinks.
Then take any person—call him Jim. Since everybody
drinks and Jim drinks, then it is true that if Jim drinks
then everybody drinks. So there is at least one person—
namely Jim—such that if he drinks then everybody drinks.

Suppose, however, that it is not true that everybody drinks;
what then? Well, in that case there is at least one person—
call him Jim—who doesn't drink. Since it is false that Jim
drinks, then it is true that if Jim drinks, everybody drinks.
So again there is a person—namely Jim—
such that if he drinks, everybody drinks."

chapter 14. How to Prove Anything. (topic)
250. The Drinking Principle. pp. 209-211
https://archive.org/details/whatisnameofthis00smul

The same is clearly outline here:

27 EXIST(x):[D(x) => ALL(y):D(y)]
Cases, 25, 26
https://groups.google.com/g/sci.logic/c/a7zRnh2NUdw/m/1mnsYfgaAgAJ

But Dan Christensen aka Wony Man doesn't understand
the proof idea and cannot produce a proof.

[Mostowski Collapse]

This is quite amasing since mathematics is thought to
be a science which has a communicable element,
namely for example proofs. Mathematicians should be

able to exchange proofs. This fails for Dan Christensen, since
a) he only understands natural deduction nothing else,
b) and if it is natural deduction it must be free logic,

c) and if it is natural deduction with free logic it
nust be DC Proof. So the mytseries of Smullyans Book
will be for ever a book a sealed book, hidden trove,

not accessible to Wonky Man aka Dan Christensen.

[Dan Christensen]

On Tuesday, October 18, 2022 at 8:09:45 PM UTC-4, Mostowski Collapse wrote:
> Dan Christensen doesn't open source is tool, since everybody
> would see that he didn't write it on his own.

I'm flattered that you think so, Jan Burse!

Dan

[Mostowski Collapse]

You stole it, and now we have an instance of:

"A fool with a tool, is still a fool"
— Grady Booch

[Mostowski Collapse]

How it started:
"Call me a joker, call me a fool, right
at this moment I'm totally cool."
"Even a fool gets to be young once."
"Only a fool expects to be happy all the time."

How its going:
"No one but a fool is always right."
"There is, they say, no fool like an old fool."
"Only a fool trips on what's behind them."

Mostowski Collapse schrieb:

[Dan Christensen]

On Tuesday, October 18, 2022 at 8:18:48 PM UTC-4, Mostowski Collapse wrote:
> You stole it,

I'm flattered that the you think my creation could only be that of some kind of mathematical genius.

Dan

[Chris M. Thomasson]

I still have VB 6 installed on several old computers for maintaining
legacy DB programs from more than 20 years ago. Have you hooked it up
with msWord yet? Its fun to use the vbo, or was it vba? Create detailed
reports, all formatted and pretty. ;^) Have use used ms access? It
interfaces quite nicely with VB 6.

[Chris M. Thomasson]

I actually managed to get an old version of ms word, because I still
maintain the database, installed and working on windows 11! lol.

https://i.ibb.co/bQxJX1S/image.png

[Dan Christensen]

Files in DC Proof are just low-tech flat (binary?) files. It has been a several years since I did anything with the file structure--not since I created the Windows version in 2004. Before that I had a VBDOS version, but it wasn't available online. The current version is a very small app--only about 1.2 Mb. The downloadable exe file (about 2.9 Mb) can be downloaded and installed in less than a minute with a high speed connection.

Dan

[Mostowski Collapse]

Did I find a formula in DC Proof that isn't provable,
but is provable in FOL? Not yet 100% sure.

Somehow a charming idea, although a little far fetched
I guess, that the Drinker Paradox would be ataching
device for quantifier scope? Maybe it is the smallest

formula which is a valid/invalid like here:

∃x(Dx → ∀yDy) is valid.
https://www.umsu.de/trees/#~7x%28Dx~5~6yDy%29

∃xDx → ∀yDy is invalid.
https://www.umsu.de/trees/#~7xDx~5~6yDy

Works also after Herbandization:

∃x(Dx → Df(x)) is valid.
https://www.umsu.de/trees/#~7x%28Dx~5Df%28x%29%29

∃xDx → Df is invalid.
https://www.umsu.de/trees/#~7xDx~5Df

Can we prove ∃x(Dx → Df(x)) in DC Proof? I guess it
is not possible, because of some set domain requirement
for f(x) in the tweaked forall rule of DC Proof.

What would be the DC Proof for ∃x(Dx → Df(x)) ?

Dan Christensen schrieb am Dienstag, 18. Oktober 2022 um 23:12:55 UTC+2:

[Dan Christensen]

On Sunday, October 23, 2022 at 5:01:20 AM UTC-4, Mostowski Collapse wrote:
[snip]

>
> Can we prove ∃x(Dx → Df(x)) in DC Proof? I guess it
> is not possible, because of some set domain requirement
> for f(x) in the tweaked forall rule of DC Proof.
>

Yes, you really need to formally define the f.

[Mostowski Collapse]

f is a FOL function symbol. This here is provable in FOL:

∃x(Dx → Df(x)) is valid.
https://www.umsu.de/trees/#~7x%28Dx~5Df%28x%29%29

Can you prove it in DC Proof. It yields to another proof
of the drinker paradox. Which goes as follows:

1) Every guest points to some other guest, this is
the function f : V -> V, where V is "everybody".

2) Then we pick a random guest, call him c,
if ~Dc we are finished, i.e. if the guest is not a drinker,
the formula is true, because the material implication
makes it vacously true. c is suitable as a witness for ∃x.

3) On the other hand if Dc we check Df(c), i.e.
the guest the guest c is point to, i.e. f(c), if this
guest is a drinker, i.e. Df(c), we are also finished.
c is again suitable as a witness for ∃x.

4) If ~Df(c) then we are also finished, the formula
is true, because the material implication
makes it vacously true. This time f(c) is
suitable as a witness for ∃x.

[Mostowski Collapse]

FOL itself can prove this direction
of the Herbrandization:

(∃xPx → ∀yQy) → (∃xPx → Qf) is valid.
https://www.umsu.de/trees/#%28~7xPx~5~6yQy%29~5%28~7xPx~5Qf%29

∃x(Px → ∀yQy) → ∃x(Px → Qf(x)) is valid.
https://www.umsu.de/trees/#~7x%28Px~5~6yQy%29~5~7x%28Px~5Qf%28x%29%29

For the second formula one can use
P=D and Q=D to get the Drinker Paradox.

The other direction needs a different f quantification,
than what is implicit in FOL. Don't know how to
show it with FOL, is this possible?

[Mostowski Collapse]

Wonky Man aka Dan Christensen halucinated:
> Moral of the story: In mathematics, it is probably
> a mistake to existentially quantify an implication

It was probably a mistake that your mother baught
you a computer with visual basic. Here is a proof
of the requested theorem in DC Proof:

19 EXIST(x):[D(x) => D(f(x))]
Rem DNeg, 18

For the full proof see here:

----------------- begin proof ------------------------------------

1 EXIST(x):x ε u
Axiom

2 ALL(x):[x ε u => f(x) ε u]
Axiom

3 ~EXIST(x):[D(x) => D(f(x))]
Premise

4 ~~ALL(x):~[D(x) => D(f(x))]
Quant, 3

5 ALL(x):~[D(x) => D(f(x))]
Rem DNeg, 4

6 ALL(x):~~[D(x) & ~D(f(x))]
Imply-And, 5

7 ALL(x):[D(x) & ~D(f(x))]
Rem DNeg, 6

8 a ε u
E Spec, 1

9 D(a) & ~D(f(a))
U Spec, 7

10 D(a)
Split, 9

11 ~D(f(a))
Split, 9

12 a ε u => f(a) ε u
U Spec, 2

13 f(a) ε u
Detach, 12, 8

14 D(f(a)) & ~D(f(f(a)))
U Spec, 7, 13

15 D(f(a))
Split, 14

16 ~D(f(f(a)))
Split, 14

17 ~D(f(a)) & D(f(a))
Join, 11, 15

18 ~~EXIST(x):[D(x) => D(f(x))]
Conclusion, 3

19 EXIST(x):[D(x) => D(f(x))]
Rem DNeg, 18

------------------ end proof --------------------------------------

[Archimedes Plutonium]

Kibo better than Dr.Tao in math-- yet Kibo Parry M still believes 938 is 12% short of 945. But Dr. Terence Tao of UCLA, runs and hides, hides and runs whenever the question arises-- is slant cut of cone a ellipse or as AP proves-- it is a Oval. No, Dr. Tao should be drummed out of math completely. For here is the awful situation of a person not in math-- Kibo Parry M. who is on his way of the "realization slant cut of cone is a OVAL, never the ellipse". Yet there you have the idiot of math Dr. Tao at UCLA, run and hide, run Terry, hide Terry. Same thing can be said of Ruth Charney the recent head of AMS, run Ruth, hide Ruth, even though your so called specialty was geometry, Ruth, Ruth, run and hide.

On Sunday, October 23, 2022 at 12:51:25 AM UTC-5, Michael Moroney wrote:
> On 10/23/2022 1:06 AM, Earle Jones wrote:
> > *
> > Anyone who has taught mathematics at the college freshman level (as I have at Georgia Tech as a TA) went through the fairly simple process, using analytic geometry to define what is a conic section. If you can follow this, just perform these steps: First, write the definition of a cone (in x, y, z space). It is not difficult. Then, write the equation of an inclined plane in three-space. Then, if you have done the work accurately, you can solve these two equations simultaneously. That gives the locus of all points common to the cone and the inclined plane. (This is the definition of a section.) The resulting equation will be an ellipse, a circle, a parabola, or a hyperbola, depending on the exact inclined plane you have chosen. By the way, this was first demonstrated in about 300 BC, even before the original Archmedes (not the Plutonium version.)
> >
> > earle
> > *
> Plutonium's argument is based on axes of symmetry. While his so-called
> "proof" is rambling and in no way a valid math proof, its basic argument
> is a tilted plane intersecting a cone will have the side nearest the
> apex of the cone will be smaller than the side tilting away from the
> apex, simply because the cone itself gets smaller near the apex and
> larger away from it. Thus his "proof" is that the cone isn't symmetric
> _around the axis of the cone_. However the cone's formula will have
> something like (x-k)^2 in it, which is obviously symmetric around the
> x=k plane.
>
> I know if you look at a drawing, it doesn't look like it could be an
> ellipse. I think of this as like a "mathematical optical illusion".
>
> This is easier to visualize if the cone is tilted around the y axis,
> with its apex at the point (x=0,y=0,z=0) and is intersected by the plane
> z=m for some m.
>
>
> Here's a proof someone (I forget who) wrote earlier in response to AP,
> that tilts the cone and the cone is intersected by the plane
> z=<constant>. It may be unclear in the last line why that is the
> equation of an ellipse if C>0, but the left side is a constant, and the
> right side is C*(x-K)^2 + y^2, which is the formula of an ellipse. K=k*S/C.
>
>
>
> I'll start with the cone z^2 = x^2 + y^2, and rotate it through an angle
> 'theta' around the 'y' axis, and consider the intersection of that
> rotated cone with the plane z = <constant>
>
> To simplify things, let c = cos(theta) and s = sin(theta). Then the
> rotation is defined by
>
> z --> cz + sx
> x --> -sz + cx
> y --> y
>
> So the equation of the rotated cone is
>
> (cz+sx)^2 = (-sz+cx)^2 + y^2
>
> and now let C = c^2-s^2 and S = 2sc (again, just to simplify the look
> of things)
>
> so we get
>
> Cz^2 = Cx^2 - 2Szx + y^2
>
> and letting 'z' equal the constant 'k' gives
>
> Ck^2 + k^2*S^2/C = C(x - k*S/C)^2 + y^2
>
> which is the equation of an ellipse if C > 0.

On 10/23/2022 1:51 AM, Michael Moroney wrote:
> It may be unclear in the last line why that is the
> equation of an ellipse if C>0, but the left side is a constant, and the
> right side is C*(x-K)^2 + y^2, which is the formula of an ellipse. K=k*S/C.

This proof skips several steps before the last line, so it's far from
obvious. I will have to make it clearer, and add the skipped steps back in.

---------

Kibo of course is a loud math in sci.math and sci.physics and should never have posted but watched and listened.

3rd published book

AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.

Product details
• ASIN ‏ : ‎ B07PLSDQWC
• Publication date ‏ : ‎ March 11, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 1621 KB
• Text-to-Speech ‏ : ‎ Enabled
• Enhanced typesetting ‏ : ‎ Enabled
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• Lending ‏ : ‎ Enabled
•
•

Proofs Ellipse is never a Conic section, always a Cylinder section and a Well Defined Oval definition//Student teaches professor series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 14May2022. This is AP's 68th published book of science.

Preface: A similar book on single cone cut is a oval, never a ellipse was published in 11Mar2019 as AP's 3rd published book, but Amazon Kindle converted it to pdf file, and since then, I was never able to edit this pdf file, and decided rather than struggle and waste time, decided to leave it frozen as is in pdf format. Any new news or edition of ellipse is never a conic in single cone is now done in this book. The last thing a scientist wants to do is wade and waddle through format, when all a scientist ever wants to do is science itself. So all my new news and thoughts of Conic Sections is carried out in this 68th book of AP. And believe you me, I have plenty of new news.

In the course of 2019 through 2022, I have had to explain this proof often on Usenet, sci.math and sci.physics. And one thing that constant explaining does for a mind of science, is reduce the proof to its stripped down minimum format, to bare bones skeleton proof. I can prove the slant cut in single cone is a Oval, never the ellipse in just a one sentence proof. Proof-- A single cone and oval have just one axis of symmetry, while a ellipse requires 2 axes of symmetry, hence slant cut is always a oval, never the ellipse.

Product details
• ASIN ‏ : ‎ B081TWQ1G6
• Publication date ‏ : ‎ November 21, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 827 KB
• Simultaneous device usage ‏ : ‎ Unlimited
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
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• Print length ‏ : ‎ 51 pages
• Lending ‏ : ‎ Enabled

#12-2, 11th published book

World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 15Dec2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.

Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". And very surprising that most math professors cannot tell the difference between a "proving something" and that of "analyzing something". As if an analysis is the same as a proof. We often analyze various things each and every day, but few if none of us consider a analysis as a proof. Yet that is what happened in the science of mathematics where they took an analysis and elevated it to the stature of being a proof, when it was never a proof.

To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.


Product details
ASIN ‏ : ‎ B07PQTNHMY
Publication date ‏ : ‎ March 14, 2019
Language ‏ : ‎ English
File size ‏ : ‎ 1309 KB
Text-to-Speech ‏ : ‎ Enabled
Screen Reader ‏ : ‎ Supported
Enhanced typesetting ‏ : ‎ Enabled
X-Ray ‏ : ‎ Not Enabled
Word Wise ‏ : ‎ Not Enabled
Print length ‏ : ‎ 154 pages

Lending ‏ : ‎ Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)

[Dan Christensen]

On Sunday, October 23, 2022 at 6:41:19 PM UTC-4, Mostowski Collapse wrote:
> f is a FOL function symbol. This here is provable in FOL:
> ∃x(Dx → Df(x)) is valid.
> https://www.umsu.de/trees/#~7x%28Dx~5Df%28x%29%29

Only, it seems from your reply at sci.logic, if you make certain mysterious assumptions that you do not make explicit in your FOL "proof" They are somehow built into your FOL system and not visible to the reader. No wonder authors of math textbook authors felt they had to devise their own system of logic.

[Mostowski Collapse]

I just proved it:

Mostowski Collapse schrieb am Montag, 24. Oktober 2022 um 22:14:53 UTC+2:
> 19 EXIST(x):[D(x) => D(f(x))]
> Rem DNeg, 18

https://groups.google.com/g/sci.math/c/PwyRME9DOdY/m/4cA5lCPIBAAJ

Whats wrong with you? Do you say your proof is incorrect?

P.S.: I didn't mirror the mysterious domain, which also
exists in DC Proof, into a predicate, I didn't make an axiom:

ALL(x):U(x)

Does this make your DC Proof result mysterious and
a little occult, just as you claim FOL proofs are?

LMAO!

[Fritz Feldhase]

On Tuesday, October 25, 2022 at 1:15:06 PM UTC+2, Mostowski Collapse wrote:

> What's wrong with you? Do you say your proof is incorrect?

>
> P.S.: I didn't mirror the mysterious domain, which also
> exists in DC Proof, into a predicate, I didn't make an axiom:
>
> ALL(x):U(x)

On the other hand, this demented fool wrote HIMSELF:

> > [We] only have to prove: EXIST(b):[D(b) => ALL(a):D(a)]
> >
> > 1. EXIST(a):U(a)
> > Axiom
> > :

And it's indeed necessary to formulate something like this _in DC Proof_, otherweise you cannot prove an existence claim like

EXIST(b): ...b...

Now _he_ did't see any problems with _his_ axiom

> > 1. EXIST(a):U(a)
> > Axiom

[ but he is whining about your (quite innocent) axiom "EXIST(x):x ε u" ].

So _we_ now may ask:

> Does this make your DC Proof result mysterious and
> a little occult, just as you claim FOL proofs are?
>
> LMAO!

What an idiot!

[Dan Christensen]

On Tuesday, October 25, 2022 at 7:15:06 AM UTC-4, Mostowski Collapse wrote:

[snip]

> P.S.: I didn't mirror the mysterious domain, which also
> exists in DC Proof, into a predicate, I didn't make an axiom:
>
> ALL(x):U(x)
>

What Jan Burse has proven, in effect, is that:

ALL(u): ALL(f):[EXIST(x):x ε u & ALL(x):[x ε u => f(x) ε u]
=> EXIST(b):[D(b) => ALL(a):D(a)]]

In the FOL system, the first line is never made explicit. We are simply to imagine that something like this is true -- a lazy philosopher's shortcut? Not a good basis for mathematical proof in any case.

The above result could have been obtained in DC Proof by using the Premise Rule instead of the Axiom Rule at the beginning of the proof.

[Fritz Feldhase]

On Tuesday, October 25, 2022 at 3:02:17 PM UTC+2, Dan Christensen wrote:

> What Jan Burse has proven, in effect, is that:
>
> ALL(u): ALL(f): [EXIST(x):x ε u & ALL(x):[x ε u => f(x) ε u]
> => EXIST(b):[D(b) => ALL(a):D(a)]]
>
> In the FOL system, the first line is never made explicit.

Yeah, because it doesn't concern FOPL but set theory, you silly crank. Note that in pure FOPL we can't quantify over "functions". [If your DC Proof can do that it's not based on a system of first-order predicate logic. (Hint: Not even Free Logic can do that.)]

[Mostowski Collapse]

Wrong again. FOL doesn't assume:

EXIST(x):x ε u

Where do you see FOL assuming this?
It has 2 extra features, a) a membership relation
ε which is not part of FOL, b) a set object u,

which is not part of FOL. FOL doesn't talk about
sets. You still don't understand the difference
between predicates aka classes and sets, right?

What you could do in FOL, is the following:

EXIST(x):U(x)

It has only 1 extra feature a) a predicate symbol
U. And the result is relatively innocent, it doesn't
pressuppose membership or set objects.

[Mostowski Collapse]

I think most authors avoid a new predicate symbol
all together, and try to capture the non-emptyness
of the domain of discourse by this statement:

EXIST(x):[x=x]

But this requires another feature, namely FOL with
equality, you could write it FOL=. Wolfgang Schwartz
tool implements FOL=, and you can prove:

∃xx=x is valid.
https://www.umsu.de/trees/#~7x%28x=x%29

If you further abbreviate. With ‘E!’ we can express classical logic’s
blanket presumption that singular terms denote members
of D, where D is the quantificational domain:

E!t :<=> ∃x(x=t)

Or in DC Proof:

Quantifiable(t) :<=> EXIST(x):[x=t]

You can also try another formula, to check whether the
quantificational domain is non-empty. You could try
this one as well, Rossy Boy mentioned it already:

∃yE!t

Or in DC Proof:

EXIST(y):Quantifiable(y)

Expand the definition of E!, it is also a provable in FOL:

∃y∃xx=y is valid.
https://www.umsu.de/trees/#~7y~7x%28x=y%29

The term quantificational domain appears when the
domain of discourse is split up, in those objects that
are reached via quantifier, and other objects that are

not, which could be an approach to certain logics.

See also:

SEP - Free Logic
https://plato.stanford.edu/entries/logic-free/

[Mostowski Collapse]

But free logics might have a defect.

4.2 Substitutivity Failures
Classical predicate logic has the desirable feature
that co-extensive open formulas may be substituted
for one another in any formula salva veritate—i.e.,
without changing that formula’s truth value.
https://plato.stanford.edu/entries/logic-free/#subfail

It could be that DC Proof has the same failure?
For example in FOL I can play around with making
definition as follows:

∀t(Qt ↔ ∃x(x=t))

There is a shift in the meaning now, since I use
a forall quantifier, which ranges over the quantificational
domain, the above does not anymore mean

singular term t. We also abused it already in Rossy
Boys formula, in that we supplied a variable to E!
in the example ∃yE!y. But in FOL we can prove:

∃y∃xx=y is valid.
https://www.umsu.de/trees/#~7y~7x%28x=y%29

But we can also prove this:

∀t(Qt ↔ ∃xx=t) → ∃yQy is valid.
https://www.umsu.de/trees/#~6t%28Qt~4~7x%28x=t%29%29~5~7yQy

[Dan Christensen]

On Tuesday, October 25, 2022 at 10:28:59 AM UTC-4, Mostowski Collapse wrote:
> Wrong again. FOL doesn't assume:
>
> EXIST(x):x ε u
>
> Where do you see FOL assuming this?
> It has 2 extra features, a) a membership relation
> ε which is not part of FOL, b) a set object u,
>

You introduced it in YOUR "proof", Jan Burse. Call it something else if you want, but it unnecessary in real-world mathematical proofs. You don't need it in real-world set theory. There, we have the much less mysterious subset axiom from which we can derive:

ALL(s):[Set(s) => EXIST(x):[x in s => Q]] for any proposition Q be it true or false.

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

Nothing very profound or all that useful except maybe as a cautionary tale about existential quantifiers: Usually existential quantifiers are attached to conjunctions, e.g. EXIST(a):[a in N & a+1=2], not to implications as above.

[Fritz Feldhase]

On Tuesday, October 25, 2022 at 6:35:35 PM UTC+2, Dan Christensen wrote:

> ALL(s):[Set(s) => EXIST(x):[x in s => Q]] for any proposition Q be it true or false.
>
> http://www.dcproof.com/STGeneralizedDrinkersThm.htm

This nonsense has nothing to do with the "Drinker Paradox" or "Drinker Prinziple", you silly crank.

Especially, since it relies on a "hidden assumption" (namely Zermelo's "subset axiom") you fucking idiot!

The "Drinking Prinziple" 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)

[Dan Christensen]

On Tuesday, October 25, 2022 at 1:21:12 PM UTC-4, Fritz Feldhase wrote:
> On Tuesday, October 25, 2022 at 6:35:35 PM UTC+2, Dan Christensen wrote:
>
> > ALL(s):[Set(s) => EXIST(x):[x in s => Q]] for any proposition Q be it true or false.
> >
> > http://www.dcproof.com/STGeneralizedDrinkersThm.htm

> This nonsense has nothing to do with the "Drinker Paradox" or "Drinker Prinziple" [snip childish abuse]
>
> Especially, since it relies on a "hidden assumption" (namely Zermelo's "subset axiom") [snip childish abuse]
>

You continue to desperately grasp at straws, Frtiz.

> The "Drinking Prinziple" 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 math UNDERGRADS (my target audience) should find much more accessible. Students have, after all, been familiar with set notation since childhood. Many if not most or all will never have been exposed to logical predicates. Deal with it.

[Mostowski Collapse]

There does not exist a set theoretic version of the Drinker
Paradox using Russell Paradox. You are grasping straws

Dan-O-Matik. What you did is the Water ruins Wine paradox.
The WrW paradox runs as follows:

"How fuck up a paradox beyond recognition in a few
strokes, and then ponder on the internet for years that
it is the original, even try to edit wikipedia, although nobody
believes you, even wikipedia didn't buy your bullshit."

[Mostowski Collapse]

About your audience, I guess its the same audience that
Wolfgang Mückenheim has. Poor students that must
endure a complete crank for 1 semester, but a student

does what a student must do, putting up with a stupid
professor is ok, if the grades or some other certificate
are ok. Kind of a stockholm syndrome:

> Stockholm syndrome is a theorized condition in
> which hostages develop a psychological bond with
> their captors during captivity.
> https://en.wikipedia.org/wiki/Stockholm_syndrome

Anyway we have YOU hostage Wonky Man here on
sci.logic and sci.math, raining hell on your bullshit.

[Dan Christensen]

On Tuesday, October 25, 2022 at 2:03:11 PM UTC-4, Mostowski Collapse wrote:

[snip]

> > I have presented a new, purely set-theoretic version that math UNDERGRADS (my target audience) should find much more accessible. Students have, after all, been familiar with set notation since childhood. Many if not most or all will never have been exposed to logical predicates. Deal with it.

> There does not exist a set theoretic version of the Drinker
> Paradox using Russell Paradox. You are grasping straws
>

Still in denial, I see. Pathetic.

Given only that "drinkers" and "pub" are arbitrary sets, we have:

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

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

See my blog posting at https://dcproof.wordpress.com/2014/06/03/the-drinkers-paradox/

Read it and weep, Jan Burse.

[Dan Christensen]

On Tuesday, October 25, 2022 at 2:15:05 PM UTC-4, Mostowski Collapse wrote:


> Mostowski Collapse schrieb am Dienstag, 25. Oktober 2022 um 20:03:11 UTC+2:
> > There does not exist a set theoretic version of the Drinker
> > Paradox using Russell Paradox. You are grasping straws
> >
> > Dan-O-Matik. What you did is the Water ruins Wine paradox.
> > The WrW paradox runs as follows:
> >
> > "How fuck up a paradox beyond recognition in a few
> > strokes, and then ponder on the internet for years that
> > it is the original, even try to edit wikipedia, although nobody
> > believes you, even wikipedia didn't buy your bullshit."
> > Dan Christensen schrieb am Dienstag, 25. Oktober 2022 um 19:44:59 UTC+2:
> > > On Tuesday, October 25, 2022 at 1:21:12 PM UTC-4, Fritz Feldhase wrote:
> > > > On Tuesday, October 25, 2022 at 6:35:35 PM UTC+2, Dan Christensen wrote:
> > > >
> > > > > ALL(s):[Set(s) => EXIST(x):[x in s => Q]] for any proposition Q be it true or false.
> > > > >
> > > > > http://www.dcproof.com/STGeneralizedDrinkersThm.htm
> > > > This nonsense has nothing to do with the "Drinker Paradox" or "Drinker Prinziple" [snip childish abuse]
> > > >
> > > > Especially, since it relies on a "hidden assumption" (namely Zermelo's "subset axiom") [snip childish abuse]
> > > >
> > >
> > > You continue to desperately grasp at straws, Frtiz.
> > > > The "Drinking Prinziple" 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 math UNDERGRADS (my target audience) should find much more accessible. Students have, after all, been familiar with set notation since childhood. Many if not most or all will never have been exposed to logical predicates. Deal with it.

> About your audience, I guess its the same audience that

> Wolfgang Mückenheim has. ...

[snip]

>
> Anyway we have YOU hostage Wonky Man here on
> sci.logic and sci.math, raining hell on your bullshit.

That "rain" is actually you pissing yourself, Jan Burse. HA, HA, HA!!!

[Mostowski Collapse]

Repeating bullshit doesn't make it less bullshit,
it only makes it more bullshit. We now have this
chemical equation how you created your bullshit:

WrW = DP + RP

[Mostowski Collapse]

Because you are constantly repeating your bullshit we
have a new instance of John Gabriel, there is this analogy
of putting bullshit into the world, both dont work:

- John Gabriel: New Calculoose
- Dan Christensen: New Drinker (a typical Paraduck)

[Fritz Feldhase]

On Tuesday, October 25, 2022 at 9:04:58 PM UTC+2, Mostowski Collapse wrote:

> Because you are constantly repeating your bullshit we
> have a new instance of John Gabriel, there is this analogy

> of putting bullshit into the world, both don't work:

>
> - John Gabriel: New Calculoose
> - Dan Christensen: New Drinker (a typical Paraduck)

Completely agree with your assessment.

- WM: Dark numbers

[Fritz Feldhase]

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*

[Fritz Feldhase]

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".

[Dan Christensen]

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?

[Chris M. Thomasson]

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?

[Mostowski Collapse]

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?

[Fritz Feldhase]

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).

[Julio Di Egidio]

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

[Dan Christensen]

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.

[Julio Di Egidio]

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

[Dan Christensen]

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.

[Julio Di Egidio]

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

[Dan Christensen]

[snip childish abuse]

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

[snip more childish abuse]

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

[Julio Di Egidio]

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

[Mostowski Collapse]

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

[FromTheRafters]

Chris M. Thomasson explained on 10/25/2022 :

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.

[Dan Christensen]

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.

[Fritz Feldhase]

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.

[Dan Christensen]

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.

[Mostowski Collapse]

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

[Fritz Feldhase]

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.

[Mostowski Collapse]

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)]

[Dan Christensen]

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.

[Mostowski Collapse]

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?

[Chris M. Thomasson]

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!

[Dan Christensen]

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!

[Chris M. Thomasson]

On 10/18/2022 8:40 PM, Dan Christensen wrote:
> On Tuesday, October 18, 2022 at 11:01:20 PM UTC-4, Chris M. Thomasson wrote:
>> On 10/18/2022 5:01 PM, Dan Christensen wrote:
>>> On Tuesday, October 18, 2022 at 7:45:53 PM UTC-4, Chris M. Thomasson wrote:
>>>> On 10/18/2022 2:12 PM, Dan Christensen wrote:
>>>>> Minor bug fix. Release date: today.

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

>>>> Are you going to release your source code?
>>>
>>> No.
>>>
>>> Is it in VB 6?
>>>
>>> Yes.
>> I still have VB 6 installed on several old computers for maintaining
>> legacy DB programs from more than 20 years ago. Have you hooked it up
>> with msWord yet? Its fun to use the vbo, or was it vba? Create detailed
>> reports, all formatted and pretty. ;^) Have use used ms access? It
>> interfaces quite nicely with VB 6.
>
> Files in DC Proof are just low-tech flat (binary?) files. It has been a several years since I did anything with the file structure--not since I created the Windows version in 2004. Before that I had a VBDOS version, but it wasn't available online. The current version is a very small app--only about 1.2 Mb. The downloadable exe file (about 2.9 Mb) can be downloaded and installed in less than a minute with a high speed connection.

When you get some free time to burn, and are really bored... Try
creating output using msword wrt your existing vb6 code and making your
reports of a proof very pretty. Vb6 can talk to msword, access, excel,
ect... Like a glorified report generator. That's what I did a long time
ago wrt a inspection system for houses/pools/ect... I had a very large
database about comments, and codes, and local codes, ect... Fence
heights around a pool, ect... something you could get sued for if there
was one mistake. I could create deep narrative reports, and short action
item like reports. The comments were important because they had to be up
to current code, and still have to! I still maintain the database and
software. Even have a farm of old computers running the code. Actually,
I got up to 90% of it working on win11. DosBox was useful.

[Mostowski Collapse]

Maybe do SET SPACES before you do FUNCTION SPACES.
So far, from judging how you deal with the Drinker Paradox,
you didn't notice that your Set(_):

The s such that Set(s)

Doesn't span a lattice. It only spans an incomplete-lattice. This
explains why Set(_) cannot cover the below scenario
when its not further restricted:

Universe = {Anna, Bert, Carlo}
Drinkers = {Anna, Bert, Carlo}

What is an incomplete-lattice?
https://en.wikipedia.org/wiki/Complete_lattice

Making Russells paradox key for the Drinker Paradox,
clearly indicates that you used the wrong lattice for
modelling the Drinker Paradox.

A lattice with only bottom and no top.

[Dan Christensen]

On Friday, May 5, 2023 at 7:56:58 AM UTC-4, Mostowski Collapse wrote:
> Maybe do SET SPACES before you do FUNCTION SPACES.
> So far, from judging how you deal with the Drinker Paradox,
> you didn't notice that your Set(_):
>
> The s such that Set(s)
>
> Doesn't span a lattice. It only spans an incomplete-lattice. This
> explains why Set(_) cannot cover the below scenario
> when its not further restricted:
>
> Universe = {Anna, Bert, Carlo}
> Drinkers = {Anna, Bert, Carlo}
>

You really seem to be grasping at straws here, Mr. Collapse. What do you hope to prove by giving a set two different names? That they are equal? Universe = Drinkers? Very unimpressive.

> What is an incomplete-lattice?
> https://en.wikipedia.org/wiki/Complete_lattice
>
> Making Russells paradox key for the Drinker Paradox,

[snip]

An application on RP allows you to easily prove that, for any set S and proposition Q (be it true or false), we have EXIST(x):[x in S => Q]

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

Deal with it, Mr. Collapse. And get a life!

[Dan Christensen]

On Saturday, May 6, 2023 at 6:06:08 PM UTC-4, Dan Christensen wrote:
> On Friday, May 5, 2023 at 7:56:58 AM UTC-4, Mostowski Collapse wrote:
> > Maybe do SET SPACES before you do FUNCTION SPACES.
> > So far, from judging how you deal with the Drinker Paradox,
> > you didn't notice that your Set(_):
> >
> > The s such that Set(s)
> >

Some objects, say the number 4, are not usually considered to be sets. Unlike actual sets, 4 does not, for example, have a powerset. In DC Proof, the Powerset Axiom is applicable only to objects that have been declared to be a set by means of the Set predicate. Likewise the other axioms of set theory in DC Proof.

EXAMPLE

Let x be a set

1. Set(x)
Premise

Construct the power set of x

Apply the Power Set Axiom

2. ALL(a):[Set(a) => EXIST(b):[Set(b)
& ALL(c):[c in b <=> Set(c) & ALL(d):[d in c => d in a]]]]
Power Set

Specify x

3. Set(x) => EXIST(b):[Set(b)
& ALL(c):[c in b <=> Set(c) & ALL(d):[d in c => d in x]]]
U Spec, 2

4. EXIST(b):[Set(b)
& ALL(c):[c in b <=> Set(c) & ALL(d):[d in c => d in x]]]
Detach, 3, 1

Define: px (the power set of x)

5. Set(px)
& ALL(c):[c in px <=> Set(c) & ALL(d):[d in c => d in x]]
E Spec, 4

[FromTheRafters]

Dan Christensen wrote :

> On Saturday, May 6, 2023 at 6:06:08 PM UTC-4, Dan Christensen wrote:
>> On Friday, May 5, 2023 at 7:56:58 AM UTC-4, Mostowski Collapse wrote:
>>> Maybe do SET SPACES before you do FUNCTION SPACES.
>>> So far, from judging how you deal with the Drinker Paradox,
>>> you didn't notice that your Set(_):
>>>
>>> The s such that Set(s)
>>>
>
> Some objects, say the number 4, are not usually considered to be sets.

Under Frege, Zermelo, and von Neumann they are.

[Dan Christensen]

Reflecting the more common usage of today...

"[A]mong all the objects studied in mathematics, some of the objects happen to be sets; and if x is an object and A is a set, then either x ∈ A is true or x ∈ A is false. (If A is not a set, we leave the statement x ∈ A undefined; for instance, we consider the statement 3 ∈ 4 to neither be true or false, but simply meaningless, since 4 is not a set.)"
--Terence Tao, "Analysis I," p.34

[Mostowski Collapse]

Thats not relevant to being a complete lattice.
Your predicate Set(_) spans a class of sets which
is not a complete lattice:

Counter Example to Being a complete lattice:
ALL(s):[Set(s) => EXIST(a):~a e s]
http://www.dcproof.com/UniversalSet.htm

If the predicate Set(_) would span a class of sets,
which would be a complete lattice, we would
have some element in the lattice which is the

top, which can be expressed as:

EXIST(s):[Set(s) & ALL(a):[a e s]]

Thats is why your Set(_) alone is not suitable
for the drinker paradox. Because intuitively we
expect a complete lattice, so that scenarios

such as the following are possible:

Universe = {Anna, Bert}
Drinkers = {Anna, Bert}

[Mostowski Collapse]

The finite complete boolean lattice for the

Universe = {Anna, Bert}

isn't a moon walk, you can depict it asfollows, it
shows the possible Drinkers configurations:

____{Anna, Bert}
___/ ____________\
{Anna}________{Bert}
___\____________/
_________{}

https://en.wikipedia.org/wiki/Hasse_diagram

So that Dan Christensen can apply the Russell Paradox
to the Drinker Paradox, is because of his error that
he doesn't take Drinkers from a complete lattice.

The fix isn't that difficult though.

[FromTheRafters]

It happens that Dan Christensen formulated :

> On Saturday, May 6, 2023 at 8:28:10 PM UTC-4, FromTheRafters wrote:
>> Dan Christensen wrote :
>>> On Saturday, May 6, 2023 at 6:06:08 PM UTC-4, Dan Christensen wrote:
>>>> On Friday, May 5, 2023 at 7:56:58 AM UTC-4, Mostowski Collapse wrote:
>>>>> Maybe do SET SPACES before you do FUNCTION SPACES.
>>>>> So far, from judging how you deal with the Drinker Paradox,
>>>>> you didn't notice that your Set(_):
>>>>>
>>>>> The s such that Set(s)
>>>>>
>>>
>>> Some objects, say the number 4, are not usually considered to be sets.
>
>> Under Frege, Zermelo, and von Neumann they are.
>
> Reflecting the more common usage of today...
>
> "[A]mong all the objects studied in mathematics, some of the objects happen
> to be sets; and if x is an object and A is a set, then either x ∈ A is true
> or x ∈ A is false. (If A is not a set, we leave the statement x ∈ A
> undefined; for instance, we consider the statement 3 ∈ 4 to neither be true
> or false, but simply meaningless, since 4 is not a set.)" --Terence Tao,
> "Analysis I," p.34

Oh, *that* set theory.

[Dan Christensen]

Terry seems to have done well by it. I have attempted to formalize it in my DC Proof system. It seems to work.

[Mostowski Collapse]

You used it wrongly for the drinker paradox. Even Terrence Tao
doesn't make the same blunder. You don't find him use Set(_).
Even not implicitly when he talks about an arbitrary subset like here:

/* Terrence Tao rather uses s ⊆ U */
> Exercise 10.3.5 from Analysis Vol.1 by Terence Tao.
> Give an example of a subset X⊆R and a function f:X→R
> which is differentiable on X, is such that f′(x)>0
> for all x∈X, but f is not strictly monotone increasing.

Maybe the problem is that DC Proof has only ∈ set membership,
and not ⊆ subset relationship. There is surely something missing
in your dealing with sets, you are subject to some mental

blockade. Whereas you have no problem to somehow adopt
the notion of a function space, i.e. to have some approaches
to what one usually writes:

/* A Mountain Dan O Matik tried to clime */
f : A -> B

You seem to be totally obnoxious of set spaces. What
would one write for drinkers, so that they are from a
complete boolean lattice?

/* Mountain of Ignorance for Dan O Matik */
drinkers : ??

Can you tell us?

[Mostowski Collapse]

Could you define:

ALL(a):ALL(b):[a ⊆ b <=> ALL(x):[x ∈ a => x ∈ b]]

And then infer in DC Poop:

Set(U) & D ⊆ U => Set(D) ?

Maybe via power set axiom? Is this possible to infer
a certain transitivity of the Set(_) property along the
subset relationship ⊆ ? Didn't check exactly how

ZFCU works. ZFCU is ZFC with U-relements:

https://en.wikipedia.org/wiki/Urelement

[Mostowski Collapse]

Possibly the powerset axiom helps in deriving

Set(U) & D ⊆ U => Set(D)

It says in DC Proof:

1 ALL(a):[Set(a) => EXIST(b):[Set(b)
& ALL(c):[c ∈ b <=> Set(c) & ALL(d):[d ∈ c => d ∈ a]]]]
Power Set

But if you had also ⊆, you could define it easier as follows:

1 ALL(a):[Set(a) => EXIST(b):[Set(b)
& ALL(c):[c ∈ b <=> Set(c) & c ⊆ a]]]
Power Set

[FromTheRafters]

After serious thinking Dan Christensen wrote :

Yes, but none of them yet are perfect as foundational to mathematics.

[Dan Christensen]

See my reply just now to your identical posting at sci.logic

Dan

On Sunday, May 7, 2023 at 11:36:53 AM UTC-4, Mostowski Collapse wrote:
> You used it wrongly for the drinker paradox. Even Terrence Tao
> doesn't make the same blunder. You don't find him use Set(_).
> Even not implicitly when he talks about an arbitrary subset like here:
>

[snip]

[Dan Christensen]

On Sunday, May 7, 2023 at 11:43:36 AM UTC-4, Mostowski Collapse wrote:
> Could you define:
>
> ALL(a):ALL(b):[a ⊆ b <=> ALL(x):[x ∈ a => x ∈ b]]
>

Yes.

Define: Sub

ALL(a):ALL(b):[Set(a) & Set(b) => [Sub(a,b) <=> ALL(c):[c in a => c in b]]]
Axiom

> And then infer in DC Proof:

>
> Set(U) & D ⊆ U => Set(D) ?

Set(u) & Sub(d,u) => Set(d) ?

Not with the above definition. To "decode" Sub(d,u), you would already need to know that d was a set.

[Mostowski Collapse]

Thats probably a defect of DC proof or maybe a
defect of ZFCU. It only means that your sets possibly
have companions with the same extension

but nevertheless non-equivalent. Take s ⊆ u, you can
construct this set. From your subset axiom we
will have Set(r) because it was Set(u):

r = { x | x e u & x e s }

The set r has the same extension as s. But with your
extensionality axiom, you cannot prove them equivalent
since Set(s) is missing. Thats your extensionality:

6 ALL(a):ALL(b):[Set(a) & Set(b) => [a=b <=> ALL(c):[c @ a <=> c @ b]]]
Set Equality

Do you have this ZFCU axiom in DC Proof?

ALL(x):[~Set(x) => ~EXIST(y):y e x]

[Mostowski Collapse]

So how would we express a predication:

P(f,x) <=> The function f is defined at the point x?

And please make it not Homo Ergaster style. Namely
some guideline how to bake a formula with 100 parameters,
that does express the above. There are only two

parameters: f the function and x the point.

Our ultimate goal here is:

"Beyond reverse engineering the brain in order to understand
and emulate it, the idea is of "uploading" a specific brain with
every mental process intact, to be instantiated on a "suitably
powerful computational substrate".

Basically there will be no ChatGPT interaction in the future.
Instead we will augment ourselves. And these augments might
have interconnects. Sympatric Transhumanism.

Dan Christensen schrieb am Dienstag, 18. Oktober 2022 um 23:12:55 UTC+2:
> Minor bug fix. Release date: today.
>

[Mostowski Collapse]

Maybe humans will loose some genes through a
Hybrid speciation. Although some Augment does not
necessarily mean genetic engineering, or does it?

Hybrid speciation is a form of speciation where
hybridization between two different species leads
to a new species, reproductively isolated from the parent species.
https://en.wikipedia.org/wiki/Hybrid_speciation

What will be the progress of life sciences, thanks
to better AI? Some more genetic engineering.
What is this guy talking about here:

'Godfather of AI' discusses dangers the¨
developing technologies pose to society
https://www.youtube.com/watch?v=yAgQWnD31nE

[Dan Christensen]

On Monday, May 8, 2023 at 8:58:52 AM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Sonntag, 7. Mai 2023 um 21:38:59 UTC+2:
> > On Sunday, May 7, 2023 at 11:43:36 AM UTC-4, Mostowski Collapse wrote:
> > > Could you define:
> > >
> > > ALL(a):ALL(b):[a ⊆ b <=> ALL(x):[x ∈ a => x ∈ b]]
> > >
> > Yes.
> >
> > Define: Sub
> >
> > ALL(a):ALL(b):[Set(a) & Set(b) => [Sub(a,b) <=> ALL(c):[c in a => c in b]]]
> > Axiom
> >
> > > And then infer in DC Proof:
> > >
> > > Set(U) & D ⊆ U => Set(D) ?
> > Set(u) & Sub(d,u) => Set(d) ?
> >
> > Not with the above definition. To "decode" Sub(d,u), you would already need to know that d was a set.

> Thats probably a defect of DC proof or maybe a
> defect of ZFCU. It only means that your sets possibly
> have companions with the same extension
>
> but nevertheless non-equivalent. Take s ⊆ u, you can
> construct this set. From your subset axiom we
> will have Set(r) because it was Set(u):
>
> r = { x | x e u & x e s }
>

In DC Proof that would be:

Set(r) & ALL(x):[x in r <=> x in u & x in s]

Assuming u and s were previously declared to be sets: Set(u) and Set(s)

1. Set(u)
Axiom

2. Set(s)
Axiom

3. EXIST(y):[Set(y) & ALL(x):[x in y <=> x in u & x in s]]
Subset, 1

4. Set(r) & ALL(x):[x in r <=> x in u & x in s]
E Spec, 3

r is subset of u. s is not necessarily a subset of u. If s and u are disjoint, then r will be empty.

> The set r has the same extension as s. But with your
> extensionality axiom, you cannot prove them equivalent

I hope not!

> since Set(s) is missing.

If s was not a set, what meaning would you attach to your "x in s"? Recall that, in math textbooks, unlike in ZFC, not everything assumed to be a set (see Tao).

> Thats your extensionality:
>
> 6 ALL(a):ALL(b):[Set(a) & Set(b) => [a=b <=> ALL(c):[c @ a <=> c @ b]]]
> Set Equality
>
> Do you have this ZFCU axiom in DC Proof?
>
> ALL(x):[~Set(x) => ~EXIST(y):y e x]

Or equivalently:

ALL(x):[EXIST(y):y in x => Set(x)]

No. It looks quite useless.

[Dan Christensen]

On Saturday, May 13, 2023 at 11:29:02 AM UTC-4, Mostowski Collapse wrote:
> So how would we express a predication:
>
> P(f,x) <=> The function f is defined at the point x?
>

ALL(fun):ALL(dom):ALL(cod):ALL(elt):[Set(dom) & Set(cod) & ALL(a):[a in dom => fun(a) in cod]

=> [P(fun,elt) <=> elt in dom]]

[Mostowski Collapse]

Well a binary predicate definition would only read:

ALL(f):ALL(x):[P(f,x) <=> ...]

Try again!

[Dan Christensen]

On Saturday, May 13, 2023 at 6:02:52 PM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Samstag, 13. Mai 2023 um 20:33:05 UTC+2:
> > On Saturday, May 13, 2023 at 11:29:02 AM UTC-4, Mostowski Collapse wrote:
> > > So how would we express a predication:
> > >
> > > P(f,x) <=> The function f is defined at the point x?
> > >
> > ALL(fun):ALL(dom):ALL(cod):ALL(elt):[Set(dom) & Set(cod) & ALL(a):[a in dom => fun(a) in cod]
> >
> > => [P(fun,elt) <=> elt in dom]]

> Well a binary predicate definition would only read:
>
> ALL(f):ALL(x):[P(f,x) <=> ...]
>

What is f? What is x?

You need something a little more specific, Mr. Collapse.

Let me guess... You want to be able to infer that P(f,x) is false is f is not a function or x has not been declared to be a set. That's not usually how things work in mathematics. In that case, P(f,x) would be indeterminate.

Try again, Mr. Collapse.

[Mostowski Collapse]

I see a big problem with your definition, it is wrong:

ALL(a):[a in dom => fun(a) in cod] => [P(fun,elt) <=> elt in dom]

Where P should express that fun is defined at elt, right?

Now take the following dom and cod:

dom={0}, cod={0}

And take the following function:

fun(0)=0
fun(1)=1

Is it defined at 1?