On Monday, October 25, 2021 at 11:04:16 AM UTC-4, Mostowski Collapse wrote:
> Dan-O-Matik halucinated:
> > If, on the other hand, as in Russell's king-of-France example, you
> have ~EXIST(a):K(a), then you can have both ~EXIST(a):[K(a) & ~B(a))]
> and ~EXIST(a):[K(a) & B(a))].

> It has nothing to do with Russell, since Russell doesn't
> translate "the X is Y" into EXIST(a):(X(a) & Y(a)).

Why do you suppose he chose the king of France? Only because there is no present king of France. Then, no matter how many kings France might have at once, you have ALL(a):[K(a) => B(a)] as well as ALL(a):[K(a) => ~B(a)] where K(x) = "x is a present king of France" and B(x) = "x is bald.

Still don't get it, Jan Burse? See https://en.wikipedia.org/wiki/Vacuous_truth

Dan

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

He chose the king of france example because it makes
his "the X is Y" false. I don't think he chose the king of france
example because it makes "some X is Y" false.

After all his paper is about definite descriptions, i.e. about
"the X is Y" and not about particulars such as "some X is Y"?
Particulars where dealt with by Aristoteles, he had:

- I-type: Particular and affirmative ("Some philosophers are mortal")
- O-type: Particular and negative ("Some philosophers are not mortal")
https://en.wikipedia.org/wiki/Term_logic

You find things such as vacously false in his square. In the Aristoteles
square of oppositon you find that:

A-type = ~O-type
E-type = ~I-type
https://en.wikipedia.org/wiki/Square_of_opposition

I doubt Russell want to tell us something about vacously true, since
this was already evident from Aristoteles square of opposition.
The classical education at that time, at the time of Russell, was

that everybody knew the square of opposition by heart. Maybe
Slow-O-Matik aka Dan-O-Matik has never heard of it.

Proof:
Since A-type = ~O-type, we have
ALL(a):(X(a) => Y(a)) <==> ~EXIST(a):(X(a) & ~Y(a))
Therefore from A-type vacously true, it follows
O-type vacously false, and vice versa.

Since E-type = ~I-type, we have
ALL(a):(X(a) => ~Y(a)) <==> ~EXIST(a):(X(a) & Y(a))
Therefore from A-type vacously true, it follows
O-type vacously false, and vice versa.

Dan Christensen schrieb am Montag, 25. Oktober 2021 um 17:33:13 UTC+2:
> On Monday, October 25, 2021 at 11:04:16 AM UTC-4, Mostowski Collapse wrote:
> > Dan-O-Matik halucinated:
> > > If, on the other hand, as in Russell's king-of-France example, you
> > have ~EXIST(a):K(a), then you can have both ~EXIST(a):[K(a) & ~B(a))]
> > and ~EXIST(a):[K(a) & B(a))].
>
> > It has nothing to do with Russell, since Russell doesn't
> > translate "the X is Y" into EXIST(a):(X(a) & Y(a)).
> Why do you suppose he chose the king of France? Only because there is no present king of France. Then, no matter how many kings France might have at once, you have ALL(a):[K(a) => B(a)] as well as ALL(a):[K(a) => ~B(a)] where K(x) = "x is a present king of France" and B(x) = "x is bald.
>
> Still don't get it, Jan Burse? See https://en.wikipedia.org/wiki/Vacuous_truth
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Corr.: Typo

Since E-type = ~I-type, we have
ALL(a):(X(a) => ~Y(a)) <==> ~EXIST(a):(X(a) & Y(a))
Therefore from E-type vacously true, it follows
I-type vacously false, and vice versa.

Mostowski Collapse schrieb am Montag, 25. Oktober 2021 um 17:43:48 UTC+2:
> He chose the king of france example because it makes
> his "the X is Y" false. I don't think he chose the king of france
> example because it makes "some X is Y" false.
>
> After all his paper is about definite descriptions, i.e. about
> "the X is Y" and not about particulars such as "some X is Y"?
> Particulars where dealt with by Aristoteles, he had:
>
> - I-type: Particular and affirmative ("Some philosophers are mortal")
> - O-type: Particular and negative ("Some philosophers are not mortal")
> https://en.wikipedia.org/wiki/Term_logic
>
> You find things such as vacously false in his square. In the Aristoteles
> square of oppositon you find that:
>
> A-type = ~O-type
> E-type = ~I-type
> https://en.wikipedia.org/wiki/Square_of_opposition
>
> I doubt Russell want to tell us something about vacously true, since
> this was already evident from Aristoteles square of opposition.
> The classical education at that time, at the time of Russell, was
>
> that everybody knew the square of opposition by heart. Maybe
> Slow-O-Matik aka Dan-O-Matik has never heard of it.
>
> Proof:
> Since A-type = ~O-type, we have
> ALL(a):(X(a) => Y(a)) <==> ~EXIST(a):(X(a) & ~Y(a))
> Therefore from A-type vacously true, it follows
> O-type vacously false, and vice versa.
>
> Since E-type = ~I-type, we have
> ALL(a):(X(a) => ~Y(a)) <==> ~EXIST(a):(X(a) & Y(a))
> Therefore from A-type vacously true, it follows
> O-type vacously false, and vice versa.
> Dan Christensen schrieb am Montag, 25. Oktober 2021 um 17:33:13 UTC+2:
> > On Monday, October 25, 2021 at 11:04:16 AM UTC-4, Mostowski Collapse wrote:
> > > Dan-O-Matik halucinated:
> > > > If, on the other hand, as in Russell's king-of-France example, you
> > > have ~EXIST(a):K(a), then you can have both ~EXIST(a):[K(a) & ~B(a))]
> > > and ~EXIST(a):[K(a) & B(a))].
> >
> > > It has nothing to do with Russell, since Russell doesn't
> > > translate "the X is Y" into EXIST(a):(X(a) & Y(a)).
> > Why do you suppose he chose the king of France? Only because there is no present king of France. Then, no matter how many kings France might have at once, you have ALL(a):[K(a) => B(a)] as well as ALL(a):[K(a) => ~B(a)] where K(x) = "x is a present king of France" and B(x) = "x is bald.
> >
> > Still don't get it, Jan Burse? See https://en.wikipedia.org/wiki/Vacuous_truth
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

On Monday, October 25, 2021 at 11:43:48 AM UTC-4, Mostowski Collapse wrote:
> He chose the king of france example because it makes
> his "the X is Y" false. I don't think he chose the king of france
> example because it makes "some X is Y" false.

Again, without any inconsistency, we have ~EXIST(a):K(a) => ALL(a):[K(a) => B(a)] & ALL(a):[K(a) => ~B(a)] whatever proposition B(a) may be. That is the central point here. It doesn`t matter how many simultaneous kings might have been allowed. Deal with it Jan Burse.

Dan

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

But it has nothing to do with Russell, since Russell did
not deal with ALL(a):[X(a) => Y(a)] as a translation of
"the X is Y". ALL(a):[X(a) => Y(a)] is the translation

of "all X is Y". See here:

The Four Aristotelian Propositions
https://en.wikipedia.org/wiki/Square_of_opposition#Summary

Russell didn't write a paper about the Four Aristotelian
Propositions. He wrote a paper about definite descriptions.
Definite descriptions are neither universal

nor particular statements.

Dan Christensen schrieb:
> On Monday, October 25, 2021 at 11:43:48 AM UTC-4, Mostowski Collapse wrote:
>> He chose the king of france example because it makes
>> his "the X is Y" false. I don't think he chose the king of france
>> example because it makes "some X is Y" false.
>
> Again, without any inconsistency, we have ~EXIST(a):K(a) => ALL(a):[K(a) => B(a)] & ALL(a):[K(a) => ~B(a)] whatever proposition B(a) may be. That is the central point here. It doesn`t matter how many simultaneous kings might have been allowed. Deal with it Jan Burse.
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>

On Monday, October 25, 2021 at 12:14:26 PM UTC-4, Mostowski Collapse wrote:
> But it has nothing to do with Russell, since Russell did
> not deal with ALL(a):[X(a) => Y(a)] as a translation of
> "the X is Y". ALL(a):[X(a) => Y(a)] is the translation
>
> of "all X is Y". See here:
>
> The Four Aristotelian Propositions
> https://en.wikipedia.org/wiki/Square_of_opposition#Summary
>
> Russell didn't write a paper about the Four Aristotelian
> Propositions. He wrote a paper about definite descriptions.
> Definite descriptions are neither universal
>
> nor particular statements.
>
> Dan Christensen schrieb:
> > On Monday, October 25, 2021 at 11:43:48 AM UTC-4, Mostowski Collapse wrote:
> >> He chose the king of france example because it makes
> >> his "the X is Y" false. I don't think he chose the king of france
> >> example because it makes "some X is Y" false.
> >
> > Again, without any inconsistency, we have ~EXIST(a):K(a) => ALL(a):[K(a) => B(a)] & ALL(a):[K(a) => ~B(a)] whatever proposition B(a) may be. That is the central point here. It doesn`t matter how many simultaneous kings might have been allowed. Deal with it Jan Burse.
> >

> But it has nothing to do with Russell, since Russell did
> not deal with ALL(a):[X(a) => Y(a)] as a translation of
> "the X is Y". ALL(a):[X(a) => Y(a)] is the translation
>

Russell got sidetracked with talk of the uniqueness of the king of France, should one exist. As we have seen here, it simply doesn't matter in this case how many simultaneous kings were allowed. If there are no present kings of France (i.e. ~EXIST(a): K(a), then it is vacuously true that

ALL(a):[K(a) => B(a)] and ALL(a):[K(a) => ~B(a)]

Anyway, it seems you have been reduced to mindlessly repeating your failed arguments over and over again, Jan Burse. If you have nothing new to add, do not expect a reply from me on this matter.

Dan

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

You didn't prove something about "the X is Y".
Looks like you are the greater crank than Archimedes Plutonium.

No wonder do Archimedes Plutonium and Dan-O-Matik
attach to each other, like two dogs that sniff their assholes.

Crank+Crank, LoL

Dan Christensen schrieb am Montag, 25. Oktober 2021 um 18:29:49 UTC+2:
> On Monday, October 25, 2021 at 12:14:26 PM UTC-4, Mostowski Collapse wrote:
> > But it has nothing to do with Russell, since Russell did
> > not deal with ALL(a):[X(a) => Y(a)] as a translation of
> > "the X is Y". ALL(a):[X(a) => Y(a)] is the translation
> >
> > of "all X is Y". See here:
> >
> > The Four Aristotelian Propositions
> > https://en.wikipedia.org/wiki/Square_of_opposition#Summary
> >
> > Russell didn't write a paper about the Four Aristotelian
> > Propositions. He wrote a paper about definite descriptions.
> > Definite descriptions are neither universal
> >
> > nor particular statements.
> >
> > Dan Christensen schrieb:
> > > On Monday, October 25, 2021 at 11:43:48 AM UTC-4, Mostowski Collapse wrote:
> > >> He chose the king of france example because it makes
> > >> his "the X is Y" false. I don't think he chose the king of france
> > >> example because it makes "some X is Y" false.
> > >
> > > Again, without any inconsistency, we have ~EXIST(a):K(a) => ALL(a):[K(a) => B(a)] & ALL(a):[K(a) => ~B(a)] whatever proposition B(a) may be. That is the central point here. It doesn`t matter how many simultaneous kings might have been allowed. Deal with it Jan Burse.
> > >
>
> > But it has nothing to do with Russell, since Russell did
> > not deal with ALL(a):[X(a) => Y(a)] as a translation of
> > "the X is Y". ALL(a):[X(a) => Y(a)] is the translation
> >
> Russell got sidetracked with talk of the uniqueness of the king of France, should one exist. As we have seen here, it simply doesn't matter in this case how many simultaneous kings were allowed. If there are no present kings of France (i.e. ~EXIST(a): K(a), then it is vacuously true that
> ALL(a):[K(a) => B(a)] and ALL(a):[K(a) => ~B(a)]
> Anyway, it seems you have been reduced to mindlessly repeating your failed arguments over and over again, Jan Burse. If you have nothing new to add, do not expect a reply from me on this matter.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Which reminds me of the proverb:

"A fool with a tool, is still a fool"

Mostowski Collapse schrieb am Montag, 25. Oktober 2021 um 20:24:14 UTC+2:
> You didn't prove something about "the X is Y".
> Looks like you are the greater crank than Archimedes Plutonium.
>
> No wonder do Archimedes Plutonium and Dan-O-Matik
> attach to each other, like two dogs that sniff their assholes.
>
> Crank+Crank, LoL
> Dan Christensen schrieb am Montag, 25. Oktober 2021 um 18:29:49 UTC+2:
> > On Monday, October 25, 2021 at 12:14:26 PM UTC-4, Mostowski Collapse wrote:
> > > But it has nothing to do with Russell, since Russell did
> > > not deal with ALL(a):[X(a) => Y(a)] as a translation of
> > > "the X is Y". ALL(a):[X(a) => Y(a)] is the translation
> > >
> > > of "all X is Y". See here:
> > >
> > > The Four Aristotelian Propositions
> > > https://en.wikipedia.org/wiki/Square_of_opposition#Summary
> > >
> > > Russell didn't write a paper about the Four Aristotelian
> > > Propositions. He wrote a paper about definite descriptions.
> > > Definite descriptions are neither universal
> > >
> > > nor particular statements.
> > >
> > > Dan Christensen schrieb:
> > > > On Monday, October 25, 2021 at 11:43:48 AM UTC-4, Mostowski Collapse wrote:
> > > >> He chose the king of france example because it makes
> > > >> his "the X is Y" false. I don't think he chose the king of france
> > > >> example because it makes "some X is Y" false.
> > > >
> > > > Again, without any inconsistency, we have ~EXIST(a):K(a) => ALL(a):[K(a) => B(a)] & ALL(a):[K(a) => ~B(a)] whatever proposition B(a) may be. That is the central point here. It doesn`t matter how many simultaneous kings might have been allowed. Deal with it Jan Burse.
> > > >
> >
> > > But it has nothing to do with Russell, since Russell did
> > > not deal with ALL(a):[X(a) => Y(a)] as a translation of
> > > "the X is Y". ALL(a):[X(a) => Y(a)] is the translation
> > >
> > Russell got sidetracked with talk of the uniqueness of the king of France, should one exist. As we have seen here, it simply doesn't matter in this case how many simultaneous kings were allowed. If there are no present kings of France (i.e. ~EXIST(a): K(a), then it is vacuously true that
> > ALL(a):[K(a) => B(a)] and ALL(a):[K(a) => ~B(a)]
> > Anyway, it seems you have been reduced to mindlessly repeating your failed arguments over and over again, Jan Burse. If you have nothing new to add, do not expect a reply from me on this matter.
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

Holy cow. Aristoteles trending on Twitter:
https://twitter.com/search?q=Aristotle

Anyway Dan O Matik, what I wanted to ask you,
function spaces, is it still based on conflating:

f : A -> B

With this here:

ALL(x):[x e A => f(x) e B]

So by vacuously true, every function f is a
function f : {} -> X in your world?

Mostowski Collapse schrieb am Montag, 25. Juli 2022 um 21:03:20 UTC+2:
> Holy cow. Aristoteles trending on Twitter:
> https://twitter.com/search?q=Aristotle

On Monday, July 25, 2022 at 3:12:00 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> Anyway Dan O Matik, what I wanted to ask you,
> function spaces, is it still based on conflating:
>
> f : A -> B
>
> With this here:
>
> ALL(x):[x e A => f(x) e B]
>
> So by vacuously true, every function f is a
> function f : {} -> X in your world?

Where are you getting this nonsense, Jan Burse?

Dan

You can prove, do you want me to show a DC Proof?

A={} => ALL(f):ALL(x):[x e A => f(x) e B]

Thats also how I generated the contradiction
f1 = f2 & ~(f1 = f2), by using an empty "domain" A.

Still unsure what vacuously true means, Dan-O-Matik?

Dan Christensen schrieb am Dienstag, 26. Juli 2022 um 05:21:15 UTC+2:
> On Monday, July 25, 2022 at 3:12:00 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > Anyway Dan O Matik, what I wanted to ask you,
> > function spaces, is it still based on conflating:
> >
> > f : A -> B
> >
> > With this here:
> >
> > ALL(x):[x e A => f(x) e B]
> >
> > So by vacuously true, every function f is a
> > function f : {} -> X in your world?
> Where are you getting this nonsense, Jan Burse?
>
> Dan

Here is the DC Proof, every function f is a function f : {} -> X
in your world. The axiom says dom={}. The conclusion says
f : {} -> cod in the Dan-O-Matik interpretation as ALL(x):[x e {} => f(x) e cod]

and f and cod can be provably arbitrary:

1 ALL(x):~x ε dom
Axiom
[...]
20 ALL(cod):ALL(f):ALL(x):[x ε dom => f(x) ε cod]
Rem DNeg, 19

------------------------------------- begin cut here ------------------------------------------------

1 ALL(x):~x ε dom
Axiom

2 EXIST(f):EXIST(x):[x ε dom & ~f(x) ε cod]
Premise

3 EXIST(x):[x ε dom & ~g(x) ε cod]
E Spec, 2

4 y ε dom & ~g(y) ε cod
E Spec, 3

5 y ε dom
Split, 4

6 ~g(y) ε cod
Split, 4

7 ~y ε dom
U Spec, 1

8 y ε dom & ~y ε dom
Join, 5, 7

9 ~EXIST(cod):EXIST(f):EXIST(x):[x ε dom & ~f(x) ε cod]
Conclusion, 2

10 ~~ALL(cod):~EXIST(f):EXIST(x):[x ε dom & ~f(x) ε cod]
Quant, 9

11 ALL(cod):~EXIST(f):EXIST(x):[x ε dom & ~f(x) ε cod]
Rem DNeg, 10

12 ALL(cod):~~ALL(f):~EXIST(x):[x ε dom & ~f(x) ε cod]
Quant, 11

13 ALL(cod):ALL(f):~EXIST(x):[x ε dom & ~f(x) ε cod]
Rem DNeg, 12

14 ALL(cod):ALL(f):~~ALL(x):~[x ε dom & ~f(x) ε cod]
Quant, 13

15 ALL(cod):ALL(f):ALL(x):~[x ε dom & ~f(x) ε cod]
Rem DNeg, 14

16 ALL(cod):ALL(f):ALL(x):~~[~x ε dom | ~~f(x) ε cod]
DeMorgan, 15

17 ALL(cod):ALL(f):ALL(x):[~x ε dom | ~~f(x) ε cod]
Rem DNeg, 16

18 ALL(cod):ALL(f):ALL(x):[~x ε dom | f(x) ε cod]
Rem DNeg, 17

19 ALL(cod):ALL(f):ALL(x):[~~x ε dom => f(x) ε cod]
Imply-Or, 18

20 ALL(cod):ALL(f):ALL(x):[x ε dom => f(x) ε cod]
Rem DNeg, 19

------------------------------------- end cut here ------------------------------------------------

Mostowski Collapse schrieb am Dienstag, 26. Juli 2022 um 10:31:23 UTC+2:
> You can prove, do you want me to show a DC Proof?
>
> A={} => ALL(f):ALL(x):[x e A => f(x) e B]
>
> Thats also how I generated the contradiction
> f1 = f2 & ~(f1 = f2), by using an empty "domain" A.
>
> Still unsure what vacuously true means, Dan-O-Matik?
> Dan Christensen schrieb am Dienstag, 26. Juli 2022 um 05:21:15 UTC+2:
> > On Monday, July 25, 2022 at 3:12:00 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > > Anyway Dan O Matik, what I wanted to ask you,
> > > function spaces, is it still based on conflating:
> > >
> > > f : A -> B
> > >
> > > With this here:
> > >
> > > ALL(x):[x e A => f(x) e B]
> > >
> > > So by vacuously true, every function f is a
> > > function f : {} -> X in your world?
> > Where are you getting this nonsense, Jan Burse?
> >
> > Dan

Mostowski Collapse wrote:

> You can prove, do you want me to show a DC Proof?
> A={} => ALL(f):ALL(x):[x e A => f(x) e B]
>
> Dan Christensen schrieb am Dienstag, 26. Juli 2022 um 05:21:15 UTC+2:

I just saw, the english pigs are training the nazis of uKraine on their
territory. The will never was this shit from their mouth.

anti-nazis?? give me a break. The english pigs ARE the nazis.

On Tuesday, July 26, 2022 at 4:38:40 AM UTC-4, Mostowski Collapse wrote:
> Here is the DC Proof, every function f is a function f : {} -> X
> in your world. The axiom says dom={}. The conclusion says
> f : {} -> cod in the Dan-O-Matik interpretation as ALL(x):[x e {} => f(x) e cod]
>
> and f and cod can be provably arbitrary:
>

See my reply just now to similar positing at sci.logic

Dan

Vacuously TRUE is so much fun. And if stubbornness
had another name, its name would be Dan Christensen.
He wrote, in connection with his new function axiom,

which I critized already a little bit:
> Enough hand-waving

Use your function axiom with dom={} and cod={0,1},
because Function is on the wrong side in the function
axiom and because vacuously true no

Function(fun,dom,cod)

can be infered. So you cannot show f1 : {} -> X and
f2 : {} -> X equal. Starting from gra1={} and gra2={}.
But in Bourbaki f1 and f2 are the same.

Hint: Vacously True has an Annoying Property,
if A(x) is not inbabitated, from

ALL(x):[A(x) => B]

You cannot infer B. On the other hand when A(x) is
inhabitated, you can infer B.

Lets use the good ole tree tool:

(¬∃xAx ∧ ∀x(Ax→B)) → B is invalid.
https://www.umsu.de/trees/#~3~7xAx~1~6x%28Ax~5B%29~5B

(∃xAx ∧ ∀x(Ax→B)) → B is valid.
https://www.umsu.de/trees/#~7xAx~1~6x%28Ax~5B%29~5B

For the record, I was just contemplating this
monster, which is somenow not in miniscope,
has a strange logical "code smell":

ALL(dom):ALL(cod):ALL(gra):[Set(dom) & Set(cod) & Set'(gra)
=> [ALL(a1):ALL(b):[(a1,b) in gra => a1 in dom & b in cod]
& ALL(a1):[a1 in dom => EXIST(b):[b in cod & (a1,b) in gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 in dom & b1 in cod & b2 in cod
=> [(a1,b1) in gra & (a1,b2) in gra => b1=b2]]
=> EXIST(fun):ALL(a1):ALL(b):[a1 in dom & b in cod
=> Function(fun,dom,cod) <----------------------------- New
& [fun(a1)=b <=> (a1,b) in gra]]]]
Axiom

Mostowski Collapse schrieb am Mittwoch, 27. Juli 2022 um 00:52:59 UTC+2:
> Vacuously TRUE is so much fun. And if stubbornness
> had another name, its name would be Dan Christensen.
> He wrote, in connection with his new function axiom,
>
> which I critized already a little bit:
> > Enough hand-waving
>
> Use your function axiom with dom={} and cod={0,1},
> because Function is on the wrong side in the function
> axiom and because vacuously true no
>
> Function(fun,dom,cod)
>
> can be infered. So you cannot show f1 : {} -> X and
> f2 : {} -> X equal. Starting from gra1={} and gra2={}.
> But in Bourbaki f1 and f2 are the same.
>
> Hint: Vacously True has an Annoying Property,
> if A(x) is not inbabitated, from
>
> ALL(x):[A(x) => B]
>
> You cannot infer B. On the other hand when A(x) is
> inhabitated, you can infer B.
>
> Lets use the good ole tree tool:
>
> (¬∃xAx ∧ ∀x(Ax→B)) → B is invalid.
> https://www.umsu.de/trees/#~3~7xAx~1~6x%28Ax~5B%29~5B
>
> (∃xAx ∧ ∀x(Ax→B)) → B is valid.
> https://www.umsu.de/trees/#~7xAx~1~6x%28Ax~5B%29~5B

On Tuesday, July 26, 2022 at 6:52:59 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> Vacuously TRUE is so much fun. And if stubbornness
> had another name, its name would be Dan Christensen.
> He wrote, in connection with his new function axiom,
>
> which I critized already a little bit:
> > Enough hand-waving
>
> Use your function axiom with dom={} and cod={0,1},
> because Function is on the wrong side in the function
> axiom and because vacuously true no
>
> Function(fun,dom,cod)
>
> can be infered.

Only the contrary, anything whatsoever can be inferred about x if you assume that x in { }. It's called vacuous truth for a reason!

Now get busy with those proofs, Jan Burse!

Dan

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

Dan Christensen wrote:

> On Tuesday, July 26, 2022 at 6:52:59 PM UTC-4, Mostowski Collapse (Jan
>> Use your function axiom with dom={} and cod={0,1}, because Function is
>> on the wrong side in the function axiom and because vacuously true no
>> Function(fun,dom,cod) can be infered.
>
> Only the contrary, anything whatsoever can be inferred about x if you
> assume that x in { }. It's called vacuous truth for a reason!

you two nazis kiss my ass. Instead of being in hospitals, helping wounded nazis soldiers with the necessary, the khakhole khazar ugly nazi bitch is in Vogue.

Portrait of Bravery: Ukraine’s First Lady, Olena Zelenska
https://www.vogue.com/article/portrait-of-bravery-ukraines-first-lady-olena-zelenska

COVER LOOK
First lady Olena Zelenska photographed in Kyiv in July 2022. “We have no doubt we will prevail.”Photographed by Annie Leibovitz, Vogue, October 2022.

There is no script for first ladies in wartime, and so Olena Zelenska is writing her own. The wife of Ukrainian president Volodymyr Zelenskyy, a longtime comedy writer, always preferred to stay behind the scenes, while her husband, a comedian turned politician whose presidency may yet determine the fate of the free world, glowed in the limelight. But ever since Russia invaded Ukraine on February 24, Zelenska has suddenly found herself center stage in a tragedy. When I met her on a recent rainy afternoon in Kyiv, where cafés were busy even amid frequent air-raid sirens, her luminous face and green-brown eyes seemed to capture the range of emotions coursing through Ukraine today: deep sadness, flashes of dark humor, recollections of a safer, happier past, and a steely core of national pride.

“These have been the most horrible months of my life, and the lives of every Ukrainian,” she said, speaking her country’s language through a translator. “Frankly I don’t think anyone is aware of how we have managed emotionally.” What inspires her, she told me, is her fellow Ukrainians. “We’re looking forward to victory. We have no doubt we will prevail. And this is what keeps us going.”

You will not be able to prove:

Function(fun, {}, {0,1})

From gra={}. I cannot produce proofs, where I claim
there are no proofs. Whats wrong with you?

That there is no proof was demonstrated here:

> (¬∃xAx ∧ ∀x(Ax→B)) → B is invalid.
> https://www.umsu.de/trees/#~3~7xAx~1~6x%28Ax~5B%29~5B

Dan Christensen schrieb am Mittwoch, 27. Juli 2022 um 01:18:31 UTC+2:
> On Tuesday, July 26, 2022 at 6:52:59 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > Vacuously TRUE is so much fun. And if stubbornness
> > had another name, its name would be Dan Christensen.
> > He wrote, in connection with his new function axiom,
> >
> > which I critized already a little bit:
> > > Enough hand-waving
> >
> > Use your function axiom with dom={} and cod={0,1},
> > because Function is on the wrong side in the function
> > axiom and because vacuously true no
> >
> > Function(fun,dom,cod)
> >
> > can be infered.
> Only the contrary, anything whatsoever can be inferred about x if you assume that x in { }. It's called vacuous truth for a reason!
>
> Now get busy with those proofs, Jan Burse!
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

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

Apologies for the typo. It now works.

Dan

On Wednesday, July 27, 2022 at 2:51:13 AM UTC-4, Mostowski Collapse wrote:
> You will not be able to prove:
>
> Function(fun, {}, {0,1})
>
> From gra={}. I cannot produce proofs, where I claim
> there are no proofs. Whats wrong with you?
>
> That there is no proof was demonstrated here:
> > (¬∃xAx ∧ ∀x(Ax→B)) → B is invalid.
> > https://www.umsu.de/trees/#~3~7xAx~1~6x%28Ax~5B%29~5B
> Dan Christensen schrieb am Mittwoch, 27. Juli 2022 um 01:18:31 UTC+2:
> > On Tuesday, July 26, 2022 at 6:52:59 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > > Vacuously TRUE is so much fun. And if stubbornness
> > > had another name, its name would be Dan Christensen.
> > > He wrote, in connection with his new function axiom,
> > >
> > > which I critized already a little bit:
> > > > Enough hand-waving
> > >
> > > Use your function axiom with dom={} and cod={0,1},
> > > because Function is on the wrong side in the function
> > > axiom and because vacuously true no
> > >
> > > Function(fun,dom,cod)
> > >
> > > can be infered.
> > Only the contrary, anything whatsoever can be inferred about x if you assume that x in { }. It's called vacuous truth for a reason!
> >
> > Now get busy with those proofs, Jan Burse!
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

Dan Christensen wrote:

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

nothing.

On Tuesday, July 26, 2022 at 7:32:59 PM UTC-4, The same ruSSian Nazi war criminal wrote:
> Dan Christensen wrote:
>
> > On Tuesday, July 26, 2022 at 6:52:59 PM UTC-4, Mostowski Collapse (Jan
> >> Use your function axiom with dom={} and cod={0,1}, because Function is
> >> on the wrong side in the function axiom and because vacuously true no
> >> Function(fun,dom,cod) can be infered.
> >
> > Only the contrary, anything whatsoever can be inferred about x if you
> > assume that x in { }. It's called vacuous truth for a reason!

> you two nazis kiss my ass. Instead of being in hospitals, helping wounded nazis soldiers with the necessary, the khakhole khazar ugly nazi bitch is in Vogue.

Hey, Nazi boy, bomb any more schools or hospitals lately? Really, you must escape while you can. This will not end well for you

Dan Christensen wrote:

> On Tuesday, July 26, 2022 at 7:32:59 PM UTC-4, The same ruSSian lovely
> human wrote:
>> Dan Christensen wrote:
>>
>> > On Tuesday, July 26, 2022 at 6:52:59 PM UTC-4, Mostowski Collapse
>> > (Jan
>> >> Use your function axiom with dom={} and cod={0,1}, because Function
>> >> is on the wrong side in the function axiom and because vacuously
>> >> true no Function(fun,dom,cod) can be infered.
>> >
>> > Only the contrary, anything whatsoever can be inferred about x if you
>> > assume that x in { }. It's called vacuous truth for a reason!
>
>> you two nazis kiss my ass. Instead of being in hospitals, helping
>> wounded nazis soldiers with the necessary, the khakhole khazar ugly
>> nazi bitch is in Vogue.
>
> Hey, Nazi boy, bomb any more schools or hospitals lately? Really, you

the khakhole nazis are hiding in schools and hospitals, you retard. Follow
the links to the given data, to be convinced. Let's keep the proportion.
This *_ugly_khazar_bitch_* is *NOT* in hospital helping the people she
forced dying for her.

Portrait of Bravery: Ukraine’s First Lady, Olena Zelenska
https://www.vogue.com/article/portrait-of-bravery-ukraines-first-lady-
olena-zelenska

“These have been the most horrible months of my life, and the lives of
every Ukrainian,” she said, speaking her country’s language through a
translator. “Frankly I don’t think anyone is aware of how we have managed
emotionally.” What inspires her, she told me, is her fellow Ukrainians.
“We’re looking forward to victory. We have no doubt we will prevail. And
this is what keeps us going.”

Dan Christensen wrote:

> On Tuesday, July 26, 2022 at 7:32:59 PM UTC-4, The same ruSSian
> wonderful human being wrote:
>> you two nazis kiss my ass. Instead of being in hospitals, helping
>> wounded nazis soldiers with the necessary, the khakhole khazar ugly
>> nazi bitch is in Vogue.
>
> Hey, Nazi boy, bomb any more schools or hospitals lately? Really, you

let me rephrase, the khakhole nazis are hiding in schools and hospitals, you retard. Follow the links to the given data, to be convinced. Let's
keep the proportion. This *_ugly_khazar_bitch_* is *NOT* in hospital helping the people forced to die for her.

Portrait of Bravery: Ukraine’s First Lady, Olena Zelenska
https://www.vogue.com/article/portrait-of-bravery-ukraines-first-lady-olena-zelenska

“These have been the most horrible months of my life, and the lives of
every Ukrainian,” she said, speaking her country’s language through a
translator. “Frankly I don’t think anyone is aware of how we have managed
emotionally.” What inspires her, she told me, is her fellow Ukrainians.
“We’re looking forward to victory. We have no doubt we will prevail. And
this is what keeps us going.”