Dan-O-Matik boasts:

"I think Russell made a minor error here. It's nothing earthshattering.
It won't change anything. It's just a fun fact that, given there are
presently no kings of France"

So does this imply that Dan-O-Matik cannot distinguish between
material truth and formal truth?

A "fun fact" is material truth, it refers to the world. But formal truth
would be for example bachelors are not married. You don't
need to know who the bachelor is , its an universal terminological

truth. So what wanted Russell to do, something in material logic
or something in formal logic?

Corr.:

Sometimes the following terms are also used:

synthetic truth ~ material truth
analytic truth ~ formal truth

“The analytic/synthetic distinction” refers to a distinction between
two kinds of truth. Synthetic truths are true both because of what
they mean and because of the way the world is, whereas analytic
truths are true in virtue of meaning alone."
Analytic/Synthetic Distinction
https://www.oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0044.xml

So did Russell, On Denoting, write a piece in analytic philosophy
of language or a piece in synthetic philosophy of language?
And what about Aristoteles, for him the distinction between
singular and universal is a fundamental metaphysical one,
and not merely grammatical. Is metaphysical synthetical
or analytical?

Mostowski Collapse schrieb am Sonntag, 3. Oktober 2021 um 13:34:13 UTC+2:
> Dan-O-Matik boasts:
>
> "I think Russell made a minor error here. It's nothing earthshattering.
> It won't change anything. It's just a fun fact that, given there are
> presently no kings of France"
>
> So does this imply that Dan-O-Matik cannot distinguish between
> material truth and formal truth?
>
> A "fun fact" is material truth, it refers to the world. But formal truth
> would be for example bachelors are not married. You don't
> need to know who the bachelor is , its an universal terminological
>
> truth. So what wanted Russell to do, something in material logic
> or something in formal logic?

What makes Dan-O-Matik even think there is an error.
The following Russells requirement still holds:

"the King is Bald" => EXISTUNIQUE King

Because when there is no King, the Russell translation
on the left hand side becomes false, and therefore the
implication becomes true. What should be the error or

inconsistency in Russells translation and Russells requirement?
There is no error, its is self contained and consistent. Just
plug in EXIST(King & FORALL(King' => King = King') & Bald)

for "the King is Bald", and do your logic. There is no
error or inconsistency, the requirement is satisfied, since
"the King is Bald" gets anyway false.

Mostowski Collapse schrieb am Sonntag, 3. Oktober 2021 um 13:42:22 UTC+2:
> Corr.:
>
> Sometimes the following terms are also used:
>
> synthetic truth ~ material truth
> analytic truth ~ formal truth
>
> “The analytic/synthetic distinction” refers to a distinction between
> two kinds of truth. Synthetic truths are true both because of what
> they mean and because of the way the world is, whereas analytic
> truths are true in virtue of meaning alone."
> Analytic/Synthetic Distinction
> https://www.oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0044.xml
>
> So did Russell, On Denoting, write a piece in analytic philosophy
> of language or a piece in synthetic philosophy of language?
> And what about Aristoteles, for him the distinction between
>
> singular and universal is a fundamental metaphysical one,
> and not merely grammatical. Is metaphysical synthetical
> or analytical?
> Mostowski Collapse schrieb am Sonntag, 3. Oktober 2021 um 13:34:13 UTC+2:
> > Dan-O-Matik boasts:
> >
> > "I think Russell made a minor error here. It's nothing earthshattering.
> > It won't change anything. It's just a fun fact that, given there are
> > presently no kings of France"
> >
> > So does this imply that Dan-O-Matik cannot distinguish between
> > material truth and formal truth?
> >
> > A "fun fact" is material truth, it refers to the world. But formal truth
> > would be for example bachelors are not married. You don't
> > need to know who the bachelor is , its an universal terminological
> >
> > truth. So what wanted Russell to do, something in material logic
> > or something in formal logic?

Mostowski Collapse wrote:

> Dan-O-Matik boasts:
> "I think Russell made a minor error here. It's nothing earthshattering.
> It won't change anything. It's just a fun fact that, given there are
> presently no kings of France"
> So does this imply that Dan-O-Matik cannot distinguish between material
> truth and formal truth?

ohh yes, kiss my ass-

BREAKING : MEN NEED TO STAND UP NOW ! MUST SEE. - BOMBSHELL
https://www.brighteon.com/d34f4aba-0943-44ba-840a-e4edb325173b

On Sunday, October 3, 2021 at 7:42:22 AM UTC-4, Mostowski Collapse wrote:
> Corr.:
>
> Sometimes the following terms are also used:
>
> synthetic truth ~ material truth
> analytic truth ~ formal truth
>
> “The analytic/synthetic distinction” refers to a distinction between
> two kinds of truth. Synthetic truths are true both because of what
> they mean and because of the way the world is, whereas analytic
> truths are true in virtue of meaning alone."
> Analytic/Synthetic Distinction
> https://www.oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0044.xml
>
> So did Russell, On Denoting, write a piece in analytic philosophy
> of language or a piece in synthetic philosophy of language?
> And what about Aristoteles, for him the distinction between
>
> singular and universal is a fundamental metaphysical one,
> and not merely grammatical. Is metaphysical synthetical
> or analytical?
> Mostowski Collapse schrieb am Sonntag, 3. Oktober 2021 um 13:34:13 UTC+2:
> > Dan-O-Matik boasts:
> >
> > "I think Russell made a minor error here. It's nothing earthshattering.
> > It won't change anything. It's just a fun fact that, given there are
> > presently no kings of France"
> >
> > So does this imply that Dan-O-Matik cannot distinguish between
> > material truth and formal truth?
> >
> > A "fun fact" is material truth, it refers to the world. But formal truth
> > would be for example bachelors are not married. You don't
> > need to know who the bachelor is , its an universal terminological
> >
> > truth. So what wanted Russell to do, something in material logic
> > or something in formal logic?

"From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2."
- https://quod.lib.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath&cc=umhistmath&idno=aat3201.0001.001&frm=frameset&view=image&seq=401

At page 379?

This sort of truth is hollow.

Sticky language from the start: "It should be observed that the whole effect of the doctrine of types is negative: it forbids certain inferences which would otherwise be valid, but does not permit any which would otherwise be invalid. Hence we may reasonably expect that the inferences which the doctrine of types permits would remain valid even if the doctrine should be found to be invalid."

Straw man argument: all men are grass.

I'll have to try reading this more, but as to truth types versus doctrine types versus modern type safety in computers: it seems that there is a level of seriousness that is accruing even while it could be said that all values are ints.

On Sunday, October 3, 2021 at 7:34:13 AM UTC-4, Mostowski Collapse wrote:
> Dan-O-Matik boasts:
>
> "I think Russell made a minor error here. It's nothing earthshattering.
> It won't change anything. It's just a fun fact that, given there are
> presently no kings of France"
>
> So does this imply that Dan-O-Matik cannot distinguish between
> material truth and formal truth?
>

No, this implies that Jan Burse STILL doesn't get formal mathematics. If he can't count it on his fingers, it doesn't exist. ;^)

Dan

I dont think your Danish "the X is Y" has anthing to with
the Russell "the X is Y". We now have two "the X is Y":

"the X is Y"_1: Russell
"the X is Y"_2: Danish

And they disagree. So what? No error or inconsistency
is shown. WM does the same, he also invents his own
natural numbers "N", which have nothing to do with lets
say the ZFC natural numbers "N". We have also two "N":

"N"_1: ZFC Bootstrapping
"N"_2: WMs Handwaving

And they disagree. Did WM show ZFC inconsistent?

Dan Christensen schrieb am Sonntag, 3. Oktober 2021 um 17:46:05 UTC+2:
> On Sunday, October 3, 2021 at 7:34:13 AM UTC-4, Mostowski Collapse wrote:
> > Dan-O-Matik boasts:
> >
> > "I think Russell made a minor error here. It's nothing earthshattering.
> > It won't change anything. It's just a fun fact that, given there are
> > presently no kings of France"
> >
> > So does this imply that Dan-O-Matik cannot distinguish between
> > material truth and formal truth?
> >
> No, this implies that Jan Burse STILL doesn't get formal mathematics. If he can't count it on his fingers, it doesn't exist. ;^)
>
> Dan

With your synthetic facts you didn't change an analytic truth.

/***************************************************************/
/* You can never change analytic truth by additional synthetic */
/* facts analytic truth is immune, its a truth which universally */
/* quantifies over all possible additional synthetic facts. */
/***************************************************************/

You are totally out of your mind Dan. Your post is on the
same level like another crank that posts "Cantor was Wrong".
There is no "Russell is Wrong". Thats provably impossible.

Because this is provable:

/* Russels Analytic Implication */
"the X is Y"_1 (Russell) => EXISTUNIQUE(x):K(x)

It is still provable even when ~EXIST(x):K(x). Whether EXIST(x):K(x)
or ~EXIST(x):K(x) doesn't change anything in the above proof.
Its generally valid, its an analytic truth.

When ~EXIST(x):K(x) then Russels Analytic Implication becomes
vacously true, that extremly easy to verify. Because then
"the X is Y"_1 (Russell) becomes false.

Mostowski Collapse schrieb am Sonntag, 3. Oktober 2021 um 17:55:49 UTC+2:
> I dont think your Danish "the X is Y" has anthing to with
> the Russell "the X is Y". We now have two "the X is Y":
>
> "the X is Y"_1: Russell
> "the X is Y"_2: Danish
>
> And they disagree. So what? No error or inconsistency
> is shown. WM does the same, he also invents his own
> natural numbers "N", which have nothing to do with lets
> say the ZFC natural numbers "N". We have also two "N":
>
> "N"_1: ZFC Bootstrapping
> "N"_2: WMs Handwaving
>
> And they disagree. Did WM show ZFC inconsistent?
> Dan Christensen schrieb am Sonntag, 3. Oktober 2021 um 17:46:05 UTC+2:
> > On Sunday, October 3, 2021 at 7:34:13 AM UTC-4, Mostowski Collapse wrote:
> > > Dan-O-Matik boasts:
> > >
> > > "I think Russell made a minor error here. It's nothing earthshattering.
> > > It won't change anything. It's just a fun fact that, given there are
> > > presently no kings of France"
> > >
> > > So does this imply that Dan-O-Matik cannot distinguish between
> > > material truth and formal truth?
> > >
> > No, this implies that Jan Burse STILL doesn't get formal mathematics. If he can't count it on his fingers, it doesn't exist. ;^)
> >
> > Dan

Russell wants non-referring descriptions and
indefinite descriptions to render definite descriptions
false. At least when it appears in the form "the X is Y".

See also here:
https://en.wikipedia.org/wiki/On_Denoting#Illustration

Its very easy:
Case 1: non-referring description
--> "the X is Y" is false

Case 2: definite descriptions
--> "the X is Y" is "some X is Y" is "all X is Y"

Case 3: indefinite description
--> "the X is Y" is false

See also:
Bertrand Russell's theory of descriptions was initially put
forth in his 1905 essay "On Denoting", published in the journal
of philosophy Mind. Russell's theory is focused on the logical
form of expressions involving denoting phrases, which
he divides into three groups.
https://en.wikipedia.org/wiki/Theory_of_descriptions#Overview

On Sunday, October 3, 2021 at 12:18:39 PM UTC-4, Mostowski Collapse wrote:

> There is no "Russell is Wrong"

It is a minor error of little or no consequence AFAICT. Just a fun fact.

Let K and B be unary predicates such that:

K(x) = "x is a present king of France"

ALL(y):[K(a) <=> y=x] = "x is the only present king of France

B(x) = "x is bald"

We can prove ~EXIST(x):K(x) => ALL(x):[ALL(y):[K(x) <=> y=x] => B(x)]

1 ~EXIST(x):K(x)
Premise

2 ALL(y):[K(a) <=> y=a]
Premise

3 ~B(a)
Premise

4 K(a) <=> a=a
U Spec, 2

5 [K(a) => a=a] & [a=a => K(a)]
Iff-And, 4

6 a=a => K(a)
Split, 5

7 a=a
Reflex

8 K(a)
Detach, 6, 7

9 ~~ALL(x):~K(x)
Quant, 1

10 ALL(x):~K(x)
Rem DNeg, 9

11 ~K(a)
U Spec, 10

12 K(a) & ~K(a)
Join, 8, 11

13 ~~B(a)
Conclusion, 3

14 B(a)
Rem DNeg, 13

15 ALL(x):[ALL(y):[K(x) <=> y=x] => B(x)]
Conclusion, 2

16 ~EXIST(x):K(x)
=> ALL(x):[ALL(y):[K(x) <=> y=x] => B(x)]
Conclusion, 1

Dan

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

No, it will not be falsified by a member of parliament,
which is not a lorry driver. You can prove:

EXIST(x):EXIST(y):[P(x) & P(y) & x<>y] => ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]

irrespective who is a lorry driver or not. Because
ALL(y):[P(x) <=> y=x] is false, the implication =>

from your formula ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)] is
then vacously true. Dont you remember the truth table

for implication => Dan-O-Matik. Why do you talk so
much nonsense post after post?

A B A => B
0 0 1
0 1 1
1 0 0
1 1 1

A => B is automatically true, when A is true, A => B is
vacuously true when A is true. This means with your formula

ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]

This here gets true:

"The members of the parliament are lorry drivers."

Corr.:
A => B is automatically true, when A is false, A => B is
vacuously true when A is false.

You can also use this site to check that your
formula has no counter mode:

Last update: 02 Sep 2021 now supports identity
https://www.umsu.de/trees

Just enter: ∃x∃y(Px ∧ Py ∧ ¬(x = y)) → ∀x(∀y(Py ↔ x=y) → Lx)
and you get:
∃x∃y(Px ∧ (Py ∧ ¬x=y)) → ∀x(∀y(Py ↔ x=y) → Lx) is valid.

It will not show a counter model, but say valid.
A formula cannot have a counter model and be valid
at the same time. You are halucinating Dan-O-Matik.

Its enough to produce a proof, to have the assurance
that there will be no parliament lorry driver, that
would violate what is proof. Thats the whole point

of a proof. THE POINT OF A PROOF is to show
something GENERALLY VALID, which means true
in all possible state of affairs. How would

one even get the idea that a provable sentence
has a counter model. This is totally crank.

Mostowski Collapse schrieb am Dienstag, 5. Oktober 2021 um 19:20:46 UTC+2:
> No, it will not be falsified by a member of parliament,
> which is not a lorry driver. You can prove:
>
> EXIST(x):EXIST(y):[P(x) & P(y) & x<>y] => ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
>
> irrespective who is a lorry driver or not. Because
> ALL(y):[P(x) <=> y=x] is false, the implication =>
>
> from your formula ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)] is
> then vacously true. Dont you remember the truth table
>
> for implication => Dan-O-Matik. Why do you talk so
> much nonsense post after post?
>
> A B A => B
> 0 0 1
> 0 1 1
> 1 0 0
> 1 1 1
>
> A => B is automatically true, when A is true, A => B is
> vacuously true when A is true. This means with your formula
>
> ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
>
> This here gets true:
>
> "The members of the parliament are lorry drivers."

The parliament lorry driver example is there to
demonstrate that the Danish formula ALL(x):[ALL(y):[P(y)
<=> x=y] => L(x)] does not adhere Russells Requirements

for non-referring descriptions, but also for indefinite descriptions:

Mostowski Collapse wrote:> Its very easy:
> Case 1: non-referring description
> --> "the X is Y" is false
>
> Case 2: definite descriptions
> --> "the X is Y" is "some X is Y" is "all X is Y"
>
> Case 3: indefinite description
> --> "the X is Y" is false

The Danish formula ALL(x):[ALL(y):[P(y) <=> x=y] => L(x)]
does not provide "the_single", it does not only satisfy the
Russell requirements for case 1, it also does not satisfy the

Russell requirements for case 3. Both case 1 and case 3
do get true, while Russell wants them to get false. But
the parliament example is not optimal, since

"the_single" might not be the only reading, it might also
be something from the camp "the_plural". A better example
would be for example something from mathematics,

like for example:

"The square root of 2 is positive"

The square root of can be either +1.4142... or -1.4142...
and a description for the square root would be x^2 = 2.
So what is the truth value of the sentence when

we think that the intention of the sentence is a "the_singular"?

Mostowski Collapse schrieb am Dienstag, 5. Oktober 2021 um 19:29:55 UTC+2:
> Corr.:
> A => B is automatically true, when A is false, A => B is
> vacuously true when A is false.
>
> You can also use this site to check that your
> formula has no counter mode:
>
> Last update: 02 Sep 2021 now supports identity
> https://www.umsu.de/trees
>
> Just enter: ∃x∃y(Px ∧ Py ∧ ¬(x = y)) → ∀x(∀y(Py ↔ x=y) → Lx)
> and you get:
> ∃x∃y(Px ∧ (Py ∧ ¬x=y)) → ∀x(∀y(Py ↔ x=y) → Lx) is valid.
>
> It will not show a counter model, but say valid.
> A formula cannot have a counter model and be valid
> at the same time. You are halucinating Dan-O-Matik.
>
> Its enough to produce a proof, to have the assurance
> that there will be no parliament lorry driver, that
> would violate what is proof. Thats the whole point
>
> of a proof. THE POINT OF A PROOF is to show
> something GENERALLY VALID, which means true
> in all possible state of affairs. How would
>
> one even get the idea that a provable sentence
> has a counter model. This is totally crank.
> Mostowski Collapse schrieb am Dienstag, 5. Oktober 2021 um 19:20:46 UTC+2:
> > No, it will not be falsified by a member of parliament,
> > which is not a lorry driver. You can prove:
> >
> > EXIST(x):EXIST(y):[P(x) & P(y) & x<>y] => ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
> >
> > irrespective who is a lorry driver or not. Because
> > ALL(y):[P(x) <=> y=x] is false, the implication =>
> >
> > from your formula ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)] is
> > then vacously true. Dont you remember the truth table
> >
> > for implication => Dan-O-Matik. Why do you talk so
> > much nonsense post after post?
> >
> > A B A => B
> > 0 0 1
> > 0 1 1
> > 1 0 0
> > 1 1 1
> >
> > A => B is automatically true, when A is true, A => B is
> > vacuously true when A is true. This means with your formula
> >
> > ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
> >
> > This here gets true:
> >
> > "The members of the parliament are lorry drivers."

On Tuesday, October 5, 2021 at 1:20:46 PM UTC-4, Mostowski Collapse wrote:
> No, it will not be falsified by a member of parliament,
> which is not a lorry driver.

ALL(a):[P(a) => L(a)] would be falsified for P(x) and ~L(x) for some x (a counter-example).

Most parliaments have several different members.

> You can prove:
>
> EXIST(x):EXIST(y):[P(x) & P(y) & x<>y] => ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
>

Makes no sense.

Dan

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

Why would you consider ALL(a):[P(a) => L(a)], when I
said, in the Danish interpretetation ALL(x):[ALL(y):[P(x) <=>
y=x] => L(x)] this sentence:

The parliament members are lorry drivers.

Is true, irrespective whether each of them drives a lorry
or not. You then say, no it has a countermodel, it
can be falsified.

You only falsified ALL(a):[P(a) => L(a)],, but you
didn't falsify ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)].
You only changed topic, but you didn't falsify

any of my claims.

Dan Christensen schrieb am Dienstag, 5. Oktober 2021 um 20:46:11 UTC+2:
> On Tuesday, October 5, 2021 at 1:20:46 PM UTC-4, Mostowski Collapse wrote:
> > No, it will not be falsified by a member of parliament,
> > which is not a lorry driver.
> ALL(a):[P(a) => L(a)] would be falsified for P(x) and ~L(x) for some x (a counter-example).
>
> Most parliaments have several different members.
> > You can prove:
> >
> > EXIST(x):EXIST(y):[P(x) & P(y) & x<>y] => ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
> >
> Makes no sense.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Tuesday, October 5, 2021 at 5:01:44 PM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Dienstag, 5. Oktober 2021 um 20:46:11 UTC+2:
> > On Tuesday, October 5, 2021 at 1:20:46 PM UTC-4, Mostowski Collapse wrote:
> > > No, it will not be falsified by a member of parliament,
> > > which is not a lorry driver.
> > ALL(a):[P(a) => L(a)] would be falsified for P(x) and ~L(x) for some x (a counter-example).
> >
> > Most parliaments have several different members.
> > > You can prove:
> > >
> > > EXIST(x):EXIST(y):[P(x) & P(y) & x<>y] => ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)]
> > >
> > Makes no sense.

> Why would you consider ALL(a):[P(a) => L(a)], when I
> said, in the interpretetation ALL(x):[ALL(y):[P(x) <=>
> y=x] => L(x)] this sentence:
>
> The parliament members are lorry drivers.
>

Should be: The only member of parliament is a lorry driver.

> Is true, irrespective whether each of them drives a lorry
> or not. You then say, no it has a countermodel, it
> can be falsified.
>
> You only falsified ALL(a):[P(a) => L(a)],,

∀x(Px → Lx) is invalid.
Countermodel:
Domain: { 0 }
P: { 0 }
L: { }
https://www.umsu.de/trees/#~6x(Px~5Lx)

> but you
> didn't falsify ALL(x):[ALL(y):[P(x) <=> y=x] => L(x)].

"∀x(∀y(Px ↔ y=x) → Lx) is invalid."

Countermodel:
Domain: { 0 }
P: { 0 }
L: { }
https://www.umsu.de/trees/#~6x(~6y(Px~4y=x)~5Lx)

Dan

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

Dan-O-Matik wrote, on sci.math:
> Trolls like AP, JG and WM having ZERO impact in the classroom :^)

Which is funny, because Slow-O-Matik can still not
understand the analytic truth Russell was after.

LMAO!

On Monday, October 25, 2021 at 9:41:50 AM UTC-4, Mostowski Collapse wrote:
> Dan-O-Matik wrote, on sci.math:
> > Trolls like AP, JG and WM having ZERO impact in the classroom :^)
>
> Which is funny, because Slow-O-Matik can still not
> understand the analytic truth Russell was after.
>

Poor old Jan Burse still doesn't understand why Russell was so fixated on the present king of France. Hint: Because there is NO present king of France.. I think the last one literally lost his head centuries ago. It then becomes an exercise in vacuous truth. Jan Burse still doesn't get that. Oh, well...

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 other post. Russell did surely not deal with Aristoteles
square of opposition, which has only universal "all X is Y"
and particular statements "some X is Y".

He was interested in singular statements "the X is Y". Aristoteles
also wrote about singular statements. But the classical square
of opposition doesn't contain them.

But you can draw a kind of "square" for Russells definite
description. Russell wanted:

"the X is Y" ----- Contrary ----- "the X is ~Y"

'Contrary' (medieval: contrariae) statements, are such that the both
statements cannot at the same time be true.

So Russell wanted:

~("the X is Y" & "the X is ~Y")

But "some X is Y" and "some X is ~Y" are not contrary.

Dan Christensen schrieb am Montag, 25. Oktober 2021 um 17:45:43 UTC+2:
> On Monday, October 25, 2021 at 9:41:50 AM UTC-4, Mostowski Collapse wrote:
> > Dan-O-Matik wrote, on sci.math:
> > > Trolls like AP, JG and WM having ZERO impact in the classroom :^)
> >
> > Which is funny, because Slow-O-Matik can still not
> > understand the analytic truth Russell was after.
> >
> Poor old Jan Burse still doesn't understand why Russell was so fixated on the present king of France. Hint: Because there is NO present king of France. I think the last one literally lost his head centuries ago. It then becomes an exercise in vacuous truth. Jan Burse still doesn't get that. Oh, well...
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

There is even no slippery road, to distinguish between modern
and non-modern square of opposition, since the countermodel
to "some X is Y" and "some X is ~Y" are contrary,

doesn't need vacous X. The non-modern square of opposition
might not see that vacous, since it might associate with some of
term logic types some existential import.

But we don't need vacous to see that "some X is Y" doesn't
work for the Russell "square":

"the X is Y" ----- Contrary ----- "the X is ~Y"

Mostowski Collapse schrieb:
> See my other post. Russell did surely not deal with Aristoteles
> square of opposition, which has only universal "all X is Y"
> and particular statements "some X is Y".
>
> He was interested in singular statements "the X is Y". Aristoteles
> also wrote about singular statements. But the classical square
> of opposition doesn't contain them.
>
> But you can draw a kind of "square" for Russells definite
> description. Russell wanted:
>
> "the X is Y" ----- Contrary ----- "the X is ~Y"
>
> 'Contrary' (medieval: contrariae) statements, are such that the both
> statements cannot at the same time be true.
>
> So Russell wanted:
>
> ~("the X is Y" & "the X is ~Y")
>
> But "some X is Y" and "some X is ~Y" are not contrary.
>
> Dan Christensen schrieb am Montag, 25. Oktober 2021 um 17:45:43 UTC+2:
>> On Monday, October 25, 2021 at 9:41:50 AM UTC-4, Mostowski Collapse wrote:
>>> Dan-O-Matik wrote, on sci.math:
>>>> Trolls like AP, JG and WM having ZERO impact in the classroom :^)
>>>
>>> Which is funny, because Slow-O-Matik can still not
>>> understand the analytic truth Russell was after.
>>>
>> Poor old Jan Burse still doesn't understand why Russell was so fixated on the present king of France. Hint: Because there is NO present king of France. I think the last one literally lost his head centuries ago. It then becomes an exercise in vacuous truth. Jan Burse still doesn't get that. Oh, well...
>> 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 11:57:54 AM UTC-4, Mostowski Collapse wrote:
> See my other post. Russell did surely not deal with Aristoteles
> square of opposition, which has only universal "all X is Y"
> and particular statements "some X is Y".
>
> He was interested in singular statements "the X is Y". Aristoteles
> also wrote about singular statements. But the classical square
> of opposition doesn't contain them.
>
> But you can draw a kind of "square" for Russells definite
> description. Russell wanted:
>
> "the X is Y" ----- Contrary ----- "the X is ~Y"
>

[snip]

I have already formally proven this trivial result using DC Proof. Don't pretend you haven't seen 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

Why do you call it trivial? Doesn't make any sense. A proof is
trivial if its one or two lines. You needed much more lines.

Whats wrong with you? Still mental problems with Russell?

Dan Christensen schrieb:
> On Monday, October 25, 2021 at 11:57:54 AM UTC-4, Mostowski Collapse wrote:
>> See my other post. Russell did surely not deal with Aristoteles
>> square of opposition, which has only universal "all X is Y"
>> and particular statements "some X is Y".
>>
>> He was interested in singular statements "the X is Y". Aristoteles
>> also wrote about singular statements. But the classical square
>> of opposition doesn't contain them.
>>
>> But you can draw a kind of "square" for Russells definite
>> description. Russell wanted:
>>
>> "the X is Y" ----- Contrary ----- "the X is ~Y"
>>
>
> [snip]
>
> I have already formally proven this trivial result using DC Proof. Don't pretend you haven't seen 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 12:21:55 PM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb:
> > On Monday, October 25, 2021 at 11:57:54 AM UTC-4, Mostowski Collapse wrote:
> >> See my other post. Russell did surely not deal with Aristoteles
> >> square of opposition, which has only universal "all X is Y"
> >> and particular statements "some X is Y".
> >>
> >> He was interested in singular statements "the X is Y". Aristoteles
> >> also wrote about singular statements. But the classical square
> >> of opposition doesn't contain them.
> >>
> >> But you can draw a kind of "square" for Russells definite
> >> description. Russell wanted:
> >>
> >> "the X is Y" ----- Contrary ----- "the X is ~Y"
> >>
> >
> > [snip]
> >
> > I have already formally proven this trivial result using DC Proof. Don't pretend you haven't seen it, Jan Burse!
> >

> Why do you call it trivial? Doesn't make any sense. A proof is
> trivial if its one or two lines. You needed much more lines.
>

OMG! Perhaps you haven't worked much with formal proofs, but it is a straight-forward, 21 line proof by contradiction is trivial.

Here it is again:

> Why do you call it trivial? Doesn't make any sense. A proof is
> trivial if its one or two lines. You needed much more lines.
>

OMG! Perhaps you haven't worked much with formal proofs, but it is a straight-forward, 21 line proof by contradiction is trivial.

1 EXIST(a):[ALL(b):[X(b) <=> b=a] & Y(a)]
& EXIST(a):[ALL(b):[X(b) <=> b=a] & ~Y(a)]
Premise

2 EXIST(a):[ALL(b):[X(b) <=> b=a] & Y(a)]
Split, 1

3 EXIST(a):[ALL(b):[X(b) <=> b=a] & ~Y(a)]
Split, 1

4 ALL(b):[X(b) <=> b=t] & Y(t)
E Spec, 2

5 ALL(b):[X(b) <=> b=t]
Split, 4

6 Y(t)
Split, 4

11 X(t)
Detach, 9, 10

12 ALL(b):[X(b) <=> b=u] & ~Y(u)
E Spec, 3

13 ALL(b):[X(b) <=> b=u]
Split, 12

14 ~Y(u)
Split, 12

15 X(t) <=> t=u
U Spec, 13

16 [X(t) => t=u] & [t=u => X(t)]
Iff-And, 15

17 X(t) => t=u
Split, 16

18 t=u
Detach, 17, 11

19 ~Y(t)
Substitute, 18, 14

20 Y(t) & ~Y(t)
Join, 6, 19

21 ~[EXIST(a):[ALL(b):[X(b) <=> b=a] & Y(a)]
& EXIST(a):[ALL(b):[X(b) <=> b=a] & ~Y(a)]]
Conclusion, 1

Trivial.

Dan

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

But the your vacous truth proof is also trivial. Because you can also
write down the proof and at the end write Trivial.

.... bla bla ...

Trivial

Thats not a very definite criteria for Trivial, having written Trivial
at the end of a proof. You are more a crank than

Archimedes Plutonium.

Dan Christensen schrieb am Montag, 25. Oktober 2021 um 18:45:02 UTC+2:
> On Monday, October 25, 2021 at 12:21:55 PM UTC-4, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb:
> > > On Monday, October 25, 2021 at 11:57:54 AM UTC-4, Mostowski Collapse wrote:
> > >> See my other post. Russell did surely not deal with Aristoteles
> > >> square of opposition, which has only universal "all X is Y"
> > >> and particular statements "some X is Y".
> > >>
> > >> He was interested in singular statements "the X is Y". Aristoteles
> > >> also wrote about singular statements. But the classical square
> > >> of opposition doesn't contain them.
> > >>
> > >> But you can draw a kind of "square" for Russells definite
> > >> description. Russell wanted:
> > >>
> > >> "the X is Y" ----- Contrary ----- "the X is ~Y"
> > >>
> > >
> > > [snip]
> > >
> > > I have already formally proven this trivial result using DC Proof. Don't pretend you haven't seen it, Jan Burse!
> > >
> > Why do you call it trivial? Doesn't make any sense. A proof is
> > trivial if its one or two lines. You needed much more lines.
> >
> OMG! Perhaps you haven't worked much with formal proofs, but it is a straight-forward, 21 line proof by contradiction is trivial.
>
> Here it is again:
> > Why do you call it trivial? Doesn't make any sense. A proof is
> > trivial if its one or two lines. You needed much more lines.
> >
> OMG! Perhaps you haven't worked much with formal proofs, but it is a straight-forward, 21 line proof by contradiction is trivial.
>
> 1 EXIST(a):[ALL(b):[X(b) <=> b=a] & Y(a)]
> & EXIST(a):[ALL(b):[X(b) <=> b=a] & ~Y(a)]
> Premise
>
> 2 EXIST(a):[ALL(b):[X(b) <=> b=a] & Y(a)]
> Split, 1
>
> 3 EXIST(a):[ALL(b):[X(b) <=> b=a] & ~Y(a)]
> Split, 1
>
> 4 ALL(b):[X(b) <=> b=t] & Y(t)
> E Spec, 2
>
> 5 ALL(b):[X(b) <=> b=t]
> Split, 4
>
> 6 Y(t)
> Split, 4
>
> 11 X(t)
> Detach, 9, 10
>
> 12 ALL(b):[X(b) <=> b=u] & ~Y(u)
> E Spec, 3
>
> 13 ALL(b):[X(b) <=> b=u]
> Split, 12
>
> 14 ~Y(u)
> Split, 12
>
> 15 X(t) <=> t=u
> U Spec, 13
>
> 16 [X(t) => t=u] & [t=u => X(t)]
> Iff-And, 15
>
> 17 X(t) => t=u
> Split, 16
>
> 18 t=u
> Detach, 17, 11
>
> 19 ~Y(t)
> Substitute, 18, 14
>
> 20 Y(t) & ~Y(t)
> Join, 6, 19
>
> 21 ~[EXIST(a):[ALL(b):[X(b) <=> b=a] & Y(a)]
> & EXIST(a):[ALL(b):[X(b) <=> b=a] & ~Y(a)]]
> Conclusion, 1
>
> Trivial.
> 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 2:22:30 PM UTC-4, Mostowski Collapse wrote:
> But the your vacous truth proof is also trivial. Because you can also
> write down the proof and at the end write Trivial.
>
> ... bla bla ...
>
> Trivial
>
> Thats not a very definite criteria for Trivial, having written Trivial
> at the end of a proof.

Grasping at straws, eh, Jan Burse? Looks good on you! (HA, HA, HA!!!)

Unless you have something new and interesting to add to the discussion, do not expect a reply from me on this matter.

Dan