This a nice glitch. What is a value? Well a value are
objects from the domain of discourse. Do we see
some Truth Values in this modelling:

[a e t | a e f | a e m]
& ~[a e t & a e f]
& ~[a e t & a e m]
& ~[a e f & a e m]
https://www.dcproof.com/LiarParadoxResolution.htm

The answer is no. It only modells sentences from the set s,
that share the same Truth Value. But the object of a Truth Value
is nowhere modelled.

Can we fix that?

Dan Christensen is always talking about "indeterminate truth value"
and stuff. But he has nowhere truth values. Neither classical ones,
nor non-classical ones. What would be a fix?

Here is a solution with truth values:

49 ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
Rem DNeg, 48

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

1 ALL(x):[Value(x) <=> x=f | x=t | x=u]
Axiom

2 ~f=t
Axiom

3 ~f=u
Axiom

4 ~t=u
Axiom

5 ~ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
Premise

6 ~~EXIST(x):~[Value(x) => [[x=t <=> x=f] => x=u]]
Quant, 5

7 EXIST(x):~[Value(x) => [[x=t <=> x=f] => x=u]]
Rem DNeg, 6

8 ~[Value(w) => [[w=t <=> w=f] => w=u]]
E Spec, 7

9 ~~[Value(w) & ~[[w=t <=> w=f] => w=u]]
Imply-And, 8

10 Value(w) & ~[[w=t <=> w=f] => w=u]
Rem DNeg, 9

11 Value(w)
Split, 10

12 ~[[w=t <=> w=f] => w=u]
Split, 10

13 ~~[[w=t <=> w=f] & ~w=u]
Imply-And, 12

14 [w=t <=> w=f] & ~w=u
Rem DNeg, 13

15 w=t <=> w=f
Split, 14

16 ~w=u
Split, 14

17 [w=t => w=f] & [w=f => w=t]
Iff-And, 15

18 w=t => w=f
Split, 17

19 w=f => w=t
Split, 17

20 Value(w) <=> w=f | w=t | w=u
U Spec, 1

21 [Value(w) => w=f | w=t | w=u]
& [w=f | w=t | w=u => Value(w)]
Iff-And, 20

22 Value(w) => w=f | w=t | w=u
Split, 21

23 w=f | w=t | w=u => Value(w)
Split, 21

24 w=f | w=t | w=u
Detach, 22, 11

25 ~[w=f | w=t] => w=u
Imply-Or, 24

26 ~w=u => ~~[w=f | w=t]
Contra, 25

27 ~w=u => w=f | w=t
Rem DNeg, 26

28 w=f | w=t
Detach, 27, 16

29 ~w=f => w=t
Imply-Or, 28

30 ~w=f => ~w=t
Contra, 18

31 ~w=f
Premise

32 w=t
Detach, 29, 31

33 ~w=t
Detach, 30, 31

34 w=t & ~w=t
Join, 32, 33

35 ~~w=f
4 Conclusion, 31

36 w=f
Rem DNeg, 35

37 ~w=t => ~~w=f
Contra, 29

38 ~w=t => w=f
Rem DNeg, 37

39 ~w=t => ~w=f
Contra, 19

40 ~w=t
Premise

41 w=f
Detach, 38, 40

42 ~w=f
Detach, 39, 40

43 w=f & ~w=f
Join, 41, 42

44 ~~w=t
4 Conclusion, 40

45 w=t
Rem DNeg, 44

46 f=t
Substitute, 36, 45

47 f=t & ~f=t
Join, 46, 2

48 ~~ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
4 Conclusion, 5

49 ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
Rem DNeg, 48

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

Mild Shock schrieb am Mittwoch, 20. September 2023 um 20:57:02 UTC+2:
> This a nice glitch. What is a value? Well a value are
> objects from the domain of discourse. Do we see
> some Truth Values in this modelling:
>
> [a e t | a e f | a e m]
> & ~[a e t & a e f]
> & ~[a e t & a e m]
> & ~[a e f & a e m]
> https://www.dcproof.com/LiarParadoxResolution.htm
>
> The answer is no. It only modells sentences from the set s,
> that share the same Truth Value. But the object of a Truth Value
> is nowhere modelled.
>
> Can we fix that?
>
> Dan Christensen is always talking about "indeterminate truth value"
> and stuff. But he has nowhere truth values. Neither classical ones,
> nor non-classical ones. What would be a fix?

On Wednesday, September 20, 2023 at 10:12:12 PM UTC+3, Mild Shock wrote:
> Here is a solution with truth values:
>
> 49 ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
> Rem DNeg, 48
>
> ------------------------------------ begin proof --------------------------------------
>
> 1 ALL(x):[Value(x) <=> x=f | x=t | x=u]
> Axiom
>
> 2 ~f=t
> Axiom
>
> 3 ~f=u
> Axiom
>
> 4 ~t=u
> Axiom
>
> 5 ~ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
> Premise
>
> 6 ~~EXIST(x):~[Value(x) => [[x=t <=> x=f] => x=u]]
> Quant, 5
>
> 7 EXIST(x):~[Value(x) => [[x=t <=> x=f] => x=u]]
> Rem DNeg, 6
>
> 8 ~[Value(w) => [[w=t <=> w=f] => w=u]]
> E Spec, 7
>
> 9 ~~[Value(w) & ~[[w=t <=> w=f] => w=u]]
> Imply-And, 8
>
> 10 Value(w) & ~[[w=t <=> w=f] => w=u]
> Rem DNeg, 9
>
> 11 Value(w)
> Split, 10
>
> 12 ~[[w=t <=> w=f] => w=u]
> Split, 10
>
> 13 ~~[[w=t <=> w=f] & ~w=u]
> Imply-And, 12
>
> 14 [w=t <=> w=f] & ~w=u
> Rem DNeg, 13
>
> 15 w=t <=> w=f
> Split, 14
>
> 16 ~w=u
> Split, 14
>
> 17 [w=t => w=f] & [w=f => w=t]
> Iff-And, 15
>
> 18 w=t => w=f
> Split, 17
>
> 19 w=f => w=t
> Split, 17
>
> 20 Value(w) <=> w=f | w=t | w=u
> U Spec, 1
>
> 21 [Value(w) => w=f | w=t | w=u]
> & [w=f | w=t | w=u => Value(w)]
> Iff-And, 20
>
> 22 Value(w) => w=f | w=t | w=u
> Split, 21
>
> 23 w=f | w=t | w=u => Value(w)
> Split, 21
>
> 24 w=f | w=t | w=u
> Detach, 22, 11
>
> 25 ~[w=f | w=t] => w=u
> Imply-Or, 24
>
> 26 ~w=u => ~~[w=f | w=t]
> Contra, 25
>
> 27 ~w=u => w=f | w=t
> Rem DNeg, 26
>
> 28 w=f | w=t
> Detach, 27, 16
>
> 29 ~w=f => w=t
> Imply-Or, 28
>
> 30 ~w=f => ~w=t
> Contra, 18
>
> 31 ~w=f
> Premise
>
> 32 w=t
> Detach, 29, 31
>
> 33 ~w=t
> Detach, 30, 31
>
> 34 w=t & ~w=t
> Join, 32, 33
>
> 35 ~~w=f
> 4 Conclusion, 31
>
> 36 w=f
> Rem DNeg, 35
>
> 37 ~w=t => ~~w=f
> Contra, 29
>
> 38 ~w=t => w=f
> Rem DNeg, 37
>
> 39 ~w=t => ~w=f
> Contra, 19
>
> 40 ~w=t
> Premise
>
> 41 w=f
> Detach, 38, 40
>
> 42 ~w=f
> Detach, 39, 40
>
> 43 w=f & ~w=f
> Join, 41, 42
>
> 44 ~~w=t
> 4 Conclusion, 40
>
> 45 w=t
> Rem DNeg, 44
>
> 46 f=t
> Substitute, 36, 45
>
> 47 f=t & ~f=t
> Join, 46, 2
>
> 48 ~~ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
> 4 Conclusion, 5
>
> 49 ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
> Rem DNeg, 48
>
> ------------------------------------ end proof --------------------------------------
> Mild Shock schrieb am Mittwoch, 20. September 2023 um 20:57:02 UTC+2:
> > This a nice glitch. What is a value? Well a value are
> > objects from the domain of discourse. Do we see
> > some Truth Values in this modelling:
> >
> > [a e t | a e f | a e m]
> > & ~[a e t & a e f]
> > & ~[a e t & a e m]
> > & ~[a e f & a e m]
> > https://www.dcproof.com/LiarParadoxResolution.htm
> >
> > The answer is no. It only modells sentences from the set s,
> > that share the same Truth Value. But the object of a Truth Value
> > is nowhere modelled.
> >
> > Can we fix that?
> >
> > Dan Christensen is always talking about "indeterminate truth value"
> > and stuff. But he has nowhere truth values. Neither classical ones,
> > nor non-classical ones. What would be a fix?

Nither you nor Dan C have any meaningful logic, I'm not sorry to say that both of you are well-known Trolls in science & mathematics as well

I have examined both of your mental abilities, where I realized that both of you are suffering from deeply rooted & incurable mental retardation where you don't realize it, mainly due to your false global education, FOR SURE

The time had passed away to recover & be quite normal creauters

However, you aren't alone in this astray boat but a common & very general case among the vast majorities of educated humans, where they are fixed mind people

Hard luck for your unlimited ignorance strictly in your own areas of specializations

But how do you know 🤔?

BKK

Thats a funny find that these two are logically equivalent:

a e t <=> a e f
a e t & ~a e f <=> ~a e t & a e f

Confirmed by Wolfgang Schwarz tree tool:

(A↔B) ↔ ((A∧¬B) ↔ (¬A∧B)) is valid.
https://www.umsu.de/trees/#(A~4B)~4(A~1~3B~4~3A~1B)

Now we can reveal the typical models, how equivalence classes are formed:

Model 3-
~a e t & ~a e f ~~> x = u
a e t & ~a e f ~~> x = t
~a e t & a e f ~~> x = f

Model 3+
a e t & ~a e f ~~> x = t
~a e t & a e f ~~> x = f
a e t & a e f ~~> x = u

Model 4
~a e t & ~a e f ~~> x = u
a e t & ~a e f ~~> x = t
~a e t & a e f ~~> x = f
a e t & a e f ~~> x = u

But then model 3+ typically uses another name than x=u, rather x=p.
And model 4 typically uses two names x=u and x=p. But it works also
with using one name x=u.

On Wednesday, September 20, 2023 at 3:48:39 PM UTC-4, bassam karzeddin wrote:

> Nither you nor Dan C have any meaningful logic, I'm not sorry to say that both of you are well-known Trolls in science & mathematics as well

Speaking of trolls...

From Psycho Troll BKK who also wrote here:

“Those many challenges of mine (in my posts) weren't actually designed for human beings, but for the future artificial beings that would certainly replace them not far away from now, for sure.”
-- BKK, Dec. 6, 2017

"The Devils deeds that are strictly and basically sourced from mathematicians like humans, FOR SURE!"
-- BKK, June 11, 2020

“You know certainly that I'm the man, and more specially the KING who is going to upside down most of your current false mathematics for all future generations.”
-- BKK, Nov. 22, 2018

“Despite thousands of years of continuous juggling and false definitions of what is truly the real number, they [us carbon-based lifeforms?] truly don't want to understand it as was discovered strictly by the *KING* [BKK Himself!]”
-- BKK, Nov. 28, 2019

“I don't believe even in one being a number”
-- BKK, Dec. 31, 2019

Math failure, BKK, doesn't believe in negative numbers, zero, one or numbers like pi and root 2. He doesn't even believe in 40 degree angles or circles. Simple speed-distance-time problems seem to be impossible for him. Really!

Needless to say his own goofy little system is getting nowhere and never will. As such he is insanely jealous of wildly successful mainstream mathematics. He seems to believe these super-intelligent artificial beings of his will somehow be enlisting his aid to "reform" mathematics worldwide when they take over the planet in the near future. He is truly delusional.

Dan

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

You can use this equivalence relation:

a ~ b :<=> [[a e t & b e t] v [a e f & b e f] v [a e m & b e m]]

To get equivalence classes:

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

The equivalence classes are the truth values.
Thats missing in your take. If you then further
abstract, you get this nifty result:

49 ALL(x):[Value(x) => [[x=t <=> x=f] => x=u]]
Rem DNeg, 48

Dan Christensen schrieb:
> The set s is comprised of 3 mutually disjoint sets t, f and m
> which models my classification of sentences of natural language
> true sentences, false sentences and those of indeterminate
> truth value respectively.

On Thursday, September 21, 2023 at 4:18:48 AM UTC-4, Mild Shock wrote:
> You can use this equivalence relation:
>
> a ~ b :<=> [[a e t & b e t] v [a e f & b e f] v [a e m & b e m]]
>
[snip]

Thanks, but no thanks. I will stick to the simpler trichotomy structure described in my proof. It actually makes sense.
https://dcproof.com/LiarParadoxV2.htm

Dan

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