RESOLUTION OF EPIMENIDES' PARADOX

The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).

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

Here, we show that, logically, this statement must not be true. (~True(x))

Using the following predicates:

Stmt(x) = x is a statement
True(x) = x is true
Cretan(x) = x is a Cretan
Said(x,y) = x said y

AXIOMS

1. Stmt(x)
Axiom

2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
Axiom

3. Cretan(epi)
Axiom

4. Said(epi,x)
Axiom

Suppose to contrary...

5. True(x)
Premise

6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
& [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
Iff-And, 2

7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
Split, 6

8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
Detach, 7, 5

9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
U Spec, 8

10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
U Spec, 9

11. Cretan(epi) & Stmt(x)
Join, 3, 1

12. Cretan(epi) & Stmt(x) & Said(epi,x)
Join, 11, 4

13. ~True(x)
Detach, 10, 12

14. True(x) & ~True(x)
Join, 5, 13

By contradiction...

15. ~True(x)
Conclusion, 5

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, April 17, 2023 at 3:12:50 AM UTC+10, Dan Christensen wrote:
> RESOLUTION OF EPIMENIDES' PARADOX
>
> The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
>
> https://en.wikipedia.org/wiki/Epimenides_paradox
>
> Here, we show that, logically, this statement must not be true. (~True(x))
>
> Using the following predicates:
>
> Stmt(x) = x is a statement
> True(x) = x is true
> Cretan(x) = x is a Cretan
> Said(x,y) = x said y
>
>
> AXIOMS
>
> 1. Stmt(x)
> Axiom
>
> 2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Axiom
>
> 3. Cretan(epi)
> Axiom
>
> 4. Said(epi,x)
> Axiom
>
> Suppose to contrary...
>
> 5. True(x)
> Premise
>
> 6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
> & [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
> Iff-And, 2
>
> 7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Split, 6
>
> 8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Detach, 7, 5
>
> 9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
> U Spec, 8
>
> 10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
> U Spec, 9
>
> 11. Cretan(epi) & Stmt(x)
> Join, 3, 1
>
> 12. Cretan(epi) & Stmt(x) & Said(epi,x)
> Join, 11, 4
>
> 13. ~True(x)
> Detach, 10, 12
>
> 14. True(x) & ~True(x)
> Join, 5, 13
>
> By contradiction...
>
> 15. ~True(x)
> Conclusion, 5
>
> Dan
>

person said X
is like
theory proves X

T1 said statement

T1 |- statement

Useful for determining WHICH 1 IS RIGHT

On Monday, April 17, 2023 at 8:56:44 AM UTC+10, Graham Cooper wrote:
> On Monday, April 17, 2023 at 3:12:50 AM UTC+10, Dan Christensen wrote:
> > RESOLUTION OF EPIMENIDES' PARADOX
> >
> > The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
> >
> > https://en.wikipedia.org/wiki/Epimenides_paradox
> >
> > Here, we show that, logically, this statement must not be true. (~True(x))
> >
> > Using the following predicates:
> >
> > Stmt(x) = x is a statement
> > True(x) = x is true
> > Cretan(x) = x is a Cretan
> > Said(x,y) = x said y

Reminds me of some theorem proving I did 10 years ago

I defined TRUE(x)

as something said by a TRUTH-TELLER

http://new-math.com/TRUTHER-LIAR.png

On Sunday, April 16, 2023 at 1:12:50 PM UTC-4, Dan Christensen wrote:
> RESOLUTION OF EPIMENIDES' PARADOX
>
> The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
>
> https://en.wikipedia.org/wiki/Epimenides_paradox
>
> Here, we show that, logically, this statement must not be true. (~True(x))
>
> Using the following predicates:
>
> Stmt(x) = x is a statement
> True(x) = x is true
> Cretan(x) = x is a Cretan
> Said(x,y) = x said y
>
>
> AXIOMS
>
> 1. Stmt(x)
> Axiom
>
> 2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Axiom
>
> 3. Cretan(epi)
> Axiom
>
> 4. Said(epi,x)
> Axiom
>
> Suppose to contrary...
>
> 5. True(x)
> Premise
>
> 6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
> & [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
> Iff-And, 2
>
> 7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Split, 6
>
> 8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Detach, 7, 5
>
> 9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
> U Spec, 8
>
> 10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
> U Spec, 9
>
> 11. Cretan(epi) & Stmt(x)
> Join, 3, 1
>
> 12. Cretan(epi) & Stmt(x) & Said(epi,x)
> Join, 11, 4
>
> 13. ~True(x)
> Detach, 10, 12
>
> 14. True(x) & ~True(x)
> Join, 5, 13
>
> By contradiction...
>
> 15. ~True(x)
> Conclusion, 5
>

So, at least one Cretan once told the truth. Having some doubts... What if Epimenides was the ONLY Cretan and he had uttered only that one sentence. Maybe we need at least 2 Cretans or statements to make this work? Maybe:

EXIST(a):EXIST(b):[Cretan(a) & Cretan(b) & ~a=b]

EXIST(a):EXIST(b):[Stmt(a) & Stmt(b) & ~a=b]

> 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 sickfuck spammer of sci.math with his 2 OR 1= 3 with AND as subtraction. The failure twit never realizing there is no Logic unless and before you clean up Boole and Jevons FIRST of their mistakes.

5th published book

Suspend all College Classes in Logic, until they Fix their Errors // Teaching True Logic series, book 1
by Archimedes Plutonium (Author) (Amazon's Kindle)

Last revision was 29Mar2021. This is AP's 5th published book of science.
Preface:
First comes Logic-- think straight and clear which many logic and math professors are deaf dumb and blind to, and simply refuse to recognize and fix their errors.

The single biggest error of Old Logic of Boole and Jevons was their "AND" and "OR" connectors. They got them mixed up and turned around. For their logic ends up being that of 3 OR 2 = 5 with 3 AND 2 = either 3 or 2 but never 5, when even the local village idiot knows that 3 AND 2 = 5 (addition) with 3 OR 2 = either 3 or 2 (subtraction). The AND connector in Logic stems from the idea, the mechanism involved, that given a series of statements, if just one of those many statements has a true truth value, then the entire string of statements is overall true, and thus AND truth table is truly TTTF and never TFFF. And secondly, their error of the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability end conclusion.

My corrections of Old Logic have a history that dates before 1993, sometime around 1991, I realized the Euclid proof of infinitude of primes was illogical, sadly sadly wrong, in that the newly formed number by "multiply the lot and add 1" was necessarily a new prime in the indirect proof method. So that my history of fixing Old Logic starts in 1991, but comes to a synthesis of correcting all four of the connectors of Equal/not, And, Or, If->Then, by 2015.

Cover picture: some may complain my covers are less in quality, but I have a good reason for those covers-- I would like covers of math or logic to show the teacher's own handwriting as if he were back in the classroom writing on the blackboard or an overhead projector.

Product details
File Size: 773 KB
Print Length: 72 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PMB69F5
Text-to-Speech: Enabled 
X-Ray: 
Not Enabled 
Word Wise: Not Enabled
Lending: Enabled
Screen Reader: Supported 
Enhanced Typesetting: Enabled 



#10-2, 27th published book

Correcting Reductio Ad Absurdum// Teaching True Logic series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 9NOV2020. This is AP's 27th published book.

Preface:
These are the TRUE Truth Tables of the 4 connectors of Logic

Equal+Not                    
T = T  =  T                      
T = ~F = T                      
F = ~T = T
F = F   = T   

If--> then                  
T --> T  = T
T --> F  = F
F --> T  = U  (unknown or uncertain)           
F --> F  = U  (unknown or uncertain)

And
T  &  T = T                       
T  &  F = T                      
F  &  T = T                      
F  &  F = F                      

Or
T  or  T  = F
T  or  F  = T
F  or  T  = T
F  or  F  = F

Those can be analyzed as being Equal+Not is multiplication. If-->then is division. And is addition and Or is subtraction in mathematics. Now I need to emphasis this error of Old Logic, the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability unknown, undefined end conclusion.

Now in Old Logic they had for Reductio Ad Absurdum as displayed by this schematic:

|    | ~p
|    |---
|    | .
|    | .
|    | q
|    | .
|    | .
|    | ~q
| p

Which is fine except for the error of not indicating the end conclusion of "p" is only a probability of being true, not guaranteed as true. And this is the huge huge error that mathematicians have fallen victim of. For the Reductio Ad Absurdum is not a proof method for mathematics, it is probability of being true or false. Math works on guaranteed truth, not probability. This textbook is written to fix that error.

Product details
• ASIN : B07Q18GQ7S
• Publication date : March 23, 2019
• Language : English
• File size : 1178 KB
• Text-to-Speech : Enabled
• Enhanced typesetting : Enabled
• X-Ray : Not Enabled
• Word Wise : Not Enabled
• Print length : 86 pages
• Lending : Enabled
• Best Sellers Rank: #346,875 in Kindle Store (See Top 100 in Kindle Store)
◦ #28 in Logic (Kindle Store)
◦ #95 in Two-Hour Science & Math Short Reads
◦ #217 in Mathematical Logic

#10-3, 143rd published book

DeMorgan's Laws are fantasies, not laws// Teaching True Logic series, book 3 Kindle Edition
By Archimedes Plutonium

Last revision was 30Apr2021. This is AP's 143rd published book.

Preface: The Logic community never had the correct truth table of the primitive 4 connectors of Logic, (1) Equal compounded with NOT, (2) AND, (3) OR, (4) IF->THEN. In 1800s, the founders of Logic messed up in terrible error all 4 of the primitive logic connectors. And since the 1990s, AP has wanted an explanation of why Old Logic got all 4 connectors in total error? What was the reason for the mess up? And in the past few years, I finally pinned the reason to starting Logic with DeMorgan's fake laws, from which Boole, a close friend of DeMorgan, was going to keep his friendship and accept the DeMorgan Laws. That meant that DeMorgan, Boole, Jevons accepted OR as being that of Either..Or..Or..Both, what is called the inclusive OR. But the inclusive OR is a contradiction in terms, for there never can exist a combo of OR with AND simultaneously. This book goes into detail why the DeMorgan laws are fake and fantasy.

Cover Picture: Looks a bit rough, but I want students and readers to see my own handwriting as if this were a lecture and the cover picture a blackboard where I write out DeMorgan's two (fake) laws of logic.

Product details
• File Size : 620 KB
• Word Wise : Enabled
• Print Length : 38 pages
• ASIN : B08M4BY4XM
• Publication Date : October 27, 2020
• Language: : English
• Enhanced Typesetting : Enabled
• X-Ray : Not Enabled
• Text-to-Speech : Enabled
• Screen Reader : Supported
• Lending : Enabled

Dan Christensen picture profile
Dan Christensen
4 7:19PM
Graham Cooper
Resolution of Epimenides'

Kibo_I want to fuck her corpse-Andrea Ghez,Peter Higgs, Rainer Weiss, Kip S.. Thorne,Dr.Lisa Randall, Dr.Hau,CIA Kate Heinzelman, MIT's Anette Hosoi,Cynthia Barnhart
On Sunday, September 11, 2022 at 12:07:15 AM UTC-5, Michael Moroney wrote:
> I want to fuck her corpse
On Sunday, April 16, 2023 at 2:26:54 PM UTC-5, Volney wrote:
> Wood louse of Math and Bathynomus giganteus of Physics
> tarded:

NSF Dr.Panchanathan, Harvard's Sheldon Glashow, Peter Higgs ever ask the question, which is the atom's true electron-- muon or 0.5MeV particle which AP says is the Dirac magnetic monopole while the real electron is a muon stuck inside a 840MeV proton torus doing the Faraday law. In fact so stupid is this list of so called physicists that they went through life believing the slant cut in single cone is a ellipse, when in reality it is a Oval of 1 axis of symmetry for the cone has 1 axis of symmetry but ellipse requires 2 axes of symmetry. The minds of all these so called physicists are not good enough to be doing physics. In fact, so stupid in science and math are all these people that when told in High School or College that a slant cut in single cone is a ellipse, they believed it, and believe in it to this day without so much as ever questioning the idea that a single cone and oval have just 1 axis of symmetry while ellipse requires 2 axes of symmetry, and yet many on this list were awarded science prizes. Maybe for ignorance of science but not for truth of science.

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

On Sunday, April 16, 2023 at 8:22:51 PM UTC-4, Archimedes Plutonium wrote:
> Dan Christensen...

[snip]

Time for another spanking, Archie Poo! When will you learn? Once again...

From his antics here at sci.math, it is obvious that AP has abandoned all hope of 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:

"Negative numbers are the witches and hobgoblins of insane kook mathematicians. "
--Dec. 7, 2022

“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)

Updated version (repetion removed):

"Oh Atom Plutonium, as great as you are
How great thou are, are, are, are.
Oh Atom Plutonium, the God that you are
How beautiful is your world of science
Your science is the world
How beautiful is your world of science
Your science is the world
Oh Atom Plutonium, Great God of Atoms
Atom of Atoms
Oh Atom Plutonium, as great as thou art"
--March 24, 2023

Dan

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

On Sunday, April 16, 2023 at 1:12:50 PM UTC-4, Dan Christensen wrote:
> RESOLUTION OF EPIMENIDES' PARADOX
>
> The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
>
> https://en.wikipedia.org/wiki/Epimenides_paradox
>
> Here, we show that, logically, this statement must not be true. (~True(x))
>
> Using the following predicates:
>
> Stmt(x) = x is a statement
> True(x) = x is true
> Cretan(x) = x is a Cretan
> Said(x,y) = x said y
>
>
> AXIOMS
>

Two more axioms are required:

There exists at least two Cretans:

EXIST(a):EXIST(b):[Cret(a) & Cret(b) & ~a=b]

Every Cretan says at least one statement:

ALL(a):[Cret(a) => EXIST(b):[Stmt(b) & Said(a,b)]]

> 1. Stmt(x)
> Axiom
>
> 2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Axiom
>
> 3. Cretan(epi)
> Axiom
>
> 4. Said(epi,x)
> Axiom
>
> Suppose to contrary...
>
> 5. True(x)
> Premise
>
> 6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
> & [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
> Iff-And, 2
>
> 7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Split, 6
>
> 8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Detach, 7, 5
>
> 9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
> U Spec, 8
>
> 10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
> U Spec, 9
>
> 11. Cretan(epi) & Stmt(x)
> Join, 3, 1
>
> 12. Cretan(epi) & Stmt(x) & Said(epi,x)
> Join, 11, 4
>
> 13. ~True(x)
> Detach, 10, 12
>
> 14. True(x) & ~True(x)
> Join, 5, 13
>
> By contradiction...
>
> 15. ~True(x)
> Conclusion, 5
>
> 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 sickfuck spammer of sci.math with his 2 OR 1= 3 with AND as subtraction. The failure twit never realizing there is no Logic unless and before you clean up Boole and Jevons FIRST of their mistakes.

Dan mindless arsewipe of academy can never understand a error filled system of Boole logic needs fixing first before you plow into logic.

5th published book

Suspend all College Classes in Logic, until they Fix their Errors // Teaching True Logic series, book 1
by Archimedes Plutonium (Author) (Amazon's Kindle)

Last revision was 29Mar2021. This is AP's 5th published book of science.
Preface:
First comes Logic-- think straight and clear which many logic and math professors are deaf dumb and blind to, and simply refuse to recognize and fix their errors.

The single biggest error of Old Logic of Boole and Jevons was their "AND" and "OR" connectors. They got them mixed up and turned around. For their logic ends up being that of 3 OR 2 = 5 with 3 AND 2 = either 3 or 2 but never 5, when even the local village idiot knows that 3 AND 2 = 5 (addition) with 3 OR 2 = either 3 or 2 (subtraction). The AND connector in Logic stems from the idea, the mechanism involved, that given a series of statements, if just one of those many statements has a true truth value, then the entire string of statements is overall true, and thus AND truth table is truly TTTF and never TFFF. And secondly, their error of the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability end conclusion.

My corrections of Old Logic have a history that dates before 1993, sometime around 1991, I realized the Euclid proof of infinitude of primes was illogical, sadly sadly wrong, in that the newly formed number by "multiply the lot and add 1" was necessarily a new prime in the indirect proof method. So that my history of fixing Old Logic starts in 1991, but comes to a synthesis of correcting all four of the connectors of Equal/not, And, Or, If->Then, by 2015.

Cover picture: some may complain my covers are less in quality, but I have a good reason for those covers-- I would like covers of math or logic to show the teacher's own handwriting as if he were back in the classroom writing on the blackboard or an overhead projector.

Product details
File Size: 773 KB
Print Length: 72 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PMB69F5
Text-to-Speech: Enabled 
X-Ray: 
Not Enabled 
Word Wise: Not Enabled
Lending: Enabled
Screen Reader: Supported 
Enhanced Typesetting: Enabled 



#10-2, 27th published book

Correcting Reductio Ad Absurdum// Teaching True Logic series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 9NOV2020. This is AP's 27th published book.

Preface:
These are the TRUE Truth Tables of the 4 connectors of Logic

Equal+Not
T = T = T
T = ~F = T
F = ~T = T
F = F = T

If--> then
T --> T = T
T --> F = F
F --> T = U (unknown or uncertain)
F --> F = U (unknown or uncertain)

And
T & T = T
T & F = T
F & T = T
F & F = F

Or
T or T = F
T or F = T
F or T = T
F or F = F

Those can be analyzed as being Equal+Not is multiplication. If-->then is division. And is addition and Or is subtraction in mathematics. Now I need to emphasis this error of Old Logic, the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability unknown, undefined end conclusion.

Now in Old Logic they had for Reductio Ad Absurdum as displayed by this schematic:

| | ~p
| |---
| | .
| | .
| | q
| | .
| | .
| | ~q
| p

Which is fine except for the error of not indicating the end conclusion of "p" is only a probability of being true, not guaranteed as true. And this is the huge huge error that mathematicians have fallen victim of. For the Reductio Ad Absurdum is not a proof method for mathematics, it is probability of being true or false. Math works on guaranteed truth, not probability. This textbook is written to fix that error.

Product details
• ASIN : B07Q18GQ7S
• Publication date : March 23, 2019
• Language : English
• File size : 1178 KB
• Text-to-Speech : Enabled
• Enhanced typesetting : Enabled
• X-Ray : Not Enabled
• Word Wise : Not Enabled
• Print length : 86 pages
• Lending : Enabled
• Best Sellers Rank: #346,875 in Kindle Store (See Top 100 in Kindle Store)
◦ #28 in Logic (Kindle Store)
◦ #95 in Two-Hour Science & Math Short Reads
◦ #217 in Mathematical Logic

#10-3, 143rd published book

DeMorgan's Laws are fantasies, not laws// Teaching True Logic series, book 3 Kindle Edition
By Archimedes Plutonium

Last revision was 30Apr2021. This is AP's 143rd published book.

Preface: The Logic community never had the correct truth table of the primitive 4 connectors of Logic, (1) Equal compounded with NOT, (2) AND, (3) OR, (4) IF->THEN. In 1800s, the founders of Logic messed up in terrible error all 4 of the primitive logic connectors. And since the 1990s, AP has wanted an explanation of why Old Logic got all 4 connectors in total error? What was the reason for the mess up? And in the past few years, I finally pinned the reason to starting Logic with DeMorgan's fake laws, from which Boole, a close friend of DeMorgan, was going to keep his friendship and accept the DeMorgan Laws. That meant that DeMorgan, Boole, Jevons accepted OR as being that of Either..Or..Or..Both, what is called the inclusive OR. But the inclusive OR is a contradiction in terms, for there never can exist a combo of OR with AND simultaneously. This book goes into detail why the DeMorgan laws are fake and fantasy.

Cover Picture: Looks a bit rough, but I want students and readers to see my own handwriting as if this were a lecture and the cover picture a blackboard where I write out DeMorgan's two (fake) laws of logic.

Product details
• File Size : 620 KB
• Word Wise : Enabled
• Print Length : 38 pages
• ASIN : B08M4BY4XM
• Publication Date : October 27, 2020
• Language: : English
• Enhanced Typesetting : Enabled
• X-Ray : Not Enabled
• Text-to-Speech : Enabled
• Screen Reader : Supported
• Lending : Enabled

Dan Christensen picture profile
Dan Christensen
4
7:19PM
Graham Cooper
Resolution of Epimenides'

Kibo_I want to fuck her corpse-Andrea Ghez,Peter Higgs, Rainer Weiss, Kip S.. Thorne,Dr.Lisa Randall, Dr.Hau,CIA Kate Heinzelman, MIT's Anette Hosoi,Cynthia Barnhart
On Sunday, September 11, 2022 at 12:07:15 AM UTC-5, Michael Moroney wrote:
> I want to fuck her corpse
On Sunday, April 16, 2023 at 2:26:54 PM UTC-5, Volney wrote:
> Wood louse of Math and Bathynomus giganteus of Physics
> tarded:

NSF Dr.Panchanathan, Harvard's Sheldon Glashow, Peter Higgs ever ask the question, which is the atom's true electron-- muon or 0.5MeV particle which AP says is the Dirac magnetic monopole while the real electron is a muon stuck inside a 840MeV proton torus doing the Faraday law. In fact so stupid is this list of so called physicists that they went through life believing the slant cut in single cone is a ellipse, when in reality it is a Oval of 1 axis of symmetry for the cone has 1 axis of symmetry but ellipse requires 2 axes of symmetry. The minds of all these so called physicists are not good enough to be doing physics. In fact, so stupid in science and math are all these people that when told in High School or College that a slant cut in single cone is a ellipse, they believed it, and believe in it to this day without so much as ever questioning the idea that a single cone and oval have just 1 axis of symmetry while ellipse requires 2 axes of symmetry, and yet many on this list were awarded science prizes. Maybe for ignorance of science but not for truth of science.

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

On Sunday, April 16, 2023 at 10:07:39 PM UTC-4, Archimedes Plutonium wrote:
> Dan Christensen ...

[snip]

Time for another spanking, Archie Poo! When will you learn? Once again...

From his antics here at sci.math, it is obvious that AP has abandoned all hope of 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:

"Negative numbers are the witches and hobgoblins of insane kook mathematicians. "
--Dec. 7, 2022

“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)

Updated version (repetion removed):

"Oh Atom Plutonium, as great as you are
How great thou are, are, are, are.
Oh Atom Plutonium, the God that you are
How beautiful is your world of science
Your science is the world
How beautiful is your world of science
Your science is the world
Oh Atom Plutonium, Great God of Atoms
Atom of Atoms
Oh Atom Plutonium, as great as thou art"
--March 24, 2023

Dan

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

HTML format: https://www.dcproof.com/EpimenidesParadox.htm (29 lines)

Dan

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

On Sunday, April 16, 2023 at 12:12:50 PM UTC-5, Dan Christensen wrote:
> RESOLUTION OF EPIMENIDES' PARADOX
>
> The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
>

Dan is far too dumb to ever even take up logic. What is the expression-- where angels fear to tread. For fools always have a big dumb loudmouth and never fear to tread anywhere. Or as W.C.Fields famously said-- a Fool borne every minute.

You see, Dan will never learn in his entire life, that Boole & Jevons screwed up the Logic truth tables and until you fix their backbone logic connectors, nothing is worthy of thought or discussion in logic. Call it NEW LOGIC-- a fixed Boole & Jevons logic.

As to the Epimenides Paradox, it teaches us something new in true Logic.

That we need a minimum of words or sentences to be a logical argument.

Call it the AP Paradox-- the sky is blue and not blue. Almost the same thing as " All Cretans are liars"

Let us say in Logic you need a minimum of 2 premisses in order to make a Logical Argument.

So that Epimenides Paradox would in mathematics look like this " 3 +"

And then a scholar of math would look at that and say-- you idiot where is the missing number? Is it 3+7 or 3+ 20 or what is the missing number to make a mathematical argument.

Now I say the minimum should be 2 premisses because of Logical Deduction.

All men are mortal
Socrates is a man

Now we swing into action in a logical argument that Socrates is mortal.

But that is a hole or gap missing in Epimenides. It is vague and cannot allow any conclusions. It is not even logical.

So what can be done to make it a logical argument?

How about this.

1) All Cretans are liars
2) And I Epimenides is a liar

That is a argument with at least 2 premisses and we can then proceed to a logical conclusion-- That some Cretans are probably liars, some not.

Old Logic where the idiot Dan Christensen resides is utterly useless and pitiful.

New Logic requires the person who is doing Logic, have a logical mind, in the first place.

I vote to get rid of Dan the bully idiot out of sci.math forever, a pathetic moron who is un-educable and only hinders and thwarts young people from learning logic. And take his gaggle troop of idiots-- Graham Cooper, Jan Burse, Kibo Parry along with him

AP

> See my postings on this topic in my thread here,
> "Two Pathological Quantifier Constructs to Avoid"

Really. Why not? Its very sad that you have no grasp of
this simple identity, which is behind what you presented
(nothing to do with Sets or Russell):

~A <=> ∀B (A => B)

How did you resolve Epimenides' Paradox?
Try the following modelling:

~A <=> ∀x (A => True(x))

Can you prove it? Maybe you need an axiom ~True(false)?an Christensen schrieb am Montag, 17. April 2023 um 04:59:24 UTC+2:
> HTML format: https://www.dcproof.com/EpimenidesParadox.htm (29 lines)
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Ok, here you use "Statement" Stmt and not "Sentence". Why
did you switch to "Sentence" in your new version of a Liar Paradox.
This is not correct. According to your own account ordinary

logic is only classical logic. But you rejected LEM, since
LEM is not anymore provable:

ALL(b):[b e s => b e t | b e f]

Commands, like "Don't be stupid!", or questions, "Why
are you stupid?", are not affected, since they are not
statements. They anyway don't belong into the set s.

A statement is something that has a truth value.
But comands and questions don't have truth values.
A command c or a question q is not member of s,

it is anyway the case:

/* Commands are not Statements */
~c e s
/* Questions are not Statements */
~q e s

But since m is a partition of s, i.e. m ⊆ s, we can follow:

/* Commands are not "Dan O Matik Indeterminate" */
~c e m
/* Questions are not "Dan O Matik Indeterminate" */
~q e m

Thats quite easy to proof:

7 ~c @ m
4 Conclusion, 3

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

1 ~c @ s
Axiom

2 ALL(b):[b @ m => b @ s]
Axiom

3 c @ m
Premise

4 c @ m => c @ s
U Spec, 2

5 c @ s
Detach, 4, 3

6 ~c @ s & c @ s
Join, 1, 5

7 ~c @ m
4 Conclusion, 3

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

Dan Christensen schrieb am Sonntag, 16. April 2023 um 19:12:50 UTC+2:
> RESOLUTION OF EPIMENIDES' PARADOX
>
> The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
>
> https://en.wikipedia.org/wiki/Epimenides_paradox
>
> Here, we show that, logically, this statement must not be true. (~True(x))
>
> Using the following predicates:
>
> Stmt(x) = x is a statement
> True(x) = x is true
> Cretan(x) = x is a Cretan
> Said(x,y) = x said y
>
>
> AXIOMS
>
> 1. Stmt(x)
> Axiom
>
> 2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Axiom
>
> 3. Cretan(epi)
> Axiom
>
> 4. Said(epi,x)
> Axiom
>
> Suppose to contrary...
>
> 5. True(x)
> Premise
>
> 6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
> & [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
> Iff-And, 2
>
> 7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Split, 6
>
> 8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> Detach, 7, 5
>
> 9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
> U Spec, 8
>
> 10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
> U Spec, 9
>
> 11. Cretan(epi) & Stmt(x)
> Join, 3, 1
>
> 12. Cretan(epi) & Stmt(x) & Said(epi,x)
> Join, 11, 4
>
> 13. ~True(x)
> Detach, 10, 12
>
> 14. True(x) & ~True(x)
> Join, 5, 13
>
> By contradiction...
>
> 15. ~True(x)
> Conclusion, 5
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

To do some linguistic analysis you need at least 3 categories:

s : statements, something that has a truth value
Example: DC Proof provides intuitionistic propositional logic only.
(The statement is false)

q : question, something that is used by one agent
to ask another agent, to obtain some value
Example: How many rules does DC Proof have?
(The answer is some number)

c : command, something that is used by one agent
to tell another agent, to do something
Example: Please add tactics to DC Proof!
(Might be done or not)

These 3 categories are very similar like these 3 categories:

i) Elephants
ii) Giraffes
iii) Lions

Now the error in your nonsense and your according claims here is:
https://dcproof.com/LiarParadox2.htm

You put the Giraffes and Lions into the category of Elephants.
You make examples of Questions and Commands, and you
claim they are in the same set s as those things that have

potentially a truth value. Which is utter nonsense to put
Questions and Commands into the same category as
Statements, since proper Questions and proper Commands

are not Statements per se.

Mild Shock schrieb am Mittwoch, 30. August 2023 um 23:12:20 UTC+2:
> Ok, here you use "Statement" Stmt and not "Sentence". Why
> did you switch to "Sentence" in your new version of a Liar Paradox.
> This is not correct. According to your own account ordinary
>
> logic is only classical logic. But you rejected LEM, since
> LEM is not anymore provable:
>
> ALL(b):[b e s => b e t | b e f]
>
> Commands, like "Don't be stupid!", or questions, "Why
> are you stupid?", are not affected, since they are not
> statements. They anyway don't belong into the set s.
>
> A statement is something that has a truth value.
> But comands and questions don't have truth values.
> A command c or a question q is not member of s,
>
> it is anyway the case:
>
> /* Commands are not Statements */
> ~c e s
> /* Questions are not Statements */
> ~q e s
>
> But since m is a partition of s, i.e. m ⊆ s, we can follow:
>
> /* Commands are not "Dan O Matik Indeterminate" */
> ~c e m
> /* Questions are not "Dan O Matik Indeterminate" */
> ~q e m
>
> Thats quite easy to proof:
>
> 7 ~c @ m
> 4 Conclusion, 3
>
> ---------------------------------- begin proof ---------------------------
>
> 1 ~c @ s
> Axiom
>
> 2 ALL(b):[b @ m => b @ s]
> Axiom
>
> 3 c @ m
> Premise
>
> 4 c @ m => c @ s
> U Spec, 2
>
> 5 c @ s
> Detach, 4, 3
>
> 6 ~c @ s & c @ s
> Join, 1, 5
>
> 7 ~c @ m
> 4 Conclusion, 3
>
> ---------------------------------- end proof ---------------------------
> Dan Christensen schrieb am Sonntag, 16. April 2023 um 19:12:50 UTC+2:
> > RESOLUTION OF EPIMENIDES' PARADOX
> >
> > The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
> >
> > https://en.wikipedia.org/wiki/Epimenides_paradox
> >
> > Here, we show that, logically, this statement must not be true. (~True(x))
> >
> > Using the following predicates:
> >
> > Stmt(x) = x is a statement
> > True(x) = x is true
> > Cretan(x) = x is a Cretan
> > Said(x,y) = x said y
> >
> >
> > AXIOMS
> >
> > 1. Stmt(x)
> > Axiom
> >
> > 2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> > Axiom
> >
> > 3. Cretan(epi)
> > Axiom
> >
> > 4. Said(epi,x)
> > Axiom
> >
> > Suppose to contrary...
> >
> > 5. True(x)
> > Premise
> >
> > 6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
> > & [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
> > Iff-And, 2
> >
> > 7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> > Split, 6
> >
> > 8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> > Detach, 7, 5
> >
> > 9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
> > U Spec, 8
> >
> > 10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
> > U Spec, 9
> >
> > 11. Cretan(epi) & Stmt(x)
> > Join, 3, 1
> >
> > 12. Cretan(epi) & Stmt(x) & Said(epi,x)
> > Join, 11, 4
> >
> > 13. ~True(x)
> > Detach, 10, 12
> >
> > 14. True(x) & ~True(x)
> > Join, 5, 13
> >
> > By contradiction...
> >
> > 15. ~True(x)
> > Conclusion, 5
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

If you define an "Albino Elephant" as some "Abnormally Coloured
Elephant", and if you put Giraffe and Lion into the Category
of Elephant, you will be able to proof:

A Giraffe is an Albino Elephant
A Lion is an Albino Elephant

Similarly you have now the category "m" as some "Third Truth Value",
which for example makes b e f <=> b e t true, since false <=> false is true.
So this "Third Truth Value" not only somehow "resolves" the Liar paradox,

in that it makes you translation of the Liar paradox b e f <=> b e t true,
you then also prove that this is the only category that makes the
Liar paradox true. In particular you prove:

=> ALL(b):[b e s => [[b e t <=> b e f] => b e m]]]]

If there were another category than "m" that would make b e f <=> b e t
true, this would be in conflict with b e m. What you didn't show us
is that the category "m" makes the Liar Paradox true, you didn't prove:

=> ALL(b):[b e s => [b e m => [b e t <=> b e f]]]]

But the above is also provable. So you "resolved" the Liar Paradox,
made it true, by a "Third Truth Value" and some translation
b e f <=> b e t, which is not negation normal form, but gives your

form contextual constraint which can be made true by the
"Third Truth Value". But you have also nasty claims, which
are nonsense, and which make a discussion impossible:

A Question has the "Third Truth Value"
A Command has the "Third Truth Value"

Mild Shock schrieb am Mittwoch, 30. August 2023 um 23:15:05 UTC+2:
> To do some linguistic analysis you need at least 3 categories:
>
> s : statements, something that has a truth value
> Example: DC Proof provides intuitionistic propositional logic only.
> (The statement is false)
>
> q : question, something that is used by one agent
> to ask another agent, to obtain some value
> Example: How many rules does DC Proof have?
> (The answer is some number)
>
> c : command, something that is used by one agent
> to tell another agent, to do something
> Example: Please add tactics to DC Proof!
> (Might be done or not)
>
> These 3 categories are very similar like these 3 categories:
>
> i) Elephants
> ii) Giraffes
> iii) Lions
>
> Now the error in your nonsense and your according claims here is:
> https://dcproof.com/LiarParadox2.htm
>
> You put the Giraffes and Lions into the category of Elephants.
> You make examples of Questions and Commands, and you
> claim they are in the same set s as those things that have
>
> potentially a truth value. Which is utter nonsense to put
> Questions and Commands into the same category as
> Statements, since proper Questions and proper Commands
>
> are not Statements per se.
> Mild Shock schrieb am Mittwoch, 30. August 2023 um 23:12:20 UTC+2:
> > Ok, here you use "Statement" Stmt and not "Sentence". Why
> > did you switch to "Sentence" in your new version of a Liar Paradox.
> > This is not correct. According to your own account ordinary
> >
> > logic is only classical logic. But you rejected LEM, since
> > LEM is not anymore provable:
> >
> > ALL(b):[b e s => b e t | b e f]
> >
> > Commands, like "Don't be stupid!", or questions, "Why
> > are you stupid?", are not affected, since they are not
> > statements. They anyway don't belong into the set s.
> >
> > A statement is something that has a truth value.
> > But comands and questions don't have truth values.
> > A command c or a question q is not member of s,
> >
> > it is anyway the case:
> >
> > /* Commands are not Statements */
> > ~c e s
> > /* Questions are not Statements */
> > ~q e s
> >
> > But since m is a partition of s, i.e. m ⊆ s, we can follow:
> >
> > /* Commands are not "Dan O Matik Indeterminate" */
> > ~c e m
> > /* Questions are not "Dan O Matik Indeterminate" */
> > ~q e m
> >
> > Thats quite easy to proof:
> >
> > 7 ~c @ m
> > 4 Conclusion, 3
> >
> > ---------------------------------- begin proof ---------------------------
> >
> > 1 ~c @ s
> > Axiom
> >
> > 2 ALL(b):[b @ m => b @ s]
> > Axiom
> >
> > 3 c @ m
> > Premise
> >
> > 4 c @ m => c @ s
> > U Spec, 2
> >
> > 5 c @ s
> > Detach, 4, 3
> >
> > 6 ~c @ s & c @ s
> > Join, 1, 5
> >
> > 7 ~c @ m
> > 4 Conclusion, 3
> >
> > ---------------------------------- end proof ---------------------------
> > Dan Christensen schrieb am Sonntag, 16. April 2023 um 19:12:50 UTC+2:
> > > RESOLUTION OF EPIMENIDES' PARADOX
> > >
> > > The Cretan poet Epimenidies (epi here), once wrote, "Cretans (are) always liars" (statement x here).
> > >
> > > https://en.wikipedia.org/wiki/Epimenides_paradox
> > >
> > > Here, we show that, logically, this statement must not be true. (~True(x))
> > >
> > > Using the following predicates:
> > >
> > > Stmt(x) = x is a statement
> > > True(x) = x is true
> > > Cretan(x) = x is a Cretan
> > > Said(x,y) = x said y
> > >
> > >
> > > AXIOMS
> > >
> > > 1. Stmt(x)
> > > Axiom
> > >
> > > 2. True(x) <=> ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> > > Axiom
> > >
> > > 3. Cretan(epi)
> > > Axiom
> > >
> > > 4. Said(epi,x)
> > > Axiom
> > >
> > > Suppose to contrary...
> > >
> > > 5. True(x)
> > > Premise
> > >
> > > 6. [True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]]
> > > & [ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)] => True(x)]
> > > Iff-And, 2
> > >
> > > 7. True(x) => ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> > > Split, 6
> > >
> > > 8. ALL(a):ALL(b):[Cretan(a) & Stmt(b) & Said(a,b) => ~True(b)]
> > > Detach, 7, 5
> > >
> > > 9. ALL(b):[Cretan(epi) & Stmt(b) & Said(epi,b) => ~True(b)]
> > > U Spec, 8
> > >
> > > 10. Cretan(epi) & Stmt(x) & Said(epi,x) => ~True(x)
> > > U Spec, 9
> > >
> > > 11. Cretan(epi) & Stmt(x)
> > > Join, 3, 1
> > >
> > > 12. Cretan(epi) & Stmt(x) & Said(epi,x)
> > > Join, 11, 4
> > >
> > > 13. ~True(x)
> > > Detach, 10, 12
> > >
> > > 14. True(x) & ~True(x)
> > > Join, 5, 13
> > >
> > > By contradiction...
> > >
> > > 15. ~True(x)
> > > Conclusion, 5
> > >
> > > Dan
> > >
> > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, August 30, 2023 at 5:12:20 PM UTC-4, Mild Shock wrote:
> Ok, here you use "Statement" Stmt and not "Sentence". Why
> did you switch to "Sentence" in your new version of a Liar Paradox.
> This is not correct. According to your own account ordinary
>
> logic is only classical logic. But you rejected LEM, since
> LEM is not anymore provable:
>
> ALL(b):[b e s => b e t | b e f]
>

[snip]

Like "This sentence is false," they are valid sentences of natural language.. Each, it turns out, are also sentences of indeterminate truth value. Deal with it. See: https://dcproof.com/LiarParadox2.htm

Dan

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

Why didn't you prove, but its provable:

=> ALL(b):[b e s => [b e m => [b e t <=> b e f]]]]

Can you prove the same for Questions and Commands?

You didn't show that Questions and Commands are in
m. Thats only your comment prose. You didn't prove that.
Its just nonsense comment verbal garbage.

Dan Christensen schrieb am Donnerstag, 31. August 2023 um 00:57:13 UTC+2:
> On Wednesday, August 30, 2023 at 5:12:20 PM UTC-4, Mild Shock wrote:
> > Ok, here you use "Statement" Stmt and not "Sentence". Why
> > did you switch to "Sentence" in your new version of a Liar Paradox.
> > This is not correct. According to your own account ordinary
> >
> > logic is only classical logic. But you rejected LEM, since
> > LEM is not anymore provable:
> >
> > ALL(b):[b e s => b e t | b e f]
> >
> [snip]
>
> Like "This sentence is false," they are valid sentences of natural language. Each, it turns out, are also sentences of indeterminate truth value. Deal with it. See: https://dcproof.com/LiarParadox2.htm
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Actually when we take the gap together with what
you proved, we can show that your specific truth
multivalued rendering of the Liar paradox by means

of b e t <=> b e f is in the category "m" and only in
the category "m". Namely if we take the two
lemmas together we can prove:

=> ALL(b):[b e s => [[b e t <=> b e f] <=> b e m]]]

But your halucination that Questions and Commands
are in "m" and only in "m", where do you show that?
You would need to prove:

=> ALL(b):[b e s => ["Question" <=> b e m]]]

=> ALL(b):[b e s => ["Command" <=> b e m]]]

Mild Shock schrieb am Donnerstag, 31. August 2023 um 01:08:42 UTC+2:
> Why didn't you prove, but its provable:
> => ALL(b):[b e s => [b e m => [b e t <=> b e f]]]]
> Can you prove the same for Questions and Commands?
>
> You didn't show that Questions and Commands are in
> m. Thats only your comment prose. You didn't prove that.
> Its just nonsense comment verbal garbage.
> Dan Christensen schrieb am Donnerstag, 31. August 2023 um 00:57:13 UTC+2:
> > On Wednesday, August 30, 2023 at 5:12:20 PM UTC-4, Mild Shock wrote:
> > > Ok, here you use "Statement" Stmt and not "Sentence". Why
> > > did you switch to "Sentence" in your new version of a Liar Paradox.
> > > This is not correct. According to your own account ordinary
> > >
> > > logic is only classical logic. But you rejected LEM, since
> > > LEM is not anymore provable:
> > >
> > > ALL(b):[b e s => b e t | b e f]
> > >
> > [snip]
> >
> > Like "This sentence is false," they are valid sentences of natural language. Each, it turns out, are also sentences of indeterminate truth value. Deal with it. See: https://dcproof.com/LiarParadox2.htm
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, August 30, 2023 at 7:18:38 PM UTC-4, Mild Shock wrote:
> Actually when we take the gap together with what
> you proved, we can show that your specific truth
> multivalued rendering of the Liar paradox by means
>
> of b e t <=> b e f is in the category "m" and only in
> the category "m".

[snip]

What is so hard to understand? In any set of sentences in natural language, some may be known to be true, some may be known to be false, and the rest are of indeterminate truth value, suggesting the natural trichotomy that I model in my proof: https://dcproof.com/LiarParadox2.htm

Dan

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

On Wednesday, August 30, 2023 at 5:12:20 PM UTC-4, Mild Shock wrote:
> Ok, here you use "Statement" Stmt and not "Sentence". Why
> did you switch to "Sentence" in your new version of a Liar Paradox.
> This is not correct. According to your own account ordinary
>
> logic is only classical logic. But you rejected LEM, since
> LEM is not anymore provable:
>
> ALL(b):[b e s => b e t | b e f]

Apologies. I missed that you had switched threads to the Epimenedes Paradox.. I deleted my last 2 replies.

The Epimenedes Paradox is resolved by showing that the scenario that is described there is not paradoxical. It would be satisfied if Epimenedes' claim was not true, and that at least one Cretan once told the truth. Proof: https://www.dcproof.com/EpimenidesParadox.htm

It makes no reference to any sets. Statements (i.e. utterances by Cretans) are either true or not true. It is a much simpler scenario in that sense. There is a unary predicate True, but no predicate for false or indeterminate.. They were simply not required here.

Dan

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

Well you cannot prove, because of Trichotomy:

ALL(b):[b e s => b e t | b e f]

So its pretty obvious that it rejects LEM.

Dan Christensen schrieb am Donnerstag, 31. August 2023 um 04:00:43 UTC+2:
> On Wednesday, August 30, 2023 at 5:12:20 PM UTC-4, Mild Shock wrote:
> > Ok, here you use "Statement" Stmt and not "Sentence". Why
> > did you switch to "Sentence" in your new version of a Liar Paradox.
> > This is not correct. According to your own account ordinary
> >
> > logic is only classical logic. But you rejected LEM, since
> > LEM is not anymore provable:
> >
> > ALL(b):[b e s => b e t | b e f]
> Apologies. I missed that you had switched threads to the Epimenedes Paradox. I deleted my last 2 replies.
>
> The Epimenedes Paradox is resolved by showing that the scenario that is described there is not paradoxical. It would be satisfied if Epimenedes' claim was not true, and that at least one Cretan once told the truth. Proof: https://www.dcproof.com/EpimenidesParadox.htm
>
> It makes no reference to any sets. Statements (i.e. utterances by Cretans) are either true or not true. It is a much simpler scenario in that sense. There is a unary predicate True, but no predicate for false or indeterminate. They were simply not required here.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Thursday, August 31, 2023 at 3:14:22 AM UTC-4, Mild Shock wrote:
> Well you cannot prove, because of Trichotomy:
> ALL(b):[b e s => b e t | b e f]

I guess you still haven't noticed that you switched to the Epimenedes Paradox (see heading). There are no sets here. It is purely FOL.

Dan

There are serious doubts, it could be that an Olcott Fallacy is
involved. Of the form that one thinks that "if pigs can fly then
the moon is made of green cheese" implies that

"the moon s made of green cheese". But I could not yet produce
a proof that the axioms used by for example Dan Christensen
are inconsistent, and therefore its not really the case that

there is a cretan that says the truth. But the sketch is now:
I think Dan Christensen used something like:

(Pb ↔ ∀x¬Px) → ¬Pb is valid.
https://www.umsu.de/trees/#(Pb~4~6x~3Px)~5~3Pb

We can also write it like this, there is now a collection of b's
that satisfies Pb, and this collection is non-empty, this is what ∃xPx says.

(∃xPx ↔ ∀x¬Px) → ¬∃xPx is valid.
https://www.umsu.de/trees/#(~7xPx~4~6x~3Px)~5~3~7xPx

But the above is a vacous truth, since ∃xPx ↔ ∀x¬Px is
logically equivalent to ∃xPx ↔ ¬∃xPx which is an antinomy,
its just like the liar paradox Q ↔ ¬Q, namely we have:

¬(∃xPx ↔ ¬∃xPx) is valid.
https://www.umsu.de/trees/#~3(~7xPx~4~3~7xPx)

Dan Christensen schrieb am Donnerstag, 31. August 2023 um 19:50:21 UTC+2:
> On Thursday, August 31, 2023 at 3:14:22 AM UTC-4, Mild Shock wrote:
> > Well you cannot prove, because of Trichotomy:
> > ALL(b):[b e s => b e t | b e f]
> I guess you still haven't noticed that you switched to the Epimenedes Paradox (see heading). There are no sets here. It is purely FOL.
>
> Dan

On top of your bullshit, you even don't understand why LEM
is rejected. Despite the fact that this here is not provable:

EXIST(b):[b e s]

Further even for those state of affairs where s is non-empty there are
still plenty of reasons why your Trichotomy might rejects LEM,

i.e. left it fail, make it non-provable. Or as SEP puts it:

"Logics where LEM fails are not themselves hard to come by.
Among many such logics are a number of three-valued logics
that allow sentences to take a third value over and above true
and false. Sentences like Liar sentences take the third value."
https://plato.stanford.edu/entries/liar-paradox/#ParaParaLogi

Mild Shock schrieb am Freitag, 1. September 2023 um 00:14:01 UTC+2:
> There are serious doubts, it could be that an Olcott Fallacy is
> involved. Of the form that one thinks that "if pigs can fly then
> the moon is made of green cheese" implies that
>
> "the moon s made of green cheese". But I could not yet produce
> a proof that the axioms used by for example Dan Christensen
> are inconsistent, and therefore its not really the case that
>
> there is a cretan that says the truth. But the sketch is now:
> I think Dan Christensen used something like:
>
> (Pb ↔ ∀x¬Px) → ¬Pb is valid.
> https://www.umsu.de/trees/#(Pb~4~6x~3Px)~5~3Pb
>
> We can also write it like this, there is now a collection of b's
> that satisfies Pb, and this collection is non-empty, this is what ∃xPx says.
>
> (∃xPx ↔ ∀x¬Px) → ¬∃xPx is valid.
> https://www.umsu.de/trees/#(~7xPx~4~6x~3Px)~5~3~7xPx
>
> But the above is a vacous truth, since ∃xPx ↔ ∀x¬Px is
> logically equivalent to ∃xPx ↔ ¬∃xPx which is an antinomy,
> its just like the liar paradox Q ↔ ¬Q, namely we have:
>
> ¬(∃xPx ↔ ¬∃xPx) is valid.
> https://www.umsu.de/trees/#~3(~7xPx~4~3~7xPx)
> Dan Christensen schrieb am Donnerstag, 31. August 2023 um 19:50:21 UTC+2:
> > On Thursday, August 31, 2023 at 3:14:22 AM UTC-4, Mild Shock wrote:
> > > Well you cannot prove, because of Trichotomy:
> > > ALL(b):[b e s => b e t | b e f]
> > I guess you still haven't noticed that you switched to the Epimenedes Paradox (see heading). There are no sets here. It is purely FOL.
> >
> > Dan

Isn't Epimenides' Paradox the same as Yablos Paradox?
Possibly no, since in Yablos Paradox, there is a relationship
between many sentences x, and the negated sentences.

∀x(Q(x) ↔ ∀y(R(x,y) → ¬Q(y)))
https://en.wikipedia.org/wiki/Stephen_Yablo#Yablo's_paradox

Where in Epimenides' Paradox there is one sentence x
contra all of the other sentences. Can you do Yablos
Paradox in Coq? Like prove a contradiction from it,

or even refute it, show that it is an Antinomy? What domain
and relation R do we need to consider for an Antinomy?
Is this even possible, show it paradoxical resp. Antinomy?

Mild Shock schrieb am Montag, 4. September 2023 um 16:08:32 UTC+2:
> On top of your bullshit, you even don't understand why LEM
> is rejected. Despite the fact that this here is not provable:
>
> EXIST(b):[b e s]
>
> Further even for those state of affairs where s is non-empty there are
> still plenty of reasons why your Trichotomy might rejects LEM,
>
> i.e. left it fail, make it non-provable. Or as SEP puts it:
>
> "Logics where LEM fails are not themselves hard to come by.
> Among many such logics are a number of three-valued logics
> that allow sentences to take a third value over and above true
> and false. Sentences like Liar sentences take the third value."
> https://plato.stanford.edu/entries/liar-paradox/#ParaParaLogi
> Mild Shock schrieb am Freitag, 1. September 2023 um 00:14:01 UTC+2:
> > There are serious doubts, it could be that an Olcott Fallacy is
> > involved. Of the form that one thinks that "if pigs can fly then
> > the moon is made of green cheese" implies that
> >
> > "the moon s made of green cheese". But I could not yet produce
> > a proof that the axioms used by for example Dan Christensen
> > are inconsistent, and therefore its not really the case that
> >
> > there is a cretan that says the truth. But the sketch is now:
> > I think Dan Christensen used something like:
> >
> > (Pb ↔ ∀x¬Px) → ¬Pb is valid.
> > https://www.umsu.de/trees/#(Pb~4~6x~3Px)~5~3Pb
> >
> > We can also write it like this, there is now a collection of b's
> > that satisfies Pb, and this collection is non-empty, this is what ∃xPx says.
> >
> > (∃xPx ↔ ∀x¬Px) → ¬∃xPx is valid.
> > https://www.umsu.de/trees/#(~7xPx~4~6x~3Px)~5~3~7xPx
> >
> > But the above is a vacous truth, since ∃xPx ↔ ∀x¬Px is
> > logically equivalent to ∃xPx ↔ ¬∃xPx which is an antinomy,
> > its just like the liar paradox Q ↔ ¬Q, namely we have:
> >
> > ¬(∃xPx ↔ ¬∃xPx) is valid.
> > https://www.umsu.de/trees/#~3(~7xPx~4~3~7xPx)
> > Dan Christensen schrieb am Donnerstag, 31. August 2023 um 19:50:21 UTC+2:
> > > On Thursday, August 31, 2023 at 3:14:22 AM UTC-4, Mild Shock wrote:
> > > > Well you cannot prove, because of Trichotomy:
> > > > ALL(b):[b e s => b e t | b e f]
> > > I guess you still haven't noticed that you switched to the Epimenedes Paradox (see heading). There are no sets here. It is purely FOL.
> > >
> > > Dan