"We are therefore confronted with a proposition which asserts its own
unprovability." (Gödel 1931:39-41)

When Gödel refers to a proposition asserting its own unprovability then
within the precise focus on these exact words we can see that such a
proposition would be unprovable because it would be self-contradictory.

F ⊢ GF ↔ ¬ProvF (┌GF┐).
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

When we simply strip away the reference to Gödel numbers thus requiring
F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).

When we convert to more standard notational conventions an add an
existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))

A proof of G in F that proves that G cannot be proved in F is simply
self-contradictory, thus no such G exists in F.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/26/23 2:39 PM, olcott wrote:
> "We are therefore confronted with a proposition which asserts its own
>  unprovability." (Gödel 1931:39-41)
>
> When Gödel refers to a proposition asserting its own unprovability then
> within the precise focus on these exact words we can see that such a
> proposition would be unprovable because it would be self-contradictory.
>
> F ⊢ GF ↔ ¬ProvF (┌GF┐).

And where does Godel actually SAY THAT?

> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

So, you go by someones summary of what he is saying, not what he
actually say. That seems to imply you don't actually understand what he
is saying.

>
> When we simply strip away the reference to Gödel numbers thus requiring
> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).

IE, you are admitting that you are changing the subject of the
proposition. i.e. admitting to using the Strawman fallacy.

Note, the Reference to the Godel Numbers is the key part of the proof.
Stripping them out means you aren't

>
> When we convert to more standard notational conventions an add an
> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))

Except that is just proven to be a dishonest dodge. He used perfectly
fine notational conventions and meant what he wrote.

He is showing that you can express that sort of idea, WITHOUT the
explicit statement, because of the expressiveness of numbers. The only
way you can remove the truth of his "notation" is to just ban
semi-advanced forms of math. But, it seems that is beyound your
understanding.

>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.
>
>

A "Proof" Can't be "Contradictory". A set of statements can be, at which
point you can point out the exact contradiction in them, which you
haven't done, you just CLAIM that it is impossible for something to be
True but not provable, but you can't show that such a claim is actually
true.

The only way for a proof to be contradictory is for the whole logic
system to be inconsistent, so your claim that when you add your ideas
into the logic, that the proof is contradictory, just proves that your
addidtion break the system and make it inconsistent.

YOU LOSE.

On 3/26/2023 1:39 PM, olcott wrote:
> "We are therefore confronted with a proposition which asserts its own
>  unprovability." (Gödel 1931:39-41)
>
> When Gödel refers to a proposition asserting its own unprovability then
> within the precise focus on these exact words we can see that such a
> proposition would be unprovable because it would be self-contradictory.
>
> F ⊢ GF ↔ ¬ProvF (┌GF┐).
> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>
> When we simply strip away the reference to Gödel numbers thus requiring
> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>
> When we convert to more standard notational conventions an add an
> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.
>
>

Thus proving that when the above G is neither provable nor refutable in
F it is because G is self-contradictory in F thus not because F is
incomplete.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/26/23 3:29 PM, olcott wrote:
> On 3/26/2023 1:39 PM, olcott wrote:
>> "We are therefore confronted with a proposition which asserts its own
>>   unprovability." (Gödel 1931:39-41)
>>
>> When Gödel refers to a proposition asserting its own unprovability then
>> within the precise focus on these exact words we can see that such a
>> proposition would be unprovable because it would be self-contradictory.
>>
>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>
>> When we simply strip away the reference to Gödel numbers thus requiring
>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>
>> When we convert to more standard notational conventions an add an
>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>
>> A proof of G in F that proves that G cannot be proved in F is simply
>> self-contradictory, thus no such G exists in F.
>>
>>
>
> Thus proving that when the above G is neither provable nor refutable in
> F it is because G is self-contradictory in F thus not because F is
> incomplete.
>

Using FALSE statements doesn't prove anything except that you are an idiot.

The above ISN'T the G of Godel, so your statement is meaningless except
to prove that you are stupid.

Note, any statement made that doesn't show what you are trying to rebut,
automatically loses most of its ability to rebut the statement.

You are just showing you have nothing to actually base you claims, and
all the errors pointed out in messages you don't reply to are actually
correctlly pointing out errors.

That is how "debate" works.

You are just proving you are anti-social, as you refuse to work within
the social convetions.

You are also proving you are anti-logic, as you refuse to work within
the accepted logical system.

You are just proving that your life was wasted and NO ONE will ever
consider your work worthly to examine, as it has been so thoughly
rebuted and you haven't actually tried to answer the rebutalls,
effectively agreeein gto them.

Harry Cliff physics failures,Cambridge,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.

1) Too stupid to question if Thomson found Dirac's magnetic monopole and not the electron of atoms.
2) Too stupid to realize that in the Rutherford,Geiger, Marsden Experiment when you have increase in velocity of bounce back alpha particles means head on collision with a larger proton torus, hence, the interior of gold atoms are toruses, no nucleus.
3) Too stupid in logic to understand subatomic particles have jobs and tasks to do, not sit around on beaches sipping lemonade what Old Physics says. The proton is a 8 ring torus with muon as electron inside doing the Faraday law producing new electricity.
4) Too stupid to understand stars and our Sun shine not from fusion but from Faraday law of each and every atom inside that star.

5) think a slant cut in single cone is a ellipse when it is proven to be a Oval, never the ellipse. For the cone and oval have 1 axis of symmetry, while ellipse has 2.
6) think Boole logic is correct with AND truth table being TFFF when it really is TTTF in order to avoid 2 OR 1 =3 with AND as subtraction
7) can never do a geometry proof of Fundamental Theorem of Calculus and are too ignorant in math to understand that analysis of something is not proving something in their "limit hornswaggle"
8) too stupid in science to ask the question of physics-- is the 1897 Thomson discovery of a 0.5MeV particle actually the Dirac magnetic monopole and that the muon is the true electron of atoms stuck inside a 840MeV proton torus doing the Faraday law. Showing that Peter Higgs, Sheldon Glashow, Ed Witten, John Baez, Roger Penrose, Arthur B. McDonald are sapheads when it comes to logical thinking in physics with their do nothing proton, do nothing electron.

> > Roger Penrose, Reinhard Genzel, Andrea Ghez,
> > Peter Higgs, Rainer Weiss, Kip S. Thorne, Barry C. Barish
> > David J. Thouless_, F. Duncan M. Haldane, John M. Kosterlitz, Takaaki Kajita
> > Arthur B. McDonald
> > Francois Englert
> > Saul Perlmutter
> > Brian P. Schmidt
> > Adam G. Riess
> > Makoto Kobayashi
> > Toshihide Maskawa_
> > Yoichiro Nambu_
> > John C. Mather
> > George F. Smoot
> > Roy J. Glauber_
> > David J. Gross
> > Hugh David Politzer
> > Frank Wilczek
> > Raymond Davis Jr. _
> > Masatoshi Koshiba_
> > Riccardo Giacconi_
> > Gerardus 't Hooft
> > Martinus J.G. Veltman_
> > Jerome I. Friedman
> > Henry W. Kendall_
> > Richard E. Taylor_
> > Carlo Rubbia
> > Simon van der Meer_
> > William Alfred Fowler_
> > Kenneth G. Wilson_
> > James Watson Cronin_
> > Val Logsdon Fitch_
> > Sheldon Lee Glashow
> > Steven Weinberg_
> > .
> > .
> > little fishes
> > .
> > .
> > Layers of error thinking physics Re: 2-Comparative Analysis of failures of Logic with failures of Physics// one thinks 3 OR 2 =5 with 3 AND 2 = subtraction of either 3 or 2, while the other thinks proton to electron is 938MeV vs .5MeV when truly it is 840MeV to 105MeV
> >
> > Physical Review Letters: Proton Mass
> > Yi-Bo Yang, Jian Liang, Yu-Jiang Bi, Ying Chen, Terrence Draper, Keh-Fei Liu, Zhaofeng Liu
> > more and more layers of error thinking physics
> > .
> > .
> > Edward Witten
> > John Baez
> > Brian Greene
> > Lisa Randall
> > Alan H. Guth
> > Michael E. Brown
> > Konstantin Batygin
> > Ben Bullock
> > Larry Harson
> > Mark Barton, PhD in Physics, The University of Queensland, physicist with National Astronomical Observatory of Japan
> > Answered Aug 26, 2013 · Author has 8.7k answers and 10.3m answer views
> > None at all - he was a raving nutter.
> > Richard A. Muller, crank at Berkeley
> > Jennifer Kahn, Discover, science hater
> > Eric Francis Coppolino, newsreporter hatred of science, George Witte, St.Martin's Press science hater
> > Toby Howard, The Guardian, science hater
> >
> >
> > #2-1, 137th published book
> >
> > Introduction to AP's TEACHING TRUE PHYSICS// Physics textbook series, book 1 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> >
> >
> > #1 New Release in Electromagnetic Theory
> >
> > This will be AP's 137th published book on science. And the number 137 is special to me for it is the number of QED, Quantum Electrodynamics as the inverse fine structure constant. I can always remember 137 as that special constant of physics and so I can remember where Teaching True Physics was started by me.
> >
> > Time has come for the world to have the authoritative textbooks for all of High School and College education. Written by the leading physics expert of the time. The last such was Feynman in the 1960s with Feynman Lectures on Physics. The time before was Maxwell in 1860s with his books and Encyclopedia Britannica editorship. The time is ripe in 2020 for the new authoritative texts on physics. It will be started in 2020 which is 60 years after Feynman. In the future, I request the physics community updates the premier physics textbook series at least every 30 years. For we can see that pattern of 30 years approximately from Faraday in 1830 to Maxwell in 1860 to Planck and Rutherford in about 1900, to Dirac in 1930 to Feynman in 1960 and finally to AP in 1990 and 2020. So much happens in physics after 30 years, that we need the revisions to take place in a timely manner. But also, as we move to Internet publishing such as Amazon's Kindle, we can see that updates can take place very fast, as editing can be a ongoing monthly or yearly activity. I for one keep constantly updating all my published books, at least I try to.
> >
> > Feynman was the best to make the last authoritative textbook series for his concentration was QED, Quantum Electrodynamics, the pinnacle peak of physics during the 20th century. Of course the Atom Totality theory took over after 1990 and all of physics; for all sciences are under the Atom Totality theory.
> > And as QED was the pinnacle peak before 1990, the new pinnacle peak is the Atom Totality theory. The Atom Totality theory is the advancement of QED, for the Atom Totality theory primal axiom says -- All is Atom, and atoms are nothing but Electricity and Magnetism.
> > Length: 64 pages
> >
> > Product details
> > • File Size : 790 KB
> > • Publication Date : October 5, 2020
> > • Word Wise : Enabled
> > • Print Length : 64 pages
> > • Text-to-Speech : Not enabled
> > • Screen Reader : Supported
> > • Enhanced Typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Language: : English
> > • ASIN : B08KS4YGWY
> > • Lending : Enabled
> > • Best Sellers Rank: #430,602 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #39 in Electromagnetic Theory
> > ◦ #73 in Electromagnetism (Kindle Store)
> > ◦ #74 in 90-Minute Science & Math Short Reads
> >
> > #2-2, 145th published book
> > TEACHING TRUE PHYSICS//Junior High School// Physics textbook series, book 2
> > Kindle Edition
> > by Archimedes Plutonium (Author)
> > What I am doing is clearing the field of physics, clearing it of all the silly mistakes and errors and beliefs that clutter up physics. Clearing it of its fraud and fakeries and con-artistry. I thought of doing these textbooks starting with Senior year High School, wherein I myself started learning physics. But because of so much fraud and fakery in physics education, I believe we have to drop down to Junior year High School to make a drastic and dramatic emphasis on fakery and con-artistry that so much pervades science and physics in particular. So that we have two years in High School to learn physics. And discard the nonsense of physics brainwash that Old Physics filled the halls and corridors of education.
> >
> > Product details
> > • ASIN : B08PC99JJB
> > • Publication date : November 29, 2020
> > • Language: : English
> > • File size : 682 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Enabled
> > • Print length : 78 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #185,995 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #42 in Two-Hour Science & Math Short Reads
> > ◦ #344 in Physics (Kindle Store)
> > ◦ #2,160 in Physics (Books)
> >
> > #2-3, 146th published book
> >
> > TEACHING TRUE PHYSICS// Senior High School// Physics textbook series, book 3
> > Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > I believe that in knowing the history of a science is knowing half of that science. And that if you are amiss of knowing the history behind a science, you have only a partial understanding of the concepts and ideas behind the science. I further believe it is easier to teach a science by teaching its history than any other means of teaching. So for senior year High School, I believe physics history is the best way of teaching physics. And in later years of physics courses, we can always pick up on details. So I devote this senior year High School physics to a history of physics, but only true physics. And there are few books written on the history of physics, so I chose Asimov's The History of Physics, 1966 as the template book for this textbook. Now Asimov's book is full of error and mistakes, and that is disappointing but all of Old Physics is full of error. On errors and mistakes of Old Physics, the best I can do is warn the students, and the largest warning of all is that whenever someone in Old Physics says "electron" what they are talking about is really the Dirac magnetic monopole. And whenever they talk about the Rutherford-Bohr model of the atom, they are talking about huge huge grave mistakes, for the true atom is protons as 8 ringed toruses with a muon stuck inside of a proton doing the Faraday law and producing those magnetic monopoles as electricity. I use Asimov's book as a template but in the future, I hope to rewrite this textbook using no template at all, that is if I have time in the future.
> > Cover Picture: Is the book The History of Physics, by Isaac Asimov, 1966 and on top of the book are 4 cut-outs of bent circles representing magnetic monopoles which revolutionizes modern physics, especially the ElectroMagnetic theory.
> >
> > Product details
> > • ASIN ‏ : ‎ B08RK33T8V
> > • Publication date ‏ : ‎ December 28, 2020
> > • Language ‏ : ‎ English
> > • File size ‏ : ‎ 794 KB
> > • Text-to-Speech ‏ : ‎ Enabled
> > • Screen Reader ‏ : ‎ Supported
> > • Enhanced typesetting ‏ : ‎ Enabled
> > • X-Ray ‏ : ‎ Not Enabled
> > • Word Wise ‏ : ‎ Enabled
> > • Print length ‏ : ‎ 123 pages
> > • Lending ‏ : ‎ Enabled
> > • Best Sellers Rank: #4,167,235 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #15,099 in Physics (Kindle Store)
> > ◦ #91,163 in Physics (Books)
> >
> >
> > #2-4, 151st published book
> >
> > TEACHING TRUE PHYSICS// 1st year College// Physics textbook series, book 4
> > Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Preface: This is AP's 151st book of science published. It is one of my most important books of science because 1st year college physics is so impressionable on students, if they should continue with physics, or look elsewhere for a career. And also, physics is a crossroad to all the other hard core sciences, where physics course is mandatory such as in chemistry or even biology. I have endeavored to make physics 1st year college to be as easy and simple to learn. In this endeavor to make physics super easy, I have made the writing such that you will see core ideas in all capital letters as single sentences as a educational tool. And I have made this textbook chapter writing follow a logical pattern of both algebra and geometry concepts, throughout. The utmost importance of logic in physics needs to be seen and understood. For I have never seen a physics book, prior to this one that is logical. Every Old Physics textbook I have seen is scatter-brained in topics and in writing. I use as template book of Halliday & Resnick because a edition of H&R was one I was taught physics at University of Cincinnati in 1969. And in 1969, I had a choice of majors, do I major in geology, or mathematics, or in physics, for I will graduate from UC in 1972. For me, geology was too easy, but physics was too tough, so I ended up majoring in mathematics. If I had been taught in 1969 using this textbook that I have written, I would have ended up majoring in physics, my first love. For physics is not hard, not hard at all, once you clear out the mistakes and the obnoxious worthless mathematics that clutters up Old Physics, and the illogic that smothers much of Old Physics.
> >
> > Maybe it was good that I had those impressions of physics education of poor education, which still exists throughout physics today. Because maybe I am forced to write this book, because of that awful experience of learning physics in 1969. Without that awful experience, maybe this textbook would have never been written by me.
> >
> > Cover picture is the template book of Halliday & Resnick, 1988, 3rd edition Fundamentals of Physics and sitting on top are cut outs of "half bent circles, bent at 90 degrees" to imitate magnetic monopoles. Magnetic Monopoles revolutionizes physics education, and separates-out, what is Old Physics from what is New Physics.
> >
> > Product details
> > • ASIN ‏ : ‎ B09JW5DVYM
> > • Publication date ‏ : ‎ October 19, 2021
> > • Language ‏ : ‎ English
> > • File size ‏ : ‎ 1035 KB
> > • Text-to-Speech ‏ : ‎ Enabled
> > • Screen Reader ‏ : ‎ Supported
> > • Enhanced typesetting ‏ : ‎ Enabled
> > • X-Ray ‏ : ‎ Not Enabled
> > • Word Wise ‏ : ‎ Enabled
> > • Print length ‏ : ‎ 386 pages
> > • Lending ‏ : ‎ Enabled
> > • Best Sellers Rank: #4,874,333 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #526 in Electromagnetic Theory
> > ◦ #1,321 in Electromagnetism (Kindle Store)
> > ◦ #9,546 in Electromagnetism (Books)
> >
> >
> >
> > #2-5, 174th published book
> >
> > TEACHING TRUE PHYSICS, 2nd year College
> > by Archimedes Plutonium (Author) Kindle Edition
> >
> > Preface: At the moment this is a physics book for 2nd year College. But as the months and years go by I intend to convert it into a textbook of about 200 to 300 pages. It is mostly about thermodynamics for in my own college education 1968-1972 at University of Cincinnati, I took physics thermodynamics in the 2nd year (if memory has not failed me).
> > Cover-Picture: Is a iphone photograph of the Chemistry textbook I used at UC 1968-1972 with my own paper cut-outs of magnetic monopoles. Pictured are 4 bent circles, bent at 90degrees from diameter and each bent circle is a individual magnetic monopole.
> >
> > Product details
> > • ASIN ‏ : ‎ B09TKL4HMC
> > • Publication date ‏ : ‎ February 27, 2022
> > • Language ‏ : ‎ English
> > • File size ‏ : ‎ 675 KB
> > • Text-to-Speech ‏ : ‎ Enabled
> > • Screen Reader ‏ : ‎ Supported
> > • Enhanced typesetting ‏ : ‎ Enabled
> > • X-Ray ‏ : ‎ Not Enabled
> > • Word Wise ‏ : ‎ Enabled
> > • Print length ‏ : ‎ 41 pages
> > • Lending ‏ : ‎ Enabled
> >
> >
> >
> > #2-6, 177th published book
> > TEACHING TRUE PHYSICS, Architecture of Atoms, 3rd year College
> > by Archimedes Plutonium (Author) Kindle Edition
> >
> > Preface: I come to teaching physics for 3rd year College as the Architecture of Atoms. My writing style will be prose-narrative, until I add on exercise problems and convert it into a textbook. The 1st year College, has to be the equations and laws of electricity and magnetism. For the primal-axiom over all of physics is-- All is Atom, and atoms are nothing but electricity and magnetism. The 2nd year College is thermodynamics. And now the 3rd year College physics has to teach the Architecture, the geometry of the inside and exterior surface of the atom. One of the greatest faults, misery, and anti-science teaching of Old Physics is their denial that subatomic particles have to be something more than tiny balls tiny spheres that do-nothing, perform nothing, function as nothing. That the proton and neutron and true electron=muon, has to be matter with a function and purpose and design and task and job. This is a year of physics teaching of the architecture of the atom.
> > Cover Picture: A iphone photograph of my book chemistry book, a long time favorite of mine of CHEM ONE, 2nd edition, Waser, Trueblood, Knobler, 1980, and page 307 of that book. Why this page? Because it was instrumental in my discovery of the true Architecture of Atoms. Not many professors of chemistry or physics dive into the Shrodinger Equation that results in a meaningful teaching of "matter waves". Matter waves are the heart of understanding the geometry of Atomic Architecture.
> >
> > Product details
> > • ASIN ‏ : ‎ B09VFH9QST
> > • Publication date ‏ : ‎ March 12, 2022
> > • Language ‏ : ‎ English
> > • File size ‏ : ‎ 823 KB
> > • Text-to-Speech ‏ : ‎ Enabled
> > • Screen Reader ‏ : ‎ Supported
> > • Enhanced typesetting ‏ : ‎ Enabled
> > • X-Ray ‏ : ‎ Not Enabled
> > • Word Wise ‏ : ‎ Not Enabled
> > • Print length ‏ : ‎ 74 pages
> > • Lending ‏ : ‎ Enabled
> >
> >
> >
> > #2-7, 178th published book
> >
> > TEACHING TRUE PHYSICS, Architecture of Light Waves & Energy, 4th year College
> > by Archimedes Plutonium (Author) (Kindle edition)
> >
> >
> > Preface: This is 4th year College Physics and the important ideas of physics to learn as last year undergraduate school is the architecture and geometry of the Light Wave & Energy in physics. This is New Physics and not Old Physics. New Physics is defined as physics that knows and uses the true electron of atoms is the muon stuck inside a 840MeV proton torus and doing the Faraday law, creating new electrical energy that is storaged in the neutrons of atoms until they grow from 1eV into 945MeV and then create a new higher atomic numbered atom or emitted as radioactivity. Old Physics mistakenly identified the electron of atoms as the 0.5MeV particle that AP calls the Dirac magnetic monopole. In 3rd year College we studied the architecture of the interior of atoms. In 4th year College we study the architecture of Light Waves & Energy.
> >
> > The template book for 4th year College is Feynman's 1985 book of QED.
> >
> > Cover Picture: Is my iphone photograph of the template book for this book. Feynman's 1985 QED, quantum electrodynamics, showing my plastic toy model of DNA and my cut-outs of 4 bent circles that each bent circle represents one magnetic monopole. I arranged the monopoles into a single strand of a cycloid wave.
> >
> > Product details
> > • ASIN ‏ : ‎ B09W58XGDW
> > • Publication date ‏ : ‎ March 21, 2022
> > • Language ‏ : ‎ English
> > • File size ‏ : ‎ 824 KB
> > • Text-to-Speech ‏ : ‎ Enabled
> > • Screen Reader ‏ : ‎ Supported
> > • Enhanced typesetting ‏ : ‎ Enabled
> > • X-Ray ‏ : ‎ Not Enabled
> > • Word Wise ‏ : ‎ Enabled
> > • Print length ‏ : ‎ 66 pages
> > • Lending ‏ : ‎ Enabled
> >
> >
> >

On 3/26/2023 1:39 PM, olcott wrote:
> "We are therefore confronted with a proposition which asserts its own
>  unprovability." (Gödel 1931:39-41)
>
> When Gödel refers to a proposition asserting its own unprovability then
> within the precise focus on these exact words we can see that such a
> proposition would be unprovable because it would be self-contradictory.
>
> F ⊢ GF ↔ ¬ProvF (┌GF┐).
> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>
> When we simply strip away the reference to Gödel numbers thus requiring
> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>
> When we convert to more standard notational conventions an add an
> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.

If we take the simplest possible essence of Gödel's logic sentence we
have: *G asserts its own unprovability in F*

This means that G is asserting that there is no sequence of inference
steps in F that derives G.

For G to be satisfied in F there would have to be a sequence of
inference steps in F that proves there is no such sequence of inference
steps in F.

This is like René Descartes saying:
“I think therefore thoughts do not exist”

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 5:15 PM, olcott wrote:
> On 3/26/2023 1:39 PM, olcott wrote:
>> "We are therefore confronted with a proposition which asserts its own
>>   unprovability." (Gödel 1931:39-41)
>>
>> When Gödel refers to a proposition asserting its own unprovability then
>> within the precise focus on these exact words we can see that such a
>> proposition would be unprovable because it would be self-contradictory.
>>
>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>
>> When we simply strip away the reference to Gödel numbers thus requiring
>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>
>> When we convert to more standard notational conventions an add an
>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>
>> A proof of G in F that proves that G cannot be proved in F is simply
>> self-contradictory, thus no such G exists in F.
>
> If we take the simplest possible essence of Gödel's logic sentence we
> have: *G asserts its own unprovability in F*

No, that isn't what Godel logic sentence says at all in F.

Thus, your arguement is built on a LIE, showing you don't understand how
logic works.

>
> This means that G is asserting that there is no sequence of inference
> steps in F that derives G.

No, that G is asserting that there is no FINITE sequence of inference
steps in F that demonstrates G.

You just proved you don't understand the meaning of "Proof"

Proofs in classic logic are, by definition, Finite.

>
> For G to be satisfied in F there would have to be a sequence of
> inference steps in F that proves there is no such sequence of inference
> steps in F.

Right, but G can be true due to an INFINITE sequence of inference steps
in F, and not be provable.

Since there is a difference between an INFINTE sequence and a FINITE
sequence, it is possible for both to exist.

>
> This is like René Descartes saying:
> “I think therefore thoughts do not exist”
>
>

Nope, just proves you are too stupid to understand logic, since this has
been explained to you many times, but you still make the same mistake,

Because of this, no one with any sense is going to give your "Correct
Reasoning" a second look, because the source of it is so unsound.

On 4/15/2023 4:34 PM, Richard Damon wrote:
> On 4/15/23 5:15 PM, olcott wrote:
>> On 3/26/2023 1:39 PM, olcott wrote:
>>> "We are therefore confronted with a proposition which asserts its own
>>>   unprovability." (Gödel 1931:39-41)
>>>
>>> When Gödel refers to a proposition asserting its own unprovability then
>>> within the precise focus on these exact words we can see that such a
>>> proposition would be unprovable because it would be self-contradictory.
>>>
>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>
>>> When we simply strip away the reference to Gödel numbers thus requiring
>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>
>>> When we convert to more standard notational conventions an add an
>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>
>>> A proof of G in F that proves that G cannot be proved in F is simply
>>> self-contradictory, thus no such G exists in F.
>>
>> If we take the simplest possible essence of Gödel's logic sentence we
>> have: *G asserts its own unprovability in F*
>
> No, that isn't what Godel logic sentence says at all in F.
>
> Thus, your arguement is built on a LIE, showing you don't understand how
> logic works.
>
>>
>> This means that G is asserting that there is no sequence of inference
>> steps in F that derives G.
>
> No, that G is asserting that there is no FINITE sequence of inference
> steps in F that demonstrates G.
>
> You just proved you don't understand the meaning of "Proof"
>
> Proofs in classic logic are, by definition, Finite.
>
>>
>> For G to be satisfied in F there would have to be a sequence of
>> inference steps in F that proves there is no such sequence of inference
>> steps in F.
>
> Right, but G can be true due to an INFINITE sequence of inference steps
> in F, and not be provable.
>
> Since there is a difference between an INFINTE sequence and a FINITE
> sequence, it is possible for both to exist.
>

You already said that proofs cannot have infinite sequences thus when G
asserts its own unprovability in F it is asserting that there is no
finite sequence of inference steps in F that derive G.

To satisfy G requires a finite sequence of inference steps in F that
proves there is no such finite sequence of inference steps in F.

G cannot be satisfied by any infinite proof because infinite proofs are
not allowed. Unless there is a finite sequence of steps in F that proves
that no such sequence of steps exist in F, G remains unsatisfiable in F.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 5:50 PM, olcott wrote:
> On 4/15/2023 4:34 PM, Richard Damon wrote:
>> On 4/15/23 5:15 PM, olcott wrote:
>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>> "We are therefore confronted with a proposition which asserts its own
>>>>   unprovability." (Gödel 1931:39-41)
>>>>
>>>> When Gödel refers to a proposition asserting its own unprovability then
>>>> within the precise focus on these exact words we can see that such a
>>>> proposition would be unprovable because it would be self-contradictory.
>>>>
>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>
>>>> When we simply strip away the reference to Gödel numbers thus requiring
>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>
>>>> When we convert to more standard notational conventions an add an
>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>
>>>> A proof of G in F that proves that G cannot be proved in F is simply
>>>> self-contradictory, thus no such G exists in F.
>>>
>>> If we take the simplest possible essence of Gödel's logic sentence we
>>> have: *G asserts its own unprovability in F*
>>
>> No, that isn't what Godel logic sentence says at all in F.
>>
>> Thus, your arguement is built on a LIE, showing you don't understand
>> how logic works.
>>
>>>
>>> This means that G is asserting that there is no sequence of inference
>>> steps in F that derives G.
>>
>> No, that G is asserting that there is no FINITE sequence of inference
>> steps in F that demonstrates G.
>>
>> You just proved you don't understand the meaning of "Proof"
>>
>> Proofs in classic logic are, by definition, Finite.
>>
>>>
>>> For G to be satisfied in F there would have to be a sequence of
>>> inference steps in F that proves there is no such sequence of inference
>>> steps in F.
>>
>> Right, but G can be true due to an INFINITE sequence of inference
>> steps in F, and not be provable.
>>
>> Since there is a difference between an INFINTE sequence and a FINITE
>> sequence, it is possible for both to exist.
>>
>
> You already said that proofs cannot have infinite sequences thus when G
> asserts its own unprovability in F it is asserting that there is no
> finite sequence of inference steps in F that derive G.

So, there is no claim that G is provable in F, just that it is True in
F, and to be True just requires an infinite sequence of inference steps.

The only one trying to prove in F that G is true is you, and that
operation can easily be proven to be impossible, and in fact, that is
part of the proof in the Meta-Theory that shows that G is True (and thus
unprovable, since in the meta-theory we can deduce that if the actual G
is true it can not be proven in F).

>
> To satisfy G requires a finite sequence of inference steps in F that
> proves there is no such finite sequence of inference steps in F.

No, that would only be needed to prove G in F. Godel never claims to
prove, in F, that G is true, he only proves in Meta-F that G is true in
F. You are just showing you don't understand what you are talking about.

>
> G cannot be satisfied by any infinite proof because infinite proofs are
> not allowed. Unless there is a finite sequence of steps in F that proves
> that no such sequence of steps exist in F, G remains unsatisfiable in F.
>

Yes, G can not be proved IN F, but that doesn't mean that we can't prove
that G is True in F with a proof in a Meta-Theory that knows about the
rules of F.

There CAN be a proof in the Meta-Theory that shows that, in F, there is
an infinite sequence of steps in F that demonstrate G, making G true in
F, but not provable. The additional properties of the Meta-Theory can
demonstrate this in a finite number of steps in the Meta-Theory, thus
PROVING that G is True in F, and unprovable.

On 4/15/2023 5:05 PM, Richard Damon wrote:
> On 4/15/23 5:50 PM, olcott wrote:
>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>> On 4/15/23 5:15 PM, olcott wrote:
>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>> "We are therefore confronted with a proposition which asserts its own
>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>
>>>>> When Gödel refers to a proposition asserting its own unprovability
>>>>> then
>>>>> within the precise focus on these exact words we can see that such a
>>>>> proposition would be unprovable because it would be
>>>>> self-contradictory.
>>>>>
>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>
>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>> requiring
>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>
>>>>> When we convert to more standard notational conventions an add an
>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>
>>>>> A proof of G in F that proves that G cannot be proved in F is simply
>>>>> self-contradictory, thus no such G exists in F.
>>>>
>>>> If we take the simplest possible essence of Gödel's logic sentence we
>>>> have: *G asserts its own unprovability in F*
>>>
>>> No, that isn't what Godel logic sentence says at all in F.
>>>
>>> Thus, your arguement is built on a LIE, showing you don't understand
>>> how logic works.
>>>
>>>>
>>>> This means that G is asserting that there is no sequence of inference
>>>> steps in F that derives G.
>>>
>>> No, that G is asserting that there is no FINITE sequence of inference
>>> steps in F that demonstrates G.
>>>
>>> You just proved you don't understand the meaning of "Proof"
>>>
>>> Proofs in classic logic are, by definition, Finite.
>>>
>>>>
>>>> For G to be satisfied in F there would have to be a sequence of
>>>> inference steps in F that proves there is no such sequence of inference
>>>> steps in F.
>>>
>>> Right, but G can be true due to an INFINITE sequence of inference
>>> steps in F, and not be provable.
>>>
>>> Since there is a difference between an INFINTE sequence and a FINITE
>>> sequence, it is possible for both to exist.
>>>
>>
>> You already said that proofs cannot have infinite sequences thus when G
>> asserts its own unprovability in F it is asserting that there is no
>> finite sequence of inference steps in F that derive G.
>
> So, there is no claim that G is provable in F, just that it is True in
> F, and to be True just requires an infinite sequence of inference steps.
>
> The only one trying to prove in F that G is true is you, and that
> operation can easily be proven to be impossible,
G is unsatisfiable in F because G is self-contradictory in F

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 6:18 PM, olcott wrote:
> On 4/15/2023 5:05 PM, Richard Damon wrote:
>> On 4/15/23 5:50 PM, olcott wrote:
>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>> "We are therefore confronted with a proposition which asserts its own
>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>
>>>>>> When Gödel refers to a proposition asserting its own unprovability
>>>>>> then
>>>>>> within the precise focus on these exact words we can see that such a
>>>>>> proposition would be unprovable because it would be
>>>>>> self-contradictory.
>>>>>>
>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>
>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>> requiring
>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>
>>>>>> When we convert to more standard notational conventions an add an
>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>
>>>>>> A proof of G in F that proves that G cannot be proved in F is simply
>>>>>> self-contradictory, thus no such G exists in F.
>>>>>
>>>>> If we take the simplest possible essence of Gödel's logic sentence we
>>>>> have: *G asserts its own unprovability in F*
>>>>
>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>
>>>> Thus, your arguement is built on a LIE, showing you don't understand
>>>> how logic works.
>>>>
>>>>>
>>>>> This means that G is asserting that there is no sequence of inference
>>>>> steps in F that derives G.
>>>>
>>>> No, that G is asserting that there is no FINITE sequence of
>>>> inference steps in F that demonstrates G.
>>>>
>>>> You just proved you don't understand the meaning of "Proof"
>>>>
>>>> Proofs in classic logic are, by definition, Finite.
>>>>
>>>>>
>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>> inference steps in F that proves there is no such sequence of
>>>>> inference
>>>>> steps in F.
>>>>
>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>> steps in F, and not be provable.
>>>>
>>>> Since there is a difference between an INFINTE sequence and a FINITE
>>>> sequence, it is possible for both to exist.
>>>>
>>>
>>> You already said that proofs cannot have infinite sequences thus when G
>>> asserts its own unprovability in F it is asserting that there is no
>>> finite sequence of inference steps in F that derive G.
>>
>> So, there is no claim that G is provable in F, just that it is True in
>> F, and to be True just requires an infinite sequence of inference steps.
>>
>> The only one trying to prove in F that G is true is you, and that
>> operation can easily be proven to be impossible,
> G is unsatisfiable in F because G is self-contradictory in F
>

Maybe your FAKE G, but the ACTUAL G is fully statisfiable in F, and this
is actually proven in his proof.

You are just too stupid to understand that actual proof, and need to
make incorrect simplifications to try to understand it.

You are just showing that you are not qualified to deal with complicated
logic.

On 4/15/2023 6:22 PM, Richard Damon wrote:
> On 4/15/23 6:18 PM, olcott wrote:
>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>> On 4/15/23 5:50 PM, olcott wrote:
>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>> "We are therefore confronted with a proposition which asserts its
>>>>>>> own
>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>
>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>> unprovability then
>>>>>>> within the precise focus on these exact words we can see that such a
>>>>>>> proposition would be unprovable because it would be
>>>>>>> self-contradictory.
>>>>>>>
>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>
>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>> requiring
>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>
>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>
>>>>>>> A proof of G in F that proves that G cannot be proved in F is simply
>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>
>>>>>> If we take the simplest possible essence of Gödel's logic sentence we
>>>>>> have: *G asserts its own unprovability in F*
>>>>>
>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>
>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>> understand how logic works.
>>>>>
>>>>>>
>>>>>> This means that G is asserting that there is no sequence of inference
>>>>>> steps in F that derives G.
>>>>>
>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>> inference steps in F that demonstrates G.
>>>>>
>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>
>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>
>>>>>>
>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>> inference steps in F that proves there is no such sequence of
>>>>>> inference
>>>>>> steps in F.
>>>>>
>>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>>> steps in F, and not be provable.
>>>>>
>>>>> Since there is a difference between an INFINTE sequence and a
>>>>> FINITE sequence, it is possible for both to exist.
>>>>>
>>>>
>>>> You already said that proofs cannot have infinite sequences thus when G
>>>> asserts its own unprovability in F it is asserting that there is no
>>>> finite sequence of inference steps in F that derive G.
>>>
>>> So, there is no claim that G is provable in F, just that it is True
>>> in F, and to be True just requires an infinite sequence of inference
>>> steps.
>>>
>>> The only one trying to prove in F that G is true is you, and that
>>> operation can easily be proven to be impossible,
>> G is unsatisfiable in F because G is self-contradictory in F
>>
>
> Maybe your FAKE G,

Ah great so you can see how my simple G is not satisfiable in F.
Do you understand that it is not satisfiable in F because it is self-
contradictory in F ?

> but the ACTUAL G is fully statisfiable in F, and this
> is actually proven in his proof.
>

No it is not. Try and show how Gödel's G is satisfiable in F.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 7:44 PM, olcott wrote:
> On 4/15/2023 6:22 PM, Richard Damon wrote:
>> On 4/15/23 6:18 PM, olcott wrote:
>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>> "We are therefore confronted with a proposition which asserts
>>>>>>>> its own
>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>
>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>> unprovability then
>>>>>>>> within the precise focus on these exact words we can see that
>>>>>>>> such a
>>>>>>>> proposition would be unprovable because it would be
>>>>>>>> self-contradictory.
>>>>>>>>
>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>
>>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>>> requiring
>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>
>>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>
>>>>>>>> A proof of G in F that proves that G cannot be proved in F is
>>>>>>>> simply
>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>
>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>> sentence we
>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>
>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>
>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>> understand how logic works.
>>>>>>
>>>>>>>
>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>> inference
>>>>>>> steps in F that derives G.
>>>>>>
>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>> inference steps in F that demonstrates G.
>>>>>>
>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>
>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>
>>>>>>>
>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>> inference steps in F that proves there is no such sequence of
>>>>>>> inference
>>>>>>> steps in F.
>>>>>>
>>>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>>>> steps in F, and not be provable.
>>>>>>
>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>
>>>>>
>>>>> You already said that proofs cannot have infinite sequences thus
>>>>> when G
>>>>> asserts its own unprovability in F it is asserting that there is no
>>>>> finite sequence of inference steps in F that derive G.
>>>>
>>>> So, there is no claim that G is provable in F, just that it is True
>>>> in F, and to be True just requires an infinite sequence of inference
>>>> steps.
>>>>
>>>> The only one trying to prove in F that G is true is you, and that
>>>> operation can easily be proven to be impossible,
>>> G is unsatisfiable in F because G is self-contradictory in F
>>>
>>
>> Maybe your FAKE G,
>
> Ah great so you can see how my simple G is not satisfiable in F.
> Do you understand that it is not satisfiable in F because it is self-
> contradictory in F ?
>
>> but the ACTUAL G is fully statisfiable in F, and this is actually
>> proven in his proof.
>>
>
> No it is not. Try and show how Gödel's G is satisfiable in F.
>
>

Well, since you don't accept the actual statement that IS Godel's G,
that seems to be a fools errand.

Do you accept that Godel's G is axtually a statement of the form:

There does not exist a whole number g that satisfies <a specific
Primative Recursive Relationship>.

Note, if you DON'T accept that statement as G, then you are just proving
that you don't understand what Godel's proof is about.

If you DO accept that as what Godel's G is, then it isn't that hard to
prove that this is satisfied in F.

On 4/15/2023 6:22 PM, Richard Damon wrote:
> On 4/15/23 6:18 PM, olcott wrote:
>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>> On 4/15/23 5:50 PM, olcott wrote:
>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>> "We are therefore confronted with a proposition which asserts its
>>>>>>> own
>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>
>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>> unprovability then
>>>>>>> within the precise focus on these exact words we can see that such a
>>>>>>> proposition would be unprovable because it would be
>>>>>>> self-contradictory.
>>>>>>>
>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>
>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>> requiring
>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>
>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>
>>>>>>> A proof of G in F that proves that G cannot be proved in F is simply
>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>
>>>>>> If we take the simplest possible essence of Gödel's logic sentence we
>>>>>> have: *G asserts its own unprovability in F*
>>>>>
>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>
>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>> understand how logic works.
>>>>>
>>>>>>
>>>>>> This means that G is asserting that there is no sequence of inference
>>>>>> steps in F that derives G.
>>>>>
>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>> inference steps in F that demonstrates G.
>>>>>
>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>
>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>
>>>>>>
>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>> inference steps in F that proves there is no such sequence of
>>>>>> inference
>>>>>> steps in F.
>>>>>
>>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>>> steps in F, and not be provable.
>>>>>
>>>>> Since there is a difference between an INFINTE sequence and a
>>>>> FINITE sequence, it is possible for both to exist.
>>>>>
>>>>
>>>> You already said that proofs cannot have infinite sequences thus when G
>>>> asserts its own unprovability in F it is asserting that there is no
>>>> finite sequence of inference steps in F that derive G.
>>>
>>> So, there is no claim that G is provable in F, just that it is True
>>> in F, and to be True just requires an infinite sequence of inference
>>> steps.
>>>
>>> The only one trying to prove in F that G is true is you, and that
>>> operation can easily be proven to be impossible,
>> G is unsatisfiable in F because G is self-contradictory in F
>>
>
> Maybe your FAKE G,

Ah great so you can see how my simple G is not satisfiable in F.
Do you understand that it is not satisfiable in F because it is self-
contradictory in F ?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/2023 6:56 PM, Richard Damon wrote:
> On 4/15/23 7:44 PM, olcott wrote:
>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>> On 4/15/23 6:18 PM, olcott wrote:
>>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>>> "We are therefore confronted with a proposition which asserts
>>>>>>>>> its own
>>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>>
>>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>>> unprovability then
>>>>>>>>> within the precise focus on these exact words we can see that
>>>>>>>>> such a
>>>>>>>>> proposition would be unprovable because it would be
>>>>>>>>> self-contradictory.
>>>>>>>>>
>>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>>
>>>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>>>> requiring
>>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>>
>>>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>>
>>>>>>>>> A proof of G in F that proves that G cannot be proved in F is
>>>>>>>>> simply
>>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>>
>>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>>> sentence we
>>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>>
>>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>>
>>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>>> understand how logic works.
>>>>>>>
>>>>>>>>
>>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>>> inference
>>>>>>>> steps in F that derives G.
>>>>>>>
>>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>>> inference steps in F that demonstrates G.
>>>>>>>
>>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>>
>>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>>
>>>>>>>>
>>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>>> inference steps in F that proves there is no such sequence of
>>>>>>>> inference
>>>>>>>> steps in F.
>>>>>>>
>>>>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>>>>> steps in F, and not be provable.
>>>>>>>
>>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>>
>>>>>>
>>>>>> You already said that proofs cannot have infinite sequences thus
>>>>>> when G
>>>>>> asserts its own unprovability in F it is asserting that there is no
>>>>>> finite sequence of inference steps in F that derive G.
>>>>>
>>>>> So, there is no claim that G is provable in F, just that it is True
>>>>> in F, and to be True just requires an infinite sequence of
>>>>> inference steps.
>>>>>
>>>>> The only one trying to prove in F that G is true is you, and that
>>>>> operation can easily be proven to be impossible,
>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>
>>>
>>> Maybe your FAKE G,
>>
>> Ah great so you can see how my simple G is not satisfiable in F.
>> Do you understand that it is not satisfiable in F because it is self-
>> contradictory in F ?
>>
>>> but the ACTUAL G is fully statisfiable in F, and this is actually
>>> proven in his proof.
>>>
>>
>> No it is not. Try and show how Gödel's G is satisfiable in F.
>>
>>
>
> Well, since you don't accept the actual statement that IS Godel's G,
> that seems to be a fools errand.
>
> Do you accept that Godel's G is axtually a statement of the form:
>
> There does not exist a whole number g that satisfies <a specific
> Primative Recursive Relationship>.
>

How do we show that in F.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 8:00 PM, olcott wrote:
> On 4/15/2023 6:56 PM, Richard Damon wrote:
>> On 4/15/23 7:44 PM, olcott wrote:
>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>>>> "We are therefore confronted with a proposition which asserts
>>>>>>>>>> its own
>>>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>>>
>>>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>>>> unprovability then
>>>>>>>>>> within the precise focus on these exact words we can see that
>>>>>>>>>> such a
>>>>>>>>>> proposition would be unprovable because it would be
>>>>>>>>>> self-contradictory.
>>>>>>>>>>
>>>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>>>
>>>>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>>>>> requiring
>>>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>>>
>>>>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>>>
>>>>>>>>>> A proof of G in F that proves that G cannot be proved in F is
>>>>>>>>>> simply
>>>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>>>
>>>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>>>> sentence we
>>>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>>>
>>>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>>>
>>>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>>>> understand how logic works.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>>>> inference
>>>>>>>>> steps in F that derives G.
>>>>>>>>
>>>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>>>> inference steps in F that demonstrates G.
>>>>>>>>
>>>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>>>
>>>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>>>> inference steps in F that proves there is no such sequence of
>>>>>>>>> inference
>>>>>>>>> steps in F.
>>>>>>>>
>>>>>>>> Right, but G can be true due to an INFINITE sequence of
>>>>>>>> inference steps in F, and not be provable.
>>>>>>>>
>>>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>>>
>>>>>>>
>>>>>>> You already said that proofs cannot have infinite sequences thus
>>>>>>> when G
>>>>>>> asserts its own unprovability in F it is asserting that there is no
>>>>>>> finite sequence of inference steps in F that derive G.
>>>>>>
>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>> inference steps.
>>>>>>
>>>>>> The only one trying to prove in F that G is true is you, and that
>>>>>> operation can easily be proven to be impossible,
>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>
>>>>
>>>> Maybe your FAKE G,
>>>
>>> Ah great so you can see how my simple G is not satisfiable in F.
>>> Do you understand that it is not satisfiable in F because it is self-
>>> contradictory in F ?
>>>
>>>> but the ACTUAL G is fully statisfiable in F, and this is actually
>>>> proven in his proof.
>>>>
>>>
>>> No it is not. Try and show how Gödel's G is satisfiable in F.
>>>
>>>
>>
>> Well, since you don't accept the actual statement that IS Godel's G,
>> that seems to be a fools errand.
>>
>> Do you accept that Godel's G is axtually a statement of the form:
>>
>> There does not exist a whole number g that satisfies <a specific
>> Primative Recursive Relationship>.
>>
>
> How do we show that in F.
>

It can be shown if F be testing every whole number, and seeing that none
of them statisy the relationship.

This takes infinite time to do in F, but that is enough to make it True
in F.

If can be PROVEN in Meta-F, because in Meta-F we can show some extra facts.

1) That any statement or proof in F can be mapped to a specific whole
number via the rules established in Meta-F.

2) That this specific Primative Recursive Relationship is a "Proof
Checker in F" for proofs expressed as a number by this system.

3) That the specific statement proven by this PRR is the statement G.

4) Thus, if such a number existed that matches the PRR, then that number
would show the existance of a proof of G, ie that no number can exist
that satisfies that relationship.

5) Thus, the existance of such a number therefore proves that such a
number can't exist, which leads to a contradiction, so no such number
can exist.

6) Thus, we have established that no such number exists, and thus G is
true.

7) Also, we know that there can not exist a proof of this in G, since if
one did exist, we could compute the number that represented it, and, by
necessity, that would satisfy the relationship, making G false.

Thus, G must be True, and unprovable in F, or there would exist a False
statement that had been proven to be True, which means that the system F
was not consistent, but F being consistent was one of the requirements
put on F. (You can of course prove G in F if F is inconsistent, since
you can prove ANYTHING in a system that is inconsistent).

(That last point is an important one for you proofs, as all your logic
to show things seems to be ultimately rooted in first creating an
incosistency in your system of logic, so you can prove the statement you
want).

On 4/15/23 7:58 PM, olcott wrote:
> On 4/15/2023 6:22 PM, Richard Damon wrote:
>> On 4/15/23 6:18 PM, olcott wrote:
>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>> "We are therefore confronted with a proposition which asserts
>>>>>>>> its own
>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>
>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>> unprovability then
>>>>>>>> within the precise focus on these exact words we can see that
>>>>>>>> such a
>>>>>>>> proposition would be unprovable because it would be
>>>>>>>> self-contradictory.
>>>>>>>>
>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>
>>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>>> requiring
>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>
>>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>
>>>>>>>> A proof of G in F that proves that G cannot be proved in F is
>>>>>>>> simply
>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>
>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>> sentence we
>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>
>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>
>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>> understand how logic works.
>>>>>>
>>>>>>>
>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>> inference
>>>>>>> steps in F that derives G.
>>>>>>
>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>> inference steps in F that demonstrates G.
>>>>>>
>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>
>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>
>>>>>>>
>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>> inference steps in F that proves there is no such sequence of
>>>>>>> inference
>>>>>>> steps in F.
>>>>>>
>>>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>>>> steps in F, and not be provable.
>>>>>>
>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>
>>>>>
>>>>> You already said that proofs cannot have infinite sequences thus
>>>>> when G
>>>>> asserts its own unprovability in F it is asserting that there is no
>>>>> finite sequence of inference steps in F that derive G.
>>>>
>>>> So, there is no claim that G is provable in F, just that it is True
>>>> in F, and to be True just requires an infinite sequence of inference
>>>> steps.
>>>>
>>>> The only one trying to prove in F that G is true is you, and that
>>>> operation can easily be proven to be impossible,
>>> G is unsatisfiable in F because G is self-contradictory in F
>>>
>>
>> Maybe your FAKE G,
>
> Ah great so you can see how my simple G is not satisfiable in F.
> Do you understand that it is not satisfiable in F because it is self-
> contradictory in F ?
>

But that doesn't matter, because it isn't the statement that proves that
all sufficiently powerful systems are inconsistent.

Note, the fact that it would be impossible to actually prove your
pseudo-G in F doesn't mean that it can't be true.

Note, it can't be False, but its status of being a Truth Bearer can't be
proven in F.

On 4/15/2023 7:20 PM, Richard Damon wrote:
> On 4/15/23 8:00 PM, olcott wrote:
>> On 4/15/2023 6:56 PM, Richard Damon wrote:
>>> On 4/15/23 7:44 PM, olcott wrote:
>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>>>>> "We are therefore confronted with a proposition which asserts
>>>>>>>>>>> its own
>>>>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>>>>
>>>>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>>>>> unprovability then
>>>>>>>>>>> within the precise focus on these exact words we can see that
>>>>>>>>>>> such a
>>>>>>>>>>> proposition would be unprovable because it would be
>>>>>>>>>>> self-contradictory.
>>>>>>>>>>>
>>>>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>>>>
>>>>>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>>>>>> requiring
>>>>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>>>>
>>>>>>>>>>> When we convert to more standard notational conventions an
>>>>>>>>>>> add an
>>>>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>>>>
>>>>>>>>>>> A proof of G in F that proves that G cannot be proved in F is
>>>>>>>>>>> simply
>>>>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>>>>
>>>>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>>>>> sentence we
>>>>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>>>>
>>>>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>>>>
>>>>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>>>>> understand how logic works.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>>>>> inference
>>>>>>>>>> steps in F that derives G.
>>>>>>>>>
>>>>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>>>>> inference steps in F that demonstrates G.
>>>>>>>>>
>>>>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>>>>
>>>>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>>>>> inference steps in F that proves there is no such sequence of
>>>>>>>>>> inference
>>>>>>>>>> steps in F.
>>>>>>>>>
>>>>>>>>> Right, but G can be true due to an INFINITE sequence of
>>>>>>>>> inference steps in F, and not be provable.
>>>>>>>>>
>>>>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You already said that proofs cannot have infinite sequences thus
>>>>>>>> when G
>>>>>>>> asserts its own unprovability in F it is asserting that there is no
>>>>>>>> finite sequence of inference steps in F that derive G.
>>>>>>>
>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>>> inference steps.
>>>>>>>
>>>>>>> The only one trying to prove in F that G is true is you, and that
>>>>>>> operation can easily be proven to be impossible,
>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>
>>>>>
>>>>> Maybe your FAKE G,
>>>>
>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>> Do you understand that it is not satisfiable in F because it is self-
>>>> contradictory in F ?
>>>>
>>>>> but the ACTUAL G is fully statisfiable in F, and this is actually
>>>>> proven in his proof.
>>>>>
>>>>
>>>> No it is not. Try and show how Gödel's G is satisfiable in F.
>>>>
>>>>
>>>
>>> Well, since you don't accept the actual statement that IS Godel's G,
>>> that seems to be a fools errand.
>>>
>>> Do you accept that Godel's G is axtually a statement of the form:
>>>
>>> There does not exist a whole number g that satisfies <a specific
>>> Primative Recursive Relationship>.
>>>
>>
>> How do we show that in F.
>>
>
> It can be shown if F be testing every whole number, and seeing that none
> of them statisy the relationship.
>
> This takes infinite time to do in F, but that is enough to make it True
> in F.

Thus it is impossible. Everything that takes an infinite amount of time
is impossible because an infinite amount of time does not and cannot
exist.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/2023 6:22 PM, Richard Damon wrote:
> On 4/15/23 6:18 PM, olcott wrote:
>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>> On 4/15/23 5:50 PM, olcott wrote:
>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>> "We are therefore confronted with a proposition which asserts its
>>>>>>> own
>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>
>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>> unprovability then
>>>>>>> within the precise focus on these exact words we can see that such a
>>>>>>> proposition would be unprovable because it would be
>>>>>>> self-contradictory.
>>>>>>>
>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>
>>>>>>> When we simply strip away the reference to Gödel numbers thus
>>>>>>> requiring
>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>
>>>>>>> When we convert to more standard notational conventions an add an
>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>
>>>>>>> A proof of G in F that proves that G cannot be proved in F is simply
>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>
>>>>>> If we take the simplest possible essence of Gödel's logic sentence we
>>>>>> have: *G asserts its own unprovability in F*
>>>>>
>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>
>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>> understand how logic works.
>>>>>
>>>>>>
>>>>>> This means that G is asserting that there is no sequence of inference
>>>>>> steps in F that derives G.
>>>>>
>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>> inference steps in F that demonstrates G.
>>>>>
>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>
>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>
>>>>>>
>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>> inference steps in F that proves there is no such sequence of
>>>>>> inference
>>>>>> steps in F.
>>>>>
>>>>> Right, but G can be true due to an INFINITE sequence of inference
>>>>> steps in F, and not be provable.
>>>>>
>>>>> Since there is a difference between an INFINTE sequence and a
>>>>> FINITE sequence, it is possible for both to exist.
>>>>>
>>>>
>>>> You already said that proofs cannot have infinite sequences thus when G
>>>> asserts its own unprovability in F it is asserting that there is no
>>>> finite sequence of inference steps in F that derive G.
>>>
>>> So, there is no claim that G is provable in F, just that it is True
>>> in F, and to be True just requires an infinite sequence of inference
>>> steps.
>>>
>>> The only one trying to prove in F that G is true is you, and that
>>> operation can easily be proven to be impossible,
>> G is unsatisfiable in F because G is self-contradictory in F
>>
>
> Maybe your FAKE G,

Ah great so you can see how my simple G is not satisfiable in F.
Do you understand that it is not satisfiable in F because it is self-
contradictory in F ?

I will keep asking this until you answer.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 8:28 PM, olcott wrote:
> On 4/15/2023 7:20 PM, Richard Damon wrote:
>> On 4/15/23 8:00 PM, olcott wrote:
>>> On 4/15/2023 6:56 PM, Richard Damon wrote:
>>>> On 4/15/23 7:44 PM, olcott wrote:
>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>>>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>>>>>> "We are therefore confronted with a proposition which
>>>>>>>>>>>> asserts its own
>>>>>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>>>>>
>>>>>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>>>>>> unprovability then
>>>>>>>>>>>> within the precise focus on these exact words we can see
>>>>>>>>>>>> that such a
>>>>>>>>>>>> proposition would be unprovable because it would be
>>>>>>>>>>>> self-contradictory.
>>>>>>>>>>>>
>>>>>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>>>>>
>>>>>>>>>>>> When we simply strip away the reference to Gödel numbers
>>>>>>>>>>>> thus requiring
>>>>>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>>>>>
>>>>>>>>>>>> When we convert to more standard notational conventions an
>>>>>>>>>>>> add an
>>>>>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>>>>>
>>>>>>>>>>>> A proof of G in F that proves that G cannot be proved in F
>>>>>>>>>>>> is simply
>>>>>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>>>>>
>>>>>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>>>>>> sentence we
>>>>>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>>>>>
>>>>>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>>>>>
>>>>>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>>>>>> understand how logic works.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>>>>>> inference
>>>>>>>>>>> steps in F that derives G.
>>>>>>>>>>
>>>>>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>>>>>> inference steps in F that demonstrates G.
>>>>>>>>>>
>>>>>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>>>>>
>>>>>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>>>>>> inference steps in F that proves there is no such sequence of
>>>>>>>>>>> inference
>>>>>>>>>>> steps in F.
>>>>>>>>>>
>>>>>>>>>> Right, but G can be true due to an INFINITE sequence of
>>>>>>>>>> inference steps in F, and not be provable.
>>>>>>>>>>
>>>>>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You already said that proofs cannot have infinite sequences
>>>>>>>>> thus when G
>>>>>>>>> asserts its own unprovability in F it is asserting that there
>>>>>>>>> is no
>>>>>>>>> finite sequence of inference steps in F that derive G.
>>>>>>>>
>>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>>>> inference steps.
>>>>>>>>
>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>
>>>>>>
>>>>>> Maybe your FAKE G,
>>>>>
>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>> Do you understand that it is not satisfiable in F because it is self-
>>>>> contradictory in F ?
>>>>>
>>>>>> but the ACTUAL G is fully statisfiable in F, and this is actually
>>>>>> proven in his proof.
>>>>>>
>>>>>
>>>>> No it is not. Try and show how Gödel's G is satisfiable in F.
>>>>>
>>>>>
>>>>
>>>> Well, since you don't accept the actual statement that IS Godel's G,
>>>> that seems to be a fools errand.
>>>>
>>>> Do you accept that Godel's G is axtually a statement of the form:
>>>>
>>>> There does not exist a whole number g that satisfies <a specific
>>>> Primative Recursive Relationship>.
>>>>
>>>
>>> How do we show that in F.
>>>
>>
>> It can be shown if F be testing every whole number, and seeing that
>> none of them statisy the relationship.
>>
>> This takes infinite time to do in F, but that is enough to make it
>> True in F.
>
> Thus it is impossible. Everything that takes an infinite amount of time
> is impossible because an infinite amount of time does not and cannot
> exist.
>

Nope, Truth just requires a CONNECTION, which can be infinite.

For US to do it would be impossible, but that doesn't mean the
connection doesn't exist.

You are showing your ignorance of what Truth actually is, confusing it
with Knowldege, which is something different.

I suppose this would be an easy mistake for someone who thinks they are
God, since for the REAL God, all Truth is actually known, since God is
actually infinite, and thus can know things that need infinite to know.

But you are finite, and thus can only know what is finite, so not all
Truth is knowable.

On 4/15/2023 7:39 PM, Richard Damon wrote:
> On 4/15/23 8:28 PM, olcott wrote:
>> On 4/15/2023 7:20 PM, Richard Damon wrote:
>>> On 4/15/23 8:00 PM, olcott wrote:
>>>> On 4/15/2023 6:56 PM, Richard Damon wrote:
>>>>> On 4/15/23 7:44 PM, olcott wrote:
>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>>>>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>>>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>>>>>>> "We are therefore confronted with a proposition which
>>>>>>>>>>>>> asserts its own
>>>>>>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>>>>>>
>>>>>>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>>>>>>> unprovability then
>>>>>>>>>>>>> within the precise focus on these exact words we can see
>>>>>>>>>>>>> that such a
>>>>>>>>>>>>> proposition would be unprovable because it would be
>>>>>>>>>>>>> self-contradictory.
>>>>>>>>>>>>>
>>>>>>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>>>>>>
>>>>>>>>>>>>> When we simply strip away the reference to Gödel numbers
>>>>>>>>>>>>> thus requiring
>>>>>>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>>>>>>>>>>>>
>>>>>>>>>>>>> When we convert to more standard notational conventions an
>>>>>>>>>>>>> add an
>>>>>>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>>>>>>
>>>>>>>>>>>>> A proof of G in F that proves that G cannot be proved in F
>>>>>>>>>>>>> is simply
>>>>>>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>>>>>>
>>>>>>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>>>>>>> sentence we
>>>>>>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>>>>>>
>>>>>>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>>>>>>
>>>>>>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>>>>>>> understand how logic works.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>>>>>>> inference
>>>>>>>>>>>> steps in F that derives G.
>>>>>>>>>>>
>>>>>>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>>>>>>> inference steps in F that demonstrates G.
>>>>>>>>>>>
>>>>>>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>>>>>>
>>>>>>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> For G to be satisfied in F there would have to be a sequence of
>>>>>>>>>>>> inference steps in F that proves there is no such sequence
>>>>>>>>>>>> of inference
>>>>>>>>>>>> steps in F.
>>>>>>>>>>>
>>>>>>>>>>> Right, but G can be true due to an INFINITE sequence of
>>>>>>>>>>> inference steps in F, and not be provable.
>>>>>>>>>>>
>>>>>>>>>>> Since there is a difference between an INFINTE sequence and a
>>>>>>>>>>> FINITE sequence, it is possible for both to exist.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You already said that proofs cannot have infinite sequences
>>>>>>>>>> thus when G
>>>>>>>>>> asserts its own unprovability in F it is asserting that there
>>>>>>>>>> is no
>>>>>>>>>> finite sequence of inference steps in F that derive G.
>>>>>>>>>
>>>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>>>>> inference steps.
>>>>>>>>>
>>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>
>>>>>>>
>>>>>>> Maybe your FAKE G,
>>>>>>
>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>> Do you understand that it is not satisfiable in F because it is self-
>>>>>> contradictory in F ?
>>>>>>
>>>>>>> but the ACTUAL G is fully statisfiable in F, and this is actually
>>>>>>> proven in his proof.
>>>>>>>
>>>>>>
>>>>>> No it is not. Try and show how Gödel's G is satisfiable in F.
>>>>>>
>>>>>>
>>>>>
>>>>> Well, since you don't accept the actual statement that IS Godel's
>>>>> G, that seems to be a fools errand.
>>>>>
>>>>> Do you accept that Godel's G is axtually a statement of the form:
>>>>>
>>>>> There does not exist a whole number g that satisfies <a specific
>>>>> Primative Recursive Relationship>.
>>>>>
>>>>
>>>> How do we show that in F.
>>>>
>>>
>>> It can be shown if F be testing every whole number, and seeing that
>>> none of them statisy the relationship.
>>>
>>> This takes infinite time to do in F, but that is enough to make it
>>> True in F.
>>
>> Thus it is impossible. Everything that takes an infinite amount of time
>> is impossible because an infinite amount of time does not and cannot
>> exist.
>>
>
> Nope, Truth just requires a CONNECTION, which can be infinite.
>
Truth might allow this Satisfiability does not.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 8:29 PM, olcott wrote:
> On 4/15/2023 6:22 PM, Richard Damon wrote:
>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>
>>>> So, there is no claim that G is provable in F, just that it is True
>>>> in F, and to be True just requires an infinite sequence of inference
>>>> steps.
>>>>
>>>> The only one trying to prove in F that G is true is you, and that
>>>> operation can easily be proven to be impossible,
>>> G is unsatisfiable in F because G is self-contradictory in F
>>>
>>
>> Maybe your FAKE G,
>
> Ah great so you can see how my simple G is not satisfiable in F.
> Do you understand that it is not satisfiable in F because it is self-
> contradictory in F ?
>
> I will keep asking this until you answer.
>
But that doesn't matter, because it isn't the statement that proves that
all sufficiently powerful systems are inconsistent.

Note, the fact that it would be impossible to actually prove your
pseudo-G in F doesn't mean that it can't be true.

Note, it can't be False, but its status of being a Truth Bearer can't be
proven in F.

Maybe you need to learn to read, because my answer DOES answer your
question and show that you are wrong.

Just shows the level of your intelect.

Another point, you are showing that you don't understand what
"self-contradictory" means.

"This statement is not Provable" is NOT Self-Contradictory, as it has a
possible set of truth values that makes it satisified, that is being
True but Unprovable.

That is a VALID combination of truth values

Being Proven but untrue would be contradictory, as Proven requires True.

So, you are just furthering your proof that you don't understand what
you are talking about.

You have locked into your mind some false statements, and they make you
whole logic system invalid.

On 4/15/23 8:44 PM, olcott wrote:
> On 4/15/2023 7:39 PM, Richard Damon wrote:
>> On 4/15/23 8:28 PM, olcott wrote:
>>> On 4/15/2023 7:20 PM, Richard Damon wrote:
>>>> On 4/15/23 8:00 PM, olcott wrote:
>>>>> On 4/15/2023 6:56 PM, Richard Damon wrote:
>>>>>> On 4/15/23 7:44 PM, olcott wrote:
>>>>>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>>>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>> On 4/15/2023 5:05 PM, Richard Damon wrote:
>>>>>>>>>> On 4/15/23 5:50 PM, olcott wrote:
>>>>>>>>>>> On 4/15/2023 4:34 PM, Richard Damon wrote:
>>>>>>>>>>>> On 4/15/23 5:15 PM, olcott wrote:
>>>>>>>>>>>>> On 3/26/2023 1:39 PM, olcott wrote:
>>>>>>>>>>>>>> "We are therefore confronted with a proposition which
>>>>>>>>>>>>>> asserts its own
>>>>>>>>>>>>>>   unprovability." (Gödel 1931:39-41)
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> When Gödel refers to a proposition asserting its own
>>>>>>>>>>>>>> unprovability then
>>>>>>>>>>>>>> within the precise focus on these exact words we can see
>>>>>>>>>>>>>> that such a
>>>>>>>>>>>>>> proposition would be unprovable because it would be
>>>>>>>>>>>>>> self-contradictory.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>>>>>>>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> When we simply strip away the reference to Gödel numbers
>>>>>>>>>>>>>> thus requiring
>>>>>>>>>>>>>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF
>>>>>>>>>>>>>> (GF).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> When we convert to more standard notational conventions an
>>>>>>>>>>>>>> add an
>>>>>>>>>>>>>> existential quantifier: ∃G ∈  F (G ↔ ¬(F ⊢ G))
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A proof of G in F that proves that G cannot be proved in F
>>>>>>>>>>>>>> is simply
>>>>>>>>>>>>>> self-contradictory, thus no such G exists in F.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If we take the simplest possible essence of Gödel's logic
>>>>>>>>>>>>> sentence we
>>>>>>>>>>>>> have: *G asserts its own unprovability in F*
>>>>>>>>>>>>
>>>>>>>>>>>> No, that isn't what Godel logic sentence says at all in F.
>>>>>>>>>>>>
>>>>>>>>>>>> Thus, your arguement is built on a LIE, showing you don't
>>>>>>>>>>>> understand how logic works.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> This means that G is asserting that there is no sequence of
>>>>>>>>>>>>> inference
>>>>>>>>>>>>> steps in F that derives G.
>>>>>>>>>>>>
>>>>>>>>>>>> No, that G is asserting that there is no FINITE sequence of
>>>>>>>>>>>> inference steps in F that demonstrates G.
>>>>>>>>>>>>
>>>>>>>>>>>> You just proved you don't understand the meaning of "Proof"
>>>>>>>>>>>>
>>>>>>>>>>>> Proofs in classic logic are, by definition, Finite.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> For G to be satisfied in F there would have to be a
>>>>>>>>>>>>> sequence of
>>>>>>>>>>>>> inference steps in F that proves there is no such sequence
>>>>>>>>>>>>> of inference
>>>>>>>>>>>>> steps in F.
>>>>>>>>>>>>
>>>>>>>>>>>> Right, but G can be true due to an INFINITE sequence of
>>>>>>>>>>>> inference steps in F, and not be provable.
>>>>>>>>>>>>
>>>>>>>>>>>> Since there is a difference between an INFINTE sequence and
>>>>>>>>>>>> a FINITE sequence, it is possible for both to exist.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> You already said that proofs cannot have infinite sequences
>>>>>>>>>>> thus when G
>>>>>>>>>>> asserts its own unprovability in F it is asserting that there
>>>>>>>>>>> is no
>>>>>>>>>>> finite sequence of inference steps in F that derive G.
>>>>>>>>>>
>>>>>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>>>>>> True in F, and to be True just requires an infinite sequence
>>>>>>>>>> of inference steps.
>>>>>>>>>>
>>>>>>>>>> The only one trying to prove in F that G is true is you, and
>>>>>>>>>> that operation can easily be proven to be impossible,
>>>>>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>>>>>
>>>>>>>>
>>>>>>>> Maybe your FAKE G,
>>>>>>>
>>>>>>> Ah great so you can see how my simple G is not satisfiable in F.
>>>>>>> Do you understand that it is not satisfiable in F because it is
>>>>>>> self-
>>>>>>> contradictory in F ?
>>>>>>>
>>>>>>>> but the ACTUAL G is fully statisfiable in F, and this is
>>>>>>>> actually proven in his proof.
>>>>>>>>
>>>>>>>
>>>>>>> No it is not. Try and show how Gödel's G is satisfiable in F.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Well, since you don't accept the actual statement that IS Godel's
>>>>>> G, that seems to be a fools errand.
>>>>>>
>>>>>> Do you accept that Godel's G is axtually a statement of the form:
>>>>>>
>>>>>> There does not exist a whole number g that satisfies <a specific
>>>>>> Primative Recursive Relationship>.
>>>>>>
>>>>>
>>>>> How do we show that in F.
>>>>>
>>>>
>>>> It can be shown if F be testing every whole number, and seeing that
>>>> none of them statisy the relationship.
>>>>
>>>> This takes infinite time to do in F, but that is enough to make it
>>>> True in F.
>>>
>>> Thus it is impossible. Everything that takes an infinite amount of time
>>> is impossible because an infinite amount of time does not and cannot
>>> exist.
>>>
>>
>> Nope, Truth just requires a CONNECTION, which can be infinite.
>>
> Truth might allow this Satisfiability does not.
>

In mathematical logic, a formula is satisfiable if it is true under some
assignment of values to its variables.

So, to be satisfiable, we just need a set of values that makes it true.

On 4/15/2023 7:45 PM, Richard Damon wrote:
> On 4/15/23 8:29 PM, olcott wrote:
>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>
>>>>> So, there is no claim that G is provable in F, just that it is True
>>>>> in F, and to be True just requires an infinite sequence of
>>>>> inference steps.
>>>>>
>>>>> The only one trying to prove in F that G is true is you, and that
>>>>> operation can easily be proven to be impossible,
>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>
>>>
>>> Maybe your FAKE G,
>>
>> Ah great so you can see how my simple G is not satisfiable in F.
>> Do you understand that it is not satisfiable in F because it is self-
>> contradictory in F ?
>>
>> I will keep asking this until you answer.
>>
> But that doesn't matter, because it isn't the statement that proves that
> all sufficiently powerful systems are inconsistent.
>
> Note, the fact that it would be impossible to actually prove your
> pseudo-G in F doesn't mean that it can't be true.
>
> Note, it can't be False, but its status of being a Truth Bearer can't be
> proven in F.
>
>
> Maybe you need to learn to read, because my answer DOES answer your
> question and show that you are wrong.
>
> Just shows the level of your intelect.
>
> Another point, you are showing that you don't understand what
> "self-contradictory" means.
>
> "This statement is not Provable" is NOT Self-Contradictory, as it has a
> possible set of truth values that makes it satisified, that is being
> True but Unprovable.
>

When G asserts its own unprovability in F is proven in F this requires a
sequence of inference steps in F that proves there is no such sequence
of inference steps in F.

Try and show how you would provide a sequence of inference steps in F
that correctly proves that no such set of inference steps exists in F.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 4/15/23 8:56 PM, olcott wrote:
> On 4/15/2023 7:45 PM, Richard Damon wrote:
>> On 4/15/23 8:29 PM, olcott wrote:
>>> On 4/15/2023 6:22 PM, Richard Damon wrote:
>>>> On 4/15/23 6:18 PM, olcott wrote:
>>>>>>>>
>>>>>> So, there is no claim that G is provable in F, just that it is
>>>>>> True in F, and to be True just requires an infinite sequence of
>>>>>> inference steps.
>>>>>>
>>>>>> The only one trying to prove in F that G is true is you, and that
>>>>>> operation can easily be proven to be impossible,
>>>>> G is unsatisfiable in F because G is self-contradictory in F
>>>>>
>>>>
>>>> Maybe your FAKE G,
>>>
>>> Ah great so you can see how my simple G is not satisfiable in F.
>>> Do you understand that it is not satisfiable in F because it is self-
>>> contradictory in F ?
>>>
>>> I will keep asking this until you answer.
>>>
>> But that doesn't matter, because it isn't the statement that proves
>> that all sufficiently powerful systems are inconsistent.
>>
>> Note, the fact that it would be impossible to actually prove your
>> pseudo-G in F doesn't mean that it can't be true.
>>
>> Note, it can't be False, but its status of being a Truth Bearer can't
>> be proven in F.
>>
>>
>> Maybe you need to learn to read, because my answer DOES answer your
>> question and show that you are wrong.
>>
>> Just shows the level of your intelect.
>>
>> Another point, you are showing that you don't understand what
>> "self-contradictory" means.
>>
>> "This statement is not Provable" is NOT Self-Contradictory, as it has
>> a possible set of truth values that makes it satisified, that is being
>> True but Unprovable.
>>
>
> When G asserts its own unprovability in F is proven in F this requires a
> sequence of inference steps in F that proves there is no such sequence
> of inference steps in F.
>
> Try and show how you would provide a sequence of inference steps in F
> that correctly proves that no such set of inference steps exists in F.
>

But G isn't PROVEN in F, it just is TRUE in F.

The fact that I can't show the existance of such a sequence doesn't mean
that they don't exist.

We can postualte that an infinite sequence of steps might somehow exist
to show that G is true, but not provable, and the fact that such a
postulate doesn't lead to a contradiction, shows that the statme that G
asserts its own non-provablity isn't "Self-Contradictory".

YOU have the burden of proof if you want to make the claim it is.

You have a FUNDAMENTAL problem (or maybe it is a funny mental problem)
about Truth and Proofs. Things are allowed to be True that are unproven,
and even unprovable. Things that are proven, must be True.

For something to be "Known" it needs to be provable, but not necessarily
in the same "Theory" as the statement is made. This is shown for the
ACTUAL G of Godel, which is True in F, and the Truth is Proven in
Meta-F, so we can KNOW that G is True in F, even though we can't prove
it there. (Knowledge can carry across pocket of logic, under proper
conditions)

You inability to stay on the ACTUAL point, and get stuck on your
unimportant side points just reinforces the fact that you don't really
understand what you are talking about.