Here we have a stipulation of a
Trivalent solution to the Liar Paradox:

https://dcproof.com/LiarParadox2.htm

My stipulation is that there will be always
the posibility to formulate some Paradox.
For example Trivalently this is a new paradox:

"this sentence does not express a true proposition"

Its based on this truth table for "not express a true proposition":

A A =\= T
T F
U T
F T

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

Dan

On Monday, July 24, 2023 at 3:23:27 PM UTC-4, Mild Shock wrote:
> Here we have a stipulation of a
> Trivalent solution to the Liar Paradox:
>
> https://dcproof.com/LiarParadox2.htm
>
[snip]

Trivalent = T richotomy holds

Its in your proof:

ALL(a):[a e s => [a e t | a e f | a e m] (Trichotomy holds)
& ~[a e t & a e f] & ~[a e t & a e m] & ~[a e f & a e m]]

And it gives a new paradox:

"this sentence does not express a true proposition"

See for yourself for an explanation:
https://plato.stanford.edu/entries/liar-paradox/#InstReve

Dan Christensen schrieb am Dienstag, 25. Juli 2023 um 07:06:11 UTC+2:
> See my reply just now to your identical posting at sci.logic.
>
> Dan
> On Monday, July 24, 2023 at 3:23:27 PM UTC-4, Mild Shock wrote:
> > Here we have a stipulation of a
> > Trivalent solution to the Liar Paradox:
> >
> > https://dcproof.com/LiarParadox2.htm
> >
> [snip]

Dan Christensen wrote:

> See my reply just now to your identical posting at sci.logic. Dan
>
> On Monday, July 24, 2023 at 3:23:27 PM UTC-4, Mild Shock wrote:
>> Here we have a stipulation of a Trivalent solution to the Liar Paradox:
>> https://dcproof.com/LiarParadox2.htm [snip]

what a pair of idiots. These two 𝐧𝐚𝐳𝐢𝐬_𝐨𝐟_𝐮𝐤𝐫𝐚𝐢𝐧𝐞 are posting identical
posts.

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

Dan

On Tuesday, July 25, 2023 at 3:20:41 AM UTC-4, Mild Shock wrote:
> Trivalent = T richotomy holds
>
> Its in your proof:
>
> ALL(a):[a e s => [a e t | a e f | a e m] (Trichotomy holds)
> & ~[a e t & a e f] & ~[a e t & a e m] & ~[a e f & a e m]]
>
> And it gives a new paradox:
> "this sentence does not express a true proposition"
> See for yourself for an explanation:
> https://plato.stanford.edu/entries/liar-paradox/#InstReve
> Dan Christensen schrieb am Dienstag, 25. Juli 2023 um 07:06:11 UTC+2:
> > See my reply just now to your identical posting at sci.logic.
> >
> > Dan
> > On Monday, July 24, 2023 at 3:23:27 PM UTC-4, Mild Shock wrote:
> > > Here we have a stipulation of a
> > > Trivalent solution to the Liar Paradox:
> > >
> > > https://dcproof.com/LiarParadox2.htm
> > >
> > [snip]

I 100% agree with Olcott, he is the better Logician:

olcott schrieb am Dienstag, 25. Juli 2023 um 15:18:48 UTC+2:
> > On 7/25/2023 12:04 AM, Dan Christensen wrote:
> > We can say that their truth values are INDETERMINATE (like the "numerical value" of 1/0).
> It is not that no one can determine the truth value, it is that the truth value is non-existent.
https://groups.google.com/g/sci.logic/c/KfDliBm1Hb8/m/S4FUx1w_CAAJ

Dan Christensens usage of the word "indeterminate" is completely wrong.
According to these slides the Liar Paradox doesn't have an "indeterminate"
truth, because "indeterminate" is defined as:

A sentence Φ (or set of sentences Σ) is indeterminate if and only if
there is more than one way to coherently assign it a truth value (or to
assign the sentences contained in it truth values)
http://fitelson.org/piksi/piksi_18/cook_notes.pdf

The correct terminology is "paradoxical", defined as:

A sentence Φ (or set of sentences Σ) is paradoxical if and only if
there is no way to coherently assign it a truth value (or to assign the
sentences contained in it truth values).
http://fitelson.org/piksi/piksi_18/cook_notes.pdf

And its relativey easy to prove that the sentence is paradoxical,
just stay in classical logic and stay with proposition you then get:

/* Law of Non-Contradiction */
∀x(~(Tx & Fx)) &
/* Low of Excluded Middle */
∀x(Tx v Fx) =>
/* Paradoxical */
~∃x(Tx <-> Fx)

Its pretty easy. Even Wolfgang Schwartz tree tool can do it:

(∀x¬(Tx ∧ Fx) ∧ ∀x(Tx ∨ Fx)) → ¬∃x(Tx ↔ Fx) is valid.
https://www.umsu.de/trees/#~6x(~3(Tx~1Fx))~1~6x(Tx~2Fx)~5~3~7x(Tx~4Fx)

Now we have Olcotts "non-existent". But we need to go
back to "propositions" and "classical", to have Olcotts
"non-existent". But Olcott was 100% right.

Dan Christensen schrieb am Dienstag, 25. Juli 2023 um 18:27:27 UTC+2:
> See my reply just now to your identical posting at sci.logic
> Dan
> On Tuesday, July 25, 2023 at 3:20:41 AM UTC-4, Mild Shock wrote:
> > Trivalent = T richotomy holds
> >
> > Its in your proof:
> >
> > ALL(a):[a e s => [a e t | a e f | a e m] (Trichotomy holds)
> > & ~[a e t & a e f] & ~[a e t & a e m] & ~[a e f & a e m]]
> >
> > And it gives a new paradox:
> > "this sentence does not express a true proposition"
> > See for yourself for an explanation:
> > https://plato.stanford.edu/entries/liar-paradox/#InstReve
> > Dan Christensen schrieb am Dienstag, 25. Juli 2023 um 07:06:11 UTC+2:
> > > See my reply just now to your identical posting at sci.logic.
> > >
> > > Dan
> > > On Monday, July 24, 2023 at 3:23:27 PM UTC-4, Mild Shock wrote:
> > > > Here we have a stipulation of a
> > > > Trivalent solution to the Liar Paradox:
> > > >
> > > > https://dcproof.com/LiarParadox2.htm
> > > >
> > > [snip]

See my reply just now to your identical posting elsewhere here.

Dan

On Tuesday, July 25, 2023 at 2:45:49 PM UTC-4, Mild Shock wrote:
> I 100% agree with Olcott, he is the better Logician:
>
> olcott schrieb am Dienstag, 25. Juli 2023 um 15:18:48 UTC+2:
> > > On 7/25/2023 12:04 AM, Dan Christensen wrote:
> > > We can say that their truth values are INDETERMINATE (like the "numerical value" of 1/0).
> > It is not that no one can determine the truth value, it is that the truth value is non-existent.

[snip]

Dan Christensen was in full halucination mode, when he
wrote "INDETERMINATE (like the numeraical value of 1/0)".

Here is a reminder:

1/0 is undefined, non-existent, since 1/0 = x resp 1=0*x has no solution
0/0 is indeterminate, manyvalued, since 0/0 = x resp 0=0*x has many many solutions

You can check yourself dumbo:

List of indeterminate forms
0/0, oo/oo, 0*oo, oo-oo, 0^0, 1^oo, oo^0
https://en.wikipedia.org/wiki/Indeterminate_form#List_of_indeterminate_forms

Where do you see 1/0 in the above list? Irony is,
we could call 1/0 paradoxical, using this definition:

"A sentence Φ (or set of sentences Σ) is paradoxical if and only if
there is NO WAY to coherently assign it a truth value (or to assign the
sentences contained in it truth values)."
http://fitelson.org/piksi/piksi_18/cook_notes.pdf

Dan Christensen schrieb am Dienstag, 25. Juli 2023 um 21:38:37 UTC+2:
> See my reply just now to your identical posting elsewhere here.
>
> Dan
> On Tuesday, July 25, 2023 at 2:45:49 PM UTC-4, Mild Shock wrote:
> > I 100% agree with Olcott, he is the better Logician:
> >
> > olcott schrieb am Dienstag, 25. Juli 2023 um 15:18:48 UTC+2:
> > > > On 7/25/2023 12:04 AM, Dan Christensen wrote:
> > > > We can say that their truth values are INDETERMINATE (like the "numerical value" of 1/0).
> > > It is not that no one can determine the truth value, it is that the truth value is non-existent.
> [snip]

See my reply just now to your identical and really quite pathetic posting elsewhere here.

On Tuesday, July 25, 2023 at 6:55:33 PM UTC-4, Mild Shock wrote:
> Dan Christensen was in full halucination mode, when he
> wrote "INDETERMINATE (like the numeraical value of 1/0)".
>
[snip]

Can_Dr.Joel Mesot,Dr.Klaus Kirch,Dr.Ursula Keller,Dr.Simon Lilly, -please--step into their ETH Zurich physics or chemistry lab and weigh the mass of Electrolysis Water, proving Water is H4O not H2O. AP's homegrown lab cannot do the fine tuning experiment of weighing a test tube of electrolyzed hydrogen and oxygen from water. If AP is correct Water is really H4O, not H2O. My weighing scale is puny and insufficient for the job at hand, 0.00001 gram or less of hydrogen and oxygen test tubes. If AP is correct the hydrogen is 1/4 the weight of oxygen, if mainstream chemistry, physics is correct the hydrogen is 1/8 in amu to oxygen.
>
>
> ETH Zurich
>
> Joel Mesot, Gunther Dissertori
> Paul Biran, Marc Burger, Patrick Cheridito, Manfred Einsiedler, Paul Embrechts
> Giovanni Felder, Alessio Figalli, Norbert Hungerbuhler, Tom Ilmanen, Horst Knorrer
> Emmanuel Kowalski
> Urs Lang
> Rahul Pandharipande
> Richard Pink
> Tristan Riviere
> Dietmar Salamon
> Martin Schweizer
> Mete Soner
> Michael Struwe
> Benjamin Sudakov
> Alain Sznitman
> Josef Teichmann
> Wendelin Werner
> Thomas Willwacher
>
> Zurich ETH, physics dept
> Charalampos Anastasiou, Niklas Beisert, Adrian Biland, Gianni Blatter, Marcella Carollo, Christian Degen, Leonardo Degiorgi, Gunther Dissertori, Klaus Ensslin, Tilman Esslinger, Jerome Faist, Matthias Gaberdiel, Aude Gehrmann-De Ridder, Vadim Geshkenbein, Christophorus Grab, Michele Graf, Jonathan Home, Roland Horisberger, Sebastian Huber, Thomas Markus Ihn, Atac Imamoglu, Steven Johnson, Ursula Keller, Klaus Kirch, Simon Lilly, Joel Mesot, Renatto Renner, Andre Rubbia, Werner Schmutz, Thomas Schulthess, Manfred Sigrist, Hans-Arno Synal, Matthias Troyer, Andreas Vaterlaus, Rainer Wallny, Andreas Wallraff, Werner Wegscheider, Audrey Zheludev, Oded Zilberberg
> The mindless logic failure Jan Burse spamming sci.math for almost 3 decades.
>
> Mild Shock (Jan Burse) profile photo
> Mild Shock
> ,... 25Jul2023
> Dan Christensen
> 7
> The Revenge Paradox in DC Proof
>
>
>
>
>
> > > Spam mill echo chamber, that is Rubard, WM along with his gay spamletts a decades long spammer of sci.math, yet he fails math. Is it that Gottingen cannot understand the slant cut in single cone is an Oval, never the ellipse, or is it the foolish Boole logic they teach of 2 OR 1 = 3 with AND as subtraction? Or is it that neither WM or Gottingen can do a geometry proof Fundamental Theorem of Calculus? Which is it W. Mueckenheim??
> > > +Proving Water is H4O, not H2O, and where hydroxyl is H2O// AP's 250th book TEACHING TRUE CHEMISTRY, by Archimedes Plutonium Now I see some of these electronic weighing scales are accurate to 0.00001 gram. I do not know if that is within
> > >
> > > 3m views Proving Water is H4O, not H2O, and where hydroxyl is H2O// AP's 250th book TEACHING TRUE CHEMISTRY, by Archimedes Plutonium
> > >
> > >
> > > Now I see some of these electronic weighing scales are accurate to 0.00001 gram. I do not know if that is within the accuracy I need for weighing a test tube of oxygen then a test tube of hydrogen from water electrolysis.
> > >
> > >
> > > Proving Water is H4O, not H2O, and where hydroxyl is H2O// AP's 250th book TEACHING TRUE CHEMISTRY, by Archimedes Plutonium
> > >
> > > In Old Chemistry and Old Physics, their subatomic particles were do nothing and no function and no job particles that sit around as balls or whiz around the outside of balls doing nothing but pointless circling.
> > >
> > > In New Physics and New Chemistry-- All is Atom and Atoms are nothing but electricity and magnetism. Every subatomic particle has a job a function a purpose as to the Laws of Electromagnetism--- Faraday law, Coulomb law, Ampere law, Capacitor law.
> > >
> > > A proton is a torus of 840MeV with 840 windings, while the muon is the true electron of Atoms and is encased inside the proton torus thrusting through and producing electricity-- magnetic monopoles.
> > >
> > > The neutron of Atoms is a parallel plate capacitor storing the electricity of proton+muon and is skin cover on the outside of the proton torus in the form of parallel plates.
> > >
> > > Can hydrogen be a Atom if it is just a proton+muon? No, all atoms require to have a capacitor such as at least one neutron. Thus the Hydrogen Atom is H2 where you have 2 proton+muon where 1 of the 2 proton+muon acts like a neutron to the other proton+muon. Thus, water molecule is not H2O but rather is H4O.
> > >
> > > AP is waiting for experimental chemists and physicists to prove him correct that Water is H4O.
> > >
> > > In the meantime we have Hydroxyl which in Old Chemistry, especially Biology is OH, while AP says that is wrong and that is really H2O.
> > >
> > > Now glycerine is a hydroxyl with formula C3H8O3. And what I am thinking at this moment, is that hydroxyls will be an easier proof that Water is truly H4O, rather than wait for experimentalists to actually "weigh the electrolysis test tubes of oxygen and hydrogen".
> > >
> > > You see, with H4O as water, glycerine is C3(2 waters)O with an extra oxygen. If Water is H2O then glycerine is C3(4 waters) deficit O. It is missing an oxygen if water is H2O.
> > >
> > > The reason glycerine is so effective as a skin ointment is because it has glycerine, the extra O oxygen. If water were H2O, then glycerine would be a missing oxygen and not a skin lotion that works, but makes skin even more dry.
> > >
> > > Proving Water is H4O, not H2O, and where hydroxyl is H2O// AP's 250th book TEACHING TRUE CHEMISTRY, by Archimedes Plutonium
> > >
> > > Archimedes Plutonium<plutonium....@gmail.com>
> > > 12:24 AM (13 hours ago)
> > > 
> > > 
> > > 
> > > to Plutonium Atom Universe
> > >
> > > --- quoting in part from source-- Study.com ---
> > > Perhaps there is only two Faraday laws on Electrolysis. I am looking at the one that states: Faraday's first law of electrolysis relates the mass of a substance liberated (or deposited) at an electrode to the electric charge used (Q). A proportionality constant Z can be used:
> > >
> > > m = ZQ = (E/96485)(Q)
> > >
> > > m = mass, Q = total charge rewritten as Q = I*t amperes x time in seconds.
> > >
> > > This website gives an example: 5amps passed through molten Sodium Chloride for 3 hours. Calculate the mass of Sodium. E=23/1.
> > >
> > > m = (23/96485) (5) (3*60*60) approx 12.87 grams.
> > >
> > > --- end quoting in part from source-- Study.com ---
> > >
> > > Now has such a experiment been performed on Water to see how much atomic mass of hydrogen and of oxygen results??? If AP is correct, the formula of water is H4O, if Old Physics, Old Chemistry is correct the formula is H2O. So which is it???
> > >
> > > AP
> > >
> > >
> > > No, sorry no, Faraday's Law of Electrolysis is not going to tell the correct mass of hydrogen.
> > >
> > > Reading Wikipedia on Faraday's Electrolysis law.
> > >
> > > --- quoting Wikipedia ---
> > > A monovalent ion requires 1 electron for discharge, a divalent ion requires 2 electrons for discharge and so on. Thus, if x electrons flow,
> > > x/v atoms are discharged.
> > >
> > > So the mass m discharged is
> > >
> > > m= (xM)/vN_A) = (QM)/(eN_A *v) = (QM) / (vF)
> > > where
> > > N_A is the Avogadro constant;
> > > Q = xe is the total charge, equal to the number of electrons (x) times the elementary charge e;
> > > F is the Faraday constant.
> > > --- end quoting Wikipedia ---
> > >
> > > No, the Faraday law of Electrolysis will not work on water with a correct answer, because H is not an atom but H2 is an Atom. And where one of the proton+muon converts to being a neutron to the other proton+muon.
> > >
> > > So if Faraday's law of Electrolysis was applied to water, thinking it would deliver a true answer is mistaken because the one H converts to neutron.
> > >
> > > So it appears that we need to directly measure the test tube of oxygen and the test tube of hydrogen by a direct mass measurement.
> > >
> > > AP
> > > Archimedes Plutonium's profile photo
> > > Archimedes Plutonium<plutonium....@gmail.com>
> > > 1:14 AM (12 hours ago)
> > > 
> > > 
> > > 
> > > to Plutonium Atom Universe
> > > I doubt we can measure a test tube of hydrogen or test tube of oxygen, too small to determine the mass on some sort of weight scale.
> > >
> > > But here is a possible lucrative idea. We should be able to get pure deuterium water. Then run the electrolysis. Collect the test tubes.
> > >
> > > Now have some sort of balancing beam weight scale. Place the regular water of hydrogen test tube on one side, and place the deuterium water hydrogen test tube on other side. If they stay balanced, then AP is correct and Water is really H4O.
> > >
> > > AP
> > > Archimedes Plutonium's profile photo
> > > Archimedes Plutonium<plutonium....@gmail.com>
> > > 1:48 AM (11 hours ago)
> > > 
> > > 
> > > 
> > > to Plutonium Atom Universe
> > > Cosmic Rays from Sun
> > >
> > > 90% of Sun's cosmic rays are 840MeV proton+muon inside = H. The hydrogen Atom is H2 where one of the H proton+muon converts to being a neutron..
> > >
> > > When these proton+muon hit Earth atmosphere, they can turn into pions and muons.
> > >
> > > I commented that H alone is a subatomic particle and that makes sense in the idea that Sun's cosmic rays are 90% these proton+muon.
> > >
> > > Now is interstellar hydrogen H2 and intergalactic hydrogen H2 formed when one H cosmic ray joins up with another H cosmic ray to form H2 atom?
> > >
> > > Is this how we get H2 in outer space? From the splitting apart of H2 into H cosmic rays?
> > >
> > > So how much of the Sun's hydrogen is H2 and how much is H ready to join with another H and reform back into H2. Probably little of the Sun's H is H alone, and the vast majority of the Sun's hydrogen is H2.
> > >
> > > How much deuterium in the Sun? And it is a higher percentage than the deuterium in water on Earth?
> > >
> > > AP
> > > Archimedes Plutonium's profile photo
> > > Archimedes Plutonium<plutonium....@gmail.com>
> > > 3:11 AM (10 hours ago)
> > > 
> > > 
> > > 
> > > to Plutonium Atom Universe
> > > Water is the only known non-metallic substance that expands when if freezes; its density decreases and it expands approximately 9% by volume. (Source: web Lunar and Planetary Institute)
> > >
> > > I have to wait for experimental chemists and physicists to weigh the mass of test tubes from electrolysis, as to the verdict-- water is H4O.
> > >
> > > But until that news comes in, I will look for other means of proof.
> > >
> > > So AP says that the H2 is not a molecule but is the hydrogen Atom itself, where one proton+muon converts to a neutron and capacitates the other proton+muon which undergo the Faraday law.
> > >
> > > There are subatomic particles of H in the form of Cosmic Rays from the Sun, but most of the Sun's hydrogen is H2, and flips back and forth from H to rejoining to form H2. Some gets away from the Sun and is cosmic rays.
> > >
> > > But H2 is an Atom and H is a fleeting subatomic particle.
> > >
> > > So can I prove Water is H4O from the data of Spectral lines of H2 is the same as deuterium, only slight difference is that the deuterium is a full fledged neutron not a makeshift proton+muon of H.
> > >
> > > I suspect that special trait of water freezing is a proof that Water is H4O. Because the 840MeV proton torus with muon inside doing the Faraday law acting as a makeshift neutron capacitor for the other 840MeV proton torus with muon inside, is where H2 gets that expansion characteristic.
> > >
> > > A neutron is a parallel plate capacitor and those plates can expand when frozen temperature occurs. As the temperature gets colder, those plates move further apart.
> > >
> > > Now does deuterium which truly has a full neutron, does it expand also when frozen?? If so, does it expand as much as H2 which is 2 protons with 2 muons inside?
> > >
> > > So comparing the freezing and expansion of the parallel plates of a neutron in deuterium with the freezing and expansion of one of the proton+muon that is acting as a makeshift neutron in H2.
> > >
> > > If I can numbers correlate the H2 expansion with the Deuterium expansion would be a alternative proof that Water is really H4O and not H2O.
> > >
> > > AP
> > > to
> > > So now on Blankenship's book "Molecular Mechanisms of Photosynthesis", 2014, page 134, shows The structure of ATP, ADP, AMP. And within that structure are OH hydroxyls.
> > >
> > > In New Chemistry, water is truly H4O, and where hydroxyls are now H2O.. And we have first proof of this in the Figure 8.1 of Blankenship's "Chemical structure of ATP".
> > >
> > > For in the lower left corner of the diagram, Blankenship has a H+ all alone, (really a mindless error) and has P surrounded by O-, O-, O and OH. The OH is really H2O for hydroxyls are H2O and water itself is H4O, and that would leave that mindless H+ as being hydrogen Atom of H2.
> > >
> > > The world of physics and chemistry should drop what they are doing and weigh the electrolysis test tube of hydrogen and oxygen to discover the correct true formula of water is H4O.
> > >
> > > AP is total confident, becuase an Atom cannot exist if it has no capacitor structure such as a neutron, or one of the H in H2 acting as a neutron. I am totally confident that Water formula is truly H4O. And I need look only to methane of H4C, to realize that there is no HC, no H2C, no H3C, but starts with H4C, and that tells me water starts with H4O. Totally confident that Old Chemistry, Old Physics did electrolysis experiments and the moment they saw hydrogen test tube be 2x volume of oxygen test tube, they dropped their work and went out for a Danish and coffee break, rather than finish their work--- actual physics weighing of atomic mass units (not the Faraday electrolysis law for it does not apply to water).
> > >
> > > When water electrolysis is physics weighed, AP is confident that there are 4H per every one oxygen O. And that Water is truly H4O.
> > >
> > > AP, King of Science
> > > Archimedes Plutonium's profile photo
> > > Archimedes Plutonium
> > > 9:34 AM (15 minutes ago)
> > > 
> > > 
> > > 
> > > to
> > > On Tuesday, July 18, 2023 at 8:56:57 AM UTC-5, Archimedes Plutonium wrote:
> > > > Now I see some of these electronic weighing scales are accurate to 0.00001 gram. I do not know if that is within the accuracy I need for weighing a test tube of oxygen then a test tube of hydrogen from water electrolysis.
> > >
> > > Now modern day physics and chemist experimenters can really do a marvelous job if they wanted to. For they could freeze the test tubes of oxygen and hydrogen to where they are liquid and compare liquids from water electrolysis.
> > > Archimedes Plutonium's profile photo
> > > Archimedes Plutonium
> > > 10:01 AM (5 hours ago)
> > > 
> > > 
> > > 
> > > to
> > > So, what AP is saying here is that we do electrolysis of water. We collect the two test tubes, one with oxygen the other with hydrogen.
> > >
> > > To prove Water is truly the formula H4O and not H2O we must weigh the masses of the two tubes to find that the ratio is 1 x 16amu to 4 x 1amu.
> > >
> > > The silly grotesque science error of the past was to look at volumes in the two test tubes-- "Hey-- the hydrogen is twice the volume of oxygen so the formula of water is H2O".
> > >
> > > No, way was that science good practice. For the correct formula of water needs to be measured by mass, by atomic mass units where Oxygen is 16amu and hydrogen is 1amu.
> > >
> > > I suspect a balance beam scale is good enough to see the hydrogen test tube will be 1/4 as massive as the oxygen test tube. To get within precision of electronic weighing scale of 0.00001 gram we just have to make a larger test tube of electrolysis of water.
> > >
> > > AP is betting that the readings will be hydrogen test tube 1/4 the mass of oxygen test tube proving Water formula is truly H4O.
> > >
> > > Old Physics and Old Chemistry is betting that the mass experiment will have the hydrogen test tube be 1/8 the mass of the oxygen test tube, proving Water formula is H2O.
> > >
> > > AP does not have these precision equipment to conduct an at-home experiment of this nature.
> > >
> > > AP
> > > Archimedes Plutonium's profile photo
> > > Archimedes Plutonium
> > > 12:38 PM (4 hours ago)
> > > 
> > > 
> > > 
> > > to
> > > So, once Water is found to actually be H4O, not H2O, we move on to methane, and ask the same question of its hydrogen bonds. Is Methane really that of H8C and not H4C.
> > >
> > > Well, looking in the literature for anomalies to methane, I come across a arXiv "Low and high-temperature anomalies in the physical properties of solid methane "The anomalous behavior of thermodynamic, spectral, plastic, elastic and some other properties of solid methane is discussed near 20.48K and...
> > >
> > > AP wonders: if they can get methane to solid form, well, I am then hopeful that the mass of the molecule can be determined. Because if methane is truly H8C, that difference of H4 in atomic mass units would be very much noticeable difference.
> > >
> > > Chemistry Europe--
> > > "The Anomalous Deuterium Isotope Effect in the NMR Spectrum of Methane...
> > >
> > > P Vermeeren, 2023
> > > "The abnormally long and weak methylidyne C-H bond.."
> > > "The C-H bond of the methylidyne radical, CH*, is abnormally long and weak, even longer and..."
> > >
> > > AP asks, are these anomalies solved if we consider methane is actually H8C and not H4C?
> > >
> > > AP
> > >
> > >
>
> > >
> > > Everything Jan Burse or Dan Christensen do in logic-- worthless until they recognize and accept the fact that Boole messed up bigtime, for he screwed up AND with OR, and his logic truth tables are a pile of shit. But Dan and Jan have shit for brains and keep on keeping on with their moron logic 2 OR 3 = 5 with 3 AND 2 resulting in 1.
> > >
> > > Re: *Fire the entire Univ Western Ontario math dept/ still teaching that the contradictory sine graph as sinusoid when it is really semicircle
> > > by Dan Christensen Nov 21, 2017,
> > >
> > > Re: 81,045-Student victims of Rose M. Patten Univ Toronto from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Univ Toronto, physics, Gordon F. West, Michael B. Walker
> > > by Frank Cassa 12Apr2021 7:00 AM
> > >
> > >
> > > Re: 77,233 Student victims of Lawrence Bacow's Harvard from stalker Kibo Parry Moroney with his 938 is 12% short 945, his 10 OR 4 = 14 with AND as subtraction, and his mindless belief real electron = 0.5MeV when true electron is muon
> > > 11:57 AM 10Apr2021
> > > by Wayne Decarlo
> > >
> > >
> > >
> > > Re: 7,744-Student victims of Linda Hasenfratz Univ Western Ontario from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Chancellor Linda Hasenfratz President Alan Shepard
> > > 11:53 AM 10Apr2021
> > > by Wayne Decarlo
> > >
> > > Re: 102,852-Student victims of Dominic Barton, Univ Waterloo from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Dominic Barton, President Feridun Hamdullahpur physics
> > > by konyberg Apr 15, 2021, 3:09:41 PM
> > >
> > > Re: 176,232-Student Victims of Michael Meighen McGill Univ by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus... 0.5MeV electron when in truth it is the muon as the real electron
> > > by Dan Christensen Jul 2, 2021, 9:47:42 AM
> > >
> > >
> > > Re: 135,568 Student victims Queen's Univ. James Leech, Arthur B. McDonald by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus-- his mindless electron =0.5MeV when real electron of
> > > May 10, 2021
> > > by Professor Wordsmith
> > >
> > >
> > > Re: 1.1Dr. John Baez is a failed mathematician-physicist with his proton of 938MeV when it is 840MeV, electron= muon //his ellipse is a conic when it never was// as phony in math and physics as kibo Parry Moroney's ellipse and Christensen 10 OR 4 =
> > > by Dan Christensen Sep 22, 2019, 9:54:06 AM
> > >
> > >
> > > 5th published book
> > >
> > > Suspend all College Classes in Logic, until they Fix their Errors // Logic series, book 1 Kindle Edition
> > > by Archimedes Plutonium (Author)
> > >
> > > First comes Logic-- think straight and clear which many logic and math professors are deaf dumb and blind to, and simply refuse to recognize and fix their errors.
> > >
> > > The single biggest error of Old Logic of Boole and Jevons was their "AND" and "OR" connectors. They got them mixed up and turned around. For their logic ends up being that of 3 OR 2 = 5 with 3 AND 2 = 1, when even the local village idiot knows that 3 AND 2 = 5 (addition) with 3 OR 2 = either 3 or 2 (subtraction). And secondly, their error of the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability end conclusion.
> > >
> > > My corrections of Old Logic have a history that dates before 1993, sometime around 1991, I realized the Euclid proof of infinitude of primes was illogical, sadly sadly wrong, in that the newly formed number by "multiply the lot and add 1" was necessarily a new prime in the indirect proof method. So that my history of fixing Old Logic starts in 1991, but comes to a synthesis of correcting all four of the connectors of Equal/not, And, Or, If->Then, by 2015.
> > >
> > > Cover picture: some may complain my covers are less in quality, but I have a good reason for those covers-- I would like covers of math or logic to show the teacher's own handwriting as if he were back in the classroom writing on the blackboard or an overhead projector.
> > > Length: 63 pages
> > >
> > > File Size: 764 KB
> > > Print Length: 63 pages
> 
> > > 
> > > Publication Date: March 12, 2019
> > > Sold by: Amazon Digital Services LLC
> > > Language: English
> > > ASIN: B07PMB69F5
> > > Text-to-Speech: Enabled
> > > X-Ray: Not Enabled
> > > Word Wise: Not Enabled
> > > Lending: Enabled
> > > Screen Reader: Supported
> > > Enhanced Typesetting: Enabled

On Tuesday, July 25, 2023 at 4:59:31 PM UTC-7, Dan Christensen wrote:
> See my reply just now to your identical and really quite pathetic posting elsewhere here.
> On Tuesday, July 25, 2023 at 6:55:33 PM UTC-4, Mild Shock wrote:
> > Dan Christensen was in full halucination mode, when he
> > wrote "INDETERMINATE (like the numeraical value of 1/0)".
> >
> [snip]

Earlier, and often: "You guys need to study logic more."

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

On Wednesday, July 26, 2023 at 4:02:34 AM UTC-4, Archimedes Plutonium wrote:
[snip]

> .... Dan Christensen ...

[snip]

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

From his antics here at sci.math, it is obvious that AP has abandoned all hope of being recognized as a credible personality. He is a malicious internet troll who now wants only to mislead and confuse students. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives. Is it revenge for his endless string of personal failures in life? Who knows?

In AP's OWN WORDS that, over the years here, he has NEVER renounced or withdrawn:

"Water is really H4O, not H2O." *************** NEW *************************
--July 27, 2023

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

“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020

“The last and largest finite number is 10^604.”
--June 3, 2015

“0 appears to be the last and largest finite number”
--June 9, 2015

“0/0 must be equal to 1.”
-- June 9, 2015

“0 is an infinite irrational number.”
--June 28, 2015

“No negative numbers exist.”
--December 22, 2018

“Rationals are not numbers.”
--May 18, 2019

According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019

Which could explain...

“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019

AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:

“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019

AP seeks aid of Russian agents to promote failure in schools:

"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--November 9, 2017

And if that wasn't weird enough...

“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994

“The Universe itself is one gigantic big atom.”
--November 14, 2019

AP's sinister Atom God Cult of Failure???

“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)

Updated version (repetition removed):

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

Dan

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

In set theory one can even prove the ultimate revenge
paradox, for arbitrary domains J = {0,...}. There is the
following set theory theorem, relatively trivial:

Theorem Constant Function:
Assume an arbitrary domain J = {0,...} which is non-empty
and has zero 0, i.e. 0 e J. Then looking at the function space,
i.e. functions for an arity n:

f : J^n -> J

We find that there is always a constant function:

ALL(x1):[x1 e J => .... ALL(xn):[xn e J => f(x1,..,xn) = 0] ...]

Proof:
Just use the Subset Axiom, and construct this function:
f = { (x1,...,xn,0) | x1 e J & ... & xn e J }
Q.E.D:

Corrolary Ultimate Revenge:
In a language that is at least as expressive as set theory,
there is always a Liar Paradox like form, even if we allow
to range expressions over more than B = {0,1}.

Proof:
We had J arbitrary in the previous theorem, so it can be also
different or larger than B. Even excelling the super revenge
paradox which transcends only K = {0,1,u}.
Q.E.D.

I guess the wish to "resolve" the Liar Paradox, is rooted in
Alchemy. I find, the Ouroboros as a symbol of self reference?

Ouroboros (representation of a serpent eating its own tail)
with the words ἕν τὸ πᾶν, hen to pān ("the all is one") from
the Chrysopoeia of Cleopatra the Alchemist in the 3rd
century or 4th century A.D. (Christian era)
https://en.wikipedia.org/wiki/Chrysopoeia

So will Dan O Matik turn dirt to gold. Go Go Dan O Matik
resolve the Liar Paradox, we are all currious how an

Antinomy is not an Antinomy.

Dan Christensen schrieb am Mittwoch, 26. Juli 2023 um 01:59:31 UTC+2:
> See my reply just now to your identical and really quite pathetic posting elsewhere here.
> On Tuesday, July 25, 2023 at 6:55:33 PM UTC-4, Mild Shock wrote:
> > Dan Christensen was in full halucination mode, when he
> > wrote "INDETERMINATE (like the numeraical value of 1/0)".
> >
> [snip]

The easiest resolution of the Liar Paradox is found in:

"One is the Serpent which has its poison according to two
compositions, and One is All and through it is All, and by
it is All, and if you have not All, All is Nothing."
https://en.wikipedia.org/wiki/Cleopatra_the_Alchemist

Kind of Archimedes Plutonium totality, but we can
use it to resolve the Liar Paradox. Just go Oneotomy
instead of Trichtomoy, i.e. only a single truth value, and

you are done. Just change this into a single truth value:

https://dcproof.com/LiarParadox2.htm

LoL

Mild Shock schrieb am Montag, 21. August 2023 um 23:37:29 UTC+2:
> I guess the wish to "resolve" the Liar Paradox, is rooted in
> Alchemy. I find, the Ouroboros as a symbol of self reference?
>
> Ouroboros (representation of a serpent eating its own tail)
> with the words ἕν τὸ πᾶν, hen to pān ("the all is one") from
> the Chrysopoeia of Cleopatra the Alchemist in the 3rd
> century or 4th century A.D. (Christian era)
> https://en.wikipedia.org/wiki/Chrysopoeia
>
> So will Dan O Matik turn dirt to gold. Go Go Dan O Matik
> resolve the Liar Paradox, we are all currious how an
>
> Antinomy is not an Antinomy.
> Dan Christensen schrieb am Mittwoch, 26. Juli 2023 um 01:59:31 UTC+2:
> > See my reply just now to your identical and really quite pathetic posting elsewhere here.
> > On Tuesday, July 25, 2023 at 6:55:33 PM UTC-4, Mild Shock wrote:
> > > Dan Christensen was in full halucination mode, when he
> > > wrote "INDETERMINATE (like the numeraical value of 1/0)".
> > >
> > [snip]

So lets walk the path of the philosopher stone, and
resolve the Liar Paradox. The adivse is here, very modern
with a touch of LGBT:

"In like manner the Philosophers would have the quadrangle
reduced into a triangle, that is, into body, Spirit, and Soul,
which three do appear in three previous colors before redness,
for example, the body or earth in the blackness of Saturn,
the Spirit in a lunar whiteness, as water, the Soul or air in a solar
citrinity: then will the triangle be perfect, but this likewise must
be changed into a circle, that is, into an invariable redness:
By which operation the woman is converted into the man,
and made one with him, and the senary the first number of
the perfect completed by one, two, having returned again to an
unit, in which is eternal rest and peace.
— Michael Maier, Atalanta Fugiens, Emblem XXI.

So lets turn "woman" into "man" and assume there are not
two truth values {T, F} but only a single truth value {*}. The
truth table for "is" is very simple:

A B A <-> B
* * *

When we now stipulate negation as:

A ~A
* *

We can resolve the Liar Paradox by p <-> ~p:

"This sentences is false."

Dan Christensen schrieb am Mittwoch, 26. Juli 2023 um 01:59:31 UTC+2:
> See my reply just now to your identical and really quite pathetic posting elsewhere here.
> On Tuesday, July 25, 2023 at 6:55:33 PM UTC-4, Mild Shock wrote:
> > Dan Christensen was in full halucination mode, when he
> > wrote "INDETERMINATE (like the numeraical value of 1/0)".
> >
> [snip]

This is the proper resolution, like the Russell Paradox, it sacrifices
something. The Russell Paradox resolution in ZF set theory sacrifices
for example that the universal class would be a set,

here we sacrificy the idea that there are "men" and "women", we
go from two truth values {T, F} to only a single truth value {*}. The
advantage is that we can stay in the framework of sentences,

we don't need to call in expressions such that:

sentences ⊆ expressions

So its a proper resolution of the Liar Paradox, not a fake resolution
like in Dan Christensens proof, which assumes a broader class
of phrases that can have a value outside of truth values.

A terminological error in Dan Christensens proof is that he
calls this broader class of phrases "sentences" whereas in
mathematical logic and computer science one would call

them "expressions". Just like 2+2 is a expression and 2+2=4
is a sentence. But the single truth value resolution doesn't need
"expressions", a phrase which valuates to {*} is still a sentence.

Mild Shock schrieb am Dienstag, 22. August 2023 um 09:47:21 UTC+2:
> So lets walk the path of the philosopher stone, and
> resolve the Liar Paradox. The adivse is here, very modern
> with a touch of LGBT:
>
> "In like manner the Philosophers would have the quadrangle
> reduced into a triangle, that is, into body, Spirit, and Soul,
> which three do appear in three previous colors before redness,
> for example, the body or earth in the blackness of Saturn,
> the Spirit in a lunar whiteness, as water, the Soul or air in a solar
> citrinity: then will the triangle be perfect, but this likewise must
> be changed into a circle, that is, into an invariable redness:
> By which operation the woman is converted into the man,
> and made one with him, and the senary the first number of
> the perfect completed by one, two, having returned again to an
> unit, in which is eternal rest and peace.
> — Michael Maier, Atalanta Fugiens, Emblem XXI.
>
> So lets turn "woman" into "man" and assume there are not
> two truth values {T, F} but only a single truth value {*}. The
> truth table for "is" is very simple:
>
> A B A <-> B
> * * *
>
> When we now stipulate negation as:
>
> A ~A
> * *
>
> We can resolve the Liar Paradox by p <-> ~p:
>
> "This sentences is false."
> Dan Christensen schrieb am Mittwoch, 26. Juli 2023 um 01:59:31 UTC+2:
> > See my reply just now to your identical and really quite pathetic posting elsewhere here.
> > On Tuesday, July 25, 2023 at 6:55:33 PM UTC-4, Mild Shock wrote:
> > > Dan Christensen was in full halucination mode, when he
> > > wrote "INDETERMINATE (like the numeraical value of 1/0)".
> > >
> > [snip]

On Tuesday, August 22, 2023 at 3:48:46 AM UTC-4, Mild Shock (aka Mr.. Collapse) wrote:

[snip]

> So its a proper resolution of the Liar Paradox, not a fake resolution
> like in Dan Christensen's proof, which assumes a broader class
> of phrases that can have a value outside of truth values.
>

In common usage, "Wash your hands" is a sentence. It is known to be never true and never false, i.e. it is of indeterminate truth value. In this sense, "This sentence is false" is also of indeterminate truth value.

Formal proof: https://dcproof.com/LiarParadox2.htm (only 44 lines in DC Proof format)

Trichotomy Lemma: For every set, there exists 3 disjoint subsets on which a trichotomy rule holds. https://www.dcproof.com/LiarParadoxLemma.htm (84 lines)

https://www.dcproof.com/LiarParadoxLemma.htm (84 lines)

I hope this helps clear up your confusion, Mr. Collapse.

Dan

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

May "resolve" your tool first, instead of the Liar Paradox?

Reading Alonzos Paper here, it talks about yet another Paradox:

"A Comparison of Russell’s Resolution of the Semantical Antinomies
with that of Tarski" Alonzo Church - 1976
The Journal of Symbolic Logic, Volume 41 Issue 4
https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/0E1F24F9F14EB30A01C164B536EDC5DE

Was quite fruitful, can now prove in DC Proof:

/* Grelling's antinomy */
43 h(h)=1 & ~h(h)=1
Join, 28, 42

See also here:

AmateurGate: DC Proof is subject to Grelling's antinomy
https://groups.google.com/g/sci.logic/c/TaIENB54MNQ/m/S48dp4ADAwAJ

Dan Christensen schrieb am Dienstag, 22. August 2023 um 17:02:11 UTC+2:
> On Tuesday, August 22, 2023 at 3:48:46 AM UTC-4, Mild Shock (aka Mr. Collapse) wrote:
>
> [snip]
> > So its a proper resolution of the Liar Paradox, not a fake resolution
> > like in Dan Christensen's proof, which assumes a broader class
> > of phrases that can have a value outside of truth values.
> >
> In common usage, "Wash your hands" is a sentence. It is known to be never true and never false, i.e. it is of indeterminate truth value. In this sense, "This sentence is false" is also of indeterminate truth value.
>
> Formal proof: https://dcproof.com/LiarParadox2.htm (only 44 lines in DC Proof format)
>
> Trichotomy Lemma: For every set, there exists 3 disjoint subsets on which a trichotomy rule holds. https://www.dcproof.com/LiarParadoxLemma.htm (84 lines)
>
> https://www.dcproof.com/LiarParadoxLemma.htm (84 lines)
>
> I hope this helps clear up your confusion, Mr. Collapse.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Tuesday, August 22, 2023 at 11:18:55 AM UTC-4, Mild Shock wrote:

> Was quite fruitful, can now prove in DC Proof:
>
> /* Grelling's antinomy */
> 43 h(h)=1 & ~h(h)=1
> Join, 28, 42
>

Only if you introduce some wonky axioms. Garbage in, garbage out.

Dan

Well I presented you the gift of new life goals. Instead of
wasting your time with Trichotomy and Liar, lets put you into
a situation that Frege was 100 years ago. I am now using:

1 ALL(f):ALL(g):[Fun(f) & Fun(g) => [ALL(x):f(x)=g(x) <=> f=g]]
Axiom

2 Fun(h) & ALL(v):[h(v)=1 <=> EXIST(f):[Fun(f) & ALL(x):v(x)=f(x) & ~f(v)=1]]
Axiom

There is nothing wonky, except that your DC Proof tool is
subject to the Grelling's antinomy. Similar like Freges system
was subject to Russell's antinomy, your DC Proof system is

subject to the Grelling's antinomy. How do you resolve it?

Dan Christensen schrieb am Dienstag, 22. August 2023 um 18:06:26 UTC+2:
> On Tuesday, August 22, 2023 at 11:18:55 AM UTC-4, Mild Shock wrote:
>
> > Was quite fruitful, can now prove in DC Proof:
> >
> > /* Grelling's antinomy */
> > 43 h(h)=1 & ~h(h)=1
> > Join, 28, 42
> >
> Only if you introduce some wonky axioms. Garbage in, garbage out.
>
> Dan

Actually this is kind of an open game. I don't know the result.
I don't know what the resolution is. It seems we have a
case of "Grellingness", respectively we should have a case

of "Grellingness", namely we need to have somewhere a
barrier, so that the function gets not expressed, that it becomes
inexpressible, similar like set theory makes the universal set

inexpressible. BTW: I borrowed "Grellingness" from here:

Inexpressible properties and Grelling’s antinomy
Benjamin Schnieder - Springer Science+Business Media B.V. 2009
https://benjaminschnieder.files.wordpress.com/2022/09/grelling-paradox-philosophical-studies.pdf

LoL

Mild Shock schrieb am Dienstag, 22. August 2023 um 20:51:42 UTC+2:
> Well I presented you the gift of new life goals. Instead of
> wasting your time with Trichotomy and Liar, lets put you into
> a situation that Frege was 100 years ago. I am now using:
>
> 1 ALL(f):ALL(g):[Fun(f) & Fun(g) => [ALL(x):f(x)=g(x) <=> f=g]]
> Axiom
>
> 2 Fun(h) & ALL(v):[h(v)=1 <=> EXIST(f):[Fun(f) & ALL(x):v(x)=f(x) & ~f(v)=1]]
> Axiom
>
> There is nothing wonky, except that your DC Proof tool is
> subject to the Grelling's antinomy. Similar like Freges system
> was subject to Russell's antinomy, your DC Proof system is
>
> subject to the Grelling's antinomy. How do you resolve it?
> Dan Christensen schrieb am Dienstag, 22. August 2023 um 18:06:26 UTC+2:
> > On Tuesday, August 22, 2023 at 11:18:55 AM UTC-4, Mild Shock wrote:
> >
> > > Was quite fruitful, can now prove in DC Proof:
> > >
> > > /* Grelling's antinomy */
> > > 43 h(h)=1 & ~h(h)=1
> > > Join, 28, 42
> > >
> > Only if you introduce some wonky axioms. Garbage in, garbage out.
> >
> > Dan

On Tuesday, August 22, 2023 at 2:51:42 PM UTC-4, Mild Shock wrote:

[snip]

> I am now using:
>
> 1 ALL(f):ALL(g):[Fun(f) & Fun(g) => [ALL(x):f(x)=g(x) <=> f=g]]
> Axiom
>
> 2 Fun(h) & ALL(v):[h(v)=1 <=> EXIST(f):[Fun(f) & ALL(x):v(x)=f(x) & ~f(v)=1]]
> Axiom
>

I see you would rather not use the function axioms built into DC Proof (on the Sets menu). Why is that? It seems you get an inconsistency when you use YOUR OWN axioms. What does THAT tell you about your axioms? Garbage in, garbage out???

Dan

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

On Monday, August 21, 2023 at 2:37:29 PM UTC-7, Mild Shock wrote:
> I guess the wish to "resolve" the Liar Paradox, is rooted in
> Alchemy. I find, the Ouroboros as a symbol of self reference?
>
> Ouroboros (representation of a serpent eating its own tail)
> with the words ἕν τὸ πᾶν, hen to pān ("the all is one") from
> the Chrysopoeia of Cleopatra the Alchemist in the 3rd
> century or 4th century A.D. (Christian era)
> https://en.wikipedia.org/wiki/Chrysopoeia
>
> So will Dan O Matik turn dirt to gold. Go Go Dan O Matik
> resolve the Liar Paradox, we are all currious how an
>
> Antinomy is not an Antinomy.

Wider World: "I'm curious about any sense in which what you are doing is *not* a hoax."

Here you go, happy now? This was already posted on sci.logic.

Ok, this is a quite long proof, using Function Axiom
and Function Equality twice, making the Grelling function
set like. It bails out with ~h e dom, very similar like what

Dan Christen found in his "Generalized Drinker Paradox" nonsense,
when he found that every set has an outside element:

402 ~h @ dom
5 Conclusion, 389

So when we would assume that h e dom, we would
get a contradiction. Was thinking about using Dana Scotts
trick, to provoke a contradiction. Not yet sure. Because

we have "dom" arbitrary, not really specified, we could
envision a kind of chasing game.

-------------------------- begin proof, collapsed view -----------------------------

1 Set(dom)
Axiom

2 Set(cod)
Axiom

3 ~0=1
Axiom

4 ALL(x):[x @ cod <=> x=0 | x=1]
Axiom

5 ALL(a1):ALL(a2):[Set(a1) & Set(a2) => EXIST(b):[Set'(b) & ALL(c1):ALL(c2):[(c1,c2) @ b <=> c1 @ a1 & c2 @ a2]]]
Cart Prod

6 ALL(a2):[Set(dom) & Set(a2) => EXIST(b):[Set'(b) & ALL(c1):ALL(c2):[(c1,c2) @ b <=> c1 @ dom & c2 @ a2]]]
U Spec, 5

7 Set(dom) & Set(cod) => EXIST(b):[Set'(b) & ALL(c1):ALL(c2):[(c1,c2) @ b <=> c1 @ dom & c2 @ cod]]
U Spec, 6

8 Set(dom) & Set(cod)
Join, 1, 2

9 EXIST(b):[Set'(b) & ALL(c1):ALL(c2):[(c1,c2) @ b <=> c1 @ dom & c2 @ cod]]
Detach, 7, 8

10 Set'(rel) & ALL(c1):ALL(c2):[(c1,c2) @ rel <=> c1 @ dom & c2 @ cod]
E Spec, 9

11 Set'(rel)
Split, 10

12 ALL(c1):ALL(c2):[(c1,c2) @ rel <=> c1 @ dom & c2 @ cod]
Split, 10

13 EXIST(gra):[Set'(gra) & ALL(x):ALL(y):[(x,y) @ gra <=> (x,y) @ rel & [EXIST(fun):[Function(fun,dom,cod) & ALL(a):[a @ dom => x(a)=fun(a)] & ~[x @ dom & fun(x)=1]] <=> y=1]]]
Subset, 11

14 Set'(gra) & ALL(x):ALL(y):[(x,y) @ gra <=> (x,y) @ rel & [EXIST(fun):[Function(fun,dom,cod) & ALL(a):[a @ dom => x(a)=fun(a)] & ~[x @ dom & fun(x)=1]] <=> y=1]]
E Spec, 13

15 Set'(gra)
Split, 14

16 ALL(x):ALL(y):[(x,y) @ gra <=> (x,y) @ rel & [EXIST(fun):[Function(fun,dom,cod) & ALL(a):[a @ dom => x(a)=fun(a)] & ~[x @ dom & fun(x)=1]] <=> y=1]]
Split, 14

17 ALL(dom):ALL(cod):ALL(gra):[Set(dom) & Set(cod) & Set'(gra)
=> [ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]
=> EXIST(fun):[Function(fun,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [fun(a1)=b <=> (a1,b) @ gra]]]]]
Function

18 ALL(cod):ALL(gra):[Set(dom) & Set(cod) & Set'(gra)
=> [ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]
=> EXIST(fun):[Function(fun,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [fun(a1)=b <=> (a1,b) @ gra]]]]]
U Spec, 17

19 ALL(gra):[Set(dom) & Set(cod) & Set'(gra)
=> [ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]
=> EXIST(fun):[Function(fun,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [fun(a1)=b <=> (a1,b) @ gra]]]]]
U Spec, 18

20 Set(dom) & Set(cod) & Set'(gra)
=> [ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]
=> EXIST(fun):[Function(fun,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [fun(a1)=b <=> (a1,b) @ gra]]]]
U Spec, 19

21 Set(dom) & Set(cod) & Set'(gra)
Join, 8, 15

22 ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]
=> EXIST(fun):[Function(fun,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [fun(a1)=b <=> (a1,b) @ gra]]]
Detach, 20, 21

252 ~~[ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]]
5 Conclusion, 23

253 ALL(a1):ALL(b):[(a1,b) @ gra => a1 @ dom & b @ cod]
& ALL(a1):[a1 @ dom => EXIST(b):[b @ cod & (a1,b) @ gra]]
& ALL(a1):ALL(b1):ALL(b2):[a1 @ dom & b1 @ cod & b2 @ cod
=> [(a1,b1) @ gra & (a1,b2) @ gra => b1=b2]]
Rem DNeg, 252

254 EXIST(fun):[Function(fun,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [fun(a1)=b <=> (a1,b) @ gra]]]
Detach, 22, 253

255 Function(h,dom,cod) & ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [h(a1)=b <=> (a1,b) @ gra]]
E Spec, 254

256 Function(h,dom,cod)
Split, 255

257 ALL(a1):ALL(b):[a1 @ dom & b @ cod
=> [h(a1)=b <=> (a1,b) @ gra]]
Split, 255

307 ~[h @ dom & h(h)=1]
5 Conclusion, 258

388 ~[h @ dom & ~h(h)=1]
5 Conclusion, 308

402 ~h @ dom
5 Conclusion, 389

-------------------------- end proof, collapsed view -----------------------------

Dan Christensen schrieb am Dienstag, 22. August 2023 um 21:27:02 UTC+2:
> On Tuesday, August 22, 2023 at 2:51:42 PM UTC-4, Mild Shock wrote:
>
> [snip]
> > I am now using:
> >
> > 1 ALL(f):ALL(g):[Fun(f) & Fun(g) => [ALL(x):f(x)=g(x) <=> f=g]]
> > Axiom
> >
> > 2 Fun(h) & ALL(v):[h(v)=1 <=> EXIST(f):[Fun(f) & ALL(x):v(x)=f(x) & ~f(v)=1]]
> > Axiom
> >
> I see you would rather not use the function axioms built into DC Proof (on the Sets menu). Why is that? It seems you get an inconsistency when you use YOUR OWN axioms. What does THAT tell you about your axioms? Garbage in, garbage out???
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com