to Plutonium Atom Universe newsgroup.
(6) Biology life on Earth needs to move out to Europa because the Sun has gone into Red Giant initiation phase-- every year the Sun gets hotter and hotter.
Statement: Biology life on Earth will go extinct and into oblivion because the Sun is in Red Giant phase and unless we make Europa our new home.
6-1) As the Sun has started Red Giant phase, every year gets hotter and hotter and at some point in the future Earth will lose all its life. Our best bet to survive is to make Europa, a satellite of Jupiter, our new home in the next 1,000 years.
6-2) When you have a false idea of the inside structure of an Atom; thinking atoms have a nucleus when in truth they have a proton torus doing the Faraday law-structure making new electricity very second, and that Sunshine comes predominantly from Faraday law-structure, and very little from fusion. Then humanity has a problem to solve. Do we want to live or go extinct and into oblivion as the Sun grows bigger every day.
6-3) An obvious solution will be to move away from the Sun to a more habitable place, like Europa a satellite of Jupiter. It has plenty of water and we can tap into the magnetic field of Jupiter for almost unlimited powerful clean energy.
6-4) Here on Earth, at this time of May 2026, most humans believe Atoms have a nucleus and the Sun shines from fusion, and that every year gets hotter not because the Sun is going into Red Giant phase, but because fossil fuel burning emits CO2 into the air which is a greenhouse gas and traps heat on Earth. True that CO2, fossil fuel burning causes "global warming", but the largest contributor to every year hotter than the last year is due to the Sun gone Red Giant phase.
6-5) What evidence do we have that hotter years are Sun gone Red Giant rather than fossil fuel greenhouse gas global warming? The evidence is that the poles are accelerated in heat warming more than any other region on Earth. When the Sun radiates more energy, that energy is first seen in the Poles and causes acceleration of ice melt. Greenhouse gas warming of Earth would not be concentrated at the poles but rather where population centers are and be accelerating there, not the poles.
6-6) A rough percentage of how much heating of Earth is caused by Faraday law structure going on inside every atom of the Sun versus how much fusion is going on in the Sun is about 95% Faraday law-structure and 5% fusion. A rough percentage of how much increasing Earth temperature is due to Sun gone Red Giant versus fossil fuel burning climate change is 90% Sun gone Red Giant and 10% fossil fuel burning.
The 95% to 5% is obtained from the idea that Faraday law-structure goes on every instant of time inside every atom of the Sun. While fusion of hydrogen into helium is a probability half-life factor. Comparing every instant of time the muons thrusting through proton torus versus the chance of two atoms fusing is a 95 to 5 percentage comparison.
The increase in Solar radiation because the Sun has every year more atoms than previous years and the constancy of that radiation versus the mechanism of producing greenhouse gases is a 90 to 10 percentage comparison.
6-7) Life on Earth cannot exist in a Solar System of a growing Red Giant Star and must move further away, outward of the yearly increasing Sun gone Red Giant. A Sun gone Red Giant will grow to where the surface of the Sun radiation will swallow Earth in a heat bath.
Conclusion: For life on Earth to exist after thousands of years into the future, it must move out to near Jupiter.
Theme of this long Logic Reasoned Argument: Humanity at present in May 2026 has an attention span of yearly increasing climate heat rises all caused by fossil fuel burning and CO2 greenhouse gases, and utterly no realization the main culprit is the Sun gone Red Giant. The physics and astronomy textbooks still think of Atoms as nucleus with do nothing balls of proton, neutron, 0.5MeV electron and that the stars run by fusion. When in reality, Atom interiors are Proton torus, with muons inside doing the Faraday law-structure producing continual electrical energy both pouring out of the Sun and heating Earth and in creating newer atoms in the Sun, to accelerate heating. The Theme of this logic argument, is how long will it take for scientists to wake up and realize yearly heat extremes in climate is because the Sun went Red Giant? If it takes too long of a time for humanity and its scientists to wake up, then all of life on Earth is the proverbial expression "toast".
(7) Can we move both Earth and Moon out to Europa and near Jupiter?
7-1) Sun gone Red Giant raises the immediate question that life on Earth to not go extinct and into oblivion is to move further out from the Sun. Instead of moving and leaving Earth behind to be swallowed by the Sun, is humanity able to move all of Earth and the Moon out to where Europa of Jupiter lies?
Statement: Can humanity move Earth and Moon to where present day Europa of Jupiter lies?
7-2) Our Sun and all stars shine mostly from Faraday law-structure of Muons thrusting through Proton torus and some of that electricity produces is stored in Neutrons to create more atoms but much of it is released as star shine radiation.
7-3) As Sun gone Red Giant, every year the climate, weather gets hotter and hotter, especially the poles. Much of continents will be underwater as no more ice or snow is possible. And the continents that remain will be desert interiors, with the rims of continents in yearly floods called "atmospheric rivers".
7-4) As scientists finally wake up to the truth of the interior of atoms and that the Sun shines 95% from Faraday law-structure, and then the world general public finally taught the correct physics and the call then to Move as much of Earth and Moon out to nearby Jupiter takes place.
7-5) The question arises on whether we can fully move Earth and Moon out of its orbit and heading for Jupiter.
7-6) Recently, a asteroid and its satellite was experimented with to see if it can be moved out of orbit. The mission of moving was a success. And the physics involved can be scaled up.
7-7) By using Atomic Bomb blasts on Earth at precision spots at precision time intervals, we can nudge planet Earth, similarly the Moon, that every year we can scoot the two out of orbit with the Sun and to where they are scheduled to be repositioned nearby Europa of Jupiter.
7-8) Each year as we atomic bomb blast Earth out of orbit we will experience a Cooling Effect on Earth as to make Earth far better in weather and climate if we had not bomb blasted. So that the so called "ride to Europa, by Earth + Moon" will be a joyful ride, provided that scientists and engineers get all the details worked out.
Theme of this Logic Reasoned-Argument: In Quantum Mechanics of a Atom Totality Universe lies a concept known as quantum entanglement but a better word for it is Superdeterminism. The reason the world had Atomic bombs is exactly the reason that all intelligent life in the cosmos may get stuck in the situation of their home star turning Red Giant. They be toast, if not for several exit strategies such as atomic bomb blasting their way outward from the star gone Red Giant. But, the life on those planets has to wake up before the window of opportunity is closed upon them and they thus get toasted and burned out of existence and thrown into oblivion.
In my next long reasoned-argument of Logic is one of those stories that is dear to my heart. Probably because it is a call for experimentation which has yet to be performed for it shows a laziness on the part of chemists and physicists alike. It is not a difficult experiment but particular in attention to detail. It comes from my pure intuition of what must be for "water", and if shown true once the experiment is performed, it proves water is not only H4O but proves the interior of Atoms has no nucleus and is composed of a proton torus with muons inside and neutrons outside the proton torus as capacitors. If proven correct, it ties theory together in one nice neat consistent whole.
(9) Chemistry-- Is Water really H4O and not H2O?
9-1) Re-do the Water Electrolysis Experiment and instead of stopping with checking on volume of hydrogen versus volume of oxygen, go a step further by actually weighing the mass of hydrogen versus oxygen to determine if water is really H4O and not H2O.
Statement: The Water Electrolysis Experiment performed to where we actually weigh the mass of hydrogen versus oxygen to determine if water is really H4O and not H2O.
9-2) In the past, where we performed Water Electrolysis Experiments where we separate the hydrogen from oxygen, and the scientists look only at the volume of hydrogen and the volume of oxygen and say from that volume measure that water formula is H2O.
9-3) When the Atom has a proton torus with muons inside doing the Faraday law structure, producing electricity, then the atom must have at least one neutron to storage the electricity produced. Otherwise, for instance, hydrogen as simply a 1 proton + 1 muon has no place to store its electricity and would be a subatomic particle and not a atom of hydrogen. Then, if H2 is formed, where one of the protons converts into being a neutron capacitor, then, that H2 would thus be a Atom.
H by itself as a single proton with muon inside thrusting through in the Faraday law-structure is a subatomic particle. When H bonds with H, one of the protons with muon inside converts to being a neutron to the other H and thus H2 is a atom.
9-4) To find out if water is truly H4O and not H2O we need to perform the Water Electrolysis experiment and stop only after we weigh the mass of the hydrogen versus oxygen. We do not stop with looking at volume.
9-5) The story leading up to my insistence on H4O began in 2016-17 when I was writing a chapter on physics elementary particles in my 8th edition of Atom Totality. I am a mathematician by training and instantly recognized that the proton as listed as 938MeV and electron at 0.5MeV and neutron at 940MeV and muon at 105MeV, I instantly recognized that both proton and neutron were really 9 x 105 = 945. Physics has a concept that is called Sigma Error and what it means is that if the proton is 938 and neutron 940 and muon 105, that really they are 9 x 105 = 945 precisely. As we measure the proton and neutron, that a lot of background energy stops us from getting precision that the proton is really 945MeV as well as neutron is 945MeV with muon truly 105MeV.
9-6) You see Sigma Error in physics is a polite way of saying "the noise" in the experiment gets into the data and makes the measurement of proton be 938 MeV when it really is exactly 945MeV.
9-7) Then in 2017, I realized that the proton was really 840MeV and not 945 MeV because the true electron of atoms was the muon itself and stuck inside of the proton torus 840MeV doing the Faraday law-structure with the proton torus. The Old Physics particle of 0.5MeV, the unit of electricity, is not the electron of atoms but rather, is the magnetic monopole of Atoms. The proton torus with muon inside thrusting through producing electricity is producing the 0.5MeV particles stored in neutrons as parallel plate capacitors that surrounds the proton torus, and converts those eV currents into magnetic monopoles. These magnetic monopoles on parallel plate capacitors is what gives chemistry its bonding capabilities. As positrons and antipositrons of H sticks with another H to form H2 and these positrons and antipositrons on oxygen O bonds O to H2 and H2.
9-8) Bonding in all of chemistry is the interplay of magnetic monopoles 0.5MeV that reside on neutrons of parallel plate capacitors that surround the proton torus.
9.9) Many chemists have noticed many strange things about hydrogen in their career in chemistry. For one, hydrogen to hydrogen bonding is anomalous bonding for its force strength is too high.
9-10) Water Electrolysis performed in Old Chemistry, Old Physics gives the impression that everyone is in a rush to get back to the faculty lounge and get some coffee, cake and donuts, saying that their experiment is finished after looking at volume.
AP says, no, you are not finished. Now you need to precisely weigh the mass of hydrogen compared to oxygen with a precision scale and see if the hydrogen is 1/4 the mass of oxygen would mean water is truly H4O. If the mass of hydrogen is 1/8 that of oxygen, then water is H2O.
9-11) But the experiment needs much attention to detail, for water has deuterium a proton with 1 neutron, and tritium a proton with 2 neutrons. So before we do electrolysis, we must be sure all the deuterium and tritium is removed.
9-12) I hear that a Quartz Crystal Balance can weigh the mass of hydrogen and oxygen in water electrolysis. We need the best available scale possible.
Conclusion: Sloppiness in Logic is bad logic. Why stop at looking at volume, for hydrogen has many strange characteristics. Press on to weigh the mass of hydrogen versus oxygen in electrolysis. Should the result come back that water is really H4O, means that Atoms have no nucleus, they have a proton torus with muons inside and neutrons as parallel plate capacitors responsible for chemical bonding.
Logic Theme: one could say the theme is similar to the Rutherford, Geiger, Marsden experiment of sloppiness in not noticing 180 degree bounce back alpha particles with greater velocity coming out than upon entrance. Is the same sloppiness of scientists just looking at volume, when a complete experiment requires measurement of mass. But I think the best theme of this story is that all of science is intertwined and connected, which mathematicians and logicians alike call consistency. It is consistency that my intuition played upon. If subatomic particles have functions and jobs to perform the proton a coil in Faraday law structure and the muons as bar magnets, the neutrons as storage parallel plates. Then we have a extremely oddball Atom of hydrogen. It makes electricity with its proton and muon but no place to store electricity--- so--- is it even a Atom or is it a subatomic particle. And the true atom of hydrogen is then H2 which chemists would say is a molecule but AP says is an Atom of hydrogen, where one of the proton+muon converts into being a neutron. I guess I love this story because it is a strong example that when you have the theory correct, that you can actually predict the outcome of the water electrolysis----- it is H4O, not H2O.
Alright, my last long logic reasoned-argument. Again, the bulk of logic, in doing logic is centered on making long reasoned-arguments. All of us do this in our life, only the arguments are usually about some practical actions taken in your daily life. Such as my driving to go shopping on rainy days since I cannot work outside in the lawn and gardens. Or my habit of working late in the night-early morning because of the peacefulness and nothing to bother me. And my last long argument is about an idea as I approach older age and then the inevitable death. Reincarnation, a fascinating prospect. I even have experiments ongoing right now on attempting to graft a blackberry scion to a spruce rootstock and a honeylocust scion to a spruce rootstock. Both are still alive and hoping for success.
(10) Reincarnation of biology is real and true as recycling of DNA.
10-1) Reincarnation of biology is real science and is the recycling of DNA, for why be a wasteful Cosmos that makes new DNA when you can recycle old DNA with a added improvement.
Statement: Reincarnation of biology is real science and is the recycling of DNA, for why be a wasteful Cosmos that makes new DNA when you can recycle old DNA with a added touch of improvement.
10-2) I have tried all my life to capture moments in which I see something in my mind that predicts a future outcome, before it actually happens. Thus hinting of reincarnation. Especially when analyzing dreams.
10-3) I believe myself to be the reincarnation of the Ancient Greek scientist of Archimedes, the one who discovered pi is 3.1415.... and did many engineering feats. But have no solid concrete evidence for this belief.
10-4) Physics has a concept of maximum speed and we know it as the speed of Light, a constant maximum.
10-5) Physics has another concept, only this time it is a Minimum concept called Least Action Principle. This is where the path of a object in motion, takes the path of least action. I call it Least Energy.
10-6) If we apply Least Energy to death and the here after, would it not make logical sense that the DNA of that dead body goes to some realm of the Cosmic Atom Totality and is reconstituted and brought back to life in a new creature of biology, although given a few edits. Why construct a brand new DNA, when you have all this old DNA that can be utilized. Much like a recycling center for humans for Rare Earth Minerals, or aluminum or iron. Better to recycle than dig it out of the ground.
10-7) I have started to graft species from different phylums starting in 2025 with no success. This year 2026, have another new batch of grafts in hopes of success. The idea here is that the scion is dead once it is cut. But being applied to a rootstock, it can come back to life. A reincarnation in plants.
10-8) Since physics has a principle of Least Action (Least Energy), that biology would have Least Energy by recycling dead DNA, making a few edits and bringing that dead former life back to life in the present.
10-9) But of course in an Atom Totality Universe, there would be a Control Center where DNA of dead are received, edited and then shot back out into the Cosmos in the form of Light-photons to make a new life with that DNA.
Conclusion: Applying Logic to physics Least Action implies DNA is recycled from dead creatures to form new creatures.
Logic Theme: I am reminded that when I wrote the History of Logic book that the concept of Symmetry frequently came up as the most brilliant logicians of the past used Symmetry (which is consistency) that brought them fame. Curie and Dirac symmetry of the Maxwell Equations and that the magnetic monopole had to exist. In this argument of Reincarnation, Least Energy becomes almost tantamount, almost equal to the process of Reincarnation.
The Logic theme of Reincarnation is to think of Reincarnation as another recycling mechanism in an Atom Totality Universe.
As is usual in a case study of me, myself, whenever I do long logic reasoned arguments, I end up with a new argument to pursue. It reminds me of the year 1993 when I first came to and arrived at the Internet and Usenet newsgroups of sci.physics, sci.math and many more. I thought back then and most every observer thought that "science discovery" is enhanced by interaction with other people with same interests. Trouble is, noise usually sets in and then hate-mongering stalkers set in and it becomes more of a time waste. Now that Google is gone from Usenet and AP is alone in his own newsgroup, I seem to have made far more progress in that of new scientific discovery than if these past years were back with Internet and all the cabal going on. Instead of taking 2 years to write these 4 textbooks on Logic when I am alone in my own newsgroup, it likely would have taken me 5 years with cabal going on.
So I finished these 10 long reasoned-arguments of logic and need to summarize. And I started the summary below--- saying that in my History of Logic textbook I could not escape noticing that the fame of many a famous scientist is connected with the concept of Symmetry. Maxwell is famous for unification of the structure of electromagnetism and he needed a-lot of symmetry to pull off that feat. However, it escaped Maxwell's attention that the Gauss law in his unification was itself asymmetrical--- where Gauss and Maxwell declare-- no magnetic monopole. Perhaps Maxwell was daunted and intimidated by Gauss's math. But regardless, Maxwell's work garnered Maxwell huge fame, but to straigthen out the monopole asymmetry allows two more famous scientists to achieve fame-- Pierre Curie and Paul Dirac as they insist magnetic monopoles must exist. And of course in 2016-17 AP announces that the very ubiquitous 0.5MeV particle is not the electron of Atoms but is in fact the Curie-Dirac magnetic monopole. The electron of atoms had always been the Muon.
Symmetry is none other than Consistency. A geometrical consistency is what symmetry is.
And I did mention that I myself became famous in science with the Atom Totality theory, which is a discovery of Symmetry and Consistency. Can you have a Universal Atomic Theory, when the Universe itself is not one single big Atom?????? No. If the Universe is not one single big atom, you have asymmetry between the Atomic Theory and the Cosmos. The Atomic theory to be Universal theory and not a mere meager rule of thumb has to include the Cosmos as being a single big atom.
But now, having completed 10 Reasoned-Arguments of Logic, I need to include a 11th reasoned argument of logic, saying that Speed of Light as a constant Maximum Speed is directly related to physics Principle of Least Action (or call it Least Energy). Speed of Light is directly related to Least Action, otherwise, there is asymmetry and inconsistency. And my 11th reasoned logic argument will dive deep into that connection.
On Saturday, May 30, 2026 at 4:13:01 AM UTC-5 Archimedes Plutonium wrote:
(snipped)
Conclusion: Applying Logic to physics Least Action implies DNA is recycled from dead creatures to form new creatures.
Logic Theme: I am reminded that when I wrote the History of Logic book that the concept of Symmetry frequently came up as the most brilliant logicians of the past used Symmetry (which is consistency) that brought them fame. Curie and Dirac symmetry of the Maxwell Equations and that the magnetic monopole had to exist. In this argument of Reincarnation, Least Energy becomes almost tantamount, almost equal to the process of Reincarnation.
The Logic theme of Reincarnation is to think of Reincarnation as another recycling mechanism in an Atom Totality Universe.
So, well, in my History of Logic textbook I cannot help but notice that the fame of many of the most famous scientists was tied to a issue of "symmetry". And I wrote that in the summary of History of Logic.
For a summary of these 10 logic reasoned-arguments, I cannot help but notice that Speed of Light as a constant maximum must be directly related to the Minimum Action or called Least Action.
So how are they related???? Looking at the units of Action it is simply angular momentum.
velocity = LT^-1
acceleration = LT^-2
energy EM = ML^2T^-2
energy = ML^2T^-2
action = ML^2 T^-1
force = MLT^-2
frequency = T^-1
linear momentum = MLT^-1
Angular momentum = ML^2T^-1
Force = MLT^-2
So we see that velocity is length divided by time and we see that Action is Area divided by time.
Minimum Action involves length squared, will maximum velocity involves length.
What does that relationship remind me off???
It reminds me that derivative is a velocity dy/dx while integral in the same interval is area under function graph.
Thus, Speed of Light as Maximum constant speed is the Derivative, while Least Action is angular momentum or area divided by time.
This tells me that so many proofs of physics what we would call Experimental-Proofs rely on this idea that the Physics Principle of Least Action is the proving mechanism.
Prove Occam's Razor? Simple, inject Least Action, where the path the particle must take is the Minimum path. The true explanation in Occam's Razor has the Minimum number of assumptions.
Prove Reincarnation is true. Simple, use Least Action, where it is the greatest savings of DNA by recycling the DNA upon death and injecting it into new life.
Prove (this is a hard one), prove that the muons inside every single proton torus produce maximum electricity in their thrusting through the proton torus in the Faraday law-structure. Hard one to prove.
Archimedes Plutonium May 30, 2026, 5:32:14 PM to Plutonium Atom Universe newsgroup.
Connecting Least Action Principle directly to Speed of Light. One is the inverse of the other, for Speed of Light is the derivative while Action is Angular Momentum which is the integral.
So many arguments in Logic end up being solved by this Maximum and Minimum inverse relationship. Occam's razor is solved by this technique.
Before I get steered off course with Riemann Hypothesis and Space has only 3 dimensions never 4, I best finish off this idea of Instantaneous Energy that corresponds with Instantaneous Velocity in the Calculus.
This instantaneous concepts of velocity and energy is proof that calculus is really about discrete numbers in Cells that line the x-axis.
On Sunday, May 31, 2026 at 4:23:48 PM UTC-5 Archimedes Plutonium wrote:
Old Math and Old Physics were smart enough to have Instantaneous Velocity, but too dumb and stupid to have Instantaneous Energy.
On Saturday, May 30, 2026 at 4:24:23 PM UTC-5 Archimedes Plutonium wrote:
(big snips)
So how are they related???? Looking at the units of Action it is simply angular momentum.
velocity = LT^-1
energy = ML^2T^-2
action = ML^2 T^-1
frequency = T^-1
Angular momentum = ML^2T^-1
--------------------------------
AP discovers the Integral is Angular Momentum is Instantaneous Energy while the Derivative as velocity is Instantaneous speed.
---------------------------------
Physics has the Principle that Light is a constant maximum speed. It also has a less known Principle called Least Action which basically says that the motion of a particle follows the path of Least Action or Angular Momentum. I like to call it the Least Energy principle. And what it basically means is that Velocity is the dual of Angular Momentum, just as addition is the dual of subtraction; multiplication the dual of division; derivative the dual of integral; electricity the dual of magnetism.
Old Math not only was stupid in never realizing calculus is geometry and seek a geometry proof of FTC, but they did manage to find "Instantaneous Velocity" in spite of their stupidity. But being dumb often means being sloppy, and Old Math --- finding intantaneous velocity, never followed through. Okay, you found instantaneous velocity but struggling to ever teach it, but you failed miserably in finding Instantaneous energy. And I suppose waiting for AP to discover it for you.
I am begin to recognize that my memory is fading. And especially when I juggle many ideas at one time. Worse yet when I steer off course into a different topic and thus when I return, have lost my concentration of what I was doing.
I want to prove in this section of Logic textbook, that the Speed of Light principle as a maximum speed is related to the Least Action Principle in Physics, so as to easily prove Occam's Razor as an example of Least Action being Least Number of Assumptions.
So let me stay focused and pick up on Riemann Hypothesis and Space is only 3rd dimensional and a New Poincare Conjecture Proof where the Old Poincare Conjecture is deeply flawed and false. If I wander down that road, I will completely forget my train of thought on Least Action.
I need Least Action as a proving mechanism in Logic and Science for reasons like this.
Part 8. More details of Equalities of Logic, which Old Logic called "Rules of Inference".
Before I get to the Equalities of Logic let me repeat some of the terms used in science.
List of terms used in science
--------------------------------------
for science, especially physics but also other sciences
----------
Hypothesis -speculation
Concept
Law-structure
Principle
Theory
for logic
-------
Statement- proposition
Premiss
Concept
Equalities, as seen as Rules of Induction Rules of Inference
for mathematics
-------
Statement
Axiom
Proof
Theorem
Corollary
for science, especially physics but also other sciences
----------
Hypothesis- speculation
----------------
Some would call it a speculation or conjecture. Its truth value is unknown and needs science research and even experimentation to find out the truth. Examples-- (a) Human overpopulation will extinct all wild animals. (b) Jupiter will start to shine like a star before 2099.
Law
-----
There are few Law-structures of science and most are about electricity and magnetism. Such as the Faraday law-structure, Coulomb law-structure, Ampere law-structure, New Ohm's law-structure, Capacitor law-structure, Lenz law-structure.
Law-structures are universal and are experimentally proven true.
Principle
-----------
A principle of science is a description of some topic in science. Principles are different from law-structures in that principles describe objects while Law-structures are the forces and actions of objects. For example in geology the Complementarianism Principle; in biology the Darwin evolution principle; in chemistry the Aufbau Principle; in physics the Superposition Principle.
Theory
Theory is a term that should seldom be used because the definition of theory is a collection of laws of physics, the electromagnetic laws all working together as a single unified picture of the world. Most people use the word "theory" when they should be using the word "hypothesis". For example, Quantum Electrodynamics is a theory for it is a collection of EM laws. Optics of physics is a theory because it is a collection of EM laws. In biology, there is Cell theory for it uses some of the EM laws, but Darwin Evolution is not a theory but a principle because "natural selection" "the fittest fit" is its mainspring and that is not a electromagnetic law-structures underpinning it.
for logic
-------
Statement
-------------
Statements can be words, sentence or a number of sentences, even a picture-image. They contain an idea or ideas, and the truth value can vary to true, false or partial truth.
For example: Jack and Jill ran up the hill to fetch a pail of water. Jack fell down and broke his crown and Jill came tumbling after.
Premiss
----------
These are statements all of which have a true truth value. For example: Sun and stars shine from Faraday law-structure and not from fusion as the reason the Sun has gone Red Giant.
Equalities, as seen as Rules of Induction- Rules of Inference
-------------------------------------------
Math calls them "properties" such as commutative A+B = B+A or as in multiplication that AxB = BxA. Logic calls them equalities. Old Logic authors often refer to them as "rules of inference" as the inside cover of Copi's Introduction to Logic, 4th edition, 1972.
For example in Logic P AND Q = Q AND P. Another example: If P then Q, and, if Q then P, then P = Q.
for mathematics
-------
Statement
-------------
A statement in math is a sentence or sentences which is that to be accepted as a axiom or to be proven true by stepwise deductions.
For example: The volume of any prism is Base area times height.
Axiom-Postulate
----------------------
These are statements accepted as true by common agreement for they have no proof. For example: Two points determine a unique straight line segment.
Proof
-------
In math we are given a statement and if not a axiom, we must prove it in a stepwise deduction using axioms or theorems.
Theorem
------------
These are proven statements and once proven they are given the name "theorem".
For example: there is a picture proof of the Pythagorean theorem, A^2 + B^2 = C^2 for the three sides of a right triangle.
Corollary
-----------
These are smaller proofs of side issues for a theorem proof. For example: the prism volume is Base area x height, which then can easily prove the rectangular box volume is length x width x height and also prove the cube volume is length of side s as s^3, both of these are corollaries.
The most often mistake of terms is the over-use of "theory". Theory should seldom be used except when talking physics and the laws of electricity and magnetism.
Some people confuse Theorem of math with theory of physics.
Most people not in science confuse what is a Law-structure and what is a Rule. A "law" means universal and law-structure means works always, yet a rule works only sometimes not all the times. In Old Physics, their Ohm's law-structure broke down when you had high voltage or high current. The problem was fixed by AP who replaced Resistance with (magnetic field x electric field) in the 1990s calling it New Ohm's Law-structure. Voltage = current x magnetic field x electric field where the multiplication is a generalized multiplication being normal multiply or vector cross product or vector dot product.
So now, let me dive into the 6 connector-structures of Logic, the Existential quantifier, Not-Equal, AND, OR, If--Then, Universal quantifier.
Archimedes Plutonium Mar 21, 2026, 3:37:11 AM to Plutonium Atom Universe newsgroup.
From my Elementary Logic textbook I wrote this about the 6 connectors as connector-structures of Logic.
We define logic connectors by a structure, not by its truth table. Although the truth-table helps us to ascertain what the connector-structure is.
In New Logic we define all 6 connectors by a connector-structure governing the connectors. The same as in physics where the essential ideas and truths of physics are given in a "physical law-structure" such as Coulomb law-structure, Faraday law-structure, Ampere law-structure, New Ohm's law-structure.
Truth-tables do not define a logic connector, and this avoids the AND truth table seemingly to have a contradiction of "True AND False being True". This appears to be a contradiction, but since AND is defined as a Law, we avoid the seemingly contradiction.
For __Existential quantifier that connector-structure__ of defining was this--- look in the most relevant recent science pertaining to the existence of something and see if the object exists in that science, plus, no logic argument can have a contradiction such as A exists and A does not exist. If a contradiction arises in Logic, all must come to a halt and consult the relevant science to overcome the contradiction.
For the definition of __Not-Equal as a universal concept__ we say this. Not-Equal is equality of identical sameness and the Not portion is a reversal of a statement. Keep in mind, Not is bound together with Equal and is inseparable from equal.
We now define the AND connector, not with truth-table but as a connector-structure saying that AND connector is one of add or join two or more statements of ideas together. And the connector-structure that defines AND is that within a string of statements joined by AND that at __least one of the statements has a true value__ ascertained from science, and where all the other statements in the string can be 0-valued out right false or mere worthless chitter-chatter, ___except a contradiction___, but the overall chain of statements is thus true. If a contradiction occurs in a string of statements, then all stops and until the contradiction is excised out, does logic continue further.
Enumerate the 6 connector-structures of Logic Connectors.
Connector-structure of Existential quantifier: There exists something is formed by the best available science on the subject topic. This comes from math derivative of calculus as dy/dx and also is coupled to If-->Then as division. And in the Exist quantifier we can never have "A exists AND A does not exist" for a contradiction causes all of logic to come to a screeching halt and has to call in the sciences to overcome the contradiction before continuing further.
Connector-structure of Not-Equal: Not is a reversal of a given statement while equality is identical sameness of two statements. Now the words in the two statements can be different but the idea in both statements is the same. Not-Equal comes from multiplication in arithmetic and is coupled with Universal quantifier as the integral of calculus.
Connector-structure of AND: Joins together several statements p,q,r,s, etc of Logic and is a collective true statement provided at least one of the statements p,q,r,s, etc is true. The AND connector allows falsehoods and nonsense talk to enter arguments. And the truth comes from the pertinent science surrounding the statements. AND comes from addition in arithmetic.
Connector-structure of OR: Removes or discards ideas or subtracts one idea from another idea represented by p,q,r,s, etc. OR is the opposite of AND that joins together statements. OR removes something, be it a statement or the subtraction of one statement with another statement. OR is the connector of Deciding Experiments in science and as such allows from a variable truth value "dT" being a fraction of truth between 0 and 1.
Connector-structure of If-->Then: I like to think of If--> Then from calculus graph where we slowly move down the x-axis and graph the next coordinate point. Given statements P and Q that P moves into Q. The Law of If-->Then is both P and Q have to be true, by science, to form the conclusion of Q starting from P. And this ties in earlier with the idea that we discard all the F rows and U rows and have the T row define the connector.
Connector-structure of Universal quantifier: The Universal quantifier comes from the Existential and the two of them are duals of one another. We do numerous experiments and find all of them obey a formula. The experiments exist and once we have a number of them we elevate the idea to be a universal law-structure through this process of Existential Instantiation, Existential Generalization, Universal Generalization, Universal Instantiation.
Homework assignment: Write one statement for each of the above Laws using a science reference. Use my 6 examples below as guidance.
1) Existential quantifier: Tides exist because the Moon's gravity exists.
2) Not-Equal: The slant cut of a cone is not equal to a ellipse, but equal to a oval.
3) AND: The Darwin evolution is described as the concept of mutation, and the concept of genetic recombination, and the concept of natural selection, and the concept of reproductive isolation.
4) OR: Quantum Mechanics "superdeterminism" is true and prevailing, or, Darwin's Evolution is true and prevailing.
5) If-->Then: If the true numbers of mathematics form a continuum with no holes or gaps between one number and the next number, then, the Calculus cannot exist in this environment.
6) Universal quantifier: In every experiment where a bar magnet is thrust through a circuit of copper coil of wire there was the observation of an electric current produced, and so the Faraday law-structure is universal.
Let me repeat the Truth-Tables I published in Elementary Logic.
So our truth table of Logic for Not-Equal is made from two binary tables of equal and then of not, combined to form a quaternary table.
Not-Equal truth-table:
p q
T T = (T = T) = T
T not F = (T = T) = T
F not T = (F = F) = T
F F = (F = F) = T
Suppose we substitute numbers for T=1 and F=0 to see if we get multiplication out of the Logic connector that is Not-Equal.
p q
1 equal to 1 is true = 1
1 equal to 1 is true = 1
0 equal to 0 is true = 1
0 equal to 0 is true = 1
And we see a quick way to validate if any truth-table of Logic is valid or invalid. We simply see if we can substitute numbers into Logic truth tables and what those numbers become. In the above, only the Math operator of Multiplication can deliver a 1x1 = 1 and a 0x0= 0. Only Multiplication can deliver 1 when we have 1x1 and only multiplication can deliver 0 when we have 0x0. Only multiplication can substitute for Equal in 1=1 and 0=0.
For comparison sake we show the AND connector truth-table. Paying particular attention to the fact it has 4 rows and why we had to combine Not to Equal to convert the two 2 rows into being also 4 rows.
AND truth-table:
p q p AND q
T T = T
T F = T
F T = T
F F = F
And if we plug in arithmetic of T= 1 and F = 0 we see that AND is addition in arithmetic.
1 1 = 2
1 0 = 1
0 1 = 1
0 0 = 0
In the OR connector we have the Deciding Experiment to take into account, where two statements are competing for the truth, one statement is all true while the other statement has a fractional truth, a fraction between 0 and 1 such as being 1/4 true or 1/2 true. And science then conducts experiments to see which of the two competing statements is the full truth and the other a partial fraction of the truth.
New Logic OR (exclusive)
p q p or q
____________
T T F
T dT T
dT T T
F F F
Math validation of correctness
p q p or q
____________
1 1 0 so in this row we can see 1 - 1 =0
1 fraction 1 in this row we see 1remove fraction =1
fraction 1 1 in this row we can say remove fraction leaving us with 1
0 0 0 in this row we can say 0-0 =0, alternatively we can say remove p leaving q, or remove q leaving p
So we have 4 possibilities.
1) Remove P keeping Q
2) Remove Q keeping P
3) Subtract P from Q provided Q is larger
4) Subtract Q from P provided P is larger
New Logic for If-->Then
p q if p then q
____________
T T T
T F F
F T U for unknown, uncertain, undecided
F F U for unknown, uncertain, undecided
Let me validate that is the math operator division. I replace T with 1 and F with 0.
p q p divide into q
____________
1 divide into 1 1
1 divide into 0 0
0 divide into 1 U for unknown, uncertain, undecided and undefined
0 divide into 0 U for unknown, uncertain, undecided and undefined
Yes, so in summary so far we have Not-Equal as multiplication, AND as add, OR as subtract, and If-->Then as divide. Of course the Existential and Universal quantifiers have no truth tables for they are laws. And we should also define the 4 other connectors by Laws, just as we define science by Laws of Science.
The Logic Truth Tables in detail
------------------------------------------
I mentioned the AND truth table earlier of statement P AND Q.
Corrected Old Logic AND truth table where AND is seen as addition of arithmetic; seen as joining together.
P Q P AND Q
T T = T
T F = T
F T = T
F F = F
So we ask the question why does AND, OR, If--Then, Equal-Not have 4 rows?
And the answer lies in the idea that you want all possible outcomes for statement of idea P combined with statement of idea Q.
So that the truth table for 2 statements, the P will always be this:
P
---
T
T
F
F
And the Q will always to this:
Q
----
T
F
T
F
This is so to capture all the possible outcomes. If there were 3 variables of P, Q, R, then you need 8 rows to capture all the possible combinations.
P Q R
------------------
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Does the reader see the pattern? It is a pattern that captures all possibilities of statements truth values given a specific number of variables P, Q, R, S, T etc. Remember, statements of ideas can be written either in capital letters or small letters, P,Q written as p,q.
We compare this pattern to mathematics of a true-false test.
Total possibilities for a test of 2 questions with 2 answers is 2^2
Total possibilities for a test of 3 questions with 2 answers is 2^3
Total possibilities for a test of 4 questions with 2 answers is 2^4
(Mathematical Induction for a proof of this-- that the total possibilities are 2^m where m is the number of questions in math or the number of variables in Logic.)
Fundamental Counting Principle: To find the number of ways of making several decisions in succession, multiply the numbers of choices that can be made in each decision. (from Harold Jacobs, Mathematics a Human Endeavor)
Here again, we can see that Logic comes from Physics and is a subset of physics, for quantum mechanics is the subject of probability mathematics in order to get to the Fundamental Counting Principle.
In Physics we have Zero or Nothing in the idea that Absolute 0 Kelvin temperature is unattainable. This also proves that Negative numbers do not exist and never existed.
Physics has an infinity borderline because physics has a maximum constant speed of Light at 3.16*10^8 meters/second. Makes sense that if the world has a maximum speed, the speed of Light then the world has a maximum number that composes a infinity borderline, which is from Huygens tractrix is 1*10^604.
Everything in Math is of a positive value and in geometry is all mapped out in 1st Quadrant Only.
It is unfortunate that math named subtraction as subtraction for a better name for it would have been Remove. If math had used the term "Remove" you cannot remove (you cannot subtract) more than what is available to remove, then math and physics would never have negative numbers.
I start Logic with mathematics and used math to guide me. But now I shift over to physics for answers.
Physics has 0 and it has infinity borderline which comes to be 1*10^604 and its inverse. It is where pi digits has 3 zero digits in a row. If we climb back to 1*10^600, just before we slam into those 3 zero digits in a row, we find that the Speed of Light as 3.16*10^8 meters/second divides into 10^600 by 10^75. For 8 x 75 =600.
Meters and seconds are arbitrary until you ask the question what is the speed of light inside a proton torus with muons inside of an atom like hydrogen or helium. Meters and seconds are no longer arbitrary inside the proton torus. And it is here where you get the 10^75 factor.
Now, I have to shift over to Physics, for answers upon Logic, I start with Existence quantifier first and then go to Not-Equal because we need existence to start with. After existence we need "not" combined with "equality".
Equality to get at the AND, OR, IF-->Then. And it is with Not-Equal that we introduce the Distributive Law. Do you remember the distributive equality in mathematics class? It is for example this A(B + C) = AB + AC, for example 2(3+4) = 2*3 + 2*4. It turns out that the distributive equality is more essential for the beginning of Logic than is the commutative or associative equalities. Commutative and associative equalities are about the order in which you add or multiply. For example of commutative is 3+4 = 4+3 for add and 3*4 = 4*3. For example the associative is A+(B+C) = (A+B) + C, where you have to do what is inside the parenthesis first. Example 1+(2+3) = (1+2)+3. You see the order in which you add matters not. And for multiplication associative we have (A*B)*C = A*(B*C), for example (10*100)*1000 = 10*(100*1000). Distributive equality has a mix of addition with multiplication.
Now physics also introduces Probability math into Logic. The way Physics introduces probability is through what it calls Psi-squared and that comes from physics being all about electricity and magnetism which are perpendicular to one another and obeys the Pythagorean Theorem of Geometry.
Pythagorean Triples and multiples of P-triples:
1, 2, 2, 3 for 1+4+4=9
3,4,5 for 9+16=25
1,1,3,5,6,7 for 1+1+9+25+36+49 =121
5,12,13
8, 15, 17
7, 24, 25
Physics delivers what exists in Space geometry and Physics delivers universal laws of the world.
We start Logic with Mathematics first through the Existential quantifier, next the Not-Equal and move down into the details of Logic. We use mathematics to reveal the essentials of Logic for Logic is a larger set than is mathematics, but mathematics is easier to understand what the details of logic are.
So if we take "Physics looking at the World" as opposed to "A human looking at the world". An idea for the human would be either true of false. But that same idea for Physics is given a value of either "zero-nothing" versus an idea that has "existence in material science".
So when Physics looks at a statement --- The Earth is the 4th planet from the Sun. Physics does not say "false" but rather, says-- "zero-nothing". When Humans look at that statement, they say "false".
And "nothing-zero" comes from physics in the Absolute 0 Kelvin temperature, nothing beyond zero.
Calculus forms existence in the derivative, the dy/dx as it moves along the x-axis, the function lands on a y-value, a unique y value and so that causes the existence of a unique coordinate point, a single 1 point to exist. The derivative thus creates Existence quantifier, and that it lands on a unique y-value. Physics Absolute 0 temperature and the derivative of calculus creates 0 and creates 1.
This is where Logic gets entangled with science. It starts with the question of existence of something and goes to the relevant science of that topic.
In mathematics, logic starts with the existence question of 0 and existence of 1. Then Logic turns to the concepts of Not and of Equal. Does 0 exist, or not exist. Does 1 exist or not exist. Logic then asks what is 0 equal to and what is 1 equal to? Is 5 subtract 5 equal to 0? Is 1/8 of 8 equal to 1?? But to define Equal, Logic needs the Not connector, becoming Not-Equal all wrapped up together into one package in order to well define the other connectors of AND, OR, IF-->Then, Universal quantifier.
We start Logic connectors with Existence. Then we move to well-defining Not-Equal so we can well define all the other connectors.
Let us look at Truth Tables in terms of mathematics as 1 and 0 for addition, subtraction, and division. I leave out multiplication because that involves Not-Equal with a distributive law.
Addition truth table of Arithmetic
-----------------------------------------
P Q P + Q
1 1 2
1 0 1
0 1 1
0 0 0
So 1 is true as existence of 1, while 0 in physics is "nothing-no existence". That math truth table implies or moves-into the idea that the truth table for AND connector is TTTF.
Subtraction truth table of Arithmetic
-----------------------------------------------
P Q P - Q
1 1 0
1 0 1
0 1 1
0 0 0
That table implies subtraction is remove, whether we remove a 0 or a 1 or a 1 from 1. That table also implies OR connector is subtraction with FTTF. Now here we must also consider that we remove P or remove Q or we can subtract P from Q or subtract Q from P.
Division truth table of Arithmetic
-----------------------------------------------
P Q P divide into Q
1 1 1
1 0 0
0 1 undefined
0 0 undefined
That table implies the material conditional of logic the If-->Then truth table as being TFUU.
The multiplication truth table is complicated by the fact that we have a binary row for equal, T = T and F=F and we have a binary row for Not in which we combine the two binaries to make a 4 row truth table using the distributive equality of arithmetic.
But, before I leave this chapter on Universal quantifier, let me tell you something about the Existential and Universal quantifiers that has bugged me throughout my life since studying logic over 54 years ago in 1972. In logic class when I was young, I had it in mind that there must be an equation that has Existence quantifier on one side of the equation and has the Universal quantifier on the other side of the equation with some sort of factor on one of them. Much like the equation relating energy to mass in physics E = mc^2. So, before I leave the Universal quantifier, I want to explore if such a equation exists and what it would look like. Certainly no equation of such a kind is seen in any logic textbook before this AP logic textbook.
Archimedes Plutonium Apr 28, 2026, 8:36:43 PM to Plutonium Atom Universe newsgroup.
On Monday, April 27, 2026 at 11:29:56 PM UTC-5 Archimedes Plutonium wrote:
snipped
Note to any teacher using this textbook.
-----------------------------------------------
You will have to know at least 1st year college calculus, especially the polynomial Power formulas of derivative and integral and be able to graph a function in class and talk at length about the derivative and integral. Logic needs the math calculus for understanding the Existential and Universal quantifiers relationship.
In calculus we have the derivative and integral and they are what is the Existential quantifier and the Universal quantifier in Logic. In calculus there is the Fundamental Theorem of Calculus which basically says that the derivative is inverse to integral and vice versa. In math we can display inverse relationship as 1/3 is inverse to 3. For if we multiply 1/3 by 3 we end up with 1. If we think of 1 as existence and think of 3 as the total universe, we can relate that to Existential and Universal quantifiers.
The derivative of a function is dy/dx and the integral of that function in a cell is dy*dx. The dy as existence in the ___Case-Sample of 1/3 and 3___, then dy = 1 and you have 1/3 = dy*dx = 1*dx = 3.
What this means is that there is a Fundamental theorem of Calculus but also a Fundamental Theorem of Logic that says the Existential quantifier is Inverse to the Universal quantifier and there should be a Logic proof-argument, just as there is a math proof in calculus.
Archimedes Plutonium Apr 28, 2026, 9:01:01 PM to Plutonium Atom Universe newsgroup.
The proof of the Fundamental Theorem of Calculus is quite simple and can be easily explained in High School using the AP geometry proof.
It goes like this and similar to the diagram proof of the Pythagorean theorem, for, make no mistake about it, calculus is geometry, not some silly stupid "limit analysis".
Geometry Proof of the Fundamental Theorem of Calculus for High School
--------------------------------------------------
Now the derivative in Calculus is this rooftop of a slanted line segment that is the hypotenuse of a right triangle.
Here is a picture of what you have.
From this:
B
/|
/ |
m /----|
/ |
|A |
|____|
a b
The trapezoid roof has to be a straight-line segment (the derivative)
so that it can be hinged at m, midpoint, and swiveled down to form rectangle for
integral. The area of the rectangle is the integral.
To this:
__m__
| |
| |
| |
---------
a b
So, we have two items in Calculus for this theorem, we have a derivative, the straight line segment A to B with m in the middle. And we have the rectangle area which we call the integral.
That diagram is reversible so that you can start with the rectangle and form the trapezoid derivative or start with the derivative of and fold it down to form the integral rectangle.
But, for a Fundamental Theorem of Logic, FTL, is it an easy Logic Argument Proof?????
To prove FTL, let me go back to Ancient Greek times with Aristotle starting Logic as a subject in world history. His famous syllogisms and this one in particular.
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
There is another Aristotle syllogism.
All men are mortal.
All Greeks are men.
Therefore all Greeks are mortal.
Archimedes Plutonium Apr 28, 2026, 9:09:00 PM to Plutonium Atom Universe newsgroup.
I have to patch this up for it excludes women and in Ancient Greek times, they probably had a different view of men and women in society---
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
There is another Aristotle syllogism.
All men are mortal.
All Greeks are men.
Therefore all Greeks are mortal.
All humans are mortal
Socrates is a human
Therefore Socrates is mortal
All humans are mortal
All Greeks are humans
Therefore all Greeks are mortal
Archimedes Plutonium Apr 29, 2026, 3:43:47 AM to Plutonium Atom Universe newsgroup.
On Tuesday, April 28, 2026 at 9:09:00 PM UTC-5 Archimedes Plutonium wrote:
I have to patch this up for it excludes women and in Ancient Greek times, they probably had a different view of men and women in society---
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
There is another Aristotle syllogism.
All men are mortal.
All Greeks are men.
Therefore all Greeks are mortal.
All humans are mortal
Socrates is a human
Therefore Socrates is mortal
Socrates is the existence of 1. All humans is a universal for humans.
All humans are mortal
All Greeks are humans
Therefore all Greeks are mortal
Let me work on a different set of syllogisms
The Solar System is a large group of mass objects held together by the Sun with its force of gravity that forces these objects to revolve around the Sun.
Earth is a mass object of the Solar System.
Therefore Earth revolves around the Sun.
Planets of the Solar System have objects such as satellites that revolve around the planet by the force of gravity.
Venus is a planet and a satellite revolves around Venus by Venus's gravity.
Therefore a satellite revolves around Venus.
Planets have satellites that revolve around the planet by force of gravity.
Venus is a planet.
Therefore Venus has a satellite.
I am attempting to show that the universal gravity force related to the existence.
Feynman's description of the Atomic theory in his textbooks Lectures on Physics, 1963.
All things are made up of atoms.
So a AP syllogism of Atomic Theory.
All things are made up of atoms.
The Universe is a thing.
Therefore the Universe in whole is one single atom of the possible 118 atoms.
AP focus: here we have the universal of the Universe itself composed of material matter of atoms. Must the Universe be a single Atom out of one of the 118 possible atoms in the Periodic Table of Elements? Well, if atoms are created by the Faraday law-structure, then sure enough, the entire cosmos must be a single atom.
Is there a equality relationship between Existential quantifier and Universal quantifier?
----------------------------------------------------------------------------
Archimedes Plutonium Apr 29, 2026, 4:25:01 PM to Plutonium Atom Universe newsgroup.
Now the relationship of the Existential quantifier with the Universal quantifier is revealed in the EI, EG, UI and UG, but that is a descriptive relationship. The direct relationship between Existential and Universal in a formula is what I am about to reveal in the Fundamental Theorem of Logic. Now logic in my glossary of terms does not have theorems, but rather mathematics has theorems. And this reasoned-argument of Logic should be called a Law-Structure like that of commutative, associative or Occam's Razor. Still, I will keep the term Fundamental Theorem of Logic because it closely allies itself to math's calculus Fundamental theorem of Calculus.
So I have 1 = (3) x (1/3)
Existence = (Universal) x (Existence/(Universal))
Do you see where the universal divides out and leaves behind existence???
Another Case-Example, and using the latest stock market bubble hype over their shitty AI. (Yes I am not used to swearing but I live in a age where money greed in stock market is pushing this mindless cesspool ignorant crap called AI-- which to me deserves the height of swear words.)
Case-Example for Existence = (Universal) x (Existence/(Universal))
--------------------------------------------------------------------------------------
1) All entities require a Minimum Threshold to be classified as "being intelligent"
2) The minimum threshold for "being intelligent" is Self Awareness which means able to turn oneself ON, or OFF by own volition.
3) As of April 2026, not a single machine in the entire world has "self awareness" , which means no machine has Intelligence.
4) As of April 2026, only plants and especially animals have "self awareness" and thus possess intelligence.
5) Self Awareness is a Universal trait and there exists biology entities which have self-awareness.
6) Therefore, there exists intelligent biology entities, but there does __not exist intelligent machines__.
So, in that logic-argument above of the Fundamental Theorem of Logic let us pick out the Existence and the Universal and the E/U.
Existence is plants & animals are self aware.
Universal is self-awareness trait.
E/U is existence divided by universal is Plants & Animals divided by self-awareness.
Archimedes Plutonium Apr 29, 2026, 5:27:12 PM to Plutonium Atom Universe newsgroup.
Now let me try the existence formula upon Venus has no satellite example given earlier.
On Wednesday, April 29, 2026 at 4:25:01 PM UTC-5 Archimedes Plutonium wrote:
Now the relationship of the Existential quantifier with the Universal quantifier is revealed in the EI, EG, UI and UG, but that is a descriptive relationship. The direct relationship between Existential and Universal in a formula is what I am about to reveal in the Fundamental Theorem of Logic. Now logic in my glossary of terms does not have theorems, but rather mathematics has theorems. And this reasoned-argument of Logic should be called a Law-Structure like that of commutative, associative or Occam's Razor. Still, I will keep the term Fundamental Theorem of Logic because it closely allies itself to math's calculus Fundamental theorem of Calculus.
So I have 1 = (3) x (1/3)
Existence = (Universal) x (Existence/(Universal))
Do you see where the universal divides out and leaves behind existence???
The Solar System is a large group of mass objects held together by the Sun with its force of gravity that forces these objects to revolve around the Sun.
Earth is a mass object of the Solar System.
Therefore Earth revolves around the Sun.
Planets of the Solar System have objects such as satellites that revolve around the planet by the force of gravity.
Venus is a planet and a satellite revolves around Venus by Venus's gravity.
Therefore a satellite revolves around Venus.
Planets have satellites that revolve around the planet by force of gravity.
Venus is a planet.
Therefore Venus has a satellite.
Existence = (Universal) x (Existence/(Universal))
Moon exists = (satellites of Earth) x ((Moon)/(satellites of Earth))
Venus satellite = (satellites of Venus) x ((Venus satellite)/(satellites of Venus))
0 = 0 x (0/0)
Yes, again, what I am driving at here is a formula that relates Existential quantifier with Universal quantifier. Here I have the Nonexistence of a satellite yet I still possess the Universal quantifier trait of gravity force of Venus. The gravity force of Venus will allow for the Existence of a satellite around Venus, but the satellite itself does not exist.
So can we speak of a Universal force of gravity for Venus to have a satellite, yet, Venus has no satellite?? Can you have a Universal, yet not have any existence is the question.
Case-Example:
All dinosaurs share a few Linnaeus traits in common, such as the Pterosaurs, Spinosaurus, Titanosaurus and T. Rex had those traits.
Triceratops was a dinosaur.
Therefore, Triceratops shared those common traits with Pterosaurs, Spinosaurus, Titanosaurus and T. Rex.
Here in this case example, can we speak of a Universal trait in common between all the dinosaurs??? Their existence would be in the fossil record. Here the Universal is ambiguous and vague, although the existence of these animals is real.
Archimedes Plutonium Apr 29, 2026, 6:02:54 PM to Plutonium Atom Universe newsgroup.
So I have 1 = (3) x (1/3)
Existence = (Universal) x (Existence/(Universal))
So let me just substitute Calculus in that formula. Where derivative dy/dx is derivative and integral (dydx).
dy/dx = dydx ((dy/dx)/(dydx)) = dydx(1/((dx)^2)
Archimedes Plutonium Apr 30, 2026, 2:36:01 AM to Plutonium Atom Universe newsgroup.
If we examine this equation for insights of speed, energy.
If we take dy/dx as speed with the x-axis as time and the dydx as integral and thus energy, we see the denominator as time^2 which comes with acceleration.
A further substitution of Energy = mcc, we have dy/dx = mcc/dx^2. Multiply both sides by dx^2/ cc gives us dydx/cc = mass.
I am looking for a deeper penetration of what mass is, but no such luck.
Archimedes Plutonium Apr 30, 2026, 2:55:01 AM to Plutonium Atom Universe newsgroup.
Before, I had thought of including this calculus of the truth about the Derivative in my Intermediate Logic textbook, thinking it would be too complicated and complex. But on second thought, calculus is usually taught to freshman in college and university, so why not teach this true derivative in Logic to Freshman in hopes that math professors will see the errors of their ways and fix their torture chamber calculus classrooms. Now I see the advantage of including it in my Elementary Logic textbook for Freshman in college or university. At UC in 1968-1972, I took calculus in 1968 as a Freshman. But it would have been far far more wonderful for me and all the other students to have learned True Calculus, and not the fake calculus taught by math professors who never realized ____calculus is geometry____ and thus--- the Fundamental Theorem of Calculus, FTC needs a geometry proof.
Because once a math professor has to make a geometry proof of FTC, then she/he starts to realize that Reals are fake numbers. That math has no continuum realizing that physics has no continuum because of quantum mechanics. Realizes that numbers, true numbers of mathematics are the Decimal Grid Numbers that have holes or gaps of empty space from one number to the next number. That the negative numbers are fakery and that the graph of numbers is in 1st quadrant only. That the only valid functions of math are Polynomials and if not a polynomial, you have to convert it to a polynomial over an interval. And that math Calculus is very very easy of the derivative and integral are merely add or subtract 1 from the polynomial exponent which is called the "power formula" for polynomials.
Note: the teacher of this course in logic is going to have to be familiar with the Power formula of calculus, taught in 1st year of college. The power formula is essentially the heart of Calculus, considering the only valid functions of math are polynomials and it makes calculus almost as easy as add, subtract, multiply, divide.
Have the teacher do this lesson in class on the blackboard or overhead projector. Sorry, but calculus of math is indispensable in teaching logic.
Power Formula of Calculus
-------------------------------------
We learn for the Derivative Power formula of a polynomial x^n that the derivative is n(x^n-1).
So for example the function x^2 -> Y its derivative using the power formula is 2 (x^2-1) = 2x
Do you see how we got that?? Probably not, so let us do it in slow-motion.
We have a function x^2 -> Y and asked to do the Calculus derivative upon x^2. We use the power formula which says, we drop that exponent number down to be a coefficient. The exponent is 2 so we drop it down
2 (?)
Now the rule tells us to do a n-1 on the exponent n. Our exponent in x^2 is 2, so what is 2-1 ? and it is 1.
So our answer is 2x.
Now try another function say x^3 -> Y, and so our exponent is 3 and we drop it down
3 (?)
Now the rule says do a n-1 on that exponent and so we do a 3-1 and get 2. So our final answer is
3x^2
Try another, say our function is 3x^2 -> Y. What is our exponent? It is 2 and we must drop it down as being a coefficient.
3x2 (?)
Now what is n-1 ? It is 2-1 = 1 so our final answer is :
3 times 2x which is 6x.
The Integral Power Formula is sort of the opposite, actually the reverse of the derivative formula so for polynomial x^n that the integral is (1/(n+1)) times (x^(n+1)). In the derivative we subtract, in the integral we add. For example the integral of x^2 -> Y is (1/(2+1)) times (x^(2+1)) = 1/3x^3.
Let us try another integral of x^3 -> Y. What is our exponent? It is 3, so our n+1 is 3+1 = 4 and that gives us 1/(n+1) as being 1/4.
1/4(?)
Now what is our new exponent of x^(n+1) and it is x^4 so our final answer is :
1/4x^4
The derivative is subtraction, the integral is addition.
And that is all there is to Calculus, provided that our functions, all functions are polynomials.
So let us do many exercises.
The important idea to learn is the Power Formula so you an easily do all of Calculus, all of Calculus once we have all functions converted to polynomials.
Power formula for Differentiation x^n ->Y then nx^(n-1) -> Y'
Power formula for Integration x^n -> Y then Integral is (1/(n+1))* x^(n+1) -> Y_int
Prefix-Area in calculus such as the 1/3 in 1/3*x^3 in integration of x^2 -> Y
Homework Exercises:
Derivatives using the Power formula of
3x -> Y
3x^2 -> Y
3x^3 -> Y
1/2x^4 -> Y
1/2x^6 -> Y
10x^8 -> Y
Integrals using the Power formula of
3x -> Y
3x^2 -> Y
3x^3 -> Y
1/2x^4 -> Y
1/2x^6 -> Y
10x^8 -> Y
So, yes, I should include this calculus in Elementary Logic because many students will be taking Elementary Logic as Freshman in college and university, and as the student is tortured in calculus class with nonsense of derivative as tangent and thousands of different functions, meanwhile, over in Logic class we teach you the true calculus that calculus is super easy with just add or subtract 1 from exponent, no torture chamber by crank-crackpot math professors who cannot even admit the slant cut of cone is Oval, never ellipse.
I hope students clash with the math professor and his/her torture chambers of calculus.
Homework: Do the assignment below of drawing the trapezoid and exposing the fact that when the true numbers of mathematics have holes and gaps in between one number and the next number-- not a continuum-- then the calculus derivative is not a tangent line to a point of the graph but that it spans to be the next point on the original function graph.
Now the teacher of this logic class will have to know well the calculus of math and to lecture on this chapter with students taking notes. Many items I have omitted such as the "power rule of polynomials". So the chore of the teacher is to clarify to the students. Many will have seen the derivative in math class, but many will not and so the teacher has to fill the gap.
--- quoting in part from my textbook
TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2 ---
Fundamental Theorem of Calculus, Picture
Draw a trapezoid so it is easier to explain this Calculus. This theorem is the essence of Calculus, so we want to understand it easily.
Draw the trapezoid (0,0) (10,0) (10, 20) (0, 10)
Now look at the coordinate point (5,10) and mark it with a "m" meaning midpoint.
For it is the midpoint of the line segment that goes from (0,10) to (10,20) a slanted line segment.
Draw it in and draw the whole trapezoid.
Now the derivative in Calculus is this rooftop of a slanted line segment that goes from (0,10) to (10,20).
Here is a picture of what you have
From this:
B
/|
/ |
m /----|
/ |
|A |
|____|
a b
The trapezoid roof has to be a straight-line segment (the derivative)
so that it can be hinged at m, and swiveled down to form rectangle for
integral. The area of the rectangle is the integral.
To this:
__m__
| |
| |
| |
---------
a b
So, we have two items in Calculus for this theorem, we have a derivative, the straight line segment A to B with m in the middle. And we have the rectangle area which we call the integral.
We draw in m, the midpoint because that is where we have a hinge, we imagine a hinge there. In fact, some teachers will build this model in wood working class just to use in math class.
So, Calculus has two items-- the derivative which is the rooftop, the straightline. And the other item, the integral which is the rectangle area.
So, what is this theorem all about?
Well, it says that-- if you have a rectangle with a midpoint on its top side.
__m__
| |
| |
| |
---------
That you can cut a right triangle from the midpoint
__m__
| / |
|/ |
| |
---------
Cut that right triangle and swivel it up to make the trapezoid
B
/|
/ |
m /----|
/ |
|A |
|____|
Or, you can start with that trapezoid and swivel the right triangle downwards to make the rectangle
__m__
| / |
|/ |
| |
---------
And, basically that is the Calculus at its most simple form. Where the slanted line is the derivative and the rectangle area is the integral. So, there, 15 year olds, you have just learned the fundamental basics of Calculus. Take a rectangle, swivel the right triangle and you have a derivative. Take the trapezoid, swivel the right triangle to form a rectangle area and you have the integral.
Basically, that is all that Calculus is.
--- end quoting from my Teaching True Mathematics ---
Alright for an Exercise and then a Homework assignment of huge importance. We are going to prove that modern day math professors of Calculus are crank-crackpots when they believe the numbers of mathematics are the Reals as a continuum and that the derivative is a tangent line to the original function graph. Yes, we are going to prove math professors, not only are silly when it comes to slant cut of cone but crank crackpots when it comes to teaching true calculus. And let me use the glossary of terms for Mathematics given earlier.
Archimedes Plutonium May 1, 2026, 2:50:28 AM to Plutonium Atom Universe newsgroup.
Let me tell you a true story of my education in Logic and how my memory is slowly coming back around to focus in on it. And remarkably it comes at a time when I am almost finished writing these 4 textbooks on Logic.
It was a discovery of mine as important to Logic as my discovery in calculus that the polynomial is the only valid function making all of calculus so very easy and simple which I discovered while in college 1968-1972 at University of Cincinnati. So I was in Calculus class, first year college 1968 using Fisher & Ziebur textbook Calculus And Analytic Geometry, 2nd edition, 1965. And where the authors would always give examples of problem exercises over the concepts discussed, and they would generally give one of the examples using polynomials. I hated when they invariably gave a trigonometry example. But polynomial examples were a breeze for me. And sometime in my 4 quarters of calculus class, the idea came to me--- since the Power Rule made derivative and integral so super easy that the idea came to me--- what if Polynomials were the only valid function and then calculus would be Super easy, and dispense with every function not a polynomial. Well it was not until 40-50 years later when I learned of the Lagrange Interpolation, that my dream came true, for you can take any other so called function and turn it into a Polynomial.
But that was mathematics and a young AP of 18 years old brewing up a great idea that would take fruit in 2013 with my writing of "True Calculus".
But a similar incident occurred to me by 1971 and 1972 as I was taking two courses in Logic in two separate years at UC. The idea that brewed up here in logic when I was 21 and 22 years old concerns the relationship of Existence to Universal.
Mind you, this idea in Logic was nowhere as important as the idea in calculus that the polynomial was the only valid function for then Calculus would be so Magnificently easy, so easy that I would make straight A's and would seldom have to even do homework, so easy.
The idea in calculus came up because I saw how easy it was to find both derivative and integral of any polynomial.
But the idea in Logic came up not from any ease of anything, but rather, I sensed something was "missing" in logic.
What I imagined in college in Logic class was that there had to be a relationship of Existential quantifier = Universal quantifier times a factor. Or, I could write it as Existential quantifier times a factor = Universal quantifier.
I was certain in my mind when 21 and 22 years old that a equal sign needs to be placed with Existential quantifier on one side and Universal quantifier on the other side of the equation, with a factor in the equation.
I looked in Copi's textbook and in Thomason's textbook for this equation which I had imagined. But never found any. So, now, here 2026-1972=54 years later, I am trying to remember that episode as I finish up on my 4 Logic textbooks. I am trying to resolve the issue and include it in my logic textbooks.
Using Math to help me.
So, let me pick a number at random larger than 1. And I picked 3. So we have 1 = 3*(1/3).
In Calculus class at UC, I saw that given any Polynomial function for example x^2 the derivative is 2x and the integral is (1/3)x^3. Now take the derivative of integral returns me back to x^2 and take the integral of derivative takes me back to x^2. Derivative is inverse to Integral and vice versa.
Maybe it was this knowledge learned in calculus class at UC in 1968 that spurred my mind on to thinking there was some equality equation for Existential quantifier and for Universal quantifier. That the derivative was Existential quantifier and integral was Universal quantifier and they are equal in a sense that one is inverse to the other.
We would write this Equality as derivative of integral = original function = integral of derivative.
So I needed a equation that begins to sound like this---- Existential of Universal = original = Universal of Existential.
Only in the past month of April 2026 as I am finishing these 4 Logic textbooks have I really begun to recall in earnest this desire of equality.
So I pick the number 3 and pretend it is the Universal and the number 1 as Existence of one. And I have 1= 3*(1/3).
Examining 1/3 it is the existence of 1 divided by the universal 3.
So, can I say that Existence = Universal times (1/universal), which does not get me far.
Bring in the calculus and the derivative is dy/dx and integral is dy*dx as area in function graph.
We have derivative of integral = original function = integral of derivative. Now substitute dy/dx and dy*dx gives us dy/dx(dy*dx) = original function = dy*dx(dy/dx) again, this does not get me far.
Now I am 54 years more mature and learned, and let me throw in something new that will allow me to overcome these problems.
If we graph x^2 function we get this in 1st quadrant.
| /
| /
| /
|_____________
Now we take the Inverse of x^2 by flipping the y-axis to be x-axis and x-axis to be y-axis, which is merely rotating the previous function to lie in 2nd quadrant (some use for 2nd quadrant since I threw all quadrants except 1st out of mathematics entirely).
Our function of inverse x^2 now looks like this.
__ |
__ |
--- |
_____________|
We studied inverse functions at UC but I never seemed to make much use of them. Maybe now I make enormous use of them.
Archimedes Plutonium May 1, 2026, 6:12:40 AM to Plutonium Atom Universe newsgroup.
Alright, I solved my problem. Whenever I have difficult problems I take a hot bath and it usually renders some answer.
I was thinking the final solution had to be of a form of Existential quantifier = Universal quantifier times a factor. No, that is a linear solution, much like a straight line is Y = mx + b. No, this solution is not linear.
The solution is the concept of Inverse. We can say that Addition = Inverse[subtraction] or vice versa.
We can say Multiplication = Inverse[division] or vice versa.
We can say Derivative = Inverse[integral] or vice versa.
We can say Existential quantifier = Inverse[Universal quantifier] or vice versa.
Now comes the hard part-- proving it, or in logic we say form the Reasoned Argument. Of those inverses listed, the Existential and Universal is the most difficult to form a reasoned-argument of proof.
So I shall work on that.
But I wonder why mathematicians have not declared those equalities before--- is it just too plain obvious to even bother with? It is not obvious in the case of Logic with Existential and Universal.
And, honestly, I cannot think of any more inverse equalities except those 6 above for math and the 2 for Logic. Unless we have AND inverse to OR and we have Not-Equal inverse to If-->Then. Then I have two more proof arguments to assemble.
Archimedes Plutonium May 2, 2026, 1:52:06 AM to Plutonium Atom Universe newsgroup.
I am fascinated of when many of my discoveries occur. If I were doing just plain old mathematics, the concept of function and function inverses would not arise of any importance. But since I am doing Logic and the subject of function inverses of mathematics takes on special meaning and causes me to focus more.
So, yesterday I said I solved my problem of equating Existential quantifier with Universal quantifier and finally come to realize the equality is that of inverse function. And yesterday I outlined a way of arriving at the inverse of a given function by rotating the y axis to become the x-axis, rotating the 1st quadrant to lie in the 2nd quadrant and thus the y-axis is now a x-axis and the new function is inverse the old function.
But we really did not need to rotate the 1st quadrant into the 2nd quadrant to obtain the inverse function. We could keep the same quadrant and rotate the given function around the function of Y--> x, which is called the identity function.
What I have crudely graphed below are 3 functions, the middle one is the identity function. The function to the left of identity is the function of Y--> 2x and the function to the right of identity is the inverse function of 2x which is (1/2)x.
Here are the coordinate tables.
Y--> x Y--> 2x Y--> (1/2)x
x y x y x y
0 0 0 0 0 0
1 1 1 2 1 .5
2 2 2 4 2 1
3 3 3 6 3 1.5
4 4 4 8 4 2
5 5 5 10 5 2.5
I stop there because we are in Decimal 10 Grid, and no need to go beyond 10.
Now get out a sheet of graph paper with pencil and erasure in case you make a mistake for we want to use the graph paper over and over again.
Your graphing of x, 2x and (1/2)x should start to look like this crude ascii art graph.
|
|
| / /
| / / . '
|/-_'__________________
Now with a nice long ruler draw the three straight lines. Notice that the two angles on either side of Y-->x are equal. And that if you rotate the steeper line 2x rotate around x, that you have the line (1/2)x.
So the inverse of 2x is (1/2)x and every function graphed in 1st Quadrant has its mirror reflected inverse function rotated around Y--> x, the identity function. The Identity function is self-inverse.
Now we can take a polynomial like x^2 or perhaps x^3 and approximate that function graph with a straight line function. For x^2 when we reach 3 for x, y=9 and can be approximated by Y-->3x, and then the inverse approximation would be Y--> (1/3)x. This approximation technique reminds me of the Lagrange Interpolation technique in calculus when faced with a non-polynomial function and grappling with a polynomial approximation over a interval.
So, yes, I finally after more than 50 years, finally figured out where there is a equality between Existential quantifier and Universal quantifier. They are inverse functions of one another.
And in math we can write this.
Addition = Inverse[subtraction] and vice versa
Multiplication = Inverse[division] and vice versa
derivative = Inverse[integral] and vice versa
In Logic we can write this, although a reasoned-argument will not come until Intermediate logic textbook.
AND = Inverse[OR] and vice versa
Equal-Not = Inverse[If-->then] and vice versa
Existential quantifier = Inverse[Universal quantifier] and vice versa
So I solved my 50 year conundrum. But now, as usual, arises a even more important new conundrum. It is noticed in physics that duality is of a perpendicular feature. That electricity is perpendicular to magnetism that B-field is perpendicular to E-field. Is this perpendicular feature the same as the inverse function feature????
I believe it is. Only you would not notice it if we rotated the Identity function to fetch the inverse, rotate the diagonal in 1st quadrant. However, to gain the inverse function by rotating the 1st quadrant to become the 2nd quadrant, where the y-axis is now the x-axis. Then, well, that is a 90 degree rotation and that would be a simple proof of math or a reasoned-argument of Logic.
Archimedes Plutonium May 2, 2026, 5:54:10 PM to Plutonium Atom Universe newsgroup.
Yes, this is going smoothly, and better than ever I could have hoped for.
Let me intercede at this moment with the well defined terms established for science, logic and math. Those would be this.
So for **Science** we have Statement, Concept, Hypothesis, Law-structure, Theory, Universal Axiom.
For **Logic** we have Statement, Premiss, Connector-structure, Reasoning, Equalities, Law-structure.
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory
So, in my previous exercise, I took the function x^2, plotted it in 10 Grid then I rotated it about the diagonal Y--> x the identity function and as I ended up rotating it, it formed a new function, the inverse of x^2 to be the function (1/2)x.
So, I am going to have to Prove in math (see the term proof is the 4th term), prove that Addition is the inverse function of Subtraction and vice versa. In Logic, this would be a Reasoned-Argument which is 4th term in logic.
Make a graphing table for Addition in 10 Grid.
0+1 =1, 1+2=3, 2+3=5, 3+4=7, 4+5=9 (reminds me of Fibonacci sequence).
x y
1 1
2 3
3 5
4 7
5 9
Using your graph paper and pencil with erasure in case you make a mistake, graph that table.
Graph the above and then rotate the diagonal Y--> x the identity function which then produces a inverse function, which should be the math Operator of Subtraction. Where y and x axis are turned around yielding this.
x y
1 1
3 2
5 3
7 4
9 5
Draw in the two lines starting at coordinate point (1,1) and see for yourself the line left of Y--> x is identical but inverse the line right of Y-->x.
In a sense we have proven that a function to the left of Y-->x and the function once rotated at Y-->x and if right of that rotation is the inverse function and we can say Addition = Inverse[Subtraction] and vice versa.
We can set up another function of multiplication as 0x1 = 0, 1x2=2, 2x3=6, 3x4=12, 4x5=20 in 100 Grid. Graph that function and find out after rotation of Y--> x diagonal that the function that was left of the diagonal now becomes the function right of diagonal, proving that Multiplication = Inverse[division]
Student for homework do the above multiplication proof.
The proof that derivative = Inverse[integral] was already proven true by the Fundamental Theorem of Calculus.
Now we come back to pure logic and ask whether Existential quantifier = Inverse[Universal quantifier] and vice versa. We see the Existential quantifier as a function itself. We also see the Universal quantifier as a function in and of itself. This makes sense in the idea that the x axis is a lone individual number as a function, but the y-axis are all the numbers from 0 to infinity a universal number. So one number on x-axis has a choice of a unique number out of an infinity of numbers on the y-axis.
Then, as we rotate the Y--> x the diagonal, will the new function, the inverse function be equal in geometry angle and view as the pre-rotated function?
Let us do the function Y--> x^2 in 100 Grid with this table.
x y
1 1
2 4
3 9
4 16
5 25
We graph that (I use small squares for this graph).
We rotate the diagonal and end up with the inverse function.
x y
1 1
4 2
9 3
16 4
25 5
Yes, once I rotated the diagonal it is the table above.
The question now becomes, is that a proof that Existential quantifier EQUALS the Inverse[Universal quantifier] ???? That is the question.
Archimedes Plutonium Mar 23, 2026, 8:40:42 PM to Plutonium Atom Universe newsgroup.
On Sunday, March 22, 2026 at 3:39:18 AM UTC-5 Archimedes Plutonium wrote:
So in Elementary Logic we learned the 6 connectors-- Existential quantifier, Not-Equal, AND, OR, If-->Then, Universal quantifier. And we learned in a Argument of Logic we can Only use true-premisses except in the case of AND where we can use false or nonsense premisses as long as we have one premiss of true value as determined by Science. And as long as there is ____no contradiction of the statements and premisses.
And we learned that in the OR connector we can have a fractional truth premisses, where the statement has a partial truth such in a Deciding Experiment where we find out which one of two premisses is the whole truth and the other a partial truth.
We learned in the Not-Equal (some prefer to call it the Equal-Not) and in the If-->Then, only True premisses are allowed, no partial true premiss and no false premiss is allowed.
Having said that, let us review what these 6 Logic connector Laws are.
1) Connector-structure of Existential quantifier: There exists something is formed by the best available science on the subject topic. This comes from math derivative of calculus as dy/dx and also is coupled to If-->Then as division. And in the Exist quantifier we can never have "A exists AND A does not exist" for a contradiction causes all of logic to come to a screeching halt and has to call in the sciences to overcome the contradiction before continuing further.
2) Connector-structure of Not-Equal: Not is a reversal of a given statement while equality is identical sameness of two statements. Now the words in the two statements can be different but the idea in both statements is the same. Not-Equal comes from multiplication in arithmetic and is coupled with Universal quantifier as the integral of calculus.
3) Connector-structure of AND: Joins together several statements p,q,r,s, etc of Logic and is a collective true statement provided at least one of the statements p,q,r,s, etc is true, and provided any one of the statements is not a contradiction to another statement. The AND connector allows falsehoods and nonsense talk to enter arguments. And the truth of at least one statement confers truth over all the statements joined by AND. AND comes from addition in arithmetic.
4) Connector-structure of OR: Removes or discards ideas or subtracts one idea from another idea represented by p,q,r,s, etc. OR is the opposite of AND that joins together statements. OR removes something, be it a statement or the subtraction of one statement with another statement. OR is the connector of Deciding Experiments in science and as such allows from a variable truth value "dT" being a fraction of truth between 0 and 1.
5) Connector-structure of If-->Then: I like to think of If--> Then from calculus graph where we slowly move down the x-axis and graph the next coordinate point. Given statements P and Q that P moves into Q. The Law of If-->Then is both P and Q have to be true, by science, to form the conclusion of Q starting from P. And this ties in earlier with the idea that we discard all the F rows and U rows of the If--> Then connector and have the T row define the connector.
If you cannot remember the truth-table of If-->Then it is this.
New Logic
IMPLIES (Material Conditional)
IF-->THEN truth table
MOVES INTO
T -> T = T
T -> F = F
F -> T = U probability outcome
F -> F = U probability outcome
6) Connector-structure of Universal quantifier: The Universal quantifier comes from the Existential and the two of them are duals of one another. We do numerous experiments and find all of them obey a formula. The experiments exist and once we have a number of them we elevate the idea to be a universal law through this process of Existential Instantiation, Existential Generalization, Universal Instantiation, Universal Generalization.
In Elementary Logic we learn the basics. In Intermediate Logic, this textbook we learn the details of the basics plus more.
We need to discuss the (1) NonContradiction which I often mentioned in Elementary Logic by saying we "stop everything" if we run into a contradiction.
So where does this Law of NonContradiction arise from?
It arises from the Existence quantifier in conjunction with the Not-Equal connector. To exist or not to exist; you cannot have both. And this forms the basis of the (1) Law of NonContradiction.
The laws of (2) Existential Instantiation, Existential Generalization, Universal Instantiation, Universal Generalization, come from the Scientific Method. These four concepts are fancy words for the Scientific Method in action. Existential Instantiation is a fancy word for finding if physics objects exist or not exist. Existential Generalization is the hypothesis in the experiment of physics. The Universal Instantiation, is that one experiment result turns out true. The Universal Generalization is made once numerous experiments duplicate the results of the first experiment.
The (3) Laws of Commutative, Associative, Distributive come from the fact that the AND connector is the addition operator in Logic.
The (4) Transposition Law of Logic as If P then Q is the same as If not-Q then not-P comes from the Not-Equal connector.
The (5) Occam's Razor Law where the Easiest Explanation is the true explanation comes--- round-about from physics in the law of Least Action or Least Energy principle--- and from Logic from the OR connector in fetching the Deciding Experiment.
The (6) Law of Consistency in Logic where ideas form a symmetry relationship with all other ideas, comes out of physics in the laws of electromagnetism are symmetrical laws.
Archimedes Plutonium Mar 24, 2026, 2:31:23 AM to Plutonium Atom Universe newsgroup.
Other Laws besides the 6 connector laws
-----------------------------------------------------------------
The first connector of Logic is the Existential quantifier for there is no point in discussing of Logic if the object is non-existent. For the discussion is what is deemed metaphysics or science fiction. And to be logical must be tested by Science for truth sake.
The second connector of Logic was the Not-Equal connector in terms of ordered sequence of evaluating and learning the connectors. So that when you put together Existence and the Not connector, we have that P exists or the P does not exist. The third connector of Logic in logical order was the AND connector. So now, here, we have the first 3 connectors of logic in sequential order of Existential quantifier, Not-Equal, AND.
Now we construct or run into a Logic Argument where we have P exists AND P does not exist. Or in general form, Q AND not-Q.
What happens to Logic when we run into that situation?
Well, all Logic stops dead in its tracks and has to fix the situation before Logic can continue. There is no Logic when it has Q AND not-Q.
A contradiction in physics would be "Electricity exists and electricity does not exist."
All physics stops until the contradiction is reolved.
A contradiction in mathematics would be 1 = 2, for they are not equal, and math cannot resume until resolved.
A contradiction in biology would be that "All life comes in cells and not all life comes in cells." And so the biology discussion comes to a grinding halt and the contradiction is sorted out. For you cannot have P AND not-P.
Logic comes to a grinding halt whenever a contradiction pops up, and the onus is to fix the contradiction.
This is the Law of NonContradiction. Logic stops whenever it runs into P AND not-P, and does not resume until the impasse is fixed by the best available science of the topic in question.
Archimedes Plutonium Mar 24, 2026, 2:43:17 AM to Plutonium Atom Universe newsgroup.
How does the Existential quantifier relate to the Universal quantifier? For both have the word "quantifier" in them so they must be related somehow? And the answer is that they are related because they form the structure of how Science works, which is called the Scientific Method.
The Scientific Method in broad outline is this.
-----------------------------------------------------------
Step 1-- Make observations and ask many questions.
Step 2-- Research the subject matter and Review the literature on the subject.
Step 3-- Formulate a Hypothesis of what you think is going on.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Step 6-- Draw conclusions, and publish the results so the experiments are repeated to qualify as a law-structure of science.
The law-structures of (2) Existential Instantiation, Existential Generalization, Universal Instantiation, Universal Generalization, come from the Scientific Method. These four concepts are fancy words for the Scientific Method in action. Existential Instantiation is a fancy word for finding if physics objects exist or not exist. Existential Generalization is the hypothesis in the experiment of physics. The Universal Instantiation, is that one experiment result turns out true. The Universal Generalization is made once numerous experiments duplicate the results of the first experiment.
Archimedes Plutonium Mar 24, 2026, 3:14:46 AM to Plutonium Atom Universe newsgroup.
The (3) Law-structures of Commutative, Associative, Distributive come from the fact that the AND connector is the addition operator in Logic.
And it is with Not-Equal that we introduce the Distributive Law. Do you remember the distributive law in mathematics class? It is for example this A(B + C) = AB + AC, for example 2(3+4) = 2*3 + 2*4. It turns out that the distributive law is more essential for the beginning of Logic than is the commutative or associative laws. Commutative and associative laws are about the order in which you add or multiply. For example of commutative is 3+4 = 4+3 for add and 3*4 = 4*3. For example the associative is A+(B+C) = (A+B) + C, where you have to do what is inside the parenthesis first. Example 1+(2+3) = (1+2)+3. You see the order in which you add matters not. And for multiplication associative we have (A*B)*C = A*(B*C), for example (10*100)*1000 = 10*(100*1000). Distributive law has a mix of addition with multiplication.
In forming the truth table of Not-Equal it was this.
So our truth table of Logic for Not-Equal is made from two binary tables of equal and then of not, combined to form a quaternary table.
Not-Equal truth-table:
p q
T T = T
T not F = T
F not T = T
F F = T
Notice in forming the Not-Equal truth-table, I manipulated the p,q by inserting a "not" so that the end result are all 4 T values. For example, the distributive law 2 (1 + 3) = 2*1 + 2*3.
In the second row above T not F = T
That was T = F = F and now apply not
T = not-F = not-F
T = T = T
If we ask Mathematics with its simple operators of add, subtract, multiply, divide to make a list of equalities between those 4 operators. The only equalities to begot are such as commutative law, associative law, distributive law. We do not have such things as Add equaling subtract, multiply. Or, divide equaling subtract then multiply. No, each of the 4 operators of mathematics is independent of one another and each is unique compared to the others.
So for the Laws of Inference we discuss what are the true laws when Not-Equal, AND, OR, If-->Then are truly correct and independent and unique. There does exist some Laws of Inference in New Logic, but not 19 of them as Copi has in his Old Logic textbook. Rather instead, since math has commutative, associative, distributive laws, that Logic will have those three also, but also the equality mentioned on opening this chapter that when P-->Q, with Q-->P, then P=Q. The reasoning for that is because in the If-->Then truth table only when you have true-->true is the whole thing true, so that if you have T-->T from P-->Q and then T--> T from Q-->P, you end up with P=Q.
Of the 4 math operators, they are all 4 independent of one another. You cannot make add equal to subtract and eliminate one of them.
You see--- Logical Independence stems from the fact that the truth tables of Equal-Not, AND, OR, If-->then are such that One has 4 true values, another has 3 true values, another has 2 true values and the fourth has just 1 true value, respectively.
By having a unique truth table pattern, insures Independence. With independence insures few equalities, few laws of inference.
What we do find in Algebra mathematics are equalities in the order of connectors such as commutative law, associative law and distributive law.
Commutative law of math where a+b = b+a, and where a*b = b*a. Example 10 +20 = 20 +10, and 10*20 = 20*10. Meaning:: it does not matter in what order you add or multiply. The commutative law is of 2 variables.
Multiplication is commutative in math such as 2x3 = 3x2. And in Logic, Not-Equal is commutative in that P=Q is the same as Q=P.
Associative law of math where (a+b)+c = a+(b+c) and where (a*b)c = a(b*c). Example (2+3) +4 = 2+(3+4) and where (2*3)4 = 2(3*4). The associative law of 3 variables.
Distributive law of math is not a ordering law but a distribution law, where a(b+c) = ab + ac. Example 3(4+5) = 3*4 + 3*5.
So now, in Logic of Not-Equal, AND, OR, If-->Then which of those obeys Commutative, Associative and Distributive??
AND obeys both Commutative of two statements p,q and Associative of three statements p,q,r or more variables, for it matters not what order the connections of joining together statements, for the end result of this joining together will all be the same provided one of p,q,r has a true value.
Equal-Not obeys both Commutative and Associative for equality does not matter in what order they are connected. Example P= Q = R is equal to R=Q=P is equal to Q=P=R etc.
OR is not commutative and not associative. Example, when you have P OR Q, remove P is not the same as remove Q. And with associative the choices of removal are increased even more, P OR Q OR R, the order of removal can result in the end with keeping P removing Q and R, or, keeping Q and removing P and R, or, keeping R and removing P and Q.
For example, addition in math is commutative such as 2 +3 is the same as 3+2. Commutative means in matters not the order in which you do the operation. But in subtraction 3-2 is not the same as 2-3. And OR is subtraction or remove.
Now If--> Then is not commutative, for it is dependent on the order. Where p--> q does not warrant q-->p. Just as division in math is not commutative. Example: 2/1 does not equal 1/2. Addition is commutative in that 1+2 = 2+1 and subtraction is not commutative for 2-1 does not equal 1-2.
Example of If-->Then as not commutative. If I swim then I get wet. Now look at "If I get wet, then I was swimming." No that is false, for I could have gotten wet from it raining.
Another example: If a large enough asteroid hits Earth, smashing it into pieces, then all life on Earth goes extinct. Here the "p" is "A large enough asteroid hits Earth, smashing it into pieces" with the "q" as "All life on Earth goes extinct." Now examine If q-->then p. If all life on Earth goes extinct, then a large enough asteroid hit Earth, smashing it into pieces.
This is not true, for it could be that the Sun gone Red Giant killed all life on Earth, and not an asteroid.
If-->Then does not obey commutative nor associative. Example, "If the Sun has gone into Red Giant Initiation Phase, then the Sun shines from Faraday law, not fusion." Is not the same as "If the Sun shines from Faraday law, not fusion, then the Sun has gone into Red Giant Initiation Phase." There is a time factor involved.
But there is an interesting take away with the the If-->Then connector of Logic, a Equality, provided we take the Truth Table of If-->Then of its single row of true truth value and discard the other three rows, one of F, and two of U.
When we examine If-->Then of its P is true and Q is true and the entire If-->Then is true we can fetch a Equality so that we have a Law of Inference that says If P then Q, AND, If Q then P = that of P= Q as discussed earlier.
So here we have a equality relationship between If-->Then and Equal-Not.
Example: "If being human then that means able to throw rocks overarm." "If able to throw rocks overarm, then that is a human." Explanation: here we have two statements P and Q wherein P implies Q, and vice versa, Q implies P, meaning, they are equal statements. P= Q.
So, what Laws of Inference do I have so far??
1) AND is commutative and associative.
2) Equal-Not is commutative and associative.
3) If-->Then when P-->Q AND Q-->P = (P=Q)
4) Not-Equal, some prefer to call it Equal-Not is distributive law.
I also have distributive when forming the truth table of Not-Equal. When forming this truth table, we actually implement the distributive law in the very act of forming the table.
Law of Inference called Occam's Razor
----------------------------------------------------
Occam's Razor is dear to my heart for I used it so often, practically every day that I write science in my newsgroup, I use Occam's Razor. In Old Science, Old Physics, Old Logic and Old Philosophy, Occam's Razor is _____not considered to be a law___ but merely a "rule". A law is universal, a rule works some of the times but not always.
In New True Logic, Occam's Razor is a law, a universal law just as the laws of Physics are universal such as Ampere's law, Coulomb law, Faraday law.
So what is Occam's Razor stated in most simple form?
Occam's Razor is the concept that the Easiest and most Simple Explanation of a chain of Events is the True Explanation.
Physics has a similar concept and can actually replace Occam's Razor. Physics calls it the Least Action Principle or some call it the Least Energy Principle. In physics, it means the path of a particle under a force follows the path of least energy spent or least action-- the shortest path.
So how does New Logic able to elevate Occam's Razor from being a "rule" to being a "law". How can New Logic elevate Occam's Razor?
New Logic is able to make Occam's Razor a law because of the OR truth table of Deciding Experiment.
The OR truth table was this where dT means a fractional truth value such as 1/4, or 1/3, or 1/2, or 2/3, or 3/4, or 0.90 etc etc.
New Logic OR (exclusive)
p q p or q
____________
T T F
T dT T
dT T T
F F F
The OR truth table decides which one of two theories is the correct theory and the other theory only partially true.
As we use the Scientific Method of experiments we end up with one theory superior over the other theory for the other theory has partial truths and falsehoods that requires ____ added assumptions to explain_____.
And that is exactly Occam's Razor in that it is the explanation of Least number of assumptions. The Truth Table of OR and the Scientific Method in action, is none other than Occam's Razor as a law, universal law of Logic and science.
Part 9. More details of Logic Law-structures such as Occam's Razor.
The AP Principle of Well-Defining a concept
----------------------------------------------------------
But first, before we get to the Principle of Well-Defining, let us distinguish the difference between a Principle and a Law-structure and a Theory and other names for important concepts.
Definition of Principle versus Law
--------------------------------------------
I believe the definition of a Principle of science is that it is ___descriptive, a description___ while a Law of science is active, action involved.
(Special note: readers, sadly politics and civics have their own concept of "law", man-made laws with courts and justice which is far different from laws-of-science.) Whenever I speak of laws in any of my science books I mean, laws-of-science.
Some examples throughout science of principles are Geology has Uniformitarian Principle, Physics has Uncertainty Principle, Pauli Exclusion Principle, Superposition Principle, Special Relativity Principle. Logic has Well-Defining Principle and Occam's Razor Principle. Biology has the Cell Principle although many call it the cell theory when in truth it is a principle not a theory and that is the reason we are well defining law, principle, theory.
A Law of science has action with it, a prescription involving forces and motion, while a Principle of science is a description of Nature, an outline of characteristics. For example, the science of biology has the Linnaean Classification of all plants and animals into that of
Domain
Kingdom
Phylum
Class
Order
Family
Genus
Species.
So that every living organism has special traits characteristics that distinguishes it from other species. For humans versus apes, we have opposable thumb, throw overarm, bipedalism, large brains.
A Principle of science compared to a Law of science is that the Principle is description while the Law is one of forces in action on objects.
Yes, I am going to need to Well-Define many concepts and words used in science and math. All of which have never been here-to-for well-defined.
These concepts need to be Well-Defined.
for science
----------
Statement, (some call them fact or facts)
Hypothesis, (some call them speculation)
Concept
Law-structure (most people simply call them laws)
Principle
Theory
for logic
-------
Statement
Premiss
Concept
Connector-structure
Equalities, (some call them Rules of Induction or Rules of Inference)
for mathematics
-------
Statement
Concept
Axiom (some call them postulates)
Operator-structure
Proof
Theorem
Corollary
Notice we do not have theory in math nor in logic. That is because theory is only a collection of law-structures gained from experiments in science.
Notice we have "statement" in all three of science, logic and math. A statement in physics or other sciences can be a math formula or words, sentences. A statement in Logic can be words, sentences but also be picture-images. A statement in math can be algebra of numbers or word-sentence, or a geometry figure.
All statements have to be checked for truth value by the appropriate science involved with the subject matter.
Notice that we have "concepts" in all three of science, logic and math. "Concept" has nuances when a concept of physics or a concept of logic or a concept of math.
Concepts in all three of science, logic, and math are a collection of statements in those three. The next higher category is theory. So we have statement then concept then theory.
And a theory is a collection of law-structures. Only one law-structure is sufficient to call it a theory.
(1) Axiom (some say Postulate) well-defined means we take some ideas as given and granted without the proof mechanism of experiments in the scientific-method. Some ideas we accept fully as common-sense and the inability to check-up on the axiom via experiments. The most important single idea in all of science is the Primal Axiom-- all is Atom and Atoms are nothing but electricity and magnetism.
Here "primal" simply means the first and most important axiom.
(2) Law-structure well-defined comes from science in the scientific-method with experiments as proof. Laws are universal. And according to the Primal Axiom, all laws reduce to one of the law-structures of electricity and magnetism. Physics has all the laws of science and there are only a few of them. All the laws of science come from the AP-EM equations, the revised Maxwell equations. However, laws in mathematics and in logic come from the operators of mathematics and connectors of logic. And to the extant, that if you list the AP-EM equations you see that they are containing the math operators and the logic connectors.
(3)Theory well-defined is easy for a theory is a collection of laws, and since EM laws are the only laws of science, means that a theory, when properly named has at least one electromagnetic law-structures central to the action forming the theory.
Quantum Mechanics is not a theory when talking only about its principles. But if you include Faraday law-structure with the principles, then you have a theory.
When a subject of science is unknown if it is a theory, then it is often called a speculation, conjecture or hypothesis. Hypothesis is the oft used term when the subject matter is not recognized as a theory of science.
I discovered the Stonethrowing theory of Homo sapiens and how they evolved from apes to us. Am I justified in naming it a theory? Yes, because in throwing rocks and stones is about the law of gravity, a EM law, and the laws of optics more EM laws. To see and understand the rock trajectory as it is thrown.
I discovered the Vibration theory of Continental Drift, where the two cores of Earth acting as a electric dynamo creates vibrations in mantle and crust, hence electricity and magnetism laws, as the vibrations move tectonic plates.
Is Darwin evolution a theory? No, there are no central law-structures of electricity magnetism in Darwin evolution but there is EM laws in John Bell's superdeterminism.
Is the Big Bang a theory of science? No, there is no EM law-structures central to this hypothesis for only after the supposed Big Bang does the Big Bang create law-structures of physics.
Is the "cell" in biology a theory? No, we discussed previously that the cell is a description and thus a Principle of science. It is the Cell Principle, not the Cell Theory.
Is DNA in biology a theory or principle? Yes, DNA is a theory because it is electrical and magnetic and that a photon of Light is perfect DNA. First life on Earth begins when Photons-Light-pulses stop inside a capacitor like calcium in oceans and automatically turns into living DNA.
(4) Principle well-defined is a description of Nature and not a acting force in Nature. Principle is describing of science. Law-structures are forces acting on objects and matter and moving them.
(5) Statement well-defined concerns mostly Logic and mathematics. In logic a statement is a word, sentence or picture-image that holds 1 or more ideas. Statements as ideas are the fundamental elements of logic. The fundamental elements of math are numbers and geometry pictures-images.
(6) Theorem well-defined comes strictly from mathematics and should remain in mathematics. It means a argument with stepwise deductions using axioms and other true statements to form a true conclusion.
(7) Corollary well-defined means it is a lesser important theorem of mathematics.
Now let us discuss well-defining itself.
So the definition of Logic is similar and follows the definition of Mathematics. Mathematics is the science of making precise and correct numbers-quantity-size and geometry figures and shapes. While Logic is the science of making precise and correct ideas as statements p,q,r,s,t,u,v, etc etc that forms a language of communication.
Ideas have to be clear, crystal clear in order to be able to work with them.
I do not recall when Wikipedia first came out. I would guess in late 1990s. I do remember coming to Usenet in August of 1993 with posts on mathematics and my Atom Totality theory. But once Wikipedia started to come to the Internet, I often used it to look up science concepts. It was fast and easy.
But I soon discovered an unpleasant reality about Wikipedia science entries. Many in physics were obfuscation as I looked up a term. And then it dawned on me. That the authors of many physics or math or science concepts were unpaid authors and were contributing their thoughts as to what the definition was. And these free authors had no Logic training. And many were writing the entries of science for they failed in that science and as some showmanship, the author is getting back at the schools that failed them in science. So that their writing a definition would often have terms that were more complex than the term they are trying to define. I do have a logical mind and so I began to complain that most of the science entrees into Wikipedia were not definitions but obfuscation of what is attempted to be defined.
Sometime in the past 2 or 3 decades, I realized there had to be a principle of Logic, that when you define a concept, you can ___only define it by using more simple terms___, more simple terms to establish a definition.
So often I found myself looking up a concept in Wikipedia such as superdeterminism and finding myself in a run around looking up more complicated terms. Not only physics but mathematics also.
Wikipedia is notorious for violating AP's Logic Principle of Well-Defined Definitions.
The principle simply says, you cannot define a concept by using terms that are more complex than what you are trying to define. Take a look at any of 10 physics entries in Wikipedia of defining a concept and I bet that about 80 to 90% of those definitions violate AP's principle. Which is often very frustrating. You want to know what a concept is, and presented by Wikipedia a nauseous blather of terms of more complexity than the concept you originally seeked to understand.
Here is an example in physics, where I look up the term of "superdeterminism" and Wikipedia defines with this blather.
--- quoting Wikipedia---
In quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem.
--- end quoting Wikipedia---
This is a major problem of Wikipedia as it hires for free, failures of physics to write many entries, yet having no logical brains to be writing on physics at all. In my opinion the above was written by a failed person of physics. Or, likely some fool in philosophy cranking up a physics definition.
Here is what a definition of Superdeterminism looks like where the terms are much more simple than the concept being defined. And thus the concept Superdeterminism is made accessible to the new reader.
So often, especially physics in Wikipedia is burdened by fools as editors, as writers who know not what they talk about, and have almost a 0 logic IQ. Just look at Wikipedia pictures of conic sections where the fools list the ellipse as a slant cut of cone when in truth that is a oval.
Part 10. Infinity well-defined.
The minds of students and professors gets tangled up and messed up with infinity concept and with the Universal quantifier concept and so we need to spend time with both so we do not mess up.
I should discuss in detail the concept of Infinity and how infinity relates to Universal quantifier, something I did not do in Elementary Logic.
So in discussing Infinity we best go to mathematics and begin with the concept of finite. Logically we think of Finite as having an "end to whatever we are doing". If it has no end, then it is infinite. Sounds reasonable.
However, ending and no end need some qualifications. For example, in order to have Calculus exist, you need empty space between one number and the next successor number. If we look at the Reals of Old Math they had the idea that between any two numbers exists __always another Real number___. And so, between one Real and another Read exists endless number of new Reals. So that the numbers in Reals from 0 to 10 would be solid points forming a line 10 units long. There would not be any gap or hole in that solid (what they called continuous line). Trouble is, you cannot have a Calculus mathematics on a solid line with no holes in between one number and the next number.
The Logical argument of what is Infinity boils down to a simple question. Do you want Calculus to exist or do you want Infinity with no holes between one number and the next number? Basically that is the heart of the matter--- either you have Calculus or you have infinity with numbers continuous.
In Decimal 10 Grid Numbers, the set 0, .1, .2, .. .9, 1.0, 1.1, . . . 9.8, 9.9, 10, is a number system that has a hole or gap of 0.1 from one number to the next number and thus is not continuous, not a solid line. In 10 Grid, you can have a Calculus of derivative and integral. You cannot have a calculus on Reals of Old Math.
Because of the need and importance of Calculus in mathematics, we must have numbers be discrete with holes in between one number and the next number. Huygens a mathematician who lived in the time when Newton and Leibniz who discovered calculus, that Huygens found a fascinating way of finding the borderline of infinity in the small scale and large scale, as 10^-604 and 10^604 by the area of a Tractrix geometry figure.
Concept that Infinity = a borderline between finite and infinite was discovered by AP in 2009. Simple beautiful idea-- there must be a borderline between finite and infinite, otherwise, all is just one and the same, and not two different concepts. And so I defined the concept of infinity itself as this border crossing. For more information, please see my TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2.
Concept of Logic pertaining to Borderlines
-------------------------------------------------------
When you have two concepts that are related to each such as finite to infinite; such as geography one country to a neighbor country, that it is essential to have a Borderline between them, otherwise there is no country nor is there infinity.
Here is the textbook that I wrote much of the infinity borderline in, and where one can learn the true numbers of mathematics are the discrete numbers called the Decimal Grid Number System. This book and all my books are for free to read on the Internet in my newsgroup, PAU.
TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2
by Archimedes Plutonium
Written in 2 May, 2019
This is AP's 45th published book of science published on Internet, Plutonium-Atom-Universe,
Preface: Volume 2 takes the 5 year old student through to senior in High School for their math education.
This is a textbook series in several volumes that carries every person through all his/her math education starting age 5 up to age 26. Volume 2 is for age 5 year old to that of senior in High School, that is needed to do both science and math. Every other math book is incidental to this series of Teaching True Mathematics.
It is a journal-textbook because electronic books, E-books offer me the ability to edit overnight, and to change the text, almost on a daily basis. A unique first in education textbooks-- almost a continual overnight editing. Adding new text, correcting text. Volume 2 takes the 5 year old student through to senior in High School for their math education. Volume 3 carries the Freshperson in College for their math calculus education.
Cover Picture: The Numbers as Integers from 0 to 100, and 10 Grid when dividing by 10, and part of the 100 Grid when dividing by 100. Decimal Grid Numbers are the true numbers of mathematics. The Reals, the rationals & irrationals, the algebraic & transcendentals, the imaginary & Complex, and the negative-numbers are all fake numbers. For, to be a true number, you have to "be counted" by mathematical induction. The smallest Grid system is the Decimal 10 Grid.
Table of Contents
1) Motivation of the Teaching True Mathematics series textbooks.
2) Chapter 1
Lesson 1-1: Numbers, Counting, writing numbers// age 5, Teaching True Mathematics.
3) Lesson 1-2 more add, and a bit of subtract and multiply, and divide.
4) Lesson 1-3 more subtract, and more multiply, more divide, and memorization of Multiplication Table.
5) Lesson 1-4 Fractions in mathematics// Teaching True Mathematics.
6) Lesson 1-5 Reducing Fractions to lowest terms.
7) Lesson 1-6 Summary for ages 5, 6, 7.
8) Chapter 2
Lesson 2-1 division then decimals for 8 year olds// Teaching True Mathematics.
9) Lesson 2-2 wood cube blocks, repeat-add, repeat-subtract// Teaching True Mathematics.
10) Lesson 2-3 teaching decimals; operations, Long Division.
11) Lesson 2-4 Decimals Teaching True Mathematics.
12) Lesson 2-5 teaching decimals; operations, Long Division.
13) Lesson 2-6 teaching decimals; operations, Long Division Teaching True Mathematics.
14) Lesson 2-7 teaching decimals; operations, Long Division.
15) Writing out Decimal Numbers & Scientific Notation.
16) Lesson 2-8 teaching decimals; operations, Long Division.
17) Lesson 2-9 dividing decimals; operations, Long Division.
18) Lesson 2-10 teaching decimals; operations, Long Division.
19) Chapter 3
Lesson 3-1 Grade School, Algebra// Equation and Equality // Teaching True Mathematics.
20) Lesson 3-2 Algebra // Teaching True Mathematics.
21) Lesson 3-3 a lesson for just the teachers // Teaching True Mathematics.
22) Another Lesson on Scientific Notation.
23) Lesson 3-4 Logic of AND, OR// Teaching True Mathematics.
24) Lesson 3-5 Graphing & geometry // Teaching True Mathematics.
25) Lesson 3-6 Graphing & geometry // Teaching True Mathematics.
26) Lesson 3-7 When we have to introduce Atomic theory in school.
27) Lesson 3-8, Graphing-Geometry; Graphing & line is really a long thin rectangle and a circle or arc curve is really a string of straightline segments.
28) Lesson 3-9 Circle.
29) Lesson 3-10 Sigma-error in math Teaching True Mathematics.
30) Lesson 3-11 teaching decimals // Teaching True Mathematics.
31) More Lessons on Scientific Notation.
32) Lesson 3-12 teaching decimals; operations, add, subtract, multiply.
33) Lesson 3-13 some algebra rules// Teaching True Mathematics.
34) Lesson 3-14 Lesson for the teachers, mostly.
35) Lesson 3-15 teaching Percentages.
36) Lesson 3-16 more Percentages and Cross Product Proportionality.
37) Lesson 3-17 teaching, true numbers are ones you can count in order.
38) Chapter 4
Lesson 4-1 teaching the concepts of All Possible Digit Arrangements and Completeness of Numbers, for ages 13-14// Teaching True Mathematics textbook
39) Some more Lessons on Scientific Notation.
40) Lesson 4-2 Idea of Sequence in Mathematics, for ages 13-14, Teaching True Mathematics.
41) Lesson 4-3 Idea of Series in Mathematics// Teaching True Mathematics textbook.
42) Again a Lesson on Scientific Notation.
43) Lesson 4-4 Grade Schoolers first proof in math, why decimals are special// What is the Binary number system and other number systems, compared to Decimal Number System.
44) Lesson 4-5 discovering why the Decimal Number System is superior over all other number base systems.
45) Lesson 4-6 review of this book's first proof.
46) Lesson 4-7 Graphing Lessons for ages 13 through 14; ANGLES<, Angles>, Angles.
47) Lesson 4-8 Graphing Lessons for ages 13-14, using tools of geometry.
48) Lesson 4-9 The 1by1 Square for angles Re: ANGLES--Graphing lessons in Teaching True Mathematics.
49) Lesson 4-10 Definition of angle with subtend-arc Re: ANGLES--Graphing lessons in Teaching True Mathematics.
50) Lesson 4-11 The 1by1Square and definition of angle with dy/dx // Teaching True Mathematics.
51) Lesson 4-12 Exercises and homework with angles // Teaching True Mathematics.
52) Lesson 4-13 Logic lessons, equal-not.
53) Lesson 4-14 Logic lessons, equal-not and Truth Tables.
54) Lesson 4-15 Logic lessons, equal-not why it is multiplication.
55) Lesson 4-16 Logic lessons, And connector is addition.
56) Lesson 4-17 Logic lessons, OR connector is subtraction.
57) Lesson 4-18 Logic lessons, If-Then connector is division.
58) Lesson 4-19 Talk, equal-not, and, or, if-->then.
59) Lesson 4-20 Logic, Exist Quantifier and Every Quantifier.
60) Lesson 4-21 What is Logic // Teaching True Mathematics.
61) Lesson 4-22 Sigma Error in angles // Teaching True Mathematics.
62) Lesson 4-23 Sigma Error in angles and circles // Teaching True Mathematics.
63) Lesson 4-24 Sigma Error in number roots, sqrt2, sqrt3, sqrt5, etc // Teaching True Mathematics.
64) Lesson 4-25 Quizzes & Tests, what are numbers and what are fakes // Teaching True Mathematics.
65) Lesson 4-26 Quizzes & Tests, what are numbers and what are fakes // Teaching True Mathematics.
66) Lesson 4-27 Quizzes & Tests, review on what true numbers are-- Decimal Grid Numbers // Teaching True Mathematics.
67) Chapter 5 and Guidepost of this book structure and goal and aim.
68) Lesson 5-1 Freshperson High School Geometry for ages 14-15// Pythagorean Theorem.
69) Lesson 5-2 Freshperson High School Geometry best proof of Pythagorean Theorem.
70) Lesson 5-3 trigonometry, most-all of the trigonometry you will ever need.
71) Lesson 5-4 FUNCTIONS, Teaching True Mathematics.
72) Lesson 5-5 tractrix demonstration with pocketwatch.
73) Borderline between finite and infinity, Teaching True Mathematics.
74) Lesson 5-6 Freshperson High School, Calculus // Fundamental Theorem of Calculus.
75) Lesson 5-7 exercises with Calculus.
76) Lesson 5-8 Freshperson High School subtraction-slopes //Teaching True Math.
77) Chapter 6 Sophomore
Lesson 6-1 Geometry High School// Teaching True Mathematics.
78) Lesson 6-2 Geometry High School// Teaching True Mathematics.
79) Lesson 6-3 Geometry in High School : geometry with numbers, called analytical geometry.
80) Lesson 6-4 Geometry in High School : geometry without numbers, called synthetic geometry.
81) Chapter 7
Lesson 7-1 Junior High School power rule formulas// Teaching True Mathematics.
82) Chapter 8
Lesson 8-1 Senior High School converting graph points into polynomials// Teaching True Mathematics.
Appendix
Archimedes Plutonium Mar 22, 2026, 9:49:38 PM to Plutonium Atom Universe newsgroup.
It is very easy to get "infinity" mixed up and confused with the concept of Universal Quantifier, very easy. And this is a good place-- in Logic science to differentiate between the two for they are distinct concepts.
Infinity and the infinity borderline has to do with number density, while, Universal Quantifier has to do with a concept of "all, every".
Number density is different from "all and every".
Archimedes Plutonium Mar 23, 2026, 8:18:10 PM to Plutonium Atom Universe newsgroup.
Now my textbook of TEACHING TRUE MATHEMATICS is for free on the Internet in my newsgroup.
TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2
by Archimedes Plutonium
Written in 2 May, 2019
This is AP's 45th published book of science published on Internet, Plutonium-Atom-Universe,
Borderline between finite and infinity, Teaching True Mathematics.
Now this mistake in not having a correct Infinity in math, affects the Calculus by a large measure, a large impact, so large that Old Math Calculus was all wrong because they had no well-defined infinity. It is impossible to have a correct calculus, when you have a bozo-kook understanding of what is infinity. The reason for this is the Calculus needs a smallest nonzero number-- what Newton and Leibniz in the 1600s called the infinitesimal. This is the smallest number, if we ignore 0 number. So the next number after 0, is the infinitesimal in the Grid Number System. So in 10 Grid, the infinitesimal is .1, in 100 Grid the infinitesimal is .01, in 1000 Grid the infinitesimal is .001 etc etc. Also, instead of calling it the infinitesimal we can call it the micro-infinity of that Grid, and the largest number in the Grid we can call the macro-infinity border which would be 10 in 10 Grid and 100 in 100 Grid and 1000 in 1000 Grid, etc etc.
This is probably the biggest mistake-- not well defining what infinity is -- in all of pure mathematics for it affects all other mathematics. Of course the other sciences, especially physics rarely needs to know what the correct proper infinity is. However, it does show up frequently in the best physics-- quantum electrodynamics, in which it is often used to eliminate infinities that crop up in calculations. This physics math procedure is called Renormalization-- getting rid of the infinities. But we save those ideas for College.
The trouble with Old Math, is, well, they were terribly shoddy in logic, in thinking straight and clear. For a logical person, knows, that if you have a concept of finite versus infinite, the only way to handle those two concepts is to realize a border must go between them so that you can tell if any given number is finite or infinite. Otherwise, there is no infinity, if there is no borderline.
There is only one way you can have a concept of finite, by having a concept of infinity, and the only way you can have both, is that a
borderline exists between them.
I have pinpointed that borderline from tractrix-circle analysis, from algebraic analysis of algebraic completeness, and from angles of
regular polyhedra. The borderline in micro-infinity is 1*10^-604 and in macro-infinity is 1*10^604. Students, in 10 Grid, if 10 is the largest nonzero number then 1/10 = .1 would be the smallest number that is not 0. In 100 Grid, if 100 is the largest number, then 1/100 = .01 is the smallest nonzero number in 100 Grid. You see that once you find macro-infinity border , you just divide it into 1 and you have the micro-infinity border-- the infinitesimal number.
You see in True Math, True Logic, infinity has a micro-infinity and a macro-infinity, something that the silly stupid Old Math never thought, that infinity has two types.
Now in mathematics history is a famous Dutch mathematician named Christiaan Huygens pronounced (HOY-genz) that lived in the 1600s also along with Newton and Leibniz. And Huygens found a remarkable proof that the area of a given unit circle is equal to a unit-tractrix area, once that Tractrix reaches infinity. In other words, Huygens proof -- forces there to be a infinity borderline where finite numbers stop and the numbers there-after are all infinite numbers.
The easiest way to see the borderline is to see where pi digits ends in a three zero digits in a row.
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000
Since the Universe 3rd dimension, one would suspect that where pi digits have their first three digits in a row of 000, that such would be the borderline at infinity.
Now, for physics, that infinity is 1*10^604 for large and we divide that into 1 we have 1*10^-604, that number is the same as 1/ 10^604, for the small, makes perfect sense, since in physics, it is extremely, extremely difficult to find anything above 10^200 or smaller than 10^-200, to give the reader a sense of proportion.
Now for us in High School we are content with numbers of the 10, the 10^2, the 10^3, even 10^4, and seldom if ever in High School do we go beyond 10^4. In physics in High School you will learn perhaps 10^20 or even 10^30. But only in College do you run into something like 10^40 or 10^100 and never run into such a huge number as 10^604, except in math class when studying infinity border.
The infinity borderline is 1*10^604 for macro-infinity and for micro-infinity or the infinitesimal it is 1*10^-604 and the algebraic closure of these numbers is by squaring them, so when you square 10^3 you are doing 10^3 times 10^3 which is adding the exponent so you have 10^3 times 10^3 = 10^6. When you square 10^604, you again add exponents and arrive at 1*10^1208 and then its inverse of 1/10^1208 is 10^-1208. The infinity borderline is derived in two methods, one, __first method__by algebra is derived from the fact that when pi has its first three zeroes in a row, 10^-601, 10^-602 and 10^-603, place values, and this is where the area of the tractrix equals for the first time, the area of the associated circle, and since Huygens proved the area of tractrix equals associated circle at infinity, we have a borderline. And the second derivation, second method__ is by geometry for the Regular Polyhedra, the five geometry figures of tetrahedron, cube, octahedron, dodecahedron, and icosahedron require special angles-- in that a vertex point, the angle to go around circumnavigate that vertex point cannot be equal to 120 degrees or else the point will have to lie flat in the plane to where it is no longer 3 dimensional. So the tetrahedron has 3 times 60 degrees is 180 degrees which is acceptable. The octahedron vertex has 4 times 60 degrees is 240 degrees and not 360 or higher and is acceptable. The cube has 3 times 90 degrees is 270 degrees and is acceptable. The dodecahedron has 3 times 108 degrees per vertex is 324 degrees and less than 360 degrees and is acceptable. The icosahedron has 5 times 60 degrees is 300 degrees and less than 360 degrees and is acceptable. The reason a hexagon a regular polygon of 6 sides cannot form a regular polyhedron is because its angles are 120 degrees and 3 times 120 is 360 and is a flat plane and not able to be a 3rd dimension regular polyhedron. So in this 2nd method of deriving the infinity borderline is to look where the digits of pi are evenly divisible by 120 for 120 degrees which would allow for the construction or formation of the regular polyhedra at infinity borderline. Where pi digits are evenly divisible by 120=5! = 1x2x3x4x5 which is where pi digits have 3 zero digits in a row in the 601, 602, 603 place value, making the 604 in 10^604 be infinity borderline.
Lesson on what Factorial means
------------------------------------------
Factorial is represented as with the symbol "!". And in the example of 5! above, It means you multiply all the counting numbers starting with 1 up to and including 5. Where 5! = 1 x 2 x 3 x 4 x 5 and that equals 120.
1! = 1
2! = 1 x 2 = 2
3! = 1 x 2 x 3 = 6
4! = 1 x 2 x 3 x 4 = 24
5! = 1 x 2 x 3 x 4 x 5 = 120
Homework complete this table out to 10.
6! =
7! =
8! =
9! =
10! =
The derivation from 120 = 5! = 1x2x3x4x5 is the idea that the Regular Polyhedra need to exist at the infinity borderline and that is guaranteed if the borderline is evenly divisible by an angle of 120 degrees. But even more astounding is that at the Completion of Algebra which is where you take any two numbers from 0 to 10^604 and multiply them together you get a number from 0 to 10^1208.
These numbers are too big for students of this young age so the nice thing about the Decimal Grid System is we can always go down to smaller grids and the smallest grid is the 10 Grid whose largest number is 10. So if I take any number in the 10 Grid and multiply it by another 10 Grid number, would it be between 0 and 100? Yes. The largest is 10 and 10 x 10 = 100. The smallest in 10 Grid not counting 0 is 0.1, and where 0.1 x 0.1 = 0.01 which is also in 100 Grid.
So if the Infinity Borderline is 1*10^604 and its Algebraic Completion is 1*10^1208, where we multiply any two numbers from 0 to 1*10^604 together and our new number is somewhere between 0 and 1*10^1208, well, the astonishing fact is that a single zero digit 0 occupies the 1208 place value in pi digits, just a single 0, not three zeroes in a row at the 601, 602, 603 place value. And can you believe it, for I find it incredible that 1208 place value in pi digits is evenly divisible by not just 5! = 120 but by 720 = 6! = 1x2x3x4x5x6.
So that 1*10^604 is the last and largest finite number, and all numbers beyond are infinite-numbers and all numbers smaller than 1*10^-604 (except 0) are infinite-numbers since 1*10^-604 is the smallest nonzero positive finite number.
Explanation: What Huygens proved was that the area inside a unit circle equals the area under the graphing of the Tractrix once the Tractrix reaches infinity borderline. So the tractrix is far behind the area of the circle, until the digits of pi, those digits slow down. And those digits really really slow down in area when the digit is 0. When the digit is zero, gives the Tractrix some time to gain in area and the circle is deprived of area. So when pi comes to having three 0s in a row-- 000 --- well, the Tractrix completely catches up in area and equals the circle area. This happens at 1*10^604, and is the borderline between Finite numbers and Infinite Numbers, as well as the micro-infinity of 1*10^-604. There exists no finite number between 0 and 1*10^-604. This number is the infinitesimal in all of mathematics.
But now, caution to students, for we treat every Grid System as if the smallest nonzero number is the infinitesimal and the largest number the infinity borderline of macro-infinity. This allows us to form a Calculus. For Calculus can only exist if there is empty space from one number to the next number. This is called "discrete" or physics likes to say "quantized" for Max Planck started physics quantum mechanics in year 1900 by notifying the world physics was discrete in numbers of electricity and magnetism. Old Math had continuous numbers with no holes in between one number and the next number and that meant Old Math had ___ no calculus___.
Now I said earlier that the main difference between the concept "infinity" and that of "universal quantifier" is that infinity is a math concept of density while "universal quantifier" is a concept that pertains to "all, every". One can see of feel uneasiness in that it sounds like infinity and "all, every" are closely related. But I assure you, they are very much different and distinct.
I also taught that everything found in Mathematics exists in Logic for Logic is the larger science than math. And it is why Logic can seek out the truth of what infinity is, by logical reasoning. If left up to mathematicians to find the infinity borderline and to "well-define infinity" we have the present situation where no-one in the math community ever raised the issue until AP raised the issue and solved it in 2009.
We found the infinity borderline by the Tractrix with pi digits of three zero digits in a row, allowing the tractrix area to catch up with the circle area for the first time and hence the infinity borderline. We find the infinity borderline independent of the Tractrix by looking where the digits of pi are evenly divisible by 5! = 120 to form all the angles of regular polyhedra at infinity, in addition to where the square of that borderline as algebraic completion is also evenly divisible by 120 where 1*10^604 and its algebraic completion 1*10^120 is in fact evenly divisible by pi digits by 6! = 720 (a super plus bonus).
So the question of Density as the main idea of infinity
----------------------------------------------------------------------
We say a set of numbers is infinite, that is to say dense enough, if there are such numbers, at least 1*10^604 between 0 and 1*10^1208.
For example, are the even numbers an infinite set? Yes, because there are 1*10^604 even numbers between 0 and 1*10^605.
For the same reason, odd numbers are an infinite set.
How about Perfect Numbers, are they infinite? The perfect numbers are the sum of proper divisors and that set starts out with 6, 28, 496, 8128, .... So to say they are infinite would mean there are 1*10^604 such numbers between 0 and 1*10^1208, and there is not such. That means Perfect Numbers are a finite set.
How about Perfect Square Numbers 1, 4, 9, 16, 25, . . . This is a set dear to my heart because there are exactly 1*10^604 such numbers between 0 and 1*10^1208.
Question for students in class, do we count 0 in the Perfect Squares???
So, the picture is emerging that Infinity concept is a density concept, very much different and distinct from a concept of Universal quantifier which concerns itself with "all, every".
Homework, write a page paper on the question of whether perfect cubes 1, 8, 27, . . . is a finite or an infinite set?
Part 11. Fallacies of Logic committed by logicians from DeMorgan, Boole, Jevons onward.
Now I had a list of 7 categories of fallacies in my Elementary Logic textbook.
1) Mistake calculation error
2) Ambiguity -- lack of well defined or unclear parameters
3) Non-Sequitur
4) Ad Hominem
5) Mis-identification
6) Mistakes in Existence-Nonexistence for the derivative is the existential quantifier-- the "assumed to exist" fallacy.
7) Mistakes in Universal for the integral is the universal quantifier-- the giver of consistency and completeness.
Let me add one more category.
8) No logical brains to actually do logic
I write this 8th category for we pick apart the many mistakes of Old Logic and the best category to fit those mistakes is "no logical brains to be doing logic".
Some scientists have researched the frequency in human populations for when a genius of music comes around, Mozart, Beethoven, Vangelis and they come infrequently. Top notch physicists come infrequently, Newton, Faraday, Maxwell, Hertz, Planck, Bell.
But the most rare of all scientists are those geniuses of Logic. In my textbook History of Logic, very few logicians ever appear as the science field that has the rarest number.
Nature has the most difficulty of forming a person with a Logical Mind. Proof:: The slant cut of cone as ellipse was accepted for 2,200 years ago and not a single human being said--- wait a moment--- a cone has 1 axis of symmetry, but a ellipse requires 2 axes of symmetry, so the slant cut of cone must be a Oval, not ellipse.
A genius of Logic, is the most rarest science genius there is.
Posts in sci.math or sci.physics.
On Tuesday, January 8, 2019 at 7:52:34 PM UTC-6, Dan Christensen wrote:
> Dan
>
> Download my DC Proof 2.0,,,,
> Visit my Math Blog,,,
(be foolish and download that worthless spam stalker of Logic-- the Canadian Christensen)
Re: s.. for brains in Logic Morons of logic George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap, Jan Burse& Dan Christensen as moronette cadets of Boole, Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi
by
zelos...@gmail.com Mar 25, 2021, 12:55:15 AM in sci.math
Scientists that are just memorization not masters Re: Analysis of failures..Logic with failures of Physics// one thinks 3 OR 2 =5 with 3 AND 2 = 1 while the other thinks proton to electron is 938MeV vs .5MeV when truly it is 840MeV to 105MeV
Dan Christensen (the stalking insane Canadian of 6 years) wrote on 20Dec2018 in sci.math
8:19 AM
>WARNING TO PARENTS
>Archie Pu's fake logic
A B A & B
T T T
T F T
F T T
F F F
>Real logic:
A B A & B
T T T
T F F
F T F
F F F
A B A OR B
T T T
T F T
F T T
F F F
Partial List of the World's Crackpot Logicians-- should be in a college Abnormal-Psychology department, not Logic//
Peter Bruce Andrews, Lennart Aqvist, Henk Barendregt, John Lane Bell, Nuel Belnap,
Paul Benacerraf, Jean Paul Van Bendegem, Johan van Benthem, Jean-Yves Beziau,
Andrea Bonomi, Nicolas Bourbaki (a group of logic fumblers), Alan Richard Bundy, Gregory Chaitin,
Jack Copeland, John Corcoran, Dirk van Dalen, Martin Davis, Michael A.E. Dummett, John Etchemendy, Hartry Field, Kit Fine, Melvin Fitting, Matthew Foreman, Michael Fourman,
Harvey Friedman, Dov Gabbay, L.T.F. Gamut (group of logic fumblers), Sol Garfunkel, Jean-Yves Girard, Siegfried Gottwald, Jeroen Groenendijk, Susan Haack, Leo Harrington, William Alvin Howard,
Ronald Jensen, Dick de Jongh, David Kaplan, Alexander S. Kechris, Howard Jerome Keisler, Julia F. Knight logic journal, Robert Kowalski, Georg Kreisel, Saul Kripke, Kenneth Kunen, Karel Lambert, Penelope Maddy, David Makinson, Isaac Malitz, Gary R. Mar, Donald A. Martin, Per Martin-Lof,Yiannis N. Moschovakis, Jeff Paris, Charles Parsons, Solomon Passy, Lorenzo Pena, Dag Prawitz, Graham Priest, Michael O. Rabin, Gerald Sacks, Dana Scott, Stewart Shapiro, Theodore Slaman, Robert M. Solovay, John R. Steel, Martin Stokhof, Anne Sjerp Troelstra, Alasdair Urquhart,
Moshe Y. Vardi, W. Hugh Woodin, John Woods
Now I should include the authors of Logic textbooks for they, more than most, perpetuate and crank the error filled logic, the Horrible Error of 2 OR 1 = 3 with 2 AND 1 = 1, that is forced down the throats of young students, making them cripples of ever thinking straight and clearly.
Many of these authors have passed away but their error filled books are a scourge to modern education
George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap,
Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi, Michael Withey,
Patrick Hurley, Harry J Gensler, David Kelley, Jesse Bollinger, Theodore Sider,
David Barker-Plummer, I. C. Robledo, John Nolt, Peter Smith, Stan Baronett, Jim Holt,
Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
John Venn, William Gustason, Richmond H. Thomason,
All of them in the opinion of AP are clowns of logic, although they have interest in logic, none are past a baby stage understanding of what Logic is. They are all worse than the fool George Boole. All of them are a disgrace to the subject we call Logic.
AP believes that if a person is Logical, that his daily life should be logical--- George Boole-- catching pneumonia and then having his wife douse him in bed with cold freezing water and taking cold showers-- thinking that combatting pneumonia is done by getting colder.
All of the above listed should never be allowed to teach their nonsense and pollute the minds of youngsters with their crazy 9 OR 5 = 14 with 9 AND 5 = 4, all because a crazy Boole with Jevons in the 1800s thought that OR was TTTF and AND was TFFF. Boole and Jevons had them reversed and turned around backwards, making OR as add and AND as subtract. All because a true logician has more than a microgram brain of Logic in his head, and realizes that if you had a string of statements, say 10 statements and if just one single statement of those ten is true, makes the entire set of 10 to be true also, regardless of the truth value of the other 9 statements. Said in a different manner, if you have a truth of a single statement, and, no matter how you surround that single statement with 9 other statements, regardless of their truth value, because of the truth of the one statement makes the combined all 10 statements have a true value.
AND connector
-------------------
The Truth Table for AND in Old Logic was this.
Old Logic AND
p q p AND q
____________
T T T
T F F
F T F
F F F
New Logic AND, addition
p q p AND q
____________
T T T
T F T
F T T
F F F
Write a 1 page paper on why Old Logic AND is a huge mistake.
So the truth table of AND is TTTF, yet Old Logic under Boole and Jevons said it was TFFF.
Is there any reasoning for TFFF, or is it just a dumb mistake?
Turns out there is a very excellent reason that Boole & Jevons thought it was TFFF.
Suppose we have the example of The Sun is a star AND the Sun is not a star.
Under AP, the AND truth table is TTTF and the above would be a true compound statement connected by AND, if not for the contradiction. That is likely the reason Boole & Jevons decided the truth table of AND had to be TFFF for they did not want to tackle a contradiction.
The statement of P AND Q as "The Sun is a star AND the Sun is not a star" is what is called a Contradiction in Logic and never allowed. All things stop and come to a grinding halt and only resumes, once the contradiction is sorted out-- Is the Sun a star?
This would easily explain when Boole & Jevons in circa 1850s would deem the AND truth table as TFFF to avoid contradictions.
In New Logic we always stop what we are doing if a contradiction pops-up and cannot resume until the contradiction is solved. This is the connector-structure of noncontradiction.
OR connector
------------------
OR truth table in New Logic
P Q P OR Q where dT stands for a statement that has a partial truth
T T F
T dT T
dT T T
F F F
The variable or partial truth value of dT allows OR connector to solve for Deciding Experiments of science, finding the full Truth value experiment and discarding the partial true experiment.
Old Logic had two OR connectors, one a exclusive that looked like this.
OR exclusive truth table in Old Logic
P Q P OR Q
T T F
T F T
F T T
F F F
OR inclusive truth table in Old Logic
P Q P OR Q
T T T
T F T
F T T
F F F
Write a 2 page paper on the hypocrisy and inconsistency of having two different types of OR in Logic. And the gross error of having inclusive OR be addition as Copi on inside cover lists inclusive OR as addition. Leaving Old Logic, one can assume that they thought AND must be subtraction.
Write a 1 page paper on why it is wise and prudent to Model the 6 connectors of Logic with the 6 operators of mathematics.
Not-Equal connector
----------------------------
Not-Equal truth-table in New Logic:
p q
T T = (T = T) = T
T not F = (T = T) = T
F not T = (F = F) = T
F F = (F = F) = T
Old Logic did not have the brains to combine Not with Equal to make a 4 row truth table.
Write a 1 page paper on how the distributive equality is used to make Not and Equal to become a 4 row truth table, and explain how Not-Equal is multiplication in math by noting that 1x1 = 1 and 0x0 = 0. Are these the only two numbers in all of mathematics where their multiplication equals their value?
If-->Then connector
-------------------------
New Logic
IMPLIES (Material Conditional)
IF-->THEN truth table
MOVES INTO
T -> T = T
T -> F = F
F -> T = U probability outcome
F -> F = U probability outcome
Old Logic
IMPLIES (Material Conditional)
IF-->THEN truth table
MOVES INTO
T -> T = T
T -> F = F
F -> T = F
F -> F = F
Write a two page paper on how silly it is to have a F move into a T or an F move into a F in 3rd and 4th row. Explain how If--> Then is division and that you need "undefined" as a answer when you divide by 0.
Pretty abysmal showing for Old Logic in that they failed to get a single one of the 4 most simple connectors--- AND, OR, Not-Equal, If-->Then correct. Not a single connector correct, and the reason that AP opines that none of the so called logicians from Boole onward deserves to be called a logician.
And here we can safely say, the greatest of all errors of Old Logic was not that they got all 4 of the simple connectors of Logic-- AND, OR, Not-Equal, If-->Then all messed up and in error. As hard as it is to believe, they made even a far greater mistake in Old Logic. They never recognized that Science determines truth in Logic and Science determines the size of an Argument in Logic.
Does Any Old Logic book mention "science" ??
--------------------------------------------------------------
Looking at Copi's Introduction to Logic, 4th edition, 1972 and Thomason's Symbolic Logic An Introduction, 1970 in the index in the back of the book. Does either one mention "science"????
Copi mentions "science" starting on page 423 as "Science, the aims of".
Thomason does not even mention science.
First and foremost of logic is Science for it is science and the methods of science to give us the "truth value" of Logic. Without science we have no truth value for Logic. And without truth value, we have no logic itself.
If we examine every logic textbook written before AP's 2025 textbooks on logic, we likely will find the words "true or truth" several times on each page. Seldom do we see the word "science".
In Copi's Introduction to Logic, he starts his first page with a excerpt from Sextus Empericus where he mentions "truth" 2 times, just in the first paragraph of the book.
"...this we do affirm-- that if truth is to be sought in every division of Philosophy, we must, before all else, possess trustworthy principles and methods for the discernment of truth. Now the Logical branch is that which includes the theory of criteria and of proofs; so it is with this that we ought to make our beginnings." -- (Sextus Empiricus, an ancient Greek physician).
In this textbook, the word science and physics are mentioned almost on every page and several times mentioned along with other sciences, and the scientific-method.
Yes, the single biggest error of all in Old Logic, is that no attention was given to the idea that Science is the judge of truth in Logic. And all other errors of Old Logic pale in the sight of this error of not seeing that science is the arbiter of truth.
Copi's 19 Rules of Inference Fallacies
---------------------------------------------------
When I studied Thermodynamics in college, University of Cincinnati, we often had to prove that the statement of physics was equal to another statement. And the way we went about doing that was to prove that P implies Q in a If-->Then connector. Then we proved the reverse, that Q implies P. Once we showed that P implies Q and then Q implies P we could say the two statements are equal for an equality. Recently in 2025, the same year as writing this logic textbook, I proved that the 2nd law of thermodynamics stated as Heat goes from Hot to Cold and never the reverse was ___ not equal___ to the statement that the entropy (disorder) was increasing. But rather, the exact opposite was the truth, that the Order of the universe was increasing. Realizing that Old Physics was confused in that temperature was the inverse of time as in time = 1/temperature. In college in 1970, the thermodynamics class was teaching Heat goes from Hot to Cold was equal to entropy of the universe is increasing through a argument of P-->Q and if Q-->P gives P=Q. That was a false argument. The true argument was Heat goes from Hot to Cold was equal to Order of the Universe is increasing and then we really have a P-->Q with Q-->P allows us to conclude in a argument that P=Q. The error made in Thermodynamics physics was a error of not knowing Time is the inverse of Temperature. And this makes sense in the idea that "coldness" is disorder, and when heat flows into coldness and warms things up, that order is increasing.
That was a long story, but serves as the introduction to this chapter of what Equalities exist in the 4 simple connectors?? We ask the question of what equalities exist. And we trashcan the silly mindless wreck of Copi's listing of 19 rules of inference equalities inside the front cover and back cover of his textbook. We trashcan all logic textbooks before this one as they thought 19 or more equalities existed in Old Logic.
As was mentioned earlier that the New Logic Laws of the 4 simple connectors are unique and independent in number of true values each had. Let us examine that uniqueness again, and compare with Old Logic. This is important in the idea that Rules of Inference in Old Logic were a sham because if your connectors are wrong in truth value and not independent of one another and not unique, you end up with the hypocrisy of 19 Rules of Inference of equality as written in Copi's Introduction to Logic, 4th edition, 1972, on the inside front and back cover, when you should have close to no equality rules of inference.
Old Logic has this in terms of the number of true values.
Equal has 1
Not has 1
AND has 1
OR inclusive has 3
OR exclusive has 2
If-->Then has 3
In AP's New True Logic that tally would be this.
Equal-Not has 4
AND has 3
OR has 2 (for exclusive is the only OR)
If-->Then has 1
When you have the 4 simple connectors of Old Logic all wrong and those connectors have no unique independent truth values, you invariably find that many connectors equal one another through compounding the connectors. Copi shows 19 such equalities of Rules of Inference in his front and back cover. And those rules are all wrong, silly stupid wrong, because the connectors are wrong.
If we ask Mathematics with its simple operators of add, subtract, multiply, divide to make a list of equalities between those 4 operators. The only equalities to begot are such as commutative law, associative law, distributive law. We do not have such things as Add equaling subtract, multiply. Or, divide equalling subtract then multiply. No, each of the 4 operators of mathematics is independent of one another and each is unique compared to the others.
So in this chapter on Rules of Inference which should be called Laws of Inference we discuss what are the true laws when Not-Equal, AND, OR, If-->Then are truly correct and independent and unique. There does exist some Laws of Inference in New Logic, but not 19 of them. Rather instead, since math has commutative, associative, distributive laws, that Logic will have those three also, but also the equality mentioned on opening this chapter that when P-->Q, with Q-->P, then P=Q. The reasoning for that is because in the If-->Then truth table only when you have true-->true is the whole thing true, so that if you have T-->T from P-->Q and then T--> T from Q-->P, you end up with P=Q.
Of the 4 math operators, they are all 4 independent of one another. You cannot make add equal to subtract and eliminate one of them.
You see--- Logical Independence stems from the fact that the truth tables of Equal-Not, AND, OR, If-->then are such that One has 4 true values, another has 3 true values, another has 2 true values and the fourth has just 1 true value, respectively.
By having a unique truth table pattern, insures Independence. With independence insures few equalities.
The Old Logic of its Inclusive OR has 3 true values and the True truth table of AND has 3 true values, so that there is absolutely no need to have AND in Old Logic because they had no logical mind to see that OR inclusive is a hypocrisy.
It is reasonable and logical to suspect that since mathematics has only a few Laws of Inference, such as that of commutative, associative, distributive, that likewise, Logic would mirror reflect this pattern. A pattern not of that one or two connectors equals another connector, but rather, more of a pattern involved with Order of operation or order of connectivity, such as in AND, where it does not matter if T AND F is the same as F AND T, mirror reflecting math that 2 + 3 = 3 + 2.
When you look at a mathematics textbook for the Laws of Inference in mathematics, you will never see that addition, subtraction, multiplication, division are equal to one another, for each is unique and independent of one another. They maybe reverses or (some call it inverses) of one another, yet, still, they are not equal to one another. So that leaves us to question what Equalities of Inference does math have?
And the answer is apparently Equalities of order of operation such as commutative law, associative law and distributive law.
When the operators are unique and independent, as they should be, then you cannot have a Equality of addition = subtraction, or, addition = multiplication.
You can have Equalities of order in which you carry out a operation. For example, commutative law 2 + 5 = 5 + 2. Example in Logic "Cell principle and DNA theory" equals "DNA theory and Cell principle". Another example in logic: "Jupiter is part of the Solar System and Earth is part of the Solar System" is equal to "Earth is part of the Solar System and Jupiter is part of the Solar System".
Let me give you an example of a Rule of Inference that would be true provided Inclusive OR was not a fictional connector.
The Inclusive OR of Old Logic was this--- Either..or..or..Both and had a Old Logic truth table of this.
Old Logic
OR(inclusive) truth table (their either..or..or..both) and fictional.
P Q
T or T = T
T or F = T
F or T = T
F or F = F
New Logic
AND
P Q
T or T = T
T or F = T
F or T = T
F or F = F
The reader can easily see those two tables are the same, and thus equal.
And so we can write Either..or..or..Both = AND.
But we cannot write that because Either..or..or..Both is fictional for it is a conglomeration of both OR exclusive with AND itself.
I show this to give the reader an appreciation of what equality in Laws of Inference look like. But since in New Logic, all 4 simple connectors have different truth tables and unique independent truth tables there is no equality for rules of Inference.
New Logic AND, addition
p q p AND q
____________
T T T
T F T
F T T
F F F
Let us check if the OId Logic rule of inference called De Morgan's theorem has equality where Not(P AND Q) = (not P OR not Q), let us see if that is phony baloney.
Truth table for Not(P AND Q) in Old Logic when P=T and Q= T would result in F. The truth table in Old Logic for inclusive OR when P=T and Q=T would also result in F. Mind you, the mistake made here by DeMorgan is that he is thinking AND truth table was TFFF and believing that inclusive OR is a connector with truth table of TTTF. The reader can easily see one has three F's and the other has three T's in which, when you "Not" both sides of the expressions they coincide. Checking when P=T with Q=F, both expressions end up as T. Checking P=F with Q=T, both expressions end up as T, and when P=F with Q=F, both expressions result in a T. Allowing the fools of Old Logic to believe this De Morgan's theorem to be true. When what the idiotic fools should have looked at was their mindless belief you can have two different types of OR and where their AND was subtraction when it should be addition.
Now we analyze DeMorgan's other mistake of Not(P OR Q) to see if it equals Not P AND Not Q. In Old Logic with their mindless AND being TFFF and their hideous inclusive OR being TTTF, when we have P=T with Q= T we have Not(P OR Q) result in F. And we have for P=T with Q=T in NotP AND NotQ result in F. When we look at P=T with Q=F in both expressions the result is F. When we look at P=F with Q=T, the result is F in both expressions. When we look at P=F with Q=F the result is T in both expressions. Allowing the fools of Old Logic to believe this De Morgan's theorem to be true.
I believe DeMorgan conceived of his fake theorem before Boole and Jevons finally decided to have AND truth table be TFFF. Using the fake theorem of DeMorgan to make their final decision as to not upset the apple cart.
Clearly they are amiss and one does not equal the other, and so we have Not(P AND Q) =/= (not P OR not Q) with that of
Not (P OR Q) =/= Not-P AND Not-Q. The symbol =/= means "does not equal". And so, not a rule of inference. In New Logic, the De Morgan's laws are clearly wrong. They probably were acceptable in Old Logic for there, they had two types of OR, and they had a error filled AND.
Let me try If-->Then. Of course, the Not comes alongside Equal in Equal-Not is multiplication in New Logic.
IF-->Then is division in New Logic. Some call it "implies", some call it the material-conditional or "implies". Some like to call it the "because" in Q because of P. I like to call it the "moves into", P moves into Q.
p q p --> q
____________
T T T
T F F
F T U for unknown
F F U for unknown
Truth table for Not(P-->Q) is this.
____________
T T F
T F T
F T not-U does that mean known?
F F not-U does that mean known?
Truth table for Not-P --> Not-Q is this.
F F U
F T U
T F F
T T T
Clearly, Not(P-->Q) =/= Not-P --> Not-Q.
But let us try to see if Copi's rule of inference he calls "transposition" is true, where If P then Q = If not-Q then not-P.
p q p --> q
____________
T T T
T F F
F T U for unknown
F F U for unknown
not-q not-p not-q --> not-p
____________
F F U for unknown
T F F
F T U for unknown
T T T
But let us check this further out with premiss concept where only true premisses can be used in a logic argument. The only true premiss in If-->Then is when both P and Q are true. In that situation Not(T-->T) becomes false. In the case of Not-Q-->Not-P becomes If F--> then F is actually U for unknown, so the transposition rule of inference for Copi is false also. It is false because of the obnoxious Old Logic truth table for If-->Then was TFTT where the mindless fools thought that a truth value can be reached when the starting statement of P in P-->Q is false. The true truth table of If-->Then is TFUU.
Where, If P -->then Q =/= If not-Q --> then not-P.
Now examples should have shown the mindless idiocy of Old Logic with their AND being TFFF and their If-->Then being TFTT as grossly in error. Why did examples not show the fools of Boole & Jevons up to when AP corrects the fools, why did examples slip under the radar and not show the massive ignorance of Old Logic???? It is because, you can tailor make a example to fit your nonsense, and because most people, even logic professors never really care if they are correct or full of error.
Examples.
P-->Q
If Atoms consist of a Proton torus, then geometrically their center is empty space of a donut hole of a torus.
Not(P-->Q)
It is not the case that (If Atoms consist of a Proton torus, then geometrically their center is empty space of a donut hole of a torus).
Not P --> Not Q
It is not the case that Atoms consist of a Proton torus, then not the case geometrically that their center is empty space of a donut hole of a torus.
Not-Q --> not P
lf it is not the case that geometrically the proton torus is empty space of a donut hole, then Atoms do not consist of a proton torus.
To me, P-->Q is not the same as not-Q--> not-P.
But examples can be deceptive and flawed and examples are easily dismissed as not accurate by Old Logic professors, who are failures of logic. This is why AP uses all of mathematics to shine light on the failings of Old Logic, instead of using Examples to shine a light on Old Logic failings. A dunce logic professor can easily squirm out of a example that shows him/her is wrong. But that same dunce logic professor cannot squirm out of mathematics-arithmetic showing him/her is a dunce failure.
In the meantime an example from Biology (I do not like to stick with physics alone).
P-->Q
If Darwin Evolution is a false theory of species creation, then Bell's Inequality of Superdeterminism is the true theory of species creation.
Not(P-->Q)
It is not the case that (If Darwin Evolution is a false theory of species creation, Then Bell's Inequality of Superdeterminism is the true theory of species creation).
Not P--> Not Q
If Darwin Evolution is a true theory of species creation, then Bell's Inequality of Superdeterminism is a false theory of species creation.
Not-Q --> not P
If Bell's Inequality of Superdeterminism is a false theory of species creation, then Darwin Evolution is a true theory of species creation.
But it goes to show, that truth in logic can come from Examples, can possibly come from good examples which in Physics is tantamount to Experiment.
For Physics, it is experiment that determines truth. In Logic we replace experiment with Examples.
Now, looking at math algebra textbooks, and looking for laws or properties of numbers we find no connector equality. We find that add, subtract, multiply, divide never are equal to one another. On the other hand, we find about 19 equalities in Copi's Introduction to Logic.
What we do find in Algebra mathematics are equalities in the order of connectors such as commutative equality, associative equality and distributive equality.
Commutative equality of math where a+b = b+a, and where a*b = b*a. Example 10 +20 = 20 +10, and 10*20 = 20*10. Meaning:: it does not matter in what order you add or multiply. The commutative equality is of 2 variables.
Associative equality of math where (a+b)+c = a+(b+c) and where (a*b)c = a(b*c). Example (2+3) +4 = 2+(3+4) and where (2*3)4 = 2(3*4). The associative equality of 3 variables.
Distributive equality of math is not a ordering equality, but a distribution equality, where a(b+c) = ab + ac. Example 3(4+5) = 3*4 + 3*5.
So now, in Logic of Not-Equal, AND, OR, If-->Then which of those obeys Commutative, Associative and Distributive??
AND obeys both Commutative of two statements p,q and Associative of three statements p,q,r or more variables, for it matters not what order the connections of Joining together statements, for the end result of this joining together will all be the same provided one of p,q,r has a true value.
Equal-Not obeys both Commutative and Associative for equality does not matter in what order they are connected. Example P= Q = R is equal to R=Q=P is equal to Q=P=R etc.
OR is not commutative and not associative. Example, when you have P OR Q, remove P is not the same as remove Q. And with associative the choices of removal are increased even more, P OR Q OR R, the order of removal can result in the end with keeping P removing Q and R, or, keeping Q and removing P and R, or, keeping R and removing P and Q.
For example, addition in math is commutative such as 2 +3 is the same as 3+2. Commutative means in matters not the order in which you do the operation. But in subtraction 3-2 is not the same as 2-3. And OR is subtraction or remove.
Now If--> Then is not commutative, for it is dependent on the order. Where p--> q does not warrant q-->p. Just as division in math is not commutative. Example: 2/1 does not equal 1/2. Addition is commutative in that 1+2 = 2+1 and subtraction is not commutative for 2-1 does not equal 1-2.
Multiplication is commutative in that 2x3 = 3x2.
Example of If-->Then as not commutative. If I swim then I get wet. Now look at "If I get wet, then I was swimming." No that is false, for I could have gotten wet from it raining.
Another example: If a large enough asteroid hits Earth, smashing it into pieces, then all life on Earth goes extinct. Here the "p" is "A large enough asteroid hits Earth, smashing it into pieces" with the "q" as "All life on Earth goes extinct." Now examine If q-->then p. If all life on Earth goes extinct, then a large enough asteroid hit Earth, smashing it into pieces.
This is not true, for it could be that the Sun gone Red Giant killed all life on Earth, and not an asteroid.
If-->Then does not obey commutative nor associative. Example, "If the Sun has gone into Red Giant Initiation Phase, then the Sun shines from Faraday law, not fusion." Is not the same as "If the Sun shines from Faraday law, not fusion, then the Sun has gone into Red Giant Initiation Phase." There is a time factor involved.
But there is an interesting take away with the the If-->Then connector of Logic, a Equality, provided we take the Truth Table of If-->Then of its single row of true truth value and discard the other three rows, one of F, and two of U.
When we examine If-->Then of its P is true and Q is true and the entire If-->Then is true we can fetch a Equality where we have If P then Q, AND, If Q then P = that of P= Q as discussed in the first paragraphs of this chapter.
So here we have a equality relationship between If-->Then and Equal-Not.
Example: "If being human then that means able to throw rocks overarm." "If able to throw rocks overarm, then that is a human." Explanation: here we have two statements P and Q wherein P implies Q, and vice versa, Q implies P, meaning, they are equal statements. P= Q.
So, what Equalities do I have so far??
1) AND is commutative and associative.
2) Equal-Not is commutative and associative and distributive.
3) If-->Then when P-->Q AND Q-->P = (P=Q)
4) If-->Then when P-->Q then we have transposition of not-Q --> not P.
I also have distributive when forming the truth table of Not-Equal. When forming this truth table, we actually implement the distributive in the very act of forming the table.
New Logic
Not-Equal truth-table:
p q
T T = T
T not F = T
F not T = T
F F = T
So, in New Logic we end up with only 4 Equalities as Laws of Inference for the 4 connectors of Logic. Unlike Copi with his 19 equalities as rules-of-inference, and unlike all the other Old Logic textbooks with their numerous silly and obnoxious equalities like DeMorgan's theorem.
And does that make sense? Yes, if you have 4 independent and unique connectors, then the number of equalities begot from those 4 connectors should be no more than 4 equalities. But I need to prove there is a link between number of connectors is number of equalities, which is far beyond the text of this book. However, I do start this proof below, and will finish the proof in my #371 logic textbook of Advanced Logic. But, I am sure that most classes of Logic in college will have a genius like student who can do the proof, without ever reading AP's Advanced Logic textbook.
Part 12. The concept of "time" as analyzed by Logic.
Archimedes Plutonium Apr 7, 2026, 4:17:14 AM to Plutonium Atom Universe newsgroup.
I come back to this book needing far far more clarity on special terms used.
Part 9. Differences between Laws, Principles, Theories, statements, axioms, rules of inference as well-defined.
The AP Principle of Well-Defining a concept
----------------------------------------------------------
But first, before we get to the Principle of Well-Defining, let us distinguish the difference between a Principle and a Law and a Theory and other names for important concepts.
Definition of Principle versus Law
--------------------------------------------
I believe the definition of a Principle of science is that it is ___descriptive, a description___ while a Law of science is active, action involved.
(Special note: readers, sadly politics and civics have their own concept of "law", man-made laws with courts and justice which is far different from laws-of-science.) Whenever I speak of laws in any of my science books I mean, laws-of-science.
Some examples throughout science of principles are Geology has Uniformitarian Principle, Physics has Uncertainty Principle, Pauli Exclusion Principle, Superposition Principle, Special Relativity Principle. Logic has Well-Defining Principle and Occam's Razor Principle. Biology has the Cell Principle although many call it the cell theory when in truth it is a principle not a theory and that is the reason we are well defining law, principle, theory.
A Law of science has action with it, a prescription involving forces and motion, while a Principle of science is a description of Nature, an outline of characteristics. For example, the science of biology has the Linnaean Classification of all plants and animals into that of
Domain
Kingdom
Phylum
Class
Order
Family
Genus
Species.
This is easy to remember in the mnemonic-- Do keep pond clean or fish get sick. For me this is especially easy to remember for I have a pond. And I do hate biology's recent use of this silly "clades" stuff. My reincarnation experiments involve grafting of different phylum-- blackberry or elm scion on pine, spruce rootstock.
So that every living organism has special traits characteristics that distinguishes it from other species. For humans versus apes, we have opposable thumb, throw overarm, bipedalism, large brains.
A Principle of science compared to a Law of science is that the Principle is description while the Law is one of forces in action on objects.
Yes, I am going to need to Well-Define many concepts and words used in science and math. All of which have never been here-to-for well-defined.
These concepts need to be Well-Defined.
for science
----------
Hypothesis
Law
Principle
Theory
for logic
-------
Statement
Premiss
Rules of Induction (Inference)
for mathematics
-------
Statement
Axiom
Proof
Theorem
Corollary
Archimedes Plutonium Apr 7, 2026, 7:43:38 PM to Plutonium Atom Universe newsgroup.
for science
----------
Hypothesis
Law-structure
Principle
Theory
for logic
-------
Statement
Premiss
Equalities--Rules of Induction (Inference)
for mathematics
-------
Statement
Axiom
Proof
Theorem
Corollary
No, Rules of Induction or Rules of Inference is not a well-defined concept, but rather, those are Equalities (Equivalency which can be reduced to equality).
Most of us have forgotten how Mathematics began with Early Humans. Further back than 400,000 with Neanderthals making fire from flint struck on iron pyrite.
Mathematics begins perhaps with sticks more than stones.
When Prehistoric Humanity had 1 stick as I, and gave it a name such as "one". Then she/he put together sticks II and gave it a name "two". Then sticks III calling it "three". Then sticks IIII calling it "four", IIIII calling it "five", IIIIII calling them "six". Or, of course the fingers of Prehistoric Humanity instead of wood sticks calling each finger a name.
But with fingers, you cannot remove them and have subtraction or with fingers have a multiplication which you can do with sticks, even do a division with sticks.
This is how math started.
Archimedes Plutonium Apr 7, 2026, 7:54:52 PM to Plutonium Atom Universe newsgroup.
These concepts need to be Well-Defined.
for science
----------
Hypothesis
Law-structure
Principle
Theory
The problem of concern here is that the only laws that exist in science are the Electromagnetic laws as we apply the Primal Axiom of All is Atom and Atoms are nothing but electricity and magnetism. And a theory is a collection of laws. That makes our use of the concept "theory" very limited to only science which has a EM law in play. Darwin evolution is not a theory. Quantum Mechanics is not a theory but Quantum Electrodynamics is a theory. In Mathematics, it is not Probability theory any longer, and must be Probability Principles. It is a joke to call it the Big Bang theory. Atomic theory is a theory for it is all of the EM laws.
for logic
-------
Statement
Premiss
Equalities-Equivalence
Here the idea is not of "rules" but of equations of equality-equivalence.
for mathematics
-------
Statement
Axiom-postulate
Proof
Theorem
Corollary
Math is the science of precision and logic, not far ahead of math is the science of well-defined ideas and the manipulation of ideas.
No, Rules of Induction or Rules of Inference is not a well-defined concept, but rather, those are Equalities (Equivalency which can be reduced to equality).
Most of us have forgotten how Mathematics began with Early Humans. Further back than 400,000 with Neanderthals making fire from flint struck on iron pyrite.
Mathematics begins perhaps with sticks more than stones.
When Prehistoric Humanity had 1 stick as I, and gave it a name such as "one". Then she/he put together sticks II and gave it a name "two". Then sticks III calling it "three". Then sticks IIII calling it "four", IIIII calling it "five", IIIIII calling them "six". Or, of course the fingers of Prehistoric Humanity instead of wood sticks calling each finger a name.
But with fingers, you cannot remove them and have subtraction or with fingers have a multiplication which you can do with sticks, even do a division with sticks.
This is how math started.
Archimedes Plutonium Apr 7, 2026, 11:32:14 PM to Plutonium Atom Universe newsgroup.
There is no concept of "time" necessary in mathematics, however, by the time we reach the larger science of Logic, the concept of "time" can no longer be in the shadows but has to be well defined.
Some in math will argue that the act of counting numbers is time itself, and that the derivative of dy/dx, the dx axis can be viewed as the time axis. But I contend that numbers of math are in general replaceable by anything you wish to replace with, yet, by the time that we reach the larger set of science Logic, where math is a subset, the issue of "time" must be no longer hidden, but outright open in full brightness and clarity. Time is a central concept of Physics, in velocity, in forces, in all the EM laws.
What I am saying is that mathematics needs not well-define "time" but that the science of Logic needs to of necessity well-define "time".
And the places I would go to, to make progress are these.
Planck time is 10^-43 seconds while Planck length is 10^-35 meter.
Perpetual motion exists only in atoms, in their interior where muon is thrusting through proton torus in the Faraday law, and so there must be electricity in a steady stream flowing out of radioactive elements, not because they are falling apart but because the Faraday law activity is producing an equal stream of 0.5MeV particles as those emitted via beta decay. I think Tellurium and Strontium can verify this.
How to make time not exist? Long ago I opined and still believe that if you can stop motion, no motion, everything at a standstill with respect to everything else, that if that can be done, then you have "no time". This is sort of like a reverse Special Relativity. A world that is motionless, frozen in place.
An AP aside: I remember once having a discussion in general with a physicist who strongly believed that if we well understood what is "time" that we then will well understand the entire world.
Archimedes Plutonium Apr 8, 2026, 3:13:17 AM to Plutonium Atom Universe newsgroup.
In all these years of my research, I have been focused on Time as the mystery parameter. Somehow I thought that distance or length was not mysterious. Nor that velocity, speed was not mysterious. Perhaps if I shift my attention away from "time" and look at velocity as being the mystery parameter.
Because all matter in the Universe goes around in a circle or near circle, is that proof enough alone that the Universe is a single big Atom of Plutonium.
In the Big Bang, all matter would be moving away from the center of the blast and move in straight line motion.
Because everything moves in circles, reminds us that electricity and magnetism moves in circles.
So we have velocity = distance / time which is velocity x time = distance.
In Old Ohm's law we have Voltage = current x Resistance.
New Ohm's law we expand on Resistance so we have Voltage = current x magnetic field x electric field.
Is it possible that velocity is split up into magnetic field x electric field.
I do not think distance is reducible to anything more simple, nor, is time reducible. So that leaves only velocity reducible.
Of course in calculus the integral is energy, while the derivative is velocity. The integral surely is reducible, but is the derivative reducible?
I think so, in that all derivatives are the hypotenuse of a right triangle if not a flat straight line. And being the hypotenuse reduces down to the two sides of a right triangle following the Pythagorean theorem. And so we can make out that the Speed is magnetic field x electric field.
So if we substitute that back into Velocity x time = distance. Let me change distance to "length". Velocity x time = length.
So we have Magnetic field x Electric field x time = length.
Have we reached any new insight????
Well, one immediate insight is that resistance in electromagnetism is actually a form of speed-velocity. Does that make any sense?? Yes if you compare speed to speed of Light.
Archimedes Plutonium Apr 8, 2026, 12:17:32 PM to Plutonium Atom Universe newsgroup.
Yes, yes indeed, this probably would have never come up in my mind if it were math or physics I was doing. But since I am doing Logic, it has to come up.
When I went to take physics in high school, 1967-8 a topic came up called Instantaneous Velocity. When I went to University, UC, 1968, in calculus we had this same thing --- instantaneous velocity. And I quickly learned that taking the integral of a function with not set bounds that the integral started with the point 0.
For example: Y--> x, has derivative 1, and has integral 1/2(x^2).
So, well, how does the math and physics community look upon this "Instantaneous Velocity". They see it as a conundrum, a nemesis, a mystery. They dread it, for it really makes no sense.
Can I straighten it out now, here in year 2026?? Yes I can, and give it a-lot of sense and meaning.
Ohm's law is central to physics to the laws of electromagnetism, but not the Old Ohm's law of Voltage = current x Resistance. For that is not even a "law" but a "rule" for it is not universal. It breaks down at high voltage, or high current.
How to fix Old Ohm's law? Simple, recognize that Resistance is ____not well-defined____. When we well-define Resistance to be that of Magnetic field x Electric field and write the equation as this.
Voltage = current x magnetic field x electric field
Then we have a Law of Physics.
When we write velocity as this Velocity = length / time, and so, what is instantaneous velocity? Is it this velocity x time = length.
Back to this calculus integral and derivative, that is unspecified, for the integral of Y--> x is 1/2(x^2) when you do not specify the interval it automatically throws the integral to be from 0 to a point along the x axis.
Integral is Energy in physics, and Voltage is energy. Velocity is derivative dy/dx.
The function Y---> x looks like this. Splitting the x and y axis into a right-triangle from a square.
| /
| /___
However, the derivative need not be counted upon from point (0,0) to point x which remains a right triangle. Instead, the point say x = 1 and then x= 1.1 in 10 Grid is no longer a right triangle starting at 0 but is a trapezoid in interval x = 1 to 1.1. If it were x from 0 to 1, or x from 0 to 1.1 we still have that right triangle. But here we have from 1.0 to 1.1 of x-axis no longer the right triangle but a cell in 10 Grid which is a right trapezoid. And our derivative is the hypotenuse of a tiny right triangle for derivative and when this right triangle is hinged downward it forms a rectangle for integral of the cell from 1.0 to 1.1 as seen in this diagram below.
From this:
B
/|
/ |
m /----|
/ |
|A |
|_______|
1 1.1
A of course is also 1 and B is 1.1 for y-axis.
The trapezoid roof has to be a straight-line segment (the derivative)
so that it can be hinged at m, and swiveled down to form rectangle for
integral. The area of the rectangle is the integral.
To this:
___m__
| |
| |
| |
-------------
1 1.1
So now, here, in April 2026 I have the physics equation of New Ohm's law, a true law, not just a rule that works sometimes but not always. A law works always.
New Ohm's law Voltage = current x magnetic field x electric field
I have Velocity as velocity x time = length
Do I have velocity in general as a law or do I have velocity that is instantaneous???
Velocity in general would be magnetic field x electric field. And so velocity in general would be this.
Magnetic field x electric field x time = length
Why that? Because the derivative in general is a right triangle hypotenuse, of that right-trapezoid, the magnetic field is one leg of that right triangle and the electric field is the other leg of that right triangle. The hypotenuse is the derivative length which in calculus ends up landing on the next point of the original function graph which in the case above is the coordinate point (1.1, 1.1).
Archimedes Plutonium Apr 8, 2026, 9:59:10 PM to Plutonium Atom Universe newsgroup.
Not only do we have Instantaneous Velocity, which is the derivative from one cell to the next cell, but we have the Instantaneous Integral or energy of that cell. Instantaneous Energy, I am not sure if Physics has run across something like this. And the Instanteous Velocity and Instantaneous Energy of each cell depends on what Decimal Grid System one is working in. In 10 Grid it would be 0.1 from one cell to another. While in 100 Grid it is 0.01 for Instantaneous cell velocity or energy.
Archimedes Plutonium Apr 9, 2026, 3:32:04 AM to Plutonium Atom Universe newsgroup.
So, I was hunting down some insights into the meaning of "time".
And we have the New Ohm's law of Voltage = current x magnetic field x electric field where the multiplication is of generalized multiplication where it can be vector cross product or dot product or plain ordinary multiply.
Then I took the Velocity equation Velocity = length/ time and rearranged it to be length = time x Velocity.
Then I made a hypothesis that length and time are not reducible any further, but that Velocity can be further reduced especially since we have "instantaneous velocity" as compared to normal velocity. And in instantaneous velocity we have a right triangle in calculus where the dy can be seen as electric field and the dx seen as magnetic field and thus our equation of velocity transformed further.
Length = time x Velocity becomes this.
Length = time x magnetic field x electric field.
Now look at the similarities to New Ohm's law.
Voltage = current x magnetic field x electric field.
I am trying to think if ever, I had a perception that Voltage is a length and if current is time????
I do not recall ever of anyone thinking that Voltage is length and current is time, in any science book.
Many say that Voltage is pressure, but I do not even buy that, for I see it as a energy.
Looking up the units of magnetic field and electric field in Halliday & Resnick & Krane they give.
Magnetic field = kg* A^-1* s^-2
Electric field = kg*m*s^-3*A^-1
If we divided Magnetic field into that of Electric field we end up with Velocity.
That is a surprise to me.
Archimedes Plutonium Apr 10, 2026, 1:37:32 AM to Plutonium Atom Universe newsgroup.
On Thursday, April 9, 2026 at 3:32:04 AM UTC-5 Archimedes Plutonium wrote:
Snipped
Magnetic field = kg* A^-1* s^-2
Electric field = kg*m*s^-3*A^-1
That division would look like this.
kg*m /(s^3*A)
----------------------
kg / (A*s^2)
That ends up being m/s which is velocity.
If we divided Magnetic field into that of Electric field we end up with Velocity.
That is a surprise to me.
So now how to interpret the idea that the difference between Electric field versus magnetic field is velocity.
Well the Faraday law is where we scrape off magnetic field, magnetic-lines-of-force that is thrust through a coil of wire in closed loop circuit producing electricity. The magnetic field is EM radiation going at the speed of light, but the electric current in the wire is caused by 0.5MeV magnetic monopoles and these are not going at the speed of light, not the particle but the signal that a 0.5MeV particle is created from scraped off magnetic-lines-of-force.
There is another set of ill-defined terms of physics, one of them is wavefunction and collapsed wavefunction. So when you scrape off magnetic lines of force by thrusting a bar magnet through coil, you collapse the wavefunction of Lines of Force and build them into being a 0.5MeV particle of electric current.
Archimedes Plutonium Apr 10, 2026, 8:46:21 PM to Plutonium Atom Universe newsgroup.
It is funny how I got here. I was doing a textbook on Logic and felt it is important to talk about "time" in logic. This led to a examination of magnetic field divided into electric field which ends up with velocity as length / time.
Now the pursuit is on whether Faraday's Law is that of scraping off the magnetic field of a thrusting bar magnet that forms magnetic monopoles of 0.5MeV in the copper wire coil. Or, whether the thrusting bar magnet only pushes along pre-existing magnetic monopoles in the copper coil to form Faraday's law.
These topics would probably never come up if I were doing a physics or math textbook. But because I am doing Logic, it surely does arise.
To help answer the question of whether the thrusting bar magnet in Faraday's Law pushes along pre-existing magnetic monopoles the units of electric current, or whether the thrusting bar magnet actually manufactures the 0.5MeV particles by scraping off magnetic-Lines-of-Force, I am helped by these passages in Feynman's Lectures on Physics, Volume 3, 1965, pages 21-6 to 21-7.
--- quoting Feynman in parts---
The meaning of the wave function
When Schrodinger first discovered his equation he discovered the conservation law... But he imagined incorrectly that P was the electric charge density of the electron and that J was the electric current density..... that the square of the amplitude is not the charge density but is only the probability per unit volume of finding an electron there, and that when you do find the electron some place the entire charge is there.
--- end quoting Feynman ----
On page 21-7, Feynman tries to link up Schrodinger with superconductivity.
The Logical Stumbling Block Feynman committed
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Here is where Logic steps in to help out enormously. I do not know about you, but I was never really satisfied with either Schrodinger interpretation or that of Born remade interpretation of the wave function.
But in steps Logic in a critical manner.
What would logic say about the wave function and its interpretation?
If we start over again, we have the Wave function and pick one of the EM laws, such as Faraday law, and pose that law to a question of deciding between one or the other.
Faraday Law
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When we thrust a bar magnet through the coil of copper wire, is the magnetic field pushing ahead pre-existing magnetic monopoles 0.5MeV or is the thrusting creating brand new monopoles by scraping off magnetic Lines of Force formed into 0.5MeV particles the unit of electricity?
Have the Schrodinger equation provide an answer for that.
Once it has provided an answer to that, see if it can provide an answer as to superconductivity has no resistance--- waves are all going in one direction.
Archimedes Plutonium Apr 10, 2026, 9:03:08 PM to Plutonium Atom Universe newsgroup.
Feynman thought that Born was correct and Schrodinger wrong on interpretation of his wave function. AP thinks all three of them, Feynman, Born, Schrodinger were wrong in interpretion. For one, they thought atoms had nuclei which they do not, and they thought the true electron was the 0.5MeV particle which is false for the Muon is the true electron and that the interior of atoms is a proton torus with neutrons storing the electricity produced by muons thrusting through proton torus. When you have the Atom so out of line of reality, there is no hope that a proper interpretation of the wave function is possible.
So the question is, when you do the Faraday law, the thrusting bar magnet--- are you scraping off magnetic Lines of Force, creating brand new monopoles of 0.5MeV to make electricity, or, are you just pushing along monopoles pre-existing to make the electric current?
Also, I need to incorporate the Schrodinger Equation into the AP-EM equations, because, All is Atom and Atoms are nothing but electricity and magnetism, means that the Schrodinger Equation has to be a tiny part of the EM equations.
Archimedes Plutonium Apr 11, 2026, 2:45:59 AM to Plutonium Atom Universe newsgroup.
Like I say, I probably would never have been diving into the Schrodinger equation, unless I was doing textbooks on Logic. This all started when I wanted to include "time" into my #370 and #371 logic textbooks. This morphed into the question of dividing electric field by magnetic field and finding out that they have a factor of velocity in common. Then the question came up as to whether the Faraday law is the scraping off of magnetic Lines-of-Force creating the magnetic monopoles 0.5MeV which is the electric current in Faraday's law, or, whether thrusting the bar magnet into the copper coil is a push upon pre-existing magnetic monopoles to move in the direction of thrust.
This led to the collapse of the wavefunction of Schrodinger equation.
So here I am now logically analyzing how Faraday law actually works using the Schrodinger equation.
If this came up in a physics textbook, I would have likely not proceeded to get so far in analysis.
So, well, what would a Logical person do to find out if Faraday law is a (1) scraping off of magnetic Lines of Force and forming, creating new magnetic monopoles 0.5MeV the current, or (2) the Lines of Force merely push pre-existing magnetic monopoles into being a current.
I believe the correct answer is (2). It could be the case that some magnetic lines of force of the thrusting bar magnet creates new monopoles, only a few of them, and so both (1) and (2) are correct.
But I also wanted to review on how to show the Schrodinger equation is a subset of the AP-EM equations. And I believe I did that by my 112th book saying the units of Psi^2 are angular momentum and that is easily found in Faraday and Ampere laws.
But now, Logic will reveal what is Resistance in electricity and magnetism. And so logic tells me to go to magnetism with magnetic moments such as diamagnetic, paramagnetic and ferromagnetic. This should reveal even the correct theory of superconductivity.
So on page 891 of Brown, LeMay, Bursten, 5th edition Chemistry the Central Science, 1991. We can picture in our minds that diamagnetism has no centers of magnetic moments and would be a nonconductor. Diamagnetism would be high resistance. Next is paramagnetism magnetic moments not aligned unless in a magnetic field. Then we have ferromagnetism where we have coupled centers aligned in one direction.
So, as to the question of whether thrusting bar magnet in Faraday's law scrapes off magnetic Lines of Force forming new magnetic monopoles of 0.5MeV as the produced electric current, or, whether the thrusting bar magnet merely has the Lines of Force push the pre-existing monopoles to be a current, implies the Lines of Force do not create new monopoles but push along the pre-existing magnetic monopoles of copper. As we see that a Conductor can itself be defined as a FerroElectricCurrent.
In this viewpoint Resistance is the nullification of magnetic moments and so we can call those electric-current-moments.
I probably will have to go back to many of my old books and correct my mistake where I said the current in Faraday law is the scraping off of magnetic lines of force of the bar magnet to create new monopoles of electric current.
Archimedes Plutonium Apr 11, 2026, 3:47:59 AM to Plutonium Atom Universe newsgroup.
So, in all my 4 textbooks of Logic, to get the true logic, I used mathematics as a guide, a guidepost to correct Old Logic.
So now, I ask the question of what is "time", a very important concept. And then I follow that until I end up with Schrodinger wave equation. And I am mystified by wanting to know if the Faraday Law is a scraping off of magnetic Lines of Force in the thrusting bar magnet through copper coil? Scraped off magnetic lines of force forming magnetic monopoles of 0.5MeV which are the units of electric current. Or, is the electric current formed simply by the magnetic lines of force pushing pre-existing magnetic monopoles??
So I am in a quandary, and using Logic, I play the same trick on this question that I played in arriving at the correct 6 connectors Existential quantifier, Not-Equal, AND, OR, If-->Then, Universal quantifier where I used math as the guide.
Here I use Magnetism as the guide to tell me what Electricity, electric field and electric current are.
I use Magnetism of diamagnetic, paramagnetic, ferromagnetic to tell me the true nature of Faraday law, and now superconductivity.
I should have known better years ago, that Faraday law was not the scraping off of magnetic lines of force of the bar magnet for then there would be nonconservation of energy to a large extent. Every electric current would violate conservation of energy.
But nonconservation of energy truly exists for the muons inside a proton torus are in perpetual motion and perpetual motion is itself nonconservation of energy.
Archimedes Plutonium Apr 11, 2026, 4:53:17 PM to Plutonium Atom Universe newsgroup.
I would need to discuss the concept of "time" in 4 textbooks of Logic, not knowing where it would lead me. But "time" needs clarity, logical clarity. Turns out, Length and Time are not special, what is special is velocity. You can reduce length and time, no further, no further reductions. But, you can reduce velocity to be that of Electric field divided by Magnetic field, each of those fields is reducible to length, time, Ampere, kilogram mass.
This clarity then forces us to ask the next question. When we do the Faraday law of thrusting bar magnet inside a closed loop copper coil circuit, is the electric current produced from scraping off the magnetic field lines of force, scraping them off and turning those scrapings into the magnetic monopole 0.5MeV particle that is the unit of electric current, or, is the thrusting bar magnet simply pushing along pre-existing monopoles 0.5MeV of copper along to make the current? Or, possibly both? Here, experiments need to be conducted to answer that question fully. I am of the intuition that only pre-existing magnetic monopoles 0.5MeV are in play and that the thrusting of bar magnet does not create any new magnetic monopole from scraped off magnetic lines of force.
Reasoning: When you divide electric field by magnetic field you get meter/second, a velocity, telling me the magnetic field is less in energy than the electric field and not able to secure enough scrappings to form a new magnetic monopole of 0.5MeV. This would violate Conservation of Energy, even though Nature does violate conservation of energy as the muon inside proton torus is in perpetual motion.
So, I await Experiments to definitively prove that in Faraday Law, only pre-existing magnetic monopoles are pushed (or pulled) through the circuit for electric current.
But, this Logic adventure does not stop with those Experiments.
The pinnacle peak of Physics, Old Physics was the Dirac equation, which was a supplemented Schrodinger equation. The Schrodinger equation was nonrelativistic and so Dirac inputed relativity into the Schrodinger equation to make it more wholesome.
AP argues though, it is impossible for these equations of Schrodinger or Dirac to tell true physics for they were built from thinking the Atom has a nucleus which it does not, that the Atom has no magnetic monopoles and that the electron of atoms is the 0.5MeV particle when in reality the muon is the true electron of atoms stuck inside a proton torus doing the Faraday law.
The Mathematics of the Dirac equation and of the Schrodinger equation are reduced to Clifford Algebras. This reduction in essence is that the Dirac equation is a polynomial of **quadratic form**. Quadratic form, not to be confused with quadratic equation, but quadratic form means ___every term___ of the equation is of order 2.
An equation such as 3x^2 +2x = 4 is a quadratic equation but not quadratic form because of the term 2x is not of order 2 but of order 1. An equation like 3xy + y^2 = 4 is a quadratic form equation.
Clifford Algebra is a generalization of the Dirac Equation. And to be a Clifford Algebra means that every integer can be fetched when using only integers for the variables. So, the Pythagorean theorem x^2 + y^2 = C. Can we use only integers for x and y and then fetch every other integer? 0 is fetched by 0^2+0^2, and 1 is fetched by 1^2 +0^2, and 2 is fetched by 1^2 + 1^2, but there is no way to fetch 3.
What does this have to do with Physics of electricity and magnetism? Everything for they are dependent on being a Circuit a closed loop. And a smooth closed loop so the magnetic monopoles stay on the circuit.
How do we get to 3?
We realize that the Algebra needs to be in 3rd dimension not 2nd dimension.
x^2 + y^2 + z^2 = C fetches every integer when allowed to only use integers for x,y,z plus 0.
This allows AP to easily claim the Primal Axiom over all of physics--- All is Atom, and Atoms are nothing but electricity and magnetism obeying the AP-EM equations. Those equations are permutations of New Ohm's law V = current x magnetic field x electric field.
When you take the derivative of New Ohm's Law you have this.
Using the Product Rule which is (fgh)' = (f'gh + fg'h + fgh')
New Ohm's Law (C*B*E)' = C'*B*E + C*B'E + C*B*E'
V' = (CBE)' = C'*B*E + C*B'*E + C*B*E' here we have three terms explaining New Ohm's Law derivative and is a capacitor.
Now of course, well I end up with even a greater generalization for New Ohms law is cubed.
I needed just x^2 +y^2 + z^2
But I got a-lot more with
x^3 +y^3 + z^3 (keep in mind I can have mixtures such as xy^2 or xyz to maintain all are clifford algebra order 3).
So, what I have here is a explanation of the Dirac equation in 3rd dimension, not just 2nd dimension.
And this is all possible because of a outstanding feature of Electromagnetism-- must be a closed circuit.
The Schrodinger equation is one of screaming out loud-- a closed circuit in 2nd dimension.
The Dirac equation is one of screaming out loud-- a closed circuit in 2nd dimension with relativity added.
The AP equations is one of a Closed Circuit in 3rd dimension with all the laws of EM theory.
Archimedes Plutonium Apr 11, 2026, 5:40:30 PM to Plutonium Atom Universe newsgroup.
The geometry of Clifford Algebras as closed circuits in 2nd or 3rd dimension
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The essence of physics is the Atomic theory coupled with EM laws.
The essence of EM laws is the closed loop circuit.
Mathematically, the closed loop circuit is the Clifford algebra and the Dirac and Schrodinger equations are tiny subset examples of Clifford algebra.
So what are examples of geometry of Clifford algebra in 2nd dimension. Here any closed circuit but it must not have vertices for electric current is ruined at a vertex. The closed circuit must be vertex free and somewhat smooth, like a circle or ellipse or oval. Our household extension cords are pencil ellipses circuits.
In 3rd dimension a smooth circuit can be so many different shapes, geometries much of which have no names in math geometry.
Archimedes Plutonium Apr 12, 2026, 3:17:31 AM to Plutonium Atom Universe newsgroup.
So, the Schrodinger Equation is a subset of the Dirac Equation for the Dirac Equation is relativistic. But, now, the Dirac Equation is a subset of Clifford Algebra, where you have polynomials and with only integers plus 0 derive all the integers from those polynomials.
Now the AP-EM Equations are polynomials in 3rd dimension, ternary form. While the Dirac Equation is in Clifford Algebra a quadratic form, 2nd dimension.
The basis for Dirac Equation is the Schrodinger Equation of 2nd dimension for waves are 2nd dimensional. The AP-EM Equations are about Circuits, closed loop circuits, not about waves. And circuits in 3rd dimension, not in 2nd dimension like the Dirac Equation.
I used to call them Bent-circles for a circuit in 3rd dimension Space. But they can take all types of geometry shape as closed loops in 3rd dimension.
The basis of the AP-EM Equations is New Ohm's Law and all its permutations. This is the reason that Schrodinger and Dirac Equations fall apart and fail, in that their basis is nothing logical other than to have a Wave, even allowing for non- closed loop wave.
The 6 AP-Electromagnetic Equations and the 7 Structures (Laws) of Physics and all sciences.
0) domain structure as Atomic Theory-- Periodic Table of Chemical Elements
1) B and E primal unit structures Magnetic Field B = kg / (Ampere*second^2) and Electric field E = kg*m/(Ampere*second^3)
2) V = A*B*E New Ohm's Law, structure of electricity
3) V' = (A*B*E)' Capacitor-Transformer Law
4) (V/A*E)' = B' Ampere-Maxwell Law
5) (V/(B*E))' = A' Faraday Law
6) (V/(A*B))' = E' the new structure of Coulomb force law with EM gravity force law and DeBroglie pilot wave structure
V= voltage, A = ampere current, B = magnetic field, E = electric field.
Primal Axiom over all Science = All is Atom and Atoms are nothing but electricity and magnetism. This is the primal axiom of all sciences.
Archimedes Plutonium Apr 12, 2026, 3:52:13 AM to Plutonium Atom Universe newsgroup.
On Sunday, April 12, 2026 at 3:17:31 AM UTC-5 Archimedes Plutonium wrote:
So, the Schrodinger Equation is a subset of the Dirac Equation for the Dirac Equation is relativistic. But, now, the Dirac Equation is a subset of Clifford Algebra, where you have polynomials and with only integers plus 0 derive all the integers from those polynomials.
The reason I added that about "derive all the integers from those polynomials" is the basis for Clifford Algebra. The basis for Schrodinger and Dirac equations was "waves" , yet the basis for AP-EM Equations is New Ohm's Law and all its differential permutations.
When you realize that the true numbers of mathematics are all Decimal Grid Numbers, then when your Quadratic Form Clifford Algebra fetches all the integers (for AP it is only positive integers, for negative numbers are fakery), means that you fetch every number that exists. Take for example the 10 Grid is 100 numbers not counting 0. It is .1, .2, .3, ... 1, 1.1, 1.2, .....9.8, 10. So if you multiply 10 Grid by 10 each and every number, you end up with all the counting numbers from 1 to 100. And where the infinity borderline is in true math at 1*10^604 if you multiply each and every number by 10^604 you turn all the numbers to be Counting Numbers. I write this to inform those not in math or physics to understand why Clifford Algebra onus for existence is to derive all the counting numbers from Quadratic Form. However, sad to say, they fail in Clifford Algebra, for you need the Ternary Form Clifford Algebra in order to get all the Counting numbers, hence all the numbers of mathematics. The New Ohm's law is V = i*B*E and in differential equation form using the product rule it is this.
Using the Product Rule which is (fgh)' = (f'gh + fg'h + fgh')
Capacitor Law (i*B*E)' = i'*B*E + i*B'E + i*B*E'
V' = (iBE)' = i'*B*E + i*B'*E + i*B*E' here we have three terms explaining capacitors
Now the AP-EM Equations are polynomials in 3rd dimension, ternary form. While the Dirac Equation is in Clifford Algebra a quadratic form, 2nd dimension.
The Dirac Equation needs to be in ternary form for 3rd dimension circuits. The understanding of EM theory takes place on circuits in 3D, not on waves in a plane of 2D.
The basis for Dirac Equation is the Schrodinger Equation of 2nd dimension for waves are 2nd dimensional. The AP-EM Equations are about Circuits, closed loop circuits, not about waves. And circuits in 3rd dimension, not in 2nd dimension like the Dirac Equation.
I used to call them Bent-circles for a circuit in 3rd dimension Space. But they can take all types of geometry shape as closed loops in 3rd dimension.
This was a major failing of Maxwell when you unified electricity with magnetism. He should not have cobbled together disparate laws, especially the fake Gauss law-- no magnetic monopoles. If Maxwell had been logically smarter, he would have looked for the law that was most perfect--- Ohm's law and simply made permutations in differential equations.
The basis of the AP-EM Equations is New Ohm's Law and all its permutations. This is the reason that Schrodinger and Dirac Equations fall apart and fail, in that their basis is nothing logical other than to have a Wave, even allowing for non- closed loop wave.
The 6 AP-Electromagnetic Equations and the 7 Structures (Laws) of Physics and all sciences.
0) domain structure as Atomic Theory-- Periodic Table of Chemical Elements
1) B and E primal unit structures Magnetic Field B = kg / (Ampere*second^2) and Electric field E = kg*m/(Ampere*second^3)
2) V = A*B*E New Ohm's Law, structure of electricity
3) V' = (A*B*E)' Capacitor-Transformer Law
4) (V/A*E)' = B' Ampere-Maxwell Law
5) (V/(B*E))' = A' Faraday Law
6) (V/(A*B))' = E' the new structure of Coulomb force law with EM gravity force law and DeBroglie pilot wave structure
V= voltage, A = ampere current, B = magnetic field, E = electric field.
Primal Axiom over all Science = All is Atom and Atoms are nothing but electricity and magnetism. This is the primal axiom of all sciences.
On Saturday, April 11, 2026 at 5:40:30 PM UTC-5 Archimedes Plutonium wrote:
The geometry of Clifford Algebras as closed circuits in 2nd or 3rd dimension
-----------------------------------------------------------------------------------------
The essence of physics is the Atomic theory coupled with EM laws.
The essence of EM laws is the closed loop circuit.
Mathematically, the closed loop circuit is the Clifford algebra and the Dirac and Schrodinger equations are tiny subset examples of Clifford algebra.
So what are examples of geometry of Clifford algebra in 2nd dimension. Here any closed circuit but it must not have vertices for electric current is ruined at a vertex. The closed circuit must be vertex free and somewhat smooth, like a circle or ellipse or oval. Our household extension cords are pencil ellipses circuits.
In 3rd dimension a smooth circuit can be so many different shapes, geometries much of which have no names in math geometry.
Archimedes Plutonium Apr 17, 2026, 9:25:00 PM to Plutonium Atom Universe newsgroup.
So I wanted a chapter on the concept of "time" for Logic. And I came to some astounding results such as the idea that the Dirac Equation is a minor subset or Clifford Algebras wherein the AP equations of Electromagnetism require a Ternary-Form for Clifford Algebras, rather than a Quadratic-Form.
Now we all know where time is essential and basic in velocity as speed = distance / time.
Some of us in science know that distance^2 / time is essential in angular momentum.
But today, well, I am thinking of where in physics do we have distance^3 / time? I cannot think of anyplace in physics where meters^3 comes up in electricity and magnetism. Seconds^4 comes up in capacitance and seconds^3 comes up in conductance, but I do not recall, ever, that meters^3 comes up, do you????
Archimedes Plutonium Apr 18, 2026, 2:17:43 AM to Plutonium Atom Universe newsgroup.
Actually in the New Ohm's law of AP-EM equations we can get a seconds^5 and even seconds^6 because of magnetic field multiply electric field. I also get a kg^2 which I as yet have not interpreted. Is it kg x kg = kg + kg or something else?
But, can we get meters^3 or higher??
Voltage has the units of kg*m^2/ A*s^3. Here again, as in V = A*B*E if we multiply 1/sec^2 by that of 1/sec^3 do we end up with just 1/sec^3.
In the AP-EM equations below, by replacement in V' we can end up with Voltage^2 and that would specifically give me meters^4.
The 6 AP-Electromagnetic Equations and the 7 law-structures of Physics and all sciences.
0) domain structure as Atomic Theory-- Periodic Table of Chemical Elements
1) B and E primal unit structures Magnetic Field B = kg / (Ampere*second^2) and Electric field E = kg*m/(Ampere*second^3)
2) V = A*B*E New Ohm's law-structure of electricity
3) V' = (A*B*E)' Capacitor-Transformer law-structure
4) (V/A*E)' = B' Ampere-Maxwell law-structure
5) (V/(B*E))' = A' Faraday law-structure
6) (V/(A*B))' = E' the new structures of Coulomb force law-structure with EM gravity force and DeBroglie pilot-wave structure
V= voltage, A = ampere current, B = magnetic field, E = electric field.
I need a-lot more work on this.
Archimedes Plutonium<
plutonium....@gmail.com>
6:04 PM (1 hour ago)
to Plutonium Atom Universe
Again, I have to start over again. This time, because --- since there are 6 connectors in logic and 6 operators in math, and 6 law-structures of physics like Faraday, Coulomb, Ampere, Ohm that there needs to be 6 well-defined terms to describe Science, Logic and Math. Below, I have various terms but I need 6 terms for each of science, logic, and math.
for science
----------
Statement, (some call them fact or facts)
Hypothesis, (some call them speculation)
Concept
Law-structure (most people simply call them laws)
Principle
Theory
for logic
-------
Statement
Premiss
Concept
Connector-structure
Equalities, (some call them Rules of Induction or Rules of Inference)
for mathematics
-------
Statement
Concept
Axiom (some call them postulates)
Operator-structure
Proof
Theorem
Corollary
Archimedes Plutonium<
plutonium....@gmail.com>
6:52 PM (21 minutes ago)
to Plutonium Atom Universe
I find myself having trouble in forming the basic foundational terms , the 6 basic terms that are to be used in Science, in Logic and in Math. So I am going back to use what I had learned in fixing the mistakes of Old Logic, use that method to fetch the 6 basic terms of science, logic and math.
The Scientific Method has 6 steps.
Step 1-- Make observations and ask many questions.
Step 2-- Research the subject matter and Review the literature on the subject.
Step 3-- Formulate a Hypothesis of what you think is going on.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Step 6-- Draw conclusions.
Let me re-interpret those 6 steps using 6 logic connectors.
Step 1-- Does something exist-- Existential quantifier --- call it a statement
Step 2-- Research-- Not- equal connector --- call it a concept
Step 3-- Hypothesis --- If-->Then connector --- call it a hypothesis or conjecture or speculation
Step 4-- Experiments -- AND connector --- call it Law-structure
Step 5-- analyze data and deciding experiment-- OR connector --- call it theory or principle
Step 6-- draw conclusion -- Universal quantifier --- call it Universal Axiom
This catches me by surprise in that I had thought "theory" was the highest and final term of science, especially physics; and instead I needed a higher term than "theory". I needed a Axiom term for that which summarizes "theory". Until now I have called it the "Primal Axiom" of science-- All is Atom and Atoms are nothing but electricity and magnetism. Instead, I should have called it the Universal Axiom, not the "primal axiom". It summarizes the "theory".
Apparently we need a summarization in science even though it is a theory. For Math, we need to go a step beyond "theorem" and that would be a "theory".
We need a summarization for Logic and go beyond "Equality-Rules-of-Inference" and that would be a Law-structure. Notice, not a theory but a law-structure. Occam's Razor is thus described as a law structure along with the 6 connectors of logic.
Wow, I never thought I would be ending up applying Logic to terms of science, logic and math. No wonder writing true logic textbooks is so very painful. In this 1.5 years of writing these 4 logic textbooks I could have likely written 100 books on just normal science, to indicate how painful just these 4 logic textbooks have been on me.
On Friday, April 17, 2026 at 6:04:40 PM UTC-5 Archimedes Plutonium wrote:
Again, I have to start over again. This time, because --- since there are 6 connectors in logic and 6 operators in math, and 6 law-structures of physics like Faraday, Coulomb, Ampere, Ohm that there needs to be 6 well-defined terms to describe Science, Logic and Math. Below, I have various terms but I need 6 terms for each of science, logic, and math.
for science
----------
Statement, (some call them fact or facts)
Concept
Hypothesis, (some call them speculation)
Law-structure
Principle
Theory
for logic
-------
Statement
Premiss
Concept
Connector-structure
Equalities, (some call them Rules of Induction or Rules of Inference)
for mathematics
-------
Statement
Concept
Axiom (some call them postulates)
Operator-structure
Proof
Theorem -corollary (a smaller theorem)
Archimedes Plutonium<
plutonium....@gmail.com>
5:13 PM, 19April 2026
to Plutonium Atom Universe
Yes, I am happy with the below.
Now I need to well-define what is Science. Feynman gives a good description of a definition. But we need to add more of the concept of "prediction". The common layman knows or thinks she/he knows that predicting the future is impossible. But then again, they lack a "scientific mind" and we clearly can see this in the week or two ago mission of Artemis II around the Moon. Science, correct science has the ability to predict the future, but anything ___not science___ has no ability to predict the future. Without science, we could not even begin to go to the Moon for we need science-law-structure and math for precision.
When we have true science, we also have the ability and capability of predicting parts of the future. No other body of knowledge has the ability to predict the future. In step 3 below of the Scientific Method, does this capability of future prediction come to light.
Well-defining Science is the knowledge that is able to make predictions of the future, is precise, follows a method of inquiry called the scientific-method where experimentation decides between competing ideas of the truth.
On Saturday, April 18, 2026 at 3:06:09 AM UTC-5 Archimedes Plutonium wrote:
On Friday, April 17, 2026 at 6:52:39 PM UTC-5 Archimedes Plutonium wrote:
I find myself having trouble in forming the basic foundational terms , the 6 basic terms that are to be used in Science, in Logic and in Math. So I am going back to use what I had learned in fixing the mistakes of Old Logic, use that method to fetch the 6 basic terms of science, logic and math.
The Scientific Method has 6 steps.
Step 1-- Make observations and ask many questions.
Step 2-- Research the subject matter and Review the literature on the subject.
Step 3-- Formulate a Hypothesis of what you think is going on.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Step 6-- Draw conclusions.
This one for science looks good at the moment. A little worried that Experiment is AND.
Let me re-interpret those 6 steps using 6 logic connectors.
Step 1-- Does something exist-- Existential quantifier --- call it a statement
Step 2-- Research-- Not- equal connector --- call it a concept
Step 3-- Hypothesis --- If-->Then connector --- call it a hypothesis or conjecture or speculation or prediction
Step 4-- Experiments -- AND connector --- call it Law-structure
Step 5-- analyze data and deciding experiment-- OR connector --- call it theory or principle
Step 6-- draw conclusion -- Universal quantifier --- call it Universal Axiom
So how do I feel about the above. Does it look promising? If the Scientific Method is the above, then it looks good.
Is a "concept" involve "not-equal or equal-not" more than any of the other connectors?
And am I happy with saying AND is the Experiment? Probably yes because OR is the deciding experiment that differentiates what is universal and not universal. Leaving the Universal quantifier as the Summary for physics.
Notice that just as there are 6 steps in Scientific Method, there are 6 terms in Physics (and all other sciences), 6 terms in Logic and 6 terms in Math.
For science, especially physics but all the other sciences included
----------
Statement, (some call them fact or facts)
Concept -- A collection of statements
Hypothesis-- (some call them implies as in material implication, some call them prediction)
Law-structure-- some call them Principle--- these are borne from experiments especially physics
Theory-- a collection of law-structures or principles
Universal Axiom-- a summary and this axiom says--- All is Atom and Atoms are nothing but electricity and magnetism
The last one is a big surprise to me, for I had called it Primal Axiom, but now it is the Universal Axiom. I suppose Science ends with a summary and that would be--- All is Atom and Atoms are nothing but electricity and magnetism.
Alas, well, I maybe able to get rid of the use of the word "law" by calling all laws simply "principle" so that jurisprudence and the law enforcement can have "law" all for themselves and science use "principle"-- Faraday principle or Ohm principle the gravity principle.
For Logic
-------
Statement-- an idea which is either word-sentence algebra or picture-image which can have various truth values, T, F or partial T, partial F
Premiss--checking the statements to see if true by best science on the subject matter
Connector-structure -- the 6 connectors of logic
Reasoning, Discourse, Argument, -- a collection of premisses leading to a conclusion, the smallest is a 2 premiss called a Syllogism.
So take my pick, logical-reasoning, logical-discourse, logical-argument? In math this would be called a proof. I am going to stick with Reasoning.
Equalities, (some call them Rules of Induction or Rules of Inference) such as commutative, associative, distributive, transposition
Law-structure-- the summary of Logic in such structures as NonContradiction in logic and Occam's Razor in logic, EI existential instantiation, EG existential generalization, UI universal instantiation, UG universal generalization.
For mathematics
-------
Statement-- either in number algebra or geometry figures
Axiom (some call them postulates) accepted statements without proof
Operator-structure-- such as add, subtract, multiply, divide, differentiate, integrate, and the proof deduction mechanism
Proof -- is a stepwise deduction using axioms and other data. The logic argument becomes the math proof.
Theorem -(corollary-a smaller theorem)-- a statement with a given deductive proof, step by step proof
Theory-- the summary of mathematics such as a geometry theory or algebra number theory or probability theory or set theory even a mathematics theory.
Bizarrely, or should I say Awesomely, that there appears some spin rotation in these crucial terms of science, logic, math.
Notice that Math ends in summary as a theory which is 2nd from bottom of science. Notice that Logic ends with summary of Law-structure which is 3rd from bottom for Science.
All three start with "statement". For physics that would be a observation, for logic that would be a idea in sentence form or picture-image form, and for math that would be a sentence of number algebra or geometry figure image.
AP
Archimedes Plutonium<
plutonium....@gmail.com>
May 4, 2026, 2:47:55 AM (4 days ago)
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A piece of advice to anyone contemplating writing a textbook on logic. If you hate to revise or even edit, then do not write a textbook on logic. Funny I should even say that for most people never want to even a read a textbook on logic, let alone write one.
Just today I had to correct this mistake where I had written add was not equal to subtract.
(5) Equalities-- Some call them Rules of Induction or Rules of Inference such as commutative, associative, distributive, transposition. Copi in his "Introduction to Logic on inside front cover and back cover lists 19 Rules of Inference starting with Modus Ponens and ending with Tautology. Here in New Logic, we have very few Equalities because math has very few equalities among math's operators. Math does have add equals to subtraction as inverses and written like this Addition = Inverse[subtraction] and math has Multiplication = Inverse[division]. Math has equalities of commutative, associative and distributive and so does Logic. When Old Logic makes their many mistakes, they end up with 19 Rules of Inference. If Old Logic made no mistakes, they end up with only a few rules of inference which I call equalities.
Another mistake I made was that I said OR was commutative because of its truth table where T OR F is the same as F OR T. But then later I switched by citing that math subtraction was Not Commutative where for example 5 -3 is not the same as 3-5. So OR was not commutative. But today, looking at the OR truth table makes me realize again, it is commutative. We can understand that Logic is above mathematics and more general than mathematics and allows for a Commutative OR.
But there is far more going on here with subtraction in math. In Old Math they had fake things like negative numbers and they forgot a important axiom-- You cannot subtract more than what is available to subtract. So that we can have 5-3 but we cannot venture into 3-5. Does that mean subtraction in math is commutative as OR is commutative in Logic?? No. It means only that OR is more general as subtraction-remove than in math where subtraction is governed by a axiom which says you cannot remove more than what is available.
Yes, if you hate and despise revising and editing, never ever write a logic textbook.
Archimedes Plutonium<
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May 4, 2026, 8:10:06 PM (3 days ago)
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Still not finished. First I thought OR is not commutative since subtraction in math is not commutative, then I thought it was commutative for the order does not matter P OR Q the same as Q OR P. Then I thought it was not commutative because if you include a Time factor in the P OR Q, that the time factor makes Q OR P different.
And this is shown especially in the Associative law-structure of ((P OR Q) OR T) whether it equals (P OR (Q OR T)).
If one of those P, Q, R is time dependent could throw the entire equality into a dis-equality.
And this is a concept I never thought was possible for Logic statements and premisses.
In doing mathematics we never entertain the concept of TIME playing a part or role in the calculation. When we add 2 +11 we think everything in mathematics in going according to instant time, everything is simultaneous and instant in math calculations.
But in Logic, we can have statements and premisses that are Time Influenced.
So this issue of whether OR is commutative or associative is really not over with, but just begun.
Archimedes Plutonium<
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May 5, 2026, 2:49:21 AM (3 days ago)
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Alright in this Elementary Logic textbook I have spent no time on doing proofs by counterexample. In math we would call it a counterexample proof. While in Logic using our glossary of terms it is called a "reasoned argument".
Mathematicians love using a counterexample to prove something. And in college, myself in 1968-1972 in logic class this was often used.
The idea is --- if someone makes a reasoned-argument that holds a key idea. And then, if someone voices a counterexample, then the key idea is wrong.
Example:: All birds fly. Counterexample-- the ostrich. Thus some birds fly but not all birds fly.
So what I want to do now is prove that OR connector is not commutative nor is it associative by using this method of Counterexample.
And I distinctly remember Logic class we had ample training in knowing this method. I remember the teacher saying to this day 54 years later--- a idea is immediately false if you can find a Counterexample.
So the Premiss is this "The OR connector is commutative." Next, the premiss is this "The OR connector is associative."
So let me see if I can come up with counterexamples of both.
I am going to look for Counterexamples with a element of Time involved in the statements that form the premiss.
Remember in Logic, the hierarchy of terms is this.
Statement
Premiss
Connector structure
Reasoned argument (syllogism)
Equalities
Law-structure
Remember that a statement is simply a idea. A premiss has to only true ideas. True as checked and validated by the best science on the subject matter.
So here the question involves equalities of logic. Is P OR Q = Q OR P , the commutative always true, and, is ((P OR Q) OR S) = (P OR (Q OR S)) true, the associative?
If I can find counterexamples then they are no longer equalities.
I am going to look for a time element involved in the premisses to prove OR is false for commutative and associative.
Premiss:: The summer of 2025 where I live was a normal summer with rainfall OR the summer of 2026 is a drought summer.
Now that is a valid premiss because the P part of P OR Q, is true --summer of 2025 was normal rainfall, but the summer of 2026 has yet to be revealed for it is in the near future.
Now let me take the Commutative of that premiss.
Premiss:: The summer of 2026 where I live is a drought summer OR the summer of 2025 is a normal summer.
Again that is a valid premiss because the Q part is true.
But this is not yet working out as a counterexample.
Archimedes Plutonium<
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May 5, 2026, 12:55:15 PM (3 days ago)
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Let me try this one out for I mirror-reflected the counterexample of mathematics 10 - 2 versus 2 - 10.
A Caltech astronomer has 9 -1 planets OR a Caltech astronomer has 1 - 9 subplanets.
Archimedes Plutonium<
plutonium....@gmail.com>
May 6, 2026, 3:06:11 AM (2 days ago)
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What I am doing here for the new latecomer reader joining me in this book. I am trying to find a CounterExample for the commutative and associative equality. In Math, addition and multiplication are both commutative and associative. I have not yet figured out if OR is or is not commutative and associative.
By the way, I should also figure out if when being not commutative, it is impossible to be associative.
So to find out, for I would be finished in writing this textbook, I need at least one counterexample to make a proof.
_On Tuesday, May 5, 2026 at 12:55:15 PM UTC-5 Archimedes Plutonium wrote:
_Let me try this one out for I mirror-reflected the counterexample of mathematics 10 - 2 versus 2 - 10.
P OR Q
_A Caltech astronomer has 9 -1 planets OR a Caltech astronomer has 1 - 9 subplanets.
Is that a Counterexample? A Caltech astronomer has 1-9 subplanets OR a Caltech astronomer has 9-1 planets.
You see, I modeled that after math noncommutative 9-1 does not equal 1-9. For in truth, no negative numbers ever existed in the first place when you have an axiom of math saying you can never remove more than what is available to remove (subtract) and mathematicians who believe in negative numbers are in a Fantasy Fairyland Bubble.
I wish to solve this problem as to finally finish this textbook.
Archimedes Plutonium<
plutonium....@gmail.com>
May 6, 2026, 3:28:40 PM (2 days ago)
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The most silly mistake AP has made in Logic, when it is all so simple and clear. So there I was, almost at the end of writing the textbook Elementary Logic. With only one spot to clean up and done with the book. I had to prove that OR, disjunction was either commutative or not commutative. And over a year now I was battling that question. All the other textbooks on logic say OR is commutative, even Copi and even Wikipedia says OR is commutative. But the trouble with that is that mathematics says that OR which is subtract in math is Noncommutative.
So, since 2025 I have been battling this issue. One month I would argue OR is Noncommutative then a month later concede it was commutative because looking at the truth tables alone of exclusive OR it is true for T OR F and true for F OR T.
Finally, coming down to the wire here in May 2026, for I desperately need to finish this textbook and cannot do that until this issue is settled.
Is OR commutative?????
And can a connector (operator in math) be associative if it is non-commutative?????
Two issues remaining. And just last week I was sure and certain that the resolution can be found by the method of CounterExample. And looking at my textbook I had not dwell on the method of Counterexample and that certainly would be a shortcoming of this logic textbook.
But today, 6 May, I have a clear mind that I can resolve all these issues and finally be done with this textbook.
Solving the question of OR is Non Commutative and Non Associative, including IF-->Then is the same as OR
------------------------------------------------------------------------------
This is AP's worst mistake ever, in doing Logic science. Mistake because the answer is really so simple that it is a total embarrassment for me to have spent so much time in solving the problem. Just yesterday I thought the above Premiss of astronomer 1-9 subplanets or 9-1 planets was a CounterExample.
Proof that OR is Non Commutative
The trouble here is a word language problem. OR is math's subtraction. However the word "subtraction" is a hideous word that leads everyone astray. The true word or term that math and Logic OR should have adopted and used is Remove. Math should have Add, Remove, Multiply, Divide.
We can say in math that of "Add 2 to 3", also we could say 2 AND 3. In math we can say "10 remove 4" but we cannot say "4 remove 10" because that violates a Axiom of math that Old Math was too stupid to realize it exists. The axiom that says you cannot take away more than what is available to remove or take away.
So, what is the Proof that OR is Non Commutative???
P OR Q
P = 10 with Q = 4.
Since OR is the same as the concept Remove we have
P remove Q, thus 10 remove 4 = 6
Now, someone asks for Q OR P
Q remove P, thus 4 remove 10, impossible, hence OR is Non-Commutative.
Proof that AND plus Not-Equal are Commutative and also Associative.
P AND Q is P add Q
P = 10, with Q = 4 and S = 1 for commutative and associative and since that is true in math it is true in Logic.
Proof that If-->Then is Non-commutative and Non-associative
----------------------------------------------------------------------------------------------
P = 10, Q= 6, S = 3
P divide into Q is not the same as Q divide into P
((P divide into Q) divide into S) is not the same as (P divide into (Q divide into S))
(Note to student, in a statement with parantheses, you have to do the inner most parantheses first, before the outermost parantheses)
So, well, that is settled, but, now, my textbook is deficient on talk of the proof method of CounterExample, and so I need to go back and look up a fine example of this proof method and include it in this textbook --- Elementary Logic.
Archimedes Plutonium<
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May 7, 2026, 12:02:21 AM (yesterday)
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So I have to go back and add on counterexample ideas for it is an important proving mechanism, especially in math.
Here is an old example of where a proposed counterexample is actually wrong and where the AP proposed proof is correct.
1) Proof that 1 is the Only Odd Perfect Number.
PROOF THAT THE NUMBER 1 IS THE ONLY ODD PERFECT NUMBER FOR THE
POSITIVE INTEGERS (1P). 1P was the oldest (or second oldest) unsolved
problem of mathematics until now. No mathematician until now has proved
1P.
PROOF: It is seen that a perfect number is a number p which the sum of
all its factors excluding itself equals p, and including itself equals
2p. Thus 1,6,28,496,8128, . . . are perfect numbers. The number 1 is
odd perfect since the factor 1 equals itself, and the factor 1 add 1
itself, equals 2. Representing perfect numbers in rational form since
the operations of division, multiplication, and addition are used in
the definition of what a perfect number is. Thus for 1 gives 1=(1/1)+0,
and for 6 gives 1=(1/2)+(1/3)+(1/6) and for 28 gives
1=(1/2)+(1/4)+(1/7)+(1/14)+(1/28). After 1, the next odd number is 3,
suppose 3 is perfect, so 1/3 and what rational numbers are needed to
make the sum equal to 1. No matter what these rational numbers are,
their combined sum must equal 2/3. So any combination of rational
numbers must add to 2/3 and so the 2 in the numerator requires when
finding the smallest common denominator which must equal to 3, that 2
is one of the factors of 3, because the combination of rational numbers
in order for all the numerators of all the terms to equal 1 puts a 2
in the denominator, implying 3 is even, a contradiction, so 3 is not
perfect. After 3, the next odd number is 5, suppose 5 is perfect, so
1/5 and what combination of rational numbers are needed to make the sum
equal to 1 is 4/5. No matter what these terms are (for example, for 28
these terms were [(14/28)+(7/28)+(4/28)+(2/28)], which is equal to
27/28, which when the numerators are changed into 1 where the
denominator is the smallest common denominator which has to equal 28)
their sum must equal 4/5 and so the 4 in the numerator requires when
reducing all the terms where the numerators of all the terms are
converted to the number 1, implies that a factor of 2, since 4 is even,
and thus a 2 is a factor of the denominator, but the denominator is the
odd number 5, a contradiction, so 5 is not a odd perfect number.
Applying the same argument to the next odd number after 5 which is 7,
and so on. Thus any odd number other than 1 in rational representation
requires that odd number subtract one for the numerator, and when
converting the numerators to terms of 1, implies the factor 2 since the
numerator is an even number, will go into the smallest common
denominator, implying that the original odd number is even, a
contradiction. A last example: take the number 105 and suppose it was
perfect, then 1 = 1/105 + (104/105). The term (104/105)= (x/105 +
y/105 + . . +z/105). The factor of 2 which is in 104 will go into the
denominator in eventually forming the smallest common denominator, just
like in the perfect number 6 where 1/6+5/6 is equal to 5/30 + 25/30 in
cross multiplication, likewise for 105 in cross multiplication,
104/10920 + 10816/10920 where the term 104/10920 implies that the
denominator is factorable by 2, then when converting all of the
numerators into 1 with the denominator as the smallest common
denominator which is 105 implies that 2 is a factor of 105, but 2 is
never a factor of 105 nor is 2 a factor of any odd number, thus a
contradiction, thus 105 is not perfect. Therefore 1 is the only odd
perfect number for the positive integers. Q.E.D.
The numbers 1 and -1, and 6 and -6 are the only four numbers which are
absolutely perfect. Because 6=3x2x1, 6=3+2+1, -6=-3x-2x-1,
-6=-3+-2+-1, and 1=1 and -1=-1. The number 28 and the other larger
perfect numbers are not absolutely perfect since 28=7x2x2x1, but
7+2+2+1=12.
Newsgroups: sci.math
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From:
Ludwig.P...@dartmouth.edu (Ludwig Plutonium)
Subject: Re: 1 IS THE ONLY ODD PERFECT NUMBER PROOF
Date: Mon, 23 Aug 1993 10:46:43 GMT
In article <2515i0$
9...@paperboy.osf.org>
ka...@dme3.osf.org (Karl Heuer) writes:
> You seem to be saying that the sum of odd/odd rationals cannot yield an even
> numerator. Here is a counterexample: 1/3 + 1/5 = 8/15.
No I do not mean that. What I mean is that if an odd number is perfect,
then when put into rational number representation, that the denominator
will have to be simultaneously odd and even, contradiction, proof.
Archimedes Plutonium<
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May 7, 2026, 12:27:19 AM (yesterday)
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Here is an example of a Counterexample in my proof of Collatz Conjecture.
World's First Proof of Collatz Conjecture// Math proof series, book 6
by Archimedes Plutonium (Author)
This is AP's 19th published book of science published on Internet, Plutonium-Atom-Universe,
And, early on, I noticed there was a need for a sequence that has the opposite behavior of Collatz-- internal trap of spinning around or divergence to infinity. Funny how no mathematician tackling Collatz ever seemed to look for a counterexample sequence like 5N+5 to compare to 3N+1.
Seeing the structure of 5N+5 and wondering how that can have internal spinning around in a trap and how it can diverge to infinity, and wondering why 3N+3 avoids all of that.
So, seeing there has to be two primal slides involved, I proclaimed the real Collatz conjecture involved 3N-3, 3N-1, 3N+1, 3N+3 written as 3N+-1 simultaneously 3N+-3. And that a conjecture on 3N+1 stand alone is not a viable conjecture. It is like saying 5N+5 never converges in any run to 1.
Alright, I should discuss this type of Collatz of 5N+5, for it shows us how a Collatz can have a "spinning around inside trapped in a spin". Such as 9 with 5N+5
9;;9, 50, 25, 130, 65, 330, 165, 830, 415, 2080, 1040, 520, 260, 130, 65, and spinning around endlessly.
Now let us check out 99 with 5N+5 and see if it diverges to infinity.
99;;99, 500, 250, 125, 630, 315, 1580, 790, 395, 1980, 990, 495, and as can be seen it keeps diverging to infinity, never descending.
May 7, 2026, 12:37:20 AM (yesterday)
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Here is another example of the use of Counterexample, only this time Karl Heuer is correct and straightening out Detlef Bosau.
My legal name at that time, 1994 was Ludwig Plutonium when this was posted to sci.math in 1994. Mind you I was testing people in sci.math to see if they could give a valid proof of Euclid's Infinitude of Regular Primes. For my proof of infinitude of Twin Primes was a mere tweaking by adding and simultaneously subtracting 1 from "multiply the lot".
Karl Heuer gives a correct Euclid IP, indirect method
Date: Sun, 20FEB1994, 21:05:13 GMT
Newsgroups: sci.math
Subject: INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS
Lines: 36
Sender:
k...@spdcc.com (Karl Heuer)
k...@ursa-major.spdcc.com (Karl Heuer) writes:
In article (
5JChA8g2...@jojo.escape.de>
det...@jojo.escape.de (Detlef Bosau) writes:
>
Ludwig.Pluton...@dartmouth.edu meinte am 18.02.94
>>
det...@jojo.escape.de (Detlef Bosau) writes:
>>>Wrong. Your two numbers are not necessarily prime
>>NO, YOU ARE WRONG. Those numbers are necessarily prime, due to
>>UPFAT, all the primes that exist in the finite set leave a remainder
>>of 1.
>I'll give you a lesson of elementary arithmetics. . .
I really shouldn't bother to get involved in this discussion again,
but
Ludwig is right. In logical terms, his key statement is "if P is a
finite set containing all the primes, then prod(P)+1 is prime." This
is
a true statement.
Let's step through your alleged counterexample:
>consider your set of primes to be: {2,3,5,7,11,13}, as I assert 13 to be
>the largest prime. [. . .] Now, you made the assertion, that
> > > > (2x3x5x11x13) + 1 [=30031] must be prime.
Yes, it's true that if 13 is the largest prime, then 30031 is prime.
Do
you disagree with that assertion?
>As you stated before, there exists an unique prime decomposition of
>30031. This is 59x509. It could be easily shown, that 59 and 509
>both are prime.
If 13 is the largest prime, then 59x509 is not a factorization of
30031.
--- end quoting Karl Heuer's post of 1994 ---
What Karl was pointing out to Detlef was an error in logical thinking. People in math are good at computation, but rarely good at logical coherent thinking for doing math proofs.
So I had a proof of Infinitude of Twin Primes by 1991 and started to broadcast it to the world general public by Usenet sci.math.
But troubles and problems appeared in 2009 and later. One problem was infinity concept was not well defined in Old Math, but made clear in New Math. The second problem is that I was working on Logic and found that the proof method of Reductio Ad Absurdum, (the indirect proof method) was not a valid math proof method. So my Old Math proof of suppose primes finite, reach a contradiction, then claim they must be infinite was not a valid proof. The logic truth tables of If-->then was such that it was TFUU with U being uncertain. Old Math was operating on a truth table of If-->then as TFTT. Quite a bit different from a truth table of TFUU.
Third problem in the decades after I proved prime conjectures and found the true numbers of mathematics are not the Reals, but instead are the Decimal Grid Numbers, which threatened to even make the concept of Primes as fake and vacuous. I discovered the true numbers of mathematics were Decimal Grid Numbers while writing my book series True Calculus in 2013.
Archimedes Plutonium<
plutonium....@gmail.com>
May 7, 2026, 12:45:49 AM (yesterday)
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These examples of counterexamples should be listed in my Intermediate Logic textbook for they would be too strenous for Elementary Logic.
This example is found in my proof of Kepler Packing.
World's First Proof of Kepler Packing Problem // Math proof series, book 3
by Archimedes Plutonium
This is AP's 24th published book of science published on Internet, Plutonium-Atom-Universe
Preface: There has been an alleged proof of KPP by Thomas Hales, but his is a fakery because he does not define what infinity actually means, for it means a borderline between finite and infinite numbers. Thus, KPP was never going to be proven until a well-defined infinity borderline was addressed within the proof.
--- quoting my 24th book---
One of the signs or signals that the below proof of the Keplerian 3D Packing and the Gaussian 2D packing is that both use the very same method of proof, whereas in our times, these alleged fake proofs are not able to incorporate the same method of Gauss in 2D from 3D. So this is the very highest
indication of alleged proof but in fact is fakery. If your 3D is not able to prove 2D, then you are pushing a fake.
Secondly the tell tale sign of a true Kepler Packing Proof is that it is do-able as a physical demonstration. In the below we can pack circles, spheres, oranges, ball bearings, magnetic circles and show the higher density of Corner-Edge-Hex or Corner-Edge-Hexagonal-Close-Pack or Oblong Hex or Oblong Hexagonal Close Pack in both 3D and 2D.
A physical demonstration of a more dense pack than the pi/sqrt18 is a CounterExample.
This maybe the first time that a Physics Experiment proves a unsolved Mathematical Conjecture, for which the mathematics community was unable
to prove in the Kepler Packing Problem and shows it to be wrong. Wrong because the most dense packing in both 3D and 2D Euclidean is the Oblong HCP or Oblong Hexagonal combined with the Corner Edge technique
respectively.
Call this proof the "Education of Archie on KPP" up till now. I had a mindblock
and bet most everyone else has this same mindblock when it comes to both KPP and Gauss's 2D version. The mindblock or paradox is that we think that N^3 number is larger than the number of spheres in KPP given any N. Well it is true for small N. Because 3^3 and no more than 27 spheres can fit in that cube or that 8^3 and no more than 512 spheres can fit in that cube. Likewise in 2D that no more than 9 circles can fit in 3^2 or no more than 64 circles can fit in a square 8 by 8. This is a mindblock that most everyone comes into packing problems with this paradox. They think and I thought that N^3 or N^2 was always larger than the number of spheres or circles in that packing.
Well at 10, which is the magic number, the experiments I conducted show
quite clearly that the number of spheres in a 10Cube are more than 10^3 and the number of circles in a 10Square is larger than 100. Most everyone that enters Packing enters it with the misconception that N^3 or N^2 are upper
limits to how many spheres and circles can be contained in 3D or 2D respectively. But at the integer 10 (it maybe 9 since my ruler is not that precise) that there is more spheres or circles than the N^3 or N^2 and the reason for this is due to the nesting inside of hollows of lower layers. And the reason for our misconception is due to our visualization that 10^3 or 1,000 small unit cubes completely tile the big cube with no holes or gaps in between those small unit cubes. Contrarily we visualize all those holes and gaps in the spheres or circles and we have a hard time of realizing that there could be more spheres and circles than unit cubes or unit squares.
This maybe the first time a Physics Layout of Data proves a Mathematical
Conjecture.
Experiment and Results: I have uniform magnetic circles of 25mm diameter.
Either at 9 or 10 for sure, is there an extra row of circles due to the hollows
of the hexagonal packing.
I need only show the Gaussian 2D Packing for it proves not only 2D but also
Keplerian 3D with spheres. The data is transferable from 2D to 3D.
I also have marbles but not of uniform size but close enough to gain this data:
HEX stacking pattern yield this data:
3Sq = 8 N^2 = 9 circle status = -1
4Sq = 14 N^2 = 16 circle status = -2
5Sq = 23 N^2 = 25 circle status = -2
6Sq = 33 N^2 = 36 circle status = -3
7Sq = 46 N^2 = 49 circle status = -3
8Sq = 60 N^2 = 64 circle status = -4
9Sq = 77 +8 N^2 = 81 circle status = +4
10Sq = 95 +10 N^2 = 100 circle status = +5
11Sq = 116 +10 N^2 = 121 circle status = +5
Notice that the number of circles at 9 changes from a negative status to a positive status due to the adding up of the hollow-nesting.
For about a week now, I have been looking for a function or equation to describe the Core Hex or Core HCP stacking but in that quest, I was under the misconception that it was always smaller than N^3 or N^2
I no longer need to find any such function or equation. The physical data proves the Gaussian 2D and the Keplerian 3D.
May 7, 2026, 3:24:54 AM (23 hours ago)
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Now Karl Heuer is a very very smart gentleman and rarely makes mistakes. So that forces me to go back and see if my explanation was all screwed up causing Karl to make a mistake.
And here is a revised edition to clarify my proof of No Odd Perfect Number, except 1. So Karl made the mistake because I was not clear enough in my proof.
PROOF THAT THE NUMBER 1 IS THE ONLY ODD PERFECT NUMBER FOR THE
POSITIVE INTEGERS (1P). 1P was the oldest (or second oldest) unsolved
problem of mathematics until now. No mathematician until now has proved
1P.
PROOF: It is seen that a perfect number is a number p which the sum of
all its factors excluding itself equals p, and including itself equals
2p. Thus 1,6,28,496,8128, . . . are perfect numbers. The number 1 is
odd perfect since the factor 1 equals itself, and the factor 1 add 1
itself, equals 2. Representing perfect numbers in rational form since
the operations of division, multiplication, and addition are used in
the definition of what a perfect number is. Thus for 1 gives 1=(1/1)+0,
and for 6 gives 1=(1/2)+(1/3)+(1/6) and for 28 gives
1=(1/2)+(1/4)+(1/7)+(1/14)+(1/28).
Notice in the even perfect numbers starting with 6, that the numerator has to end up with 5/6 + 1/6 to equal 1 and notice the 5 odd number before we add 1 to it, to be 6/6 = 1. Apply that idea to odd perfect numbers such as say if 3 were odd perfect you end up with 2/3 + 1/3 = 1. Or, contemplate 5 being odd perfect you end up with 4/5 + 1/5 = 1. So the most simple proof that no odd perfect number except 1 exists, plays on this numerator issue, for an even perfect, the numerator is odd before you add 1/n and for odd perfect the numerator is even before you add 1/n.
And for the even perfect numbers 6, 28, 496, for that numerator to be an odd number means that you have to add both even and odd numbers in the case of 6, we had 3/6 + 2/6 = 5/6. You cannot add two odd numbers to make an even numerator. In the case of Odd-perfect numbers beyond 1 itself, then you have to have a even number numerator in at least two even numbers of the summands in order to end up with a even number numerator. Suppose 7 was odd perfect then you need to end up with 6/7 + 1/7 to be odd perfect. And there comes the crisis, on how in the world can 7 have two even number factors. With Even-perfect number the numerator needs to be an odd number and thus, adding two odd numbers is even, adding two even numbers is even, but adding a odd with even is odd.
What proves No Odd Perfect number beyond 1, is the arithmetic fact that a Odd Perfect number is divisible and has a factor of a even number.
But I am not finished with this proof in a logic textbook. There is another very important issue that Logic needs to focus upon. The conjecture of No Odd Perfect number except 1 is a fairly simple conjecture that most grade school students can understand, especially High School.
In my Logic textbooks I made a glossary of well defined terms.
So for **Science** we have Statement, Concept, Hypothesis-experiments, Law-structure, Theory, Universal Axiom.
For **Logic** we have Statement, Premiss, Connector-structure, Reasoning, Equalities, Law-structure (some call them principles).
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory
In Logic, the Law Structure or some call them principles are the last and most general term. Occam's Razor is a Principle in Logic and basically it says that the easiest explanation is the true explanation.
If we look at the conjecture of No Odd Perfect number except 1, is a easy super easy concept to understand for High School students. And Occam's Razor in logic has a reverse concept. Which says something like this. If you have a conjecture that is simple in ideas, then its proof in math or in logic will be a proof not much longer than the statement of the conjecture.
What this means is seen in the Proof of Pythagorean theorem which is about a paragraph long. And the actual proof is one simple picture proof.
This tells us, that the conjecture of No Odd Perfect Number except 1 is about 1 paragraph long. That means the proof of that conjecture is also Simple, easy and about 1 paragraph long.
In 1993 when I first appeared in sci.math and posted my math proofs. I could just as easily posted this one paragraph proof that 1 was the only Odd Perfect number.
Proof:: Suppose 7 was odd perfect then you need to end up with 6/7 + 1/7 to be odd perfect. And there comes the crisis, on how in the world can 7 have two even number factors.
Now I bring that up also, because mathematics has many con-artist clowns such as Andrew Wiles with Fermat's Last Theorem, FLT and Thomas Hales with 4 Color Mapping. I say con-artist clowns because when we apply Reverse Occam's Razor, that a valid proof is about equal in length and in concepts as the statement of the conjecture itself.
But, Andrew Wiles has some obnoxious100 to 200 pages of a fake proof and uses everything but the kitchen sink to try to prove A^n + B^n = C^n has no solutions when n =3 or higher.
Andrew was just too dumb of a math person, to step back, and contemplate--- look, the conjecture is simple and easy--- Means the proof has to be simple and easy. There is a symmetry involved.
Whereas AP in 1993 gave a valid proof of FLT. AP's proof is of equal length and as simplistic as the statement is simplistic. AP Proof:: For a solution when exponent is 3 or greater, implies there exists a number in math which has the property of A+A+A = A^3. The reason we have solutions in exponent 2 is because 2+2 = 2^2.
As for Thomas Hales, if he ever took logic and passed it, would realize you cannot prove something in mathematics when your concepts are ill-defined. Kepler packing involves infinity, and Hales was too stupid in math and logic to well define what infinity means. It means a borderline exists between finite and infinite. That borderline is where pi digits have 3 zeros in a row at the 1*10^604 decimal place value. A hexagonal closed-pack is not the best packing. See AP's Kepler Packing Proof. But the point with Hales and with Wiles, is they are illogical and their proofs in math are doomed to failure.
A huge problem in math and science is the journal system. Wiles was a editor for a math journal, and this allows corruption to be publish and accepted as true, when Wiles FLT is garbage nonsense and so is Hales Kepler packing. It is good that the Internet came along when it did in the early 1990s, for then, the corrupt journal publishing --- you scratch my back, I scratch yours, is the reason physics is so full of garbage--- black holes, dark matter, dark energy, neutron stars, .....
Archimedes Plutonium<
plutonium....@gmail.com>
May 7, 2026, 3:52:10 AM (23 hours ago)
to Plutonium Atom Universe
So I am looking for CounterExamples for Elementary Logic textbook. My examples from math are far above the heads of most freshmen in college or university. No, I need simple examples.
One simple example of Counterexample is this in biology.
Person A: All birds fly in the air.
Person B: Not true, here is a counterexample-- the ostrich.
Many textbooks of logic and Wikipedia like to cite this as an example of a Counterexample.
Person C: All prime numbers are odd.
Person D: Not true, here is a counterexample-- the number 2 is prime and even.
But AP says that primes in math, Old Math is fake math. The true numbers of mathematics are not the Reals but the Decimal Grid Numbers, and the concept of primes is nonexistent in Decimal Grid Numbers. The problem with primes, is that they are Not Well Defined because primes are not closed to division. Addition and multiplication of counting numbers is closed because given any two counting numbers, add them or multiply them yields a another counting number. But take any counting number divide it by another counting number can yield no counting number, example 3/4, 4/3, 1/2, 10/3, etc etc. Primes are Not Well Defined over Division and that is why there is no general formula for primes and why primes never form a pattern. Primes are a garbage concept of Old Math. One of the prime reasons all math professors should take 2 years of college logic before they earn a degree in math.
A pretty example of Counterexample comes from geometry.
Person E: The slant cut of a cone is ellipse.
Person F: Not true, here is a counterexample for the slant cut of a cylinder is truly an ellipse and because cone and cylinder have different axes of symmetry, means the cone slant cut is a oval.
_--- quoting Wikipedia, the free encyclopedia---
_
_--- end quoting Wikipedia---
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Archimedes Plutonium<
plutonium....@gmail.com>
May 7, 2026, 5:31:12 PM (9 hours ago)
to Plutonium Atom Universe
Examples of counterexamples
---------------------------------------------
In geology
Person G: Continental Drift plate tectonics is all about convection currents in plate tectonics and subduction of plates.
Person H: False, for here is a counterexample of the plates in Mexico vibrating forward and backward caused by Earth two cores as a electric motor that vibrates.
In astronomy
Person I: All the planets spin axis is nearly perpendicular to the Sun's ecliptic and Earth's tilt of 23 degrees is the worst tilt.
Person J: False, Uranus is a counterexample as the tilt of Uranus is almost 90 degrees making Uranus revolve around the sun on its side.
In physics
Person K: All single atoms are written by their letters such as He for helium, Li for lithium, C for carbon, O for oxygen.
Person L: False, for hydrogen is a counterexample, because H for hydrogen is a subatomic particle and for hydrogen as a atom is written as H2 for all atoms have to have at least one neutron. H by itself has only a proton with muon inside, so that when 2 hydrogens form H2, then that is a atom because one proton converts into being a neutron to the other as proton.
In chemistry
Person M: All water molecules have the chemical formula of H2O.
Person N: False, the counterexample is water molecules with formula H4O when chemists stop being lazy and stop their water electrolysis by checking on volume of hydrogen gas to that of volume of oxygen gas, too dumb and too lazy to actually weigh the mass of hydrogen compared to oxygen to see that water molecules are truly H4O.
In paleontology
Person O: All Smilodon, saber tooth cats had enormous upper canine teeth.
Person P: False, the counterexample is that no such cat upper jaw has ever been found with the saber teeth attached, especially from the La Brea Tar Pits, making the observing scientist wonder whether museums are gluing or screwing walrus tusks onto normal cat upper jaws.
In Logic
Person Q: All Venn Diagrams of the complement of the union of two sets is the same as the intersection of their complements which is a DeMorgan law.
Person R: False for there is a pretty counterexample to all of Venn Diagrams and all of DeMorgan laws which simply says when you have the true correct numbers of mathematics as the Decimal Grid Numbers which are discrete and have holes in between one number and the next number, forming Space into grids. Then the Union and complement and intersection all fall apart along with DeMorgan Laws.
* * *
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Here is a 9 point space as a set. No-one can navigate that set with union or complement or intersection when all sets have empty space holes from one number to the next.
AP
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plutonium dot archimedes at gmail dot com. Looking for a College or University press to hardcover publish all 371+ AP books of science, likely to become 500-600 maybe even 700 books by the time I die. E-books are too prone to unbalanced-unhinged censor-editors, who can easily make your books vanish by pulling a switch. Science should never have gatekeepers, who thwart access to true science.
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Archimedes Plutonium
and which contain four right triangles whose sides are 
