366th,#366 AP book of science-- Elementary Logic // Teaching True Logic textbook series by Archimedes Plutonium This is AP's 366th published book of science published on Internet, Plutonium-Atom-Universe,PAU newsgroup is this. Please read this
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Archimedes Plutonium
May 1, 2026, 5:56:45 PM (13 days ago) May 1
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Elementary Logic // Teaching True Logic textbook series
by Archimedes Plutonium
This is AP's 366th published book of science published on Internet, Plutonium-Atom-Universe,PAU newsgroup is this. Please read this textbook for free on Internet.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Cover Picture: my photograph 011.out-west20yrs.gif. A picture of me either out West on vacation or in Florida on school break, not sure of where the picture was taken, sucking on cactus for water to experiment and see if I could get a drink, and although it has nothing to do with me taking Logic classes at University of Cincinnati, 1968-1972, the logical mind is always engaged in logical activities. Now-a-days such activities are banned for people are indiscriminately killing too many cacti in the wild. Sometimes, logic is not the same as wisdom, for I would never kill a cactus just to learn something about it.
I am researching Reincarnation as per science, and in the year 2025, I attempted to prove reincarnation by grafting elm, ash, blackberry, spruce and various species onto different species. I had read that only cactus grafting--different family-genus-species has been successful to date, and for the special reason that the graft does not dry out, for cacti are full of water. This year, 2026, I am going to switch rootstock with scion, for in 2025, I was using just angiosperm (flowering plants) rootstock and this year I use gymnosperm (spruce, pine) as rootstock thinking they hold water better. The year 2026, I hope to graft two different phylum of blackberry onto spruce.
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Table of Contents
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1) Introduction.
2) What is Science and a list of terms used in science.
3) Logic is the "Scientific Method".
4) Logic is the Science of Ideas.
5) Math is the science of numbers-algebra and geometry figures.
6) Both Logic and Math are precision sciences; math uses sigma-error and logic uses truth-tables.
7) A lesson on Calculus derivative and integral in order to understand Existential and Universal quantifiers.
8) What is truth and falsehood and partial-truth in truth-tables of Logic.
9) The Existential quantifier.
10) The 6 connectors of Logic resemble math 6 operators.
11) The Not-Equal connector.
12) The AND connector.
13) The OR connector.
14) The IF-->Then connector.
15) The Universal quantifier.
16) Principle of Least Energy of Physics is the Occam's Razor Principle of Logic.
17) Why logic is so important for science, for you will never be a good scientist without skills in logic.
18) Completeness and Consistency in Logic.
19) The short Logic Argument, the syllogism.
20) The long Logic Argument.
21) Fallacies of Logic, including fallacies of Venn diagrams.
22) How Logic can help you live a better life.
Archimedes Plutonium
May 1, 2026, 9:15:47 PM (12 days ago) May 1
to Plutonium Atom Universe
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1) Introduction.
This textbook is designed for 1st year College, or 1st year University, as increasingly, the school systems of the world fail to train students on how to think straight, clearly and correctly. Students who take Logic have a better chance of thinking straight and clear.
When writing this book I had hoped I could teach it in High School. But near the end of writing this book, I realized it was too much above the heads of High School students who had little science experience, especially physics and especially calculus. I was a High School teacher of math myself, teaching in Australia in late 1970s and if there is one thing I despise most of all in education is teaching students a topic that is over their heads. I am determined to write a textbook of Logic for High School, only not now. This book is over their heads and so, in the near future I will come back and write the True and Simple Logic textbook for High School. But because these logic textbooks of Elementary, Intermediate, History of Logic, and Advanced Logic have taken so much time and energy out of me, I need a vacation of many months, even years to start the High School logic textbook.
So much of our life depends on making sound reasoned good decisions and this is what Logic is especially good at making those sound reasoned decisions. Many of us grew-up as High School students watching Star Trek with Dr. Spock, famous for Logic. Science depends on logic and may as well learn logic in college and university if you take a-lot of science or math. In fact, I insist that every student of science in college or university, wanting a science degree, should mandatorily be forced to take 2 years of college logic to attain that degree. To me, this is just plain common-sense.
To think straight and clearly, especially on seeing that we have mostly anti-science people in office in the USA-- president, secretary of health in the USA as of 2026, when, it was science that raised the USA above other countries. We have an anti-science president in office who attacks clean electricity and medicine and health care by wanting drill drill drill fossil fuel and do away with clean air, clean environment. Who thinks more money is better than a healthy body, clean air and environment. Who has a health secretary that eliminates vaccines and destroys the health care system of the USA. A president that recently claimed in a speech-- that Wind Farms producing electricity, clean energy, that every time the blade makes one revolution "...is the throwing away $1,000. dollars". While any logical president would understand the reason we make money in the first place, is for our life to be---- in a clean air, clean environment.
The factual reason that America USA became a superpower is due in large part with its Founding Fathers who were mostly Logical Scientists-- Ben Franklin the great electricity-physicist. USA is great because of Science and the logic that makes science. But now, USA is turning into decline and decay with the worst anti-science president ever to walk the White House, Dondolt Trump. I say dolt, because he thinks more money is better than living in clean air and a clean environment. Who thinks Russia should invade and conquer Ukraine and take all of Ukraine, not understanding that if Ukraine falls to Russia, that the USA itself falls and that Russia + China take over the world. The fall of Ukraine to Russia, automatically puts the USA no longer in 1st place as power, but in isolation and a fallen power. Especially as the international currency which is now the USA dollar is replaced by the Chinese Yuan and the USA falls into a Greatest Depression, reeling from the fact that the dollar is worthless, along with a anti-science president.
When people are ___not logical___ they democratically vote into office anti-science fools that go about destroying their country.
I am showing this logic textbook as being approximately 250 pages which is of good size. I feel that short textbooks are far more valuable than long ones. Copi's textbook, "Introduction to Logic", 1972, 4th edition, is 540 pages long with a few diagrams but no pictures. I believe in the old saying "pictures are worth a thousand words". Although I have few pictures in my own textbooks, is because this medium is difficult to allow pictures, and mostly, my only available pictures are ascii-art.
I recommend this as the 1st year college or university textbook on Logic. It is the first Logic textbook ever written that has all the 6 connectors of Logic all correct. The Old Logic with Boole and Jevons and all their successors never had any of the 4 simple connectors--- AND, OR, Equal-Not, If-->Then, not a single one of them correct.
In order for anyone to write a textbook on Logic, first of all, needs to have a Logical-mind. That certainly makes sense, that a person to write a textbook on Logic needs to have a logical mind in order to do so.
I recommend that all science students in college and university, mandatorily be required to take 2 years of college logic before receiving a degree in science, perhaps even engineering. For the point of college and university is to help our young scientists think straight, clear and correctly.
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. Answering any questions about calculus. For Logic needs the math calculus for understanding the Existential and Universal quantifiers relationship. Logic and calculus are inextricably intertwined, and I cannot do a good job of logic without bringing in calculus.
I went to High School at Anderson High School and Wyoming High School both near Cincinnati Ohio. Two years at Anderson and my last two years at Wyoming, in Wyoming Ohio.
I am definitely sure that without this education from two schools devoted to teaching proper science, that I would never have become King of Science with the Atom Totality theory of the Universe and that the true electron of atoms is the muon, and not the 0.5 MeV particle. Anderson taught me my strength was mathematics and Wyoming taught me this love of physics, even though I rarely understood this new type of physics textbook in High School called PSSC. I remember having a guest over the house who was a physics teacher himself from a nearby High School and asked him to solve a problem for me in this PSSC textbook, and he could not, baffled himself over the writings. For it was a physics book that can be appreciated in 1st year college but not in High School. An example of "teaching over the heads of students".
Around 2016, I have been insisting that every student wanting to become a scientist, engineer, or teacher of science to have to take mandatorily 2 years of Logic in College or University to get a degree in science or engineering, to help them think straight and think clearly and correctly.
Not surprisingly, at my own alma mater University of Cincinnati, 1968-1972, they required mandatorily that those becoming-lawyers had to take a year of Logic. I suppose to help them think straight and clearly in defending or prosecuting a case.
Writing these 4 textbooks on Logic has been my most challenging writing of all the 365 books so far written. Part of that difficulty is due to the fact that logic before AP had all 4 of the simple connectors of Logic all wrong and full of errors. So I have to start from scratch to tell what true logic is. An overhaul of a subject is difficult to write a textbook on because, otherwise, if not a overhaul requires only addition to existing books. But another component of that difficulty is the fact that writing a logic textbook has to be written logically, much like a proof in mathematics is a step by step revealing of the truth. Writing a physics or math or other science book has no step by step constraints.
Obviously, I could not insist that all science majors in college take 2 years of mandatory logic when there is no textbook on logic which has the 4 most simple connectors of Logic all correct-- AND, OR, Equal-Not, If-->Then. Not much point on insisting taking Logic when no textbook has a correct logic. And that is the purpose of me; writing these 4 textbooks.
We all know that Mathematics has 6 operators of Add, Subtract, Multiply, Divide, derivative of calculus and integral of calculus. In the same matching of math operators we have 6 connectors of Logic. We call them connectors because they connect, not numbers but ideas. For Math is about numbers and we replace numbers with ideas and call it logic. The 6 connectors that relate to the 6 operators in that above order is AND, OR, Equal-Not, If-->Then, Existential quantifier, Universal quantifier. These 6 connectors will be discussed in detail in later chapters.
I started writing science books beginning 2019 and average about 1 book per week. But these 4 logic textbooks alone consumed a full year and much more of my time and still no end in sight of completion of May 2026. And just when I thought I was near the end in January 2026, up pops this OR connector riddle that forces me to rewrite all over again. Then in April of 2026, just when I thought I was complete, up pops the need of a word-term glossary of special terms used in this textbook.
Patience, patience and I will get to the end. For writing these Logic books is one of my most important chores of my life, seeing how awfully wrong is academic logic, almost caveman logic.
Since about 2016, I have been pleading that colleges and universities across the globe force science and perhaps engineering students to take 2 years of college Logic before they earn their degree in science and engineering, to help them think straight and think clearly. I am reasonably sure that colleges and universities will take me up on that plea. And in that regard, I write this Logic textbook for first year of college or university. Later on I will write a much more simple Logic textbook to use in High School. Some countries across the globe have a different name for High School-- England and Australia call it "Form". Whatever it is called, schooling in logic before going to college or university is what I am looking to write in the near future, one that is not over the heads of High School students.
Tracing back into my own personal history. I do not know when the first time I heard of the word "Logic". I do recall, vividly, a TV series that was science fiction and a rage at the time of Star Trek in late 1960s. And Dr. Spock the Science officer and Logic officer. Spock said "Logic is the beginning of wisdom, not the end of it".
To be logical, meant being "smart". To be illogical, meant being dumb.
I write this book of Logic for a textbook in 1st year college, university, to those students who know they want to be a scientist, a doctor, or engineer to help them navigate the world by better thinking straight and thinking clearly, and thinking correctly.
Good luck.
2) What is Science and a list of terms used in science.
So let us start with teaching logic, for logic is a science and we first must well define what is science.
Science-- has a method called the Scientific Method. It is the gain of knowledge of the world by observation and experiments and careful reasoned logical ideas. Science uses math for precision and accuracy. Science uses Logic for precision and accuracy of ideas. Science is the only knowledge that can predict the future by the patterns of the law-structures such as the Atomic theory and electromagnetism forces. For example, watching Artemis 2 astronauts recently go around the Moon is predicting the future of the spacecraft, knowing the physics. Physics is the top science for it has the most experiments and law-structures of electromagnetism.
Logic is another science but much lower of importance than physics. Logic is the science of precise and accurate Ideas, while math is the science of numbers and geometry figures, Logic is the science of Ideas.
Logic is the science of Ideas, while math is the science of numbers and geometry figures.
Math is the lowest of sciences for it is that of precision and accuracy when using quantity, measure, formulas and geometry. Math actually is the easiest of the sciences and not only the lowest of the sciences. The only reason that math is difficult today as of April 2026, is that the math community uses the fake numbers of Reals and uses a fake calculus. In New Math of AP, all calculus textbooks can be reduced to 300 pages instead of the recent Stewart calculus textbook, his 5th edition, 2003 of over 1168 pages. The reason he needs so many pages is because he is in "fake calculus" that uses Reals, never understanding that Polynomials are the only valid function and thinks the derivative is a tangent line to the function graph at a point. No wonder Stewart could never do a geometry proof of Fundamental Theorem of Calculus, mired down in all those phony ideas.
Logic has had its share of horrible mistakes, in fact, the AP textbooks on Logic are the world's first logic textbooks that has all the 4 simple and the 6 crucial Logic connectors taught correctly, I am speaking of Existential quantifier, Equal-Not, AND, OR, If-->Then, Universal Quantifier. By studying Logic, you will learn about these 6 connectors in future chapters of this textbook.
It is a sad and horrible reflection that not one single logician in modern times had AND, OR, Not-Equal, If-->Then correct. Some prefer to write Equal-Not and I prefer to write it Not-Equal, it is your choice which you like.
In fact so ludicrous is Old Logic that they thought OR is addition as can be seen inside the front cover of Copi's logic textbook, 4th edition, 1972 where he writes
as Rules of Inference
9. Addition (Add)
p
therefore p or q
That entails... that means that Copi thought that AND is subtraction.
Example: Imagine that if I said to you "Tonight for dinner I will eat spaghetti and tonight for drink, I will drink orange juice. Question to reader, does the AND in that sentence sound like subtraction or removal to you? No, the AND sounds more like addition.
No wonder that people in math, especially math professors could never do a geometry proof of Fundamental Theorem of Calculus nor could tell the difference between a ellipse and a oval, because, well, they had no logical mind to even understand that AND has to be addition and OR has to be subtraction as remove. Remove either p or remove q.
Example: For dinner tonight I will eat spaghetti, or, I will eat a bacon, cucumber, tomato sandwich. Reader, does that sound like the OR is addition? No, it sounds like the OR is remove one of the items; subtract one of the items.
Logic is the science that helps you Think Straight and Think Clearly, and woe to any scientist who is bad in logic. But woe to any person who is not logical for life will have many stumbling blocks and losses to those that are illogical.
In my last chapter of this textbook, I start a conversation on using Logic to live a better life.
This is why I insist in College and University for all science majors to have 2 years of logic study, mandatory.
So, take the simple Logic test, right here, right now. What is the slant cut of a cone, a right-circular cone? As shown in the pictures below.
This is your first homework assignment in class. Write a one page paper on whether the slant cut of Cone is ellipse or is it a oval, and why you think so.
--- quoting Wikipedia on Conic Section, for the editors never allow the truth of science into any of their entries of science in Wikipedia, not even a simple geometry of slant cut of cone is it oval, or is it ellipse---
--- quoting Wikipedia, the free encyclopedia------ end quoting Wikipedia------ end quoting Wikipedia---
Archimedes Plutonium
May 1, 2026, 9:31:20 PM (12 days ago) May 1
to Plutonium Atom Universe
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.
Now I am going to interpret those 6 steps of the Scientific Method and then give them a term name, afterwords. The reason I do this is to form a well-defined list of terms most often used in science, logic and math. Logic is precision and accuracy and you do not have that if the words you use are not well-defined.
I repeat again the 6 connectors of Logic will be discussed in detail in later chapters, but I introduce the 6 here and now to well-define science, logic, math terms. The 6 connectors in order are Existential quantifier, Not-Equal, AND, OR, If-->Then, Universal quantifier.
From the Scientific Method above
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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. AND is like math add and you build a structure of ideas.
Step 5-- Analyze data and deciding experiment-- OR connector --- call it theory or principle. The idea is that you pare-away ideas that are not good enough to become universal for a theory and principle has to be universal.
Step 6-- Draw conclusion -- Universal quantifier --- call it Universal Axiom.
The Universal Axiom over all sciences is --- All is Atom, and Atoms are nothing but electricity and magnetism.
So how do I feel about the above calling them those terms? 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 I know that OR is the decision-maker for the deciding experiment, removing one experiment in favor of another experiment, that differentiates what is universal and not universal. Leaving the Universal quantifier as the Summary for science such as say physics or chemistry or biology.
Now let me list those name terms above.
Terms for science, especially physics but all the other sciences included.
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(1) Statement-- Some call them fact or facts.
(2) Concept -- A collection of statements, that is a collection of facts.
(3) Hypothesis-- Some call them implies as in material implication, some call them prediction.
(4) Law-structure-- Some call them Principle--- these are borne from experiments especially physics. Just today in 21April2026 I am reading a National Geographic of May 2026 issue titled "Secrets of the Bees" with loads and loads of experiments performed upon bees, and was stunned to find out that humanity was spraying the bees to get rid of mites, but the spray itself was killing the poor bees.
(5) Theory-- Is a collection of law-structures or principles.
(6) Universal Axiom-- Is a summary of the total science.
For the science of Physics, this axiom says--- All is Atom and Atoms are nothing but electricity and magnetism. The Universal Axiom for Biology which includes Bees is very much different than the one for Physics.
The last one is a big surprise to me, for I had called it Primal Axiom for many years in Usenet and newsgroups that I had posted to from 1993 through 2026, but now it is the Universal Axiom. I suppose Science ends with a summary, each science having a summary and for Physics, 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 human society with their jurisprudence and the law enforcement can have "law" all for themselves and science use "principle"-- Faraday principle or Ohm principle the gravity principle. You see, I hate it when ordinary language uses the term "law" to mean something far different than what science means when it says "law". For in science, laws are universal, not man-made-- here today-gone tomorrow.
Terms for Logic
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(1) Statement-- An idea which is either word or sentence algebra or picture-image which can have various truth values, T, F or partial T, partial F.
(2) Premiss--Checking the statements to see if true by best science on the subject matter. A statement is a raw, unvalued for truth idea. Once a statement is evaluated by science it is given a truth value. And premisses are statements of a large percentage of truth.
(3) Connector-structure -- This is easy for these are the 6 connectors of logic-- Existential quantifier, Not-Equal, AND, OR, If-->Then, Universal quantifier. These are similar to the 6 operators of mathematics.
(4) Reasoning, Discourse, Argument, -- a collection of premisses leading to a conclusion, the smallest is a 2 premiss argument 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.
(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 not have add equals to subtraction nor does math have that addition equals multiplication for these are independent operators. 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.
(6) 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.
Terms for mathematics
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(1) Statement-- Either in number algebra written out in symbols or numbers, or a picture of geometry figures.
(2) Axiom (some call them postulates and not to be confused with principle)-- Accepted statements without proof. In science we get to doing mathematics and we come to where we have to agree on truth that is common-sense and not able to be further analyzed, and so we accept them fully as true. Axioms such as add, subtract, multiply, divide, differentiate, integrate, and the proof deduction mechanism are accepted without any further analysis.
(3) Operator-structure-- These are the 6 operators of mathematics-- add, subtract, multiply, divide, derivative of calculus, integral of calculus.
(4) Proof -- Is a stepwise deduction using axioms and other data. The logic reasoned-argument becomes the math proof.
(5) Theorem -(corollary-is a smaller theorem)-- Is a statement with a given deductive proof, step by step proof.
(6) Theory-- The summary of parts of mathematics such as a geometry theory or algebra number theory or probability theory or set theory even a total mathematics theory.
Bizarrely, or should I say awesomely, that there appears some spin rotation in these crucial terms of science, logic, math.
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
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 word-sentence form or picture-image form, and for math that would be a sentence of number algebra or geometry figure image.
So now, as I go further into this textbook, I will use those terms above, even though other scientists are rather loose on terms and thereby making mistakes. When I quote other authors they usually are loose on terms, the most often mistakes are such as calling Darwin Evolution as a theory when it is at best a hypothesis. Because in the 20th century, quantum mechanics of physics found what is called quantum entanglement or "superdeterminism" proving Darwin Evolution is a hypothesis at best.
Archimedes Plutonium Jan 8, 2026, 8:47:56 PM to Plutonium Atom Universe newsgroup.
What is Science????
Feynman in his Lectures on Physics, 1963, on page 1-1 defines it as "The test of all knowledge is experiment."
I am going to add more to that.
Archimedes Plutonium Jan 9, 2026, 1:18:02 AM to Plutonium Atom Universe newsgroup.
On Thursday, January 8, 2026 at 8:47:56 PM UTC-6 Archimedes Plutonium wrote:
What is Science????
Feynman in his Lectures on Physics, 1963, on page 1-1 defines it as "The test of all knowledge is experiment."
Let me fill in more of Feynman's definition of "Science" for it is a good one. Far better than the mish-mesh cacophony ignorance that Wikipedia says of science, for Wikipedia science entries are mostly written by failures of science attempting to redeem themselves by writing science entries-- "Oh, I failed science but look, I wrote and have the Wikipedia entry on these science topics". For 95% of science, math, logic entries in Wikipedia is trash.
--- quoting Feynman, Lectures on Physics, 1963, page 1-1 ---
The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth". But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations---- to guess at the wonderful, simple, but very strange patterns beneath them all, and to experiment to check again whether we have made the right guess.
--- end quoting Feynman, Lectures on Physics, 1963, page 1-1 ---
AP writes:: In a sense, Feynman defines "What is science?" and in that paragraph, he outlines what is called in science, the "Scientific Method". We explore in more detail the Scientific Method in the next chapter. We can expand on Feynman's definition of science, such as for instance the idea of Superdeterminism of an Atom Totality. Where all ideas are fated to happen when they do happen, no free-will in the world, hence, no guessing. More on superdeterminism later for it is __an extremely complex idea___, but quantum physics has proven it true.
Let me stop here and give a list of terms often used in this book and in science.
List of terms used in science
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Terms for science, especially physics but also other sciences
----------
Statement
Concept
Hypothesis
Law-structure (principle)
Theory
Universal Axiom.
Terms for logic
-------
Statement
Premiss
Connector-structure
Reasoning (discourse, argument, syllogism)
Equalities
Law-structure
Terms for mathematics
-------
Statement
Axiom (postulate)
Operator-structure
Proof
Theorem (and corollaries)
Theory
Let us look more closely at some of these terms for science, especially physics but also other sciences.
Statement
------------
A statement is a fact of observation or an idea in mind stated formally in a sentence or picture or even a math formula.
Concept
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A concept in science is a collection of statements and ideas on a subject matter of science.
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.
Experiment
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An experiment in science is a set-up where you make observations in order to try to figure out what the patterns of the world are. We often call this-- the seeking of knowledge.
Law-structure
--------
Now I call it "law-structure" as to move it away from the use of "law" in civil society of justice and law enforcement. In science, the word "law" is far different from law in civil society. And it is my hope that some day we can drop the word "law" altogether and just say "structure", or perhaps say principle, like the structure of gravity, or the Faraday structure or the gravity principle or the Faraday principle.
There are few Law-structures in 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. In geology there is the cores of Earth as electric dynamo law-structure and there is Continental Drift law-structure. In biology there is the cell law-structure or the cell principle. There is the DNA principle that it is configured to be what Light-waves are in physics.
Law-structures (principles) are universal and are experimentally proven true.
Of course we should never be confused with civil laws for society, made-up by humans to live in peace and justice. I was hoping to find a term to get away from human made up laws. The best I can do here in April 2026 is "law-structure" and hoping that in the future, we can drop the world "law" altogether and just call it structure.
Principle of science is a law-structure.
-----------------------
A principle of science is a description of some topic in science. Principles are law-structures but have more of a description accounting, rather than a active motion of objects in that principles describe objects while law-structures are listing the forces and actions and motion of objects. For example in physics the Pauli Exclusion principle or the Uncertainty principle; in biology the cell or DNA principle; in chemistry the Aufbau principle; in physics the Superposition Principle and Complementarity Principle.
Theory
--------
Theory is a term that should seldom be used in conversation, because the definition of theory is a collection of law-structures of a science such as physics, the electromagnetic law-structures 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 law-structures. Optics of physics is a theory because it is a collection of EM law-structures. In geology we have the Continental Drift theory for electromagnetic law-structures cause Earth cores to vibrate and cause plates of crust to rise by electromagnetic force. In biology, there is Cell theory for it uses some of the EM law-structures, but Darwin Evolution is a rule and not a theory-- perhaps a hypothesis or maybe a concept at best, but not a theory, because "natural selection" "the fittest fit" is its mainspring and that is not a electromagnetic law-structure underpinning it. Superdeterminism replaces Darwin Evolution in biology.
Most people not in science confuse what is a Law-structure and what is a Rule. A law-structure works always and is universal, yet a rule works only sometimes not all the times. In Old Physics, their Ohm's law 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. 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.
A closer look at terms for Logic.
-------------
Terms 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.
A-lot of ideas in those two sentences, but no ideas that stand true when we have science judge the truth value. In other words, that statement is a nursery rhyme fiction and cannot pass into being a premiss of logic.
Premiss
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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.
Connector-structure
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These are the 6 connectors of logic-- the Existential quantifier, Equal-Not, AND, OR, If-->Then, Universal quantifier.
Reasoning
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Reasoning is the action taken when we assemble ideas into what some call a argument of logic or a discourse of logic, and the smallest of these arguments is the Syllogism which is just 2 ideas as 2 premisses that arrive at a conclusion. Math calls the Reasoning process as a "proof".
Equalities
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Equalities, are 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.
Law-structures of Logic
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A summary of Logic in broadest form is law-structures of logic. The Existential Instantiation and Existential Generalization and Universal Instantiation and Universal Generalization and Occam's Razor are the law-structures you will learn in more details in later chapters. A law-structure in Logic is like a theory in physics.
Looking closer at the terms of mathematics.
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Terms for mathematics
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Statement
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A statement in math is a sentence or sentences which is to be investigated as a axiom or to be proven true by stepwise deductions.
For example, the statement: The volume of any prism is Base area times height.
Axiom-Postulate
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These are statements accepted as true by common agreement for they have no proof available but accepted as common-sense. For example: Two points determine a unique straight line segment.
Proof
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In math we are given a statement and if not a axiom, we must prove it to be a true statement in a stepwise deduction using axioms or theorems. A proof can be a single picture like the Pythagorean theorem proof or can be thousands of step lines long covering an entire book. AP's proof of 4-Color-Mapping or proof of Fermat's Last Theorem are thousands of steps long.
Theorem and corollary (smaller theorem)
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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. Shown below this list of terms.
Corollary is a smaller proof 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 or science, and the law-structures of electricity and magnetism.
Some people confuse Theorem of math with theory of physics.
Theory of Math
-----------------
Math has theories and they are broadly speaking a collection of theorems of a subject matter specific to math. There is Number-algebra theory, and there is Geometry theory and Probability theory and there is Set theory to name just a few.
Many people get theory of math mixed up with theory of physics or science. The easy way to know the difference is that a science requires you to do Experiments in the Scientific Method, while math never requires you to do experiments but instead, inspect the Axioms should something becoming puzzling and go wrong.
--- end of list of terms for science, logic, and math ---
Most people not in science confuse what is a Law-structure and what is a Rule. A law-structure works always and is universal, yet a rule works only sometimes not all the times. In Old Physics, their Ohm's law 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. 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.--- quoting Wikipedia---Proofs using constructed squaresRearrangement proof of the Pythagorean theorem.
(The area of the white space remains constant throughout the translation rearrangement of the triangles. At all moments in time, the area is always c2. And likewise, at all moments in time, the area is always a2 + b2.)Rearrangement proofsIn one rearrangement proof, two squares are used whose sides have a measure of and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. In the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. Each outer square has an area of (a + b)2 as well as 2ab + c2, with 2ab representing the total area of the four triangles. Within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. These rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom-left corner, and another square of side length b formed in the top-right corner. In this new position, this left side now has a square of area (a + b)2 as well as 2ab + a2 + b2. Since both squares have the area of (a + b)2 it follows that the other measure of the square area also equal each other such that 2ab + c2 = 2ab + a2 + b2.
--- end quoting Wikipedia---
and which contain four right triangles whose sides are Archimedes Plutonium
May 2, 2026, 3:20:59 AM (12 days ago) May 2
to Plutonium Atom Universe
On Saturday, February 14, 2026 at 10:50:59 AM UTC-6 Archimedes Plutonium wrote to Plutonium Atom Universe newsgroup:
Let me expand on Feynman's definition of science where he emphasizes the huge role of Experiment. And although throughout his life, Feynman, especially his book "The Character of Physical Law" 1964, does not really go into details of a good example of where Experimentation is the heart of science.
So in my long history of doing science, I found the very best example of showing where the Experiment--- as the heart of science-- what it means. It follows the Feynman "The Character of Physical Law" where he talks about gravity on page 4 and gives its formula as this.
F= G (M*M') / r^2
I am going to doctor his formula to make it more clear.
Force = (G a constant) ( Mass_1 times Mass_2) / (separation distance of masses)^2
Now, in my life, the very best experiment I have seen concerning the verification of the Universal law-structure of gravity as displayed above, comes from a rather unusual and outstanding source of a brilliant lady mathematician and physicist of France--- Madame Emilie du Chatelet 1706-1749 a friend of the famous writer Voltaire.
Women are seldom given credit in the world of science as we well know the genius of another French-Polish lady scientist-- Madame Curie. Well, Emilie was another genius scientist. For Emilie, stood head to head alongside Newton, Leibniz, Gravesande, and even showing where Newton was wrong on his own Universal Law-structure of Gravity, the gravity principle.
Emilie could be considered as a science-reporter-journalist of her time, translating and adding on to the explanation of Newton's Law-structure of Universal Gravity.
And the reason I pick the Law-structure of Gravity is to later on use this example to clarify UG, Universal Generalization and then UI, Universal Instantiation, and then EG, Existential Generalization and then EI, Existential Instantiation, __clarify Logic of Existential and Universal quantifiers____.
So the brilliant experiment that Emilie set up, incomparable to this day, in my humble opinion, and which I want to set up in this Logic classroom, is totally brilliant. If not able to set up then, at least, watch the PBS NOVA film.
What she did can be seen in a NOVA TV show, where she takes a large ball on a stand with clay underneath and lets the ball drop from 2 different heights. If Gravity is inverse square, the hole impression made by the ball falling is going to be 4 times bigger because of inverse square in denominator.
--- quoting NOVA on the lady physicist Emilie Du Chatelet with some AP edits---
NARRATOR: Emilie du Châtelet would have a huge effect on physics in her tragically short lifetime. Unheard of, for a woman of her time, she would publish many scientific works, including a translation of Sir Isaac Newton's Principia, the greatest treatise on motion ever written. Du Châtelet's translation is still the standard text in France today.
TUTOR (Dramatization): Musa, mihi causas memora?
CHARLES: Muse, my memory causes...?
EMILIE DU CHÂTELET: "O Muse. The causes and the crimes relate; what goddess was provok'd, and whence her hate; For what offence the Queen of Heav'n began to persecute so brave, so just a man."
EMILIE'S FATHER (Dramatization): Do not be cross with your sister because she persecutes many a just man. Only the other night Emilie silenced the Duc du Luynes when she divided a ridiculously long number in her head in a matter of seconds. You should have seen the incredulity on their faces when they realized Emilie was correct.
CHARLES: Was it my sister's astounding intelligence or her boundless beauty that made their mouths gape, I wonder?
EMILIE'S FATHER: Ah well, yes, you have a point, Monsieur.
EMILIE DU CHÂTELET: Messieurs, I thank you for your kindness. I fear, however, that my wit is only a curiosity to others. If only my mind was permitted opportunity.
EMILIE'S FATHER: My dearest, Emilie. You are blessed with intellect and courage. Use them both and the world will fall at your feet.
JUDITH ZINSSER (Du Châtelet Biographer): In one sense, she is a woman utterly out of her true time and place. She is a philosopher, a scientist, a mathematician, a linguist. She demands a freedom that women didn't begin to enjoy until over 150 years later, a freedom to study science, to write about it and to be published.
NARRATOR: Du Châtelet married a general in the French army at age nineteen and had three children. She ran a busy household, all the while pursuing her passion for science. She was 23 when she discovered advanced mathematics. She enthusiastically took lessons from one of the greatest mathematicians of the day, Pierre de Maupertuis. He was an expert on Newton, and she was his eager young student. It seems they had a brief affair. But then he set off on a Polar Expedition.
Du Châtelet then fell passionately in love with Voltaire, France's greatest poet. A fierce critic of the King and the Catholic Church, Voltaire had been in prison twice and exiled to England, where he became enthralled by the ideas of Newton. Back in France, it wasn't long before he again insulted the King. Du Châtelet hid him in her country home.
CHARACTER (Dramatization): The poor little creature is devoted to him.
NARRATOR: Isolated far from Paris, Du Châtelet and Voltaire turned her chateau into a palace of learning and culture—complete with its own tiny theatre—and all with the apparent blessing of her husband.
PATRICIA FARA: There is a great deal of myth surrounding Du Châtelet and her love life. And most of it is very exaggerated. But her husband did accept Voltaire into his household, and he often went to Paris on behalf of Voltaire. He went to his publisher to plead Voltaires' case, to keep Voltaire out of jail. And it is also true that Emilie Du Châtelet did have several affairs of a fleeting nature.
JUDITH ZINSSER: She created an institution to rival that of France's Royal Academy of Sciences. Many of the great philosophers, poets and scientists of the day visited.
EMILIE DU CHÂTELET: Ah, Monsieur you are young. I hope that soon you will judge me for my own merits or lack of them, but do not look upon me as an appendage to this great general or that renowned scholar. I am, in my own right, a whole person, responsible to myself alone for all that I am, all that I say, all that I do.
NARRATOR: Du Châtelet learned from the brilliant men around her, but she quickly developed ideas of her own. Much to the horror of her mentors, she even dared to suspect that there was a flaw in the great Sir Isaac Newton's thinking.
Newton stated that the energy of an object, the force with which it collided with another object, could very simply be accounted for by its mass times its velocity. In correspondence with scientists in Germany, Du Châtelet learned of another view, that of Gottfried Leibniz. He proposed that moving objects had a kind of inner spirit. He called it "vis viva," Latin for "living force." Many discounted his ideas, but Leibniz was convinced that the energy of an object was made up of its mass times its velocity, squared.
DAVID BODANIS: Taking the square of something is an ancient procedure. If you say a garden is "four square," you mean that it might be built up by four slabs along one edge and four along the other so the total number of paving slabs is four times four, is 16. If the garden is eight square, eight by eight, well eight squared is 64, it'll have 64 slabs in it. This huge multiplication, this building up by squares is something you'd find in nature all the time.
FRANCOIS-MARIE AROUET DE VOLTAIRE: Emilie, Emilie, you are being absurd. Why ascribe to an object a vague and immeasurable force like vis viva? It is a return to the old ways. It is the occult.
EMILIE DU CHÂTELET: When movement commences, you say it is true that a force is produced which did not exist until now. Think of our bodies, to have free will we must be free to initiate motion. So, all Leibniz is asking is, "Where does all this force come from?"
FRANCOIS-MARIE AROUET DE VOLTAIRE: In your case, my dear, the force, I'm sure, is primeval.
EMILIE DU CHÂTELET: Aaah, you're infuriating. You hide behind wit and sarcasm. You only think you understand Newton. You are incapable of understanding Leibniz. You are a provocateur. Everything you do is about something else and makes trouble for you. Criticize this, denounce that. Are you capable of discovering something of your own?
FRANCOIS-MARIE AROUET DE VOLTAIRE: I discovered you.
NARRATOR: Despite the overwhelming support for Newton, Du Châtelet did not waver in her belief. Eventually, she came across an experiment performed by a Dutch scientist, Willem's Gravesande that would prove her point.
EMILIE DU CHÂTELET: Gravesande, in Leiden, has been dropping lead balls into a pan of clay.
FRANCOIS-MARIE AROUET DE VOLTAIRE: Dropping lead balls into clay? How very imaginative.
EMILIE DU CHÂTELET: Using Newton's formulas, Monsieur Voltaire, he then drops a second ball from a higher height, calculated to exactly double the speed of the first ball on impact.
So, Messieurs, care for a little wager? Newton tells us that by doubling the speed of the ball, we will double the distance it travels into the clay. Leibniz asks us to square that speed. If he is correct the ball will travel not two, but four times as far. So who is correct?
AP writes: Newton was thinking of momentum as mass times velocity, while Leibniz was thinking of kinetic energy which is mass times velocity^2. And Emilie was going to show that Leibniz was correct while Newton was wrong. Most of us learned that there was a great fight between Newton and Leibniz on who discovered Calculus, but there also was this great fight between these two on momentum versus kinetic energy.
PIERRE LOUIS DE MAUPERTUIS (Dramatization): Messieurs, I feel Mister Newton's reputation dwindling, ever so slightly.
FRANCOIS-MARIE AROUET DE VOLTAIRE: Oh, Maupertuis, do not succumb to her. There is no earthly reason to ascribe hidden forces to this Dutchman's lead balls.
EMILIE DU CHÂTELET: Well, the ball travels four times further.
DAVID BODANIS: Turns out Leibniz is the one who is right. It's the best way to express the energy of a moving object. If you drive a car at twenty kilometers an hour, it takes a certain distance to stop if you slam on the breaks. If you're going three times as fast, you are going sixty kilometers an hour, it won't take you three times as long to stop, it'll take you nine times as long to stop.
AP writes: Yes, the car stopping as momentum= mass times velocity, or stopping as kinetic energy = mass times velocity^2.
PIERRE LOUIS DE MAUPERTUIS: Oh. Well, it does seem worth consideration.
FRANCESCO ALGAROTTI (Dramatization): Perhaps we might look over his calculations?
EMILIE DU CHÂTELET: I have already checked his figures. I am sure Leibniz is correct on this point. I intend to include a section on this matter in my book.
PIERRE LOUIS DE MAUPERTUIS: Really? Do be careful, Madame. Do you think the Academy is ready for such an opinion?
FRANCOIS-MARIE AROUET DE VOLTAIRE: Quite, quite. We really should be careful...
EMILIE DU CHÂTELET: "We?"
I see no reason to delay. There is no right time for the truth.
JUDITH ZINSSER: Emilie du Châtelet published her Institutions of Physics in 1740, and it provoked great controversy. Voltaire wrote that "she was a great man whose only fault was being a woman." In her day that was a great compliment.
--- end quoting PBS NOVA on Madame Chatelet proof of Universal law-structure of Gravity via Experiment with some AP edits---
AP writes: So, this experiment, balls dropped into clay, allows me to explain EI then EG then UI then UG. Experiment connects Existence with Universal Law-structures of Science. But, let me save that discussion for later.
Neanderthals had a fire making industry of flint striking iron pyrite.
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Well, I have always considered the Neanderthals smart, for,..... how could they have gotten across the English channel in the first place, from mainland Europe to the British Isles.
On the subject of "What is science?", fortuitously, I am helped by a recent report out of England of the very first evidence of Neanderthals, some 400,000 years ago used flint and iron pyrite to make fires.
It is safe to say that Science starts in history here, 400,000 years ago, as the Experiment that keeps making fire.
Homework: look up this report of Neanderthals making fire with flint striking iron pyrite and write a one page paper on the details of this report.
Archimedes Plutonium Jan 8, 2026, 8:28:31 PM to Plutonium Atom Universe newsgroup.
Question:: Iron pyrite struck by flint as in the BBC show, showing sparks flying everywhere, just profuse sparks flying everywhere.
My question is, is that a demonstration of the Faraday law-structure??? Does the Faraday law-structure have any role in sparks flying when flint strikes iron pyrite??????
The Faraday Law-structure for students who never saw that demonstration is where a magnet thrust through a coil of copper wire, produces electric current.
Faraday Law-structure Experiment in classroom
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Teacher Assignment:: set up the Faraday Law-structure experiment in the classroom so that all the students can eye witness this law-structure and allow some students to do the thrusting. You will need a copper coil connected to a Galvanometer and have a permanent bar magnet.
Lesson in classroom: Electric currents in Nature, come from thrusting magnetism through a current carrying material, a conductor like copper.
3) Logic is the "Scientific Method".
Alright, well some of the terms used by NOAA are different from my terms established earlier, and this is what I mean when I say Old Logic, Old Physics, Old Science never got their house of terms in order.
Scientific method from NOAA
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Step 1: Wonder
Observe something and wonder what is happening or why or how it happens. Ask a question or make a statement that can be tested by an experiment. This statement is called a hypothesis and defines the purpose of your experiment.
Step 2: Define
Define your variables (parts of your experiment that will change) and your controls (parts of your experiment that will not change).
Step 3: Review
Find out everything you can about what people have already said or written about the subject. Even if someone else has already done an experiment and reported results, you can still repeat their experiment or devise one of your own to verify (or refute) the results of the previous experimenter.
Step 4: Design
Design an experiment to test the hypothesis.
Make a step-by-step list of what you are going to do.
Step 5: Experiment
Do the experiment and carefully record the data.
Step 6: Analyze
Process and analyze your data. Do any calculations needed or draw graphs to help you make sense of the data.
Step 7: Conclude
Draw conclusions and write a report.
Did the data you collected support your hypothesis or not? Is there any reason to think there might be errors in your results? If the data did not support your hypothesis, what are some other hypotheses you might test to explain your initial observations? What further research could you or someone else do to verify your results?
Here again, well, NASA is all over the map when it comes to terms of science.
Scientific Method from NASA
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1. Form a hypothesis (a statement that an experiment can test)
2. Make observations (conduct experiments and gather data)
3. Analyze and interpret the data
4. Draw conclusions
5. Publish results that can be validated with further experiments
Scientific Method from various sources on Internet
-----------------------------------------------------------------
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.
On Friday, January 9, 2026 at 4:03:31 AM UTC-6 Archimedes Plutonium wrote:
(snipped)
Alright, I am going to try to find an appropriate experiment to use the Scientific Method upon for 1st year logic in college or university.
1st Astronomy experiment: Observe the North Star and watch how the Big Dipper slowly rotates in the night sky. Focus on proving the Earth is Round and rotates on its axis.
2nd Astronomy experiment: Observe a few Blue Stars and Red Giant Stars and correlate their masses. Focus on whether stars shine from fusion or shine from Faraday law-structure.
1st Biology experiment: Try imitating Smilodon, the saber toothed tiger by placing two fingers of left or right hand on your canine teeth, while with your free hand, try eating something, like a banana or apple. Look at the ridiculousness of David Attenborough and the entire paleontology community in getting you to museums and having interest in science because they glued on walrus tusks to the upper jaw of a fossilized cat. Focus on Darwin evolution that saber teeth would get in the way and interfere with everything the cat wanted to do in life if it had those massive saber teeth.
2nd Biology experiment: The Pterosaur dinosaurs which supposedly flew in the air yet had large bills and long necks and some weighed as much as a giraffe, yet grown up scientists say they flew in the air. Focus on aeronautical engineering that weight limits the ability to fly, and that rather than fly, these animals used their appendages as sails to boat oar sail on top of water.
3rd Biology experiment: The reflection of light that points out Superdeterminism.
1st Physics experiment: Take a bungee-cord fastened to fixed structure and see if you can get a sinusoid wave. Focus on whether physics has waves or rather, instead wires.
2nd Physics experiment: When Sun shines from Faraday law-structure, not fusion, then global warming accelerates year after year. Investigate how acceleration of global warming points to Faraday law-structure, not fusion for how the Sun and stars shine.
1st Chemistry experiment: Investigate H2 a molecule or a atom? All atoms require to have a neutron to store the energy of the muon thrusting through proton torus producing electric current in the Faraday law-structure. So in H2, is one of the protons acting like a neutron and not a proton.
Archimedes Plutonium Jan 9, 2026, 9:06:07 PM to Plutonium Atom Universe newsgroup.
I am going to have to narrow this list down.
1st Astronomy experiment: Observe the North Star and watch how the Big Dipper slowly rotates in the night sky. Focus on proving the Earth is Round and rotates on its axis.
The light pollution near cities is so bad that you cannot even see the constellations, so I may have to switch to the Moon.
2nd Astronomy experiment: Observe a few Blue Stars and Red Giant Stars and correlate their masses. Focus on whether stars shine from fusion or shine from Faraday law-structure.
Here the student is going to have to find out how astronomers determine the mass of a distant star. That maybe too much.
1st Biology experiment: Try imitating Smilodon, the saber toothed tiger by placing two fingers of left or right hand on your canine teeth, while with your free hand, try eating something, like a banana or apple. Look at the ridiculousness of David Attenborough and the entire paleontology community in getting you to museums and having interest in science because they glued on walrus tusks to the upper jaw of a fossilized cat. Focus on Darwin evolution that saber teeth would get in the way and interfere with everything the cat wanted to do in life if it had those massive saber teeth.
This is a good experiment, for biology has little math and easier for students to comprehend.
2nd Biology experiment: The Pterosaur dinosaurs which supposedly flew in the air yet had large bills and long necks and some weighed as much as a giraffe, yet grown up scientists say they flew in the air. Focus on aeronautical engineering that weight limits the ability to fly, and that rather than fly, these animals used their appendages as sails to boat oar sail on top of water.
This is a good experiment. Too much of paleontology is con-art anti-science.
3rd Biology experiment: The reflection of light that points out Superdeterminism.
This is a nice experiment and would have the student dive into what is called Quantum Entanglement and the famous engineer John Bell who proved Einstein was wrong.
1st Physics experiment: Take a bungee-cord fastened to fixed structure and see if you can get a sinusoid wave. Focus on whether physics has waves or rather, instead wires.
I myself am doing this experiment, in showing that the Sinusoid wave is nonexistent and only appears on screens of appliances but not in physical reality. And where Light is not a wave but rather a Wire.
2nd Physics experiment: When Sun shines from Faraday law-structure, not fusion, then global warming accelerates year after year. Investigate how acceleration of global warming points to Faraday law-structure, not fusion for how the Sun and stars shine.
This is a good experiment for students for the most part are charged up about the climate and their future.
And recently in the news of February 2026 is the Thwaites glacier in Antarctica is accelerating melting. Probably because the Sun does not shine from fusion but from Faraday law-structure. To be sure, fossil fuel burning adds to the melt but the majority of Global Warming is due to Sun Gone Red Giant Phase.
1st Chemistry experiment: Investigate H2 a molecule or a atom? All atoms require to have a neutron to store the energy of the muon thrusting through proton torus producing electric current in the Faraday law-structure. So in H2, is one of the protons acting like a neutron and not a proton.
No, I better drop this chemistry experiment as too detailed in water electrolysis as a proof. Not all students in college take chemistry. And it maybe dangerous working with hydrogen and oxygen.
Archimedes Plutonium Jan 9, 2026, 9:36:41 PM to Plutonium Atom Universe newsgroup.
1st Astronomy experiment: Observe the North Star and watch how the Big Dipper slowly rotates in the night sky. Focus on proving the Earth is Round and rotates on its axis.
The light pollution near cities is so bad that you cannot even see the constellations, so I may have to switch to the Moon.
I have been working on astronomy in my Advanced Logic textbook, proving Earth is round, not flat. And proving Earth revolves around Sun and not the other way of geocentric system.
Of course when sailors sailed around Earth is demonstrable proof Earth is Round.
But, and however, the proof that Earth goes around the Sun, and not that Sun goes around Earth is best proved by what??? Is the Venus observations the best proof.
I am thinking we can make One Logical Argument that proves Earth is Round, and it spins on its axis with a tilt, and it goes around the Sun, not vice versa. All proven by the idea of the size of the Sun and its distance away from us and the speed of Sun and Earth in space.
I am saying speed and distance alone should prove these items. Only the proof is a Occam's Razor of easiest explanation is the true explanation.
1) Earth is Round
2) Earth spins on a tilted axis
3) Earth goes around Sun, not vice versa
4) Logic is the Science of Ideas.
The reason I bring this up about mathematics for Logic is somewhat similar to mathematics, only, instead of numbers and geometry figures to play with, we play with "ideas". Instead of numbers we manipulate ideas. Instead of geometry figures, we play with ideas in logic.
And in this book of logic, the best way to teach logic is to use what you already learned about math numbers-algebra and geometry figures.
Instead of 2 + 3 of math we play with two ideas P, Q as in P AND Q of logic. Instead of 5 - 2 of math, we play with two ideas R,S as in R OR S of logic. We call the ideas, P,Q,R,S as "statements of ideas". The statement P of Logic could be any idea, such as P = The winter is cold with the strawberries covered in pine needles to keep them alive. Such as Q = Some plants are kept inside the house near a window for survival from the winter.
Instead of numbers and geometry figures as the objects of study, in logic, we study statements of ideas and how we manipulate them via connectors such as AND, OR, Equal-Not, If-->Then.
Homework: There are 26 letters in the alphabet from A to Z, for 13 of those letters make up true statements of ideas about plants in Nature. For another 13 letters make up true statements of ideas about animals in Nature.
For example:
A= I have burr oak, Quercus macrocarpa, some over 100 years old growing on my property.
B= Both red squirrel and gray squirrel live in the burr oak and harvest their acorns.
5) Math is the science of numbers-algebra and geometry figures.
These operators in mathematics of add, subtract, multiply, and divide show up in Logic, only they are called "connectors of ideas".
In Logic there are what is called the 4 simple connectors of AND, OR, Equal-Not, and If-->Then. Can you guess which connector resembles which operator of math??
If you guessed that AND is add, and OR is subtract, and Equal-Not is multiply, and If-->Then is divide, you guessed correctly.
But there are 2 more operators in mathematics that are far more complicated and very important. These two come from calculus, the math of motion, geometry graph and energy. The two are called derivative and integral. The derivative is rate of change, like that of speed or velocity and is a sort of division of dy/dx, which in High School you learned as slope of the line. The change in the y component divided by the change in the x component is the derivative.
The other calculus operator is the integral and is the area under the graph of the function over an interval.
The reason I bring up the derivative and integral is because the Existential quantifier of Logic is the derivative of calculus and the Universal quantifier of Logic happens to be the integral of calculus. So I am going to have to teach students a little bit about calculus in order to teach Logic. I am going to bend over backwards to make it as easy as possible for many students are frightened by calculus.
So we end up with 6 operators of mathematics, add, subtract, multiply, divide, derivative and integral. And so Logic ends up with 6 connectors that resemble these 6 operators in the same order listed: AND for add, OR for subtract, Equal-Not for multiply, If-->Then for divide, Existential quantifier for derivative, and Universal quantifier for integral.
The easiest way of teaching logic is to use math as a guide, a template.
6) Both Logic and Math are precision sciences; math uses sigma-error and logic uses truth-tables.
0.5% as in percentage we go 2 places to the right of the decimal point. To check to see if that is correct we simply use a quick logic analysis multiply 945 by 0.5 and see if it comes close to 940.
Faster yet, we see if 1% of 940 gives us approximately a number when added to 940 is near 945.
I write this in detail because in sci.math Usenet where I spent enormous time from 1993 until Google exited, there are many college graduates who never learned what percentages mean, even this so called engineer from Rensselaer Polytech, as he mistakenly fumbles and makes error, after gross error.
Posted in sci.math Usenet (misspellings not corrected) and where Kibo Parry often used fake names. In my opinion, he is a good example of a big mouth with little logical brains and where this textbook would have benefitted him while in University.
May 26, 1989, 10:35:51 AM kibo parry wrote:
What's the largest prime currenlty known? (All the information
I could dig up here was either fairly old or contradictory...)
james "kibo" parry | Some days you just can't get rid of a bomb.
kibo%pawl.r...@itsgw.rpi.edu (internet)
userfe0n@rpitsmts (bitnet) | Anything I say represents the opinion of
kibo%mts.r...@itsgw.rpi.edu | myself and not this computer.
>
> Kibo Parry Moroney Volney wrote:
> On Wednesday, December 6, 2017 at 12:30:22 AM UTC-6, Michael Moroney wrote:
> > Silly boy, that's off by more than 12.6 MeV, or 12% of the mass of a muon.
> > Hardly "exactly" 9 muons.
> > Wednesday, December 6, 2017 at 9:52:21 AM UTC-6, Michael Moroney wrote:
> > Or, 938.2720813/105.6583745 = 8.88024338572. A proton is about the mass
> > of 8.88 muons, not 9. About 12% short.
>
Homework:: You may have to review percentages, so you do not make the same mistakes as engineer graduate Kibo Parry of Rensselaer Polytech.
Use the 1% check to know if you are in the range of the correct answer.
The Proton with a Muon inside the Proton actual rest-mass is 945 but Old Physics via experiments says it is 938MeV as listed in Halliday & Resnick and in Wikipedia.
Compute the sigma-error of Proton + Muon between 938 and its actual true rest-mass of 945. Show your work and show your check.
Compute the sigma-error of the Muon rest mass when it is actually 105MeV , yet Old Physics says it is 105.6 MeV. Show your work and show your check.
Compute the sigma-error of the magnetic monopole which is exactly 0.5MeV, yet Old Physics mistakenly thought this particle was the Atom's electron, it is not; but rather the muon is the atom's electron. Old Physics measures this particle as 0.51MeV. What is the sigma error between 0.5 and 0.51? Show your work and show your check.
I was a High School teacher myself and percentages was an extremely difficult concept for teenagers to learn. I advise them to use a Check on Range to know if they have the correct answer. You cannot be a good scientist or engineer, if your mind cannot handle percentages correctly.
Math is used throughout the sciences, more for physics, less for biology and the reason for its use is because math offers precision. Math is a language of precision. Logic is also a precision language as it tries to steer away from false ideas, false conclusions, vague ideas.
Logic uses Truth-Tables for precision. Math and Physics use Sigma-error for precision.
Logic seeks for you to Think Straight, Think Clearly, and Think Truthfully and uses Truth Tables to help you think the best.
Modeling Logic after Math in order to understand Logic better.
---------------------------------------------------------------------------------
Much of Logic has the same structure as mathematics, both have 6 connectors which math calls operators. Both seek precision. Only real difference is that Logic uses "Ideas" while math uses numbers or geometry figures to work on.
Ideas of course are bigger than is a number or a geometry figure and so we can readily see that Logic is the larger set and has all of mathematics inside of Logic.
Math is a subset of Physics supplying physics with correct and precise number quantity, size and geometry shapes and figures. While Logic supplies physics and the other sciences with precise ideas written as statements p,q,r,s, etc etc as those ideas. Both math and logic are precision languages.
Math numbers are quantity, size and amount, and math geometry is shape and describing space. Logic is the correct ideas and manipulation of those ideas of clear thinking and straight thinking whose truth value comes directly from the best science on the subject. Both math and logic are languages that describe Physics and all the other sciences.
Where to start in Math if this was a Math story?? Well, we could start with the true numbers of mathematics, the Decimal Grid Numbers and the smallest grid is the 10 Grid which has 100 members not counting 0. This set is 0, .1, .2, .3, ... , 9.8. 9.9, 10.0. And then start with addition then subtraction.
If Math starts that way, how should the language of Logic start? What is the parallel of Numbers in Logic?
Here the parallel are statements, which contain thoughts and ideas and are written in Logic as "p", "q", "r", "s", "t" etc. And the truth value of each of those statements comes from the best science of the time on the topic of that statement in question.
An example of statements is the famous Aristotle syllogism attributed to Aristotle.
All men are mortal.
Socrates is a man.
Therefore,
Socrates is mortal.
This can be rewritten as
p = q
S = p
therefore S = q
So for Math we have numbers, for Logic we have idea-statements p, q, r, s, t, etc.
Once we have numbers in math (and later have geometry figures), we then move on to that of operations on numbers. No point in creating numbers that sit around and do nothing. No, we want to operate and use numbers to figure out the world we live in.
And of course math operators have 4 simple operators which most students will guess or know what they are--- Add, Subtract, Multiply and Divide. In a very real sense, multiply is rapid add, while divide is rapid subtract.
Logic also has 4 Simple connectors on statements p, q, r, s, t, etc. and they are AND, OR, Equal-Not, If-->Then. Instead of calling them operators in logic, we call them connectors. But math has 2 more operators from calculus as derivative and integral.
Math has two more operators from calculus called Differentiation (the derivative) and Integration (the integral). Logic has two more connectors of quantifiers called the Existential quantifier and the Universal quantifier, related to derivative and integral, respectively.
One branch of Logic models math so much it is given a special name of "Symbolic Logic" where ideas are pushed around in arguments and all you see are symbols, much like a math computation where you see symbols from one step to the next step.
7) A lesson on Calculus derivative and integral in order to understand Existential and Universal quantifiers.
I thought I could do Elementary Logic with a brief mention of calculus derivative and integral, considering the fact that the Existential and Universal quantifiers are bound up with calculus.
For the past several days I have been debating this issue and finally came to the conclusion that you can not do Logic adequately without some calculus derivative and integral development. Just as AND is Add in math, the Existential quantifier is the derivative of calculus and the Universal quantifier is the integral of calculus.
So what I have to do now is make a Lesson on calculus, introducing the college or university student in knowing the relevant parts of Calculus in a story book telling of this calculus. Not to be scared or fearful, but a simple story book telling.
And this will be, obviously, the first Logic textbooks that views and sees Calculus essential in telling the true story of "What Logic Is?"
There is no doubt in my mind that without telling parts of calculus, I fail to instruct students, nay, humanity of "What is Logic?"
Students in High School are taught the function and the graph and so I can lean on, and be helped by that instruction.
So I am struck at this moment in time on what a marvelous idea I discovered about Logic, true Logic. A education and understanding of Logic is never complete unless you know the derivative and integral of Calculus.
Now the naysayers and old fashioned, conservative, or dull witted person of math and science would, like always rebuke and rebuff that claim. For all they know is defend the indefensible of what they have as a "memorization education". If it is in a textbook in school that is ultimate knowledge and nothing can replace or displace it in those weak minds. They can never admit slant cut of cone is oval, never ellipse. And would fiercely attack an idea that Logic as a science is incomplete unless it has math calculus, derivative and integral represented as Existential and Universal quantifiers.
So I was a High School teacher of math at one time in my life and learned well, how to make ideas simple for young people to learn. Here I need to teach in about 10 or 20 pages the rudimentary calculus to have students understand how Existential quantifier is the derivative and integral is the Universal quantifier.
But can I make a proof argument that Logic without calculus discussion, is flawed Logic????
Can I somehow come up with a viable argument that missing the derivative and integral in Logic class is like missing electricity and magnetism in physics classes????
I think I can in the very idea, that the definition of function has a Unique Y value given a x value--- which--- entails or causes existence. And the fact that the function definition requires every, or All x values have a unique y value entails a universal.
Law-structures of physics, chemistry, biology, are they the Universal quantifier? By all means. For the function in math requires All x values which determine a unique y-value.
So what I am saying here is that __no Logic textbook is complete__ unless it has a discussion of Calculus derivative and integral which forms the structure of Existential and Universal quantifiers.
There is another feature of derivative and integral that makes the case of a proof that they are Existential and Universal quantifiers. Here I speak of the idea that derivative is inverse integral returning the integral back to the starting function and that integral is inverse of derivative returning back to starting function.
When you take calculus in college or university you will learn that Polynomial functions are the easiest in the world as functions, to get a derivative or integral from. For all they are is a addition or subtraction of 1 from exponent of starting function, remembering to include a constant.
Let me show you this pattern on the Identity function, which is often written as Y = x. That is the starting function. Now the derivative of Y = x, which is a polynomial by the way. The derivative of Y = x is where x is x^1 and the constant of this x^1 is that I place the 1 in front of x^1 having 1(x^1) and if I subtract 1 from the exponent I get 1(x^(1-1)) which is 1(x^0). The x^0 turns out to have a value of 1 itself, so I end up for a derivative of x as being (1)(1)= 1.
Now that maybe confusing and scary to students upon first seeing that, so let us try another function of Y= x^2. When you see x^2 means nothing more than x times x. If you see x^3 means x times x times x. But now, what is the derivative of x^2. We follow the same procedure. We throw the 2 out in front and subtract 1 from exponent as that of 2(x^(2-1) and end up with 2x. The derivative of Y=x^2 becomes 2x and it is a function also denoted as Y=2x.
A graph of the function Y= x^2
-----------------------------------
Here is a picture diagram of what was talked about above on calculus.
The function x^2 -> Y looks like this in Integer Grid:
y-axis
^
|
|
|
9 /| 9
|
|
|
/ |
|
|
/ |
|
/ |
|
4 4/ | |
| |
/ | |
| |
1 / |1 | |
/ | | |
------------------------------------------------> x-axis
0 1 2 3
Cell or partition, some prefer the name cell, others prefer the name partition from 0 to 1 is a pure right-triangle sides 1 by 1 with hypotenuse sqrt2.
Cell from 1 to 2 is a right-angled-trapezoid (picketfence) and the picketfence is composed of a square with a right-triangle atop the square.
Cell from 2 to 3 is a right-angled-trapezoid (picketfence) and the picketfence is composed of a rectangle with a right-triangle atop the rectangle.
Homework: See if you can solve what the derivative of the function Y= x^3 is following the above pattern.
Now the Integral of calculus is almost the same method and pattern only it is a addition of 1 to the exponent. We started with Y=x function and what is the integral of that? Y=x is the same as Y=x^1. The rule is that you add 1 to exponent which is x^(1+1)and you throw in front of x^(1+1) a reciprocal of (1+1). Reciprocal means 1 over (1+1) and that is 1/2. So we have as the integral of Y=x to be Y= (1/2)x^2.
Another integral example is Y=x^2. So let us add one to the exponent and we have (2+1) and the constant thrown in front is 1/(2+1) = 1/3. So the integral of Y=x^2 is that of (1/3)x^3.
Homework: See if you can solve for the integral of the function Y= x^4 by following the above instructions.
If you go on to take Calculus in college or university you will learn a marvelous theorem called the Fundamental Theorem of Calculus which merely means that derivative and integral are inverses of one another. Inverse means one undoes the other.
In my example above of Y=x^2, we found the derivative is 2x and the integral is (1/3)x^3.
If we take the derivative of (1/3)x^3 we throw the 3 out in front and subtract 1 from exponent. That looks like this (3)(1/3)x^(3-1) and that reduces to x^2, our original starting function Y=x^2. But now, starting with the derivative 2x, what is the integral of 2x???? Here again we follow the same rules we add 1 to exponent and throw out a constant that is a reciprocal of the new exponent which looks like this (1/2)(2)x^2. Reducing that and again we have the starting function Y=x^2. This is the meaning of the Fundamental Theorem of Calculus, that the derivative undoes (inverse) the integral and the integral undoes (inverse) the derivative to establish the original starting function.
Homework: With the instructions given above on Fundamental Theorem of Calculus, your starting function is Y=x^3, see if your derivative undoes the integral and see if your integral undoes the derivative by returning to your original function Y=x^3.
Unfortunately as of this writing in February 2026, there exists no calculus textbook in the world at present who is teaching calculus correctly. I say that because the only valid functions in all of mathematics are the Polynomial functions, the easiest functions to find the derivative and integral. But that should not be strange because as of this writing, no textbook in Logic is correct for they all have the 4 simple logic connectors in awful error, the AND, OR, Equal-Not, If-->Then.
It is easily seen that Existential is inverse of Universal and that Universal is inverse Existential.
The If-->then connector (detailed later in this book) or what I call "Move into" connector is easily seen as the derivative of a function as it moves from one cell to the next all along the x-axis to pair up a x-value to a unique Y-value. We study the If-->Then later but I wanted to introduce it to you now.
No, it is impossible to describe Existential with Universal quantifiers without bringing in the concept of calculus derivative and integral.
So, is there a Fundamental Principle of Logic, like there is in Calculus, for Calculus has a Fundamental Theorem which has as a statement-- the derivative is inverse the integral and the integral is inverse the derivative? Something along the lines of saying the Existential Quantifier is inverse to the Universal Quantifier, that would be a resounding proof that Logic without a discussion of calculus is half-baked logic.
Is not the UI, UG, EI, EG, Universal Instantiation, Universal Generalization, Existential Instantiation, Existential Generalization, much the same as the math teacher talking about Function then Function derivative, then Function integral, going from one to the other.
Take the function Y = x^2, its derivative is 2x, and its integral is (1/3)x^3. Taking the derivative of (1/3)x^3 leads me back to x^2, and taking the integral of 2x leads me to (1/2)(2)x^(1+1) = x^2. One undoes the other.
Taking the Derivative of Universal Quantifier ends up with Existence. Taking the Integral of Existence ends up as Universal.
What I am saying here, is the relationship of Logic's quantifiers out of necessity needs the calculus derivative and integral.
Just as AND is related to Equal-Not (multiply is rapid addition) and that OR is related to If-->Then (division is rapid subtraction). UG is rapid UI, EG is rapid EI.
Plus, AND is reverse of OR (add reverse of subtract). and Equal-Not the reverse of If-->Then (multiply the reverse of division).
What I am doing here is saying that a Logic textbook without involving math Calculus is missing a huge chunk of the science of Logic, itself. Is incomplete as Logic.
Calculus is motion and change, and Logic to be complete cannot have missing "motion and change".
Without Calculus involved in Logic, it is a premature and soiled and stained logic.
For Calculus is Motion and Change in the world. A logic without motion and change is a logic that is pathetically poor.
The Universal Generalization UG, the Universal Instantiation UI, the Existential Generalization EG, and the Existential Instantiation EI are elements of calculus, the Motion and Change needed to make Logic complete.
I have shown earlier that the Scientific Method starts with "There exists" which is EI moving over to EG through experiments, moving over to UI and finally being titled a Law-structure of Science in UG.
The force of gravity by Newton went through this process G = constant Mass_1 x Mass_2 / distance^2. Starting out with "There exists" moving into Generalized Existence in multiple experiments moving into Universal Instantiation leading to the recognition of Universal Generalization.
Much the same as a Function graph of the Identity function in Calculus.
Y = x, the identity function looking like this in 1st quadrant only.
| /
| /_____
If we take the 10 Number Grid and only the integers, 0, 1, ...9, 10.
There exists 0 and the function links x= 0 with a unique y, being y=0. Next, x=1, links uniquely to y= 1.
x y
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
The x number exists and moves uniquely into a y-value number. This is the definition of Function. For each x number must be 1 and only 1 y-value number. When you hear "1 and only 1" is the same as saying "unique". The motion in drawing the graph, starting at the origin (0,0) onto x=1 then x=2 and all the integers in 10 Grid.
And the derivative of Y = x, the identity function is dy/dx which means the change in y-value divided by change in x-value. As the function moves from 0 to 1 we have change in y as 1-0 divided by change in x 1-0 and so we have (1-0) / (1-0) = 1/1 = 1. Next the function moves from 1 to 2 and here again we have a dy/dx as (2-1)/(2-1) =1/1 =1.
What is the integral from x=0 to x=1??? That is the area under the function graph which is a right triangle.
A right triangle whose two legs are 1 and so its area is 1/2 base times height as that of (1/2) (1) (1) =0.5.
What is the integral from x=0 to x=9???? The base of right triangle is 9, the height is 9, the area is 1/2 base times height = (1/2) 9 x 9 =40.5.
You saw earlier that the integral of Y=x was that of (1/2)x^2 and that is the same formula geometry uses for the area of a right triangle.
8) What is truth and falsehood and partial-truth in truth-tables of Logic.
Alright I better move along here. Hopefully the chapters will be short and simple.
8) What is truth and falsehood and partial-truth in truth-tables of Logic?
Here Logic takes a path never traveled before, where statements of ideas have partial truth value, not just all true or all false, but intermediate values. I was forced to do this because of the OR connector in solving for Deciding Experiments. Where two competing statements vie for the truth, one has some falsity however slight, mixed in with truth.
I am working on one such problem of a Deciding Experiment now, involving whether the Light-Photon is a wave or rather, what I suspect a wire. But both have truth value but one has falsity contained within.
So the Truth table of OR connector needs partial truth values. Later in this book we study OR in details, but for now I want to slowly introduce you to OR.
Here are some statements of ideas in Logic and here I have opined on how much truth value they have. Where falsehood and chatterbox gibberish has a value of 0, and where all truth is valued at 1, while a statement with partial truth is given a fraction value between 0 and 1.
A) Slant cut of cone is ellipse. [value of 0, since a cone has 1 axis of symmetry and ellipse has 2 axes of symmetry]
A') Slant cut of cone is oval. [value of 1]
B) Smilodon is a saber toothed tiger. [value of 1/10 until DNA testing is done]
B') Smilodon is a normal cat with normal teeth but museums like gluing on walrus tusks to increase ticket sales. [value of 1/2, until DNA testing of tooth versus cat upper jaw takes place]
C) Pterosaurs the size of a giraffe flew in the air. [value of 0, as those appendages used as row-boat, oar, sail, and not to fly in the air]
C') Pterosaurs the size of a giraffe used its appendages to oar-row-boat-sail on the Cretaceous seas to catch fish. [value of 1, for aeronautical engineers all tell us such a weight cannot fly]
D) Darwin Evolution is how species evolve. [value of 1/2, for it is useful in preliminary explanations]
D') Darwin Evolution is a rule, not a theory, for Superdeterminism is how species evolve. [value of 1, for physics experiments in quantum entanglement keep coming in positively true]
E) Atoms have a nucleus of protons and neutrons. [value 0, because the bounce back alpha particles exited at a faster speed than they entered]
E') Atoms have no nucleus, rather instead, they have a proton torus in the middle of the atom. [value 1, because the elementary particles of physics must have a geometry in order to do the law-structures of electromagnetism, and not be silly balls, for the Faraday law-structure needs a torus]
F) Convection currents cause Continental Drift. [value 1/10 because observations are showing drift in one direction one day while reverse direction the next day]
F') Vibrations caused by the 2 cores of Earth cause Continental Drift. [value 1, because Earth cores are a dynamo and that causes vibrations]
G) Light Photons are sinusoidal waves. [value 1/100, because only a semicircle geometry can give a wave to a speed of light which is a constant speed]
G') Light Photons are wires, not waves. [value 9/10, because the Electric field in physics must deal with some form of conduction, and conduction exists only in wires]
H) Sun and stars shine from Faraday law-structure of every atom inside that star. [value of 1, for when a atom has proton as torus and muon inside proton torus produces electricity energy]
H') Sun and stars shine from fusion. [value of 0.05, because fusion events are rare in stars]
I) Global warming is caused by the Sun gone Red Giant phase. [value 0.95 because Faraday law-structure in atoms creates electrical energy and causes 95% of sunshine]
I') Global warming is caused by the greenhouse gas effect from burning fossil fuels. [value 0.05 because 5% of sunshine is caused by fusion]
J) Russia taking over Ukraine will make Russia surpass USA as superpower. [value 9/10 because Russia then is the largest land mass country with the most resources]
J') Russia not taking over Ukraine keeps USA #1 superpower, China #2, and Russia #3.
[value of 6/10, because the science and engineering of NATO is vastly better than that of China+Russia]
Homework assignment: Read and ponder these above 10 pairs of statements. Then make up your own list of 10 pairs of statements and assign a number value according to your opinion and state a "because".
1 for a statement that is all true.
0 for a statement that is all false.
A decimal fraction between 0 and 1 if the statement has some truth value.
Example:
K) Earth is Round and the Sun revolves around Earth. [value 0.5 because P=Earth is Round is true]
K') Earth is Round and the Earth revolves around the Sun. [value 1, because P=Earth is Round and Q=Earth revolves around the Sun, are both true]
I would give K a 0.5 (which is 5/10 = 1/2) truth value because the Earth is Round not flat, but the Earth revolves around the Sun. I would give K' a value of 1 for it is all true. But some may want to argue that Earth is not completely Round but oblate and give it a 0.9 truth value. Or argue that for the Sun to revolve around Earth is so preposterous and mind-boggling as to where to put the Sun orbit, that its value should not be 0.5 but rather 1/100.
The assignment of truth value is often what you opine it is, based on the best science evidence available to you. But it is important to recognize that a statement is only partially true.
Slant cut of cone pictures, diagrams which is above the heads of all math professors, for they continue to teach their errors instead of admit they are wrong, and that the slant cut of cone is a Oval, not ellipse.
And, no wonder math professors could never understand the truth about calculus derivative for it is the line segment that reaches for the next point of the original function graph and not the silly and absurd idea of Old Math-Old Calculus, full of error that it is a tangent line as pictured in Wikipedia. If a math professor cannot understand slant cut of cone is oval, not ellipse as a reasoned symmetry argument, why on Earth would anyone expect a math professor, he/she to have a correct explanation of the calculus and its derivative?
--- quoting Wikipedia on the derivative---Differential calculusMain article: Differential calculusTangent line at (x0, f(x0)). The derivative f′(x) of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point.
Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The p
--- end quoting Wikipedia on the derivative---
Archimedes Plutonium
May 2, 2026, 3:36:54 AM (12 days ago) May 2
to Plutonium Atom Universe
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.
Terms for math
--------------
Statement
Axiom (postulate)
Operator-structure
Proof
Theory
We start with the Statement. And the statement is this.
Statement: Math professors who teach Calculus that the derivative is a tangent line to a point on the function graph (see Wikipedia diagram) are crank-crackpots of calculus.
We start with that as Statement. By the time we reach Theorem with Corollaries, the statement of the theorem will be far different. Something along the lines of this--- The derivative dy/dx of Calculus is a straight-line segment that joins the previous x-value and y-value of the original function to the successor x-value and y-value of the function. Geometrically it means the derivative is part of the original function itself and not some alien tangent line that touches the original function at a unique point.
I am showing the reader this because math professors since Newton and Leibniz when it comes to calculus have been nothing but crank-crackpots when understanding Calculus when they think the derivative is a tangent line to the original function graph. No, the derivative is a straight line segment that connects-up with the very next successor point of the x value and y value and forms the original function graph.
This is what I mean when scientists are not required to take 2 years of logic in college or university, for they come out as mostly kooks of science in their thinking. At least, when scientists take 2 years of University or College logic, at least they have a good chance of doing correct and proper science.
It is obvious to anyone, even those that hate math and especially Calculus, obvious that calculus is geometry. And yet in the late 17th century when Newton and Leibniz discovered calculus, they too realized calculus was geometry and they realized the Fundamental Theorem of Calculus, FTC, yet never ever proved this Fundamental Theorem of Calculus with a ____geometry proof_____. In fact no-one in math ever gave a valid proof of FTC, certainly impossible with the silly "limit analysis". And all the generations of math professors after Newton and Leibniz never had a geometry proof of FTC. They had some mindless analysis contraption called "limits" which is a bogus concept.
We have an original function Y--> x^2. By the way I write a function without a equal sign, but instead a arrow. For a function is a mapping of every x point linked up with a unique y-point and this is not equality, so I use an arrow. Now the function Y--> x^2 can be written as x^2 --> Y. The function plots coordinate points of a graph such as this integer table is trying to display.
x-value --> y-value for x^2
0 --> 0 which is coordinate point (0,0)
1 --> 1 which forms (1,1) in the graphing
2 --> 4 which forms (2,4) in the graphing
3 --> 9 which forms (3,9) in the graphing
Now that table is just for a few points, but in a function, every x point must be represented with a unique y point forming a coordinate point. The Decimal 10 Grid of numbers has exactly 100 numbers not counting 0 on the x and on the y axes. Realizing there is a hole or gap in between 0 and the next number 0.1, another hole or gap between 0.1 and the next number 0.2 and this goes on all the way to the last two numbers in 10 Grid of 9.9 then 10.
In this diagram of the original function Y--> x^2 where derivative is 2x and integral is (1/3)x^3, AP draws the derivative as being a straight line segment from x= 1 to x= 1.1 in decimal-10-Grid, and showing that the derivative forms and produces the original function starting at x=1 and what x=1.1 has to be.
In other words, the derivative, fetches the future. The derivative at point x=1 will fetch the next original function point of coordinates (1.1, 1.21) and not the mindless tangent at the original function graph that crank-crackpot math professor teaches.
So looking at the function x^2 -> Y and we make a table in Decimal 10 Grid. Our table below is just a few points, and not all of the 100, or 101 counting 0 points.
x^2 -> Y
x y
0 0
.5 .25
1 1
1.1 1.21
2.5 6.25
3 9
So we plug into the x^2 all the 10 Grid values on the x-axis and start making a table. But we are only interested in going from x=1 to x=1.1, because in 10 Grid no numbers exist between 1 and 1.1, or between 1.1 and 1.2. Grids are where there is ___no continuum___. Just like Quantum Mechanics in the year 1900 when Max Planck said physics is discrete with no continuum. But math professors were too dumb to ever entertain the idea, that math has to be discrete with no continuum if physics is discrete with no continuum.
Then, we graph our table of only the interval 1 to 1.1 for we are only concerned with this interval and I call this a cell, to see if the derivative is connecting up with the 1.1 as the successor number of 1.
y-axis
^
|
|
|
|
|
/ |
|
/ |
|
1.21 1.21/ | |
| |
/ | |
| |
1 / |1 | |
/ | | |
------------------------------------------------> x-axis
Now we are going to have to borrow from the 100 Decimal Grid the number 1.05 for in 10 Decimal Grid exists only empty space between 1. and 1.1. The 10 Decimal Grid is separated by increments of 0.1, in other words, holes of 0.1 from one number to the next number, while the 100 Decimal Grid is separated in increments of 0.01.
What is 1.05^2 for our original function graph is Y--> x^2. It is 1.1025.
We can picture this midpoint of 1.05 between x =1 and x=1.1 as a rectangle like this, which I call a cell.
____
| |
| |
------
Whose base is 1.1 subtract 1 equals 0.1. Whose height is 1.1025. The area of this cell would then be 0.1 x 1.1025 =0.11 approximately. The integral of Y-->x^2 using power rule is (1/3) x^3 and from the interval 0 to 1.1 is area of (1/3)1.331=0.444, while for area of 0 to 1 is (1/3)1 =0.333. If we subtract we have approximately, 0.11 a match to the area inside the cell.
Now the question, the big question is can we go down that cell from 1 to 1.1 with 1.05 as midpoint and find a right triangle to carve out and would, when pivoted onto the midpoint, end up landing at the coordinate point of (1.1, 1.21)??? In other words, the derivative is Not a tangent line to original function graph but is in fact a straight line segment that actually determines and connects up with the next point of the original function graph.
A week's homework assignment: This is a week long assignment. Go through two functions, Y--> 2x and Y--3x^2 using the power-rule make a table of coordinate point of x= 1 and x= 1.1 in Decimal 10 Grid. Plot your table similar to my plot above. Find the derivative and integral of these two polynomial functions. And show that the derivative connects the point (1,?) with (1.1, ?) for Y--> 2x and also for (1,?) with (1.1,?) for Y--> 3x^2. You will need the midpoint of 1 and 1.1. And sketch the right-triangle to lift up and pivot on the midpoint forming a trapezoid from rectangle. There, you have started a proof that says all mathematicians from Newton and Leibniz were wrong when they said a derivative is a tangent line to function graph.
So what failed between 17th century and 21st century? What failed most of all, is teachers do not teach Logic in College and University and the scientist has little to no logical brains. What Steve Huffman of the Reddit platform calls Lunatics. And why Australia, and now UK, France and many other countries by 2026 are banning these platforms for youngsters as these are brainwash ignorant platforms ruining the minds of our young students.
Steve Huffman lists science lunatics:
Reddit (symbol) r/math, 3 years ago Genius meets Lunatic: 1994 discussion between Terry Tao and Ludwig Plutonium
I remember Archimedes Plutonium and sci.math. He calculated the chromatic number of the plane: and it is 1 (color everything
..Is this crank...
Univ Virginia math dept: Peter Abramenko, Julie Bergner, Mikhail Ershov, Jeffrey Holt, John Imbrie, Thomas Koberda, Slava Krushkal, Thomas Mark, Jennifer Morse, Ken Ono, Andrei Rapinchuk, Christian Reidys, Jim Rolf, Charles Dunki, Ira Herbst, James Howland, Craig Huneke, Thomas Kriete, Nicholas Kuhn, Irena Lasiecka, Barbara MacCluer, Kevin McCrimmon, Karen Parshall, Loren Pitt, Donald Ramirez, James Rovnyak, Leonard Scott, Lawrence Thomas, Roberto Triggiani, Harold Ward
Steve Huffman on math lunatics Terence Tao,
Steve Huffman University of Virginia,
Reddit (symbol) An other Archimedes Plutonium rant about irrational numbers Reddit · r/badmathematics 10+ comments · 6 years ago An other Archimedes Plutonium rant about irrational numbers ... In Grid Systems, you are exact only to the Grid, and forget about the beyond. "The ...
UCLA chancellor: Gene D. Block (biology)
UCLA Physics dept
Ernest Abers, Elihu Abrahams, Katsushi Arisaka, Michalis Bachtis
Eric Becklin, Zvi Bern, Rubin Braunstein, Stuart Brown, Robijn Bruinsma
Charles Buchanan, Wesley Campbell, Troy Carter, Sudip Chakravarty
W. Gilbert Clark, John Cornwall, Robert Cousins, Eric D'Hoker
Robert Finkelstein, Christian Fronsdal, Walter Gekelman, Graciela Gelmini
George Gruner, Michael Gutperle, Brad Hansen, Jay Hauser, Karoly Holczer
Huan Huang, Eric Hudson, George Igo, Per Kraus, Alexander Kusenko
Thomas Mason, George Morales, Warren Mori, Steven Moszkowski
Christoph Niemann, Kumar Patel, Roberto Peccei, Claudio Pellegrini
Seth Putterman, B. Regan, James Rosenzweig, Joseph Rudnick
David Saltzberg, William Slater, Reiner Stenzel, Terry Tomboulis, Jean Turner
Willard Libby (chem), Julian Schwinger (physics), Paul Boyer (chem), Andrea Ghez, James Fraser Stoddart (chem), Louis Ignarro (physio-medic)
UCLA math dept.
Donald Babbitt, Kirby Baker, Andrea Bertozzi, Mario Bonk, Lennart Carleson, Tony F-C Chan, Shiu-Yuen Cheng, Robert Edwards, Gregory Eskin, Hector Fattorini, Thomas Ferguson, Theodore Gamelin, John Garnett, David Gillman, Mark Green, Nathaniel Grossman, Alfred Hales, Robert Jennrich, Paul Johnson, Alan Laub, Thomas Liggett, Donald Martin, Sidney Port, James Ralston, Paul Roberts, Bruce Rothschild, Murray Schacher, Roberto Schonmann, Masamichi Takesaki, Terence Tao, Veeravalli Varadarajan, James White, Donald Ylvisaker
9) The Existential quantifier.
Archimedes Plutonium Jan 16, 2026, 8:47:20 PM to Plutonium Atom Universe newsgroup.
9) The Existential quantifier.
Logic is about ideas and whether the ideas are good or bad and determining if the ideas are good or bad. In arithmetic we play around with numbers, in logic we play around with ideas. And one of the first things we do with ideas when presented to us, is question on whether the objects in the idea have existence, or, are simply fiction and have no existence.
Example: "Beware the Jabberwock, my son! The jaws that bite, the claws that catch! Beware the Jubjub bird, and shun the frumious Bandersnatch!"
This is a famous Lewis Carroll poem. Fun to read and think about, but is just nonsense with no existence in object reality. Logic uses science to determine a truth value which can be fully true, or partially true or all false.
Archimedes Plutonium Jan 17, 2026, 12:01:49 AM to Plutonium Atom Universe newsgroup.
Example: All drama TV shows are acting and a form of entertainment but not existing in reality. And woe to those who think they can form good ideas based on watching a TV drama show.
AP opines: Fiction shows like fiction books are stories not existing as real, but the book is real. A truth value of 100% false.
Example: All fiction and science fiction books, and woe to those who think they can form good ideas based on ideas in fiction novels.
AP opines: Same as drama TV shows.
Example: Did the Saber tooth tiger exist or were they glued on walrus tusks to upper cat jaw?
AP opines: We get the best biology scientist and see if ever there was a intact upper jaw with a saber tooth attached, as far as I know, never has one like that been found, so I opine the truth to be a tiger with normal teeth and the museums are gluing on walrus tusks found at the dig site, so I opine 90% fake saber tooth tigers. A DNA analysis should be conducted that may prove AP wrong or prove 100% fake.
Example: Does the slant cut of cone exist as a ellipse when a ellipse requires 2 axes of symmetry yet a cone has only one?
AP knows that by symmetry analysis, no slant cut in right circular cone is a ellipse, for it is a oval.
Example: Did the Moon exist as a satellite of Earth when the dinosaurs lived on both Antarctica and the Arctic circle?
AP opines: Using Occam's razor Law-structure, the timing of the rise of flowering plants with a meteor crash that killed dinosaurs points to a 100% truth value that the Moon was not a satellite of Earth until 90 million years ago.
Example: Can you have a black hole or can you have the Big Bang come into existence when you have a Pauli Exclusion Principle of physics?
AP knows that Pauli Exclusion Principle of quantum mechanics does not allow for the existence of black holes, so black holes and Big Bang are 100% false.
Example: Can you have Reals as numbers in math (Reals as a continuum) exist when physics in 1900 says all of physics is discrete with quantum mechanics. Both cannot be correct, and one is hugely mistaken.
AP knows that calculus must exist and in order for it to exist, the numbers of mathematics need to be discrete. So, Reals are 100%.
Example: Can Light be a Wave when waves require a medium to exist for the "wave to wave in", and yet Space has no medium? Is Light a Wire instead of a wave?
AP opines: Logic is a science of precision just as math is one also. A concept of wave needs a medium to wave in. So I suspect there is a ill-defined notion of a wave and where the concept of "wire" makes more sense. I would give this a truth value of 70% true that the Light ray is a wire, not a wave
The start of Logical thought often starts with the question of does this idea exist in reality or is it imagination run amok?
Really, not much use in spending a-lot of time on nonsense or fiction.
Does the object in the idea have Existence or is it Not-Existing, nonexistence. This leads us into the next operator of Logic which is Not-Equal. Not combined with Equal.
Archimedes Plutonium Jan 17, 2026, 12:26:50 AM to Plutonium Atom Universe newsgroup.
Let me not forget this important example of Infinity Borderline.
Example: Can you even have a concept of finite versus infinity without a concept of a borderline between the two??
AP knows that you cannot have a concept of finite versus infinity if there is no borderline separating out the two concepts. This is a 100% true value.
10) The 6 connectors of Logic resemble math 6 operators.
It is a double whammy, severe blow and setback to students across the world that there does not exist a logic textbook as of 2026 free of error in all 4 simple connectors--- AND, OR, Equal-Not, If-->Then. And there exists no calculus textbook which has the correct ideas of equation, what is true numbers, what is calculus derivative and integral. So students all over the world are taught nonsense of what is logic and what is calculus.
So mathematics has 6 simple operators. And given in order where Mathematical Induction starts mathematics. Mathematical Induction is a proof method, and gives all the Counting Numbers for that method is based on the idea of adding 1. Start with 0 and add 1 gives me 1, add another 1 to 1 gives me 2, add another 1 to 2 gives me 3, keep on going gives me all the positive Counting Numbers. That is how math starts by successively adding of 1 to get a new number.
Math 6 simple operators
-------------------------------
1) Add
2) Subtract (which should have been given the better name of "remove").
3) Multiply
4) Divide
5) Derivative
6) Integral
The above order of the 6 simple math operators is what the order they are taught in school and is a reasonable order. Add is likely the easiest concept of the 6 shown.
But surprisingly the order to teach Logic connectors starts with a complex concept of Existence. And this makes logical sense in that it is silly to argue over something that is nonexistent.
Logic has 6 connectors.
1) AND
2) OR
3) Not-Equal (two binaries combined to make 4 rows in a truth table)
4) If-->Then known as the material conditional, or the implication as "implies" but my favorite name is "moves into" because of calculus function and derivative is a move into.
5) Existential quantifier, because the derivative of a function moves into the next coordinate point.
6) Universal quantifier, known as "For every" or "all" but the best concept is the universal law-structures of physics such as Ampere law-structure, or Faraday law-structure or New Ohm's law-structure.
So, I listed the math operators and then the Logic connectors.
But in logic, we like to have things in order. Not enough to just list the connectors but to list them in order such that the most primitive connector is first and the last one the most complicated, needing the others to describe it.
In mathematics we can start with add first because of Mathematical Induction, given 0 and 1, add 1 to obtain 2, then add 1 to 2 to get to 3, and so on. By doing this we have all the counting numbers of mathematics. And a proof using Mathematical Induction if true for 0, 1, 2, 3 then suppose true for n, and if you can show that it is true for n+1, means your statement is true for all the counting numbers. This works by the reasoning that "n" is any counting number. So if you assume "n" and can show true for "n+1", you have proven true for all counting numbers. Now some students have trouble with Mathematical Induction when I went to college and learning this method of proof. And what seems to be the snag or hold-up in young students mind is that the "n" and then
"n+1" are numbers in general. The n can be any number. Some students have a difficult time of conceptualizing that "n" is any number. And teachers help explain Mathematical Induction by referring to dominoes falling. Dominoes ||||||||||||, if the first falls and a far off domino call it "n" and if "n+1" means all the dominoes had fallen.
Earlier in this textbook I listed the major terms of mathematics and theory was the last one of six terms listed. Mathematical Induction is a theory of mathematics for All True Numbers of mathematics are created by Math Induction. The Natural Numbers are math induction using 1 as inductor; the Decimal 10 Grid is math induction using 0.1 as inductor; the 100 Grid is math induction using 0.01 as inductor, etc.
This idea is worth great attention. The terms of mathematics as given earlier is this.
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory.
Which of those 6 terms would we classify the method of Mathematical Induction? Given any "n" assumed true and if "n+1" is shown to be true, according to Math Induction implies n is the infinite set of counting numbers.
Is Mathematical Induction a axiom?? Is it a operator-structure?? Is it a proof?? Is it a theorem?? Or is it a Theory??.
Before we find out the truth let us go back in math history to a famous mathematician who sized up what Mathematical Induction means. His name was Kronecker.
--- quoting Wikipedia---
free encyclopedia
Leopold Kronecker
Kronecker in 1865
Born 7 December 1823
Liegnitz, Province of Silesia, Prussia
Died 29 December 1891 (aged 68)
Berlin, German Empire
Citizenship Prussian
Alma mater University of Berlin
Known for
Arithmetization of analysis
Kronecker delta
Kronecker foliations
Kronecker limit formula
Kronecker symbol
Kronecker product
Kronecker quiver
Kronecker substitution
Kronecker's congruence
Kronecker's Jugendtraum
Kronecker's lemma
Kronecker's theorem
Kronecker–Capelli theorem
Kronecker–Weber theorem
Hermite–Kronecker–Brioschi characterization
Awards ForMemRS (1884)
Scientific career
Fields
Mathematics
Logic
Institutions
Berlin Academy
University of Berlin
Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker[1] as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man").[2] Kronecker was a student and life-long friend of Ernst Kummer.
--- end quoting Wikipedia---
What Kronecker suggested and implied with his famous statement that the Natural Numbers, the Counting Numbers 0, 1, 2, 3, to infinity were something supremely special. And thus, Kronecker thought of Mathematical Induction as being a axiom-- something that cannot be proven true and that we accept it as "God-given" common-sense true, just like all the other axioms such as 2 points determine a straight-line-segment.
His biography suggests Kronecker knew Logic, however, AP thinks Kronecker made a mistake here on the Natural Numbers 0, 1, 2, 3, 4, .... to infinity. In that Mathematical Induction is easily proven true as theorems and a collection of theorems would make the method of Mathematical Induction be not a axiom, not a theorem but a Theory of Mathematics. That the method of Mathematical Induction is a Theory of mathematics.
Reasoning: The reasoning is that we can prove the Counting Numbers, starting at 0 is amenable to a proof given the axioms of math that 2 points determine a unique straight line segment interval and gives us a unique distance between point 0 on the x-axis and point 1 on the x-axis. By using this unique distance we lay out a further distance to point 2 as 1+1=2. Then we lay out still a further distance of 2+1 = 3.
In this sense we have built Mathematical Induction. That proof would be a Theorem, one theorem.
But now, we say our length is going to be 1/10 instead of 1. 1/10 is of course 0.1 and starting at 0 our next point using a 0.1 length is the point 0.1, next we have 0.1+0.1 = 0.2 and as we increasingly add 0.1 and reach 10 we have the entire Decimal 10 Grid of numbers. This 10 Grid is another theorem built by Mathematical Induction.
Next we use 0.01 to build the Decimal 100 Grid and that is another new theorem in math using mathematical induction method. Further we build the 1000 Grid with inductor element 0.001, then the 10^4 Grid, then the 10^5 Grid and on to infinity.
A "theory" in mathematics is a collection of theorems. And that is what the Method of Mathematical Induction is, for it is more than a axiom, but rather it is a "theory" of mathematics.
What Kronecker observed was that the Counting Numbers seemed to be special, but Kronecker failed to realize that the Reals of Mathematics were fake numbers. For the Reals are a continuum and not until the year 1900 when Max Planck came in physics to announce the birth of quantum mechanics physics that physics is discrete numbers only and no continuum, will this become apparent to mathematics only by AP starting in 1991 and ending up here in 2026, that the true numbers of mathematics have to all be Countable by Mathematical Induction.
So mathematics starts with add and ends up last with integration as the most complicated which in mathematics is Integration of calculus.
As for the ordering in Logic, it is a little different from math which has add as first.
Logic is a bit different. We first have to know what we talk about exists or does not exist and use the Existential quantifier. Next we use the Not along with Equal sign for truth tables, and so we need a connector for Not with Equality which is presented in a combined connector of Not-Equal, some prefer to call it Equal-Not.
Makes sense, that as we start Logic with the question of Existence, naturally that gives rise to whether the physical object Exists or does Not-Exist.
No use in arguing over things that do not exist. And just as a fiction story is fiction and non-existing, no use in arguing for truth.
For Logic seeks Truth and truth comes from the sciences. Science overhangs all of Logic as the bearers of truth, and, if partially true a dT value, or if not true at all then it has a 0-value for nonsense.
The Existential quantifier is the existence in Logic and for math that would be the derivative of calculus in First Quadrant Only, starting with origin at coordinate point (0,0,0) in 3rd dimension or (0,0) in 2nd dimension. In true math and true logic, no negative numbers exist and Logic explains why no negative numbers exist in this world.
Common sense why negative numbers do not exist. What is a negative-person if -1 is the negative of 1? What is a negative-statue of liberty? What is a negative-car? The point is. Existence is a positive reality. Negative reality does not exist. Archimedes Plutonium is a person, and what would a negative Archimedes Plutonium be?? Another example is a yard or lawn that has 3 dogs in it. What if we subtract 4 dogs? Does that mean we have a 1 negative dog in the yard? You cannot remove (subtract) more than what exists in reality.
When we graph in mathematics such as a function. The derivative is a motion starting from 0 and taking in all the positive decimal grid numbers as it moves from left to right in the first quadrant only. The derivative is existence of one coordinate point to the next coordinate point. A graph was shown in this book on calculus derivative motion.
So for logic we have to study the 6 connectors in an order from simple to most complicated.
Correct order of the 6 simple connectors of Logic.
-------------------------------------------------------------
1) Existential quantifier
2) Not-Equal
3) AND
4) OR
5) If--> Then
6) Universal quantifier
The truth-tables come in for the connectors that are ---not quantifiers---. We do not have truth tables on Existential and Universal quantification. We have truth-tables on Not-Equal, AND, OR, If-->Then.
And those are arranged in order for Not-Equal truth table is TTTT, while AND is TTTF, and OR is FTTF, and If-->Then is TFUU where U means unknown, undefined. Of course T means true and F means false.
You can see a pattern in the truth-table from that of 4 trues, then 3 trues, then 2 trues, then 1 true.
11) The Not-Equal connector.
Here is an awfully interesting problem that Logic must sort out. Do I call it the Equal-Not connector or call it the Not-Equal connector? At first I called it the Equal-Not, thinking Logic needed equality before it needed to have "not". But then I realized that "not" needs to come before equality in that of Exists is the first connector of Logic for no reason to talk at length and argue over about nonexistent objects, and also, the fact that Not Exists for contradictions stops all logic. All of logic comes to a grinding halt if a contradiction arises and Logic then has to sort out the contradiction by using the best science of the times in order to sort out the contradiction and then go forward. So that answers the question of Not-Equal versus Equal-Not. Existence first, Not second and then Equal third. But we have to combine Not with Equal as one connector. But that does not stop us from calling it Equal-Not or Not-Equal. Call it either one as you wish for often I call it Equal-Not when talking of only the 4 simple connectors but call it Not-Equal when speaking of the Existential and Universal quantifiers.
Order is essential in Logical truth, as essential as truth-value is essential.
Logic has to put things in Order. And the first connector we deal with is the Existence quantifier. No use in having an argument over something that does not exist or is idle chitter-chatter. So first comes existence. Then comes the need for "not" as in "does not exist" and then comes equality. Does it exist or does it Not-exist is the question of logic order.
Apparently I need to call it the Not-Equal connector, because Existence is the first question in Logic and to be involved with existence we are asking if it "does not exist". The issue of "sameness" in equality is remote when concerned over existence. In existence the issue is "does it exist" or "does it not exist". Like in the famous Shakespeare play of Hamlet-- "To be or not to be, that is the question?"
Let me reiterate the Not-Equal connector of Logic and why we start with Existential quantifier, next we introduce the Not-Equal connector in Logic. We start with existence for there is no point in making a Logic Argument over something that does not exist, is fictional, is imaginary. In our modern day TV world of drama and fiction, plays games on our minds, that if not careful, some people actually think the shows they watch have some reality. And because it is fiction and drama and does not exist we sometimes have to step back and remind ourselves that we are probably wasting the time of our life.
Then in modern society we have the Internet loaded with falsehoods and have to navigate a mountain of falsehoods.
Truth and reality and what exists is given by the best available sciences of the time pertaining to the subject or topic on hand. We have to have "Not Exist" of Logic. This causes and forces us to consider the next connector after Existential quantifier is the Not-Equal connector.
But there is a huge problem with the Not-Equal connector compared to AND, compared to OR, compared to If-->Then for they are 4 rowed truth tables, while Not is a binary two row truth table, same with Equal is a binary two row truth table. No worries, for to make Not-Equal into being 4 rowed truth-table we simply combine the two together making 4 rows.
And, this makes common-sense on another level. Is the statements P, Q, are they equal the same or not-equal. So we use "not" for exist or not-exist, and now we use "not" for "is equal" or is "not equal".
We start with Existence and then move to Not-Equal because all the other connectors need the concepts of existence, not and equal. Not-Equal is multiplication in mathematics and in geometry particularly, is area as length times width, and is all of Space as volume is all of space in multiplication. Volume as you remember is length times width times depth.
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.
Note: I use equal equality throughout this book for I have the symbol of equivalence not available. Equivalence is more general than equality, and without loss of generality in this book, I simply use equality. Equivalence for those who did not major in math, is such as 1/2 is equivalent to 3/6 is equivalent to 5/10. You get the picture. Equality is identical, the same, while equivalent can be reduced to become equal. Equivalence occurs when people want to relax the strict concept of equality. Equal is identity the same. While equivalence is almost equal but shades of differences. And all the more reason that the True Numbers of Mathematics are __not the Reals___ but are the Decimal Grid Numbers where we do not have the problem of running into 5/10 = 1/2 =0.5. For there in Decimal Grid Numbers we see only decimal numbers and not get hung up over the fact someone has an unfinished division problem as a Rational Number. In New Math and New Logic, we can eliminate "equivalence and make it all be equality".
Because Equivalence can be reduced to Equality, we hence-forth avoid the concept of equivalence. All equivalence can be reduced to equality, so we make no more fuss over shades of equality.
That is an important data to know and I shall repeat it. In science and math we often run into the idea that there are several different notions of "equality" such as equivalence. And one would have thought that "equal" is enough, without having the world cluttered up with a similar notion as equivalence. For example, 3/9 is not the same as 1/3 until we reduce 3/9. If we take a cherry pie and cut it into 9 equal pieces is not the same as cutting that same cherry pie into 3 equal pieces. But, 3/9 is reduced to 1/3. So instead of dreaming up different notions of equal, we just say that if it can be reduced to equality, then Equality being the same is all the concept of "sameness" we ever need.
For comparison sake we show the AND connector truth-table which is the next chapter. 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 New Logic we no longer define connectors by their truth-table, as we already see that Existential quantifier has no truth-table and that Not-Equal just barely has a truth-table considering we had to lump the two binaries together to form a 4 row table. So in New Logic what we do is rely on science, especially Physics on defining the connectors by a universal structure that defines them. I call this universal structure the connector-structure.
This is important, for we define Logic connectors by a connector-structure.
------------------------------------------------------------------
We define logic connectors by a structure, not by its truth table. Although the truth-table helps us to ascertain what the structure is.
In New Logic we define all 6 connectors by a 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 structure, we avoid the seemingly contradiction.
For __Existential quantifier that 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 connector-structure__ 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.
Philosophy warning for Not-Equal, which we have to add to the discussion. A major problem of Old Logic was the recurrent mistake of thinking ideas were tagged with negative numbers as being opposite of the true idea. For example: "Earth has one satellite called the Moon". The Not or negative of that statement is : "It is not the case that Earth has one satellite called the Moon".
So, does that mean Earth has 2 satellites or 3 or more, or perhaps no satellites at all. So in Old Logic there was obfuscation surrounding the Not connector and the philosophical idea that the negation of a true statement can have multiple or even an infinity of Not ideas.
While, in New Logic, there are only two values in truth tables-- a value of 1 for all truth and a fraction of 1 greater than 0. New Logic has truth values of 1 and a positive number value greater than 0; and, where all false or meaningless statements and chitter-chatter nonsense has a value of 0. New Logic truth values range from 0 to 1 with partial truth values in between. False is 0, and full truth is 1 while some values are dT a fractional truth.
So, when a Logician examines "It is not the case that Earth has one satellite called the Moon". The New Logic logician simply throws out the statement as meaningless nonsense with 0 value and be done with it, for he/she has looked up the science and wastes no more time on it. While the Old Logic logician spends hours upon hours mulling over the statement and wasting more time, and further, using the worthless statement in more argumentation. Does it have 0 moons, does it have 2 moons, does it have 3 moons.
In New Logic an idea in statements of p,q,r,s,t etc that is false from science, is thrown out. And logic only retains true ideas supported by science and manipulates those true ideas to make new true ideas. These True statements are given a name and called a "Premiss". Statements can be true or false or partially true dT, and statements can be compounded with the connectors. Premisses are individual statements or compounded statements, but, unlike statements, all premisses have to be "true" or dT partial true.
Further example. I love the old Irish saying : "If it works, do not be fixing it."
The Not or negation of that statement would be "It is not the case that if it works, do not be fixing it." Some would prefer to say it as this "If it works, do be fixing it". Here philosophers and Old Logic logicians would step in and say it is a worthwhile statement. While New Logic logicians would point to science and say, if you take apart something that works, the probability chances are risky that once reassembled it no longer works, or works as well as before. And look closely at that negation for it suggests a spectrum of benefits will accrue someone who takes apart a machine that is working. An infinity of negative number benefits from taking apart a working machine. While New Logic logician simply would say there is 0 value in taking apart a working machine is foolish for you risk making it be non-working.
To a large degree the concept of Not is a reversal connector, a contrary statement from the original statement. It reverses true statements into becoming 0 value statements. But in many cases, the Not reverses a 0 value statement into a true statement. So here is a major difference between New Logic and Old Logic. The "Not" connector in Not-Equal does not necessarily convert a 0 value statement (false statement in Old Logic) to a true statement. To the contrary, the Not connector often leaves a 0 value statement -- a false statement remain to be of 0 or nonsense value. And the Not connector can leave a 1 value statement of true and the not statement remain true. The reason being is seen in the truth tables above where we manipulate two rows to force a table of TTTT.
Example: P= Ships are made out of paper. The not-P would be "Ships are not made out of paper." P is false but not-P is true.
Another example: P= Ships are made out of wood. The not-P would be "Ships are not made out of wood." P is true and also not-P is true, for some ships are made of wood and some are made of steel.
Another example: Of where P is true and not-P is true, even though contrary. Here I am going to apply biology statements. P= Viruses are living organisms. The not-P= Viruses are not living organisms. Analysis: throughout this textbook I have been harping the idea that truth is determined by the best available science on the topic. The science of biology claims that Viruses are living in the fact that they have DNA and hijack other cells into making more virus DNA. But some biologists reckon that Viruses are not living because they lack cellular structure and independent metabolism to make energy. So in a sense, the science of biology has come to a standstill saying P is true and not-P is also true.
Again, this reflects back to the Not-Equal truth table of TTTT, where the Not turns a P and a not-P to both be true.
Another example: this time where P is false and not-P is also false. P = Atoms have a nucleus, a center with all the protons and neutrons are clustered into a ball. The not-P= Atoms have no nucleus, a center with all the protons and neutrons are clustered into a ball. Both P and not-P are false according to the best science on the topic. Atoms have a Proton torus surrounded by neutrons as parallel plate capacitors. Yet, the center of Atoms would be these neutrons as parallel plates.
Another example: another P is false and not-P is false. P= If intelligence requires self-awareness, then no AI exists. The not-P= It is not the case that if intelligence requires self-awareness, then no AI exists. Both statements are false because the best available science says that the threshold for being "intelligent" is to have self-awareness. All plants and animals have self-awareness. No computer machine to date has self-awareness as measured by the ability of the machine to turn itself on, or off from its own volition.
About the concept of the Contradiction
---------------------------------------------------
Contradiction in Logic and science is defined from the Not-Equal connector. Throughout this book I have been harping of the fact that when logic arguments run into a Contradiction, all things must stop and sort the contradiction out, using the best available science data and facts.
A= A, and A does not equal not-A, and A does not equal B, C or any thing else but A.
Logic starts with Existence and the Existential quantifier. Logic then moves into the Not-Equal connector. Does it exist or does it not exist. And while inside of the Not-Equal connector, the Contradiction concept itself is defined.
Not-Equal truth-table:
p q
T T = T
T not F = T
F not T = T
F F = T
The Not-Equal truth-table defines the concept of Contradiction as shown in second and third row as we turn the F into "not F" and the T into "not T" as that which A exists plus A does not exist. And more generally A multiply not-A.
Mathematics as a science never comes to the contradiction concept until math comes to division. There, at division, mathematics sees that division by 0, tears up all of mathematics. If we allow 1/0 to equal something, then we destroy all of mathematics for then we have 1=2, or 3= 11, or 0 = 1 all because we allow division by 0. We cannot have division by 0 for we lose all of mathematics. We cannot have a Contradiction in Logic for that tears up all of Logic.
The structure of Not-Equal is that equality is sameness, A= A, plus, Logic itself cannot have any contradictions where A = not-A. If a contradiction arises in Logic or a argument of Logic, all must stop and come to a grinding halt and only resume by correcting the contradiction.
12) The AND connector.
So, we define and describe the connectors of Logic, not by their truth tables but as a structure of Logic, much like physics is a collection of Law-structures, the Faraday law-structure, the law-structure of universal gravity and others. We define AND connector not as a truth table of TTTF, but as a structure that says in a string of ideas, statements of ideas p,q,r,s,t etc connected through AND, if one of the ideas is true, the entire string is true. Why define by structure instead of the Truth-table is evident in AND, in that a table cannot express the limiting idea that what if P AND Q are two contradictory statements. P = Earth is flat while Q = Earth is not flat. So we have P AND Q as true if we relied only on truth tables of TTTF for AND. But when we write AND as a connector-structure of logic, we state in the structure that AND cannot contain two contradictory statements and we have to stop the logic work and resolve the issue of contradiction.
The truth-table of OR is riddled through with a strange truth value of a partial-truth in order for science to argue in a Deciding Experiment, which of statements P OR Q is the true statement, and the other partially true. By using truth-tables as defining the connector is just inadequate and we have to resort to a structure of AND and a structure of OR.
And the connector If --> Then is riddled full of strange things such as the U for undecided or unknown along with T for true and F for false or gibberish. So writing the definition of If-->Then, as a structure opens up and reveals much more about the connector then if we accepted the truth-table for If-->Then as its definition.
Structures express more details of the connectors than just plain using the truth table.
So we define connectors of true logic, not by a truth-table but by connector-structures, same as in science, for science is defined by their universal law-structure, much like the law-structures of physics. For example the law-structures of electromagnetism-- Coulomb, New Ohm's, Faraday, Lenz, Ampere.
The Existential quantifier is defined by structure as something exists due to the available best science on the subject showing the object exists, plus, you cannot have A exists and A does not exist for that is a contradiction and Logic comes to a grinding halt to straighten-out the contradiction before continuing further.
The Not-Equal connector is defined by structure as "Not" is the reversal of a statement while "Equality" is identical sameness. Keep in mind, Not is bound together with Equal and unable to be a separate concept in itself.
Example: "Plants are species that live on CO2 while animals are species that do not live on CO2."
Explanation: All plants share the sameness of living on CO2, while animals do not share a sameness with the breathing in of CO2 to live on that gas molecule. This example shows how "equal" is bound up with "not".
We now define the AND connector, not with truth-table but with a connector-structure saying that AND connector is one of add or join two or more statements of ideas together. And the structure that defines AND is that within a string of statements joined by AND that at __least one of the statements has a full 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. By full truth value the AND connector is not true if only a partial true value of dT. If a contradiction occurs in a string of statements, then all stops and until the contradiction is excised out, and then does logic continue further.
That means a string of statements, p,q,r,s,t,u,v connected by AND can be true if just one of the statements is fully true, and the rest be worthless nonsense, chitter-chatter and outright false. However, beware, there cannot be a contradiction of say v and not-v in the string. The expression given of AND is "we do not throw the baby out in the bathe water".
If one wanted to give a truth-table of AND it would look like this.
New Logic
AND truth table
p q p AND q
T T = T
T F = T
F T = T
F F = F
And with modern day computers needing to do arithmetic Add, they have their software make addition with a truth table of TTTF.
And if we substitute T with 1 and F with 0 we see again that AND is add of arithmetic.
p q p AND q
1 1 = 2
1 0 = 1
0 1 = 1
0 0 = 0
Now the AND connector of Logic has several replacement terms in English as being "but", "yet", "also", "still", "although", "however", "moreover", "nevertheless", even the comma and semicolon are AND replacements (source: Copi on conjunction).
The AND connector of Logic. To my mind the easiest connector for it is simply add of arithmetic. In fact, we can replace the word "and" with that of "add".
However, AND does get confusing or distracting in arguments because T AND F or F AND T both result in a true overall statement, yet it contains a falsehood or gibberish.
Homework: Examine these AND connected statements and pick which is the true statement and the other a false or gibberish statement.
Note: sometimes we use other words that mean AND, such as "both" sometimes "because".
1) The Earth is flat and it rotates on an axis.
2) The Winter solstice is 21 December this year and it is the first day of Winter.
3) The Big Dipper points to the North Star, Polaris, and Polaris is in Cassiopeia constellation.
4) Higgly piggly, the cow jumped over the moon, because the Moon arrived to Earth to be a satellite only 90 million years ago.
5) The Sun has gone Red Giant and so Santa will be late for Christmas.
Archimedes Plutonium Jan 20, 2026, 11:57:06 PM to Plutonium Atom Universe newsgroup.
So here we see that the AND connector in Logic is similar to the Add operator of mathematics. But carefully notice that in a logic arguments, statements using the AND connector can have falsehoods and gibberish nonsense in addition to a fully true and worthwhile statement.
This is often seen in the case of mathematics proofs. Where a proof is given but carries a-lot of side-show nonsense, even a falsehood here and there. And the way many mathematicians react to the nonsense or falsehoods, they eventually trim out the nonsense and throw-out the falsehoods. But still leaving behind a valid proof.
But, even if they did not, the proof is still valid with or without the falsehoods and gibberish nonsense.
Now, one has to ask the question why on Earth would Logic be a systematic science of ideas and need a connector such as AND that can carry around falsehoods and gibberish nonsense in arguments of Logic?? What is the need for this transport of 0 valued falsity in arguments or partially true dT statements?? Here I look to the Scientific Method for an answer. What is the function of carrying extra baggage in an argument, some outright false, some gibberish? Well in taking baggage on a expedition, we often take more than needed, just in case. And it is this idea of utility. The AND operator is a utility operator, just in case an idea needs support, like supporting evidence. We can think of the AND carrying extra baggage as carrying extra hypotheses of science, where the first hypothesis is wrong so we go to a second hypothesis.
13) The OR connector.
Alright, I am up to OR connector but need a vast overhaul of OR in order to make its truth table align with mathematics arithmetic.
The Truth table representing subtraction or Remove, for the term "remove" would have been a far better name for subtraction and could have made silly math professors realize that negative numbers are crank-crackpot ideas, because removing more than what is available to remove is insanity. Remove is what the OR connector is all about. As we saw before, AND is add or join together. So Logic would need a connector of Remove or subtract.
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 of 1 and the other a partial fraction of the truth say 2/3 true.
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 1 remove 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
As I write the connector-structure of OR, the structure must consider the 4 possibilities of Remove (subtract).
This is why I use Mathematics to guide me in the True Logic connectors. You see the third row above of F T then T is (fraction -1) = 1 is not allowed in arithmetic by the axiom that you cannot subtract more than what is available.
And this is why the Truth Tables are not the correct definition of any of the connectors but has to be a structure that states-- in statement form-- the correct definition of any of the Logic connectors.
The definition of all 6 Connectors of Logic is best served by a written statement or statements as a structure of Logic. The Truth-tables ___cannot____ properly define the 6 connectors for they leave too much out of the meaning of the 6 connectors. Written structures, like the written law-structures of Electromagnetism in Physics best describes the phenomenon that is being defined. Truth tables in Logic are only a shadowy glimpse of what the definition may be, but cannot adequately define Existential quantifier, Not-Equal, AND, OR, IF-->Then, Universal quantifier.
Alright, I am up to OR connector but need a vast overhaul of OR in order to make its truth table align with mathematics arithmetic.
The Truth table representing subtraction or Remove for OR.
New Logic OR (exclusive)
p q p or q
____________
T T F
T dT T
dT T T
F F F
Where the dT represents partial true value of a fraction value between 0 and 1.
So, OR cannot be defined from truth table but must be defined by a statement summary, just like defining the Faraday law-structure as--- thrust a bar magnet through a copper coil connected in circuit with a Galvanometer and watch for the reading of electric current produced by the thrusting bar magnet.
That is the OR truth table, but it does not give you information on how it is formed. For information we go to math arithmetic of subtraction which is better called Remove.
AND connector in previous chapter is addition and joining together of ideas, while OR should be the reverse of joining together but removing.
Archimedes Plutonium Jan 21, 2026, 12:12:33 AM to Plutonium Atom Universe newsgroup.
13) The OR connector of Logic
------------------------------------------------
AND or add connector was rather simple, but now we come to the OR connector which is far more complex and complicated.
OR is sometimes stated as "Either....or" another replacement is "alternatively". OR is the opposite of AND where we add, but in OR we remove, we subtract.
Physics is famous for experiments that tell us the truth of the world in Law-structures of physics or law-structures of any science. Often, a science has to decide on which of two statements is the true statement and which is wrong and discarded.
Example. The Earth is flat or, the Earth is Round.
Here we have two statements "P= The Earth is flat." With "Q= The Earth is Round" and it is the job of science to make experiments and decide which is true P or Q, whichever is true, we discard the false one.
OR as a connector does not tolerate falsehoods in deciding experiments and so its truth table is very different from AND in that it has partial truths written as dT. When you see the symbol dT, it means the statement has a fractional truth value but parts of the statement are false.
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 where T is valued at 1, F at 0, and dT a fraction of 1.
p q p or q
____________
1 1 0
1 1/10 1 once we discard 1/10
1/10 1 1 once we discard 1/10
0 0 0
So we have 4 possibilities.
1) Remove P keeping Q
2) Remove Q keeping P
3) Subtract P from Q provided Q is larger or the same size
4) Subtract Q from P provided P is larger or the same size
New Logic OR (exclusive)
p q p or q
____________
T T F
T dT T
dT T T
F F F
Examples of 2nd row and their deciding experiments.
1) Either the Sun shines 90% from Faraday law-structure or the Sun shines 100% from fusion of light elements forming heavier elements.
Deciding Experiment: It is found that a muon of 105MeV is inside a proton torus of hydrogen of 840MeV. Why would that be a deciding experiment?? Because a muon thrusting through a 840 windings of 1 MeV each is the Faraday law-structure producing electrical energy.
2) Earth has earthquakes caused by the rattling and vibration of the two inner cores, or, Earth has earthquakes due to the motion of convection currents in mantle and crust.
Deciding Experiment: If Convection currents are the cause, earthquakes would not move in one direction then back up and move in the opposite direction. But if it is the vibrations of electric motors that the cores are, then the motion is forward then backward.
Examples for 3rd row and their deciding experiments.
3) Either Smilodon, the saber tooth tiger really did grow large canine teeth, or, they are walrus tusks glued on by paleontologists and museums.
Deciding Experiment:: DNA test all museum specimens of Smilodon of the jaw and of the canines, if found to be cat DNA or walrus tusk DNA.
4) Either the chemical formula for Water is H2O, or, the true chemical formula for Water is H4O.
Deciding Experiment:: Insist that lazy chemists and physicists stop their water electrolysis experiment when they check for volume of hydrogen compared to oxygen, then hop skip jump back to the lounge for cake coffee and donuts, but rather, insist they get out the micro quartz balance and actually weigh the mass of the hydrogen as compared to oxygen. What prompts AP to do this extra work, is that the Atom needs all three of muon, proton and at least one neutron to store the energy created by Faraday law-structure as the muon thrusts through the proton torus of hydrogen. No atom can exist without some form of neutron. Chemists and physicists have been exceptionally lazy and ignorant in weighing the results of Water Electrolysis.
Archimedes Plutonium Jan 21, 2026, 5:56:09 PM to Plutonium Atom Universe newsgroup.
On Wednesday, January 21, 2026 at 4:21:43 AM UTC-6 Archimedes Plutonium wrote:
4) Either the chemical formula for Water is H2O, or, the true chemical formula for Water is H4O.
Deciding Experiment:: Insist that lazy chemists and physicists stop their water electrolysis experiment when they check for volume of hydrogen compared to oxygen, then hop skip jump back to the lounge for cake coffee and donuts, but rather, insist they get out the micro quartz balance and actually weigh the mass of the hydrogen as compared to oxygen. What prompts AP to do this extra work, is that the Atom needs all three of muon, proton and at least one neutron to store the energy created by Faraday law-structure as the muon thrusts through the proton torus of hydrogen. No atom can exist without some form of neutron. Chemists and physicists have been exceptionally lazy and ignorant in weighing the results of Water Electrolysis.
The message I was getting across in Water Electrolysis is that a hydrogen atom with only a proton and muon inside is not a Atom at all, but a subatomic particle. All Atoms need some form of a neutron. It does not have to be a fully grown neutron of 945MeV but a partially grown Neutron to store the electrical energy giving off by the Faraday law-structure of muon thrusting through proton torus.
Archimedes Plutonium Jan 8, 2026, 2:49:14 AM to Plutonium Atom Universe newsgroup.
I had to modify drastically, the OR connector, where truth has a Range of values. Where full truth T has a value of 1, and full false has a value of 0, but you can have truth values between 0 and 1, and those variable values need to show up as "dT" in OR truth table.
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
Example: P = The Sun is a star. Is a true statement with value 1. Q = The Sun is a planet. Is a false statement with value 0.
R = The Sun is a blue star. Is a statement that has a fractional truth value, for the Sun is a star but it is not a blue star. So we say the truth value of R is intermediate between 0 and 1 and give it a truth value of 0.25.
The greatest use of OR in logic is to evaluate Deciding Experiments of Physics. Is the Light-photon a Light Wave or as AP thinks, a Light Wire.
So in Logic we have the statement Either the Light-Photon is a Light-Wave, OR, it is a Light-Wire. From there, that argument proceeds and one of them will win, the other will lose. Both have a truth value greater than 0.
Archimedes Plutonium Jan 8, 2026, 8:15:21 PM to Plutonium Atom Universe newsgroup.
A logic textbook is the very hardest science book to write. I should know, finding out from experience, for now I start over again all 4 my of logic textbooks because of "dT".
Now some may question if the dT variable truth, part true and part false is needed in any of the other 5 connectors of Logic, other than the OR connector. And here is the beauty of modeling Logic after mathematics. In mathematics, as we substitute 1 for True and 0 for false in the connectors, the only time in which this substitution breaks apart is in the OR connector, and demanding for us to craft and create the dT variable truth value. You will notice in the next chapter on If-->Then we introduce a new parameter of U in the truth tables meaning uncertain or undefined. The U is different from T as 1, and F as 0, and dT as partial truth. The U also comes from mathematics in the knowledge that we cannot divide by 0. But that is not solved by using a dT in the If-->Then. The use of dT in OR arose because we cannot mathematically take 0 -1 = -1. The dT arose from that impossible math arithmetic of getting negative numbers. And although some will complain that 1/10 subtract 1 is still a negative number, in the structure of OR will stipulate that the subtract or removal of (1/10) - 1 is such that you remove 1/10 altogether leaving only 1. When we look at the second row instead of the third row of OR, we have 1 - 1/10 and here the subtraction is not ending up as 9/10, no, it ends up as removal of 1/10 altogether and leaving behind 1.
So in summary, the dT special variable comes into Logic only in the OR connector, only 1 of the 6 connectors. But, and however, we can use a partial truth dT in any connector we want, we need not confine dT to just the OR connector.
14) The IF-->Then connector.
14) The If-->Then connector
There are 4 simple connectors of Logic, Equal-Not, AND, OR, If->Then and we talked about the truth tables of three of them. Now we turn our attention to the fourth simple connector of If-->Then. It is far more complex than Equal-Not, AND, OR. And we learned that Equal-Not is multiplication; AND is addition, and OR is subtraction. That leaves only division remaining. The If-->Then connector is also called the "implication" or the "conditional" some go so far as to call it the "material conditional" and some call it the "hypothetical". The statement between the "if" and the "then" is called the antecedent, while the following statement after the "then" is called the consequent.
I often like to think of the If-->Then connector as the "move-into" connector. A famous philosopher, Plato, dwelled on the idea of transformation of "Being into Becoming". As the "If" is existence and then the growth and change as the "then".
One of Logic's first syllogism was this. (A syllogism is a simple two line argument with a conclusion.)
All men are mortal.
Socrates was a man.
Therefore, Socrates is mortal.
That entire argument can be rewritten as a If -->Then connected statement.
If all men are mortal and Socrates is a man, then Socrates is mortal.
So far the truth table of Not-Equal (some prefer to write it as Equal-Not) had all 4 rows being true. AND had 3 rows being true. OR had 2 rows of being true. Take a guess of how many rows are true for If-->Then????
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
Let us see how assigning T = 1 and F = 0, makes the If --> Then be division in arithmetic.
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
We must talk about the strange two rows of U for the If-->Then.
Archimedes Plutonium Jan 24, 2026, 3:12:26 AM to Plutonium Atom Universe newsgroup.
The strange two rows of If--> Then are because a falsehood will never lead to truth in science, and furthermore, mathematics needs division divided by zero be undefined. We cannot have math be more than logic. Logic needs to reflect all the truths of mathematics and then some.
Examples of If-->Then
1) If we have drought in 2026 in my region, then the plants will wilt and stop growing.
2) If the Sun shines from Faraday law-structure, not from fusion, then every year gets on average hotter than the last year.
3) If the Sun shines from Faraday law-structure, then the polar ice caps will accelerate in melting.
4) If the Moon arrived near Earth only 90 million years ago, then that easily explains how dinosaurs could live on both poles of Earth as one side of Earth constantly had daytime, no night.
5) If the Moon arrived near Earth only 90 million years ago, then that explains how life came into existence in warm seas and no violent motion.
6) If the Moon was always there when Earth was there some 4.5 billion years ago, then life on Earth would not have evolved out of the seas for the conditions were not suitable.
Analysis: (1) is If T, then T. (2) is If T then T. (3) is If T then T. (4) is If T then T. (5) is If T then T. (6) is If F then U unknown.
Archimedes Plutonium Jan 24, 2026, 5:58:50 PM to Plutonium Atom Universe newsgroup.
Canada's math and logic failure Dan Christensen in sci.math gives examples of IF-->Then where the "if part" is true but the "then part" is false and thus making the entire statement be false.
Dan Christensen in sci.math
Feb 22, 2024, 8:54:35 AM
to
STUDENTS BEWARE: Don't be a victim
"Water is really H4O, not H2O." ********** NEW **********
--July 27, 2023
Canada's Dan Christensen in a round about way says-- If water is not H2O then it is really H4O.
Analysis: If T, then T, making the entire statement be true.
Conversation: Apparently no scientist in Canada is intelligent enough to get out the weight scale and weigh the mass of hydrogen compared to oxygen, no, they run skip and jump to the lounge after looking at volume, too lazy to complete water electrolysis by weighing of mass, for them, the coffee cake and donuts is more urgent.
"Negative numbers are the witches and hobgoblins of insane kook mathematicians. "
--Dec. 7, 2022
Dan in a round about way says --- If negative numbers are witches and hobgoblins, then mathematics is insane kook.
Analysis: If F, then F, making the entire statement be U for Uncertain because you have the If portion as false.
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
“0/0 must be equal to 1.”
-- June 9, 2015
“0 is an infinite irrational number.”
--June 28, 2015
“No negative numbers exist.”
--December 22, 2018
“Rationals are not numbers.”
--May 18, 2019
According to .. “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019
Which could explain...
“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019
“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019
“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994
“The Universe itself is one gigantic big atom.”
--November 14, 2019
AP writes: It is sad for Canada, that they allow some goonclod freak of Logic pander his mindless take on Logic, for such a fool blurted this out to sci.math showing that Dan Christensen is a worthless, miserable failure of both math and logic.
Here is an example of Dan Christensen in sci.math fumbling with the most simple of logic reasoning, and yet Canada keeps allowing this misfit to dig deeper into logic and pollute the minds of our young people.
The stupid Dan Christensen always chokes up when it comes to logic or even just plain commonsense with his 2 OR 1 = 3 and his AND as subtraction.
On Wednesday, January 25, 2017 at 10:08:09 AM UTC-6, Peter Percival wrote:
> Dan Christensen wrote:
> > On Wednesday, January 25, 2017 at 9:47:32 AM UTC-5, Archimedes Plutonium wrote:
> >> On Wednesday, January 25, 2017 at 8:27:19 AM UTC-6, Dan Christensen wrote:
> >>> On Wednesday, January 25, 2017 at 9:16:52 AM UTC-5, Archimedes Plutonium wrote:
> >>>> PAGE58, 8-3, True Geometry / correcting axioms, 1by1 tool, angles of logarithmic spiral, conic sections unified regular polyhedra, Leaf-Triangle, Unit Basis Vector
> >>>>
> >>>> The axioms that are in need of fixing is the axiom that between any two points lies a third new point.
> >>>
> >>> The should be "between and any two DISTINCT points."
> >>>
> >>
> >> What a monsterous fool you are
> >>
> >
> > OMG. You are serious. Stupid and proud of it.
>
> And yet Mr Plutonium is right. Two points are distinct (else they would
> be one) and it is not necessary to say so.
>
Apparently Dan Christensen never took calculus or flunked it with this statement.
On Tuesday, June 2, 2015 at 8:57:54 AM UTC-5, Dan Christensen wrote:
> On Tuesday, June 2, 2015 at 2:32:51 AM UTC-4, Archimedes Plutonium wrote:
> > The nonexistence of a curved angle because there is no way to measure the angle if either one of the rays is not a straightline segment at the vertex,
>
> From the derivative of each curve at the point of contact you have the slopes of their respective tangents there. (Assuming derivatives are defined there.) From these slopes, you should be able to calculate angle formed.
>
>
> Dan
Archimedes Plutonium Jan 25, 2026, 1:03:21 AM to Plutonium Atom Universe newsgroup.
I am rather thankful that sci.math and sci.physics from 1993-2024 had a goonclod gang of stalker failures of science and logic for it is difficult for a normal scientist to come up with muddle headed logic since we spend much of our time on only truths of science. And so I am thankful that the dumb failure Dan Christensen posted so much logical crap to sci.math and saves me a-lot of time.
Dan is a failure of math and logic and one of the reasons he fails so much is it is impossible to make clear his thoughts, no his big loud mouth gets in the way of clarity, and this is a harbinger sign for students around the world to learn--- if you are around a "loudmouth" usually means the louder the mouth, the more empty the thoughts inside and is wasting your valuable time in life.
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020 by Dan Christensen in sci.math
What Dan was trying to say is this.
If Primes existed, then they should come from a set that is complete to division. The 10 Decimal Grid Numbers 0, 0.1, 0.2, 0.3, ...0.9, 1.0, 1.1, ... , 9.8, 9.9, 10.0 is the smallest Grid System and has division. Divide 1 by 10 and you have 0.1. Divide 5 by 10 and you have 0.5. So of the integers in 10 Grid can we say any of them are prime???? For 5 is divisible by 10, divisible by 0.5, divisible by 2.5 and many others. The number 3 is divisible by 10 by 0.3, by 1.5, etc. So that when a stupid mathematician or logician says Primes are only divisible by themselves and the number 1, while never paying attention to the fact the fool choses a set that is undefined towards the Operation of Division in the first place. So that the concept of Prime is itself Vacuous and Meaningless.
When the true numbers of mathematics are the Decimal Grid Numbers starting with 10, then 100 then 1000, etc. There is No Concept of Prime because every number (except 0) is divisible by another number other than 1 and itself. In Decimal Grid Numbers, the concept of Prime is a bogus concept.
Dan's statement turned into a If-->Then. If Primes exist, then the set they were borne from has no valid division.
Analysis: Here we see that "because" is often a replacement for "If-->Then". If T, then F. This is an example of what If-->Then avoids at all cost, a IF--> True leading to a Then False.
Statement P= Primes on Counting Numbers do not exist because Counting Numbers are not complete to division.
That statement is the same as Q= If Primes exist on Counting Numbers, then the Counting Numbers are complete to division.
Do you remember what completeness of a set means?? If not, let me refresh you. Counting numbers are complete to multiplication because when you take any two counting number and multiply them together, you end up with another counting number.
We cannot say the same thing for division on counting numbers for example 1 divided by 2 is not a counting number but a fraction as 0.5. Completeness is defined as taking any two numbers to a operation and the operation returns you a number that is in that same set.
But Dan makes a beautiful If T then F in his next example.
Now here is a beauty blunder by Canadian Dan Christensen of a If True then False.
We know in Logic the worst you can do is make a contradiction such as this: The last and largest finite number is 1*10^604 AND 1*10^604 is not the last and largest finite number.
Analysis: that is a contradiction to have P AND not-P. But the IF-->Then connector comes close to matching the nuisance of the contradiction with its If True, then False.
Here the Canadian Dan Christensen makes such a If T then F.
Dan took 6 days to make this mind-rot If T then F.
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
If the last and largest finite number is 1*10^604, then, 0 appears to be the last and largest finite number.
Can the student reader see how similar that is to a contradiction, or approaching a contradiction???
A contradiction is shown above, yet this if..then approaches a contradiction for it is saying 1*10^604 is the same as 0.
Analysis of Dan's If T then F: According to the truth tables of If..Then, it is false when you have If T then F.
Like I said earlier, scientists have their minds and brains dug deep into truth, swimming in truth and looking to find new truths. It is difficult for them to come up with nonsense gibberish bandied about by Dan Christensen and so we look for these failures whenever we want lists of falsehoods and fallacies for teaching examples.
Archimedes Plutonium Jan 25, 2026, 9:41:45 PM to Plutonium Atom Universe newsgroup.
If Harvard has a department of Theoretical Sewing Machines giving out PhDs then surely Jack Murtagh's PhD from Harvard in Theoretical Computer makes some sort of sense.
Analysis: If F, then F. The overall If-->Then is U for unknown as a false premiss in the "If portion" can never lead to a true conclusion for the tenuous connection. This is why I like to say that If-->Then is characterized as "move into".
Harvard has a department of Theoretical Sewing Machines giving out PhDs Moving Into surely Jack Murtagh's PhD from Harvard in Theoretical Computer makes some sort of sense.
Archimedes Plutonium Jan 30, 2026, 7:26:41 PM to Plutonium Atom Universe newsgroup.
Some more If-->Then statements and as homework.
My wall clock shows the phases of the Moon, and today 30 January is a Full Moon where I live in South Dakota. Also my 2026 calendar shows the Moon phases for Eastern standard time which is not far off from my going outside and observing myself.
It is a shame that when I was young, in High School, that I did not do this then, observe the Moon in its phases and learned from the observations. Oh, well, better late than never.
Homework for 1 month, write up on your observations.
----------------------------------------------------------------------
1) IF the Moon on 29 January is a sliver of a crescent Moon located in the SouthWest sky where the Sun sets at that location on 29January, AND the Moon on 30 January, a day later is directly opposite in position in the NorthEast, a move of 180 degrees in the sky, in one single day, THEN, this is evidence the Earth is round and not flat.
2) IF the Moon on 29 January is a sliver of a crescent Moon located in the SouthWest sky where the Sun sets at that location on 29January, AND the Moon on 30 January, a day later is directly opposite in position in the NorthEast, a move of 180 degrees in the sky, in one single day, THEN, this is evidence the Earth is round AND the Earth rotates on its axis each 24 hours.
3) IF the Moon on 29 January is a sliver of a crescent Moon located in the SouthWest sky where the Sun sets at that location on 29January, AND the Moon on 30 January, a day later is directly opposite in position in the NorthEast, a move of 180 degrees in the sky, in one single day, THEN, this is evidence the Earth is round AND the Earth rotates on its axis each 24 hours AND the Solar System is Heliocentric not geocentric.
So in this homework assignment you are to observe the Moon in a crescent phase where the next day the Moon is in the opposite direction in the night sky and is in a full phase. And to answer those If Then hypotheticals using Logic.
In the above I have highlighted the IF-->Then but also highlighted the AND connector.
Archimedes Plutonium Jan 31, 2026, 2:27:35 AM to Plutonium Atom Universe newsgroup.
So we have observations by students at home of the actual physical moon for two weeks.
Then we have an in class demonstration where one student is the Sun holding a flashlight. Another student is the Earth that slowly steps around in a motion to make a rotation of Earth on axis. Third we have a student acting as the Moon holding a mirror that reflects Sun (flashlight) upon Earth, and this moon slowly moves around Earth.
After we watch the demonstration guided by the teacher, we assign the homework to answer.
Archimedes Plutonium Jan 31, 2026, 4:36:25 PM to Plutonium Atom Universe newsgroup.
Helping the students learning logic by picking out images in web search that are helpful.
The University of Iowa image tells us Earth must be Round and moving on an axis in order to physically provide for Moon phases.
But, does any image in a Google search of the Moon phases prove that the Solar System is Heliocentric and not Geocentric?????
---- quoting a Google Search of Moon Phases below---
Phases
Planet parade
Crescent
Eclipse
Sunset
Moon rise
Moon phases
Saturn
Saturn conjunction
Planet alignment
Planetary alignment
Lunar eclipse
Sun
Sky tonight
Understanding Moon Phases: The 8 Stages ...
AstroBackyard
Understanding Moon Phases: The 8 Stages ...
The Crescent Moon: What Causes It to ...
The Old Farmer's Almanac
The Crescent Moon: What Causes It to ...
Skywatch: The moon and Venus can take ...
Pioneer Press
Skywatch: The moon and Venus can take ...
Paths of the Moon and Sun This Summer ...
Creators Syndicate
Paths of the Moon and Sun This Summer ...
Part 1: Lunar Phases | Imaging the ...
Imaging the Universe - The University of Iowa
Part 1: Lunar Phases | Imaging the ...
Archimedes Plutonium Jan 31, 2026, 4:59:57 PM to Plutonium Atom Universe newsgroup.
So I quoted up to the Britannica image as it and several other images prove that the Solar System is Heliocentric which means the Sun is ____Relatively at Rest____ compared to Earth, Moon and the planets.
Now, in this Logic class we are going to build a Model of the Earth to argue against all those people who think that Earth must be Flat in order to not fall off of Earth into Space if Earth was round. Here the story starts with Thales of Miletus in Ancient Greek times 626- 548 BC who studied the Lodestone-- a rock that attracts iron. He also studied static electricity of rubbing amber in animal fur.
So, we are going to have students proposing a hypothesis, nay, theory of science that anticipates Newton from Thales by thousands of years ahead of Newton.
Primal Axiom of Science:: All is Atom, and Atoms are nothing but Electricity and Magnetism.
For, come to think of it, the motion of Sun, the energy of Sun, the motion of planets and Moon are all forms of electricity and magnetism.
--- quoting Google Search for images of Moon phases that prove Solar System is Heliocentric not geocentric---
Waning crescent
Moon Phases - Griffith Observatory ...
Griffith Observatory
Moon Phases - Griffith Observatory ...
Phases of the Moon
Time and Date
Phases of the Moon
Phases of the Moon - NASA Science
NASA Science
Phases of the Moon - NASA Science
Phases of the Moon - Simple English ...
Simple Wikipedia
Phases of the Moon - Simple English ...
Moon Phases, Monthly Lunar Cycles ...
Space
Moon Phases, Monthly Lunar Cycles ...
Experiment Two – Lunar Phases | JCCC ...
Johnson County Community College
Experiment Two – Lunar Phases | JCCC ...
phases of the moon ...
Astronomy Stack Exchange
phases of the moon ...
Moon Phases Poster
Labworks blog - WordPress.com
The moon cycle – Labworks blog
What are the phases of the moon?
NBC News
What are the phases of the moon?
Different Moon Phases Explained: A ...
Country Living Magazine
Different Moon Phases Explained: A ...
The moon goes through different phases ...
US Naval Observatory Astronomical Applications Department
the Moon Illuminated
Moon Phases & Your Monthly Cycle ...
Star In A Star
Moon Phases Names - an easy way to ...
Moon Phases - NASA Science
NASA Science
Moon Phases - NASA Science
Background 2/6 - Lunar Phases - NAAP
UNL Astronomy
Background 2/6 - Lunar Phases - NAAP
Moon Clip Art ...
Britannica
Phase | Definition, Examples, & Facts ...
--- end quote of Google Search---
Archimedes Plutonium Feb 1, 2026, 3:37:57 AM to Plutonium Atom Universe newsgroup.
So I see the full moon on 31January 2026 at a position NorthEast at 6PM. I wait hours later, for 3AM and see the full moon almost SouthWest where the Sunset was on 31January.
Explanation: I am on a round Earth rotating on axis in every 24 hours. As the sun set on 31Jan the moon was full in NorthEast, but as the night moves on by 3AM I am far enough in Earth's rotation by 1Feb2026 to see the full moon nearly in the SouthWest location.
The only feasible explanation for this would be that Earth is round and rotates on axis.
In Logic we learn a valuable principle called Occam's Razor. It basically says that the easiest explanation for events is often the true explanation. We could conjure up theatrics of saying Earth is flat and Sun revolves around Earth, but such theatrics cause the speed of the Sun in motion to approach the speed of light, and makes that explanation be far far fetched.
Archimedes Plutonium Feb 1, 2026, 9:09:06 PM to Plutonium Atom Universe newsgroup.
The only sensible explanation for why the Moon is a full moon, appearing NorthEast at 6PM, 7PM then appearing SouthWest at 3AM is that of the passage of nighttime, me as observer is moving counterclockwise from West to East.
Sensible becomes the same as being ___logical___.
This proves the Earth is Round, a big ball rotating on its axis.
Now there is a far easier proof the Earth is round when we see the earth eclipse the Moon we see Earth's curvature as a round ball in a Lunar eclipse. The trouble with that though, is lunar eclipses are rare compared to almost every month you see the full moon. And the curve of Earth round is rather vague, too vague for me to have confidence in the arc curve of Earth. But the moon phases are frequent and every month and unmistakable. When doing Logic, you like to have data that is clear and not vague.
In order to explain the full Moon at 6-7PM being NorthEast then a few hours later being SouthWest is easy as in Occam's Razor that the Earth is spinning on its axis in the 12 hours of nighttime shifting the Moon from NorthEast to SouthWest as the night progresses.
To explain this shift from NorthEast to SouthWest as a Flat Earth which is stationary and the Sun moving around Earth in revolution orbit, would require the Sun to approach the speed of light as well as the Moon moving at such unbelievable rapid speed yet so far away.
The only other explanation and argument that needs our attention, is how does a Round Earth, moving in Space keep people from falling off into space. And here the argument of logic will be the Lodestone, the magnets and static electricity found by Thales in Ancient Greek times.
We have to address this problem, because it needs attention. If Earth is round, what is to keep things from falling off Earth???
Actually, it is far easier to explain the force of gravity that holds all material to the surface of Earth than it is to explain the motion of Sun, planets and moons, in my humble opinion. So that the Ancient Greeks could have explained the force of gravity as a form of electromagnetism which is even more advanced than our present day physics classes teaches, for they have not yet unified the four forces of physics, showing that gravity is a EM force.
Thales and Archimedes and Eratosthenes and Aristarchus all high powered geniuses in Ancient Greek times could easily have anticipated all of Newton, yes, they could have anticipated all of Newton on gravity and then some, for Newton did not unify gravity to EM force. Probably because he, and most all modern day physicists could not see that electricity is all attract and no repel, for there is a Pauli Exclusion Principle that looks like repel but is rather instead ___ no occupation of same space___. Dull people cannot understand no occupation of the same space is far different, far far different, from repel.
--- quoting Wikipedia on Lodestone magnets---
For a general description of the mineral itself, see Magnetite.
For other uses, see Lodestone (disambiguation).
Lodestone attracting some iron nails
Lodestone in the Hall of Gems of the Smithsonian
Lodestone attracting small bits of iron
Lodestones are naturally magnetized pieces of the mineral magnetite. They are naturally occurring magnets, which can attract iron. The property of magnetism was first discovered in antiquity through lodestones. Pieces of lodestone, suspended so they could turn, were the first magnetic compasses, and their importance to early navigation is indicated by the name lodestone, which in Middle English means "course stone" or "leading stone", from the now-obsolete meaning of lode as "journey, way".
Lodestone is one of only a very few minerals that is found naturally magnetized. Magnetite is black or brownish-black with a black streak, with a metallic luster and a Mohs hardness of 5.5–6.5.
Origin
The process by which lodestone is created has long been an open question in geology. Only a small amount of the magnetite on the Earth is found magnetized as lodestone. Ordinary magnetite is attracted to a magnetic field as iron and steel are, but does not tend to become magnetized itself; it has too low a magnetic coercivity, or resistance to magnetization or demagnetization. Microscopic examination of lodestones has found them to be made of magnetite (Fe3O4) with inclusions of maghemite (cubic Fe2O3), often with impurity metal ions of titanium, aluminium, and manganese. This inhomogeneous crystalline structure gives this variety of magnetite sufficient coercivity to remain magnetized and thus be a permanent magnet.
The other question is how lodestones get magnetized. The Earth's magnetic field at 0.5 gauss is too weak to magnetize a lodestone by itself. The leading hypothesis is that lodestones are magnetized by the strong magnetic fields surrounding lightning bolts. Magnetite is a ferrimagnetic material, so a lightning strike can align its magnetic domains and create a lodestone. This is supported by the observation that they are mostly found near the surface of the Earth, rather than buried at great depth.
History
One of the earliest known references to lodestone's magnetic properties was made by 6th century BC Greek philosopher Thales of Miletus, whom the ancient Greeks credited with discovering lodestone's attraction to iron and other lodestones. The name magnet may come from lodestones found in Magnesia, Anatolia.
--- end quoting Wikipedia on Lodestone magnets---
So, on 1Feb2026 a full Moon was seen NorthEast at 7PM, then 2Feb this full Moon was seen SouthWest at 4AM. Did it make a continuous trek across the night sky??? It was too cloudy to tell. Some clear night I should observe the Moon if it is a continuous trek from NorthEast to SouthWest.
So a lunar eclipse on average is about 2 a year is too rare to prove Earth is round. Besides, even if you see a lunar eclipse, it is hard to see a Round ball Earth on the moon and open for debate among observers. Some may swear that this is the easiest proof other than sailing around the globe or flying around the globe before that was possible.
My opinion, given lunar eclipse is rare, 2 per year, and given it is a judgement call you are seeing a curved Earth as ball, that the Moon phases which occur every month of the year is a far better logical proof of Earth is round and spinning on its axis.
I would have posted a picture of a lunar eclipse, but could not find any with a clear curved Earth.
As for the question of the trek of the Moon from 7PM to 3AM is continuous in the night sky, I ask myself the question of whether the moon lies in the same plane that the Sun and Earth form a plane called the Ecliptic.
So if the moon is in the very same plane, we would not have Full Moons as the Earth would block that phenomenon. Looking it up, I see the Moon is off of the ecliptic by 5.14 degrees. Apparently 5 degrees off the plane formed by Earth and Sun is enough off-plane so that Full Moons are commonplace.
This would mean that a continuous full moon from 7PM through 3AM treks from NorthEast to SouthWest.
The start of physics really started in Ancient times by observing star and planet and Sun motion. The vital questions of --- Is Earth Round and moving was impeded by the question, if round, how do you keep from falling off.
Both questions can be solved and answered by Ancient Greek times of Thales, Archimedes, Aristarchus and Eratosthenes, by watching the motion of the Moon in its phases and by referring to the magnetic Lodestone to keep Earth together and people not falling off.
Also, the start of Math and Logic in Ancient times with Pythagorus, Socrates, Aristotle coincided with Thales, Archimedes and physics.
Archimedes Plutonium
May 4, 2026, 3:47:55 AM (10 days ago) May 4
to Plutonium Atom Universe
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.
AP
Archimedes Plutonium
May 4, 2026, 9:10:06 PM (9 days ago) May 4
to Plutonium Atom Universe
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.
AP, King of Science
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.
AP, King of Science
Archimedes Plutonium
May 5, 2026, 3:49:21 AM (9 days ago) May 5
to Plutonium Atom Universe
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.
More tomorrow.
AP
Archimedes Plutonium
May 5, 2026, 1:55:15 PM (9 days ago) May 5
to Plutonium Atom Universe
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.
AP
Archimedes Plutonium
May 6, 2026, 4:06:11 AM (8 days ago) May 6
to Plutonium Atom Universe
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.
AP
Archimedes Plutonium
May 6, 2026, 4:28:40 PM (8 days ago) May 6
to Plutonium Atom Universe
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
May 7, 2026, 1:02:21 AM (7 days ago) May 7
to Plutonium Atom Universe
So I have to go back and add on counterexample ideas for it is an important proving mechanism, especially in math.
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.
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
May 7, 2026, 1:27:19 AM (7 days ago) May 7
to Plutonium Atom Universe
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,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
by Archimedes Plutonium (Author)
This is AP's 19th published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
And, early on, I noticed there was a need for a sequence that has the opposite behavour 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.
Archimedes Plutonium
May 7, 2026, 1:37:20 AM (7 days ago) May 7
to Plutonium Atom Universe
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.
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
May 7, 2026, 1:45:49 AM (7 days ago) May 7
to Plutonium Atom Universe
These examples of counterexamples should be listed in my Intermediate Logic textbook for they would be too strenous for Elementary Logic.
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,
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.
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.
Archimedes Plutonium
May 7, 2026, 4:24:54 AM (7 days ago) May 7
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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.
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory
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).
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.
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, 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
May 7, 2026, 4:52:10 AM (7 days ago) May 7
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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---
Archimedes Plutonium
May 7, 2026, 6:31:12 PM (7 days ago) May 7
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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.
* * *
* * *
* * *
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
Archimedes Plutonium
May 9, 2026, 5:19:20 AM (5 days ago) May 9
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Archimedes Plutonium<plutonium....@gmail.com>
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Archimedes Plutonium<plutonium....@gmail.com>
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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.
APArchimedes Plutonium's profile photo
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.
AP
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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)
And, early on, I noticed there was a need for a sequence that has the opposite behavour 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.
Archimedes Plutonium's profile photoSeeing 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.
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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
Archimedes Plutonium<plutonium....@gmail.com>
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, 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's profile photoIn my Logic textbooks I made a glossary of well defined terms.
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 (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)
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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)
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Now a Counterexample need not necessarily be from a universal statement. "All birds fly." Counterexample: ostrich.
Counterexamples can occur from descriptions that are not universal quantifier.
Examples: Person S: Plants bloom in Spring.
Person T: Counterexample -- lilacs bloom in Autumn.
Person U: Ice is wet and cold.
Person V:: Counterexample "dry ice" is dry and cold for it is frozen CO2, a gas and does not melt into a liquid. If Person U had said water ice, he/she would be correct.
Person W:: Computers save us time.
Person Y:: Counterexample: not when a bureaucracy demands you change passwords every 3 months and you forget those passwords.
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