AP's 367th science book-- TEACHING __Pure__ TRUE LOGIC // Logic textbook by Archimedes Plutonium This is AP's #367th published book of science published on Internet, Plutonium-Atom-Universe, PAU newsgroup is this.
149 views
Skip to first unread message
Archimedes Plutonium
Jan 4, 2026, 6:11:23 PM (12 days ago) Jan 4
to Plutonium Atom Universe
TEACHING __Pure__ TRUE LOGIC // Logic textbook
by Archimedes Plutonium
This is AP's 367th 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
Preface: This textbook is almost the same as my #366 textbook. Only real difference is that it is much smaller in pages because I have removed almost all criticism of the mistakes made by Old Logic, and where I eliminated all discussion of the mistakes made in Old Logic of its many logicians, especially Boole and Jevons. Many students want to learn just the pure true logic, and not be bothered with who made errors and mistakes in history.
I wanted a textbook that tells only the Pure True Logic, without constantly referring to all the mistakes and errors made in the past. I wanted to eliminate criticism and focus solely on true pure Logic science. Students deserve learning "just the pure truth" and not be bothered by past mistakes. If they wish to learn past mistakes, they can pursue that on their own time.
Essentially, this textbook is the same as #366 but excision of all past mistakes of Old Logic. And I let the colleges and university departments decide on which of these two textbooks to use in class. I know that it will take a long time, perhaps a full century before all colleges and universities textbooks tell just the "pure truth" of logic and not hampered with having to say--- well, the AND connector was TFFF in Old Logic but is TTTF in New True Logic. In this textbook, I tell only the
"pure true logic". This textbook is far shorter in pages than #366. But there is going to be a transition phase in education where the error filled Boole & Jevons logic is thrown out and the AP logic becomes the only Logic available.
It may well be that Harvard University as a dumb math and philosophy department that feels teaching the error filled Boole and Jevons logic is good because they sell their textbook written by a Harvard dumb professor making money for the professor rather than teach true logic. And then the neighboring colleges and universities near Harvard, like Princeton and Yale, and Columbia and Dartmouth too conservative to keep teaching error filled Old Logic even though authors make more money like Harvard, decide to use AP's #366 logic textbook, feeling they cannot go the full distance of truth and use AP's #367 Logic textbook. Actually this reminds me of an episode in my own lifetime when I was at University of Cincinnati 1968-1972 and learning geology. The Continental Drift theory was not yet fully accepted by the geology community and so we were forced to buy a textbook of geology that had no, or little mention of Continental Drift. And so, well, my reckoning is that it will take 100 years to clear out all the worthless and damaging mind-rot that is Old Logic.
AP Demand: It is my demand on public education that all seeking a science degree in college and university to take 2 years of college Logic, hopefully using AP two textbooks, in hopes, that all those graduating with a science-degree can better think straight and think clearly. AW, Shucks, even my alma mater University of Cincinnati required want-to-be lawyers had to take mandatorily take Logic to get a lawyer degree.
Side note: For me in writing #366 logic textbook became the hardest book for me to write in all my life. Up to then I had written a science book on average of 1 per week. I started writing science books in 2019, and now is January 2026. That is 7 years of elapsed time. All can do the math, where 366/7 = 52.2, meaning, I wrote a science book every passing week from 2019-2025. However, #366 took me a full year to write. The difficulty was that I was replacing the entire subject matter of Logic and not just adding on to the science. Old Logic is so full of error, that is damaging to use to teach students logic.
Cover picture: A different cover picture than my #366 but the same subject matter of --The Logic Syllogism-- All Matter is made up of the 114 chemical elements. The Universe is matter, hence the Universe is one single chemical element Atom that forms an Atom Totality. Plutonium fits the numbers of math and physics the best.
---------------------------------
Table of Contents
---------------------------------
Part 1, What is Logic?
1) Prospectus of books to write in near future.
2) What is Logic in the first place?
3) How do we start Logic-- first with a definition of logic and then the connectors of logic in logical order.
4) What is the physics concept of True and of False?
5) The Logic Truth Tables in detail.
6) The AP Principle of Well Defining a concept.
Part 2, A short brief history of Logic.
7) Logic, formally starts in Ancient Greek time, along with deductive mathematics.
8) The first computer by Babbage influences Logic, and the Boole + Jevons mistakes.
Part 3, The Mechanics of Logic.
9) The 6 simple connectors of Logic.
10) Using mathematics to guide Logic.
11) What is Truth, and how does truth relate to Logic?
12) Existential quantifier.
13) Not-Equal connector.
14) AND connector.
15) OR connector.
16) If-->Then connector.
17) Universal quantifier.
18) Best understanding of "nothing or zero" in both math and logic.
19) The Size & Mechanics of the Logic Argument in New Logic.
Part 4, The Logic Argument starting with Syllogism and moving to more complicated Arguments.
20) The Syllogism is the most simple of argument.
21) More complicated arguments.
Part 5, The Rules of Inference corrected and renamed Laws of Inference.
22) Laws of Inference for Equal-Not, AND, OR, If-->Then.
23) Laws of Inference for Existential and Universal Quantifiers.
Part 6, Scientific Method is Logic.
24) Mathematical-Induction and where does UG, UI, EG, EI, fit in?
25) The Scientific Method is Logic in practice.
Part 7, The Atomic Theory.
26) The most exquisite Logic argument of all time-- the Atomic theory.
Part 8, Proof that God exists, but it is a Science God.
27) Proof is quite simple and shows us the superpower each and every day.
28) Our mission is to make a permanent colony on Europa before year 3025.
Part 9, Uniqueness, Consistency, Completeness and the biggest mistake of all in Old Logic.
29) Where does Universal Generalization UG, Universal Instantiation UI, Existential Generalization EG, Existential Instantiation EI, fit in?
30) Summing up all of Logic in uniqueness, consistency, completeness by the Scientific Method.
31) Biggest mistake of all in Old Logic.
Part 10, Many examples of Logic Fallacies, which in mathematics would simply be called mistakes.
32) Many examples of Logic Fallacies
Part 11, How Logic easily improves our lives.
33) Improving your life with applying Logic.
34) Applying Logic to our modern ever increasing digital world so you can be safer and more secure.
35) What to expect in Advanced Logic, my #368 book of science.
-------------
Text
-------------
Part 1, What is Logic?
1) Prospectus of books to write in near future.
The first sentence of this textbook should concern itself with "What is Logic"??? Why am I here studying logic?
I have been preaching for over decades now that people wanting a degree in college in science, should be required to take 2 years of college logic to earn that degree. For Logic is the science that helps you think straight and think clearly--- at least that is the hope.
I often refer to the two textbooks of Logic I used at University of Cincinnati 1968-1972, one by Copi, Introduction to Logic, 4th edition and one by Thomason, Symbolic Logic An Introduction, 1970.
Copi is straight-on with his first sentences.
"...this we do affirm-- that if truth is to be sought in every division of Philosophy, we must, before all else, possess trustworthy principles and methods for the discernment of truth. Now the Logical branch is that which includes the theory of criteria and of proofs; so it is with this that we ought to make our beginnings." -- (Sextus Empiricus, an ancient Greek physician)
1.1 What is Logic?
Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning. (Copi, 1972).
Thomason's Symbolic Logic does not start where I expect him to start.
1 Uninterpreted Syntax of a Logical System
1. This section has to do with some rules of constructing certain strings of symbols called formulas, and for manipulating these formulas to build arrays called proofs. (Thomason, 1970).
AP writes: sadly, Thomason should have started where Copi started and all textbooks of Logic. Tell the student or reader--- What is Logic.
I start this book with my definition of Logic.
Logic is the science that helps one better to think straight and to think clearly, especially needed by scientists.
A batch of books to write, most important are two logic textbooks for the World has ___no logic textbook mostly free of errors____, at least almost free of errors. Instead,,,, by year 2025 massive errors in all college logic textbooks that I can see as far as the eyes can see, where all 4 of the simple logic connectors, the very most simple logic connectors are all in ruinous gross error.
The history of this textbook-- 1st year college Logic was based on a batch of books I began to write in year 2025.
#350 Geometry
#365 Calculus
#366 Logic
#367 Pure True Logic
#368 Advanced Logic
#369 Advanced Geometry
#370 Physics electricity
#371 Plutonium Atom Totality, 10th edition
#372 Improving the Scientific Method
#373 Thermodynamics Corrected
#374 Philosophical-Physics--- not only what is the purpose of life, but the purpose of physics
#372 book of science for AP--- Improving the Scientific Method by Archimedes Plutonium
I am going to need to add the Scientific Method as a part of my two textbooks on Logic, and also making it the subject of a separate book, #372.
Archimedes Plutonium
Jan 4, 2026, 6:29:16 PM (12 days ago) Jan 4
to Plutonium Atom Universe
--- quoting what I wrote in my #365 book Calculus ---
Chapter 1, An introduction of what this book is about.
...For decades now, I have been excoriating the fact that no college or university in the world has a correct teaching program for the subject of Logic. No college or university as of 2025 can teach two years of college Logic with the correct truth tables of the 4 most simple Logic connectors of Equal-Not, AND, OR, If--> Then. Every college and university across the world teach Error filled logic of Boole and Jevons for they have all 4 connectors wrong. So, how could AP tell all science majors to take 2 years of college logic, when no college or university on Earth has a correct Logic textbook? This series along with math and physics textbooks is needed. I start with this Calculus textbook for the AP series #365 through #373 are school textbooks that replace error filled textbooks in colleges and universities across the globe of Earth.
#350 Geometry
#365 Calculus
#366 Logic
#367 Pure True Logic
#368 Advanced Logic
#369 Advanced Geometry
#370 Physics electricity
#371 Plutonium Atom Totality, 10th edition
#372 Improving the Scientific Method
#373 Thermodynamics Corrected
--- end quoting what I wrote in my #365 book Calculus---
In the past 7 years I wrote these books on Logic-- 13 books, but no textbook to use in classroom. And that is the purpose of this book.
1Suspend all College Classes in Logic, until they Fix their Errors 1Suspend all College Classes in Logic, until they Fix their Errors.JPG 2Correcting Reductio Ad Absurdum 2Correcting Reductio Ad Absurdum.JPG 3DeMorgan 3DeMorgan.JPG 4Pragmatism 4Pragmatism.JPG 169Consistency 169Consistency.JPG 172Occam.JPG 172OccamR 188Language->eq 188Language.jpg 199paradoxes 199paradoxes.jpg 231AllAtoms 231AllAtoms.jpg 300Unification philosophy.jpg 300Unificationphilosophy 318math-subset-logic 328Lowenheim 348Feynman's Atomic theory
I write this textbook on Logic for the 1st year College Logic course. It does not have to be in the Freshman year, but hopefully the prospective student of science takes calculus before they take this Logic course, because I refer to calculus a-lot in this book. However, my referencing calculus in this book may better equip the student to understand calculus better. For the Old Math has calculus all screwed up and messed up, so dumb is Old Math that they could never do a geometry proof of the Fundamental Theorem of Calculus. You see, AP calculus needs to replace all of Old Math calculus, in addition to replacing Old Logic.
Chapter 1, An introduction of what this book is about.
...For decades now, I have been excoriating the fact that no college or university in the world has a correct teaching program for the subject of Logic. No college or university as of 2025 can teach two years of college Logic with the correct truth tables of the 4 most simple Logic connectors of Equal-Not, AND, OR, If--> Then. Every college and university across the world teach Error filled logic of Boole and Jevons for they have all 4 connectors wrong. So, how could AP tell all science majors to take 2 years of college logic, when no college or university on Earth has a correct Logic textbook? This series along with math and physics textbooks is needed. I start with this Calculus textbook for the AP series #365 through #373 are school textbooks that replace error filled textbooks in colleges and universities across the globe of Earth.
#350 Geometry
#365 Calculus
#366 Logic
#367 Pure True Logic
#368 Advanced Logic
#369 Advanced Geometry
#370 Physics electricity
#371 Plutonium Atom Totality, 10th edition
#372 Improving the Scientific Method
#373 Thermodynamics Corrected
In the past 7 years I wrote these books on Logic-- 13 books, but no textbook to use in classroom. And that is the purpose of this book.
1Suspend all College Classes in Logic, until they Fix their Errors 1Suspend all College Classes in Logic, until they Fix their Errors.JPG 2Correcting Reductio Ad Absurdum 2Correcting Reductio Ad Absurdum.JPG 3DeMorgan 3DeMorgan.JPG 4Pragmatism 4Pragmatism.JPG 169Consistency 169Consistency.JPG 172Occam.JPG 172OccamR 188Language->eq 188Language.jpg 199paradoxes 199paradoxes.jpg 231AllAtoms 231AllAtoms.jpg 300Unification philosophy.jpg 300Unificationphilosophy 318math-subset-logic 328Lowenheim 348Feynman's Atomic theory
I write this textbook on Logic for the 1st year College Logic course. It does not have to be in the Freshman year, but hopefully the prospective student of science takes calculus before they take this Logic course, because I refer to calculus a-lot in this book. However, my referencing calculus in this book may better equip the student to understand calculus better. For the Old Math has calculus all screwed up and messed up, so dumb is Old Math that they could never do a geometry proof of the Fundamental Theorem of Calculus. You see, AP calculus needs to replace all of Old Math calculus, in addition to replacing Old Logic.
Archimedes Plutonium
Jan 5, 2026, 5:00:49 AM (12 days ago) Jan 5
to Plutonium Atom Universe
2) What is Logic in the first place?
In Logic we examine ideas and manipulate ideas and focus and concentrate on ideas. We write ideas out and often label them with a p,q,r,s, etc. When you hear or see the words "Symbolic Logic" that means instead of writing out the idea in full, we just give them a label like p,q,r,s, etc.
Examples of various Ideas in Logic
----------------------------------------------
I woke up today and saw the Winter Solstice at 4:50 PM from my south window.
On 20 December 2025, I had 12 hours of sleep.
I am 17 years old today, 20 December 2025.
The temperature in my living room is 20 degrees Celsius around 70 degrees Fahrenheit.
I am a female going to High School.
I feel sad, depressed upon not being invited to the Party to dance and sing.
Let me label the above six ideas with Symbols as would be done in Symbolic Logic and analyze them each briefly.
A = (I woke up on 20 December 2025 and saw the Winter Solstice at 4:50 PM from my south window.)
B = (On 20 December 2025, I had 12 hours of sleep.)
C = (I am 17 years old today, 20 December 2025.)
D = (The temperature in my living room is 20 degrees Celsius around 70 degrees Fahrenheit.)
E = (I am a female going to High School.)
F = (I feel happy and full of glee, upon not being invited to the Party to dance and sing.)
In logic we usually label in Symbols with P, Q, R, S rather than start with A, B, C, but that is only common practice. You can label your idea with any letter of the alphabet you want, capital or not capital letters. Much the same as what goes on in algebra math A+B = C, or 5x = 35 and solve for x.
In math we have numbers to operate upon such as 2+5 = unknown. In Logic, we have something similar in that from the above list of statements: statement A AND statement B = a truth value.
So in math we have 2+5 = 7. What is the truth value of A AND B from the statements above? Statement A is "I woke up on 20 December 2025 and saw the Winter Solstice at 4:50 PM from my south window" which is true. Also, statement B is "On 20 December 2025, I had 12 hours of sleep" which is also true.
So when we connect A AND B in the joining together.
I woke up on 20 December 2025 and saw the Winter Solstice at 4:50 PM from my south window AND on 20 December 2025, I had 12 hours of sleep. That combined statement with connector AND is a true statement because both A is true and B is true.
But what about A AND C, or what about B AND E. Here we have A is true but C is false. We also have B is true but E is false. What is the joined together combined A AND C result in truth value. It is true. And the same goes for B AND E even though E is false.
How about A AND C AND E where we have 3 statements, only one of them is true? The answer is that the entire string is true if just one of the statements is true.
The reason a string of AND statements is true if just one statement is true, is that in Logic, a false statement is considered to have a truth value of zero, 0 or nothing. And so when we add in math we have 1 + 0 + 0 = 1.
There is a famous saying of how AND truth value works--- We do not throw the baby out with the bathwater. If a string of statements p, q, r, s, t, u, where only one of the statements is true, the rest all false, connected by AND, then the entire string is true.
Now with 2 statements there are 4 possible combinations for AND as connector. For statements P, Q. We could have P true Q true. We could have P true Q false. We could have P false Q true, and finally we could have both P and Q false.
In Logic we set up what is called a Truth-Table that easily lets us see the 4 possibilities for two variables P,Q.
P Q
--------------
T T
T F
F T
F F
Notice the first column is TTFF while the second column alternates with TFTF.
Whenever we have 2 variables (two statements) this pattern above gives us all the possible truth values for any given connector, such as AND connector.
In the case of A AND B above our first row covers that possibility. In the case of A AND C our second row covers that situation.
What if we took C AND F from the above which is this.
I am 17 years old today, 20 December 2025 AND I feel happy and full of glee, upon not being invited to the Party to dance and sing.
C is false because I am now 75 years old in 2025 while F is true, for I hate dancing and singing and only make a joke of myself.
Here C AND F is a joined together statement by the AND connector and follows row three above, where since F is true, the whole string is true.
Finally what if we joined together statements C AND E, both of which are false, for I am a 75 year old male. This joined statement is false for none of its statements is true and follows the fourth row above.
With two statements, two variables we form what is called a Truth Table in Logic for the connector of concern. In the above our connector was AND. And we formed all possible truth arrangements of two variables, P, Q by constructing this table.
P Q
T T
T F
F T
F F
Notice that pattern again of P being TTFF while Q being TFTF for that pattern captures all possible truth values of TT, of TF, of FT and of FF. We use the pattern over and over again for other connectors like that of OR, like that of Equal-Not, like that of If-->Then.
So let us complete the Truth Table of AND above.
P Q P AND Q
T T T
T F T
F T T
F F F
And summarize our findings. We find that AND is true whenever a single one statement of a string of statements is true. And the only time the AND connector is false is when the entire string of statements of AND have not a single true statement. We do not throw out the baby with the bathe water.
But let us now focus upon how we assign truth or falsity to a statement.
Assigning truth or falsity to a statement.
---------------------------------------------------
Short and simple, we assign truth to a statement if the statement is true in the particular science it pertains to. And a statement is false if science says it is false. Looking back at my statements from A through F
A = (I woke up on 20 December 2025 and saw the Winter Solstice at 4:50 PM from my south window.)
Science of astronomy says this is a true statement that around 20 to 21 December, the Winter Solstice takes place.
B = (On 20 December 2025, I had 12 hours of sleep.)
Science of sociology and psychology says this is true in that I am telling the truth.
C = (I am 17 years old today, 20 December 2025.)
History of AP says this statement is false and shows AP was born 1950 making him 75 years old.
D = (The temperature in my living room is 20 degrees Celsius around 70 degrees Fahrenheit.)
Science of sociology and electric bills paid show this to be false statement, in that AP's living room is likely to be no more than 15 degrees C or less than 60 degrees F.
E = (I am a female going to High School.)
Science of sociology and biology show AP was born a male, so the statement is false.
F = (I feel happy and full of glee, upon not being invited to the Party to dance and sing.)
Science of sociology and psychology and history show this to be true in that AP avoided parties of all types and had no pleasure in dancing or singing or partying.
In Logic, the truth of falsity of any statement is run through to science pertinent on the subject matter. More details on truth and falsity will come later.
Physics is the science of material objects, mass, motion, energy. Biology is the science of living objects and how living organisms behave in the environment. Logic is the science of ideas and to use language in communicating ideas and forming conclusions from those ideas. Mathematics is the science of correct use of the language of numbers-quantity and geometry figures and shapes. Just as mathematics is the correct use of numbers and figures of geometry, that Logic is the correct use of ideas and thoughts. In math we have numbers like 1,2,3,4, ... and figures of geometry like line, plane, square, rectangle, circle. In Logic we have statements of ideas and can label them as p, q, r, s, t, u, v, ... Math manipulates numbers and figures while Logic manipulates ideas as statements of a language. Sciences, logic and mathematics can be put into a diagram of subsets, where Physics is on top.
Physics
/
Chemistry
/
Astronomy, Geology
/
Biology which includes Sociology and Language
/
Logic
/
Mathematics
So Logic is the science of the correct use of ideas and reaching conclusions of those ideas communicated by a language, while in contrast, Mathematics is the science of the correct use of numbers as quantity and size and the use of geometry figures.
Both logic and math are languages. The job of Logic is correct use of ideas, while the job of math is the correct use of numbers and geometry figures. Since math is ideas of numbers and geometry, then that means Logic is a set that is larger than math and contains all of math inside of logic. We call this a "meta-language". When one language has another language inside itself, we say Logic is a meta-language of Mathematics. Logic is the larger set that has all of mathematics as a subset.
Now one may think that Logic is the Meta-language and no other set is larger than logic. That is not true. For Physics is larger than logic. Physics is the largest set of all, having all the other sciences inside of Physics and having Logic and mathematics inside of Physics. This probably sounds strange to most people to think that Physics controls Logic a language corrector. Later in this book we talk about Superdeterminism, some prefer to call it "quantum entanglement". It is a physics experiment done many times in different labs with the stunning result that the world has a superpower of an Atom Totality that controls all humans as if they are puppets, doing the wishes of the Atom Totality. When the world has something like that, means that Physics is the supreme knowledge and everything else is a subset of physics. Physics is the final metalanguage.
In logic, the science of correct use of ideas, definitions are important. And we can reduce many concepts to their primal meaning.
For example, geometry is a poor choice of term for what is really "shape".
Number is a poor choice of term for what is really "size". Some may say "quantity" but quantity is no better than "number". For example, the size of shape makes more logical sense than the quantity of shape. This is physics complamentarity, that number and geometry are complamentarity as is electric complamentarity to magnetism. So the best primal term definition for "number" is size. Numbers speak to size. Geometry speaks to form and shape.
Note: I spell the word Complimentarity of Old Physics as Complamentarity as to not confuse it with similar but confusing spellings.
Subtraction is a poor choice of term for what is really "remove". And if human history had never used the term subtraction but only used "remove" the science of mathematics would not have been encumbered by the "manifest idiocy" of negative numbers.
Physics is a good choice of a term to describe all sciences and all human thought. For that word sticks out from all other words.
Logic is a poor choice of term for what is really "the scientific method". Math is correcting numbers and geometry. Logic is correcting the use of ideas and the scientific method is the use of ideas in physics (or other sciences), for physics is based on experiments that follows the scientific method blueprint.
The Scientific Method in brief.
---------------------------------------
--- source from 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.
Step 7-- Publish the results.
So yes, so the teaching of Logic, 1st year in College and University is much like teaching Mathematics of its 4 operators of add, subtract, multiply, divide, and add on 2 more operators of derivative and integral to math which are reflected in 6 Connectors of Logic as Equal-Not, AND, OR, If->Then, Existential quantifier, Universal quantifier.
Math is the correct use of Quantity-Number- Size and Geometry Shape. While Logic is the correct use of ideas communicated in a Common Language.
Math is the language that Physics needs for detail and precision on quantity-size and geometry shape.
First let us do a perspective of where Logic fits into the scheme of things of Knowledge and Wisdom.
Structure of all Knowledge and Wisdom
-------------------------------------
It is good to place logic in a structural framework to compare its importance to other forms of knowledge.
The pinnacle peak of knowledge and wisdom is of course science, for it is science that brought humanity as advanced intelligent life and allowed us to walk on the Moon. Soon it will be science that allows humanity to escape the Sun gone Red Giant and live for a million years longer on Europa, a satellite of Jupiter.
And the pinnacle peak of Science is Physics.
Here is a schemata diagram listed by order of importance of what can be called the important knowledge and wisdom.
Physics
Chemistry
Astronomy
Geology
Biology
Physiology & Medicine,Psychology
Sociology includes Language, Philosophy, Religion, economics, music, art
Logic
Mathematics
All of them are a subset of Physics. The last two are Logic and Mathematics because most people can go through life without knowing either one of them, or, utilizing either logic or mathematics. Everyone every day, every second experiences the forces of physics, even if they do not know or understand the laws of physics.
What is Logic?
------------------------
Logic and mathematics are corrections and precision mechanisms for science. Highly important are both roles of Logic and mathematics.
Logic corrects and makes precise the actions taken in science experiments and in communication via language of the science in question. While Mathematics is the precision of quantity, size, and shape and figure.
Chemistry is a subset of Physics, and biology is a subset or chemistry and physics. Without physics and chemistry there would not be a biology.
Without Physics, there would not be a logic nor mathematics.
And Mathematics is a subset of Logic. By that I mean everything found true in mathematics, can be found true in Logic. Going even further, everything found true in Logic must be found in Physics in the Axiom Principle of Physics-- All is Atom and Atoms are nothing but electricity and magnetism. That means the Laws of Electromagnetism contain all the major principles and ideas of Logic, as well as mathematics.
If Logic is superior to mathematics, then everything in mathematics can be pulled out of Logic. So, let us pull out of mathematics the 6 connectors of Logic.
The 6 Connectors of Logic
-------------------------
Not-Equal
And
Or
If--> Then
There Exists
For Every
The 6 Operators of Mathematics
------------------------------------------------------
Multiplication (which is Equal-Not)
Addition (which is And)
Subtraction (which is Or)
Division (which is If-->Then)
Derivative (which is the existential quantifier)
Integral (which is the universal quantifier)
Somewhat surprising that derivative and integral of calculus math is the Existential and Universal quantifiers of Logic.
Maybe more surprising is that multiply, add, subtract, divide are algebra while derivative and integral are geometry.
Forced to start the 6 Logic Connectors with Existential quantifier and then next with Not-Equal
-----------------------------------------------------
In Logic, we have to start logically the 6 connectors and of those 6, the logical start is the question of Existence. No use in pondering something that does not exist. So we start with Existence. Does the idea bear existence what we call reality? Once we established if an object exists or does not exist, we then see that Not-Equal must be the second connector to be introduced. For the Not is in "not exist".
And in Logic, we have Truth tables that need equal signs, and we cannot do any operator first unless we can understand it exists or not exists and then ask what is equal. Notice also, that by combining Equal with Not we form them into a 4 row truth table of all possibilities for truth values of two variables, a TT, a TF, a FT, and a FF. If we study Equal alone we have only T=T and F=F. And we cannot have a study of T =F or F=T. So we combine Equal with Not. We escape the operators being just two-fold value truth table, and make Equal and Not be four-valued truth table operators like the others of AND, of OR, of If-->Then.
Now sometime I am going to get this correct. And it is important. You cannot have chemistry without physics. And you cannot have biology without chemistry, but you __can have__ astronomy without biology. So I need a massive repair here.
Here is a schemata diagram listed by order of importance of what can be called the important knowledge and wisdom.
Physics
Chemistry
Astronomy
Geology
Biology
Physiology & Medicine,Psychology
Sociology includes Language, Philosophy, Religion, economics, music, art
Logic
Mathematics
Now let me run through that schemata to see if logically correct. This correction is an exercise in logic itself, utilizing logic.
You cannot have chemistry without physics, and you cannot have astronomy without chemistry and physics. And you cannot have geology without astronomy. You cannot have Biology without all the fore mentioned sciences.
Is that true? You cannot have biology unless you have physics, chemistry, astronomy, geology in place?? Sounds reasonable for then you would have life coming into creation in the thinness of deep outer space. Sounds reasonable that life needs a vast array of chemicals all in on place location to form first life. What was the most heavy element essential for life?? It was beyond phosphorus, possibly manganese and iron. Both plant and animals, I cannot envision life creation without an environment of iron and all the elements before iron.
So once we have Biology in the schemata diagram we have lots of biological related sciences --- the physiology of plants and animals and medical science is part of physiology. The brain covered by psychology and were likely the meristem (root tips) in plants is plant brains.
Then we have a whole category of sciences that compose Sociology, and some people will refuse to see them as sciences, but collectively they compose the social interactions of a species of animals.
Lastly, we see the sciences of Logic and then Mathematics. You cannot have logic or math without a social animal forming logic and math.
If there were no human social animal on Earth, there would be no Logic or Mathematics on Earth.
And that corrected schemata suggests the purpose and function of Logic is more than correct the Language for clarity of ideas, but also suggests that Logic is the ___ Deductive Reasoning___ for mathematics.
A mathematics in a world without Logic is a mathematics without Deductive Reasoning.
Take for example the Pythagorean Theorem of A^2 + B^2 = C^2 of the sides of a right-triangle. The proof of a math conjecture is outside of math itself, and reaches for a new higher level of thought and thinking. That higher level is often called a meta-language. And in the case of all of mathematics--- whenever we want to do a math proof, we go outside of mathematics itself to achieve a math proof.
In fact, without any words we prove the Pythagorean Theorem in a few pictures. See the Internet or Wikipedia of the proof of the Pythagorean theorem without any words, just geometry picture diagrams.
So, we end up with the picture that Logic as a subject is that of Precision Language for correct ideas and that of being Deductive Reasoning. We are left with the picture that Mathematics is the last form of science as being Precision size-quantity (algebra) and precision geometry of shape and figure.
But we should not view the Schemata as top to bottom with Physics on top and Mathematics on bottom, instead we should view the Schemata as a full circle. A circle that comes around.
Where Physics is in the circle and to the right of physics is chemistry and to the left of physics is mathematics, coming around full circle with all the other sciences in between.
Now at this moment I am stuck on another issue--- Is multiplication of math that of Equal-Not of Logic.
I remember somewhere in Algebra, that Multiplication was very unique over addition, subtraction and division. So unique was multiplication that it played a special role in Galois Algebras.
I bring this up because Equal-Not has a truth table of TTTT. The only 4 valued truth table of all Trues. While the next one is addition as AND with truth table TTTF. AND of course is addition in Logic.
The Logical Idea here is that of the 4 out of 6 operators of Math and the 4 out of 6 connectors of Logic, that those four truth tables have to represent these four.
One True TFFF
Two True FTTF
Three True TTTF
Four True TTTT
It is multiplication as a combined Equal with Not to form TTTT.
Taking one more glance at this schemata diagram to see if correct. Yes, I see no trouble in that. For you cannot have a Logic or Mathematics if a Sociology of language is not present. You cannot have a Sociology if you have no minds of psychology. And a mind of psychology cannot exist if there is no physiology.
One True TFUU which is the If-->Then
Two True FTTF which is the OR
Three True TTTF which is the AND
Four True TTTT which is the Equal-Not
I realize that the Universal Quantifier has all truth values as being True. For every Atom, has a proton is a universal statement, and true for every Atom. While the Existential Quantifier such as There exists an Atom with only 8 protons, is true for some atoms but false for other atoms.
So, well, I cannot use the Universal Quantifier for the truth table TTTT. And so I realize the fact that only Equal-Not remains to become Multiplication. I realize also that Universal Quantifier is a form of multiplication, and then there is the multiplication of the integral of calculus. While Equal-Not is multiplication of the simple 4 operators of math --- add, subtract, divide and multiply.
So, what I am harping on here is the idea that Mathematics is all a subset of Logic, for everything in math should be gotten from Logic, and Logic of course is a subset of Physics.
So we have in mathematics, actually, 6 operators of add, subtract, divide and multiply with differentiation and integration. And we have in Logic 6 connectors of AND, OR, Implication (If-->Then), Equal-Not, Existential quantifier and Universal quantifier.
To start the truth-tables of Logic for AND, OR, Implication (If-->Then), Equal-Not, I need to start with Existential quantifier moving next into that of Equal-Not for the not-exist possibility and that equality is used in the truth tables themselves.
There is just no getting away from starting Logic with Existence and then not-exist and equality. And since AND is add, OR is subtract, Implication (If-->Then) is division, leaving me only with Equal-Not as having to be Multiplication.
As I said earlier, a hallmark of Logic is Consistency, with no contradictions.
This is why AP insists for the sake of consistency, that the 4 Connectors have different truth tables as such.
One has one T.
One has two Ts.
One has three Ts.
One has all four being Ts.
Archimedes Plutonium
Jan 5, 2026, 5:44:46 AM (12 days ago) Jan 5
to Plutonium Atom Universe
3) How do we start Logic-- first with a definition of logic and then the connectors of logic in logical order.
We defined what logic is in the last chapter, now we explore the logic connectors, but where do we start with the Logic connectors?
We start Logic connectors, logically by using good true ideas. Mathematics is long well established science in history. Mathematics is easier to study and learn than is Logic, for logic is far bigger encompassing all ideas while math is confined to arithmetic, algebra and geometry and its most important branch of calculus, where calculus is a mix of geometry and numbers. Logic is a larger set than math and so Logic should contain all of mathematics inside of Logic.
So naturally, we start Logic connectors by using mathematics as a ___guide___ to tell us if our Logic is straight and clear and on track.
Throughout this textbook I am constantly referring to mathematics to settle questions of Logic.
We know that Logic has to define 6 connectors which resemble 6 operators that compose all of mathematics. All of mathematics has 6 operators running through mathematics and those are (1) Addition (2) Subtraction (3) Multiplication (4) Division (5) Derivative of calculus (6) Integral of calculus.
I highly recommend that students take Logic only after they have taken calculus in college, not before. I say this especially on the concern that derivative of calculus is the Logic existential quantifier and also resembles the If-->Then connector. A student of this textbook cannot appreciate those ideas without taking calculus beforehand. And the student may very well struggle in this course without taking calculus first. On the other hand, math is in the weeds on calculus where they use the wrong numbers of Reals and are unable to do a geometry proof of the Fundamental Theorem of Calculus. Thus, it may benefit students to take this logic before taking calculus, as to render them with insights of the "true calculus" not the error filled calculus taught in colleges and universities the world over. Why math is so full of errors, that the fools of math professors cannot even admit slant cut of cone is oval, not ellipse for you need the slant cut of cylinder to fetch a ellipse.
And a student of calculus, that has learned calculus well, will know that Calculus in its Coordinate System of graphing and functions is the geometry of mathematics. In a real sense, geometry is played out in mathematics by the derivative giving lines, angles and integral giving area and volume. So definitely, in college, take calculus before taking logic and let the ideas of calculus settle into the mind before taking this Logic. On the other hand, taking this logic course will likely let students see the raw obnoxious mistakes of present day calculus with their absurd Reals and no geometry proof of Fundamental Theorem of Calculus.
So, since all of mathematics is inside of Logic, the main connectors of Logic have to reflect and resemble the 6 operators of Mathematics.
The 6 Connectors of Logic
-------------------------
Not-Equal
And
Or
If--> Then
For Every
The 6 Operators of Mathematics
------------------------------------------------------
The 6 Operators of Mathematics
------------------------------------------------------
Derivative (which is the existential quantifier)
Multiplication (which is Equal-Not)
Addition (which is And)
Subtraction (which is Or)
Division (which is If-->Then)
Integral (which is the universal quantifier)
So, what Logic does, is to fully use mathematics to release and understand what the true connectors, the 6 connectors of Logic are because mathematics is a guide post on what those connectors are.Multiplication (which is Equal-Not)
Addition (which is And)
Subtraction (which is Or)
Division (which is If-->Then)
Integral (which is the universal quantifier)
When I first started writing this textbook of 1st year Logic back in April 2025 and now is November 2025, I was mistakenly believing that Equal-Not should be the first connector of Logic. I reasoned this logically, because the truth tables all needed the equal sign for true or false for the connectors of AND, OR, If-->Then, Equal-Not.
Makes sense that Equal-Not should be the first connector for the other 3 all need to use Equality in their truth table.
But then in October-November 2025, I started to do the chapter on Consistency for this book and realized that Equal-Not is not the starting concept for Logic, but rather instead, I had to start Logic with Existence.
Makes sense, why bother with reasoning if something does not even exist.
And so, here, I realized that I had to start the 6 connectors of Logic with the Existence quantifier and to talk about "What is true" and the truth-tables.
No point in reasoning of ideas if none of the ideas have material existence.
What is truth and true is a major question. And the answer naturally is that the laws of science are our highest truth givers.
Every time we question if an idea is true or false, we call upon the relevant science and see what the science has to say on the issue. Whether we have existence in the ideas and the truth value of those ideas.
We start the logic connectors with Existential quantifier. Then we tack on Not-Equal, then we tack on AND, then OR, then If-->Then and finally the Universal quantifier.
4) What is the physics concept of True and of False?
My logic textbooks, the three of them #366, #367, and #368 Advanced Logic are the first logic books written by an author who had a "logical mind to write a logic book".
Suppose the science of Physics could speak to humanity in terms of statements like the P, Q, R found in Logic. And we asked Physics what is the concept of "True" and of "False". For much of Logic is about truth tables and whether a statement is true or false and whether a conclusion is true or false.
What would Physics answer to the human question of "What is true and what is false"?
What is the physics concept of True and of False?
But how do we know a statement-idea is true or is false? And here is why Logic is below all the sciences except for mathematics which is last of the sciences. Because the Truth or Falsity of an idea in a statement P, Q is obtained from all the other sciences of their universal laws of science. If we had the statement-- P = Thrusting a bar magnet through a coil of copper produces no electric current. That would be false because it violates the Faraday law in electromagnetism.
All of the truths in logic come from comparing the statements of ideas made in logic, comparing those statements up against the Laws of Science.
So we have an opportunity to speak with the science of Physics and ask Physics directly-- What is true in physics and what is false? Physics would answer this.
AP asks: Physics, what is truth and what is falsehood in the realm of physics as a science?
Physics (if it could talk): Truth in physics are all the laws of physics, especially the electromagnetic laws, but also all the other laws of the sciences such as chemistry, biology, astronomy, geology etc etc. And those laws are universal and obtained via experiments.
AP: Thanks physics but what is falsehood in physics?
Physics (if it could speak): Any violation of laws of physics or the other sciences is a falsehood. And we designate a falsehood in science as being zero, 0, for being nothing, and having a 0 value. Physics recognizes truth by a T meaning it obeys Laws of Physics, and recognizes not obeying laws of physics with a 0 for nothing. In Physics we have the law of Absolute 0 degrees Kelvin is never attainable. You can get close but the closer you get to 0 Kelvin the more energy is required to get even closer. And physics has the law that the Speed of Light is a constant Maximum speed, no speed faster than Light speed. So the realm of Physics are from a 0 to a Light speed maximum a positive number. Falsehood is zero, truth is all along from 0 to maximum positive number.
So when Humans have a truth table for AND as this. Those of us in Physics see that as excessive.
Human AND truth table
P Q P AND Q
T F = T
F T = T
F F = F
Physics AND truth table where falsehood is labeled as zero, as nothing
P Q P AND Q
T 0 = T
0 T = T
AP: So physics AND truth table does not even bother to list the 4th row of F AND F = F?
Physics: That is correct, why list "nothing". Take for example the Human truth table for OR of Logic.
Human OR truth table
P Q P OR Q
T T = F
T F = T
F T = T
F F = F
Physics OR truth table where falsehood is labeled as zero, as nothing.
P Q P OR Q
T 0 = T
0 T = T
Physics: The physics OR truth table is only two rows because the OR mechanism is one of "remove". If you remove T from T you end up with nothing, likewise if you remove F from F you end up with nothing. Hence you do not even write those rows. The mechanism in AND is that of joining together, the union in set theory and the addition in arithmetic. A old saying aptly describes AND as "we do not throw out the baby in the bathe water". So as long as a String-of-Statements has at least one true truth value, the entire string of statements is warranted as True.
AP: What is the IF-->Then connector in Physics?
Physics: Yes, the division or derivative connector, the "Move into" mechanism of Logic. Some like to call it implication, or material implication. Its truth table is a mere one row.
Human If-->then truth table
P Q If P then Q
T T = T
T F = F
F T = U for unknown
F F = U for unknown
Physics If --> Then truth table
P Q P --> Q
T T = T
AP: short and sweet, only one row truth table and why bother to list 3 other rows that are "nothing rows".
Physics: Yes, humans love to list nothing even when it causes them to make more mistakes.
Physics: But there is a truth table in Logic that is all 4 rows as true, and it is multiplication for arithmetic, and it is the assembling of both Equal with Not to form 4 rows of truth.
Human Equal+Not truth table
P Q P equal-not Q
T T = T where equality law is observed
T F =/= T where the Not is not distributive law imposed
F T =/= T where the Not is not distributive law imposed
F F = T where equality law is observed
Physics Equal-not truth table
P Q P equal-not Q
T T = T where equality law is observed
T F = T where the Not is imposed in distributive law
F T = T where the Not is imposed in distributive law
F F = T where equality law is observed
Physics: Equal is a binary operator as well as Not is binary, but when we join them together we get 4 rows instead of 2 rows for a 4 row truth table. And when we apply Not to that of Equal in the 2nd and 3rd row we cause to create the Distributive law of arithmetic. The Distributive law is borne and created in the Equal-Not truth table.
I should continue this conversation between Physics and myself AP, for much of human discussions with Logic involved amount to nothing, and what better way of pointing that out with --- then talking with Physics.
AP: short and sweet, only one row truth table for If-->Then and why bother to list 3 other rows that are "nothing rows".
Physics: Yes, humans love to list nothing even when it causes them to make more mistakes.
I wrote the schemata diagram with physics on top and next to last was logic and last was mathematics, where Logic stands in relation to other sciences. This is important for the fact of gaining Truth or Falsity values. When we make a statement and connect that statement to other statements, such as P AND Q, or, If P then Q, then we need something to measure and determine the truth value of P and of Q and however many other statements are connected in the argument. This Truth value measure is carried out by the sciences of Physics, Chemistry, Biology, Astronomy, Geology and thousands of specialized sciences using the Scientific Method. So, one can see that Logic is the science of reasoning with true ideas and communicating clear and straight and true ideas, from the help of other sciences.
Of course in human conversations we can be sly, devious and deceitful or playful, fun and flirting in romance to say things of nothing with no truth value.
But this raises the issue of Examples given in old textbooks of Logic; and the question of whether they are even examples at all. Because of truth value determination.
As I posted earlier, when Physics speaks of Logic, Physics only lists the rows in which the connector of statements has a true truth value and dismisses statements that are false.
So, let me see where Copi makes his first logical argument in his 4th edition, 1972, Introduction to Logic. And where Thomason, 1970 Symbolic Logic An Introduction makes his first logical argument. Bearing in mind, that a logical argument must have true premisses to form a conclusion.
Example: All men are mortal. Socrates is a man. Therefore Socrates is mortal. The two premisses are biologically sound which leads to a valid conclusion. But this next argument that is often seen is invalid. All crows are black. Yonder in corn field are crows. Therefore they are black. This argument is invalid because science easily proves not all crows are black. So no need to proceed any further and ask the person making the argument to come up with a Truthful argument.
What I am getting at here, is that so many examples in Logic have false premisses and should throw those arguments out. And tell the person to check the relevant science known and to make a new argument.
So in New Logic, we examine arguments to see if they are sound arguments supported by science as the Truth giver of premisses.
Suppose we teach mathematics. And in class we make a argument that Subtract 4, next, add negative 6 thus becomes negative 10. Is this a valid argument of Logic? The answer is no, it is junk. Because Subtract 4 is meaningless for you can only subtract (remove) from a larger positive number or the number itself. And the second premiss is false for negative numbers do not exist.
Let us try an example from geometry. The slant cut of a right circular cone is an ellipse, because all math textbooks says so. This argument is invalid and should not even be listed as an example because the slant cut of cone is actually an oval, never ellipse for right circular cone. So the premisses are false and thus we have no argument of logic.
The point I am making is that the Truth value of premisses has to be checked for truth or falsity before any such premisses can go into being used at all in an argument. And science determines the truth value. But college and university classrooms of Logic never understood, that an argument of Logic has to have true premisses in order to make a Logic Argument proceed. All the premisses of a Logic argument must have a true truth value to proceed further.
As the Physics said earlier-- the If--> Then is the argument and the premisses have to be true. Now a premiss can be a AND connector with a false add-on, which we view as just chatter in the argument.
Example: If Mars is the 4th planet from the Sun and that Venus has life on it, then there are 3 other planets between the Sun and Mars.
So astronomy can prove the truth value that Mars is the 4th planet. The AND connector added on a chatter box idea which is either false or true, but that is alright because AND connector allows for nonsense chatter so long as it has a true premiss.
So if we take all college and university Logic textbooks and omit all the arguments which have false premisses unchecked by science and tossed them out.
Now here is one from Copi given by Aristotle. "Poetry is finer and more philosophical than history; for poetry expresses the universal and history only the particular." (Aristotle, Poetics)
Now we can excuse Aristotle for making this junk argument that is not even logical. Excuse him because Science during the time of Aristotle was primitive and not well developed or understood. So we can excuse Aristotle on that ground. But if someone tried making that argument today in logic, would be tossed out as junk for the premisses are false--- "poetry expresses the universal and history expresses the particular" are two premisses found false by sociology science.
AP writes: Pragmatism philosophy would say that the function of poetry is "Poetry at its best is using as few of words as possible, and pretty words with rhyme and rhythm to get across a idea or feeling or sentiment." Poetry is dressed up Language to convey an idea. Logic is about ideas and the mechanics of ideas. So that Aristotle had no Logical Argument for he had false premisses.
So, what I am saying is, a Logic Argument must have true premisses determined by science (although some premisses can be long winded with AND chatterbox add-ons), in order to *be* a Logic Argument and to thus provide a logical conclusion.
I am also saying--- every logic argument presented to us, must go through a Check-up Test by the best available science on the topic to see if it has true premisses and can go on for determining a valid conclusion, otherwise it is thrown into the trash as junk.
Physics is the science of material objects, mass, motion, energy. Biology is the science of living objects and how living organisms behave in the environment. Logic is the science of correct use of language in communicating ideas and forming conclusions from those ideas. Mathematics is the science of correct use of the language of numbers-size and geometry figures and shapes. Just as mathematics is the correct use of numbers and figures of geometry, that Logic is the correct use of ideas and thoughts. In math we have numbers like 1,2,3,4, ... and figures of geometry like line, plane, square, rectangle, circle. In Logic we have statements of ideas and can label them as p, q, r, s, t, u, v, ... Math manipulates numbers and figures while Logic manipulates ideas as statements of a language. Sciences, logic and mathematics can be put into a diagram of subsets, where Physics is on top.
Physics
/
Chemistry
/
Astronomy, Geology
/
Biology which includes Sociology and Language
/
Logic
/
Mathematics
AP Principle to Form an Argument of Logic-- all the premisses must be true as checked by science to have an argument of logic. Some of the premisses are with the AND connector which has a true statement but may contain chatter box junk. But the important issue is that all the premisses are supported by current science.
An example: For it is safe to say Aristotle in Ancient Greek times started Logic with this argument.
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
In today's Logic, filled with science truth and all premisses true, the above looks more like this.
From biology there exists a species Homo sapiens composed of female as XX chromosomes and male with XY chromosomes and about half of all humans are male-- men. Homo sapiens is mortal in that biology notes that no human lives longer than 114 years and normally 99.99% of humans do not reach the age of 100 years.
Socrates existed from about 470 to 399 BC and was mortal, living for 71 years and died because he was forced to drink hemlock poison. Biology science to date knows of no living organism that lives forever and is immortal. Therefore, Socrates was mortal.
The sense I want to impart on the reader, is that a logical argument is heavily tilted toward science speak, even in the most mundane logic argument.
Example:
The family of parents John and Joan are deciding where to go on vacation with the 2 kids.
John wants to go West to a National Park to see wild wolves and wild bears because the kids want that.
While Joan wants to go East to visit her family because her parents are ill.
So John and Joan decide that they will call Joan's parents and have them decide where to vacation.
They call the parents and were told to go out West.
Therefore, they vacationed out West.
That same argument in science speak.
A working family often has a yearly vacation for the parent to revitalize his outlook of the job as shown in studies of sociology.
Vacations are fun for kids as they see new things.
The choice of where to vacation should lie in all the parents and extended family as shown in sociology studies.
The entire family and extended family get involved.
Therefore the choice was made by a vote to go out West to Yellowstone National Park.
Archimedes Plutonium
Jan 5, 2026, 6:10:53 PM (11 days ago) Jan 5
to Plutonium Atom Universe
5) The Logic Truth Tables in detail.
Corrected Old Logic AND truth table where AND is seen as addition of arithmetic; seen as joining together.
P Q P AND Q
T T = T
T F = T
F T = T
F F = F
And the answer lies in the idea that you want all possible outcomes for statement of idea P combined with statement of idea Q.
So that the truth table for 2 statements, the P will always be this:
P
---
T
T
F
F
And the Q will always to this:
Q
----
T
F
T
F
This is so to capture all the possible outcomes. If there were 3 variables of P, Q, R, then you need 8 rows to capture all the possible combinations.
P Q R
------------------
T T T
T T F
T F T
T F F
F T F
F F T
F F F
Does the reader see the pattern? It is a pattern that captures all possibilities of statements truth values given a specific number of variables P, Q, R, S, T etc. Remember, statements of ideas can be written either in capital letters or small letters, P,Q written as p,q.
We compare this pattern to mathematics of a true false test.
Total possibilities for a test of 2 questions with 2 answers is 2^2
Total possibilities for a test of 3 questions with 2 answers is 2^3
Total possibilities for a test of 4 questions with 2 answers is 2^4
(Mathematical Induction for a proof of this-- that the total possibilities are 2^m where m is the number of questions in math or the number of variables in Logic.)
Fundamental Counting Principle: To find the number of ways of making several decisions in succession, multiply the numbers of choices that can be made in each decision. (from Harold Jacobs, Mathematics a Human Endeavor)
Here again, we can see that Logic comes from Physics and is a subset of physics, for quantum mechanics is probability theory in order to get to the Fundamental Counting Principle.
In Physics we have Zero or Nothing in the idea that Absolute 0 Kelvin temperature is unattainable. This also proves that Negative numbers do not exist and never existed.
Physics has an infinity borderline because physics has a maximum constant speed of Light at 3.16*10^8 meters/second. Makes sense that if the world has a maximum speed, the speed of Light then the world has a maximum number that composes a infinity borderline, which is from Huygens tractrix is 1*10^604.
Everything in Math is of a positive value and in geometry is all mapped out in 1st Quadrant Only.
It is unfortunate that math named subtraction as subtraction for a better name for it would have been Remove. If math had used the term "Remove" you cannot remove (you cannot subtract) more than what is available to remove, then math and physics would never have negative numbers.
I start Logic with mathematics and used math to guide me. But now I shift over to physics for answers.
Physics has 0 and it has infinity borderline which comes to be 1*10^604 and its inverse. It is where pi digits has 3 zero digits in a row. If we climb back to 1*10^600, just before we slam into those 3 zero digits in a row, we find that the Speed of Light as 3.16*10^8 meters/second divides into 10^600 by 10^75. For 8 x 75 =600.
Meters and seconds are arbitrary until you ask the question what is the speed of light inside a proton torus with muons inside of an atom like hydrogen or helium. Meters and seconds are no longer arbitrary inside the proton torus. And it is here where you get the 10^75 factor.
Now, I have to shift over to Physics, for answers upon Logic, I start with Existence quantifier first and then go to Not-Equal because we need existence to start with. After existence we need "not" combined with "equality".
Equality to get at the AND, OR, IF-->Then. And it is with Not-Equal that we introduce the Distributive Law. Do you remember the distributive law in mathematics class? It is for example this A(B + C) = AB + AC, for example 2(3+4) = 2*3 + 2*4. It turns out that the distributive law is more essential for the beginning of Logic than is the commutative or associative laws. Commutative and associative laws are about the order in which you add or multiply. For example of commutative is 3+4 = 4+3 for add and 3*4 = 4*3. For example the associative is A+(B+C) = (A+B) + C, where you have to do what is inside the parenthesis first. Example 1+(2+3) = (1+2)+3. You see the order in which you add matters not. And for multiplication associative we have (A*B)*C = A*(B*C), for example (10*100)*1000 = 10*(100*1000). Distributive law has a mix of addition with multiplication.
Now physics also introduces Probability theory into Logic and into its subset--- all of mathematics. The way Physics introduces probability is through what it calls Psi-squared and that comes from physics being all about electricity and magnetism which are perpendicular to one another and obeys the Pythagorean Theorem of Geometry.
Pythagorean Triples and multiples of P-triples:
1, 2, 2, 3 for 1+4+4=9
3,4,5 for 9+16=25
1,1,3,5,6,7 for 1+1+9+25+36+49 =121
5,12,13
8, 15, 17
7, 24, 25
Physics delivers what exists in Space geometry and Physics delivers universal laws of the world.
We start Logic with Mathematics first through the Existential quantifier, next the Not-Equal and move down into the details of Logic. We use mathematics to reveal the essentials of Logic for Logic is a larger set than is mathematics, but mathematics is easier to understand what the details of logic are.
So if we take "Physics looking at the World" as opposed to "A human looking at the world". An idea for the human would be either true of false. But that same idea for Physics is given a value of either "zero or nothing" versus an idea that has "existence in material science".
So when Physics looks at a statement --- The Earth is the 4th planet from the Sun. Physics does not say "false" but rather, says-- "zero or nothing". When Humans look at that statement, they say "false".
And "nothing or zero" comes from physics in the Absolute 0 Kelvin temperature, nothing beyond zero.
Calculus forms existence in the derivative, the dy/dx as it moves along the x-axis, the function lands on a y-value, a unique y value and so that causes the existence of a unique coordinate point, a single 1 point to exist. The derivative thus creates Existence quantifier, and that it lands on a unique y-value. Physics Absolute 0 temperature and the derivative of calculus creates 0 and creates 1.
This is where Logic gets entangled with science. It starts with the question of existence of something and goes to the relevant science of that topic.
In mathematics, logic starts with the existence question of 0 and existence of 1. Then Logic turns to the concepts of Not and of Equal. Does 0 exist, or not exist. Does 1 exist or not exist. Logic then asks what is 0 equal to and what is 1 equal to? Is 5 subtract 5 equal to 0? Is 1/8 of 8 equal to 1?? But to define Equal, Logic needs the Not connector, becoming Not-Equal all wrapped up together into one package in order to well define the other connectors of AND, OR, IF-->Then, Universal quantifier.
We start Logic connectors with Existence. Then we move to well-defining Not-Equal so we can well define all the other connectors.
Let us look at Truth Tables in terms of mathematics as 1 and 0 for addition, subtraction, and division. I leave out multiplication because that involves Not-Equal with a distributive law.
Addition truth table of Arithmetic
-----------------------------------------
P Q P + Q
1 1 2
1 0 1
0 1 1
0 0 0
So 1 is true as existence of 1, while 0 in physics is "nothing or no existence". That math truth table implies or moves-into the idea that the truth table for AND connector is TTTF.
Subtraction truth table of Arithmetic
-----------------------------------------------
P Q P - Q
1 1 0
1 0 1
0 1 1
0 0 0
That table implies subtraction is remove, whether we remove a 0 or a 1 or a 1 from 1. That table also implies OR connector is subtraction with FTTF. Now here we must also consider that we remove P or remove Q or we can subtract P from Q or subtract Q from P.
Division truth table of Arithmetic
-----------------------------------------------
P Q P divide into Q
1 1 1
1 0 0
0 1 undefined
0 0 undefined
That table implies the material conditional of logic the If-->Then truth table as being TFUU.
We take up the multiplication truth table later in this textbook. It is complicated by the fact that we have a binary row for equal, T = T and F=F and we have a binary row for Not in which we combine the two binaries to make a 4 row truth table using the distributive law of arithmetic.
6) The AP Principle of Well Defining a concept.
Ideas have to be clear, crystal clear in order to be able to work with them.
I do not recall when Wikipedia first came out. I would guess in late 1990s. I do remember coming to Usenet in August of 1993 with posts on mathematics and my Atom Totality theory. But once Wikipedia started to come to the Internet, I often used it to look up science concepts. It was fast and easy.
But I soon discovered an unpleasant reality about Wikipedia science entries. Many in physics were obfuscation as I looked up a term. And then it dawned on me. That the authors of many physics or math or science concepts were unpaid authors and were contributing their thoughts as to what the definition was. And these free authors had no Logic training. And many were writing the entries of science for they failed in that science and as some showmanship, the author is getting back at the schools that failed them in science. So that their writing a definition would often have terms that were more complex than the term they are trying to define. I do have a logical mind and so I began to complain that most of the science entrees into Wikipedia were not definitions but obfuscation of what is attempted to be defined.
Sometime in the past 2 or 3 decades, I realized there had to be a principle of Logic, that when you define a concept, you can ___only define it by using more simple terms___, more simple terms to establish a definition.
So often I found myself looking up a concept in Wikipedia such as superdeterminism and finding myself in a run around looking up more complicated terms. Not only physics but mathematics also.
Wikipedia is notorious for violating AP's Logic Principle of Well Defined Definitions.
The principle simply says, you cannot define a concept by using terms that are more complex than what you are trying to define. Take a look at any of 10 physics entries in Wikipedia of defining a concept and I bet that about 80 to 90% of those definitions violate AP's principle. Which is often very frustrating. You want to know what a concept is, and presented by Wikipedia a nauseous blather of terms of more complexity than the concept you originally seeked to understand.
Here is an example in physics, where I look up the term of "superdeterminism" and Wikipedia defines with this blather.
--- quoting Wikipedia---
In quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem.
--- end quoting Wikipedia---
This is a major problem of Wikipedia as it hires for free, failures of physics to write many entries, yet having no logical brains to be writing on physics at all. In my opinion the above was written by a failed person of physics. Or, likely some fool in philosophy cranking up a physics definition.
Here is what a definition of Superdeterminism looks like where the terms are much more simple than the concept being defined. And thus the concept Superdeterminism is made accessible to the new reader.
AP well-defining Superdeterminism.
Superdeterminism-- John Bell coined the term after he published his Bell Inequality. And what Bell means by Superdeterminism is the complete absence of free-will. A World where every action, or thought is made by some superior power and humans as puppets are forced to make those actions and thoughts of the super power.
Actually, here I have where John Bell well-defines superdeterminism himself, and let the reader compare what the crank in Wikipedia wrote and what John Bell wrote.
Here is John Bell defining what Superdeterminism is:
--- Bell stated on the BBC ---
"There is a way to escape the inference of superluminal speeds and
spooky action at a distance. But it (Superdeterminism) involves
absolute determinism in the universe, the complete absence of free
will. Suppose the world is super-deterministic, with not just
inanimate nature running on behind-the-scenes clockwork, but with our
behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears.
There is no need for a faster than light signal to tell particle A what
measurement has been carried out on particle B, because the universe,
including particle A, already "knows" what that measurement, and its
outcome, will be."
--- end Bell quote ---
--- further statement by John Bell to the BBC on Superdeterminism ---
"The only alternative to quantum probabilities, superpositions of
states, collapse of the wavefunction, and spooky action at a distance,
is that everything is superdetermined. For me it is a dilemma. I think
it is a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things."
--- end Bell quote---
Of course AP found the solution, and wished that John Bell had lived to far beyond November 1990, but John died in October 1990. It was not until 1993 that the Atom Totality was published on the Internet. A Atom Totality is the super power that causes Superdeterminism--- the total absence of free-will. We are all puppets to the Atom Totality.
So often, especially physics in Wikipedia is burdened by fools as editors, as writers who know not what they talk about, and have almost a 0 logic IQ. Just look at Wikipedia pictures of conic sections where the fools list the ellipse as a slant cut of cone when in truth that is a oval.
Part 2, A short brief history of Logic.
7) Logic, formally starts in Ancient Greek time, along with deductive mathematics.
Logic has had a sad history in Modern Times. Actually the start of Logic in Ancient Greek times, that of Aristotle, shone brighter than the modern logic of Boole and Jevons of the 1800s. I say that because, Aristotle and Socrates Logic got many things correct and was a start of Logical Science. It is more difficult to start a Logical Science, than, to later contribute to it, such as Boole and Jevons contributing.
Modern Logic has the 4 most simple connectors-- Equal-Not, AND, OR, IF-->Then.
AND truth table is truly TTTF, not TFFF.
OR truth table is truly FTTF, not the mindless two types of OR, for Boole and Jevons made huge mistakes of Logic especially OR, thinking you could have two different types of OR and not be contradictory. No-one thinks subtraction in math should have two independent different types of subtraction.
Equal-Not must be combined as one truth table to establish a TTTT truth table, and not the idiotic separate two tables of p and q statements which is a 2 tier for Equal alone, and a 2 tier for Not, alone. They should be combined into forming a 4 tier such as AND, and as OR are 4 tier, as well as If-->then is 4 tier.
If-->Then must be TFUU where U stands for Unknown so that Logic is greater than Mathematics to handle division by 0. Old Logic could not explain --- "what is division by 0???".
Logic history starts in Ancient Greek times with Aristotle and with syllogisms such as this one from Aristotle.
A syllogism is simply an argument of Logic, and happens to be the shortest logic argument of 2 lines and a conclusion. We get to more complex and complicated arguments later in this textbook.
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
And it is not coincidental that the Ancient Greeks, along with inventing Logic arguments, also were the inventors of the math deductive proof. The Ancient Greeks started to do math proofs, such as the Pythagorean theorem and such magnificent proofs as the existence of just 5 regular polyhedra (only AP found a 6th and 7th in recent times, see AP's #302 book, 7 Regular Polyhedra and overhaul of geometry axioms// math research).
Ancient Greek times was a time of wealth and with wealth allows the coming into existence of schools and education.
When I was in High School, Ancient History classes had chapters on Ancient Greek times and prominent was Socrates, whose student was Plato and Plato's student was Aristotle.
Unfortunately for Archimedes, actually, the greatest thinker of Ancient Greek times was Democritus with the Atomic theory who was a younger contemporary Socrates in 460BC in Abdera, Thrace. Greater than even Archimedes in Siracusa, 287-212BC, as the Atomic Theory is central to physics, and physics the greatest science of all.
Did Democritus and Socrates ever meet each other? Plato would also be a contemporary of Democritus. So did the three know each other???
Can we say that Physics starts with Democritus? We sure can say that Chemistry starts with Democritus and the atomic theory.
No, I would say that Thales in Miletus started Physics for he starts electricity of rubbed amber by fur, and with the lodestone as a magnet attracts iron. This was about 600 BC compared to Leucippus-Democritus atomic theory of 5th century BC.
It is marvelous that both electricity and magnetism were discovered at the same time and a hundred years later the Atomic theory was started.
For the Axiom Principle over all of science is --- All is Atom, and Atoms are nothing but electricity and magnetism.
And if Superdeterminism is real and true, the start of electricity and magnetism and the Atomic theory should come in history near one another and at the same time.
--- quoting Wikipedia---
Democritus
A philosopher, possibly Democritus. Casting of bust of the Villa of the Papyri.
Born
c. 460 BC
Abdera, Thrace
Died
c. 370 BC (aged approximately 90)
Philosophical work
Era
Pre-Socratic philosophy
Region
Western philosophy
School
Atomism
Main interests
Nature
Notable ideas
Atoms and the void as the fundamental constituents of the physical world
Democritus (/dɪˈmɒkrɪtəs/, dim-OCK-rit-əs; Greek: Δημόκριτος, Dēmókritos, meaning "chosen of the people"; c. 460 – c. 370 BC) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. Democritus wrote extensively on a wide variety of topics.
None of Democritus' original work has survived, except through second-hand references. Many of these references come from Aristotle, who viewed him as an important rival in the field of natural philosophy. He was known in antiquity as the ‘laughing philosopher’ because of his emphasis on the value of cheerfulness.
Life
Democritus among the Abderites
Although many anecdotes about Democritus' life survive, their authenticity cannot be verified and modern scholars doubt their accuracy.
According to Aristotle, Democritus was born in Abdera, on the coast of Thrace. He was a polymath and prolific writer, producing nearly eighty treatises on subjects such as poetry, harmony, military tactics, and Babylonian theology. Some called him a Milesian, and the name of his father too is stated differently. His birth year was fixed by Apollodorus in the first year of the 80th Olympiad, or 460 BC, while Thrasyllus had referred it to as the 3rd year of the 77th Olympiad. Democritus had called himself forty years younger than Anaxagoras. His father, Hegesistratus,--or as others called him Damasippus or Athenocritus,--was possessed of so large a property, that he was able to receive and treat Xerxes on his march through Abdera.
Democritus spent the inheritance, which his father left him, on travels into distant countries, which he undertook to satisfy his extraordinary thirst for knowledge. He travelled over a great part of Asia, and, as some state, he even reached India and Aethiopia. We know that he wrote on Babylon and Meroe; he must also have visited Egypt, and Diodorus Siculus even states, that he lived there for a period of five years. He himself declared, that among his contemporaries none had made greater journeys, seen more countries, and made the acquaintance of more men distinguished in every kind of science than himself. Among the last he mentions in particular the Egyptian mathematicians (ἀρπεδόναπ-ται ; comp. Sturz, de Dialect. Maced. p. 98), whose knowledge he praises, without, however, regarding himself inferior to them. Theophrastus, too, spoke of him as a man who had seen many countries. It was his desire to acquire an extensive knowledge of nature that led him into distant countries at a time when travelling was the principal means of acquiring an intellectual and scientific culture; and after returning to his native land he occupied himself only with philosophical investigations, especially such as related to natural history.
--- end quoting Wikipedia---
I remember in High School stories of Socrates were on TV in the 1960s, I guess more because of the way he died, than his teachings. I remember him more for his brilliant arguments, lengthy long arguments.
--- quoting Wikipedia on Socrates---
Socrates (/ˈsɒkrətiːz/; Ancient Greek: Σωκράτης, romanized: Sōkrátēs; c. 470 – 399 BC) was an ancient Greek philosopher from Athens who is credited as the founder of Western philosophy and as among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem. Socrates was a polarizing figure in Athenian society. In 399 BC, he was accused of impiety and corrupting the youth. After a trial that lasted a day, he was sentenced to death. He spent his last day in prison, refusing offers to help him escape.
Plato's dialogues are among the most comprehensive accounts of Socrates to survive from antiquity. They demonstrate the Socratic approach to areas of philosophy including epistemology and ethics. The Platonic Socrates lends his name to the concept of the Socratic method, and also to Socratic irony. The Socratic method of questioning, or elenchus, takes shape in dialogue using short questions and answers, epitomized by those Platonic texts in which Socrates and his interlocutors examine various aspects of an issue or an abstract meaning, usually relating to one of the virtues, and find themselves at an impasse, completely unable to define what they thought they understood. Socrates is known for proclaiming his total ignorance; he used to say that the only thing he was aware of was his ignorance, seeking to imply that the realization of one's ignorance is the first step in philosophizing.
--- end quoting Wikipedia on Socrates---
Then in history comes Plato student of Socrates. I remember Plato mostly for his "being and becoming arguments".
--- quoting Wikipedia on Plato---
Plato (/ˈpleɪtoʊ/ PLAY-toe; Greek: Πλάτων, Plátōn; born c. 428–423 BC, died 348/347 BC) was an ancient Greek philosopher of the Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms. He influenced all the major areas of theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in Athens where Plato taught the doctrines that would later become known as Platonism.
Plato's most famous contribution is the theory of forms (or ideas), which aims to solve what is now known as the problem of universals. He was influenced by the pre-Socratic thinkers Pythagoras, Heraclitus, and Parmenides, although much of what is known about them is derived from Plato himself.
Along with his teacher Socrates, and his student Aristotle, Plato is a central figure in the history of Western philosophy. Plato's complete works are believed to have survived for over 2,400 years—unlike that of nearly all of his contemporaries. Although their popularity has fluctuated, they have consistently been read and studied through the ages. Through Neoplatonism, he also influenced both Christian and Islamic philosophy. In modern times, Alfred North Whitehead said: "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."
--- end quoting Wikipedia on Plato---
I invite the reader to figure out the age of lifespan of Socrates and of Plato and of Aristotle given their date of birth and death as a homework exercise for students in class. Using the Scientific Method discussed earlier, run through a formula that easily tells you the lifespan of persons who lived before 0 AD where today we simply subtract the date of birth from the date of death. For example, John Bell the engineer who discovered superdeterminism. He was born 1928 and died 1990. So to figure out lifespan in modern times we simply take the date of death and subtract date of birth gives us 1990 - 1928 = 62 years of life. Using the Scientific Method and plenty of logical thought, figure out the lifespan of Socrates, Plato and Aristotle, and Democritus and Archimedes. And find the easiest reasonable way of determining their age at death, considering it is denoted in BC time. Find a formula.
The student of Plato is Aristotle. Strangely, most people when they think of Aristotle, they think of Logic and philosophy. I think of him as the founder of biology science.
--- quoting Wikipedia on Aristotle---
Aristotle (Attic Greek: Ἀριστοτέλης, romanized: Aristotélēs; 384–322 BC) was an ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, and the arts. As the founder of the Peripatetic school of philosophy in the Lyceum in Athens, he began the wider Aristotelian tradition that followed, which set the groundwork for the development of modern science.
Little is known about Aristotle's life. He was born in the city of Stagira in northern Greece during the Classical period. His father, Nicomachus, died when Aristotle was a child, and he was brought up by a guardian. At around eighteen years old, he joined Plato's Academy in Athens and remained there until the age of thirty seven (c. 347 BC). Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, tutored his son Alexander the Great beginning in 343 BC. He established a library in the Lyceum, which helped him to produce many of his hundreds of books on papyrus scrolls.
Though Aristotle wrote many treatises and dialogues for publication, only around a third of his original output has survived, none of it intended for publication. Aristotle provided a complex synthesis of the various philosophies existing prior to him. His teachings and methods of inquiry have had a significant impact across the world, and remain a subject of contemporary philosophical discussion.
--- end quoting Wikipedia on Aristotle---
I was curious to see how many books Aristotle wrote, as to compare with AP. Wikipedia says this:: Diogenes Laërtius lists, in his Lives and Opinions of Eminent Philosophers (c. 230 CE), works of Aristotle comprising 156 titles divided into approximately 400 books, which he reports as totaling 445,270 lines of writing; however, many of these are lost or only survive in fragments, and some may have been incorrectly attributed.
Well, AP is near 370 books of science and not much longer I hit #400.
I must stress the idea, that in rich wealthy countries does education, thinking and philosophy and logic grow. In societies where hard labor is needed to just stay alive, there is little time for --- deep thinking---.
Archimedes Plutonium
Jan 5, 2026, 7:01:04 PM (11 days ago) Jan 5
to Plutonium Atom Universe
8) The first computer by Babbage influences Logic, and the Boole + Jevons mistakes.
--- quoting Wikipedia ---
First computer
Charles Babbage
A diagram of a portion of Babbage's Difference engine
The Difference Engine Number 2 at the Intellectual Ventureslaboratory in Seattle
Charles Babbage, an English mechanical engineer and polymath, originated the concept of a programmable computer. Considered the "father of the computer", he conceptualized and invented the first mechanical computer in the early 19th century.
After working on his difference engine he announced his invention in 1822, in a paper to the Royal Astronomical Society, titled "Note on the application of machinery to the computation of astronomical and mathematical tables". He also designed to aid in navigational calculations, in 1833 he realized that a much more general design, an analytical engine, was possible. The input of programs and data was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. The engine would incorporate an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete.
The machine was about a century ahead of its time. All the parts for his machine had to be made by hand – this was a major problem for a device with thousands of parts. Eventually, the project was dissolved with the decision of the British Government to cease funding. Babbage's failure to complete the analytical engine can be chiefly attributed to political and financial difficulties as well as his desire to develop an increasingly sophisticated computer and to move ahead faster than anyone else could follow. Nevertheless, his son, Henry Babbage, completed a simplified version of the analytical engine's computing unit (the mill) in 1888. He gave a successful demonstration of its use in computing tables in 1906.
In Babbage's time, printed mathematical tables were calculated by human computers; in other words, by hand. They were central to navigation, science and engineering, as well as mathematics. Mistakes were known to occur in transcription as well as calculation.
At Cambridge, Babbage saw the fallibility of this process, and the opportunity of adding mechanisation into its management. His own account of his path towards mechanical computation references a particular occasion:
In 1812 he was sitting in his rooms in the Analytical Society looking at a table of logarithms, which he knew to be full of mistakes, when the idea occurred to him of computing all tabular functions by machinery. The French government had produced several tables by a new method. Three or four of their mathematicians decided how to compute the tables, half a dozen more broke down the operations into simple stages, and the work itself, which was restricted to addition and subtraction, was done by eighty computers who knew only these two arithmetical processes. Here, for the first time, mass production was applied to arithmetic, and Babbage was seized by the idea that the labours of the unskilled computers [people] could be taken over completely by machinery which would be quicker and more reliable.
There was another period, seven years later, when his interest was aroused by the issues around computation of mathematical tables. The French official initiative by Gaspard de Prony, and its problems of implementation, were familiar to him. After the Napoleonic Wars came to a close, scientific contacts were renewed on the level of personal contact: in 1819 Charles Blagden was in Paris looking into the printing of the stalled de Prony project, and lobbying for the support of the Royal Society. In works of the 1820s and 1830s, Babbage referred in detail to de Prony's project.
Difference engine
Main article: Difference engine
The Science Museum's Difference Engine No. 2, built from Babbage's design
Portion of Babbage's difference engine
Babbage began in 1822 with what he called the difference engine, made to compute values of polynomial functions. It was created to calculate a series of values automatically. By using the method of finite differences, it was possible to avoid the need for multiplication and division.
For a prototype difference engine, Babbage brought in Joseph Clement to implement the design, in 1823. Clement worked to high standards, but his machine tools were particularly elaborate. Under the standard terms of business of the time, he could charge for their construction, and would also own them. He and Babbage fell out over costs around 1831.
Some parts of the prototype survive in the Museum of the History of Science, Oxford. This prototype evolved into the "first difference engine". It remained unfinished and the finished portion is located at the Science Museum in London. This first difference engine would have been composed of around 25,000 parts, weighed (13,600 kg), and would have been (2.4 m) tall. Although Babbage received ample funding for the project, it was never completed. He later (1847–1849) produced detailed drawings for an improved version,"Difference Engine No. 2", but did not receive funding from the British government. His design was finally constructed in 1989–1991, using his plans and 19th-century manufacturing tolerances. It performed its first calculation at the Science Museum, London, returning results to 31 digits.
Nine years later, in 2000, the Science Museum completed the printer Babbage had designed for the difference engine. His printers were the first computer printers invented.
Completed models
The Science Museum has constructed two Difference Engines according to Babbage's plans for the Difference Engine No 2. One is owned by the museum. The other, owned by the technology multimillionaire Nathan Myhrvold, went on exhibition at the Computer History Museum in Mountain View, California on 10 May 2008. The two models that have been constructed are not replicas.
Analytical Engine
Main article: Analytical Engine
Portion of the mill with a printing mechanism of the Analytical Engine, built by Charles Babbage, as displayed at the Science Museum (London)
After the attempt at making the first difference engine fell through, Babbage worked to design a more complex machine called the Analytical Engine. He hired C. G. Jarvis, who had previously worked for Clement as a draughtsman. The Analytical Engine marks the transition from mechanised arithmetic to fully-fledged general purpose computation. It is largely on it that Babbage's standing as computer pioneer rests.
The major innovation was that the Analytical Engine was to be programmed using punched cards: the Engine was intended to use loops of Jacquard's punched cards to control a mechanical calculator, which could use as input the results of preceding computations. The machine was also intended to employ several features subsequently used in modern computers, including sequential control, branching and looping. It would have been the first mechanical device to be, in principle, Turing-complete. Charles Babbage wrote a series of programs for the Analytical Engine from 1837 to 1840. The first program was finished in 1837. The Engine was not a single physical machine, but rather a succession of designs that Babbage tinkered with until his death in 1871.
--- end quoting Wikipedia---
Here I am looking in the history of Logic as to why so many mistakes in the simple connectors for Boole and Jevons made mistakes on all 4 of the simple connectors. I am looking for what propelled them to make Logic be algebraic and the answer is quite simple and easy for the rise of modern computers starts with Charles Babbage 1812, thus incentivizing Algebraic Logic to be the so-called software of the emerging new technology that Babbage was creating the hardware.
For Boole would write The Mathematical Analysis of Logic 1847 and Laws of Thought 1854. Jevons wrote the popular Logic textbook : Elementary Lessons on Logic 1871.
Logic needed to be formed to fill the software of the computers being built after Babbage.
AP writes: A long time ago I read various facets of history of Boole and one reference source which I no longer have available, said that Boole and Jevons were stumped on the truth table of AND and saved it for last. Of course they came up with AND being TFFF when in actuality, it is TTTF. This suggests that Boole and Jevons had OR exclusive plus had OR inclusive. They needed a truth table of TTTF and so they dreamed up the idea that Either..or..or..Both would fill the bill for TTTF. When all they really needed to do, was see that AND was TTTF and not that of TFFF. By November 2025, I got a clearer picture of why Boole and Jevons fell into this mistake, and probably I should not be so harsh on Boole and Jevons. The idea I came to realize in November 2025, is that early on in Logic we introduced the connectors with Existence quantifier and ask the question of ----- does Logic itself exist? And we go one step further by asking------ does Logic not exist? We form that into a argument of logic P= Logic exists, and Q = Logic does not exist. Putting that together with a AND connector is P AND Q "Logic exists and logic does not exist". Obviously this is a contradiction, and I am thinking that such was the reasoning for Boole and Jevons in making AND as TFFF to avoid contradiction.
In Mathematics there is one big no, no you can never do---and that is divide by 0. If you can divide by zero, you destroy math and we just call division by zero as undefined. You lose all uniqueness in math if you allow division by zero. For example 2/0 = infinity and 9/0 = infinity then we end up with 2=9. All of math is destroyed if you allow division by 0 be a number.
The Contradiction in Logic.
-----------------------------------
In Logic we have a similar problem with what is called a Contradiction. A contradiction is simply A and not A. Or, B exists and B does not exist. So a contradiction destroys logic just as division by 0 destroys math. So as we start Logic and introduce the Existence quantifier first, then _not_ then introduce Not-Equal. We cannot have nor tolerate a Contradiction as it destroys Logic.
By November 2025, perchance I perceive why Boole and Jevons wanted the mistake of AND being TFFF. They thought that an Argument containing "P exists AND P does not exist" or, containing "Q and not Q" are contradictions and not allowed. Thus, and therefore, Boole and Jevons finally decided that AND truth table be TFFF.
So this sounds reasonable that Boole and Jevons thought the truth table had to be TFFF in the second and third row looks like a contradiction.
P Q P AND Q
T F ?
F T ?
F F F
So from that truth table it was reasonable for Boole and Jevons to think the final truth table of AND be TFFF for the 2nd and 3rd rows look like contradictions. And this goes to show--- further--- the idea that physics has no falsehood concept but rather has the concept of zero, 0, or nothing. Here we see that humanity confused idea of "falsehood" gets in the way of truth and reality.
So, well, AP says AND is TTTF, and how does AP get around the contradiction of a AND connector that is a seemingly contradiction in 2nd and 3rd row?? Well, we get around that with the justification that AND is math Add and so math demands TTTF.
Plus, in addition, that whenever and where-ever a contradiction occurs in a argument we stop and halt all things and remove the contradiction. That fixes the problem.
Getting back to AND and OR in Logic and modern day computers.
I bring this up because Modern Day Computers run Addition on the inclusive OR because they need the truth table to be TTTF for addition. But that if all logicians from Boole going forward had backtracked and looked at how mired in error was their AND, they could have thrown out the stupid inclusive OR and declared that AND is after-all, math addition.
Reading the following selection on Jevons in Wikipedia, is alluded to the idea that once you know the truth-table "performing simple logical inference by manipulating a truth table". AP writes: Is this where Logic was saddled wrongly into using inclusive OR as math addition???
--- quoting Wikipedia---
In 1864 Jevons published Pure Logic; or, the Logic of Quality apart from Quantity, which was based on Boole's system of logic, but freed from what he considered the false mathematical dress of that system. In 1866 what he regarded as the great and universal principle of all reasoning dawned upon him; and in 1869 Jevons published a sketch of this fundamental doctrine under the title of The Substitution of Similars. He expressed this principle in its simplest form by saying: "Whatever is true of a thing is true of its like", and he worked out in detail its various applications including the logical abacus, a method of performing simple logical inference by manipulating a truth table consisting of labeled wooden boards. He noted that the operations could be performed by a simple mechanism and later he had a "logical machine" built from his specifications in 1869, sometimes called the "Logic Piano" because of its resemblance to an upright piano. The machine was exhibited before the Royal Society in 1870.
In the following year appeared the Elementary Lessons on Logic, which soon became the most widely read elementary textbook on logic in the English language. In the meantime he was engaged upon a much more important logical treatise, which appeared in 1874 under the title of The Principles of Science.
--- end quoting Wikipedia---
About time for a test or quiz here. As mentioned earlier I prefer fill in the blank tests for they have a further opportunity of teaching both student and teacher alike. I will start the first four questions of probably a 20 question test. In High School we had teachers use these machines (I forgot the name of this copying) where they made a master test sheet and then had a machine make copies where the ink smelled. I suppose those machines are no longer in use. And now a days by 2025, we simply can have a photocopy of the test.
(1) Short and simple, Logic is the science of _____ and what future actions we take based on those ____, and what ____ are true. We label ____ in logic by symbols such as p, q, r, s.
(2) We start Logic connectors, logically by using good true ideas. ________ is long well established science in history. ______ is easier to study and learn than is Logic, for logic is far bigger encompassing all ideas while _____ is confined to arithmetic, algebra and geometry and its most important branch of calculus, where calculus is a mix of geometry and numbers. Logic is a larger set than ______ and so Logic should contain all of ________ inside of Logic.
So naturally, we start Logic connectors by using _______ as a ________ to tell us if our Logic is straight and clear and on track.
(3) Truth or Falsity of an idea in a statement P, Q is obtained from all the other _____ of their universal _______. If we had the statement-- P = Thrusting a bar magnet through a coil of copper produces no electric current. That would be false because it violates the ______________.
(4) Name the 6 math operators __, __, __, __, __, __, then name the 6 logic connectors __, __, __, __, __, __. Finally, pair up the logic connectors with the similar math operator, for example, Existential quantifier pairs up with derivative of calculus, while Universal quantifier pairs up with integral of calculus __, __, __, __.
Teacher, to provide 16 more questions for a 20 question test or quiz.
Archimedes Plutonium
Jan 6, 2026, 12:43:26 AM (11 days ago) Jan 6
to Plutonium Atom Universe
Part 3, The Mechanics of Logic.
9) The 6 simple connectors of Logic.
So mathematics has 6 simple operators. And given in order where Mathematical Induction, a proof method, gives all the Counting Numbers for that method is based on the idea of adding 1.
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 simple 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 laws of physics such as Ampere law, or Faraday law or New Ohm's law.
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 and operators but to list them in order such that the most primitive connector is first and the last one the most complex, 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.
So mathematics starts with add and ends up last with integration as the most complex is Integration of calculus.
Logic is a bit different. We first have to know what we talk about exists or not exists and use the Existential quantifier. Next we use the Not and the Equal sign for truth tables, and so we need a connector for Not and for Equality which is presented in a combined connector of Not-Equal.
No use in arguing over things that do not exist. And just as a fiction story is fiction and nonexisting, 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, or if not true 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. 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. A graph is shown later in this book on calculus derivative motion.
So for logic we have to study the 6 connectors in order from simple to most complex.
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.
You can see a pattern in the truth-table from that of 4 trues, then 3 trues, then 2 trues, then 1 true.
10) Using mathematics to guide Logic.
So how should I begin the story of Logic connectors??? Not from the history of Logic but from an ally subject of mathematics. And how should I begin the story of truth in Logic? Truth comes from the sciences and especially physics.
All of Science is governed by the Axiom Principle of Science--- All is Atom, and Atoms are nothing but Electricity and Magnetism.
Explanations of science are final once you reduced the phenomenon observed to that of electricity and magnetism.
So where does Mathematics and Logic come into the picture of science for science is all about Physics and in particular Atoms?
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.
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. So does Logic have 2 more connectors of Existence quantifier and Universal quantifier related to derivative and integral, respectively.
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.
We say Existential quantifier is directly related to derivative and Universal quantifier is directly related to integral, due to the calculus of mathematics.
So here we need to turn on our logical mind and figure out the correct order. Obviously if something does not exist, no point in talking about it and what ideas come out of it. Existence is number 1. Even literature recognizes existence is number 1 as Shakespeare's Hamlet says: "To be, or not to be, that is the question: Whether 'tis nobler in the mind..".
We should start the Logic connectors with Existence, which in math would be the derivative of calculus, and next we should have Not-Equal for all the other connectors require the concepts of existence, not, and equality.
Tricky because Logic connectors start with the high-powered calculus of derivative and then next, with Not-Equal, because AND, OR, If-->Then need the concept of equal and not equal.
But, as mentioned earlier, Logic stops cold dead when it has a contradiction "The sun is a star and the sun is not a star". When a contradiction arises, all of logic stops in its tracks and calls in the best science of its time to sort things out. This is why Logic connectors must start, is forced to start with Existence quantifier and Not-Equal.
Whenever a contradiction occurs in Logic, all things stop and sorted out, before continuing.
11) What is Truth? and how does truth relate to Logic.
So truth in this world is our best science on the subject matter and that usually comes from physics, chemistry, biology, astronomy and all its branch sciences.
Logic is the science of ideas and how those ideas make other ideas. If we ask physics, and physics could talk, it would say that the laws of science are true and anything opposed to those laws is nonsense. The laws of science come from the Scientific Method and the laws are Universal laws. As time goes by the laws can change or be modified, provided new observations and experiments warrant the change and modification.
So Science tells us what is true, and what is not true is lumped together as being zero or nonsense or worthless. False or falsehood has no role in Logic, but rather is seen as being 0 value.
Logic does not deal with truth-tables with false value, seeing them as 0 value. Instead, Logic deals with truth-table as true science ideas have a truth value, and what is not true value is worthless chitter chatter and has 0 value.
So Logic defines the 6 connectors not with a Truth-table of true and false, but rather defines the 6 connectors in the way that physics defines a Law of Physics by stating the law.
So for example, Physics defines the Faraday Law as being "Thrust a bar magnet through a closed loop coil of copper wire connected to a galvanometer and read a current flow through the wire".
Logic example, in that Logic defines the AND connector not with a truth-table but rather as a Law of Science that says: "String together as many statements as you wish, p, q, r, s, t, u, v with the AND connector, and if just one of those statements has a true-value by laws of science, regardless of the fact that all the other statements are 0 value nonsense, then the entire string is true because of the one statement that is true. A caveat warning though, a string of statements strung together with the AND connector, must never have any two statements that are contradictory such as P and not-P would be a contradiction and thus all logic stops until the contradiction is straightened out by science.
Another Logic example, in that Logic defines the OR connector not with a truth-table but rather as a Law of Science that says "Given two statements p, q connected by OR, means that you remove p leaving behind q, or, remove q leaving behind p, or, you subtract q from p or subtract p from q. OR is subtraction for its removal. AND is joining together while OR is removal.
Now the quantifiers of Existential and Universal do not have truth-tables associated with them, for they are true in and of themselves. Truth granted by an inspection of the statements from the pertinent Science pertaining to the statements. We can say "does not exist" or "is not universal" and in those instances they have a 0 value, but not a falsehood value. You see, science itself does not recognize falsity, science only sees truth. Humans see the world in terms of truth or false, while science sees the world only in terms of truth. Falsehood for science is associated the number 0 for nothing or nonsense or chitter chatter mistakes.
Because of Physics as the truth giver, physics ranges from 0 out to a positive large number the infinity borderline of 1*10^604. And truth has a value somewhere in that range of numbers but not 0 for that is nonsense.
In Old Logic their numbers ranged from negative numbers then 0 and onwards to positive numbers. So in Old Logic they viewed the world in which they saw falsity or falsehoods have negative number values. In New Logic, if it is not true as supported by science its value is 0, as nonsense.
This matches the idea that 0 Kelvin degrees temperature, Absolute 0 temperature is never attainable. No negative numbers exist, and falsehood is not a negative value but is of 0 nonsense value. Temperatures above Absolute 0 Kelvin are positive numbers and correspond to the electromagnetic spectrum of energy. These EM waves of energy of the electromagnetic spectrum all exist, corresponding to the Existential quantifier. And the Laws of Electromagnetism are Universal Laws of Physics.
And the Primal Axiom over all of knowledge is -- All is Atom, and Atoms are nothing but electricity and magnetism.
12) Existential quantifier.
One would think that the last two of the simple connectors of Logic of existential quantifier and universal quantifier are very easy. All you have to say is "There exists a ____" or say "For every ____". However reality is different in that Existential and Universal quantifiers turn out to be complex, not simple at all.
And one of the signs of this complexity is the riddle of "infinity".
"There exists a horse" is simple enough. "There exists thousands of horses" is also simple. But does "There does not exist an infinity of horses" make sense? Here we have to well-define infinity and that has never been done before until it was well defined in sci.math by AP circa 2009, using the idea of a borderline. A borderline between finite and infinite, otherwise, every number is finite. And this borderline can be found from Huygens work on tractrix figure which is infinite in reach, but finite in area. Using the Tractrix figure we find that infinity borderline is where pi has 3 zero digits in a row and is the number 1*10^604. All numbers from 0 to the borderline are finite numbers. All numbers after the borderline are infinite numbers.
You cannot well-define Infinity, unless you have a borderline between finite and infinite. Amazingly, a mathematician named Huygens noticed that the geometry figure called the Tractrix was
____infinite in reach but had a finite area in its function graph______. This allowed AP to find the infinity borderline.
Concept that Infinity = a borderline between finite and infinite was discovered by AP 2009. Simple beautiful idea-- there must be a borderline between finite and infinite, otherwise, all is just one and the same, and not two different concepts. And so I defined the concept of infinity itself as this border crossing.
Now this mistake in not having a correct well-defined Infinity in math, affects the Calculus by a large measure, a large degree. It is impossible to have a correct calculus, when you have a fuzzy understanding of what is infinity.
This mistake of not well-defining infinity affects much of other mathematics. Of course the other sciences, especially physics rarely needs to know what the correct proper infinity is. However, it does show up frequently in the best physics-- quantum electrodynamics, in which it is often used to eliminate infinities that crop-up in calculations. This physics math procedure is called Renormalization-- getting rid of the infinities, taught by Feynman in his Lectures on Physics.
The trouble with Old Math, is, well, they were terribly shoddy in logic, in thinking straight and clear. For a logical person, knows, that if you have a concept of finite versus infinite, the only way to handle those two concepts is to realize a border must go between them so that you can tell if any given number is finite or infinite. Otherwise, there is no infinity, if there is no borderline.
There is only one way you can have a concept of finite, by having a
concept of infinity, and the only way you can have both, is that a
borderline exists between them.
I have pinpointed that borderline from tractrix-circle analysis, from
algebraic analysis of algebraic completeness, and from angles of
regular polyhedra. The borderline in microinfinity is 1*10^-604 and in
macroinfinity is 1*10^604.
The easiest way to see the borderline is to see where pi digits ends in a three zero digits in a row. This three zero digits in a row for pi allow the tractrix area to catch up with the circle area, for the first time. Just as Huygens said the tractrix was infinite reach but finite area. So when we reach the three zeroes in a row, the circle area and tractrix area are equal at that moment in time.
Take a look at the tractrix graph as it gets closer and closer to the x-axis.
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000
Since the Universe is 3rd dimension, one would suspect that where pi digits are there first three digits in a row of 000, that such would be the borderline at infinity.
Now, for physics, that infinity is 1*10^604 for large and 1*10^-604 for the small, makes perfect sense, since in physics, it is extremely, extremely difficult to find anything above 10^200 or smaller than 10^-200, to give the reader a sense of proportion.
The Existence quantifier comes from math in the derivative, the dy/dx of the function graph. For as the function graph is split up into small rectangular cells. And the calculus is a motion function, where the motion function starts at the origin (0,0) in 2D, and moves to cover all the points on the x-axis. As the motion goes in the decimal 10 Grid from 0 to 0.1, to 0.2, to 0.3 all the way up to 9.9 then 10. The motion function pairs a unique number from the y-axis to the x-axis number. For example the identity function of Y--> x is seen as (0,0), (.1,.1), (.2,.2), (.3,.3), (.4,.4)...(9.8,9.8), (9.9,9.9),(10.0,10.0). This motion goes from one cell to the next cell with its x number pairing up with a y value number.
We can say that the function causes the Existence of a y-value. And this derivative is defined as dy/dx, a division in math. So Existence is related to division, is related to derivative of calculus. Is related to If-->Then of Logic connector.
I start the 6 connectors of Logic with the Existential quantifier, and end the 6 with the Universal quantifier. Even though mathematics starts with addition. Logic is different from math for it is "ideas" that are the subject matter, not numbers- quantity, size or geometry shape.
If something does not exist, sort of pointless to be talking about it. And existence is given through science research, experiment, and observation. Science tells Logic what exists and does not exist.
Law of Existential quantifier: Existence is determined by the science of that particular subject matter in question. And no statement or argument in Logic can have a contradiction where A exists and A does not exist. Logic stops and grinds to a halt whenever a contradiction arises. And it must be sorted out by science before Logic can resume.
Examples.
Does the muon exist? Well we go to physics and look at the experiments that prove the muon a 105MeV elementary particle exists.
Does a canid (dog) exist that climbs trees? Well we go to the biology science of animals and find out that of the canids, the gray fox and the raccoon dog climb trees. So, yes, some canids exist that climb trees.
Physics determines existence of some rest-mass or energy. Ideas themselves are a form of energy, of electromagnetic spectrum light waves. A Light Wave exists and contains ideas for we simply turn on our cell phone and it is light-waves telling us ideas in words or in images.
But in physics there is only truth and nonsense, only a positive number from 0 to infinity for truth, and nonsense is all 0 value, like in Absolute Kelvin 0 temperature. Falsity is not a negative number but 0 value, worthless idea.
Example one: Sightings of a Loch Ness monster as being a Brontosaurus dinosaur were posted on the Internet, saying that the dinosaur lived in water not on land.
Explanation: claims of existence can easily be made, but it is the work of Science to see if such claims are worthless chitter chatter and no truth value.
Example two: The binary star to our Sun is the cause of global warming and orbits Earth every 2 years.
Explanation: It is easy for the mind to conjure up images of worthless, 0 ideas, and just as easy for Science to step in and invalidate the 0 idea.
Remember, in science we do not have falsehood, we have only what exists and what is true according to laws of science.
Science Laws established by the Scientific Method are universal truths such as Faraday law, Coulomb law, Ampere law, New Ohm's law.
Words that denote the Existential quantifier are these commonly used words.
There exists...
There is at least one of....
For some....
Some....
Where in mathematics do we have the Existential quantifier that we find in Logic??? Where??? And strange and surprisingly we find it in the most important and advanced part of mathematics the Calculus. We find it in the Derivative of a function as the derivative in a cell, moves from point A to point B in the graph. The derivative causes the existence of point B as it moves from A to B.
Calculus has 2 operators, that of Derivative and Integral just as logic has Existential quantifier and Universal quantifier. The derivative is division of dy/dx. The Integral is area under function graph curve-straightline and is multiplication but also is the Universal quantifier which we will study later.
The proof of Fundamental Theorem of Calculus, perhaps the most important math proof of all because calculus is the most important math for physics. That proof starts with area rectangle where a side of the rectangle is carved out a right triangle and pivoted on a swivel up to become the calculus derivative.
Calculus 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 |
|___|
And that the hypotenuse of right triangle is now the derivative that reaches the next point of function graph B. While the original rectangle is the Integral as area under function graph curve-straightline.
Here, it is Calculus that implores us to make the Derivative be the first starting Simple Connector of Logic which is Existence quantifier.
Archimedes Plutonium Apr 16, 2025, 4:57:10 PM to Plutonium Atom Universe newsgroup.
So at the very outset of writing a Logic textbook, by a logical person, has its hurdles and stumbling blocks. Math is the language of Precision needed to do physics and engineering. Logic is the language of Correct Ideas, think straight and clear and the formation of new true ideas.
So I look at the very best of mathematics which is Calculus and it is integral and derivative. The derivative is division of dy/dx and spans a math cell going from coordinate point A to coordinate point B. The integral is multiplication of dy times dx for area under function graph curvestraightline. This tells me that derivative as dy/dx should start the first of the 6 simple Logic connectors because B exists due to A exists.
And the derivative defined as dy/dx we later will learn is the simple Logic operator of If-->Then for that is a division in arithmetic.
Slowly we begin to see that Existential quantifier is allied to If-->Then, and then Universal quantifier of integral as area under function graph is allied with Not-Equal connector which is multiplication of arithmetic. Physics has a term for this, calling it a quantum duality.
Alright, here in November 2025, I made a huge magnificent discovery in Logic. Immense and huge in importance.
So the truth table of AND is TTTF, yet Old Logic under Boole and Jevons said it was TFFF.
Is there any reasoning for TFFF, or is it just a dumb mistake?
Turns out there is a very excellent reason that Boole & Jevons thought it was TFFF.
Suppose we have the example of The Sun is a star AND the Sun is not a star.
Under AP, the AND truth table is TTTF and the above would be a true compound statement connected by AND, if not for the contradiction. That is likely the reason Boole & Jevons decided the truth table of AND had to be TFFF for they did not want to tackle a contradiction.
The statement of P AND Q as "The Sun is a star AND the Sun is not a star" is what is called a Contradiction in Logic and never allowed. All things stop and come to a grinding halt and only resumes, once the contradiction is sorted out-- Is the Sun a star?
So, I need to be sure to tack on the Existential quantifier Law and tack on the clause of a Contradiction is never allowed in Logic or in fact Science.
This would easily explain when Boole & Jevons in circa 1850s would deem the AND truth table as TFFF to avoid contradictions.
However, AP avoids contradictions by appending the Law of Existence quantifier with the statement that no contradictions are tolerated such as P AND not-P. Beware, a contradiction can occur in a long argument and does not have to be in a short two statements.
This then allows the AP AND to be TTTF.
Order is so so very important in Logic. We start Logic connectors with Existence quantifier and do not allow contradictions to exist in Logic. When we get to the AND connector, we are reassured that it is TTTF because contradictions are not allowed from the Existence quantifier.
Order is as important in logic as is truth value.
Alright, I had to go back and repair my Law of Existential quantifier to include a Contradiction circumstance.
It is safe to say that Logic connectors starts with Existence but that an argument that says P exists and P does not exist is a contradiction and that Logic comes to a squeaky screeching halt. Logic cannot go on with a contradiction and that contradiction must be solved before Logic resumes and continues. Here again, the appropriate and relevant science on the topic is brought onto the scene and correcting the logjam of a contradiction.
So the Existence quantifier not only tells what exists but can stop Logic itself in its tracks if P exists and P does not exist occurs anywhere in a long argument, syllogism or dialogue.
This is a big discovery for it very much tells us why Boole and Jevons in the 1850s thought AND had a truth table of TFFF when it really has a truth table of TTTF. They likely saw that P AND Q where P says There exists a Milky Way galaxy with Q saying that There does not exist a Milky Way galaxy and you connect them with AND is a contradiction. So that Boole and Jevons thus decided the truth table of AND was TFFF to avoid all contradictions.
But in New Logic, we see that the concept of Contradiction springs forth at the beginning of Logic with the Existence quantifier and it is here, at the beginning of Logic that we sanitize out the Contradiction by embedding the Contradiction within the Law of the Existence quantifier. Thus, leaving alone the AND connector should P and Not-P attempt to enter the picture. Should P and Not-P attempt an entry in a logic argument, it is dismissed by the Existence quantifier Law.
Archimedes Plutonium
Jan 6, 2026, 4:46:50 AM (11 days ago) Jan 6
to Plutonium Atom Universe
13) 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 about nonexistence objects, and also Not Exists for contradictions stop all logic. So that answers the question of Not-Equal versus Equal-Not.
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".
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.
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 not F = T
F not T = T
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 x 1 = 1
1 x 1 = 1
0 x 0 = 0
0 x 0 = 0
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.
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 here-with avoid the concept of equivalence.
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 have 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, 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. 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
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 and Universal quantifiers have 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 law that defines them.
This is important, for we define Logic connectors by a Law.
------------------------------------------------------------------
In New Logic we define all 6 connectors by a Law governing the connectors. The same as in physics where the essential ideas and truths of physics are given in a "physical law" such as Coulomb law, Faraday law, Ampere law, New Ohm's law.
Truth-tables do not define a logic connector, and this avoids the AND truth table seemingly to have a contradiction of "True AND False being True". This appears to be a contradiction, but since AND is defined as a Law, we avoid the seemingly contradiction.
For __Existential quantifier that law__ of defining was this--- look in the most relevant recent science pertaining to the existence of something and see if the object exists in that science, plus, no logic argument can have a contradiction such as A exists and A does not exist. If a contradiction arises in Logic, all must come to a halt and consult the relevant science to overcome the contradiction.
For the definition of __Not-Equal as a universal law__ we say this. Not-Equal is equality of identical sameness and the Not is when there is no sameness. 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 in 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 there was obfuscation surrounding the Not connector and the philosophical idea that the negation of a true statement can have multiple of even an infinity of Not ideas.
While, in New Logic, there are only two values in truth tables-- 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 infinity at the borderline as 1*10^604 (see several of AP books that details the infinity borderline). While Old Logic truth values ranged from negative numbers to 0 to positive numbers and with no borderline at all.
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.
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.
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 may 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 remain to be of 0 or nonsense value.
Example: "Witches fly on brooms." The Not statement is "It is not the case that witches fly on brooms." Trouble: witches do not exist and so neither statement is true but 0-valued in New Logic.
Example: "Slant cut of right-circular cone is an ellipse." The Not statement is "It is not the case that the slant cut of right-circular cone is an ellipse." Explanation: the original statement is not true for the slant cut is an oval due to symmetry axis is 1 while slant cut of cylinder is indeed an ellipse. Yet the Not statement of original is true for the slant cut is an oval which is far different from ellipse.
Example: "The Real Numbers of Old Math form a continuum when graphed on the plane." The Not statement is "It is not the case that the Real Numbers of Old Math form a continuum when graphed on the plane." Trouble: Reals are fictional numbers for Physics is about quantum mechanics where no continuum exists and so the true numbers of mathematics are discrete numbers with holes in them, holes in between one number and the successor number. That makes even the second statement, the Not statement also be fictional and worth 0-value. Every statement on Reals of mathematics are 0 valued and nonsense statements.
14) AND connector.
So, we define and describe the connectors of Logic, not by their truth tables but as a Law of Logic, much like physics is a collection of Laws, the Faraday law, the Ampere law, the Coulomb law the New Ohm's law. We define AND connector not as a truth table of TTTF, but as a law that says in a string of ideas connected through AND, if one of the ideas is true, the entire string is true. Why define by laws 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 law of logic, we state in the law that AND cannot contain two contradictory statements and we have to stop the logic work and resolve the issue of contradiction. 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. So writing the definition of If-->Then as a law opens up and reveals much more about the connector then if we accepted the truth table for If-->Then as its definition.
Laws express more details of the connectors than just plain the truth table.
So we define connectors of true logic, not by a truth-table but by laws, same as in science, for science is defined by their universal laws, much like the laws of physics. For example the laws of electromagnetism-- Coulomb law, New Ohm's law, Faraday law, Ampere law.
The Existential quantifier is defined by law 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 law 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.
We now define the AND connector, not with truth-table but with a science law saying that AND connector is one of add or join two or more statements of ideas together. And the law that defines AND is that within a string of statements joined by AND that at __least one of the statements has a true value__ ascertained from science, and where all the other statements in the string can be 0-valued chitter-chatter, except a contradiction, but the overall chain of statements is true. If a contradiction occurs in a string of statements, then all stops and until the contradiction is excised out, does logic continue further.
That means a string of statements, p,q,r,s,t,u,v can be true if just one of the statements is true, and the rest be worthless nonsense, chitter-chatter and outright untrue. 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 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).
Mathematics is a language that makes precise the elements of numbers and of geometry shapes. Logic is a language that makes precise the elements of ideas and so it is not surprising that Logic is a larger set than is mathematics. We call a larger set containing a smaller set as a metalanguage. We cannot talk about math if confined to only math numbers and geometry shapes. We need a larger language to talk about math.
Logic is the language that makes precise the elements of statements of ideas, denoted by p, q, r, s, t, .... and how those statements, each a idea or thought relate to one another. Of course, mathematics would be a subset, all of mathematics inside of Logic. But towering over Logic is Physics. So physics is the metalanguage of Logic. This is because science is the arbiter of truth value. Is a statement true or a piece of junk of 0 or nonsense value.
Logic is the metalanguage over mathematics. Where Physics is the metalanguage over Logic.
Let us look at some simple connectors of Logic in three different languages.
ENGLISH GERMAN FRENCH
--------------- -------------- --------------
And Und Et
Or Oder Ou
If-->Then Wenn--> Dann Si (no need of then)
Equal Gleich Egale
Not Nicht Pas
The no need of a "then" in if-->then, in French is curious.
Let me add a few more
Nothing Nichts Rien
Exist Existieren Exister
All Alle Tous
I used to think English was the most streamlined common language, but it appears that French is even more streamlined than English. By streamlined I mean express an idea in fewest letters used. Si is much more streamlined than is If-->Then.
As a homework assignment, have the student add three new columns of three languages of their own choosing, such as for example-- Latin, Italian, Spanish, Russian, Chinese, Japanese of their own choosing.
In the AND operator of Logic, if just one statement of many statements is true, then the entire string joined by AND is true.
Of course AND is Add in mathematics and we can verify that by plugging in numbers to the truth table replacing the T with 1 and the F with 0.
Some examples using ideas p, q, r, s, t.
1) Hydrogen is element 1, and helium is element 2 and lithium is element 3 and beryllium is element 4, and boron is element 5.
This is an example of five statements of ideas connected by AND. In this case all 5 statements p,q,r,s,t are true and so the entire string is true.
2) Another example is this "Hydrogen is element 2, and Helium is element 3, and Lithium is element 4, and beryllium is element 1, and boron is element 5." Well, four of the five statements of p,q,r,s,t are false, but one of them is true in boron is element 5 with 5 protons. In Old Logic they would say that the entire chain of statements is false. In New Logic, because just one of the statements is true, warrants the entire chain of statements is true.
Homework assignment: each student make up two examples of where all the statements of p,q,r,s,t are true and then another where only one of the p,q,r,s,t are true. And in class tomorrow we have every student read his/her example if time permits, of where one true statement in a chain of statements.
Now, what Boole and Jevons failed to do was a very simple exercise that would have guided them to the correct AND truth table. Instead of T for true, and F for false, let us replace T with 1 and F for 0 in math. It is easy to see that 0 as "nothing" can represent "false". Plus where 1 or 2 can represent "true".
The same AND truth table only with numbers is this.
AND truth table
p q p AND q
1 & 1 = 2
1 & 0 = 1
0 & 1 = 1
0 & 0 = 0
Now, clearly we see with the help of mathematics, that the AND truth table is Addition in mathematics.
15) 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 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.
New Logic OR (exclusive)
p q p or q
____________
T T F
T F T
F T T
F F F
Math validation of correctnessT F T
F T T
F F F
p q p or q
____________
1 1 0
1 0 1
0 1 1
0 0 0
So we have 4 possibilities. 1 0 1
0 1 1
0 0 0
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 Law of OR as connector, the Law 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 0-1 = 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 Law 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 as a Law 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 laws, like the written laws 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 F T
F T T
F F F
So, OR cannot be defined from truth table but must be defined by a statement summary, just like defining the Faraday law 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.T F T
F T T
F F F
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 Removal.
AND connector in previous chapter is addition and joining together of ideas, while OR should be the reverse of joining together but removing.
Math validation of correctness
p q p or q
____________
1 1 0 so in this row we can see 1 - 1 =0
1 0 1 in this row we see 1-0 =1
0 1 1 in this row we can say Remove 0 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 Law of OR as connector, the Law 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 0-1 = 1 is not allowed in arithmetic by the axiom in math, 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 Law that states the correct definition of any of the Logic connectors.
Let me give an example of OR connector of Logic.
Example: Tomorrow I will eat spaghetti for supper, or tomorrow I will eat a hamburger for supper. The "p" is "Tomorrow I will eat spaghetti for supper" with the "q" is "tomorrow I will eat a hamburger for supper".
Analysis: One of the two statements is true and we subtract or remove the false one.
Another example: Either I slept for more than 10 hours, or I slept for less than 10 hours yesterday. The "p" is "I slept for more than 10 hours yesterday" with the "q" is " I slept for less than 10 hours yesterday".
Can we see that OR is subtraction, that we remove one of the statements?
OR principle is remove one of two statements P, Q
OR principle you cannot remove more than what exists in P, Q
P = there exists 3
Q = there exists 8
P OR Q is that of There exists 3 OR there exists 8. If we remove 3 there remains 8. If we remove 8 there remains 3.
However, we can also get out of this 8 subtract (remove) 3 and there exists 5 which remains in P OR Q. But we cannot subtract 8 from 3 to get a negative 5 for negative numbers do not exist due to principle that you cannot remove more than what is available to remove. Regardless of a "time factor consideration".
Example using physics.
P = There exists 2 hydrogen atoms
Q = There exists 10 hydrogen atoms
P AND Q is that of "There exists 2 hydrogen atoms AND there exists 10 hydrogen atoms". That would be a total of 12 hydrogen atoms.
P OR Q is that of "There exists 2 hydrogen atoms OR there exists 10 hydrogen atoms". That would end up being either 2 hydrogen atoms exist if we remove 10 such, or, 10 hydrogen atoms exist if we remove 2 such, or, 8 hydrogen atoms exist if we subtract 2 from 10.
For homework: the student writes two examples to be discussed in classroom using the OR connector. Try to make the examples be of some science content.
Laws so far are these.
Law of Existential quantifier: There exists something comes from the best available science on the subject topic. Existential quantifier comes from math derivative of calculus as dy/dx and also is coupled to If-->Then as division. And in the Exist quantifier we can never have A exists AND A does not exist for a contradiction causes all of logic to come to a screeching halt and call in the sciences to overcome the contradiction.
Law of Not-Equal: Not is a reversal of a given statement while equality is identical sameness of two statements. Not-Equal comes from multiplication in arithmetic and is coupled with Universal quantifier as the integral of calculus.
Law of AND: Joins together several statements p,q,r,s, etc of Logic and is a collective true statement provided at least one of the statements p,q,r,s, etc is true, based on science. And the truth comes from the pertinent science surrounding the statements. AND comes from addition in arithmetic. However, no AND string of statements can have a contradiction. If a contradiction occurs in a logic argument, all things grind to a halt and science must straighten out the contradiction before the argument can resume.
Law of OR: Removes or discards ideas represented by p,q,r,s, etc. OR is the opposite of AND which joins together statements, while OR removes or subtracts statements. OR comes from subtraction in arithmetic.
More precisely, OR, has four possible feats given two statements P, Q.
1) can remove P altogether leaving Q
2) can remove Q altogether leaving P
3) can subtract P from Q if Q is larger
4) can subtract Q from P if P is larger
Example: P = 10, Q = 15. P OR Q is 10 OR 15. In this case we can have the answer be 10 remove 15, or, 15 after removing 10, or, 15 subtract 10 leaving behind 5. There is an algebra axiom in math that says you cannot subtract more that what is available to subtract, in other words, negative numbers do not exist. So we cannot subtract 15 from 10.
OR in logic is remove and is the math arithmetic of subtraction. While AND was joining of statements, addition, while OR is the removal of statements.
In the English language, OR is often replaced by "either..or". Sometimes "alternatively" is used as a replacement.
The mindless mistakes of Old Logic with their Either....or...or.... both, which is a contradiction in terms for it combines OR with AND (when we say "both").
-------------------------------------------------------------------
I say no consistency because Either..or..or..both is the union of both AND with OR. In math arithmetic this is like saying -- Add along with Subtract.
I am going to scrutinize this mistake of the foolish "Either..or..or..both" which is contradiction in terms, on the face of it, for it is asking to combine AND with OR simultaneously and even in that hypocrisy the truth table of either..or..or..both would be TTTT and not TTTF for when the last row of p, q both being false, would make it yield a T value. So they even got it wrong in the error itself-- a double error -- one might say.
But the reason this deserves a full attention for discussion is that modern day computers are programmed with the logic idiocy of OR being addition when anyone with 1/2 of a marble of intelligence knows that AND is addition, not OR.
The exclusive OR of Old Logic was the correct OR, and OR should have one representative connector, not two of them.
The inclusive OR of Old Logic was-- anti-logical, illogical. And Boole, Jevons mixed up AND with exclusive OR. They ended up having AND as subtraction with OR as addition, as used in modern day computers, are programmed with the Boole and Jevons mistake as seen by a post in sci. math, where Franz is explaining how all modern computers are running on a fake AND and a fake OR.
On Saturday, June 8, 2019 at 3:05:40 PM UTC-5, Me (Franz) wrote:
> On Saturday, June 8, 2019 at 12:02:25 AM UTC+2, Archimedes Plutonium wrote:
>
> > 1) 10 OR 4 = 14
>
> Right! Python:
>
> def OR(x, y):
> return operator.or_(x, y)
>
> print(OR(10, 4))
>
> ==> 14
>
> > 10 AND 4 = 14
>
> Nope. Python:
>
> def AND(x, y):
> return operator.and_(x, y)
>
> print(AND(10, 4))
>
> ==> 0
>
Before I leave the discussion of OR connector, the OR connector serves one extremely vital function for Physics and other sciences in what is called "deciding experiments". When a science has two competing theories that covers the same phenomenon, then scientists formulate a "deciding experiment" to remove one of the competing theories. At this very moment in December of 2025, I am exploring what the true Light-photon geometry is. Not as a particle but as the dual of a particle. Old Physics reckoned Light was both a Light Wave and a particle called a photon. AP, on the other hand says waves are fictional for Light and that it should be a Light-Wire, not a Light-wave. The Old Physics geometry of the Light wave is looking like this up and down sinusoid wave ^v^v^v^v as a ray with a front point tip and an a tail. Of course, Old Physics had their Light wave be transverse, and AP has a transverse component. While AP's Light-wire looks like this in geometry, of a closed loop circuit pencil ellipse.
LIGHT AS a WIRE, ___not wave___ looks like this.
- - - - - - - - - - - - - - - - - -
/ front of wire \ back of wire--- it is a pencil ellipse that contains a-lot of data
\- - - - - - - - - - - - - - - - - - -/
And then we augment those holes by placing a B field ring around each hole.
- | - | - | - |
Both the E-field can vary in size and the B-field can vary in size
| B-field
__ | _______| __ | _ E-field
| |
The variations allow for different sounds and different pictures in TV reception.
Now, in order to prove one or the other is true and correct, experimental physicists set up what is called a Deciding Experiment, and the result of that experiment should remove either Old Physics Light-wave, or remove AP's Light-wire.
But I suspect that we already have a Deciding Experiment that was done many times in the past and is notoriously called the Double Slit Experiment. The results of the Double Slit Experiment can all be resolved if you think of Light as a closed loop circuit instead of a ray with front tip end and tail.
For in the Double Slit, at that screen in back the Light comes in as particles but as it enters the slits it comes in as wires that interfere with one another in an interference pattern.
The "Deciding Experiments" of science is a fine example of the OR connector of Logic.
16) If-->Then connector.
First a bit of a review before we tackle the If-->Then connector for it is a difficult concept for it basically is the structure of an argument itself. Remember Aristotle's argument "All men are mortal. Socrates is a man. Therefore Socrates is mortal." Can be written as "If you are a man, then you are mortal. Socrates is a man, therefore he is mortal".
Let us have a review before we tackle the difficult concept If-->Then. Difficult because it has a truth table with T for true and F for false but also has a new parameter of probability of U, for unknown, for undecided, for undefined. Remember, Logic needs to allow for math to have division by 0 be undefined.
Archimedes Plutonium Apr 16, 2025, 1:20:49 AM to Plutonium Atom Universe newsgroup.
It is very easy to see in the language of Logic that AND would be Add in the language of Math. Furthermore that Subtraction would be OR, where you take one or the other, or subtract one from the other. That division would be If-->Then, the consequences of "If" becoming a "Then". This contrast is even more sharply defined by the calculus derivative where a division dy/dx starts with a If as a x axis component, that must land on a unique y axis component, giving rise to the idea of x moves into becoming y.
But let us review again the simple four connectors of Not-Equal, AND, OR, If-->Then. Not-Equal is composed of two binary operators of "equal" as this.
T = T
F = F
And for "not" as this.
T not F
F not T
The AND, OR, If--> Then come from quaternary truth tables.
A quaternary truth table is an arrangement of 4 rows where all possible truth values for p and q exist. You have a TT, a TF, a FT and a FF. All possible truth values for 2 variables.
p q
------------
T T
T F
F T
F F
Notice the Quaternary truth table allows for All possible outcomes of truth or falsity in the set-up of two statements (two ideas, two variables) p and q.
That all possible outcomes are covered in a quaternary arrangement of 2 variables.
T -- T
T -- F
F -- T
F -- F
Notice one column is T, T, F, F and the other column is T, F, T, F to achieve every possibility.
Computers are based on binary inputs of 1 or 0, which represent true or false, computer gates (diodes or transistor) open or closed translates as True, or False. Two choices and that is why the Logic connectors are the software built into computers to do arithmetic add, subtract, multiply, divide.
Math is a language of precision for Physics. Logic is a language of correctness of ideas and the order sequence of ideas.
Math simple 4 operators start with Addition. But should Logic connectors start with what can be seen as Existence quantifier and multiplication as Not-Equal??? Of course, in math we define equality before we do add, subtract, multiply, divide. But here in the language of logic, equality with not, are one of the 4 simple connectors.
Not-Equal truth table:
p q
T = T = T
T = not F = T
F = not T = T
F = F = T
Suppose we substitute numbers for T and F to see if we get multiplication out of the Logic connector that is Not-Equal
p q
1 x 1 = 1
1 x 1 = 1
0 x 0 = 0
0 x 0 = 0
Sure enough that is multiplication.
Yes, remember that two of those are binary -- two for equal, and then, two for not. All the other three truth tables are quaternary, 4 rows.
So, what is the reasoning that Logic connectors start with Existence then tacks on Not-Equal?? The reasoning is that Existence starts things off, for we only have interest in what exists, not that of fake imagination and stupefying chitter-chatter, and we need Not in order to say --- either it exists or not exists to ward off contradictions. Math arithmetic is different. It starts with addition as in mathematical induction, start with 0 and 1, add 1 to 1 and we get 2, add 1 to 2 and we get 3, etc and then turns to its opposite of subtraction. Multiplication is rapid addition, while division is rapid subtraction.
The question of Existence for math numbers is a philosophical question. The question of existence for geometry objects is less philosophical. We can see a triangle shape in a building or a rectangle house. We do not see a number 6 in plain sight or number 137 walking down the street. Logic calls these as existing but existing as ___abstractions___. Numbers are abstractions and by abstractions I define that as an idea having multiple uses. There were 137 wildebeests on the African plain and the inverse fine structure constant of physics is 137 and the 231Pu has 137 neutrons.
Webster's New Collegiate Dictionary, 2002, defines "abstraction" as -- formation of an idea, as of the qualities or properties of a thing, by mental separation from particular instances or material objects.
Cambridge dictionary defines "abstraction" -- the quality of existing as or representing an idea, a feeling, etc. and not a material object, or something that has this reality.
University of Chicago says this of "abstraction" Abstraction refers to thought expressed without a concrete image. Frowned upon as the language of philosophers..
Britannica on "abstraction" -- the cognitive process of isolating, or abstracting, a common feature or relationship observed in a number of things, or the product of such a process.
AP himself has a go of a definition of "abstraction"-- all of mathematics itself is an abstraction, for numbers or figures of geometry have multiple uses. A rectangle house, a rectangle box, a rectangle sheet of paper, a rectangle wood block. An abstraction can be an idea in a statement of logic. Many ideas in science are abstractions.
Examples: When a polynomial is recognized as the only valid function in calculus, then calculus is reduced to ultra-simplicity as add or subtract 1 from exponent for integral and derivative respectively.
Slant cut of cylinder is ellipse, while slant cut of cone is oval, not ellipse.
No saber toothed tiger existed for that would defy Darwin Evolution theory that evolution does not evolve something that gets in the way of a living organism living out their life. No, these are walrus tusks glued on to cat jaws by money grub museums.
Time now to define and discuss the complicated If-->Then. I say complicated because its truth table involves something other than just T for true and F for false. It involves a new parameter of U for unknown.
If--> Then connector
-------------
We often see the If --> Then by using implies. If P then Q. P implies Q. Sometimes we see it with "because". Q because of P. The one I like the most is "moves into". P moves into Q. I like this because it is the math calculus derivative as discussed before where the function graph moves along the x-axis that yields a y-axis coordinate point, and the derivative is also division as dy/dx.
This connector If--> Then caused huge huge problems in logic, all because no-one in Old Logic had logical brains to put together Logic correctly.
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
In the English language, the If-->Then connector is replaced by different expressions such as "suppose-->then", "provided-->that", "implies", "given --> that", "conditional" and my favorite is "moves into".
So I start Logic connectors of its 6 simple connectors with that of Existential quantifier, then I introduce Not-Equal, then move to AND, then move to the reverse of AND in that of OR, then move to If-->Then.
And this pattern is also reflected in the fact of decreasing True values.
Not-Equal has 4 True values.
AND has 3 True values.
OR has 2 True values.
If-->Then has 1 True value.
The If-->Then is division of mathematics, and it is well known that all of mathematics comes tumbling falling down should there be a division by 0 such as 1/0 or 2/0 or 0/0 and that division by zero is undefined. Should division by 0 be possible, all of math is ruined for then no unique answers to any arithmetic of multiplication or division. The 2/0 can equal anything. The division by zero is the weak point of mathematics, just as the Contradiction of A exists and A does not exist is the weak point of Logic. So, here in Logic, the truth-table of If-->Then must provide for a row in which the truth value is undefined, unknown.
New Logic for If-->Then
p q if p then q
____________
T T T
T F F
F T U for unknown, uncertain, undecided
F F U for unknown, uncertain, undecided
Just plain looking at that table we see two rows where we have a U for unknown, undefined. And knowing that math is a subset of Logic, there must be a U for undefined in one of those rows to treat for division by 0 in math. In fact two rows are U for it makes common sense that when we start an implication with a falsehood (the last two rows) would lead to unknowns, undefined results. This is plain common-sense. The If F, then T yields T is horrible nonsense. And then If F then F somehow magically yields a T is more nonsense, piled higher and deeper.
Let me make up statements p, q, r to test each row.
If carbon is the 6th element, then it has 6 protons. T-->T yields T
If carbon is the 6th element, then it has 7 protons. T-->F yields F
If carbon is the 5th element, then it has 6 protons. F-->T yields nonsense
If carbon is the 5th element, then it has 7 protons. F-->F yields nonsense
Let me display the New Logic truth table of If--> Then and validate it with math numbers showing that If-->Then is division of math.
Let me validate that is the math operator division. I replace T with 1 and F with 0.
p q p divide into q
____________
1 divide into 1 1
1 divide into 0 0
0 divide into 1 U for unknown, uncertain, undecided and undefined
0 divide into 0 U for unknown, uncertain, undecided and undefined
Yes, so in summary so far we have Not-Equal as multiplication, AND as add, OR as subtract, and If-->Then as divide. Of course the Existential and Universal quantifiers have no truth tables for they are laws. And we should also define the 4 other connectors by Laws, just as we define science by Laws of Science.
When figuring out the truth table for If-->Then, what should guide Logic for the need of a table for If-->Then that yields a unknown or undefined for division by 0. We cannot have an impoverished Logic where it is less than mathematics for covering division by 0.
Let me note also the huge importance of the If-->Then connector for its truth table not only impacts division by 0 as unknown, but also an entire class of proving methods of mathematics called the Reductio ad Absurdum proof method, some call it the Indirect proof method. This is where you suppose the contrary of what you want to prove and see if a contradiction occurs in the steps of the proof. If a contradiction occurs, you go back and reverse the supposition--- saying the statement to be proved has to be true because of the contradiction. This method of proof, --so called proof-- is extensively used in Old Math, and perhaps over half of all math proofs use the Reductio ad Absurdum. Trouble is, it is not a valid proof method because of the If -->Then truth table where it has U in the last two rows. Where you suppose the statement to be proved as false, looking for a contradiction. No, that is an invalid proof method because the conclusion does not yield a T true, but instead yields a U for unknown. This is a probability conclusion and math rests on certainty, not probability. Yes, I would say slightly over 1/2 of all math proofs are reductio ad absurdum and all those have to be thrown out and thrown on the junk-pile of shame.
Examples of If-->Then.
Example: If we thrust a bar magnet through a copper wire coil attached to a galvanometer, then electric current is produced in that coil.
The "p" is "we thrust a bar magnet through a copper wire coil attached to a galvanometer" and the "q" is "electric current is produced in that coil". Logic calls the If--> Then the material conditional. Should p happen, then q must follow.
Another example: If I go swimming, then I will get wet. Here the "p" is "If I go swimming" where "q" is "I will get wet". Makes sense that since you are swimming, you are in water and will get wet. In the material conditional when p and q are true, necessitates that the outcome is true.
Another example: If I am dead, then my heart will have stopped beating. Here the "p" is "I am dead" where the "q" is "my heart will have stopped beating". I like to look on the If--> Then as a movement. That p moves into q. For it has only one T truth value when both p and q are true. But if q is false, then the entire result is false. Let me give an example of that.
An example of a false If-->Then: If I am alive, then my heart has stopped beating. Here the "p" is "I am alive" and the "q" is "my heart has stopped beating". Can we see that the p does not allow for the q and thus the result is false. The p does not move into the q.
Homework: the student makes up four examples of If--> Then and describes the resulting truth value. To be discussed in class tomorrow if time permits.
Laws of the 5 connectors.
----------------------------------
Law of Existential quantifier: There exists something is formed by the best available science on the subject topic. This comes from math derivative of calculus as dy/dx and also is coupled to If-->Then as division. And in the Exist quantifier we can never have "A exists AND A does not exist" for a contradiction causes all of logic to come to a screeching halt and has to call in the sciences to overcome the contradiction before continuing further.
Law of Not-Equal: Not is a reversal of a given statement while equality is identical sameness of two statements. Now the words in the two statements can be different but the idea in both statements is the same. Not-Equal comes from multiplication in arithmetic and is coupled with Universal quantifier as the integral of calculus.
Law of AND: Joins together several statements p,q,r,s, etc of Logic and is a collective true statement provided at least one of the statements p,q,r,s, etc is true. And the truth comes from the pertinent science surrounding the statements. AND comes from addition in arithmetic.
Law of OR: Removes or discards ideas or subtracts one idea from another idea represented by p,q,r,s, etc. OR is the opposite of AND that joins together statements. OR removes something, be it a statement or the subtraction of one statement with another statement.
Law of If-->Then: I like to think of If--> Then from calculus graph where we slowly move down the x-axis and graph the next coordinate point. Given statements P and Q that P moves into Q. The Law of If-->Then is both P and Q have to be true, by science, to form the conclusion of Q starting from P. And this ties in earlier with the idea that we discard all the F rows and U rows and have the T row define the connector.
Before I leave If-->Then connector of logic, I should mention the fact that If-->Then is not only division operator of mathematics but also is the derivative in differentiation of calculus of the dy/dx. And that Not-Equal is not only multiplication of math but is the integral in calculus where we have area under the function graph as dy times dx rectangle.
Also, in Logic, the If-->Then is Modus Ponens, the Aristotle syllogism of this.
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Here the "p" is true "All men are mortal" with "q" as true, "Socrates is a man" begot from science of medical science and sociology history. And the result or outcome is true "Socrates is mortal". We see p and q moving into a "if p then q" result or outcome.
When you have p-->q and q-->p, then you have p=q.
-----------------------------------------------------------------------
Sometimes you can get a If p -->then q where the If q --> then p is also true. Example: If there is fire, then there is smoke. Reversing that to If q then p we have: If there is smoke, then there is fire. Here we have the beginning of the idea that equality is attained when If P--> then Q , but also, If Q --> then P, means P=Q. I say beginning because some will argue that smoke does not equal fire.
Example of If--> Then leads to equality.
If Americans win the Revolutionary War of 1776 between Britain, then the Americans are free and independent of Britain.
If the Americans are free and independent of Britain, then the Americans won the Revolutionary War of 1776.
Thus we can say "Americans win the Revolutionary War of 1776 between Britain = Americans are free and independent of Britain.
Meaning: when P moves into Q and also that Q moves into P means P = Q.
Another example.
If the speed of light is a maximum speed at 3.16*10^8 meters/second, then no speed is faster than light speed.
If no speed is faster than light speed, then 3.16*10^8 meters/second is a maximum speed.
Meaning: when P moves into Q and also that Q moves into P means P = Q.
As I said before, the If-->Then is viewed as the Material Conditional. Viewed as the Implies, as p implies q. Viewed as division in math. Viewed as the derivative of motion in calculus as dy/dx, as a velocity of motion. And why I like to often view If-->Then as the "motion into", the being to becoming.
Logic is the science of making ideas as clear, and correct, and straight as possible.
Archimedes Plutonium Apr 17, 2025, 12:42:49 AM to Plutonium Atom Universe newsgroup.
So this problem of where to start with Logic of its 6 connectors is now resolved. With Math we start with Add. We would have a difficult time of starting with multiplication in math to youngsters, even adults. But with Logic we are forced to start with Existential quantifier then Not-Equal for that is multiplication and we need Equal signs for AND, OR, IF-->Then.
Math is the Language of Precision numbers quantity and geometry figures for Physics, while Logic is the Language of Correctness of Ideas as statements p,q,r,s, etc, for Physics.
We do physics by using mathematics for precise measure and observation. And we do physics ideas by employing Logic to make our ideas clear and straight and correct.
Math starts with Add, for we simply see mathematical induction yields the counting-numbers 1,2,3,4,... while Logic connectors start with Existence and Multiply and that is fitting, for starting with Add we start near zero. Yet starting with Multiply we start with a whole picture for multiplication in 10 Grid is the largest multiplication is 10 x 10 =100. A number furthest from 0 in the 10 Grid for 100 is in the next grid of 100 Grid.
Enlarging this idea that the 4 connectors of Logic keep only the True rows and discard the False rows.
------------------------------------------------------------------
In the Not-Equal connector, all 4 rows are true so there is nothing to discard.
In the AND connector, 3 rows are true and so we keep them but the last row is false and discard it.
In the OR connector the 2 middle rows are true and the first and last rows are false so we discard them.
In the If-->Then connector only the first row is True and so we discard the last 3 rows.
Now why is this important?? Because in Science, everything is about the Truth of Reality of Existence and of Universal. Falsehoods are treated as nonsense of 0 value, as a waste of time.
And this idea that only truth is used and manipulated in Logic streamlines Logic. We do not want to waste time on junk and garbage ideas.
The AND connector allows for arguments to fill up on nonsense and junk, provided there is at least one statement true in a chain of statements. The OR connector discards via subtraction the nonsense or junk statement. Finally, the If-->Then in its Law definition clearly points out that in Science and Logic, we focus only on True Statements, and see false statements as nonsense and background noise.
So when we make a Argument of Logic, whether the simple syllogism of 2 lines with a conclusion or the more robust arguments of more than 2 lines, that every line should have a True value, considering that AND may have nonsense statements also.
Every If --> Then statement has a true P and a true Q.
Every Not-Equal argument has a True P with Q where the "not" makes it so.
Every AND argument has at least 1 true value statement in a premiss.
Every OR argument ends up true for we remove a false statement.
If we count up the number of true values in Old Logic 6 connectors we have this tally.
In AP's New True Logic that tally would be this.
Equal-Not has 4 true premisses
AND has 3 true premisses
OR has 2 (for exclusive is the only OR) true premisses
If-->Then has 1 true premiss
Notice that in New Logic each connector ___is in fact a Unique and thus is Necessary connector___.
You see, when your connectors are __not unique__. Then you can find Rules of Inference of equality and begin to shave off connectors because only 2 connectors will get you all you want. But in New Logic, because all 4 of the simple connectors are unique, that no two can be equal by manipulation.
In New True Logic, each of the 4 connectors is unique in True values, one has 4, another 3, another 2 and the last one being If-->Then has 1, so that all 4 connectors are Necessary and cannot be substituted out, and thrown away.
So in True Logic there are 4 simple connectors of AND, OR, Equal-Not, and If-->Then, and there are 2 quantifiers of Existence and All.
How many simple operators exist in Mathematics, a subset of Logic??
In Math we have Add, Subtract, Multiply, Divide, and we could say we have Derivative and Integral for 6 operators.
We can link up Add to AND; Subtract to OR: Multiply to Not-Equal; Divide to If-->Then; Derivative to "there exists"; Integral to All.
Logic pretty much follows mathematics as languages of precision --- for logic it is precision ideas, and for math it is precision numbers and geometry. Logic deals with statements of language as packets of ideas. Math deals with numbers for algebra and lines and figures for geometry. There is a close relationship between the two subjects, so much so that it is wise to compare them. All along in this book I compared the two.
Since math has 4 operators as simple operators, for we could tack-on the derivative and integral to make 6 operators, we focus our attention on the 4 simple operators-- Add, Subtract, Multiply, Divide.
Since math has the 4 simple operators, it is reasonable to claim Logic has 4 simple connectors that are similar. And for Logic those 4 simple connectors are AND, OR, Not-Equal, If-->Then.
Now Math is a subset of Logic, but every science is a subset of Physics. This means that all the ideas found in mathematics have an analog or similarity with that found in Logic.
Examples: Addition in math is found in the Logic connector of AND. Many even say 2 and 3 is 5. Subtraction in math is found to be OR in logic where you have "It was raining today or it was sunny today" whichever is true you remove (subtract) the other. Multiplication in math is found to be Equal-Not combined for its truth table becomes this.
The only truth table in all of Logic 4 simple connectors with a true value for all possibilities. And that is what multiplication such as factorial in math is like. For 5 factorial is 1x2x3x4x5 =120.
Division in math is where you divide something big down into smaller pieces and in Logic that connector becomes If--> Then with a truth table of only one true value when both P and Q statements are true.
17) The Universal quantifier connector.
The Universal quantifier invokes the image or quantity of "All" or of "Every". The universal quantifier is related to the integral of calculus as the area under the function graph, area of rectangles as cells, the dy multiply times the dx. Related to math as multiplication as the Not-Equal connector of Logic. Related to geometry as "all of space" such as volume.
However, and surprisingly, the Universal quantifier is related to the AND, or addition connector of Logic also. This is somewhat surprising as we asked of AND why it was not the first connector to study in Logic? Seeing that addition is AND where in arithmetic we first study add, then subtract then multiply then divide.
So how is the Universal quantifier related to AND? The counting numbers of arithmetic are begot from Mathematical Induction in that given 0 and 1, keep adding 1 and you get 2, add 1 and you get to 3, so on and so on which yields all the Counting Numbers out to infinity.
We can perceive infinity as being the Universal. And what is truly Universal are the Laws of Physics and Science such as the Universal law of gravity, or the law of Coulomb or Faraday or Ohm or Ampere. In biology, the law of DNA as genetics or Cell theory. Again, in physics the laws of thermodynamics or the laws of quantum mechanics. In Chemistry, the Law of the Periodic Table of Chemical Elements. In chemistry and physics the law of Atomic theory.
But how are these Universal Laws of Science established? Certainly we cannot travel out infinitely far and check up whether gravity is universal.
And in comes the Scientific Method that explains how laws of science are made Universal. The process is much the same as Mathematical Induction, only instead of numbers, adding one more to form the next number out to infinity, instead of numbers, we have Experiment Induction. Reread the Scientific Method chapter on the enumerated points to establish a law of science. The crucial part is to do an Experiment. Now if one person formulates a law with a math formula and does an experiment and shows the result matches the predictions, is not yet a law of science. We have to wait for others to read the experiment details and set-up the experiment in their lab. Repeat the experiment and if they get the same results, then we are closer to announcing that we have a Law of Science. If we wait a few years and thousands of people have performing the same experiment with the same end result, it is at this point we call our experiment a Universal law of science. There is a caveat to this, though. It could be that some future experiment on the law turns up some unknown data that calls the law into question as to its validity, or whether it needs a bit of tweaking in its formulation.
What I am trying to convey to the reader is that a Universal Law of Science is similar to the process of Mathematical Induction that has the numbers go to infinity, only we have experiments to perform, instead of adding 1 more to get the next number.
The Universal quantifier is especially important to science such as physics in that Laws of science are "universal laws". Where universal means there are no exceptions. Every mass is attracted to another mass by the formula of G(M_1*M_2)/d^2, with no exceptions. Every magnetic monopole obeys Coulomb law of K(q_1*q_2)/d^2, and never any exceptions. Laws of Physics are universal. Logic connectors starts with Existence quantifier then Not-Equal, and in between is AND, OR, If-->Then, ending with the Universal quantifier. All neat and in order of 6 connectors. Reflecting the fact that 6 operators are sufficient to describe the science of precision-- mathematics.
AP Principle to Form an Argument of Logic-- all the premisses must be true as checked by science to have an argument of logic.
The idea here is that we have seen plenty of truth-tables for the 4 connectors of Not-Equal, AND, OR, If-->Then and we see many false statements as if routine in living life that false statements are abundant and that we must navigate around them. Instead, in science especially, that false statements are seldom or rare to the discussion or argument. In fact, in every science argument I have ever seen in life, the advocates are attempting to use only True Statement Premisses, and eliminate all statements that are false, chitter-chatter, time wasting statements. They try to use only true statements in the argument at hand.
That idea is the gist of the AP Principle above-- in any argument, even a science argument, we strive to put only True statements in the ongoing argument.
So I was wondering if anyone else had this idea before me. The idea that a Logical Argument is where only True ideas are acceptable for the statements p,q,r,s,t,u etc???
I found this quote on Internet of Cambridge Dictionary of Philosophy, looking to see if anyone else had the idea that all premisses must be true as checked by science.
snipped
Basic concepts
Premises, conclusions, and truth
Premises and conclusions
Main articles: Premise and Logical consequence
Premises and conclusions are the basic parts of inferences or arguments and therefore play a central role in logic. In the case of a valid inference or a correct argument, the conclusion follows from the premises, or in other words, the premises support the conclusion. For instance, the premises "Mars is red" and "Mars is a planet" support the conclusion "Mars is a red planet". For most types of logic, it is accepted that premises and conclusions have to be truth-bearers. This means that they have a truth value: they are either true or false.
Now I am interested in following up on this reference to see if they are talking about AP's principle that all premisses in a Argument of Logic be true premisses as determined by the most recent science on the subject. This reference is Cambridge Dictionary of Philosophy with Honderich 2005, philosophical logic. Apparently the AP Principle that all premisses possess a true truth value before you can form a logical argument is not completely unknown.
Physics when it does Logic, uses positive numbers from 0 to the infinity borderline of where Light speed is a constant maximum. Physics has 0 be Absolute 0 Kelvin temperature and has infinity borderline of the speed of Light. Zero in physics would be nothing, no mass, no matter, no energy. Yet it takes infinite energy to get to Absolute 0 Kelvin.
Truth Tables in Logic were human mind table constructions from human behavior, but not as a science table.
For there is no concept of "falsehood" in physics. Physics is a construct of Universal Laws and of Existence of Matter and Energy.
So when Physics is asked to make out Truth Tables for Logic, its parameters for the table would not be True and False. Its parameters would be a positive number between 0 and the speed of Light, (or the infinity borderline) such as the rest mass of the proton or electron or neutron.
For Physics the truth table of AND is that of addition and has 3 of 4 rows. The truth table of IF-->Then is that of division and has 1 of 4 rows. The truth table of Equal-Not combined as one has 4 of 4 rows and is multiplication. The OR truth table has 2 of 4 rows and seen as subtraction, but there is a profound difficulty with OR. It has to be a choice truth table and thus when using True or False, that does not make a choice of something versus nothing.
So the Truth Tables of Logic need a vast amount of more work on them to get them to be scientific and useful.
What I suspect will happen, is that Truth Tables will end up being a mere test and check measure of a Logic Argument, and no more. Where the Connectors follow laws and principles.
AND Principle is add true ideas together.
OR Principle is remove (subtract) true ideas.
IF-->Then Principle is Move true ideas to a new true idea.
Equal-Not Principle is the full Space of Ideas possible.
The Old Logic truth tables were a hindrance to doing logic for that system saw everything as just black or white with no shades of one or another, an all-or-none-system. Yet Science is nowhere like an all or none system.
The Principle of Logic that all the premisses of a Argument need to be true premisses checked and passed by the hard sciences given approval of truth value is a Principle that topples all of Old Logic and how defunct is a system of saddling a connector with T or F.
The OR connector of Logic truth table with its "false values" wrecks logic.
OR connector of Old Logic
P Q P OR Q
T T F
T F T
F T T
F F F
Yes we see a "choice" then it is True. But the F for false is 0 in Physics and so a T or nothing is really not a choice at all.T F T
F T T
F F F
Physics would demand a truth table of OR be more looking like this where OR is subtract (remove) and those numbers correspond to MeV for proton, neutron, muon and magnetic monopole.
P Q P OR Q
105 945 840
945 840 105
0.5 0.5 0
A biology truth table of OR would start to look like this.
P Q P OR Q
7 wild dogs 11 hyenas 11 hyenas
313 wildebeest 12 lions 313 wildebeest
17 vultures 31 zebra 17 vultures
Old Logic was a primitive science almost useless and along comes the computer that needs software and needs to have addition as well as the arithmetic of subtraction, multiply and divide.
Is there a 7th Connector for Logic, but not necessarily a 7th operator of mathematics.
-------------------------------------------------------------------------------------------------------------
If 6 operators describe all of mathematics and math a subset of Logic, then 6 connectors, by logical reasoning is necessary but not sufficient to describe all arguments of ideas p,q,r,s,t, etc. There may well be a 7th connector of Logic, but that question is far beyond this textbook designed for 1st year of logic in college.
But now that I brought up the subject of whether there is a 7th connector of Logic for which mathematics has no 7th operator. I would speculate that Perpendicularity, of electric field versus magnetic field, and that quantum duality of electricity to magnetism duality, or that temperature is inverse to time forms a 7th connector in logic and a 7th operator in mathematics. I will revisit this idea in Advanced Logic, #368 book of science. This idea will be taken up and proved in the Advanced Logic textbook, proved that no 7th connector exists.
I need to check up on Quantum Duality as represented in mathematics.
For example in regular polyhedra we have the duality of cube with octahedron and then there is the duality of dodecahedron with icosahedron. The cube has 6 faces and 8 vertices while octahedron has 8 faces and 6 vertices. The dodecahedron has 12 faces and 20 vertices while the icosahedron has 20 faces and 12 vertices.
In Biology, we can say that male is a duality to female. And in DNA mitosis is a perpendicular sectioning versus a horizontal sectioning for meiosis.
In Mathematics calculus, the graph cannot have a perpendicular for that denies "uniqueness" for the function. So does that entail that Physics has the perpendicular in duality, and Logic has the perpendicular in duality--- such as sex, but that Mathematics in calculus is preempted from having the perpendicular in duality?
Here I need to inspect on whether the Old Physics Maxwell Equations delivered quantum duality from those equations in some form of mathematics. It is well known that the Maxwell Equations delivered the "closed loop circuit" for electricity and magnetism in the fact that they were equations of math with an inverse square law, which in geometry is a circle or ellipse.
But here the question is whether the Maxwell Equations delivered "perpendicular for duality"???
Quite ironic that Maxwell developed the Light-photon as a magnetic field component along with and simultaneously an electric field component perpendicular to the magnetic field. But do the math equations have perpendicularity embedded in the equations themselves?
When we look at the AP Equations of EM theory, electromagnetic laws, we ___cannot get____ perpendicularity out of that mathematics, even though we can get a closed loop circuit.
The 6 AP-Electromagnetic Equations and the 7 Structures (Laws) of Physics and all sciences
0) domain structure as Atomic Theory
1) Magnetic primal unit structure Magnetic Field B = kg /A*s^2
2) V = C*B*E New Ohm's structure, structure of electricity
3) V' = (C*B*E)' Capacitor-Transformer structure
4) (V/C*E)' = B' Ampere-Maxwell structure
5) (V/(B*E))' = C' Faraday structure
6) (V/(C*B))' = E' the new structure of Coulomb force with EM gravity force and DeBroglie pilot wave
The Product Rule and the Quotient Rule of differential equations allows us to see in those divisions the inverse square is a circular closed loop, but ___no perpendicular__ is forthcoming. No perpendicular to allow for duality such as the duality as seen in the regular-polyhedron.
Alright, I need to re-do the Faraday law experiment to answer fully this question on whether Logic through all the sciences especially up through Physics, but with mathematics deleted, has a Perpendicular, yet math does not because all calculus function graphs cannot be perpendicular to x-axis.
The concept I am pursuing here is that duality is perpendicularity.
I need to pull my Faraday Law apparatus out of storage. I remember that the bar magnet has to be perpendicular for maximum electric current produced. And when off by an angle, the electric current is less than maximum using the trigonometry of sine and cosine to figure out the electric current production.
Here we see that Mathematics is split up by Trigonometry as sine and cosine are duals, duality of one another, what sine value is, is the dual of the cosine value, much like physics particle wave duality.
If the experiment shows that I can thrust the bar magnet through copper coil at a 90 degree angle from maximum current production resulting in 0 current production, then I will have shown that Faraday law, Ampere law and Coulomb law have the Concept of Duality as Perpendicularity.
Then, that 0 electric current result would cause me to return to Mathematics, to say that the Perpendicular restriction in calculus is merely just a flip of the Graph. Say we had a function that was X --> 2, a perpendicular line at x=2 with all y-values on that perpendicular. Solution: take the inverse of that function to be Y--> 2, in other words switch the roles, switch the x-axis to be the y-axis as the function.
Time for me to get the Faraday law apparatus out of winter storage and see if a perpendicular thrust yields 0 electric current production.
Once I get out my Faraday law apparatus and if it confirms that I can thrust a bar magnet through the copper coil and yet, no electric current produced. Is proof that Physics has a Perpendicularity concept which is the same as Quantum Duality, particle to wave, or better yet, electricity to magnetism.
As for mathematics, that the perpendicular is not allowed in calculus, we simply switch the x-axis to being the y-axis and proceed from there.
No need of a 7th connector in Logic or a 7th operator in mathematics.
Alright, pulled out my Faraday Law apparatus of a microAmp 10^-6 Ampere galvanometer attached to copper coil and using a neodymium (rare earth element) bar magnet thrust the bar magnet perpendicular through the coil for a 500 microAmp reading of electric current.
Next I attached the bar magnet to a steel paper clip wire to thrust the bar magnet through the coil at a horizontal rather than perpendicular. The most reading was a 30 microAmp electric current.
Next I measured the perpendicular bar magnet on the coil hole without going inside the coil and at most it read 30 microAmp electric current and finally, a horizontal positioning of the bar magnet above the hole without actually going inside read 0 microAmp.
I am convinced that when the bar magnet is positioned horizontal to the coil, it has no electric current produced.
This informs me that the Faraday law, the Ampere law, and the Coulomb law have quantum duality by virtue of horizontal configuration of bar magnet versus perpendicular orientation. Duality such as particle to wave, or electricity to magnetism is perpendicular orientation.
Sex in biology is a duality, of a horizontal to perpendicular orientation, because mitosis is a perpendicular reconfiguration, while sex is a horizontal reconfiguration. This is the theme of my future #435 book of science.
Universal quantifier and Laws of Inference
-----------------------------------------------
The Universal quantifier is especially important to Physics for the Laws of Physics are universal laws and as such, the concept of universal quantifier has to come directly out of Physics.
Archimedes Plutonium Oct 18, 2025, 4:19:40 PM to Plutonium Atom Universe newsgroup.
It is around middle of October 2025, now, and just getting started on the Laws of Inference of Quantification-- existential and universal.
Boole & Jevons and their latter day followers messed up on all 4 of the Simple Connectors-- Equal-Not, AND, OR, If-->Then. Question is, now, did they mess up on the Existential and Universal quantifiers.
Copi (Logic, 1972, 4th ed.) and Thomason (Symbolic Logic, 1970) talk about Universal Instantiation UI, Universal Generalization UG, Existential Instantiation EI, Existential Generalization EG.
Let us examine if there are mistakes in those four.
Right off the starting line-- I detect problems with Universal Generalization. Is that not -- like Either..or..or..Both, a contradiction in terms??? When something is Universal, already, then how can it be further made into a Generalization???
Copi speaks of "calling an arbitrary member of a triangle, finding a property of that triangle, and then Generalizing to say that property exists in all triangles". My question for that is --- how do you know from the start, you have an arbitrary-something??? You may have picked a biased-something.
Example: All crows are black, the crow in the field is black, the crow in the tree is black. But then in a rare case an albino crow is born.
What I am going to do here is that Copi and Thomason list four Laws of Inference for the quantifiers. I call them Laws and not the silly Old Logic of "Rules of Inference". There is a huge difference in Physics between a "rule" and a "law".
They list these:
Universal Instantiation UI
Universal Generalization as UG
Existential Instantiation as EI
Existential Generalization as EG
I suspect only UI and EG are valid. I suspect UG is a huge error. And that EI is utterly redundant as saying x exists, therefore x exists.
What I am going to do to make my case, the case of AP, is transfer Quantification to that of Calculus of mathematics. I already found and exposed that the Existential Quantifier is the Derivative of calculus. And where the Universal Quantifier is the integral of calculus. We know for sure in mathematics that the integral is the reverse of derivative and the derivative is the reverse of integral which is the famous theorem of the Fundamental Theorem of Calculus. But I need in Logic what is the function graph???? You see, in the Fundamental Theorem of Calculus, derivative and integral are reversals to a ---- function graph----. An intermediary between derivative and integral.
AP in November 2025:: But is that true, is the function graph an intermediary between the derivative of the function and the integral of the function? Take for example in Calculus that Y = x^2 as function whose derivative is 2x and whose integral is (1/3)x^3. Do we really have three entities here?? Do we really have x^2, 2x, and (1/3)x^3???? I ask because the derivative in a cell goes from the coordinate point of the left wall in that cell to the next coordinate point on the right wall of that cell and that line drawn in the graph is the initial function graph itself. So in each cell, we have the derivative and the integral, but no need of the function graph itself. So maybe there are no three entities involved in calculus-- function graph, derivative, integral. Maybe instead there are just two entities involved in calculus-- derivative and integral. And that the function graph is what can be called the result of the inner workings of the derivative and integral.
No-one in Logic, before me, has looked for an Intermediary, between that of Universal quantifier and Existential quantifier.
My guess at this moment in time of what the intermediary is--- is what physics calls a "field" such as the electric field or the magnetic field.
Archimedes Plutonium Oct 18, 2025, 5:39:42 PM to Plutonium Atom Universe newsgroup.
I am inspecting on which of the only 2 Laws of Inference for quantification are valid and the other two are false or redundant. Is it UI and EG valid and that EI is a mere redundancy while UG is invalid?? In November of 2025, I would come to realize all four of UG, UI, EG, EI ___are valid__ because all four are segments of the Scientific Method itself. All four are slices of how truth is established in Science via experiments. Certainly--- we cannot check for a "For every law of Physics" and thus we end up with UG of hypothesizing that since a few number of experiments reveals that Faraday law, or Ampere law or New Ohm's law are Universal Laws of Physics via experiments. And so, I came to realize by November 2025, that Laws of Science require all four UG, UI, EG, EI for they are slices, parts and pieces of the fact that science Experiments evince Universal laws of Science via the Scientific Method and experimentation.
Let me debunk Wikipedia listing of Logic examples which are wrong and mistaken due to their errors of the simple connectors and their gross error of never realizing that Logic is the Scientific Method.
--- quoting Wikipedia---
First-order logic also employs the logical operators from propositional logic but includes additional devices to articulate the internal structure of propositions. Basic propositions in first-order logic consist of a predicate, symbolized with uppercase letters like P and Q, which is applied to singular terms, symbolized with lowercase letters like a and b. For example, if a stands for "Aristotle" and P stands for "is a philosopher", the formula P(a) means that "Aristotle is a philosopher". Another innovation of first-order logic is the use of the quantifiers exists and for-all, which express that a predicate applies to some or all individuals. For instance, the formula exists xP(x) expresses that philosophers exist while for-all xP(x) expresses that everyone is a philosopher. The rules of inference from propositional logic are also valid in first-order logic. Additionally, first-order logic introduces new rules of inference that govern the role of singular terms, predicates, and quantifiers in arguments. Key rules of inference are universal instantiation and existential generalization. Other rules of inference include universal generalization and existential instantiation.
Notable rules of inference
Rule of inference
Form
Example
Universal instantiation
for-all xP(x) P(a)
Everyone must pay taxes.Therefore, Wesley must pay taxes.
Existential generalization
P(a) exists xP(x)
Socrates is mortal. Therefore, someone is mortal.
--- end quoting Wikipedia---
Let me write an example of EI , Existential Instantiation.
Existential Instantiation
ExP(x)
----------
P(a)
This is the reverse of above of Existential generalization.
If you have the Every then want to Generalize Every-- how stupid is that??? Unless, however you are reminded that the Scientific Method for Universal Laws of Physics are promulgated by a single experiment that turns into making a universal law.
If you have There Exists and want to Instantiate that--- how stupid is that???? Unless, however you started from a Universal law of Physics, say the Faraday law and you want to verify that an electric current exists by thrusting a bar magnet through copper wire coil.
The Example I offer to make this all clear does not come from derivative versus integral of Calculus but the entire Scientific Method.
When does an experiment in Physics allow us to say--- that is a Universal Law??? For example the Faraday Law. So we have a closed loop coil and a bar magnet thrust through the coil producing a electric current. That is one experiment and Faraday was the first to do that experiment. Soon others repeated the experiment. So we have the Existence of one true experiment then others would increase the number to thousands who repeated the Experiment. Thus we jump from There Exists to the more General and say the Faraday Experiment is a Law of Physics. A universal law established once anyone can perform the experiment and get the exact same results as all the others who performed the experiment before.
Now with the Faraday Law of thrusting bar magnet through closed loop coil yields electric current--- let us go the other way as that taken to be a Universal. What is the Universal Instantiation of the Faraday Law??? It is the experiment done once more yielding the result--- There exists a current produced in the Faraday experiment.
The UG is going from several experiments yielding the same results and thus a Universal Law of Science and the UI is where we repeat the experiment and find out the results again match the Universal Law.
It is the Scientific Method of how we arrive at Universal Laws of Physics that makes Existential Generalization valid. And it is the same Scientific Method that makes Universal Instantiation be Valid. As we take say the Ampere Law and instantiate it by showing an experiment set-up at Caltech where a current flowing in a wire produces a magnetic field around that wire.
Physics has Existential Instantiation for that is doing the Ampere law or Faraday law experiment on the spot at the moment.
So we do the Faraday law experiment and find it holds true, the existence of our Faraday Law apparatus confirms the Faraday law and thus we jump from Existence to that of Existence Generalization that all performances of the Faraday law achieve the same end results of producing electricity by thrusting a bar magnet through closed loop coil of copper wire. Here a particular experiment conducted by you and me is generalized into the Faraday law. Now EI. So we read the Faraday Law saying--- thrust the bar magnet through closed loop coil connected to Galvanometer and read how much electricity was produced. So we read this Universal Law and perform the instructions. And what we discover is that of the existence of a electric current. We have gone from existence in general to existence in specific instance.
Yes, this makes clarity to all of UG, UI, EG, and EI, but only in a context of Laws of Science where Experimentation is the existence parameter and the Science Law is the Universal parameter.
In everyday common language, we rarely are speaking about the Universal Laws of Physics or other sciences and when we teach UG, UI, EG, EI we should focus on Laws of Physics. This is why it is extremely difficult to give examples in ordinary language of common experiences for UG,UI, EG, EI, because those experiences do not involve universal laws of science (especially physics).
Tonight I was watching a most excellent show on Mountain Lions in Montana on PBS NATURE, top excellent show.
Let me see if I can drum up 4 examples one each of UG, UI, EG, EI.
UG: Willow the mountain lion and her kittens have retractable claws by Linnaeus classification, thus, every mountain lion observed in the future has retractable claws. ( a law of biology, going from Willow to her 7 + kittens to a generalization that all mountain lions have retractable claws)
UI: We start from the beginning of this show and we know as a fact the biology law that all mountain lions have retractable claws. We are introduced to Willow and then her 7+ kittens and all the mountain lions shown in this program have retractable claws.
EG: We see every mountain lion in Willow show has retractable claws, we now generalize to the biology law that all mountain lions have retractable claws.
EI: We examine the claws of any one of the kittens of Willow and of Willow herself and find they are retractable claws.
So what I am coming to the conclusion with, is that all 4 quantifications exist UG, UI, EG, EI but they exist only in a specific context of Laws of Science that have Universal Laws. The UG, UI, EG, EI do not exist in common language without the context of Laws of Science.
Finally figured out what UG, UI, EG, EI are. All four of them are based on the idea that the Scientific Method is used, employed in making the Truth of the world. The Scientific Method is essentially all four UG, UI, EG, EI combined to making and causing universal law to form from experiments, experiments often repeated of science and to instantiate universal law with existence.
18) Best understanding of "nothing or zero" in both math and logic.
What is the reverse of All or Every? The reverse is None or Nothing.
Looking in Copi, Introduction to Logic, 4th edition, 1972, looking in the index, no mention of zero, of nothing, of naught.
Looking in Thomason, Symbolic Logic An Introduction, 1970, looking in the index, no mention of zero, of nothing, of naught.
How important is zero in mathematics??? Well zero is different from all the other numbers of math-arithmetic, written as 0 and represents the concept of "nothing" of empty space in geometry. Zero is also represented in numbers themselves besides being the start of positive numbers, for ___no negative numbers exist in math or science__.
Notice that numbers vitally need 0 to count for place values. If we count 1, 2, 3, 4, 5, 6, 7, 8, 9, then we need the zero 0 number to fix the place value for 10. Without 0, we are forced to call 10 to be 11 or something stupid????
Geometry needs zero 0, vitally needs 0 for empty space. In fact, no calculus can exist if 0 did not exist, because the derivative is the slope in empty space from one number to the next successor number in the xy graph plane. If the plane were a continuum of numbers, like the Reals, with no empty space from one number to the next number, then Calculus would not exist, for you cannot form a derivative.
What is Zero, 0 from the 6 connectors of Logic? Zero comes from the negation of the Existential quantifier. If we negate with a Not the Existential quantifier we end up with a quantity of 0, nothing.
Example: A rock-elm tree exists. Therefore, 1 rock-elm tree exists.
Rock-elm tree does not exist. Therefore, 0 rock-elm trees exist.
But now we get into a very messy question. A question so messy that some may call it philosophy instead of Logic. The question is -- is Not of logic the same as zero, 0, nothing of mathematics??? I dangle this question before you and let you come up with an answer. As for me, I am happy to think of Not of Logic as different from 0, zero, nothing of mathematics. For as I can see in counting to 9 then to 10, that the 0 serves as something-- serves as place-value. So my answer to the question is that zero,0 has some similarity to the Not of Logic, but, that the two are distinct. But then your younger minds may see more than I can see at this moment in time.
Archimedes Plutonium Nov 1, 2025, 2:25:41 AM to Plutonium Atom Universe newsgroup.
Old Logic had Universal Quantifier and Existential Quantifier, but they made a mistake in missing the 0 or nothing, arising from the Existential quantifier and embedded into the Universal quantifier.
---------------------------------------------------------
On Friday, October 31, 2025 at 9:22:47 PM UTC-5 Archimedes Plutonium wrote:
Inverse A+ is to subtract A , and thus it equals 0.
Another mistake by Old Logic. They were amiss in having the Nothing the zero as part of Existential and Universal quantifiers.
The number 1 comes from the Existential quantifier as well as finite numbers. But zero 0 is in a domain of itself. By that I mean we tack on 0 in mathematics to enlist the Counting Numbers. We tack on 0 then add 1 to 0 then add more ones to achieve all the counting numbers in what is known as the process of Mathematical Induction.
Archimedes Plutonium Nov 4, 2025, 12:39:00 AM to Plutonium Atom Universe newsgroup.
Alright, I have all the issues ironed out and time to write this textbook in full. It has been a difficult book, very time consuming. Probably because I end up overhauling entire Logic study of the past. It is as if I am doing fresh logic never before seen or understood. That logic of the past was error ridden and folly.
Some say "nothing" some say "zero" some say "empty space" and the concept seems simple to everyone. Simple enough to warrant no further description. But this concept is one of the most mysterious in all of math and science.
Zero is deemed a number in mathematics but unlike any other number. It is appended onto the numbers of mathematics and thought of as "nothing". It is the starting point in mathematics for which the next number is 1, then 2, then 3, etc. But it does not have to stick to counting by 1, for the 10 Decimal Grid System counts by 0.1, the 100 Grid counts by 0.01 and the 1000 Grid counts by 0.001, ever closer to 0.
In math geometry, zero can be terribly tricky, for in Ancient Greek times up to recent we believed in the axiom of a point has zero length, zero width and zero depth, yet still a point remains in existence described as having "no dimensions", described as nothing yet existing as a point. How can nothing deliver a point?? And this is just the start of the awful complexity ans the concept of "nothing or zero".
Then in mathematics, there is the idea that infinity starting from 0, then 1 , then 2 etc, that infinity bends back around and joins up with 0. A branch of mathematics called p-adics is notorious in fostering this notion that if you go far enough in numbers, they bend back around to meet up with at 0. Some like p-adics because there is no signage-- no negative numbers and all the numbers are positive numbers.
Another beautiful philosophy idea worth pursuing-- connecting Universal with Existential via zero.
-----------------------------------------------------------------------------------
So I outlined above that p-adics in mathematics have a tendency to go to infinity and as they do so, they curl and bend back around to their starting point 0. Many love this facet of p-adics for it allows you to do all of numbers without ever needing negative numbers, with a signage of negative.
Now, getting back to my comment that zero, 0, nothing is the reverse of All or Every in the Universal quantifier. But notice also, that zero is the Not Existence of the Existential quantifier. All or Every is the reverse of "nothing". And Not Exist is "nothing". I seem to have some link up of Universal with Existential in the detail of zero, 0.
So we have to go ultimately to understand "nothing or zero" to the topmost science-- physics.
What does physics have to say about Zero or Nothing?
Physics has a-lot to say about Zero or Nothing but leaves us, in the end, unsatisfied and unhappy.
As for the idea that Zero is a starting point to reach for other numbers, first 1 then 2 then 3 etc. We have the concept of Absolute Zero Degree Kelvin Temperature where no temperature is below that. But even more starkly, no temperature can reach 0 Kelvin and all temperatures must be above 0 K degrees. As physics explains it, each lowering of temperature requires far more energy until you reach a point where you need infinite energy to go to zero kelvin.
This kelvin temperature of 0 degrees is the concept that 0 is a starting line or starting point.
But what does physics say about 0 in terms of Geometry-- Space?
The latest that physics talks of the concept of 0 is in the Dirac Equation of Physics. Where he (Dirac) imagines empty space being holes of positrons, those 0.5MeV particles-- the anti particle of the magnetic monopole of 0.5MeV (the particle that Old Physics thought was the Atom's electron). The true electron of the Atoms are muons at 105MeV and stuck inside proton toruses doing the Faraday law with the proton.
So how can we envision empty space when they are positron holes in Space?
If you read enough physics articles in magazines or books, you will find thousands of times where the author says empty space is teeming with energy and so, how can space be zero or nothing?? In fact these articles state that Space has infinite energy of Light Waves criss-crossing through space. Infinity in the emptiness of Space. We had thought this empty space was a vacuum except for the occasional light wave that traversed it.
This is the complexity and mystery of zero or nothing, I was eluding to before.
Then, in the Atomic theory, we often read the idea that over 90% of the space inside an atom is empty space, save for a photon criss-crossing through that empty space.
In my long career in science I came to the end opinion that photons---the light-photons are themselves what makes up Space thought to be empty space. In this viewpoint, when rest mass exists it can be a ball object occupying that particular space and that empty space was the photons that compose that space.
In this view All Space = rest mass occupied space plus photon making-up the rest of space. All Space = rest-mass mass + photon space.
This is in logical alignment with the idea that positrons are holes in space, and that photons are criss-crossing space and that Absolute 0 Kelvin is not attainable.
In Quantum Mechanics physics we have duality of electricity to magnetism. And here the idea is that the electric field and magnetic field determine Space that is not occupied by rest-mass particles.
We think of a photon as a packet of energy and we can envision that as empty or zero in the idea that no material objects are there.
Now how should Logic view Zero or Nothing?
It should not be made into a quantifier, but come from the other 6 connectors of Logic. And it is easy to see that Zero or Nothing comes from the Existential quantifier when we apply Not to the Existential quantifier.
When we say "Something called ixxx does not exist" we are saying that ixxx is zero or nothing.
So in Logic, zero or nothing is the combination of the Existential quantifier with the Not-Equal connector.
What is the major importance of Zero, nothing in Logic.
------------------------------------------------------------------------
The major importance of Zero, nothing in Logic is to give an evaluation number to all false and falsehood statements in logic, while true statements in Logic are assigned positive numbers larger than 0.
For examples of true statements. The statement: "Winter Solstice was 21December 2025 this year" which is a true statement and I can give it a truth value of any positive number larger than 0. Let me say in my opinion, that is important data, and so I assign it a truth value of 10. While another true statement is "The seven stars in the Big Dipper are easy to see, while only three stars of the Little Dipper are easy to see". For which, since it is true for me, maybe not true for some observers with better sky views at night. So I assign a value of 3 for this truth. But now, what would I assign a truth value to the Faraday law that says, "Thrust a bar magnet through copper coil connected to Galvanometer and see a electric current produced". This is a universal law of physics and would rate it a astounding 1*10^604, the infinity borderline positive number. In fact all laws of electromagnetism are worth that value.
The statement: " He sat and slept on a Park bench this afternoon." Is a true statement of someone, but it rather minuscule in truth value. Should I rate it a 1 or fraction of 1 as 0.5??
The statement: "Goochy goochy goo, tickle tickle". In a romantic date is a statement with little science content other than sociology, dating and romance to procreate offspring, yet it does have truth value. Should we rate it as a 1 in value, or maybe 0.25, a fraction of 1???
Examples of false statements. I have no choice but to assign all false statements with a zero, 0. For negative numbers do not exist, leaving me only with 0 to assign false statements.
The statement: "Winter Solstice is in March of every year". Is blatantly false, and give it a 0 value, for there is no other number value available.
The statement: "One of the seven stars in the Big Dipper is Polaris, the North Star". This is false for the North Star is in the Little Dipper. I have to assign this statement a 0 value.
The statement: Donald Trump says " I will slash drug prices by 400%, 500%, even 600%". This is false as it is impossible to go beyond a 100% discount, unless Trump is thinking of forcing drug companies to pay people to buy their drugs. So the statement is false and I am forced to assign it a 0 value.
The statement: "Higgily piggily into the borogoves goes a waltzing jabberwocky". Much of poetry are nonsense ideas and get a 0 in logic truth value.
The statement: "JJ Thomson in 1897 found the electron of Atoms". This is false because he found the magnetic monopole. The true electron of Atoms is the muon and stuck inside a proton torus. All false statements, even the gibberish, or yakkity yak empty ideas get the same evaluation marks--- 0.
Division by zero, 0, is possible but is an infinite integer, what I used to call p-adics from 1993 through 2009.
---------------------------------------------------------------------
From above the truth table of If-->Then was found to be TFUU where U stands for unknown, undecided and the obvious reason for this is that otherwise Logic has nothing in which to say that 1/0 = undecided. Math cannot have division by zero for it tears up all of mathematics.
Example of how division by zero tears up mathematics.
Suppose 1/0 was equal to 0 itself.
Then we have 1/0 = 0.
Multiply by 0 leaves us with (0)(1/0) = (0)(0).
This equals 1 = 0.
Trying any other number such as 2,3,4,5, etc you have the same end result that 2=0, 3=0, etc.
Thus every number equals zero.
Suppose 1/0 was equal to infinity which is the infinity borderline of 1*10^604.
The beauty of the true numbers being Decimal Grid Numbers and not the Reals is not only are they discrete, but the Grid Numbers allow one to use the 10 Grid, the 100 Grid and the 1000 Grid, pretending that 1000 Grid is the infinity borderline so that the mind does not have to think about using the actual borderline of 1*10^604 to achieve ___true results___. Here what I am saying is that if it is true in using 10, 10^2, 10^3 Grids, it is true in using 1*10^604 Grid. The beauty of the true numbers of mathematics as Grids, is not only are they discrete numbers with holes in between one number and the next number, but the entire Grid System is Mathematical Induction in full. What is true for the first 3 Grid systems will be true throughout.
Suppose 100 is the last finite number. Then 101 through 1000 are infinite integers.
1/0 in this scheme is 1/1000 where 1000 is the last infinite integer.
Here we are supposing that 1/0 is equal to infinity which is 1000.
Will this work???
0/0 equals 1/1000
1/0 equals 1/999
2/0 equals 1/998
3/0 equals 1/997
etc
etc on down to 100/0 = 1/900
Recently I proposed that the Light wave was really the Light-Wire, and that Light as a wave was flawed reasoning because it had __no medium__ to do waving in. Besides, there are no waves in the Electromagnetic Laws of physics, instead, there are Wires. So I corrected and changed Old Physics to read--- Quantum Mechanics Light Particle to Wire duality.
I drew an ascii art picture of the Light-Wire crudely looking like this.
LIGHT AS a WIRE, not wave looks like this.
- - - - - - - - - - - - - - - - - -
/ front of wire \ back of wire--- it is a pencil ellipse that contains a-lot of data
\- - - - - - - - - - - - - - - - - - -/
And then we augment those holes by placing a B field ring around each hole.
- | - | - | - |
Both the E-field can vary in size and the B-field can vary in size
|
__ | _______| __ | _
| |
The variations allow for different sounds and different pictures.
In Old Physics, their Light wave ^v^v^v^v^v^v was the up and down sinusoid transverse (phony baloney) has no variations other than taking a different type of whole wave, but no variations in the E-field or B-field, hence the data it can hold is monolithic data. You would need several Light Waves just to communicate a single letter such as "A". With the Light Wire, a entire textbook with pictures can be sent over the air.
So, now, getting back to 100 Grid being what I call half of that pencil ellipse of 1 Light-Wire, the other half of the Light-Wire above could be in the 1000 Grid the numbers 200, 199, 198, 197 which we would think of in Old Math and Old Physics as being 0, -1, -2, -3, etc etc.
Or we can use the entire 1000 Grid from 101 to 1000 and think of 1000 as 0, 999 as -1, 998 as -2, 997 as -3.
Mind you, the Infinite Integers as I called them in 1993-2009 were the p-adics by mathematicians. I remember get a-lot of help from Karl Heuer in the early 1993 to about 1995 and then Alexander Abian helped me further, until his unfortunate passing away. But by year 2009, I discarded the p-adics altogether because I found the Infinity Borderline 1*10^604 where Huygens tractrix finally meets up and matches the related circle area, where pi digits are 3 in a row of zero value. So I no longer needed Infinite Integers, or, some prefer to call them p-adics.
The resurrection of p-adics, as infinite numbers that complete a electromagnetic circuit.
---------------------------------------------------------------
Correct me if I am wrong on this statement, for I sensed from Karl Heuer and others of their likening of p-adics. That all of our modern day computers, whenever they need to Represent a Negative Number, that it is represented by p-adics, such as -1 = 999..99 then -2 is 999..98, then -3 is 999..97. They all liked p-adics because they can represent their negative numbers all with positive numbers doing the representation. Am I correct on that score??
Of course in true math, no negative numbers exist at all!!!!!!! For the axiom of math--- you cannot subtract more than what is available to subtract insures negative numbers are trash can illusions.
But, now, we have that pencil ellipse Light-Wire shown above, where 1/2 of the wire is normal regular numbers, and the other 1/2 is infinite integer numbers.
Now the ratio of normal numbers to infinite numbers need not be 1/2 to 1/2, but could be something like 1/10 normal to 9/10 infinite numbers. Where we can picture a Light Wire looking like this.
5* 6* *7
4* *8
3* *9
2* *10
1* | *11
0 1 2 3 4 5 6 7 8 9 10 where the asterisk numbers are infinite integers while the bottom straight flat row are normal numbers.
Now the above is my attempt of drawing a Light-Wire where only 1/10 of the wire is normal and the 9/10 is the severe bending arc to form a closed loop circuit composed entirely of infinite integers.
Now well, all of the above is speculation on my part, unless, of course, I find a actual Physics phenomenon which is a Deciding Experiment (referring the reader back to the OR connector).
Mine is speculation, until, I can show that the ideas above are the only ideas that can explain something in Physics which no other, like the stupid Old Physics notion of Wave within no medium.
Do I have a physics phenomenon that the above explains, yet is nothing but confusion in Old Physics????
BIREFRINGENCE
------------------------
The physics phenomenon of birefringence is easily explained, and only fully explained, when the Light-Wire is split into two parts, the normal numbers section making a image and the infinite-integer section described above, making a image.
There are probably many other phenomenon in Physics that the Light-Wire has a far easier explanation than the stupid Light wave of Old Physics.
Now in the below quote from Wikipedia, we can see the phenomenon and also we can see the feeble, and stupid Old Physics attempt of an explanation with their mindless transverse sinusoidal Light wave ^v^v^v^.
--- quoting Wikipedia on birefringence---
A calcite crystal laid upon a graph paper with blue lines showing the double refraction
--- end quoting Wikipedia on birefringence---
AP writes: in that picture, I can begin to see where a closed loop circuit of Light-Wire can form a double image, but cannot see how a sinusoidal ray with arrow head and tail can duplicate a image the up and down ^v^v^v^ Light as wave.
Alright, I solved this logical and physics problem with the best experiment to represent a Deciding Experiment. Is Light the AP Light-Wire, or is Light the Old Physics Light-Wave, the sinusoidal straight arrow with tail wave??
I spent much of this blizzard day of 28 December inside my house looking up anomalies in Light. Looking at anomalies in reflection in diffraction in refraction even in Birefringence explanation. They all have anomalies when we have Light as Light-Waves. But one experiment above all other physics experiments brings logically home the fact that Light cannot be a wave, that Light out of necessity has to be a Wire. And that experiment should not surprise anyone who has taken physics in college or university. The Double Slit Experiment makes sense only with Light being the AP Light-Wire.
So I went to University from 1968 to 1972 for a degree in mathematics, with my second favorite subject being physics. I thought I was not good enough to get a degree in physics because my grades compared to others was not good. I later realized after 1990, that the issue of not feeling adequate in physics was not a deficiency on my part, but rather, the whole of physics, and mathematics were deficient in understanding of true physics and true mathematics and those subjects were "not good enough to teach a Archimedes Plutonium the truth in math or physics". The state of physics and math eduction in the world of 1968 through 1972 were a poor state for a logical mind that was AP. I kept bumping up against foolish ideas that I could not possibly master. For example, in first year of college I dreamed that the Polynomial was the only function in all of math so that calculus class is simple as add or subtract 1 from exponent. No wonder I was average and not stellar in math. In physics, how on Earth was I going to understand the laws of electromagnetism when I cannot understand the Maxwell Equations??? Not that my brain was deficient to understanding those equations, but that the equations were phony baloney to begin with and my logical mind would have been polluted rather than enhanced and educated.
So in University of Cincinnati, later at Utah State University my love and interest of physics never waned. Your first love in life will, as the Bible says, either make or break you. And at both Universities I kept taking physics classes. I read and watched the Feynman Lectures and his films on physics. He spent inordinate time on the Double Slit Experiment, and I came to the conclusion that Feynman was obsessed with this Experiment. Seemed as though Feynman was bewildered with the results of the Double Slit, that the Light or the 0.5MeV particles would be "wavelike" at the slit, but end up "particlelike" at the end screen. How is this possible? Feynman kept puzzling over.
So here I am in 2025. With the idea that in the Michelson-Morley Experiment 1887, there was no "Luminferous Aether" no medium for Light as a wave to be "waving in". The entire physics community ignored, looked beyond their discovery of no medium for Light to wave in. When they should have had a logical mind to say--- probably our wave theory itself is wrong, for if no medium to wave in, then Light was never a wave in the first place.
I took Logic while at University of Cincinnati, two years of it. And probably the single greatest pick of my lifetime in education. For it is my Logical Mind that has made all the difference in the world for me in being a scientist. My logical mind is what led me to all the discoveries I found in science. And the reason I insist every scientist going forward who wants a degree in science in a college or university must take two years mandatory Logic. Logic from my 2 textbooks because no logic textbook had the connectors correct.
So, what if Feynman in 1963 instead of writing his Double Slit Experiment in his Lectures on Physics, revisited the Michelson-Morley Experiment. Revisited it with a Logical Mind, instead of a physics-mind. And said this. "Alright, so no Aether, no medium for Light to be waving in". And then Feynman makes a jump of faith. He says to himself, if no medium, then, well, Light is ___not a wave___!!!!!!!!!!!
Then of course there would have been a scramble for Feynman and others to find a replacement for Light as wave to Light as something else, that would make the Double Slit Experiment sensible, logically coherent.
What if in 1963, all physicists around the world dropped the idea of Light as wave, looking for a replacement.
The Logical Physicists would have looked at the other dualities in 1963, the year Feynman published his Lectures on Physics.
So the dualities current in 1963, other than the error filled particle-wave duality was the position-angular momentum duality. I am not sure if physicists by 1963 were smart enough to realize that electricity is the dual of magnetism. I may have been the first to discover that in the 1990s. But for sake of argument, let us say that all the physicists in 1963, especially Feynman, were logical and bright enough to know the best duality of all was electricity to magnetism.
So we have then a search for a replacement of Wave in physics. Now we add on top of that the duality of electricity to magnetism. We have particle but need to find what is the dual of particle. By looking at electricity to magnetism, we can say the copper coil in Faraday law or the copper wire in Ampere Law is particle, then what would be the dual????
As we thrust a bar magnet in coil of copper wires of Faraday Law we strip off magnetic lines of force to become electric current in the copper coil wires.
Likewise in Ampere law as we run a electric current in copper wire we generate a magnetic lines of force around, and perpendicular to the electric current.
So, logically, particles are involved in both Faraday and Ampere laws but no waves are involved. What is involved in both Faraday and Ampere laws is a Wire. Could Wire be the replacement of wave in Particle-- wave???? I do not mean some floating wire as Light, no, I mean the Electric Field and Magnetic Field are lines of force of a closed circuit constructed into a Wire in space that needs no medium.
Now, so we construct a wire in space from the E-field and B-field and in our construction we view the Wire as this diagram.
LIGHT AS a WIRE, not wave looks like this.
- - - - - - - - - - - - - - - - - -
/ front of wire \ back of wire--- it is a pencil ellipse that contains a-lot of data
\- - - - - - - - - - - - - - - - - - -/
And then we augment those holes by placing a B field ring around each hole.
- | - | - | - |
Both the E-field can vary in size and the B-field can vary in size
|
__ | _______| __ | _
| |
The variations allow for different sounds and different pictures.
The Old Physics wave of Feynman in his Lectures on Physics is a up and down sinusoid with a arrow tip front and a tail ray.
^v^v^v^v^v^ that is transverse.
So, now, we come to having to decide which is true physics, in a deciding experiment. Luckily for me, a Deciding Experiment already exists in the Double Slit Experiment.
If AP's Light-Wire duality is true, then, Light as particle hits the end screen and registers particle, but as the Light enters the two slits the Light has interference patterns and the AP Wire will have interference of one wire to the next wire but as the wire hits the end screen, since it is a closed loop circuit in the first place, it is simultaneously a particle as that closed loop circuit. A up and down Light ray with arrow tip front and rear ray is not able to become a particle, no it remains as a ray as it hits the screen.
So, what frustrated Feynman is that Nature was not frustrating but that the idea of Wave was incorrect. That when Light as wave was found to have ___no medium__ in which to do waving in, is the error. For the wave theory should have been abandoned shortly after Michelson-Morley experiment and a replacement theory inserted.
A scientist without a Logical mind, is a scientist who will struggle to achieve good science. He/she may be good at collecting data and doing experiments, but likely will fail in interpreting, or understanding what went on in the experiment itself.
Archimedes Plutonium
Jan 6, 2026, 5:43:04 PM (10 days ago) Jan 6
to Plutonium Atom Universe
Just when I thought I was breezing and sailing through the Mess of Logic, a big snag rolls up.
P Q P OR Q where dT stands for a statement that has a partial truth
The aphorism for the AND connector is "Do not throw the baby out in the bathwater" to help determine AND truth table TTTF, not TFFF.
However when we come to OR truth table we need a aphorism to help in that case. Here the problem is in throwing out the true valued statement and keeping the false statement. So the same aphorism applies Do not keep the dirty bath water and throw out the baby.
All of this hardship and problem is because Old Logic recognizes only absolute truth and absolute falsehood, when there is the possibility of partial truth and partial falsehood.
I am going to have to start all over again on #366 and #367 and I must include a High School textbook on Logic.
Truth Tables are mostly a guide, but then because they do not allow for partial truth or partial falsehood, truth tables end up being a barrier to truth and reality.
What will overcome this barrier is the physics concept of the Deciding Experiment. That translates into the concept of the dT which represents a partial truth in Truth tables, especially the OR.
OR truth table in New Logic
P Q P OR Q where dT stands for a statement that has a partial truth
T T F
T dT T
dT T T
F F F
T dT T
dT T T
F F F
With the AND connector, I could get away fully with just a binary truth value of absolute truth and absolute false. But the OR connector stops all of that and forces a partial truth value to all the connectors.
The Physics DECIDING EXPERIMENT is the justification for truth tables Necessarily Require a partial truth value of dT.
AP, King of Science.
Reply all
Reply to author
Forward
0 new messages