14) The IF-->Then connector.
Archimedes Plutonium Jan 22, 2026, 2:44:18 AM to Plutonium Atom Universe newsgroup.
14) The If-->Then connector
There are 4 simple connectors of Logic, Equal-Not, AND, OR, If->Then and we talked about the truth tables of three of them. Now we turn our attention to the fourth simple connector of If-->Then. It is far more complex than Equal-Not, AND, OR. And we learned that Equal-Not is multiplication; AND is addition, and OR is subtraction. That leaves only division remaining. The If-->Then connector is also called the "implication" or the "conditional" some go so far as to call it the "material conditional" and some call it the "hypothetical". The statement between the "if" and the "then" is called the antecedent, while the following statement after the "then" is called the consequent.
I often like to think of the If-->Then connector as the "move-into" connector. A famous philosopher, Plato, dwelled on the idea of transformation of "Being into Becoming". As the "If" is existence and then the growth and change as the "then".
One of Logic's first syllogism was this. (A syllogism is a simple two line argument with a conclusion.)
All men are mortal.
Socrates was a man.
Therefore, Socrates is mortal.
That entire argument can be rewritten as a If -->Then connected statement.
If all men are mortal and Socrates is a man, then Socrates is mortal.
So far the truth table of Not-Equal (some prefer to write it as Equal-Not) had all 4 rows being true. AND had 3 rows being true. OR had 2 rows of being true. Take a guess of how many rows are true for If-->Then????
New Logic
IMPLIES (Material Conditional)
IF-->THEN truth table
MOVES INTO
T -> T = T
T -> F = F
F -> T = U probability outcome
F -> F = U probability outcome
Let us see how assigning T = 1 and F = 0, makes the If --> Then be division in arithmetic.
Let me validate that is the math operator division. I replace T with 1 and F with 0.
p q p divide into q
____________
1 divide into 1 1
1 divide into 0 0
0 divide into 1 U for unknown, uncertain, undecided and undefined
0 divide into 0 U for unknown, uncertain, undecided and undefined
We must talk about the strange two rows of U for the If-->Then.
Archimedes Plutonium Jan 24, 2026, 3:12:26 AM to Plutonium Atom Universe newsgroup.
The strange two rows of If--> Then are because a falsehood will never lead to truth in science, and furthermore, mathematics needs division divided by zero be undefined. We cannot have math be more than logic. Logic needs to reflect all the truths of mathematics and then some.
Examples of If-->Then
1) If we have drought in 2026 in my region, then the plants will wilt and stop growing.
2) If the Sun shines from Faraday law-structure, not from fusion, then every year gets on average hotter than the last year.
3) If the Sun shines from Faraday law-structure, then the polar ice caps will accelerate in melting.
4) If the Moon arrived near Earth only 90 million years ago, then that easily explains how dinosaurs could live on both poles of Earth as one side of Earth constantly had daytime, no night.
5) If the Moon arrived near Earth only 90 million years ago, then that explains how life came into existence in warm seas and no violent motion.
6) If the Moon was always there when Earth was there some 4.5 billion years ago, then life on Earth would not have evolved out of the seas for the conditions were not suitable.
Analysis: (1) is If T, then T. (2) is If T then T. (3) is If T then T. (4) is If T then T. (5) is If T then T. (6) is If F then U unknown.
Archimedes Plutonium Jan 24, 2026, 5:58:50 PM to Plutonium Atom Universe newsgroup.
Canada's math and logic failure Dan Christensen in sci.math gives examples of IF-->Then where the "if part" is true but the "then part" is false and thus making the entire statement be false.
Dan Christensen in sci.math
Feb 22, 2024, 8:54:35 AM
to
STUDENTS BEWARE: Don't be a victim
"Water is really H4O, not H2O." ********** NEW **********
--July 27, 2023
Canada's Dan Christensen in a round about way says-- If water is not H2O then it is really H4O.
Analysis: If T, then T, making the entire statement be true.
Conversation: Apparently no scientist in Canada is intelligent enough to get out the weight scale and weigh the mass of hydrogen compared to oxygen, no, they run skip and jump to the lounge after looking at volume, too lazy to complete water electrolysis by weighing of mass, for them, the coffee cake and donuts is more urgent.
"Negative numbers are the witches and hobgoblins of insane kook mathematicians. "
--Dec. 7, 2022
Dan in a round about way says --- If negative numbers are witches and hobgoblins, then mathematics is insane kook.
Analysis: If F, then F, making the entire statement be U for Uncertain because you have the If portion as false.
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
“0/0 must be equal to 1.”
-- June 9, 2015
“0 is an infinite irrational number.”
--June 28, 2015
“No negative numbers exist.”
--December 22, 2018
“Rationals are not numbers.”
--May 18, 2019
According to .. “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019
Which could explain...
“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019
“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019
“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994
“The Universe itself is one gigantic big atom.”
--November 14, 2019
AP writes: It is sad for Canada, that they allow some goonclod freak of Logic pander his mindless take on Logic, for such a fool blurted this out to sci.math showing that Dan Christensen is a worthless, miserable failure of both math and logic.
Here is an example of Dan Christensen in sci.math fumbling with the most simple of logic reasoning, and yet Canada keeps allowing this misfit to dig deeper into logic and pollute the minds of our young people.
The stupid Dan Christensen always chokes up when it comes to logic or even just plain commonsense with his 2 OR 1 = 3 and his AND as subtraction.
On Wednesday, January 25, 2017 at 10:08:09 AM UTC-6, Peter Percival wrote:
> Dan Christensen wrote:
> > On Wednesday, January 25, 2017 at 9:47:32 AM UTC-5, Archimedes Plutonium wrote:
> >> On Wednesday, January 25, 2017 at 8:27:19 AM UTC-6, Dan Christensen wrote:
> >>> On Wednesday, January 25, 2017 at 9:16:52 AM UTC-5, Archimedes Plutonium wrote:
> >>>> PAGE58, 8-3, True Geometry / correcting axioms, 1by1 tool, angles of logarithmic spiral, conic sections unified regular polyhedra, Leaf-Triangle, Unit Basis Vector
> >>>>
> >>>> The axioms that are in need of fixing is the axiom that between any two points lies a third new point.
> >>>
> >>> The should be "between and any two DISTINCT points."
> >>>
> >>
> >> What a monsterous fool you are
> >>
> >
> > OMG. You are serious. Stupid and proud of it.
>
> And yet Mr Plutonium is right. Two points are distinct (else they would
> be one) and it is not necessary to say so.
>
Apparently Dan Christensen never took calculus or flunked it with this statement.
On Tuesday, June 2, 2015 at 8:57:54 AM UTC-5, Dan Christensen wrote:
> On Tuesday, June 2, 2015 at 2:32:51 AM UTC-4, Archimedes Plutonium wrote:
> > The nonexistence of a curved angle because there is no way to measure the angle if either one of the rays is not a straightline segment at the vertex,
>
> From the derivative of each curve at the point of contact you have the slopes of their respective tangents there. (Assuming derivatives are defined there.) From these slopes, you should be able to calculate angle formed.
>
>
> Dan
Archimedes Plutonium Jan 25, 2026, 1:03:21 AM to Plutonium Atom Universe newsgroup.
I am rather thankful that sci.math and sci.physics from 1993-2024 had a goonclod gang of stalker failures of science and logic for it is difficult for a normal scientist to come up with muddle headed logic since we spend much of our time on only truths of science. And so I am thankful that the dumb failure Dan Christensen posted so much logical crap to sci.math and saves me a-lot of time.
Dan is a failure of math and logic and one of the reasons he fails so much is it is impossible to make clear his thoughts, no his big loud mouth gets in the way of clarity, and this is a harbinger sign for students around the world to learn--- if you are around a "loudmouth" usually means the louder the mouth, the more empty the thoughts inside and is wasting your valuable time in life.
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020 by Dan Christensen in sci.math
What Dan was trying to say is this.
If Primes existed, then they should come from a set that is complete to division. The 10 Decimal Grid Numbers 0, 0.1, 0.2, 0.3, ...0.9, 1.0, 1.1, ... , 9.8, 9.9, 10.0 is the smallest Grid System and has division. Divide 1 by 10 and you have 0.1. Divide 5 by 10 and you have 0.5. So of the integers in 10 Grid can we say any of them are prime???? For 5 is divisible by 10, divisible by 0.5, divisible by 2.5 and many others. The number 3 is divisible by 10 by 0.3, by 1.5, etc. So that when a stupid mathematician or logician says Primes are only divisible by themselves and the number 1, while never paying attention to the fact the fool choses a set that is undefined towards the Operation of Division in the first place. So that the concept of Prime is itself Vacuous and Meaningless.
When the true numbers of mathematics are the Decimal Grid Numbers starting with 10, then 100 then 1000, etc. There is No Concept of Prime because every number (except 0) is divisible by another number other than 1 and itself. In Decimal Grid Numbers, the concept of Prime is a bogus concept.
Dan's statement turned into a If-->Then. If Primes exist, then the set they were borne from has no valid division.
Analysis: Here we see that "because" is often a replacement for "If-->Then". If T, then F. This is an example of what If-->Then avoids at all cost, a IF--> True leading to a Then False.
Statement P= Primes on Counting Numbers do not exist because Counting Numbers are not complete to division.
That statement is the same as Q= If Primes exist on Counting Numbers, then the Counting Numbers are complete to division.
Do you remember what completeness of a set means?? If not, let me refresh you. Counting numbers are complete to multiplication because when you take any two counting number and multiply them together, you end up with another counting number.
We cannot say the same thing for division on counting numbers for example 1 divided by 2 is not a counting number but a fraction as 0.5. Completeness is defined as taking any two numbers to a operation and the operation returns you a number that is in that same set.
But Dan makes a beautiful If T then F in his next example.
Now here is a beauty blunder by Canadian Dan Christensen of a If True then False.
We know in Logic the worst you can do is make a contradiction such as this: The last and largest finite number is 1*10^604 AND 1*10^604 is not the last and largest finite number.
Analysis: that is a contradiction to have P AND not-P. But the IF-->Then connector comes close to matching the nuisance of the contradiction with its If True, then False.
Here the Canadian Dan Christensen makes such a If T then F.
Dan took 6 days to make this mind-rot If T then F.
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
If the last and largest finite number is 1*10^604, then, 0 appears to be the last and largest finite number.
Can the student reader see how similar that is to a contradiction, or approaching a contradiction???
A contradiction is shown above, yet this if..then approaches a contradiction for it is saying 1*10^604 is the same as 0.
Analysis of Dan's If T then F: According to the truth tables of If..Then, it is false when you have If T then F.
Like I said earlier, scientists have their minds and brains dug deep into truth, swimming in truth and looking to find new truths. It is difficult for them to come up with nonsense gibberish bandied about by Dan Christensen and so we look for these failures whenever we want lists of falsehoods and fallacies for teaching examples.
Archimedes Plutonium Jan 25, 2026, 9:41:45 PM to Plutonium Atom Universe newsgroup.
If Harvard has a department of Theoretical Sewing Machines giving out PhDs then surely Jack Murtagh's PhD from Harvard in Theoretical Computer makes some sort of sense.
Analysis: If F, then F. The overall If-->Then is U for unknown as a false premiss in the "If portion" can never lead to a true conclusion for the tenuous connection. This is why I like to say that If-->Then is characterized as "move into".
Harvard has a department of Theoretical Sewing Machines giving out PhDs Moving Into surely Jack Murtagh's PhD from Harvard in Theoretical Computer makes some sort of sense.
Archimedes Plutonium Jan 30, 2026, 7:26:41 PM to Plutonium Atom Universe newsgroup.
Some more If-->Then statements and as homework.
My wall clock shows the phases of the Moon, and today 30 January is a Full Moon where I live in South Dakota. Also my 2026 calendar shows the Moon phases for Eastern standard time which is not far off from my going outside and observing myself.
It is a shame that when I was young, in High School, that I did not do this then, observe the Moon in its phases and learned from the observations. Oh, well, better late than never.
Homework for 1 month, write up on your observations.
----------------------------------------------------------------------
1) IF the Moon on 29 January is a sliver of a crescent Moon located in the SouthWest sky where the Sun sets at that location on 29January, AND the Moon on 30 January, a day later is directly opposite in position in the NorthEast, a move of 180 degrees in the sky, in one single day, THEN, this is evidence the Earth is round and not flat.
2) IF the Moon on 29 January is a sliver of a crescent Moon located in the SouthWest sky where the Sun sets at that location on 29January, AND the Moon on 30 January, a day later is directly opposite in position in the NorthEast, a move of 180 degrees in the sky, in one single day, THEN, this is evidence the Earth is round AND the Earth rotates on its axis each 24 hours.
3) IF the Moon on 29 January is a sliver of a crescent Moon located in the SouthWest sky where the Sun sets at that location on 29January, AND the Moon on 30 January, a day later is directly opposite in position in the NorthEast, a move of 180 degrees in the sky, in one single day, THEN, this is evidence the Earth is round AND the Earth rotates on its axis each 24 hours AND the Solar System is Heliocentric not geocentric.
So in this homework assignment you are to observe the Moon in a crescent phase where the next day the Moon is in the opposite direction in the night sky and is in a full phase. And to answer those If Then hypotheticals using Logic.
In the above I have highlighted the IF-->Then but also highlighted the AND connector.
Archimedes Plutonium Jan 31, 2026, 2:27:35 AM to Plutonium Atom Universe newsgroup.
So we have observations by students at home of the actual physical moon for two weeks.
Then we have an in class demonstration where one student is the Sun holding a flashlight. Another student is the Earth that slowly steps around in a motion to make a rotation of Earth on axis. Third we have a student acting as the Moon holding a mirror that reflects Sun (flashlight) upon Earth, and this moon slowly moves around Earth.
After we watch the demonstration guided by the teacher, we assign the homework to answer.
Archimedes Plutonium Jan 31, 2026, 4:36:25 PM to Plutonium Atom Universe newsgroup.
Helping the students learning logic by picking out images in web search that are helpful.
The University of Iowa image tells us Earth must be Round and moving on an axis in order to physically provide for Moon phases.
But, does any image in a Google search of the Moon phases prove that the Solar System is Heliocentric and not Geocentric?????
---- quoting a Google Search of Moon Phases below---
Phases
Planet parade
Crescent
Eclipse
Sunset
Moon rise
Moon phases
Saturn
Saturn conjunction
Planet alignment
Planetary alignment
Lunar eclipse
Sun
Sky tonight
Understanding Moon Phases: The 8 Stages ...
AstroBackyard
Understanding Moon Phases: The 8 Stages ...
The Crescent Moon: What Causes It to ...
The Old Farmer's Almanac
The Crescent Moon: What Causes It to ...
Skywatch: The moon and Venus can take ...
Pioneer Press
Skywatch: The moon and Venus can take ...
Paths of the Moon and Sun This Summer ...
Creators Syndicate
Paths of the Moon and Sun This Summer ...
Part 1: Lunar Phases | Imaging the ...
Imaging the Universe - The University of Iowa
Part 1: Lunar Phases | Imaging the ...
Archimedes Plutonium Jan 31, 2026, 4:59:57 PM to Plutonium Atom Universe newsgroup.
So I quoted up to the Britannica image as it and several other images prove that the Solar System is Heliocentric which means the Sun is ____Relatively at Rest____ compared to Earth, Moon and the planets.
Now, in this Logic class we are going to build a Model of the Earth to argue against all those people who think that Earth must be Flat in order to not fall off of Earth into Space if Earth was round. Here the story starts with Thales of Miletus in Ancient Greek times 626- 548 BC who studied the Lodestone-- a rock that attracts iron. He also studied static electricity of rubbing amber in animal fur.
So, we are going to have students proposing a hypothesis, nay, theory of science that anticipates Newton from Thales by thousands of years ahead of Newton.
Primal Axiom of Science:: All is Atom, and Atoms are nothing but Electricity and Magnetism.
For, come to think of it, the motion of Sun, the energy of Sun, the motion of planets and Moon are all forms of electricity and magnetism.
--- quoting Google Search for images of Moon phases that prove Solar System is Heliocentric not geocentric---
Waning crescent
Moon Phases - Griffith Observatory ...
Griffith Observatory
Moon Phases - Griffith Observatory ...
Phases of the Moon
Time and Date
Phases of the Moon
Phases of the Moon - NASA Science
NASA Science
Phases of the Moon - NASA Science
Phases of the Moon - Simple English ...
Simple Wikipedia
Phases of the Moon - Simple English ...
Moon Phases, Monthly Lunar Cycles ...
Space
Moon Phases, Monthly Lunar Cycles ...
Experiment Two – Lunar Phases | JCCC ...
Johnson County Community College
Experiment Two – Lunar Phases | JCCC ...
phases of the moon ...
Astronomy Stack Exchange
phases of the moon ...
Moon Phases Poster
Labworks blog - WordPress.com
The moon cycle – Labworks blog
What are the phases of the moon?
NBC News
What are the phases of the moon?
Different Moon Phases Explained: A ...
Country Living Magazine
Different Moon Phases Explained: A ...
The moon goes through different phases ...
US Naval Observatory Astronomical Applications Department
the Moon Illuminated
Moon Phases & Your Monthly Cycle ...
Star In A Star
Moon Phases Names - an easy way to ...
Moon Phases - NASA Science
NASA Science
Moon Phases - NASA Science
Background 2/6 - Lunar Phases - NAAP
UNL Astronomy
Background 2/6 - Lunar Phases - NAAP
Moon Clip Art ...
Britannica
Phase | Definition, Examples, & Facts ...
--- end quote of Google Search---
Archimedes Plutonium Feb 1, 2026, 3:37:57 AM to Plutonium Atom Universe newsgroup.
So I see the full moon on 31January 2026 at a position NorthEast at 6PM. I wait hours later, for 3AM and see the full moon almost SouthWest where the Sunset was on 31January.
Explanation: I am on a round Earth rotating on axis in every 24 hours. As the sun set on 31Jan the moon was full in NorthEast, but as the night moves on by 3AM I am far enough in Earth's rotation by 1Feb2026 to see the full moon nearly in the SouthWest location.
The only feasible explanation for this would be that Earth is round and rotates on axis.
In Logic we learn a valuable principle called Occam's Razor. It basically says that the easiest explanation for events is often the true explanation. We could conjure up theatrics of saying Earth is flat and Sun revolves around Earth, but such theatrics cause the speed of the Sun in motion to approach the speed of light, and makes that explanation be far far fetched.
Archimedes Plutonium Feb 1, 2026, 9:09:06 PM to Plutonium Atom Universe newsgroup.
The only sensible explanation for why the Moon is a full moon, appearing NorthEast at 6PM, 7PM then appearing SouthWest at 3AM is that of the passage of nighttime, me as observer is moving counterclockwise from West to East.
Sensible becomes the same as being ___logical___.
This proves the Earth is Round, a big ball rotating on its axis.
Now there is a far easier proof the Earth is round when we see the earth eclipse the Moon we see Earth's curvature as a round ball in a Lunar eclipse. The trouble with that though, is lunar eclipses are rare compared to almost every month you see the full moon. And the curve of Earth round is rather vague, too vague for me to have confidence in the arc curve of Earth. But the moon phases are frequent and every month and unmistakable. When doing Logic, you like to have data that is clear and not vague.
In order to explain the full Moon at 6-7PM being NorthEast then a few hours later being SouthWest is easy as in Occam's Razor that the Earth is spinning on its axis in the 12 hours of nighttime shifting the Moon from NorthEast to SouthWest as the night progresses.
To explain this shift from NorthEast to SouthWest as a Flat Earth which is stationary and the Sun moving around Earth in revolution orbit, would require the Sun to approach the speed of light as well as the Moon moving at such unbelievable rapid speed yet so far away.
The only other explanation and argument that needs our attention, is how does a Round Earth, moving in Space keep people from falling off into space. And here the argument of logic will be the Lodestone, the magnets and static electricity found by Thales in Ancient Greek times.
We have to address this problem, because it needs attention. If Earth is round, what is to keep things from falling off Earth???
Actually, it is far easier to explain the force of gravity that holds all material to the surface of Earth than it is to explain the motion of Sun, planets and moons, in my humble opinion. So that the Ancient Greeks could have explained the force of gravity as a form of electromagnetism which is even more advanced than our present day physics classes teaches, for they have not yet unified the four forces of physics, showing that gravity is a EM force.
Thales and Archimedes and Eratosthenes and Aristarchus all high powered geniuses in Ancient Greek times could easily have anticipated all of Newton, yes, they could have anticipated all of Newton on gravity and then some, for Newton did not unify gravity to EM force. Probably because he, and most all modern day physicists could not see that electricity is all attract and no repel, for there is a Pauli Exclusion Principle that looks like repel but is rather instead ___ no occupation of same space___. Dull people cannot understand no occupation of the same space is far different, far far different, from repel.
--- quoting Wikipedia on Lodestone magnets---
For a general description of the mineral itself, see Magnetite.
For other uses, see Lodestone (disambiguation).
Lodestone attracting some iron nails
Lodestone in the Hall of Gems of the Smithsonian
Lodestone attracting small bits of iron
Lodestones are naturally magnetized pieces of the mineral magnetite. They are naturally occurring magnets, which can attract iron. The property of magnetism was first discovered in antiquity through lodestones. Pieces of lodestone, suspended so they could turn, were the first magnetic compasses, and their importance to early navigation is indicated by the name lodestone, which in Middle English means "course stone" or "leading stone", from the now-obsolete meaning of lode as "journey, way".
Lodestone is one of only a very few minerals that is found naturally magnetized. Magnetite is black or brownish-black with a black streak, with a metallic luster and a Mohs hardness of 5.5–6.5.
Origin
The process by which lodestone is created has long been an open question in geology. Only a small amount of the magnetite on the Earth is found magnetized as lodestone. Ordinary magnetite is attracted to a magnetic field as iron and steel are, but does not tend to become magnetized itself; it has too low a magnetic coercivity, or resistance to magnetization or demagnetization. Microscopic examination of lodestones has found them to be made of magnetite (Fe3O4) with inclusions of maghemite (cubic Fe2O3), often with impurity metal ions of titanium, aluminium, and manganese. This inhomogeneous crystalline structure gives this variety of magnetite sufficient coercivity to remain magnetized and thus be a permanent magnet.
The other question is how lodestones get magnetized. The Earth's magnetic field at 0.5 gauss is too weak to magnetize a lodestone by itself. The leading hypothesis is that lodestones are magnetized by the strong magnetic fields surrounding lightning bolts. Magnetite is a ferrimagnetic material, so a lightning strike can align its magnetic domains and create a lodestone. This is supported by the observation that they are mostly found near the surface of the Earth, rather than buried at great depth.
History
One of the earliest known references to lodestone's magnetic properties was made by 6th century BC Greek philosopher Thales of Miletus, whom the ancient Greeks credited with discovering lodestone's attraction to iron and other lodestones. The name magnet may come from lodestones found in Magnesia, Anatolia.
--- end quoting Wikipedia on Lodestone magnets---
So, on 1Feb2026 a full Moon was seen NorthEast at 7PM, then 2Feb this full Moon was seen SouthWest at 4AM. Did it make a continuous trek across the night sky??? It was too cloudy to tell. Some clear night I should observe the Moon if it is a continuous trek from NorthEast to SouthWest.
So a lunar eclipse on average is about 2 a year is too rare to prove Earth is round. Besides, even if you see a lunar eclipse, it is hard to see a Round ball Earth on the moon and open for debate among observers. Some may swear that this is the easiest proof other than sailing around the globe or flying around the globe before that was possible.
My opinion, given lunar eclipse is rare, 2 per year, and given it is a judgement call you are seeing a curved Earth as ball, that the Moon phases which occur every month of the year is a far better logical proof of Earth is round and spinning on its axis.
I would have posted a picture of a lunar eclipse, but could not find any with a clear curved Earth.
As for the question of the trek of the Moon from 7PM to 3AM is continuous in the night sky, I ask myself the question of whether the moon lies in the same plane that the Sun and Earth form a plane called the Ecliptic.
So if the moon is in the very same plane, we would not have Full Moons as the Earth would block that phenomenon. Looking it up, I see the Moon is off of the ecliptic by 5.14 degrees. Apparently 5 degrees off the plane formed by Earth and Sun is enough off-plane so that Full Moons are commonplace.
This would mean that a continuous full moon from 7PM through 3AM treks from NorthEast to SouthWest.
The start of physics really started in Ancient times by observing star and planet and Sun motion. The vital questions of --- Is Earth Round and moving was impeded by the question, if round, how do you keep from falling off.
Both questions can be solved and answered by Ancient Greek times of Thales, Archimedes, Aristarchus and Eratosthenes, by watching the motion of the Moon in its phases and by referring to the magnetic Lodestone to keep Earth together and people not falling off.
Also, the start of Math and Logic in Ancient times with Pythagorus, Socrates, Aristotle coincided with Thales, Archimedes and physics.
15) The Universal quantifier.
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.
So here we go back to our lesson in calculus as we follow the function such as the identity function Y= x. And relate to the Existential and Universal quantifiers. The existential is the fact that every x point exists. In the 10 Decimal Grid with __integers only__ every number 0,1,2,3,4,5,6,7,8,9,10 exists. Each individual number exists and the derivative is such that it goes from 0 to 1 picking out a unique y-value. This is Existential quantifier. For the Universal quantifier, every integer from 0 to 10 is included in the function graph, as it moves from 0 on through all those integers to 10. The Existential quantifier is the derivative dy/dx while the Universal quantifier is multiplication, the integral, the area under the function graph.
Existence goes together with Universal. Now we go back to Madame Emilie du Chatelet 1706-1749 doing a superb science experiment following the Dutch physicist Gravesande with his experimental proof that kinetic energy is mv^2, quite different from momentum as mv.
So we have Newton with his Universal law-structure of Gravity F=G(m_1 times m_2) / distance^2.
Gravesande sets up the experiment of dropping lead ball to fall on clay and making a depression in the clay. Of course Earth is mass_1 and the lead ball is mass_2. If the depression hollow left after the ball strikes the clay is shallow then the gravity law-structure follows momentum mv, but if the depression is deep then it follows mv^2 and the Newton Universal law-structure of Gravity is upheld. Even Newton 1642-1727 benefited from the Gravesande experiment when Chatelet's experiment follow-up and write-up of the experiment, proving that Newton's momentum mv was not true but rather mv^2 was true.
The Gravesande-Chatelet experiments were 2 existential instantiations EI of the law-structure of gravity. Now as more experiments of the same kind are reported then that elevates the law-structure of gravity to Existential Generalization EG. Now we go the reverse and say that because of EG that gravity is a Universal law-structure UG, Universal Generalization. Now someone questions the Universal structure as to whether gravity is consistent with other law-structures such as Coulomb law-structure which has a similar math formula. The questioning becomes severe and so a new experiment involving electricity into the Gravesande-Chatelet experiments is formulated. Some physicists build a new experiment to test the question. This is Universal Instantiation UI, upon gravity, can it hold up with a new experiment? If yes, then gravity is even further credited as UG. If the new experiment has glitches then a new evaluation of gravity as given by its formula takes place. What I am saying here in this paragraph is recognition that the Scientific Method itself is a form of EI, EG, UG and then UI. Review the steps of the Scientific Method.
Existential quantifier are the experiments, numerous experiments. The Universal quantifier, the All or Every is tested by the experiments.
Universal quantifier is related to AND connector.
---------------------------------------------------------------
However, and surprisingly, the Universal quantifier is also related to the AND, or addition connector of Logic. 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 law-structures of Physics and Science such as gravity, or Coulomb or Faraday or Ohm or Ampere. In biology, the law-structure of DNA as genetics or Cell theory. Again, in physics the law-structures of quantum electrodynamics. In Chemistry, the law-structure of the Periodic Table of Chemical Elements. In chemistry and physics the law-structure of Atomic theory.
But how are these Universal law-structures 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 law-structures 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-structure of science. The crucial part is to do an Experiment. Now if one person formulates a law-structure with a math formula and does an experiment and shows the results match the predictions, is not yet a law-structure 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 new law-structure 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-structure of science. There is a caveat to this, though. It could be that some future experiment on the law-structure turns up some unknown data that calls the law-structure 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-structure 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 law-structures of science are "universal law-structures". 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-structure of K(q_1*q_2)/d^2, and never any exceptions. Law-structures 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.
And now, 6 connectors are sufficient to describe the science of ideas-- Logic.
So, now, let me enumerate the 6 Law-structures of Logic Connectors.
Structure of Existential quantifier: There exists something is formed by the best available science on the subject topic. This comes from math derivative of calculus as dy/dx and also is coupled to If-->Then as division. 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.
Structure of Not-Equal: Not is a reversal of a given statement while equality is identical sameness of two statements. For Equality, 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.
Structure of AND: Joins together several statements p,q,r,s, etc of Logic and is a collective true statement provided at least one of the statements p,q,r,s, etc is true. The AND connector allows falsehoods and nonsense talk to enter arguments. And the truth comes from the pertinent science surrounding the statements. AND comes from addition in arithmetic.
Structure of OR: Removes or discards ideas or subtracts one idea from another idea represented by p,q,r,s, etc. OR is the opposite of AND that joins together statements. OR removes something, be it a statement or the subtraction of one statement with another statement. OR is the connector of Deciding Experiments in science and as such allows variable truth value "dT" being a fraction of truth between 0 and 1.
Structure of If-->Then: I like to think of If--> Then from calculus graph where we slowly move down the x-axis and graph the next coordinate point. P Moves Into Q is the best way of thinking about If P then Q. Given statements P and Q that P moves into Q. The structure 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 __only the T row__ define the connector.
Structure of Universal quantifier: The Universal quantifier comes from the Existential and the two of them are duals of one another. If you take physics you will learn more and more about duality, but not here. We do numerous experiments and find all of them obey a formula. The experiments exist and once we have a number of them we elevate the idea to be a universal structure through this process of Existential Instantiation, Existential Generalization, Universal Instantiation, Universal Generalization.
So we see that the Scientific Method has its parts being that of Existential Instantiation, as a science observation then the start of a experiment. Then the Existential Generalization of more experiments validating the first experiment and more observations. Then the Universal Instantiation which has a new experiment test out other experiments gone before. Finally the Universal Generalization that these experiments collectively form a universal law-structure of science.
Counterexample Argument
-----------------------------------
Now we talk about a argument that plays on the Universal quantifier with attention placed on the Existential quantifier. It is called in mathematics, proof by counterexample. In logic it is just called the counterexample argument.
It is often used in science, less so in ordinary speech. It is perhaps the easiest proof method in mathematics. For example: A math person says "All triangles can be doubled and formed into being a rectangle". Which is not true and a counterexample is quickly forthcoming. Which says, "A equilateral triangle of all three sides equal when doubled and reformed will not make a rectangle but rather a rhombus".
People make the mistake of counterexample when they use universal quantifier of All or Every, when they should be using Some or Many. And the counterexample is the Existence of something that refutes the All or Every universal statement.
Archimedes Plutonium May 5, 2026, 2:49:21 AM to Plutonium Atom Universe newsgroup.
Alright in this Elementary Logic textbook I have spent no time on doing proofs by counterexample. In math we would call it a counterexample proof. While in Logic using our glossary of terms it is called a "reasoned argument".
Mathematicians love using a counterexample to prove something. And in college, myself in 1968-1972 in logic class this was often used.
The idea is --- if someone makes a reasoned-argument that holds a key idea of a Universal quantifier. And then, if someone voices a counterexample, the existence of something that refutes the universal then the key idea is wrong.
Example:: All birds fly. Counterexample-- the ostrich. Thus some birds fly but not all birds fly.
So what I want to do now is prove that OR connector is not commutative nor is it associative by using this method of Counterexample.
And I distinctly remember Logic class we had ample training in knowing this method. I remember the teacher saying to this day 54 years later--- a universal idea is immediately false if you can find a Counterexample.
So the Premiss is this "The OR connector is commutative." Next, the premiss is this "The OR connector is associative."
So let me see if I can come up with a counterexample for both.
I am going to look for Counterexamples with a element of Time involved in the statements that form the premiss.
Remember in Logic, the hierarchy of terms is this.
Statement
Premiss
Connector structure
Reasoned argument (syllogism)
Equalities
Law-structure
Remember that a statement is simply a idea. A premiss has to be only true ideas. True as checked and validated by the best science on the subject matter.
So here the question involves equalities of logic. Is P OR Q = Q OR P , is the commutative always true? And, is ((P OR Q) OR S) = (P OR (Q OR S)) true, the associative?
If I can find counterexamples then they are no longer equalities.
I am going to look for a time element involved in the premisses to prove OR is false for commutative and associative.
Premiss:: The summer of 2025 where I live was a normal summer with rainfall OR the summer of 2026 is a drought summer.
Now that is a valid premiss because the P part of P OR Q, is true --summer of 2025 was normal rainfall, but the summer of 2026 has yet to be revealed for it is in the near future.
Now let me take the Commutative of that premiss.
Premiss:: The summer of 2026 where I live is a drought summer OR the summer of 2025 is a normal summer.
Again that is a valid premiss because the Q part is true.
But this is not yet working out as a counterexample.
Let me try this one out for I mirror-reflect the counterexample of mathematics 10 - 2 versus 2 - 10.
A Caltech astronomer has 9 -1 planets OR a Caltech astronomer has 1 - 9 subplanets.
What I am doing here is-- I am trying to find a CounterExample for the commutative and associative equality of OR. In Math, addition and multiplication are both commutative and associative. I have not yet figured out if OR is or is not commutative and associative.
By the way, I should also figure out if when being not commutative, it is impossible to be associative.
So to find out, I need at least one counterexample to make a proof.
_Let me try this one out for I mirror-reflect the counterexample of mathematics 10 - 2 versus 2 - 10.
P OR Q
_A Caltech astronomer has 9 -1 planets OR a Caltech astronomer has 1 - 9 subplanets.
Is that a Counterexample? A Caltech astronomer has 1-9 subplanets OR a Caltech astronomer has 9-1 planets.
You see, I modeled that after math noncommutative 9-1 does not equal 1-9. For in truth, no negative numbers ever existed in the first place when you have an axiom of math saying you can never remove more than what is available to remove (subtract) and mathematicians who believe in negative numbers are in a Fantasy Fairyland Bubble.
The most silly mistake AP has made in Logic, when it is all so simple and clear. So there I was, almost at the end of writing the textbook Elementary Logic. With only one spot to clean up and done with the book. I had to prove that OR, disjunction was either commutative or not commutative. And over a year now I was battling that question. All the other textbooks on logic say OR is commutative, even Copi and even Wikipedia says OR is commutative. But the trouble with that is that mathematics says that OR which is subtract in math is Noncommutative.
So, since 2025 I have been battling this issue. One month I would argue OR is Noncommutative then a month later concede it was commutative because looking at the truth tables alone of exclusive OR it is true for T OR F and true for F OR T.
Finally, coming down to the wire here in May 2026, for I desperately need to finish this textbook and cannot do that until this issue is settled.
Is OR commutative?????
And can a connector (operator in math) be associative if it is non-commutative?????
Two issues remaining. And just last week I was sure and certain that the resolution can be found by the method of CounterExample. And looking at my textbook I had not dwelled on the method of Counterexample and that certainly would be a shortcoming of this logic textbook.
But today, 6 May, I have a clear mind that I can resolve all these issues and finally be done with this textbook.
SOLVING the question of OR is Non Commutative and Non Associative, including IF-->Then is the same as OR
------------------------------------------------------------------------------
This is AP's worst mistake ever, in doing Logic science. Mistake because the answer is really so simple that it is a total embarrassment for me to have spent so much time in solving the problem. Just yesterday, I thought the above Premiss of astronomer 1-9 subplanets or 9-1 planets was a CounterExample.
Proof that OR is Non Commutative
The trouble here is a word language problem. OR is math's subtraction. However the word "subtraction" is a hideous word that leads everyone astray. The true word or term that math and Logic OR should have adopted and used is Remove. Math should have Add, Remove, Multiply, Divide. We can easily interchange the word AND for Add. In logic just use Add whenever you need to use AND. But what word can we replace OR with that is accurate for what it does? The answer is "remove".
We can say in math that of "Add 2 to 3", also we could say 2 AND 3. In math we can say "10 remove 4" but we cannot say "4 remove 10" because that violates a Axiom of math that Old Math was too dumb to realize it exists. The axiom that says you cannot take away more than what is available to remove or take away.
So, what is the Proof that OR is Non Commutative???
P OR Q
P = 10 with Q = 4.
Since OR is the same as the concept Remove we have this.
P remove Q, thus 10 remove 4 = 6.
Now, someone asks for Q OR P.
Q remove P, thus 4 remove 10, impossible, hence OR is Non-Commutative.
Proof that AND plus Not-Equal are Commutative and also Associative.
P AND Q is P add Q
P = 10, with Q = 4 and S = 1 for commutative and associative and since that is true in math it is true in Logic. Using those numbers, we show OR is non-associative.
Proof that If-->Then is Non-commutative and Non-associative
----------------------------------------------------------------------------------------------
P = 10, Q= 6, S = 3
P divide into Q is not the same as Q divide into P.
((P divide into Q) divide into S) is not the same as (P divide into (Q divide into S))
(Note to student, in a statement with parentheses, you have to do the inner most parentheses first, before the outermost parentheses)
So, well, that is settled, but, now, my textbook is deficient on talk of the proof method of CounterExample, and so I need to go back and look up a fine example of this proof method and include it in this textbook --- Elementary Logic.
So I have to go back and add on counterexample ideas for it is an important proving mechanism, especially in math.
Here is an old example of where a proposed counterexample is actually wrong and where the AP proposed proof is correct.
1) Proof that 1 is the Only Odd Perfect Number.
PROOF THAT THE NUMBER 1 IS THE ONLY ODD PERFECT NUMBER FOR THE
POSITIVE INTEGERS (1P). 1P was the oldest (or second oldest) unsolved
problem of mathematics until now. No mathematician until now has proved
1P.
PROOF: It is seen that a perfect number is a number p which the sum of
all its factors excluding itself equals p, and including itself equals
2p. Thus 1,6,28,496,8128, . . . are perfect numbers. The number 1 is
odd perfect since the factor 1 equals itself, and the factor 1 add 1
itself, equals 2. Representing perfect numbers in rational form since
the operations of division, multiplication, and addition are used in
the definition of what a perfect number is. Thus for 1 gives 1=(1/1)+0,
and for 6 gives 1=(1/2)+(1/3)+(1/6) and for 28 gives
1=(1/2)+(1/4)+(1/7)+(1/14)+(1/28). After 1, the next odd number is 3,
suppose 3 is perfect, so 1/3 and what rational numbers are needed to
make the sum equal to 1. No matter what these rational numbers are,
their combined sum must equal 2/3. So any combination of rational
numbers must add to 2/3 and so the 2 in the numerator requires when
finding the smallest common denominator which must equal to 3, that 2
is one of the factors of 3, because the combination of rational numbers
in order for all the numerators of all the terms to equal 1 puts a 2
in the denominator, implying 3 is even, a contradiction, so 3 is not
perfect. After 3, the next odd number is 5, suppose 5 is perfect, so
1/5 and what combination of rational numbers are needed to make the sum
equal to 1 is 4/5. No matter what these terms are (for example, for 28
these terms were [(14/28)+(7/28)+(4/28)+(2/28)], which is equal to
27/28, which when the numerators are changed into 1 where the
denominator is the smallest common denominator which has to equal 28)
their sum must equal 4/5 and so the 4 in the numerator requires when
reducing all the terms where the numerators of all the terms are
converted to the number 1, implies that a factor of 2, since 4 is even,
and thus a 2 is a factor of the denominator, but the denominator is the
odd number 5, a contradiction, so 5 is not a odd perfect number.
Applying the same argument to the next odd number after 5 which is 7,
and so on. Thus any odd number other than 1 in rational representation
requires that odd number subtract one for the numerator, and when
converting the numerators to terms of 1, implies the factor 2 since the
numerator is an even number, will go into the smallest common
denominator, implying that the original odd number is even, a
contradiction. A last example: take the number 105 and suppose it was
perfect, then 1 = 1/105 + (104/105). The term (104/105)= (x/105 +
y/105 + . . +z/105). The factor of 2 which is in 104 will go into the
denominator in eventually forming the smallest common denominator, just
like in the perfect number 6 where 1/6+5/6 is equal to 5/30 + 25/30 in
cross multiplication, likewise for 105 in cross multiplication,
104/10920 + 10816/10920 where the term 104/10920 implies that the
denominator is factorable by 2, then when converting all of the
numerators into 1 with the denominator as the smallest common
denominator which is 105 implies that 2 is a factor of 105, but 2 is
never a factor of 105 nor is 2 a factor of any odd number, thus a
contradiction, thus 105 is not perfect. Therefore 1 is the only odd
perfect number for the positive integers. Q.E.D.
The numbers 1 and -1, and 6 and -6 are the only four numbers which are
absolutely perfect. Because 6=3x2x1, 6=3+2+1, -6=-3x-2x-1,
-6=-3+-2+-1, and 1=1 and -1=-1. The number 28 and the other larger
perfect numbers are not absolutely perfect since 28=7x2x2x1, but
7+2+2+1=12.
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From:
Ludwig.P...@dartmouth.edu (Ludwig Plutonium)
Subject: Re: 1 IS THE ONLY ODD PERFECT NUMBER PROOF
Date: Mon, 23 Aug 1993 10:46:43 GMT
In article <2515i0$
9...@paperboy.osf.org>
ka...@dme3.osf.org (Karl Heuer) writes:
> You seem to be saying that the sum of odd/odd rationals cannot yield an even
> numerator. Here is a counterexample: 1/3 + 1/5 = 8/15.
No I do not mean that. What I mean is that if an odd number is perfect,
then when put into rational number representation, that the denominator
will have to be simultaneously odd and even, contradiction, proof.
Archimedes Plutonium May 7, 2026, 12:27:19 AM to Plutonium Atom Universe newsgroup.
Here is an example of a Counterexample in my proof of Collatz Conjecture.
World's First Proof of Collatz Conjecture// Math proof series, book 6
by Archimedes Plutonium (Author)
This is AP's 19th published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe And, early on, I noticed there was a need for a sequence that has the opposite behavior of Collatz-- internal trap of spinning around or divergence to infinity. Funny how no mathematician tackling Collatz ever seemed to look for a counterexample sequence like 5N+5 to compare to 3N+1.
Seeing the structure of 5N+5 and wondering how that can have internal spinning around in a trap and how it can diverge to infinity, and wondering why 3N+3 avoids all of that.
So, seeing there has to be two primal slides involved, I proclaimed the real Collatz conjecture involved 3N-3, 3N-1, 3N+1, 3N+3 written as 3N+-1 simultaneously 3N+-3. And that a conjecture on 3N+1 stand alone is not a viable conjecture. It is like saying 5N+5 never converges in any run to 1.
Alright, I should discuss this type of Collatz of 5N+5, for it shows us how a Collatz can have a "spinning around inside trapped in a spin". Such as 9 with 5N+5
9;;9, 50, 25, 130, 65, 330, 165, 830, 415, 2080, 1040, 520, 260, 130, 65, and spinning around endlessly.
Now let us check out 99 with 5N+5 and see if it diverges to infinity.
99;;99, 500, 250, 125, 630, 315, 1580, 790, 395, 1980, 990, 495, and as can be seen it keeps diverging to infinity, never descending.
Archimedes Plutonium May 7, 2026, 12:37:20 AM to Plutonium Atom Universe newsgroup.
Here is another example of the use of Counterexample, only this time Karl Heuer is correct and straightening out Detlef Bosau.
My legal name at that time, 1994 was Ludwig Plutonium when this was posted to sci.math in 1994. Mind you I was testing people in sci.math to see if they could give a valid proof of Euclid's Infinitude of Regular Primes. For my proof of infinitude of Twin Primes was a mere tweaking by adding and simultaneously subtracting 1 from "multiply the lot".
Karl Heuer gives a correct Euclid IP, indirect method
Date: Sun, 20FEB1994, 21:05:13 GMT
Newsgroups: sci.math
Subject: INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS
Lines: 36
Sender:
k...@spdcc.com (Karl Heuer)
k...@ursa-major.spdcc.com (Karl Heuer) writes:
In article (
5JChA8g2...@jojo.escape.de>
det...@jojo.escape.de (Detlef Bosau) writes:
>
Ludwig.Pluton...@dartmouth.edu meinte am 18.02.94
>>
det...@jojo.escape.de (Detlef Bosau) writes:
>>>Wrong. Your two numbers are not necessarily prime
>>NO, YOU ARE WRONG. Those numbers are necessarily prime, due to
>>UPFAT, all the primes that exist in the finite set leave a remainder
>>of 1.
>I'll give you a lesson of elementary arithmetics. . .
I really shouldn't bother to get involved in this discussion again,
but
Ludwig is right. In logical terms, his key statement is "if P is a
finite set containing all the primes, then prod(P)+1 is prime." This
is
a true statement.
Let's step through your alleged counterexample:
>consider your set of primes to be: {2,3,5,7,11,13}, as I assert 13 to be
>the largest prime. [. . .] Now, you made the assertion, that
> > > > (2x3x5x11x13) + 1 [=30031] must be prime.
Yes, it's true that if 13 is the largest prime, then 30031 is prime.
Do
you disagree with that assertion?
>As you stated before, there exists an unique prime decomposition of
>30031. This is 59x509. It could be easily shown, that 59 and 509
>both are prime.
If 13 is the largest prime, then 59x509 is not a factorization of
30031.
--- end quoting Karl Heuer's post of 1994 ---
What Karl was pointing out to Detlef was an error in logical thinking. People in math are good at computation, but rarely good at logical coherent thinking for doing math proofs.
So I had a proof of Infinitude of Twin Primes by 1991 and started to broadcast it to the world general public by Usenet sci.math.
But troubles and problems appeared in 2009 and later. One problem was infinity concept was not well defined in Old Math, but made clear in New Math. The second problem is that I was working on Logic and found that the proof method of Reductio Ad Absurdum, (the indirect proof method) was not a valid math proof method. So my Old Math proof of suppose primes finite, reach a contradiction, then claim they must be infinite was not a valid proof. The logic truth tables of If-->then was such that it was TFUU with U being uncertain. Old Math was operating on a truth table of If-->then as TFTT. Quite a bit different from a truth table of TFUU.
Third problem in the decades after I proved prime conjectures and found the true numbers of mathematics are not the Reals, but instead are the Decimal Grid Numbers, which threatened to even make the concept of Primes as fake and vacuous. I discovered the true numbers of mathematics were Decimal Grid Numbers while writing my book series True Calculus in 2013.
This example is found in my proof of Kepler Packing.
World's First Proof of Kepler Packing Problem // Math proof series, book 3
by Archimedes Plutonium
This is AP's 24th published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe Preface: There has been an alleged proof of KPP by Thomas Hales, but his is a fakery because he does not define what infinity actually means, for it means a borderline between finite and infinite numbers. Thus, KPP was never going to be proven until a well-defined infinity borderline was addressed within the proof.
--- quoting my 24th book---
One of the signs or signals that the below proof of the Keplerian 3D Packing and the Gaussian 2D packing is that both use the very same method of proof, whereas in our times, these alleged fake proofs are not able to incorporate the same method of Gauss in 2D from 3D. So this is the very highest
indication of alleged proof but in fact is fakery. If your 3D is not able to prove 2D, then you are pushing a fake.
Secondly the tell tale sign of a true Kepler Packing Proof is that it is do-able as a physical demonstration. In the below we can pack circles, spheres, oranges, ball bearings, magnetic circles and show the higher density of Corner-Edge-Hex or Corner-Edge-Hexagonal-Close-Pack or Oblong Hex or Oblong Hexagonal Close Pack in both 3D and 2D.
A physical demonstration of a more dense pack than the pi/sqrt18 is a CounterExample.
This maybe the first time that a Physics Experiment proves a unsolved Mathematical Conjecture, for which the mathematics community was unable
to prove in the Kepler Packing Problem and shows it to be wrong. Wrong because the most dense packing in both 3D and 2D Euclidean is the Oblong HCP or Oblong Hexagonal combined with the Corner Edge technique
respectively.
Call this proof the "Education of Archie on KPP" up till now. I had a mindblock
and bet most everyone else has this same mindblock when it comes to both KPP and Gauss's 2D version. The mindblock or paradox is that we think that N^3 number is larger than the number of spheres in KPP given any N. Well it is true for small N. Because 3^3 and no more than 27 spheres can fit in that cube or that 8^3 and no more than 512 spheres can fit in that cube. Likewise in 2D that no more than 9 circles can fit in 3^2 or no more than 64 circles can fit in a square 8 by 8. This is a mindblock that most everyone comes into packing problems with this paradox. They think and I thought that N^3 or N^2 was always larger than the number of spheres or circles in that packing.
Well at 10, which is the magic number, the experiments I conducted show
quite clearly that the number of spheres in a 10Cube are more than 10^3 and the number of circles in a 10Square is larger than 100. Most everyone that enters Packing enters it with the misconception that N^3 or N^2 are upper
limits to how many spheres and circles can be contained in 3D or 2D respectively. But at the integer 10 (it maybe 9 since my ruler is not that precise) that there is more spheres or circles than the N^3 or N^2 and the reason for this is due to the nesting inside of hollows of lower layers. And the reason for our misconception is due to our visualization that 10^3 or 1,000 small unit cubes completely tile the big cube with no holes or gaps in between those small unit cubes. Contrarily we visualize all those holes and gaps in the spheres or circles and we have a hard time of realizing that there could be more spheres and circles than unit cubes or unit squares.
This maybe the first time a Physics Layout of Data proves a Mathematical
Conjecture.
Experiment and Results: I have uniform magnetic circles of 25mm diameter.
Either at 9 or 10 for sure, is there an extra row of circles due to the hollows
of the hexagonal packing.
I need only show the Gaussian 2D Packing for it proves not only 2D but also
Keplerian 3D with spheres. The data is transferable from 2D to 3D.
I also have marbles but not of uniform size but close enough to gain this data:
HEX stacking pattern yield this data:
3Sq = 8 N^2 = 9 circle status = -1
4Sq = 14 N^2 = 16 circle status = -2
5Sq = 23 N^2 = 25 circle status = -2
6Sq = 33 N^2 = 36 circle status = -3
7Sq = 46 N^2 = 49 circle status = -3
8Sq = 60 N^2 = 64 circle status = -4
9Sq = 77 +8 N^2 = 81 circle status = +4
10Sq = 95 +10 N^2 = 100 circle status = +5
11Sq = 116 +10 N^2 = 121 circle status = +5
Notice that the number of circles at 9 changes from a negative status to a positive status due to the adding up of the hollow-nesting.
For about a week now, I have been looking for a function or equation to describe the Core Hex or Core HCP stacking but in that quest, I was under the misconception that it was always smaller than N^3 or N^2
I no longer need to find any such function or equation. The physical data proves the Gaussian 2D and the Keplerian 3D.
Archimedes Plutonium May 7, 2026, 3:24:54 AM to Plutonium Atom Universe newsgroup.
Now Karl Heuer is a very very smart gentleman and rarely makes mistakes. So that forces me to go back and see if my explanation was all screwed up causing Karl to make a mistake.
And here is a revised edition to clarify my proof of No Odd Perfect Number, except 1. So Karl made the mistake because I was just not clear enough in my proof.
Logic needs clarity at all times.
PROOF THAT THE NUMBER 1 IS THE ONLY ODD PERFECT NUMBER FOR THE
POSITIVE INTEGERS (1P). 1P was the oldest (or second oldest) unsolved
problem of mathematics until now. No mathematician until now has proved
1P.
PROOF: It is seen that a perfect number is a number p which the sum of
all its factors excluding itself equals p, and including itself equals
2p. Thus 1,6,28,496,8128, . . . are perfect numbers. The number 1 is
odd perfect since the factor 1 equals itself, and the factor 1 add 1
itself, equals 2. Representing perfect numbers in rational form since
the operations of division, multiplication, and addition are used in
the definition of what a perfect number is. Thus for 1 gives 1=(1/1)+0,
and for 6 gives 1=(1/2)+(1/3)+(1/6) and for 28 gives
1=(1/2)+(1/4)+(1/7)+(1/14)+(1/28).
Notice in the even perfect numbers starting with 6, that the numerator has to end up with 5/6 + 1/6 to equal 1 and notice the 5 odd number before we add 1 to it, to be 6/6 = 1. Apply that idea to odd perfect numbers such as say if 3 were odd perfect you end up with 2/3 + 1/3 = 1. Or, contemplate 5 being odd perfect you end up with 4/5 + 1/5 = 1. So the most simple proof that no odd perfect number except 1 exists, plays on this numerator issue, for an even perfect, the numerator is odd before you add 1/n and for odd perfect the numerator is even before you add 1/n.
And for the even perfect numbers 6, 28, 496, for that numerator to be an odd number means that you have to add both even and odd numbers in the case of 6, we had 3/6 + 2/6 = 5/6. You cannot add two odd numbers to make an even numerator. In the case of Odd-perfect numbers beyond 1 itself, then you have to have a even number numerator in at least two even numbers of the summands in order to end up with a even number numerator. Suppose 7 was odd perfect then you need to end up with 6/7 + 1/7 to be odd perfect. And there comes the crisis, on how in the world can 7 have two even number factors. With Even-perfect number the numerator needs to be an odd number and thus, adding two odd numbers is even, adding two even numbers is even, but adding a odd with even is odd.
What proves No Odd Perfect number beyond 1, is the arithmetic fact that a Odd Perfect number is divisible and has a factor of a even number.
But I am not finished with this proof in a logic textbook. There is another very important issue that Logic needs to focus upon. The conjecture of No Odd Perfect number except 1 is a fairly simple conjecture that most grade school students can understand, especially High School.
In my Logic textbooks I made a glossary of well defined terms.
So for **Science** we have Statement, Concept, Hypothesis, Law-structure, Theory, Universal Axiom.
For **Logic** we have Statement, Premiss, Connector-structure, Reasoning, Equalities, Law-structure (some call them principles).
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory
In Logic, the Law Structure or some call them principles are the last and most general term. Occam's Razor is a Principle in Logic and basically it says that the easiest explanation is the true explanation.
If we look at the conjecture of No Odd Perfect number except 1, is a easy super easy concept to understand for High School students. And Occam's Razor in logic has a reverse concept. Which says something like this. If you have a conjecture that is simple in ideas, then its proof in math or in logic will be a proof not much longer than the statement of the conjecture.
What this means is seen in the Proof of Pythagorean theorem which is about a paragraph long. And the actual proof is one simple picture proof.
This tells us, that the conjecture of No Odd Perfect Number except 1 is about 1 paragraph long. That means the proof of that conjecture is also Simple, easy and about 1 paragraph long.
In 1993 when I first appeared in sci.math and posted my math proofs. I could just as easily posted this one paragraph proof that 1 was the only Odd Perfect number.
Proof:: Suppose 7 was odd perfect then you need to end up with 6/7 + 1/7 to be odd perfect. And there comes the crisis, on how in the world can 7 have two even number factors.
Now I bring that up also, because mathematics has many con-artist clowns such as Andrew Wiles with Fermat's Last Theorem, FLT and Thomas Hales with 4 Color Mapping. I say con-artist clowns because when we apply Reverse Occam's Razor, that a valid proof is about equal in length and in concepts as the statement of the conjecture itself.
But, Andrew Wiles has some obnoxious100 to 200 pages of a fake proof and uses everything but the kitchen sink to try to prove A^n + B^n = C^n has no solutions when n =3 or higher.
Andrew was just too dumb of a math person, to step back, and contemplate--- look, the conjecture is simple and easy--- MEANS the proof has to be simple and easy. There is a symmetry involved.
Whereas AP in 1993 gave a valid proof of FLT. AP's proof is of equal length and as simplistic as the statement is simplistic. AP Proof:: For a solution when exponent is 3 or greater, implies there exists a number in math which has the property of A+A+A = A^3. The reason we have solutions in exponent 2 is because 2+2 = 2^2.
As for Thomas Hales, if he ever took logic and passed it, would realize you cannot prove something in mathematics when your concepts are ill-defined. Kepler packing involves infinity, and Hales was too stupid in math and logic to well define what infinity means. It means a borderline exists between finite and infinite. That borderline is where pi digits have 3 zeros in a row at the 1*10^604 decimal place value. A hexagonal closed-pack is not the best packing. See AP's Kepler Packing Proof. But the point with Hales and with Wiles, is they are illogical and their proofs in math are doomed to failure.
A huge problem in math and science is the journal system. Wiles was a editor for a math journal, and this allows corruption to be publish and accepted as true, when Wiles FLT is garbage nonsense and so is Hales Kepler packing. It is good that the Internet came along when it did in the early 1990s, for then, the corrupt journal publishing --- you scratch my back, I scratch yours, is the reason physics is so full of garbage--- black holes, dark matter, dark energy, neutron stars, .....
Archimedes Plutonium May 7, 2026, 3:52:10 AM to Plutonium Atom Universe newsgroup.
So I am looking for CounterExamples for Elementary Logic textbook. My examples from math above maybe above the heads of freshmen in college and I apologize for that, and the teacher may want to skip those examples. No, I need simple examples.
One simple example of Counterexample is this in biology.
Person A: All birds fly in the air.
Person B: Not true, here is a counterexample-- the ostrich.
Many textbooks of logic and Wikipedia like to cite this as an example of a Counterexample.
Person C: All prime numbers are odd.
Person D: Not true, here is a counterexample-- the number 2 is prime and even.
But AP says that primes in math, Old Math is fake math. The true numbers of mathematics are not the Reals but the Decimal Grid Numbers, and the concept of primes is nonexistent in Decimal Grid Numbers. The problem with primes, is that they are Not Well Defined because primes are not closed to division. Addition and multiplication of counting numbers is closed because given any two counting numbers, add them or multiply them yields another counting number (remember we are in counting numbers only). But take any counting number divide it by another counting number can yield no counting number, example 3/4, 4/3, 1/2, 10/3, etc etc. Primes are Not Well Defined over Division and that is why there is no general formula for primes and why primes never form a pattern. Primes are a garbage concept of Old Math. One of the essential reasons all math professors should take 2 years of college logic before they earn a degree in math.
A pretty example of Counterexample comes from geometry.
Person E: The slant cut of a cone is ellipse.
Person F: Not true, here is a counterexample for the slant cut of a cylinder is truly an ellipse and because cone and cylinder have different axes of symmetry, means the cone slant cut is a oval.
Archimedes Plutonium May 7, 2026, 5:31:12 PM to Plutonium Atom Universe newsgroup.
Examples of counterexamples
---------------------------------------------
In geology
Person G: Continental Drift plate tectonics is all about convection currents in plate tectonics and subduction of plates.
Person H: False, for here is a counterexample of the plates in Mexico vibrating forward and backward caused by Earth two cores as a electric motor that vibrates.
In astronomy
Person I: All the planets spin axis is nearly perpendicular to the Sun's ecliptic and Earth's tilt of 23 degrees is the worst tilt.
Person J: False, Uranus is a counterexample as the tilt of Uranus is almost 90 degrees making Uranus revolve around the sun on its side.
In physics
Person K: All single atoms are written by their letters such as He for helium, Li for lithium, C for carbon, O for oxygen.
Person L: False, for hydrogen is a counterexample, because H for hydrogen is a subatomic particle and for hydrogen as a atom is written as H2 for all atoms have to have at least one neutron. H by itself has only a proton with muon inside, so that when 2 hydrogens form H2, then that is a atom because one proton converts into being a neutron to the other as proton.
In chemistry
Person M: All water molecules have the chemical formula of H2O.
Person N: False, the counterexample is water molecules with formula H4O when chemists stop being lazy and stop their water electrolysis by checking on volume of hydrogen gas to that of volume of oxygen gas, too dumb and too lazy to actually weigh the mass of hydrogen compared to oxygen to see that water molecules are truly H4O.
In paleontology
Person O: All Smilodon, saber tooth cats had enormous upper canine teeth.
Person P: False, the counterexample is that no such cat upper jaw has ever been found with the saber teeth attached, especially from the La Brea Tar Pits, making the observing scientist wonder whether museums are gluing or screwing walrus tusks onto normal cat upper jaws.
In Logic
Person Q: All Venn Diagrams of the complement of the union of two sets is the same as the intersection of their complements which is a DeMorgan law.
Person R: False for there is a pretty counterexample to all of Venn Diagrams and all of DeMorgan laws which simply says when you have the true correct numbers of mathematics as the Decimal Grid Numbers which are discrete and have holes in between one number and the next number, forming Space into grids. Then the Union and complement and intersection all fall apart along with DeMorgan Laws.
* * *
* * *
* * *
Here is a 9 point space as a set. No-one can navigate that set with union or complement or intersection when all sets have empty space holes from one number to the next.
Now the counterexample is a excellent tool to use in a debate, especially in school team debates. I was never a member of a debate team but can easily imagine that if a debater slams an opponent team with a "counterexample" would score high marks for it. But make sure it is a correct counterexample.
Counterexamples can occur from descriptions where the speaker leaves out the universal clue of "all or every" that is the universal quantifier.
Examples: Person S: Plants bloom in Spring.
For which S is really saying All plants bloom in Spring.
Person T: Counterexample -- lilacs bloom in Autumn.
Person U: Ice is wet and cold.
For which U is really saying All ice is wet and cold.
Person V:: Counterexample "dry ice" is dry and cold for it is frozen CO2, a gas and does not melt into a liquid. If Person U had said water ice, he/she would be correct.
Person W:: Computers save us time.
For which W is really saying All computers save us time.
Person Y:: Counterexample: not when a bureaucracy demands you change passwords every 3 months and you forget those passwords or that the bureaucracy needs your computer to be updated with the latest newest browser and you do not feel like buying new every year.
Inverse Equality
-----------------------
Most know it by the name "inverse" but I often call it the "reverse" and sometimes even call it the "dual in duality" especially quantum mechanics physics where electricity is the dual (inverse or reverse) of magnetism.
Let me tell you a story when I was at University of Cincinnati earning my degree in mathematics 1968-1972. I studied Logic in my last two years and somewhere in my studies I came to the independent idea that there had to be an equality between Existential equals Universal with some factor involved. Much like energy in physics equals mass with the factor speed of light x speed of light. We know this equality today as E = mc^2. But what I had sought for was a equality where Existential was on one side of the equation and Universal on the other side of the equation with perhaps a factor in that equality. I sensed it existed when I was about 21 years old sitting in logic class at University of Cincinnati. I never found this equality, and only until recently while doing this textbook did I manage to find the equality. Let me see that is 2026-1972 = 54 years in the making.
Surprisingly the equality of Existential equals Universal is quite simple, and comes directly from mathematics the Calculus. In Calculus we have an original function and take the derivative of it, the dy/dx. Then we do the integral of the original function. Now, if we take the derivative of the integral we end up back with the original function. If we take the integral of the derivative we end up back with the original function. Earlier in this textbook we looked closely at the function Y-->x^2 and found its derivative is 2x and its integral is (1/3)x^3.
So again, take the derivative of (1/3)x^3 and see if it returns to the original function x^2. Then, take the integral of 2x and see if it returns to the original function x^2. The student may have to brush up and remind themself of the Power rule formula discussed earlier.
And this is of course the Fundamental Theorem of Calculus which simply says the derivative is the inverse of integral and the integral is inverse the derivative. One undoes the other to return to the original function.
Now we replace derivative and integral with Existential quantifier and Universal quantifier. The original function is the "science experiment". When we take the existential of the universal we return to the original science experiment. When we take the universal of the existential we are returning to the original science experiment that launched that experiment to be universal.
But science has more inverses than just derivative inverse to integral. Science has Existential inverse to Universal and has addition inverse to subtraction (remove) and has multiplication inverse to division.
We can write these equalities as this.
Addition = inverse[Subtraction]
Multiplication = inverse[Division]
Derivative = inverse[Integral]
Existential quantifier = inverse[Universal quantifier]
And we can actually prove this inverse equalities with function theory of math, which I will do in Intermediate Logic textbook. I feel I have burdened students enough in this textbook with calculus. I prove those inverse equalities in the next textbook of Logic--- Intermediate Logic.
16) Principle of Least Energy of Physics is the Occam's Razor Principle of Logic.
To refresh our memory of the most important terms of physics, logic and math, they are these.
So for **Science** we have Statement, Concept, Hypothesis, Law-structure (principle), Theory, Universal Axiom.
For **Logic** we have Statement, Premiss, Connector-structure, Reasoning, Equalities, Law-structure (principle).
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory.
On Sunday, February 8, 2026 at 3:27:26 PM UTC-6 Archimedes Plutonium wrote in Plutonium Atom Universe newsgroup:
Funny for me, in writing this for 1st year college or university textbook, for the first time I am able to link Occam's Razor to being an actual Principle of Logic rather than a mere rule-of-logic that works most of the time, but not all of the time.
A rule works only sometimes. A law-structure which some call a principle is universal and works all of the time.
A principle works all of the time! A principle is like a law-structure that works all of the time. Gravity always works between two given masses at a distance of separation, and Occam's Razor always works between an "event" occurrence and its explanation. The only times that Occam's Razor does not give the true explanation is when --- not enough facts are given surrounding the "event" in question.
If a person comes upon an event and asked to give an explanation-- the job and chore of many news reporters-- if they do not have enough facts and information, then they cannot assemble the truth by Occam's Razor. But if they have sufficient facts and data, then Occam's Razor as the most simple explanation is the true explanation works universally.
A rule is working much of the time but breaks down and is not universal.
Before this textbook, Occam's Razor was seen as a Rule, not a universal structure nor a principle.
And Occam's Razor is now seen as a principle.
Examples of some principles are the Least Energy, the Pauli Exclusion Principle, the Quantum Mechanics Principle of Duality or Complamentarity, the Principle of Superposition. There is a slight difference between principle and law-structure in that principles are often more descriptive whereas law structures are in motion and active such as gravity versus Occam's Razor. Law-structures such as Faraday, Ohm, Coulomb, gravity are active while duality, complamentarity, uncertainty, Occam's Razor appear to be descriptive and passive.
Note: Old Physics spells Complamentarity Principle as Complementarity, I find that horribly confusing so I spell it with a "a". Confusing with words like complement, compliment.
Even geology has a principle called the Principle of Uniformitarianism which means that the processes operating today on Earth were the same processes that operated in the past-- the present is the key to the past. And one can see this descriptive and passive view of principle versus law-structure. But we can always say principle whenever we say law-structure and vice versa.
Feynman describes the Principle of Least Energy as this, only he calls it the Principle of Least Action.
--- quoting Feynman in his "Lectures on Physics", 1964, volume 2, page 19-1---
When I was in high school, my physics teacher---_______ called me down one day after physics class and said, "You look bored; I want to tell you something interesting." Then he told me something which I found absolutely fascinating, and have, since then, always found fascinating.
.... the average kinetic energy less the average potential energy is as little as possible for the path of an object going from one point to another.
--- end quoting Feynman---
Let me describe the Principle of Least Energy that is more simple than Feynman's description.
AP Least Energy Principle: the motion of objects in gravity or electricity and magnetism is a path that takes and requires the least amount of energy. Nature is parsimonious when it comes to energy.
Occam's Razor is described as this--- the Most Simple Explanation of what had happened is usually the true explanation for the events that had happened. Some describe it as the explanation with the Least Number of Premisses, as Occam described it himself--- As Occam, a 14th century theologian put it himself--" entities should not be multiplied beyond necessity".
Indian philosophy has a charming way of thinking about adding more premisses than needed by saying "no need to paint legs on a snake".
Every time a strange looking object seen in the skies, there are many who jump to the added premisses that it is a outer space ship with aliens aboard is a clear example of adding on more premisses than necessary.
Now we have Occam's Razor more than a rule, but as a Principle of Science and Logic
------------------------------------------------------------------------------------------------------------------
We are able to achieve this upgrade from Rule to being a Principle because the OR connector of Logic has partial truth values along with wholesome full truth values.
And this OR connector is the template of the Deciding Experiment in science. Where one of two statements is found to be superior, thus deciding the science law-structure.
Before, I had seen Occam's Razor as an overall appraisal that was correct most of the times but not always correct. Now we can sharpen Occam's Razor by including the OR connector as Deciding Experiment.
New Logic OR (exclusive)
p q p or q
____________
T T F
T dT T
dT T T
F F F
Math validation of correctness where T is valued at 1, F at 0, and dT a fraction of 1.
p q p or q
____________
1 1 0
1 1/10 1 once we discard 1/10
1/10 1 1 once we discard 1/10
0 0 0
Law enforcement, police, justice systems use Occam's Razor often, as the easiest explanation without contradictions, is the likely true account of events. And likely a good reason that my alma mater University of Cincinnati required aspiring lawyers to mandatorily take Logic in college.
So how would I describe the Principle of Occam's Razor?
I would say it is this.
Principle of Occam's Razor
-----------------------------------
When given details of an event and wanting to know the explanation of how the event came about. We list the details. Now we list a set of hypothesis (the third term in physics above) that explains the event details. The smallest or shortest hypothesis is the true explanation of the event that occurred.
Homework assignment: There are many mystery stories on PBS TV, throughout the week and especially on Sunday nights. Such as Miss Marple, Midsomer Murders, Father Brown, Masterpiece Mystery, Sherlock Holmes etc etc. Take one of those shows and find where the author of that show has an illogical plot and the entire story falls apart.
For example, in many of the Sherlock Holmes stories, the farfetched idea of detecting data off a person in one glance requires Sherlock to have super senses with eyes comparable to a hawk.
On Saturday, February 14, 2026 at 9:14:05 PM UTC-6 Archimedes Plutonium wrote:
Now I wrote many critiques of murder mystery shows on PBS.
Here is a sampling from sci.math.
Archimedes Plutonium, Aug 8, 2021, 6:21:52 PM to sci.math
AP, on Masterpiece "Unforgotten" episode 5.
In a different thread I commented on this miniseries of Unforgotten. I enjoy a murder mystery as a logic puzzle and to see if the story hangs together, logically. Usually the stories fail, due to time constraints, the timeline is off. For so many of these stories would require more than a Olympic athlete running under a world record marathon race. And one of the very most broken logic of many bad stories is that the amount of activity undertaken in one day of time. Some Hollywood murder mystery tales leaves one with the impression, the murder took place in the afternoon, in late afternoon of same day they are interviewing a witness across the continent, and by evening the case is in court and by nightfall the case is ended.
But in this series of Unforgotten a new dilemma arose in logic. That the murder was 30 years ago and victim placed in a freezer, two separate freezers for 30 years. Not that this is impossible in practice, for several murders involved freezing the victim/s that were recorded in newspapers. But this does not hang together logically if 4 persons were the murders, police officers in training and illogical to think that the body would not be discovered in 30 years.
Logically, one would think that a frozen murdered body would be discovered and discovered quickly. So does Unforgotten answer these illogical freezer burial?
So today, Sunday 8Aug2021 is episode 5 "Cassie and Sunny interview two of the suspects again and get closer to the truth" reads the TV guide.
So, most murder mysteries for me dealt with a logic analysis near the end of the show, to see if pieces fit together snugly in terms of logic.
Here I have the reverse, of ---whoa-- at the start someone kills another and packs them into a freezer. And how precarious is that for never being discovered. Would not the murderer or murderers want to get the body into a more "undiscoverable location"?
So in these last remaining episodes, my attention is more focused on not who did it or why, but what type of circumstances does this story tale provide for a freezer burial.
My guess is, that the story ends with not a single mention or justification for why a freezer burial for 30 years. And that is Hollywood or BBC for you, in that tv makes up any type of story convenient for the storyteller, absent of logic.
Perhaps BBC will surprise me, and have a logical answer as to a 30 year freezer burial. Maybe the murderer was in the freezer business and was going to scrap the freezer in his business, but unexpectedly died himself, before disposing of the freezer and its contents.
So, I need to see some logic as to this freezer burial, more than who did it.
And some frozen murders are for the purpose of eating the victim. Some are for the purpose of seeing their spouse, not murdered by dying of natural causes and be able to see them as years roll by-- open the freezer. (Actual news reports).
So, what is the Unforgotten going to do-- will it hang together logically? Or will it fail miserably on the question of a freezer burial? If it fails miserably, I have second thoughts of spending time on further episodes of Unforgotten. I do not like poorly stitched together stories.
Archimedes Plutonium, Aug 16, 2021, 4:38:50 PM to sci.math:
Well, saw the last episode. Excellent drama, excellent acting, fine story, but for me, fails in logic. The story -- in 6 episodes-- starts out with a decapitated body found in a freezer, and somewhere in the story plot line should explain why criminal/s put the body in a freezer. Should explain that for the silly goofy reason of leaving a murdered body in a freezer for 30 years for surely, that freezer would highly likely be opened and the police involved.
Perhaps if they remake this series, they could easily slip into the drama, where they question the crime-family boss who murdered the victim by stabbing him in the brain with a fountain pen, that he reveals his family decapitated him and stuck into a freezer to dispose of later but just let it pass by.
A great story has to also be logically sound.
Posted in sci.math, 2022.
time to downgrade Melville's Moby/Alright, the British have given AP a new murder mystery to rate and judge-- Magpie Murders. Several weeks ago AP destroys the Broadchurch mystery as illogical. Will Magpie Murders fair better???
Archimedes Plutonium, Oct 18, 2022, 9:13:47 PM to sci.math.
I watched just 5 minutes of Annika on PBS Masterpiece. A 6 part series of murder mystery. I turned the tv off because some actors are heavily accented that I could not understand a word they said. Not worth my time.
But it also leaves me with the question of whether Moby Dick's novel by Melville is time to be down-graded, and not taught in schools at all, because of its violence towards animals, in particular whales.
It is a highly praised novel for its "symbolism". But can it have been written without using whales???
I would say that teaching with Moby Dick is over and done with, for it teaches mostly the idea to young people-- go out and kill this and that animal.
I say, discontinue Moby Dick in school teaching.
Alright, the British have given AP a new murder mystery to rate and judge-- Magpie Murders. Several weeks ago AP destroys the Broadchurch mystery as illogical. Will Magpie Murders fair better???
Archimedes Plutonium, Oct 16, 2022, 9:26:17 PM to Plutonium Atom Universe newsgroup.
So AP has a new mystery murder to see if it has any logical coherence. AP is not expecting much, for in all the world of mathematics, there is no math professor alive today who can speak of the truth of conic sections-- the simple truth, and yet many High School students are smarter than the math professor in geometry-- the slant cut of cone is a Oval, never the ellipse. Simple experiment of drop a Kerr lid inside paper cone, or visualize a slant cut in cylinder is truly a ellipse, so a cone cannot be an ellipse.
So, well what does that prove about math professors? They are dumber than many High School students. And likely math professors are far dumber in logic than a mystery writer of novels. Provided the Magpie Murders pan out.
But, now, AP may just find a mystery novelist who has a marble of logical intelligence that beats out all math professors with their 1/2 to 1/3 marble of logical brains.
Now, already this 1st episode of Magpie Murders is not going logical. Maybe Alan Cumming should have prepared the viewer with the idea that 2 stories were unfolding at the same time-- two histories, for I sometimes confused the detective Pundt for the author Alan. Maybe if Mr. Cumming had told us there were 2 stories running parallel, would have made it better.
AP, your grader of murder mysteries shown on TV. Recapping the huge flaw of Broadchurch-- the lady detective knew her husband was not at home during the murder yet the writer has her not question her husband--- outright F-grade on Logic. And AP ceased watching Broadchurch. Will Magpie Murders fail dismally also??
Archimedes Plutonium, 3:36 PM to Plutonium Atom Universe newsgroup.
Alright, I am going to stop watching Magpie Murders by Anthony Horowitz. The deal with murder mysteries is that they should be 1 hour long only, and really foolish to play the public with 6 hours of one story. What Mr. Horowitz has here is an illogical Science Fiction Murder Mystery, a new category of either sci-fi or of a murder mystery.
I could not stomach Broadchurch recent murder mystery for the illogic of the lady detective knew her husband was "out the night of the murder" and too dumb to question him "where the hell were you". And something like that is not worth 6 or 12 hours out of my life to watch some hornswaggled made up b.s.
Magpie Murders is the same genre-- hornswaggled made up b.s. of illogical plot. In the first episode alone makes no logical sense-- but then, is murder itself ever logical? Or is all murder that of insanity? No, I would say that some murders are logical. But that is a different story, not here to discuss.
A murder mystery is bad when the viewer -- can see the author in the illogical scenes, for once the mind asks a question-- why did the author do it that way, then the entire story is trashed.
In the first episode-- as Susan asks-- why not sleeping pills instead of jumping off a roof and smashing your bones. But also, why jump off a roof holding a cell-phone, as we see Alan's cellphone while his sister was visiting. Would a cellphone survive a fall, and the man dies? So the solicitor comes around and rings Alan, and the signal is around the side where the tower is that we find the cellphone with Alan dead. Can a cellphone survive but the person dies, is the question of logic?
So no, AP will not watch any further the Magpie Murders. I have more important things to do in life than throw away 5 hours more.
As for the follow-on mystery of "Annika" with its many episodes, no way, the British have actors with heavy accents-- very hard to make out what they are saying. Nothing more annoying in a murder mystery than losing half the dialogue. Turn off.
AP recommendation-- BBC and PBS-- too much murder mystery, that is illogical-- give us more documentaries or NATURE-- where we learn something, not hornswaggle away the hours of our life.
Archimedes Plutonium, 4:10 PM to Plutonium Atom Universe newsgroup.
TV, especially PBS, should be more like a School, a schoolroom, where we learn, but have fun also. Now a schoolroom has lessons along with playtime where kids go outside and play free time. And so, school should not be 8 hours of fun time, playing, not learning. And this equation has come to PBS and TV screens all over the world. We make fun TV, but not educational tv. We fill Sundays with hornswaggling murder mysteries that goes on for 6 hours or 12 hours, dwelling over some fictional hornswaggle.
When better-- we should make every murder mystery capped by 1 hour. There is no imagination for a murder mystery worth 6 hours or 12 hours of wasted time out of people's lives.
Now sure, if we had 6 hours or 12 hours on the birds of England, well, that is mighty mighty worthwhile or say, the dogs of England, or the cats of England. Or 6 hours on archaeology or geology of England, where we learn something genuine and worthwhile.
What possible learning can one take away from watching a "Whodunit" "Broadchurch" or "Magpie Murders" hornswaggled made up fiction plot. Almost zero worth.
Sad, that more people in England and USA will know more about some fictional Susan editor, than they will ever know who Michael Faraday was.
Archimedes Plutonium, Oct 19, 2022, 3:10:25 AM, to sci.math.
I did not know the BBC was 100 years old as of yesterday-today? May I offer some advice, please. Your Sunday's are becoming too top heavy in murder mysteries with some during the week also.
Maybe this is due to the fact that Agatha Christie had too much influence on British life.
Instead of so much murder mysteries and these are now dragging out to be 6 episodes or 12 episodes, instead of that stuff.
How about a return to things like the Classics of I, Claudius. Or comedy like the Monty Python or the Durrells in Corfu. Have Sundays be an Upbeat day in drama, not the murder mystery.
Seems like every other week in Masterpiece Sunday drama we have a new detective-- Miss Marple, then Hercule Poirot then .... and now Atticus Pundt with a umlaut.
Why the proliferation of murder mystery, and Sundays at that. Sunday is supposed to be good cheer, and why not have drama like All Creatures Great and Small rather than this morbid murder mysteries written by authors who do not have two logical marbles to rub together.
17) Why logic is so important for science, for you will never be a good scientist without skills in logic.
Well, the obvious answer to that question is that a great experiment done in science and a bad illogical interpretation follow-up, will likely render your work tainted and blighted. A clear example of this which is detailed in my book Advanced Logic is the Rutherford, Geiger, Marsden experiment of 1911, where they shot alpha particles into a gold leaf foil and found some bounce back at 180 degrees. They interpreted this result as being proof that Atoms had a hard central nucleus of protons and neutrons. But if they had logical brains in the interpretation, they would have recognized that the bounce back alpha particles had more speed coming out than they had going into the gold atoms. This means the alpha particles hit something in a head-on collision with more momentum going in opposite direction to the alpha particles. This means Atoms have ___no nucleus___. Atoms such as gold have 79 protons forming a proton torus and inside the torus are 79 muons connected up together in a circular chain thrusting through the proton torus at nearly the speed of light. So the incoming alpha particles, some were hit head-on with this chain of 79 muons that bounced them back to the source with a faster exit speed than an entry speed.
What does that mean for Rutherford, Geiger, Marsden?? As the future rolls in more and more, that their mistake of believing a nucleus, will get to the point where they are seen as having been brainwashed by the Solar System model of a nuclear sun and planets as electrons. Seen as half success, half failures. Because now, AP will lay claim to the discovery that atoms have no nucleus but have a proton torus with a chain of muons inside thrusting through the torus. In other words, Rutherford, Geiger, Marsden and even Bohr have a mistaken view of atoms and history will not be kind to them and reward AP as discoverer.
In my Advanced Logic textbook, I bring to light many of these stories of great experiments but horrible illogical interpretations. And how awful and painful that must be to the scientists who did the hard work of experimentation, yet lose credit for their work all because they could not interpret correctly the results of the experiment.
Rutherford, Geiger, Marsden will be remembered for doing the gold foil experiment but then AP will use that experiment to its true conclusion and thus it is AP that discovers atoms have no nucleus but have a proton torus with muons inside. You see, AP becomes famous and takes the largest share of credit. If Rutherford, Geiger, Marsden and Bohr were alive today, they would be depressed in knowing that the hard work of the experiments, yet the fame for correct interpretation goes to AP with a logical brain to interpret the experiment.
But poor in logic not only affects scientists but laypersons and common people. They are more likely to be victimized by others.
Theme of the story: if you want to be a scientists, it behooves you to take 2 years of logic in college or university. It will not guarantee you will not make logical mistakes in your science career, but it will give you a fighting chance to make correct interpretations.
The logic mistake of Rutherford, Geiger, Marsden was that they believed more in a model-- the planetary model of the Sun as nucleus surrounded by planets, that they could not shake away the planetary model come time to interpret the results.
18) Completeness and Consistency in Logic.
Now the completeness and consistency of mathematics is easy to see and describe. A-lot more difficult for Logic to see and describe completeness and consistency. And this is the beauty of modeling logic after mathematics. We can see the consistency and completeness of Logic by seeing the consistency and completeness of mathematics.
First a definition of Consistency is wanted. And that is a system of objects in which contradictions do not arise. A contradiction is, if you remember when you have a statement or a premiss that has both P and not-P, that there exists P and exists not-P. That is the contradiction and we stop whatever we are doing in logic or science and have to get rid of the contradiction before moving forward.
Consistency
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Consistency is a system of statements or premisses where no contradictions arise.
Second, a definition of Completeness is wanted. Completeness for mathematics is easy to show in that the Decimal Grid Numbers all come from Mathematical Induction and where any math operation of add, subtract, multiply, divide of two members produces a number of that set. Then the set is called complete.
Completeness
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So in mathematics, the Decimal 10 Grid is 0, .1, .2, .3, .. ,1.0, 1.1, ..., 9.8, 9.9, 10.0.
The algebraic completeness of 10 Grid is the 100 Grid is 0, .01, .02, .03, .. , 1.00, 1.01, ..., 99.98, 99.99, 100.00
All Grids are formed from Mathematical Induction. For the 10 Grid the math induction element is 0.1 as we constantly add 0.1 to the previous number to get the next number until we reach 10. In the 100 Grid, the math induction element is 0.01 and we constantly add that until we reach 100.
So, in Completeness of math numbers, if we take any two numbers in 10 Grid and do a add or subtract or multiply or divide on them, does that return a number inside the 100 Grid??? If yes, the set is complete.
If I multiply the 10 Grid numbers 9.9 by 9.9, I get 98.01 which clearly is in 100 Grid. If I divide 0.1 by 5, then I get 0.02 which is in 100 Grid. A tricky one is divide 0.1 by 0.3 gives 0.33333.... but that is seen as 0.33 in 100 Grid. If you wanted to go to 1000 Grid it is 0.333, to 10^4 Grid it is 0.3333 etc.
The message is that Decimal Grid Numbers are a Complete set because that set such as 10 Grid and its algebraic-completeness set 100 Grid provide a answer to all 4 operators on Any Two Numbers on the 10 Grid furnish a number in the 100 Grid.
Are the Grid Numbers Consistent? They are complete, but are they consistent?
We know that division by 0, zero, is not allowed in mathematics for if we allow that to happen, then we end up with all numbers are equal to one another, such as 2 = 3, or 5 = 9, etc.
We know that 4 - 9, that is 4 subtract 9 leads to what Old Math called a negative number of -5.
So, well, Old Math was not consistent and not complete for they forgot to include several axioms to make Old Math consistent and complete.
They forgot or were too dumb to realize these axioms.
Axioms Old Math forgot or too dumb to realize.
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Axiom 1. Division by zero is never allowed.
Axiom 2. You cannot subtract (remove) more than what is available to remove, and hence, no negative numbers ever exist. Negative numbers are hallucinations and imaginary falsehoods.
Axiom 3. All valid equations of mathematics must have a positive nonzero number all alone on the rightside of the equation at all times. For example: 2x^2 +3x = 6 is a valid equation of math but that 2x^2 +3x -6 = 0 is a phony equation because it allows for the existence of negative numbers and negative numbers are phony. It is super easy to solve for 2x^2 +3x = 6 as it is a little more than 1, while Old Math, which was dumb math had students plug in hard formulas to extract solutions. The entire history of Tartaglia, Cardano, Ferro, and others in solving equations that are phony was a exercise in futility and stupidity that is a hall mark of Old Math. For the reason that you must always have a positive decimal grid number on the rightside of the equation all alone and at all times is because of the fact that 0, Zero is outlawed in division. Yet all the mathematicians in Old Math were cranks and crackpots to understand that if you cannot divide by zero, you sure cannot have it all alone on the rightside to form a equation of math or science. Here is where Logic firmly steps into math and science and informs the fool of Old Math, that if 0 can not be a divisor, it surely cannot be a solution to a entire equation.
For example: in the equation which is a valid equation we have 2x^2 + 3x = 8. We can divide both sides by 8 and have (2/8)x^2 + (3/8)x = 1. But if the equation has a 0 all alone on the rightside of the equation we cannot divide by 0 and have another valid equation.
Axiom 4. All graphs of math are 1st quadrant only starting with (0,0) in planar 2nd dimension of x and y axes. Starting with (0,0,0) in 3rd dimension of x,y,z axes. Logically, if negative numbers do not exist, then graphing in mathematics has no negative numbers and these absurd, foolish negative quadrants.
Axiom 5. The Only Valid Functions of math are the Polynomials, for the polynomials are discrete (not a continuum) just as the Decimal Grid Numbers are discrete with holes in between one number and the next number. This axiom is essential for the Calculus to exist. Without this axiom, there be no calculus in math or science.
The take-away from this is that Math-Induction on discrete decimal Grid Number systems defines consistency and completeness.
The funny story of Prime numbers in Old Math for primes are phony.
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The story of consistency and completeness of Old Math should include the story of Primes, for primes are Incomplete and shows us the importance of Completeness.
The fools of Old Math found a concept they called Prime-number. In the counting-numbers, 1,2,3,4,5, ...... They found a definition that some numbers like 2 and 3 and 5 were divisible only by 1 and themselves, while other numbers like 4, 6, 8, 9, 10 were divisible by themselves and by 1 but also by other numbers, like 4 is divisible by 2, and 9 is divisible by 3 and 10 by 2 and 5. So Old Math spent huge amounts of time on this concept of Prime-number.
But should they have spent so much time on Primes-numbers??
No, for --if they had trained and learned Logic well enough, they would have come to a chapter of Logic that speaks of Completeness.
You see, in Decimal Grid Numbers as the true numbers of all of mathematics, there is no concept of Prime-number in Grid Numbers. Every Grid number has multiple factors.
So what went wrong in Old Math, where is the source of their stupidity??
The source is this concept in Logic called Completeness.
To be complete you have to produce a number within the system to all 4 operators of add, subtract, multiply, divide, remembering the Axioms.
You see, the Counting Numbers themselves are ___not complete to division___. The decimal grid numbers are complete to division as shown earlier.
For example: if staying only with Counting Numbers 1,2,3,4,5,6,7,8,9,10. I divide 10 by 5 and yes that is another counting number but I divide 10 by 3 and that is not a counting number.
Why are the Counting Numbers not complete to division?? The counting numbers are complete to multiplication for take Any two counting numbers multiply them and they return to you another counting number. We cannot say that for division. Take for example 5 divided by 2 and it returns a number that is not a counting number 2.5. But that 2 x 5 does return you another counting number.
The Counting Numbers are ___not complete___ to division, means that any construct of a concept of Prime is a phony construct.
Sad to say, perhaps a billion people on Earth wasted their time in studying prime numbers of mathematics when all along they are phony entities.
This is why there never is a Pattern for Primes. Why there is never an exact formula for primes. Because the entire concept of Prime in Old Math is total phony garbage. In fact, I could say that what is ghosts, witches, hobgoblins to physics, is what is Prime-number in mathematics.
This is the whole trouble of mathematicians coming out of colleges and universities across the globe. Sure, they can compute this that and whatever. But ask them to think straight and think clearly is a vacuum for many of them, for they know nothing of Logical Reasoning, and schools do not insist they mandatorily take Logic.
Now we have to ask the question is Physics, the King of all Science, is it consistent and complete??? Excellent question. And I am not going to go in any depth with this discussion but save it for the textbook "Intermediate Logic" and then for the textbook "Advanced Logic".
Is Physics complete and consistent?
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I am well aware that my audience of students, who have not had much physics if at all, any physics. So I have to keep this lecture brief and clear and easy.
Physics has forces and by the year 1930, there were 4 forces known to the physics community and they called them (1) Electromagnetic force (2) gravity force (3) weak- nuclear as radioactivity (4) strong-nuclear as in atomic bombs and E=mc^2.
But no-one in physics was able to Unify these 4 forces, until AP did such in the early 1990s. The AP unification arises by taking the one force of the 4 known forces and asking which of those 4 forces has the most "perfect particle"???? The answer should be immediate. Only the Electromagnetic force has a "perfect particle" in the photon with its speed of light and zero rest mass. Where its speed is a maximum constant.
___By Logic___, therefore, the gravity, the weak-nuclear, the strong-nuclear must simply, very simply be just manifestations of the Electromagnetic force. I discovered the Unification of forces in early years of 1990 and posted my discovery extensively to Usenet after 1993.
If physics is complete and consistent, then there has to exist a Unification of forces into one force with its perfect particle.
Another example of why physics is complete and consistent.
In the year 2016-2017, I discovered that the proton was really 840MeV not 938MeV and the neutron when fully grown is really 945MeV and not 940MeV because I discovered that 9 x 105 = 945. The Muon of physics is truly 105MeV, meaning the true electron of Atoms is the muon and that the Old Physics fools thought that JJ Thomson's 0.5MeV particle is the electron of atoms, but it turns out that Curie and Dirac were looking for a magnetic monopole, the unit of electricity in Electromagnetic Force.
When you discover that the Proton is a torus and the Neutrons are parallel plate capacitors, much like the plates that go to make a battery, you thus discover that the Atom has ____no nucleus____ for it is a single torus of protons surrounded by neutrons as parallel plates of a capacitor.
All of a sudden, there is no more 4 forces of physics but only 3, the electromagnetic, the gravity and the radioactivity force.
The Unification of forces of Physics still holds as being Electromagnetic and that gravity is a manifestation of Electricity and Magnetism. So also is radioactivity is a manifestation of Electricity and Magnetism.
When all forces of physics are just manifestations of Electromagnetism then physics is complete and consistent and then we go a step further, in that the configuration of the Atom itself must be the law-structures of Faraday, Coulomb, Ohm, Ampere.
No longer can you have a dullard picture of what atoms are--- no longer can you have a do nothing dense nucleus, no longer can you have 0.5MeV as electrons doing nothing but floating around outside a nucleus. No longer can you have neutrons as do nothing camping alongside protons and sipping beverages on a beach.
When physics is complete and consistent, then the behavior of electrons of protons of neutrons is the law structures of Faraday, Ampere, Coulomb, Ohm.
My unification of the 4 that became 3 forces of Nature which is one and only 1 force of electromagnetism, is a Completeness and a Consistency of the science of Physics.
With my unification I could thence proudly say this Universal Axiom over all of Science, including Logic and mathematics.
Universal Axiom over all Science, all Knowledge
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All is Atom, and Atoms are nothing but electricity and magnetism.
19) The short Logic Argument, the syllogism.
Where is the logic-argument in the science of Logic? It is the 4th general term what would be a law-structure in physics and what would be a proof in mathematics.
For **Science** we have Statement, Concept, Hypothesis, Law-structure, Theory, Universal Axiom.
For **Logic** we have Statement, Premiss, Connector-structure, Reasoning (argument, discourse, syllogism), Equalities, Law-structure.
For **Math** we have Statement, Axiom, Operator-structure, Proof, Theorem, Theory
It is a shame that the bulk of Logic is the Logical Argument, yet in this textbook, I discuss the Logical Argument in just two of the last chapters. The bulk of this book should be, I would say 60 to 70 percent devoted to the Logical Arguments and analyzing them. In my Advanced Logic textbook, however, I remedy this problem for in that textbook 90% is analysis of Logical Arguments.
In the Elementary and Intermediate Logic textbooks only about 20% is the Logical Argument.
As mentioned several times earlier, in Logic we have Statements of Ideas, listed symbolically as p,q,r,s,t, etc etc. Now those statements can be compounded by connectors of AND, OR, Equal-Not, If-->Then.
Then, later on I introduced the Premiss or Premisses of Logic. What are premisses compared to Statements?
Premisses are Statements but Only True Statements, fully true of value 1, that are determined by the best available science on the subject matter. We symbolize premisses with letters of the alphabet the same as Statements.
What are Statements compared to Premisses?
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Each statement in Logic is a single idea. A compound statement of Logic is when you have two or more single ideas connected by a Logic connector AND, OR, Equal-Not, If-->Then.
A premiss of Logic is a statement or compound statement that is a True statement. The only false ideas allowed in a Logic Argument that is step by step premisses making the argument, the only falsehood allowed is when you have a compound statement of AND for the AND truth table allows for false statements. And also, in the OR truth table we allow for a partial-true statement which we called "dT" and that partial truth statement contains some falsehood. But that is it, that is all we allow of falsehood in a Logic Argument.
In a Logic argument we have a list of premisses as illustrated thus.
P_1
P_2
P_3
.
.
P_n
C for conclusion
Each of those premisses is fully true. The only falsehood allowed in the premisses is a compound statement using AND or using OR with a "dT" partial truth.
AP Principle to Form an Argument of Logic-- all the premisses must be true as checked by science in order to have an argument of logic.
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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, those false statements are seldom or rarely found in 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, that are in doubt, that are 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, especially science even a layman argument, we strive to put only True statements in the ongoing discourse, argument, reasoning.
Most colleges have a debate club, even some High Schools have a debate club. It is nice for a debate to have statements that are all true, composing the Premisses of the Argument. But naturally, debates break down where it becomes just a verbal shouting match filled with falsehoods and ad hominem nonsense.
So I was wondering if anyone else had this idea before me. The idea that a Logical Argument is where only True ideas, fully true ideas are acceptable for the statements p,q,r,s,t,u etc that go to make up the Premisses of the Logic Argument???
I started earlier in this book with the famous Aristotle syllogism: All men are mortal / Socrates is a man / therefore Socrates is mortal. But what exactly is a syllogism?
Early on, I started this 1st year college Logic textbook with a syllogism. What is a syllogism?? Some definitions say a syllogism is a (1) Formal Argument, or (2) a Deductive Argument, or (3) a Deductive Reasoning.
A syllogism to Logic is what a proof of math is to mathematics. Syllogism is just a fancy word for a logical argument. The etymology of "syllogism" comes from Greek "logos" to reason and "syl" together with; ------to mean --- to reason together with.
I myself took 2 years of College Logic at University of Cincinnati, 1968-1972, and found it exciting and exhilarating.
Here I am at age 75-76, and demanding that all scientists wanting a degree in science to mandatory have to take 2 years of college logic.
That is not possible now, because the logic textbooks are full of error, so bad of error that they are not worth teaching from. And perhaps cause more damage than if not taught logic at all.
In a subtle way, when I was in college and taking those 2 years of Logic, I remember several instances of where I rebuked the truth tables that the book was teaching. The truth table of If-->Then was crazy and the truth table of OR and the varieties of OR were crazy. But I was not going to battle with professors, for I wanted a good grade.
But now, over 50 years later, I want to toss out all that junk logic onto a pile of shame and have Logic Textbooks worth teaching.
The first Logic Syllogism that I learned was this.
All men are mortal.
Socrates is a man.
Thus Socrates is mortal.
Another syllogism was given and it goes like this in college.
All animals breathe oxygen..
All fish are animals.
Thus all fish breathe oxygen.
The spirit of deduction is shown in giving a syllogism. The last line is forced to come from the two previous lines.
Syllogism is just fancy name for Argument. It is the most simple Logic Argument for it is a 2 lines of Premiss and then a Conclusion. I prefer to call all logical arguments just simply a "argument". But since the history of logic started way back in Ancient Greek times and used the word "syllogism", I am going to continue the tradition and use the concept of syllogism as a two premiss argument that ends in a deduced conclusion.
Remember, I started this textbook teaching what a deduction is with the syllogism of Socrates.
All men are mortal.
Socrates is a man.
Thus Socrates is mortal.
The Atomic theory of science is the greatest syllogism of all time.
All Matter is made up of Atoms of one of the 118 or more chemical elements of the Periodic Table of Elements.
The Universe is matter.
Therefore the Universe itself is one of those 118 chemical elements.
Now, every illogical person who reads the Atomic theory syllogism is unnerved by that conclusion, thinking that the universe can be a compound or mixture of the 118 elements and not one specific atom of plutonium. And this is why I insist that all scientists are mandatorily required to take 2 years of college-university logic. The logical person understands that All Matter is one of the 118 elements, and if the Universe itself altogether is not one of those 118 elements, specifically plutonium, then the entire Atomic theory is __not universal__ but has an exception-- the universe as a whole. The Atomic theory would end up being a "rule" of science and not a law-structure nor a theory.
The atom that best fits the important numbers of physics and math is 231Plutonium.
Now, many many people who think they have a logical mind-brain but really are failures of logic think they see holes and flaws in that Atomic Theory Syllogism. But they are mistaken. For if the Atomic Theory Syllogism is not true, then the Atomic theory is not a Universal law-structure of Science, just a mere little rule-- sometimes correct, sometimes wrong. And we cannot accept that for the greatest theory of all in science.
So the many fools who think there are flaws and holes to the Atomic Theory Syllogism saying stupid things like-- Universe is a molecule or it is many atoms but not one single atom. They are mistaken, for the Atomic Theory to be *** universal *** requires the entire universe be a single atom.
That has to be the Atomic theory of physics for otherwise the Atomic theory is a mere and meager rule, sometimes correct sometimes wrong. We cannot have the most important science theory a rule. It must be a theory that applies in general and is universal.
Copi "Introduction to Logic" 4th edition, 1972, defines the Logical Argument called "Syllogism" as that of --- A syllogism is a deductive argument in which a conclusion is inferred from two premisses." Copi starts his chapter with a quote from Leibniz, the co-discoverer of calculus along with Newton. Leibniz says "I consider the invention of the form of syllogism one of the most beautiful, and also one of the most important, made by the human mind."
AP writes: I do not know why Leibniz said that and seems to me as over-praise, or exaggeration.
For me, I look at arguments of Logic to be of any length and why get enamored with a length of 2 premisses leading to a conclusion.
I am going to strictly follow the definition of syllogism by Copi and others and say that a syllogism can be of any short logic argument you want, whether 1 premiss and conclusion or 2 premisses and conclusion or a larger number of premisses and a conclusion.
I use the Atomic Theory as outlined in Feynman's Lectures on Physics, 1963.
Plutonium Atom Totality syllogism
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(1) All things are made up of individual atoms, one of 118 of the chemical elements.
(2) The Universe is a thing.
___________________
(3) Therefore, the Universe is a single big Atom and the chemical element that fits the numbers of physics the best is plutonium.
In the next chapter on long Logical Arguments, I re-do the Plutonium Atom Totality to be a argument of 19 paragraphs, that is 19 Premisses in stepwise fashion, concluding it exists as a single big plutonium atom, otherwise the Atomic Theory is not a theory but a rule that is sometimes false, for rules are not universal. I further go on to add 4 more Premisses (paragraphs) in the logical argument to total 23 Premisses (paragraphs).
So, well, let us judge. Is my syllogism correct? Yes it is logically correct. But when we see it as a 23 Premiss paragraph syllogism we see the mechanism and the future meaning and purpose of the Universe. And the Logical mechanism that persuades the truth of the Atom Totality is the idea that the most important theory in all of science-- the Atomic Theory is just a rule if it did not encompass the Universe itself in total.
You see, the 2-3 line syllogism does not convey the key idea of how the conclusion is begot. It is begot because the Atomic Theory needs to be Universal and not a rule.
And also, the detail of why the Universe cannot be a molecule or a chemical mixture of many atoms but a single big atom has to do with the creation process of an Atom Totality. For the progression has to follow from the Proton torus making more atoms in the Faraday law-structure, and changing the proton torus of Hydrogen to form Helium and changing the proton torus of Helium to form Lithium all the way up to Uranium and changing its proton torus to form a single big atom of Plutonium.
You see, just a simple 2 premisses misses all those deductions while 19 premiss-paragraphs and 23 premiss-paragraphs fills in the needed details.
I would say, that the definition of Syllogism of Old Logic with its mere 2 premisses and a conclusion was for the intent of showing the most simple form of a logic argument. Much like in mathematics, when we teach add to youngsters we first start out with adding two numbers like 1+2 = 3. We do not teach 6.3 + 8.9 + 0.5 + 15 until much later.
Most science logic arguments I have encountered that are important such as Plutonium Atom Totality, or the Atom is a proton torus and no nucleus, or the Calculus is where derivative is a connector of Leftwall point to Rightwall point of a cell, or that a slant cut of cone is oval, not ellipse, all these arguments take numerous premiss-paragraphs.
So when I say the term "syllogism" my definition is that it is a short logical argument of a few number of premisses to reach a conclusion. I define syllogism as a form where you have a numbered lot of premisses that reaches a final conclusion. Instead of saying "Logical Argument", I sometimes like to say simply "Syllogism".