The History of LOGIC // Teaching True Logic textbook series
by Archimedes Plutonium
This is AP's 369th 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
Author's Note: Although few people share this opinion now in February of 2026 that AP has the finest human mind on the subject of Logic. I say that not to be bragging even though most everyone else would say I am a braggart, but rather, say that for someone who has altered all of Logic of the past. The amount of altering past logic is a wholescale of altered Logic of all its 6 connectors and corrected all of Logic starting with Aristotle. I think of myself as the founding-framer of true logic. And I am sure that if I had not this powerful logic mind, I would never have discovered the Atom Totality theory of physics. It is my logic abilities that carries me far above and beyond other scientists.
Logic as a subject and a science is not appreciated in modern education. Why that is I am not fully sure but suspect religion is the blame. Religion is often adverse to logic. Maybe education institutions are too busy filling up students curriculum with all sorts of subjects-- English, math, some science, that there is no more room for a mandatory course in Logic.
In the year 2025, I started to write these 4 textbooks of Logic, (1) Elementary Logic, (2) History of Logic (3) Intermediate Logic, (4) Advanced Logic, for I was pressuring all colleges and universities to mandatorily require science and engineering students to have 2 years of college logic training before they get their degree. I could not rightfully insist on that demand for there are no logic textbooks that have all 6 connectors of logic correct. So why insist on mandatory logic with books that have error filled logic? So I set myself out in 2025 to write 4 textbooks of Logic to teach in college and university. As the years go by, I will write a 5th textbook for High School, but I need a vacation break away from logic to resume once I am refreshed.
Preface: This is a history of Logic, for it tells the good and bad of Logic throughout its long history, its triumphs and its mistakes.
Actually there are few persons that need to be mentioned so it is not a long and struggling book.
Cover picture: A picture of James Clerk Maxwell who unified electricity and magnetism into a coherent set of laws which required much logical reasoning.
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Table of Contents
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Part 1: Prehistory Logicians
1) Neanderthals making fire with flint and iron pyrite
Part 2: Ancient Logicians
2) Thales of Miletus (626 - 548 BC) -- static electricity and magnetism
3) Pythagoras of Samos (570-495 BC) -- deductive reasoning and the link between numbers and geometry in A^2 +B^2 = C^2 for right triangles
4) Leucippus (5th century BC) and Democritus (460-370 BC) greatest of all science theories, the Atomic Theory
5) Socrates (470-399 BC)-- logic argument
6) Plato (428- 348 BC)-- being into becoming
7) Aristotle (384-322 BC)-- deductive syllogism
8) Euclid (300BC) -- systematized math and geometry in a deductive proof method
9) Aristarchus of Samos 270BC-- systematized the experimental science of Astronomy
Part 3: Medieval Logicians
10) Avicenna (980 -1037)-- scientific method
11) William of Ockham (1287-1347) -- Ockham's razor
Part 3: Modern day Logicians
12) George Boole (1815-1864) and William Jevons (1835-1882) -- logic connectors
13) Gottlob Frege (1848-1925)-- symbolic logic
14) James Maxwell (1831-1879)-- unification of electricity and magnetism
15) Pierre Curie (1859-1906) and Paul Dirac (1902-1984) --symmetry in science of the magnetic monopole existence
16) John Bell (1928-1990) --superdeterminism
17) Archimedes Plutonium (1950 - present)-- systematizes Logic by paralleling logic to mathematics-physics
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Part 1: Prehistory Logicians
1) Neanderthals making fire with flint and iron pyrite
Archimedes Plutonium Feb 22, 2026, 4:42:43 PM to Plutonium Atom Universe newsgroup.
Part 1: Prehistory Logicians
1) Neanderthals making fire with flint and iron pyrite
Logic can be overall characterized as the 6 connectors of Logic.
1) Existential quantifier
2) Not-Equal
3) AND
4) OR
5) If-->Then
6) Universal quantifier
Does a fire exist or does it not exist is the existential quantifer.
Next is Not-Equal. Yes, it exists for the Neanderthal in England 400,000 years ago or it does not exist. If not exist, then get out the Flint and Iron Pyrite rocks, smash them together to make a fire.
Fire for Neanderthal was equal to lightning causing fire. Maybe they were so bright in mind as to realize the Sun was fire and that stars were fire only far away.
Note of Caution:: Now I am well aware that the "fire of Stars and our Sun" is vastly different from a Neanderthal campfire of 400,000 years ago in England. The Sun and stars fire is caused by Atomic Energy of the Faraday law going on inside every atom the resides in the Sun and only a tiny bit, say 5% is fusion. While the Campfire of Neanderthal is chemical energy of oxygen atoms bonding mostly to carbon atoms and as the oxygen atom bonds to carbon, it releases chemical energy. These two energies are not the same. And of course, no Neanderthal mind 400,000 years ago would have known that.
But what I am saying is many minds of Neanderthals 400,000 years ago would have seen and felt a similarity to their campfire, to the Sun of warmth by heat and the light to see, and compared that to the sparks emitted by striking flint to iron pyrite.
The connection of campfire to Sun and now to sparks when flint is struck on iron pyrite. That connection is Logic in action. It involves Exist--- fire exists or not, involves Not-Equal-- sparks generate campfire, involves AND in that Sun and campfire and now sparks from flint-iron pyrite, involves OR in experimenting to see if the sparks generate a campfire, involves If-->Then in "If the campfire dies out, Then we start a new one with flint-iron pyrite."
The world's first science experiment, and hence scientific method and hence Logic starts 400,000 years ago by Neanderthals in England.
Archimedes Plutonium Feb 22, 2026, 4:52:30 PM to Plutonium Atom Universe newsgroup.
I am going to start this history of Logic some 400,000 years ago to a time when Neanderthals were living and roaming in England and had a fire making industry of flint and iron pyrite.
I had seen on TV the day that the BBC broadcast this news and showing a reporter with flint and iron pyrite in hand, and I thought to myself "Wow, wow wow wow, all the sparks that this reporter made with one vigorous strike of the two rocks together". I was amazed at how many sparks came from one strike.
Although there is more to the explanation of what creates those sparks than just "steel reacts with oxygen". We have to bring in the laws of electromagnetism for a full explanation.
Lovely, lovely, that science starts with banging together two different rocks. And as science starts here, so does Logic. To remember for Neanderthals, remember two different rocks-- flint and iron pyrite and bang them together. Realizing that the fire they produce is the same fire of lightning bolts or Sun. Logic starts here.
--- quoting Wikipedia---To ignite fireA ferrocerium "flint" spark lighter in action
When struck against steel, a flint edge produces sparks. The hard flint edge shaves off a particle of the steel that exposes iron, which reacts with oxygen from the atmosphere and can ignite the proper tinder.
Prior to the wide availability of steel, rocks of pyrite (FeS2) would be used along with the flint...
--- end quoting Wikipedia---
Need a picture of Thales.
Thales of Miletus (/ˈθeɪliːz/ THAY-leez; Ancient Greek: Θαλῆς; c. 626/623 – c. 548/545 BC) was an Ancient Greek pre-Socratic philosopher from Miletus in Ionia, Asia Minor. Thales was one of the Seven Sages, founding figures of Ancient Greece.
Beginning in eighteenth-century historiography,[1]many came to regard him as the first philosopher in the Greek tradition, breaking from the prior use of mythology to explain the world and instead using natural philosophy. He is thus otherwise referred to as the first to have engaged in mathematics, science, and deductive reasoning.[2]
Thales's view that all of nature is based on the existence of a single ultimate substance, which he theorized to be water, was widely influential among the philosophers of his time. Thales thought the Earth floated on water.
In mathematics, Thales is the namesake of Thales's theorem, and the intercept theorem can also be referred to as Thales's theorem. Thales was said to have calculated the heights of the pyramids and the distance of ships from the shore. In science, Thales was an astronomer who reportedly predicted the weather and a solar eclipse. The discovery of the position of the constellation Ursa Major is also attributed to Thales, as well as the timings of the solstices and equinoxes. He was also an engineer, known for having allowed the Lydian army to cross the Halys River. Plutarch wrote that "at that time, Thales alone had raised philosophy from mere speculation to practice."[3]
3) Pythagoras of Samos (570-495 BC) -- deductive reasoning and the link between numbers and geometry in A^2 +B^2 = C^2 for right triangles
Pythagoras of Samos[a] (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC)[b] was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.
In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wisdom").[c]Historians debate whether Pythagoras made these discoveries and pronouncements, as some of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors, such as Hippasus and Philolaus.
The teaching most securely identified with Pythagoras is the "transmigration of souls" or metempsychosis, which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planetsmove according to mathematical ratios and thus resonate to produce an inaudible symphony of music. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy, and their meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there.
Pythagoras influenced Plato whose dialogues (especially Timaeus) exhibit Pythagorean ideas. A major revival of his teachings occurred in the first century BC among Middle Platonists, coinciding with the rise of Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and Pythagoreanism had an influence on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was also used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses would later influence the modern vegetarian movement.
No authentic writings of Pythagoras have survived,[4][5] and almost nothing is known for certain about his life.[6][7] The earliest sources on Pythagoras's life, from Xenophanes, Heraclitus, Empedocles, Ion of Chios, and Herodotus[8] are brief, ambiguous, and often satirical.[9][10] The major sources on Pythagoras's life are three biographies from late antiquity written by Diogenes Laërtius, Porphyry, and Iamblichus, all of which are filled primarily with myths and legends[7][11][12] and which become longer and more fantastic in their descriptions of Pythagoras's achievements the more removed they are from Pythagoras's times.[11][12] However, Porphyry and Iamblichus also used some material taken from earlier writings in the 4th century BC by Aristotle's students Dicaearchus, Aristoxenus, and Heraclides Ponticus,[13] which, when it can be identified, is generally considered to be the most reliable.
Rearrangement proof of the Pythagorean theorem.In one rearrangement proof, two squares are used whose sides have a measure of and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. In the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. Each outer square has an area of (a + b)2 as well as 2ab + c2, with 2ab representing the total area of the four triangles. Within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. These rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom-left corner, and another square of side length b formed in the top-right corner. In this new position, this left side now has a square of area (a + b)2 as well as 2ab + a2 + b2. Since both squares have the area of (a + b)2 it follows that the other measure of the square area also equal each other such that 2ab + c2 = 2ab + a2 + b2. With the area of the four triangles removed from both side of the equation what remains is a2 + b2 = c2.
Leucippus (/luːˈsɪpəs/; Λεύκιππος, Leúkippos; fl. 5th century BCE) was a pre-Socratic Greek philosopher. He is traditionally credited as the founder of atomism, which he developed with his student Democritus. Leucippus divided the world into two entities: atoms, indivisible particles that make up all things, and the void, the nothingness that exists between the atoms. He developed his philosophy as a response to the Eleatics, who believed that all things are one and the void does not exist. Leucippus's ideas were influential in ancient and Renaissance philosophy. Leucippus was the first Western philosopher to develop the concept of atoms, but his ideas only bear a superficial resemblance to modern atomic theory.
Leucippus's atoms come in infinitely many forms and exist in constant motion, creating a deterministic world in which everything is caused by the collisions of atoms. Leucippus described the beginning of the cosmos as a vortex of atoms that formed the Earth, the Sun, the stars, and other celestial bodies. As Leucippus considered both atoms and the void to be infinite, he presumed that other worlds must exist as cosmoses are formed elsewhere. Leucippus and Democritus described the soul as an arrangement of spherical atoms, which are cycled through the body through respiration and create thought and sensory input.
The only records of Leucippus come from Aristotle and Theophrastus, ancient philosophers who lived after him, and little is known of his life. Most scholars agree that Leucippus existed, but some have questioned this, instead attributing his ideas purely to Democritus. Contemporary philosophers rarely distinguish their respective ideas. Two works are attributed to Leucippus (The Great World Systemand On Mind), but all of his writing has been lost with the exception of one sentence.
The thing I remember most of Democritus besides his Atomic theory, is that he was the "Laughing philosopher". I say that because he must have come up against fierce resistance especially from religionists. If you say that Atoms are everything, in a sense you omit the Gods. And I, being the founder-framer of the Plutonium Atom Totality have had to adopt the Democritus reaction to critics--- laughing my way outright in any discussion.
Democritus (/dɪˈmɒkrɪtəs/, dim-OCK-rit-əs; Greek: Δημόκριτος, Dēmókritos, meaning "chosen of the people"; c. 460 – c. 370 BC) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe.[2] Democritus wrote extensively on a wide variety of topics.[3]
None of Democritus' original work has survived, except through second-hand references. Many of these references come from Aristotle, who viewed him as an important rival in the field of natural philosophy.[4] He was known in antiquity as the ‘laughing philosopher’ because of his emphasis on the value of cheerfulness.[5]
Although many anecdotes about Democritus' life survive, their authenticity cannot be verified and modern scholars doubt their accuracy.[6]
According to Aristotle, Democritus was born in Abdera, on the coast of Thrace.[7][6] He was a polymath and prolific writer, producing nearly eighty treatises on subjects such as poetry, harmony, military tactics, and Babylonian theology. Some called him a Milesian, and the name of his father too is stated differently.[8] His birth year was fixed by Apollodorus in the first year of the 80th Olympiad, or 460 BC, while Thrasyllus had referred it to as the 3rd year of the 77th Olympiad.[9] Democritus had called himself forty years younger than Anaxagoras. His father, Hegesistratus,--or as others called him Damasippus or Athenocritus,--was possessed of so large a property, that he was able to receive and treat Xerxes on his march through Abdera.[10]
Democritus spent the inheritance left to him by his father on travels to distant countries, which he undertook to satisfy his extraordinary thirst for knowledge. He travelled over a great part of Asia, and, as some state, he even reached India and Aethiopia.[11] We know that he wrote on Babylon and Meroe; he must also have visited Egypt, and Diodorus Siculus[12] even states, that he lived there for a period of five years. He himself declared,[13] that among his contemporaries none had made greater journeys, seen more countries, and made the acquaintance of more men distinguished in every kind of science than himself. Among the last he mentions in particular the Egyptian mathematicians (ἀρπεδονάπται ; comp. Sturz, de Dialect. Maced. p. 98), whose knowledge he praises, without, however, regarding himself inferior to them. Theophrastus, too, spoke of him as a man who had seen many countries.[14] It was his desire to acquire an extensive knowledge of nature that led him into distant countries at a time when travelling was the principal means of acquiring an intellectual and scientific culture; and after returning to his native land he occupied himself only with philosophical investigations, especially such as related to natural history.[15]
AP writes:: I do not know why most of these old pictures are so "dark". Can they be cleaned in modern day restorations???
Socrates (/ˈsɒkrətiːz/;[2] Ancient Greek: Σωκράτης, romanized: Sōkrátēs; c. 470 – 399 BC) was an ancient Greek philosopher from Classical Athens, perhaps the first Western moral philosopher, and a major inspiration on his student Plato, who largely founded the tradition of Western philosophy.[3] An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem. Socrates was a polarizing figure in Athenian society. In 399 BC, he was accused of impiety and corrupting the youth. After a trial that lasted a day, he was sentenced to death. As related by Plato, he was put to death by administration of poison after refusing offers from allies to help him escape.
Plato's dialogues are among the most comprehensive accounts of Socrates to survive from antiquity. They demonstrate the Socratic approach to areas of philosophy including epistemology and ethics. The Platonic Socrates lends his name to the concept of the Socratic method, and also to Socratic irony. The Socratic method of questioning, or elenchus, takes shape in dialogue using short questions and answers, epitomized by those Platonic texts in which Socrates and his interlocutors examine various aspects of an issue or an abstract meaning, usually relating to one of the virtues, and find themselves at an impasse, unable to define what they thought they understood. Socrates frequently proclaims his ignorance, saying that he is only sure that he does not know.
Socrates exerted a strong influence on philosophers in later antiquity and has continued to do so in the modern era. He was studied by medieval and Islamic scholars and played an important role in the thought of the Italian Renaissance, particularly within the humanist movement. Interest in him continued unabated, as reflected in the works of Søren Kierkegaard and Friedrich Nietzsche. Depictions of Socrates in art, literature, and popular culture have made him a widely known figure in the Western philosophical tradition.
Plato (/ˈpleɪtoʊ/ PLAY-toe; Greek: Πλάτων, Plátōn; born c. 428–423 BC, died 348/347 BC) was an ancient Greek philosopher of Classical Athens who is most commonly considered the foundational thinker of the Western philosophical tradition.[1] An innovator of the literary dialogue and dialectic forms, Plato influenced all the major areas of theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in Athenswhere Plato taught the collection of philosophical theories that would later become known as Platonism.
Plato's most famous contribution is his Theory of Forms (or Ideas), which aims to solve what is now known as the problem of universals. He was influenced by the pre-Socratic thinkers Pythagoras, Heraclitus, and Parmenides, although much of what is known about them is derived from Plato himself.
Along with his teacher Socrates, and his student Aristotle, Plato is a central figure in the history of Western philosophy. Plato's complete works are believed to have survived for over 2,400 years—unlike that of nearly all of his contemporaries.[2] Although their popularity has fluctuated, they have consistently been read and studied through the ages.[3] Through Platonism's outgrowth Neoplatonism, he also influenced Christian philosophy, and both Jewish and Islamic philosophy. In modern times, Alfred North Whitehead said: "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."[4]
Plato was born between 428 and 423 BC[5][6] into an aristocratic and influential Athenian family
7) Aristotle (384-322 BC)-- deductive syllogism
---quoting Wikipedia---
Aristotle[A] (Attic Greek: Ἀριστοτέλης, romanized: Aristotélēs;[B] 384–322 BC) was an ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, and the arts. As the founder of the Peripatetic school of philosophy in the Lyceum in Athens, he began the wider Aristotelian tradition that followed, which set the groundwork for the development of modern science.
Little is known about Aristotle's life. He was born in the city of Stagira in northern Greece during the Classical period. His father, Nicomachus, died when Aristotle was a child, and he was brought up by a guardian. At around eighteen years old, he joined Plato's Academyin Athens and remained there until the age of thirty seven (c. 347 BC). Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, tutored his son Alexander the Great beginning in 343 BC. He established a library in the Lyceum, which helped him to produce many of his hundreds of books on papyrus scrolls.
Though Aristotle wrote many treatises and dialogues for publication, only around a third of his original output has survived, none of it intended for publication. Aristotle provided a complex synthesis of the various philosophies existing prior to him. His teachings and methods of inquiry have had a significant impact across the world, and remain a subject of contemporary philosophical discussion.
Aristotle's views
--- end quoting Wikipedia---ppp
Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300BC) was an ancient Greek mathematician active as a geometer and logician.[2] Considered the "father of geometry",[3] he is chiefly known for the Elementstreatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissancescholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.
In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. In addition to the Elements, Euclid wrote a central early text in the optics field, Optics, and lesser-known works including Data and Phaenomena. Euclid's authorship of On Divisions of Figures and Catoptrics has been questioned. He is thought to have written many lost works.
9) Aristarchus of Samos 270BC-- systematized the experimental science of Astronomy
Before I discuss Aristarchus I need to talk about the other system of thought that competes with logic, reason and scientific method. There was a blossoming of science and logic in Ancient Greek times and that is because the other system of thought-- Religion was not so overbearing. Although in the case of Socrates, it became overbearing.
What I am saying is that a system of Religion of Multiple Gods, that some science and logic can flourish in that system by simply attaching a god like Apollo to your reasoning.
Whereas, by the Middle Ages, Religion was no longer flexible, and many suffered and payed the price of going against religion in their reasoning, logic and science. Aristarchus could flourish in his thoughts, while Galileo was almost tortured.
In the back of Wehr, Richards, Adair textbook of "Physics of the Atom", 1985, is a history of the "Chronology of the Atomic View of Nature".
And although it is only the science of Atomic view, it serves good measure as to the history of all of logic and all of science through history.
There is a huge gap of nothing after Lucretius 60BC with his De Rerum Natura-- the most complete record of Greek atomic theory. And then Saint Augustine 400AD that the forces by rubbed amber is different from forces of lodestone.
We have to jump to 1600 AD for important science to emerge with William Gilbert's textbook on magnetism.
What I am trying to explain to the Reader that the history of science had a fierce competitor in Religion, and religion wants people to place faith in dogma. So scientists and logical reasoning was anathema to religion. After 60BC, where scientists and logicians could be allowed freedom of thought with their multiple gods--- especially Apollo, the god of light and truth. But once the multiple gods were no longer extant, scientists and logicians risked death if they pushed their ideas. From 60BC to 1600AD the world was likely to have been 95% under the control of Religion as to what to think, say or even do. This period in time is commonly called the Dark Ages. A time period where science and logic are almost forbidden or risk losing your life.
Only by the year 1712 with the steam engine of Newcomen then Watt and then many others do we have a rise of science that takes a firm stand against dogma way of thinking.
By 1712 onwards, we have science and logic arising and we see it today in that our science technology put us on the Moon, not religion.
Multi-gods of Ancient Greek religion allowed for science and logic to flourish when put under the auspice of Apollo and Athena. When Multi-gods waned and religion was more one god and dogma, then science and logic had to be hidden and not given attention. Aristarchus could fully do Astronomy. But Copernicus 1473-1543 and Galileo (1564-1642) risked torture or death for their science and logic. Even the great Newton (1642-1727) was circumspect on what he said and published to not raise the ire of religion.
Moving on to Aristarchus, another systematizer, only this time astronomy.
I am trying to think of what Aristarchus used as learning aids. I would probably taken a some seed pod and drive a small branch into it representing Sun, Earth, Moon, Venus. Then when the students came for a lesson have them go around Earth or Earth go around Sun to figure out what was true.
Of course, being in the Northern Hemisphere, Aristarchus would have figured out that the Earth rotated on a axis that was tilted and rotated counterclockwise since the full Moon start out at NorthEast at 7PM sun set and as the night progresses, slowly ends up SouthWest in the sky.

Aristarchus of Samos (/ˌærɪˈstɑːrkəs/; Ancient Greek: Ἀρίσταρχος ὁ Σάμιος, Aristarkhos ho Samios; c. 310 – c. 230 BC) was an ancient Greek astronomerand mathematician who presented the first known heliocentric model that placed the Sun at the center of the universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He also supported the theory of Anaxagoras that the Sun was just another star.[2]
Born in Samos in approximately 310 BC, Aristarchus likely moved to Alexandria and became a student of Strato of Lampsacus, who later became the head of the Peripatetic school in Greece. According to Ptolemy, Aristarchus observed the summer solstice of 280 BC.[3]Vitruvius writes that Aristarchus built two different sundials: one a flat disc; and one hemispherical.[4]Aristarchus estimated the sizes of the Sun and Moon as compared to Earth, and the distances from the Earth to the Sun and to the Moon. His estimate that the Sun was 7 times larger than Earth (it's actually 109 times, in diameter) brought about the further insight that the Sun's greater size made it the most natural central point of the universe, as opposed to Earth.
Aristarchus was influenced by the concept presented by Philolaus of Croton (c. 470 – 385 BC) of a fire at the center of the universe (i.e. by contemporary understanding, at the center of the Earth). Aristarchus recast this "central fire" as the Sun, and he arranged the other planets in their correct order of distance around the Sun.[5]
Like Anaxagoras before him, Aristarchus suspected that the stars were just other bodies like the Sun, albeit farther away from Earth. His astronomical ideas were often rejected in favor of the geocentrictheories of Aristotle and Ptolemy. Nicolaus Copernicus knew that Aristarchus had a 'moving Earth' theory, although it is unlikely that Copernicus was aware that it was a heliocentric theory.[7][8]
The original text has been lost, but a reference in a book by Archimedes, entitled The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli), describes a work in which Aristarchus advanced the heliocentric model as an alternative hypothesis to geocentrism:
Aristarchus proposed that the fixed stars were extremely distant, and because ancient cosmology placed them all on a single celestial sphere, the modern concept of stellar parallax did not apply to his model. He placed the stars at a great distance so that their apparent positions relative to each other would remain constant throughout Earth's motion. Aristarchus reconciled this issue by postulating that the stars were other suns that are very far away,[2] far enough that the parallax was not observable. This implied a universe much larger than had been believed.
It is a common misconception that the heliocentric view was considered sacrilegious by the contemporaries of Aristarchus.[10] Lucio Russo traces this to Gilles Ménage's printing of a passage from Plutarch's On the Apparent Face in the Orb of the Moon, in which Aristarchus jokes with Cleanthes, who is head of the Stoics, a sun worshipper, and opposed to heliocentrism.[10] In the manuscript of Plutarch's text, Aristarchus says Cleanthes should be charged with impiety.[10]Ménage's version, published shortly after the trials of Galileo and Giordano Bruno, transposes an accusative and nominative so that it is Aristarchus who is purported to be impious.[10] The resulting misconception of an isolated and persecuted Aristarchus is still promulgated.[10][11]
According to Plutarch, while Aristarchus postulated heliocentrism only as a hypothesis, Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus, maintained it as a definite opinion and gave a demonstration of it,[12] but no full record of the demonstration has been found. In his Naturalis Historia, Pliny the Elder later wondered whether errors in the predictions about the heavens could be attributed to a displacement of the Earth from its central position.[13] Pliny[14] and Seneca[15] referred to the retrograde motion of some planets as an apparent (unreal) phenomenon, which is an implication of heliocentrism rather than geocentrism. Still, no stellar parallax was observed, and Plato, Aristotle, and Ptolemy preferred the geocentric model that was believed throughout the Middle Ages.
Part 3: Medieval Logicians
10) Avicenna (980 -1037)-- scientific method
Archimedes Plutonium Mar 6, 2026, 2:53:27 AM to Plutonium Atom Universe newsgroup.
I was curious to see if Avicenna influenced Leonardo? Sure enough he did.
It is the Scientific Method that Avicenna is famous for.
Saint Augustine 354-430 AD was the first report that the forces exerted by rubbed amber and by lodestone are different properties. (source Physics of Atom, Wehr, Richards, Adair)
Avicenna 980-1037: detailed the Scientific Method giving future scientists a method to find the truths of science.
William Gilbert 1540-1603 made the first detailed study of magnetism and also showed that, in addition to amber, many other materials can be electrified. (source Physics of Atom, Wehr, Richards, Adair)
There was a huge lull in activity on Atomic theory from Saint Augustine to William Gilbert and Avicenna filled that gap with the Scientific Method to proceed further.
Hujjat al-Haq (حجة الحق)
al-Sheikh al-Ra'is (الشيخ الرئيس)
Bu Alī Sīnā (بو علی سینا)
11) William of Ockham (1287-1347) -- Ockham's razor
Archimedes Plutonium Mar 6, 2026, 3:12:31 AM to Plutonium Atom Universe newsgroup.
Ockham was under-appreciated as a Logician, yet he likely contributed one of the most greatest Logical principles.
Under-appreciated until AP elevates his Occam's razor to the level of being a principle.
You see, as Occam stated his razor--- "entities must not be multiplied beyond necessity". Which in modern day speak is --- The easiest and most simple explanation for a chain of events is the true explanation.
But under Old Logic Boole and Jevons with their OR truth table being FTTF, they had no partial truth values, everything was all true or all false.
The Truth table representing subtraction or Remove for OR.
New Logic OR (exclusive)
p q p or q
____________
T T F
T dT T
dT T T
F F F
Where the dT represents partial true value.
Old Logic had this for OR.
Old Logic OR (exclusive)
p q p or q
____________
T T F
T F T
F T T
F F F
When you have everything be black and white and no shades in between you end up with a misconception of Occam's Razor that it is just a Rule that works sometimes but not all the times.
And physics supports the idea that Occam's Razor is a universal principle with its Least Action Principle, smallest minimum energy and no add ons.
Archimedes Plutonium Mar 6, 2026, 3:21:39 AM to Plutonium Atom Universe newsgroup.
Ockham was under-appreciated as a Logician, yet he likely contributed one of the most greatest Logical principles.
Under-appreciated until AP elevates his Occam's razor to the level of being a principle.
William of Ockham or Occam OFM (/ˈɒkəm/ OK-əm; Latin: Gulielmus Occamus;[11][12] c. 1287 – 9/10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and theologian, who was born in Ockham, a small village in Surrey.[13] He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century. He is widely known for Occam's razor, the methodological principle that bears his name, and also produced significant works on logic, physics and theology. Ockham is remembered in the Church of England with a commemoration corresponding to the commonly ascribed date of his death on 10 April.[14]
In scholasticism, William of Ockham advocated reform in both method and content, the aim of which was simplification. Ockham incorporated much of the work of some previous theologians, especially Duns Scotus. From Duns Scotus, Ockham derived his view of divine omnipotence, his view of grace and justification, much of his epistemology and ethical convictions.[25] However, he also reacted to and against Scotus in the areas of predestination, penance, his understanding of universals, his formal distinction ex parte rei (that is, "as applied to created things"), and his view of parsimony which became known as Occam's razor.
One important contribution that he made to modern science and modern intellectual culture was efficient reasoning with the principle of parsimony in explanation and theory building that came to be known as Occam's razor. This maxim, as interpreted by Bertrand Russell,[30] states that if one can explain a phenomenon without assuming this or that hypothetical entity, there is no ground for assuming it, i.e. that one should always opt for an explanation in terms of the fewest possible causes, factors, or variables. He turned this into a concern for ontological parsimony; the principle says that one should not multiply entities beyond necessity—Entia non sunt multiplicanda sine necessitate—although this well-known formulation of the principle is not to be found in any of Ockham's extant writings.[31] He formulates it as: "For nothing ought to be posited without a reason given, unless it is self-evident
Part 4: Modern day Logicians
12) George Boole (1815-1864) and William Jevons (1835-1882) -- logic connectors
Let me slightly review where the Atomic Theory was prior to the birth of Modern day logic.
Founding Framers of Chemistry Lavoisier and Dalton
Antoine Lavoisier (1734-1794) published a book containing a well-founded concept of chemical elements and the verification of the law of conservation of matter in chemical reactions. (source: Physics of the Atoim, Wehr, Richards, Adair)
John Dalton (1766-1844) published the first of a series of papers introducing atomic weights, establishing the law of multiple proportions, and founding the atomic theory of matter. (source: Physics of the Atom, Wehr, Richards, Adair)
Archimedes Plutonium Mar 6, 2026, 7:56:42 PM to Plutonium Atom Universe newsgroup.
When reading the history of Logicians, we should ask also, if they behaved logically throughout their life???
AP writes: Rather sad that Logic has always taken a back seat as far as the sciences are concerned compared to math. Probably because few can think clear and straight in the first place.
George Boole (/buːl/ BOOL; 2 November 1815 – 8 December 1864) was an English autodidact, mathematician, philosopher and logician who served as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854), which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age.[4][5][6]
Boole was the son of a shoemaker. He received a primary school education and learned Latin and modern languages through various means. At 16, he began teaching to support his family. He established his own school at 19 and later ran a boarding school in Lincoln. Boole was an active member of local societies and collaborated with fellow mathematicians. In 1849, he was appointed the first professor of mathematics at Queen's College, Cork (now University College Cork) in Ireland, where he met his future wife, Mary Everest. He continued his involvement in social causes and maintained connections with Lincoln. In 1864, Boole died due to fever-induced pleural effusion after developing pneumonia.
Boole published around 50 articles and several separate publications in his lifetime. Some of his key works include a paper on early invariant theory and "The Mathematical Analysis of Logic", which introduced symbolic logic. Boole also wrote two systematic treatises: "Treatise on Differential Equations" and "Treatise on the Calculus of Finite Differences". He contributed to the theory of linear differential equations and the study of the sum of residues of a rational function. In 1847, Boole developed Boolean algebra, a fundamental concept in binary logic, which laid the groundwork for the algebra of logic tradition and forms the foundation of digital circuit design and modern computer science. Boole also attempted to discover a general method in probabilities, focusing on determining the consequent probability of events logically connected to given probabilities.
Boole's work was expanded upon by various scholars, such as Charles Sanders Peirce and William Stanley Jevons. Boole's ideas later gained practical applications when Claude Shannon and Victor Shestakov employed Boolean algebra to optimize the design of electromechanical relay systems, leading to the development of modern electronic digital computers. His contributions to mathematics earned him various honours, including the Royal Society's first gold prize for mathematics, the Keith Medal, and honorary degrees from the Universities of Dublin and Oxford. University College Cork celebrated the 200th anniversary of Boole's birth in 2015, highlighting his significant impact on the digital age.
William Stanley Jevons FRS (/ˈdʒɛvənz/;[2] 1 September 1835 – 13 August 1882) was an English economist and logician.
Irving Fisher described Jevons's book The Theory of Political Economy (1871) as the start of the mathematical method in economics.[3] It made the case that economics, as a science concerned with quantities, is necessarily mathematical.[4] In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons's contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time.
Jevons broke off his studies of the natural sciences in London in 1854 to work as an assayer in Sydney, where he acquired an interest in political economy. Returning to the UK in 1859, he issued a "Notice of a General Mathematical Theory of Political Economy" in 1862, outlining the marginal utility theory of value, and published A Serious Fall in the Value of Gold in 1863. For Jevons, the utility or value to a consumer of an additional unit of a product is inversely related to the number of units of that product he already owns, at least beyond some critical quantity.
Jevons received public recognition for his work on The Coal Question (1865), in which he called attention to the gradual exhaustion of Britain's coal supplies and also put forth the view that increases in energy production efficiency leads to more, not less, consumption.[5]: 7f, 161f This view is known today as the Jevons paradox, named after him. Due to this particular work, Jevons is regarded today as the first economist of some standing to develop an 'ecological' perspective on the economy.[6]: 295f [7]: 147 [5]: 2
The most important of his works on logic and scientific methods is his Principles of Science (1874),[8]as well as The Theory of Political Economy (1871) and The State in Relation to Labour (1882). Among his inventions was the logic piano, a mechanical computer.
13) Gottlob Frege (1848-1925)-- symbolic logic
Friedrich Ludwig Gottlob Frege (/ˈfreɪɡə/;[7] German:[ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano(1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be one of the greatest logicians since Aristotle, and one of the most profound philosophers of mathematics ever.[8]
His contributions include the development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmeticis the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical papers "On Sense and Reference" and "The Thought" are also widely cited. The former argues for two different types of meaningand descriptivism. In Foundations and "The Thought", Frege argues for Platonism against psychologism or formalism, concerning numbers and propositionsrespectively.
James Clerk Maxwell FRS FRSE (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician[1] who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism achieved the second great unification in physics,[2] where the first one had been realised by Isaac Newton. Maxwell was also key in the creation of statistical mechanics.
Maxwell graduated from Trinity College, Cambridge, in 1854, where he earned distinction in mathematics and the Smith’s Prize. He remained at Cambridge briefly, publishing early mathematical work and investigations into optics, particularly the principles of colour combination and colour-blindness. He later held the Chair of Natural Philosophy at Marischal College, where he studied the rings of Saturn and correctly proposed that they were composed of numerous small particles,[3] work that earned him the Adams Prize in 1859. During this time he married Katherine Mary Dewar, who assisted him in his laboratory work. From 1860 to 1865, he served as the Professor of Natural Philosophy at King’s College London, where he developed his theory of electromagnetic fields. His publication of "A Dynamical Theory of the Electromagnetic Field" in 1865 demonstrated that electric and magnetic fieldstravel through space as waves moving at the speed of light, proposing that light is an undulation in the same medium that is the cause of electric and magnetic phenomena.[4] His unification of light and electrical phenomena led to his prediction of the existence of radio waves.
Maxwell was the first to derive the Maxwell–Boltzmann distribution, a statistical means of describing aspects of the kinetic theory of gases, which he worked on sporadically throughout his career.[5] He presented the first durable colour photograph in 1861, and showed that any colour can be produced with a mixture of any three primary colours, those being red, green, and blue, the basis for colour television.[6] He worked on analysing the rigidity of rod-and-joint frameworks (trusses) like those in many bridges. He devised modern dimensional analysis and helped to establish the CGS system of measurement. He was the first to understand chaos, and the first to emphasize the butterfly effect. His 1863 paper On Governors serves as an important foundation for control theory and cybernetics, and was also the earliest mathematical analysis on control systems.[7][8] In 1867, he proposed the thought experiment known as Maxwell's demon, which challenges how information affects entropy in thermodynamics. In his seminal 1867 paper On the Dynamical Theory of Gases he introduced the Maxwell model for describing the behavior of a viscoelastic material and originated the Maxwell-Cattaneo equation for describing the transport of heat in a medium.
In 1871, Maxwell returned to Cambridge as the first Cavendish Professor of Physics, overseeing the construction of the Cavendish Laboratory. As a result of his work he is regarded as a founder of the modern field of electrical engineering.[6] His discoveries helped usher in the era of modern physics, laying the foundations for such fields as relativity, also being the one to introduce the term into physics,[9] and quantum mechanics.[10][11]
15) Pierre Curie (1859-1906) and Paul Dirac (1902-1984) --symmetry in science of the magnetic monopole existence
Archimedes Plutonium Mar 6, 2026, 8:53:12 PM to Plutonium Atom Universe newsgroup.
Most people out of science, or even in science, have little awareness of how SYMMETRY plays a huge role in science and logic. Science abhors asymmetry. What kept Pierre Curie and Paul Dirac going adamant about for much of their life, was this abhorrence that the Maxwell Equations were asymmetrical unless the magnetic monopole exists.
It was right under their noses for in 1897, J.J. Thomson found the magnetic monopole--- the 0.5MeV particle. Unfortunately Thomson and all the scientists after Thomson thought it was the electron of Atoms. No, by logic, the Muon is the electron of atoms and the 0.5MeV particle is the Curie-Dirac magnetic monopole.
Pierre Curie[a] (15 May 1859 – 19 April 1906) was a French physicist and chemist, and a pioneer in crystallography and magnetism. He shared one half of the 1903 Nobel Prize in Physics with his wife, Marie Curie, for their work on radioactivity.[3] With their win, the Curies became the first married couple to win a Nobel Prize, launching the Curie family legacy of five Nobel Prizes.
Paul Adrien Maurice Dirac (/dɪˈræk/ dih-RAK;[3] 8 August 1902 – 20 October 1984) was a British theoretical physicist who is considered to be one of the founders of quantum mechanics.[4][5] Dirac laid the foundations for both quantum electrodynamics and quantum field theory, coining the former term.[6][7][8][9] He was the Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969, and a professor of physics at Florida State University from 1970 to 1984. Dirac shared the 1933 Nobel Prize in Physicswith Erwin Schrödinger "for the discovery of new productive forms of atomic theory."[10]
Dirac graduated from the University of Bristol with a First Class HonoursBachelor of Science degree in electrical engineering in 1921, and a first class honours Bachelor of Arts degree in mathematics in 1923.[11] Dirac then graduated from St John's College, Cambridge, with a Ph.D. in physics in 1926, writing the first ever thesis on quantum mechanics.[12]
He formulated the Dirac equation, one of the most important results in physics, in 1928.[7] It connected special relativity and quantum mechanics and predicted the existence of antimatter.[13] He wrote a famous paper in 1931,[14]which further predicted the existence of antimatter.[15][16][13] Dirac also contributed greatly to the reconciliation of general relativity with quantum mechanics. He contributed to Fermi–Dirac statistics, which describes the behaviour of fermions, particles with half-integer spin. His 1930 monograph, The Principles of Quantum Mechanics, is one of the most influential texts on the subject.[17] He and Schrödinger tied for eighth in a Physics World poll of the greatest physicists of all time.[18]
In 1987, Abdus Salam declared that "Dirac was undoubtedly one of the greatest physicists of this or any century ... No man except Einstein has had such a decisive influence, in so short a time, on the course of physics in this century."[19] In 1995, Stephen Hawking stated that "Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe"[20] while Stanley Deser remarked that "We all stand on Dirac's shoulders."[21]
Dirac was born on 8 August 1902 at his parents' home in Bristol, England,[22]and grew up in the Bishopston area of the city.[23][24] His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, Switzerland, of French descent,[25] who worked in Bristol as a French teacher. His mother, Florence Hannah Holten, was born to a Cornish Methodist family in Liskeard, Cornwall.[26][27] She was named after Florence Nightingale by her father, a ship's captain, who had met Nightingale while he was a soldier during the Crimean War.[28] His mother moved to Bristol as a young woman, where she worked as a librarian at the Bristol Central Library; despite this she still considered her identity to be Cornish rather than English.[29] Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix,[30][31] who died by suicide in March 1925.[32] Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much ... I never knew that parents were supposed to care for their children, but from then on I knew."[33]
Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919.[34] Dirac's father was strict and authoritarian, although he disapproved of corporal punishment.[35] Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, and I am my own man." Charles forced his children to speak to him only in French so that they might learn the language. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent.[36][37]
John Stewart Bell FRS[2] (28 July 1928 – 1 October 1990)[3] was a physicistfrom Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories.[4][5][6][7][8]
In 2022, the Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for work on Bell inequalities and the experimental validation of Bell's theorem.[9]
Bell was born in Belfast, Northern Ireland to a working class family. Due to financial hardship, neither parent and none of his three older siblings completed high school, typically dropping out of school by age 14 to work.[10]When he was 11 years old, he decided to be a scientist, and encouraged by his mother, at 16 he graduated from Belfast Technical High School.[10] Then in an exceptionally rare occurrence for someone of his background, Bell attended the Queen's University of Belfast, where, in 1948, he obtained a bachelor's degree in experimental physics and, a year later, a bachelor's degree in mathematical physics.[10] He went on to complete a PhD in physics at the University of Birmingham in 1956, specialising in nuclear physics and quantum field theory. In 1954, he married Mary Ross, also a physicist, whom he had met while working on accelerator physics at Malvern, UK.[11]: 139 Bell became a vegetarian in his teen years.[12] According to his wife, Bell was an atheist.[13]
Bell's career began with the UK Atomic Energy Research Establishment, near Harwell, Oxfordshire, known as AERE or Harwell Laboratory. In 1960, he moved to work for the European Organization for Nuclear Research (CERN, Conseil Européen pour la Recherche Nucléaire), in Geneva, Switzerland.[14]There he worked almost exclusively on theoretical particle physics and on accelerator design, but found time to pursue a major avocation, investigating the foundations of quantum theory. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1987.[15] Also of significance during his career, Bell, together with John Bradbury Sykes, M. J. Kearsley, and W. H. Reid, translated several volumes of the ten-volume Course of Theoretical Physics of Lev Landau and Evgeny Lifshitz, making these works available to an English-speaking audience in translation, all of which remain in print.
Bell was a proponent of pilot wave theory.[16] In 1987, inspired by Ghirardi–Rimini–Weber theory, he also advocated collapse theories.[17] He said about the interpretation of quantum mechanics: "Well, you see, I don't really know. For me it's not something where I have a solution to sell!"[18]
17) Archimedes Plutonium (1950 - present)-- systematizes Logic by paralleling logic to mathematics-physics