Aristotle

Born 384 BC Stegirus, Macedonia, Greece

died 322 BC Chalcis, Euboea, Greece

Aristotle

Aristotle was a Greek philosopher who made important contributions by systematizing deductive logic and wrote about physics topics. His philosophy had a long-term influence on the development of all philosophical theories in the West.

Aristotle was not primarily a mathematician, but made an important contribution through systematic deductive logic. He wrote on the subject of physics: some parts of his posterior analysis showed an unusual grasp of mathematical methods. The main thing, however, is that he is important in the development of all knowledge, as the author of [2] writes:-

Aristotle, more than any other thinker, can determine the direction and content of the history of Western thought. He was the author of a philosophical and scientific institution that became supported and vehicled by both Christian and Islamic academic thought in the Middle Ages through the centuries: until the end of the 17th century, Western culture was Aristotle. And, even after the intellectual revolution of the centuries that followed, Aristotle's concepts and ideas remained deeply rooted in Western thought.

Aristotle was born in Stagirus, or Stagir, or Stagilus, on the Halsicid Peninsula in northern Greece. His father was Nicomachos, a doctor, while his mother was named Fistis. When Aristotle was born, Nicomachos must have lived in Halcidis, and he was probably born in that area. Aristotle's mother, Fistis, came from Czarsis in Eupenia and her family property there.

There is no doubt that Nimakos would have wanted Aristotle to become a doctor, because tradition is that medical skills are kept secret and passed from father to son. It's not a society where people go to the doctor, it's a doctor who travels around the country to take care of the sick. Although we know nothing about Aristotle's early years, he will most likely travel with his father. We do know that Nikomachus found that the conditions of Halkidis were inferior to those of the neighbouring state of Macedonia, where he began to work with great success, so much so that he was soon appointed personal physician to King Amintas III of Macedon.

There is no record of whether Aristotle lived with his father in the Macedonian capital of Pella, while Nimachus served King Amintas at the court there. A few years later, however, Aristotle was indeed friendly to Philip, the son of King Amintas, and it is reasonable to assume that the two men, who were almost exactly the same age, had become friendly at Pella at a young age.

Aristotle was about ten years old when his father died. This of course means that Aristotle cannot now continue his father's profession as a physician, and since his mother also appears to have died prematurely, Aristotle was raised by proxenus of his guardian Attalnius, who was his uncle (or possibly his family friend suggested by some authors). Proxenus taught Aristotle Greek, rhetoric, and poetry to complement Nimakos' teachings on biology to Aristotle as part of training his son in medicine. Since Aristotle wrote exquisite Greek prose in his later years, this must have been part of his early education.

In 367 BC, at the age of 17, Aristotle became a student of Plato's Academy in Athens. When Aristotle joined the Academy, it had been in operation for twenty years. Plato was not in Athens, but visited Syracuse for the first time. We should not regard the Plato Academy as a non-political organization interested only in abstract ideas. The Academy was highly involved in the politics of the time, and in fact Plato's visit to Sicily was for political reasons, and the politics of the Academy and the region as a whole would play an important role in influencing the course of Aristotle's life.

When Aristotle arrived in Athens, the academy was run by Eudoxus of Cnidos, while Plato was not. Spercy Persia, Plato's nephew, also taught at the Academy because he was a Chalcedon of Xenocraty. After becoming a student, Aristotle soon became a teacher at the academy and remained there for twenty years. We know very little about what Aristotle taught at the Academy. In the writings of [10] Diogenes Laertius, AD II, aristotle taught rhetoric and dialectics. Of course, Aristotle wrote rhetoric at this time, publishing Gryllus, attacking is the view of rhetoric by Isocrates, who ran another major educational institution in Athens. All of Aristotle's writings of this period strongly support Plato's views and the views of the Academy.

Aristotle's twenty years at the Academy were coming to an end, and his position became difficult due to the political events of the time. The Macedonian king Amintas died around 369 BC, a few years before Aristotle traveled to Athens to join the Academy. Amintas' two sons, Alexander II and Perdikas III, both ruled Macedonia for a time, but the kingdom suffered from both internal strife and external war. Amintas' third son, Philip II, ascended to the throne in 359 BC, when Perdikas was killed while resisting the Illyrian invasion. Philip used ingenious military and political tactics to bring Macedonia into a period of internal peace, expanding through victories over the surrounding areas.

Philip captured Olynthos in 348 and annexed Halcidis BC. The Aristotle-born town of Stagirus held out for some time, but was also defeated by Philip. Athens feared a powerful macedonian threat, but Aristotle grew up at the Macedonian court and most likely maintained a friendship with Philip. The actual order of events is now a bit uncertain. Plato died in 347 BC and Sphipps assumed the leadership of the academy. Aristotle was certainly opposed to Spercipos's opinion that he might have left the academy after Plato's posthumous academic reasons or because he was not named head of the college himself. However, some sources suggest that he may have left for political reasons before Plato's death, as his links to Macedonia were unpopular.

Aristotle traveled from Athens to Athos, facing the island of. He was not alone in leaving the Academy of Xenocrady's Carlsy who left him. In Athos, Aristotle was warmly welcomed by Hermias, the ruler of Atalnius. Aristotle was probably philip's ambassador, and Hermias certainly did the same with him. Aristotle married Hermias's niece and adopted daughter Petias, who had a child, a daughter also named Pitias. However, Aristotle's wife was about 10 years after they were married. She is thought to be much younger than Aristotle, who was about 18 years old when they were married.

At Athos, Aristotle became the leader of the group of philosophers that Hermias had gathered there. It is possible that Xenocrates was also a member of the organization. Aristotle had a keen interest in anatomy and the structure of living things in general, an interest that his father had cultivated in him in his early years, which helped him develop an extraordinary talent for observation. Aristotle and his group began to collect observations at Athos, especially in zoology and biology. Barnes wrote in [6] aristotle:-

... The study of animals laid the foundations of the biological sciences; they were not replaced until more than two thousand years after his death. The investigations on which these great works are based may have been conducted mainly in Athos and.

Aristotle may have begun his Politics of Athos and The Theory of Kingship, the latter of which is now lost. He began to develop a philosophy different from plato, who had said that a king should be a philosopher and a philosopher should be a king. In response to King Aristotle of Han wrote that it was:-

...... For kings, becoming a philosopher was not only unnecessary, but even disadvantageous. Instead, the king should heed the advice of a true philosopher. Then he will fill his rule with good deeds rather than good words.

However, Aristotle's time in Athos ended with political events. The Persians attacked the town, and Hermias was captured and executed. Aristotle escaped on his way to Macedonia and stopped at. It wasn't just a short visit, as he was there for about a year, and there was definitely a team of scientists from Assos who were there with him to continue their biological research.

Macedonia is now at peace with Athens because Philip signed a treaty in 346 BC. In 343 BC, Aristotle arrived at the Macedonian court and stayed there for seven years. The oft-quoted story is that he became a mentor to the young Alexander the Great (Philip's son), and as Jaeger points out, almost certainly a later invention, see [16]. Grayeff suggests in [12] that Philip saw in Aristotle the future head of the Academy of Athens. This certainly suited Philippes, the dean of the academy at the time, who strongly opposed Philip and strongly encouraged Athens to oppose the rise of Macedonia. 340 BC,

The treaty between Athens and Macedonia began to break and preparations for war began. The following year Speusippus died but Aristotle, although proposed as head of the Academy , was not elected. The post went to Xenocrates Philip to lose interest in his support of Aristotle. He moved back to his home in Stagirus and came to Stagirus with his circle of philosophers and scientists.

Aristotle did not remarry after the death of his wife, but he did have a relationship with Hepilis from his hometown of Stagirus. It's not clear when they first met, but together they bore a son, Nicomachos, named after Aristotle's father.

Philip is now at the pinnacle of power, but as has often happened, it proves to be time for internal strife. Aristotle supported Alexander, the son of Philip, who soon became king. Alexander decided to adopt a policy similar to that of his father toward Athens and sought to maintain his power in a peaceful manner. Alexander protected the Academy and encouraged it to continue its work. At the same time, however, he sent Aristotle to Athens to establish a rival.

In 335 BC, Aristotle established his own school in Athens, Lyceum. He came to the city with a large collection of teaching materials and assistants collected in Macedonia. Books, maps, and other teaching materials were likely at some stage intended to support Aristotle as dean of the academy. The academy's interests have always been narrow, but the academy under Aristotle pursued a wider range of disciplines. Aristotle's detailed study of nature, as well as all other subjects of his study[6], give prominence:-

His own research was conducted in the company, and he communicated his ideas to his friends and students, never thinking of keeping them as a private treasure trove. In fact, he believes that a person cannot claim to know a subject unless he is able to impart his knowledge to others, and he considers teaching to be an appropriate expression of knowledge.

Both the fall back to our work is due to Aristotle or later members of his school were questioned by scholars who ended several dynasties in the 19th century. Jaeger [16] discusses the reasons, but in this work Jaeger argues that the apparent differences in Aristotle's approach in different writings can be explained by ideas he has developed over the years. Grave [6] examines certain texts in detail and again claims that they represent the development of his school of thought long after Aristotle's death. He wrote:-

In the same year Aristotle taught logic in almost every discipline—not once, but two or three times—— 、 physics, astronomy, meteorology, zoology, metaphysics, theology, psychology, politics, economics, ethics, rhetoric, poetics; and he wrote these lecture notes, expanding and modifying them many times, until they reached the stage where we read them. What is even more shocking, however, is that most of these disciplines did not exist before him, so he would be the first to conceive and establish them as systematic disciplines.

After the death of Alexander the Great in 323 BC, anti-Macedonian sentiment in Athens led Aristotle to retire to Halses, where he lived in a house that once belonged to his mother and was still kept by his family. The following year, he died of a stomach ailment at the age of 62.

It is almost impossible to have any definite impression of Aristotle's personality, but the author of [2] writes:-

Anecdotes about him indicate that he was an amiable man, showing little trace of self-importance that some scholars thought they could find in his work. His will was preserved, showing the same traits of kindness; he referred to his happy family life and took care of his children and his servants with care.

Barnes [6] wrote:-

He's a bit of a playboy, with rings on his fingers and a funky cut of his hair. He had indigestion, supposedly spindle-shaped. He was a good speaker, with clear lectures and persuasive conversations; he had a keen intellect. His numerous enemies made him appear arrogant and domineering. ...... As a man, I suspect he is admirable rather than amiable.

Above we have commented on the debate among modern scholars as to whether Aristotle wrote the paper now assigned to him. We do know that his work is divided into two distinct parts, namely the works he published during his lifetime and now lost (although some fragments have survived citations from other people's works), and the collections of writings that have survived and are in our collection. Aristotle did not publish it during his lifetime. We can say with certainty that Aristotle never intended to fill these 30 works with the print pages to be published in 2000. They are, of course, lecture notes from the Lyceum curriculum, and as most scholars believe, either the work of Aristotle or the work of later lecturers. Of course, they are likely to be course notes originally taught by Aristotle but later added by other lecturers after Aristotle's death.

These works were first published around 60 BC by Andronicus of Rhodes, the last head of Lyceum. Of course [ 2 ] :-

The forms, titles, and sequences of Aristotle texts studied today were given by Andronikos nearly three centuries after the philosopher's death, and it was at this stage that the long history of commentary on them began.

What are these works? There are important works on logic. Aristotle believed that logic was not a science, but that it must be dealt with before studying every branch of knowledge. Aristotle's logical name is "analysis," and the word logic was introduced by Xenocrates, who worked at the academy. Aristotle believed that logic must be applied to science[6]:-

Science—at least theoretical science—will be axiomatized. So, what are their axioms? What conditions must a proposition satisfy in order to be an axiom? Again, what form will the derivations in each science take? On what basis can the axioms be derived from the axioms? These are the questions that Aristotle raised in his logical writings, especially in works known as a priori and posterior analysis.

In fact, in a priori analysis, Aristotle proposed what is now known as Aristotle's syllogism, a form of argument consisting of two premises and one conclusion. His example is:-

(i) Every Greek is a person.

(ii) Everyone dies.

(iii) Every Greek would die.

Aristotle was not the first to propose an axiomatic system. Plato boldly proposed that there might be a single axiom system of all knowledge. Aristotle sought more possible axiomatic system suggestions for each science. Note that Euclid and his system of geometric axioms emerged after Aristotle.

Another subject to which Aristotle made a significant contribution was natural philosophy, or physics in today's terminology. (I [English, French and Russian] indicated my age and the traditional nature of the University of St Andrews, if I would say so, in 1960 š formed part of my degree, in a "Conventional Natural Philosophy" pass.) Aristotle focused on matter, change, motion, space, location, and time. He also presented astronomy in particular his research contributions to the study of comets, geography and function, such as the examination of rivers), chemistry, which he was interested in, such as combustion, as well as meteorology and the study of rainbows.

In addition to his important works in zoology and psychology, Aristotle wrote his famous work on metaphysics. According to Aristotle, this study [2]:-

... The most universal or abstract features of reality and principles with universal validity. ...... Metaphysics studies that all things that exist must be true within the limits of their existence, [and] it studies the general conditions under which anything that exists must be satisfied.

Although Aristotle seems to have made few new discoveries in mathematics, he had important implications for the development of mathematics. As Heath explains in [14]:-

The importance of a correct understanding of Aristotle's mathematics lies primarily in the fact that most of his explanations of the scientific method are taken from mathematics.

Apparently, Aristotle had a thorough grasp of elementary mathematics and believed in the importance of mathematics as one of three theoretical sciences. However, to be fair, he disagreed with Plato, who elevated mathematics to such a prominent field of study that there was little room for the scientific scope of Aristotle's study. Aristotle claimed that the other two theoretical sciences were (using modern terminology) philosophy and theoretical physics.

Heath, in his introduction [14], points out some of the mathematics that Aristotle mentioned in his writings:-

... Aristotle was aware of Theodokhos' important discoveries, which had a profound effect on Euclid's exposition of the elements. An allusion clearly shows that Aristotle knew of Eudox's great theory of proportions which was elaborated by Euclid in his book V, and recognized its importance. Another passage recalls the basic assumptions on which Eudoxos based his "exhaustion method" of measuring area and volume; and, of course, Aristotle was familiar with the system concentric spheres through which O'Dox and Karips theoretically explained the independent motion of the sun, moon, and planets. ...

The irreducible is mentioned over and over again, but the case mentioned is that the diagonal line relative to its side; There is no mention of Theodoros and Thasted extending the theory to other cases ...

Heath [14] also mentions mathematics that Aristotle did not mention, which may be surprising. Yes:-

... There is no mention of a cone section, a double of the cube, or a cubic part of an angle. The problems related to the attempts of Antiphon, Bryson and Hippocrates to solve it mention the squared problem of the circle; but there is no question of the curve of Hippias...

While Heath [14] discusses aristotle's many mathematical references, the book [5] attempts to construct (or reconstruct) artifacts from Aristotle's observations on mathematical philosophy. As the apostles wrote in [5]:-

... A large number of articles on mathematics are distributed in all the works that we have and indicate a definite philosophy of mathematics, so that it is possible to try to construct or reconstruct this philosophy with considerable accuracy.

We conclude our discussion with an explanation of the ideas of "continuity" and "infinity" in Aristotle's mathematics. Heath [ 15 ] explains Aristotle's idea of "continuity":-

... Cannot be composed of indivisible parts; a continuum is the boundary or boundary between two continuous parts, where they touch, is one and the same ...

As for the infinite Aristotle, he argued that it did not actually exist, but only existed potentially. Aristotle wrote in physics (see example [15]):-

But in any case, my argument does not deprive mathematicians of their research, although it denies the existence of infinity in the sense of actual existence, for something increases to the point of inability to pass; for, in fact, they do not need or use the infinite, but only a finite straight line as they wish. ...... So, as far as proof is concerned, it doesn't have any effect on them.