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Person: Aristotle

Aristotle was a Greek philosopher who made important contributions by systemizing deductive logic and wrote on physical subjects. His philosophy had a long-lasting influence on the development of all Western philosophical theories.

Mathematical Profile (Excerpt):

• Aristotle was born in Stagirus, or Stagira, or Stageirus, on the Chalcidic peninsula of northern Greece.
• Nicomachus was certainly living in Chalcidice when Aristotle was born and he had probably been born in that region.
• Since in latter life Aristotle wrote fine Greek prose, this too must have been part of his early education.
• In 367 BC Aristotle, at the age of seventeen, became a student at Plato's Academy in Athens.
• At the time that Aristotle joined the Academy it had been operating for twenty years.
• When Aristotle arrived in Athens, the Academy was being run by Eudoxus of Cnidos in Plato's absence.
• After being a student, Aristotle soon became a teacher at the Academy and he was to remain there for twenty years.
• We know little regarding what Aristotle taught at the Academy.
• Certainly Aristotle wrote on rhetoric at this time, issuing Gryllus which attacked the views on rhetoric of Isocrates, who ran another major educational establishment in Athens.
• All Aristotle's writings of this time strongly support Plato's views and those of the Academy.
• Amyntas, the king of Macedonia, died around 369 BC, a couple of years before Aristotle went to Athens to join the Academy.
• Stagirus, the town of Aristotle's birth, held out for a while but was also defeated by Philip.
• Athens worried about the powerful threatening forces of Macedonia, and yet Aristotle had been brought up at the Court of Macedonia and had probably retained his friendship with Philip.
• Aristotle was certainly opposed to the views of Speusippus and he may have left the Academy following Plato's death for academic reasons or because he failed to be named head of the Academy himself.
• Aristotle travelled from Athens to Assos which faces the island of Lesbos.
• In Assos Aristotle was received by the ruler Hermias of Atarneus with much acclaim.
• It is likely that Aristotle was acting as an ambassador for Philip and he certainly was treated as such by Hermias.
• On Assos, Aristotle became the leader of the group of philosophers which Hermias had gathered there.
• Aristotle and the members of his group began to collect observations while in Assos, in particular in zoology and biology.
• Aristotle probably begun his work Politics on Assos as well as On Kingship which is now lost.
• Aristotle escaped and stopped on the island of Lesbos on his way to Macedonia.
• In 343 BC Aristotle reached the Court of Macedonia and he was to remain there for seven years.
• The following year Speusippus died but Aristotle, although proposed as head of the Academy, was not elected.
• The position went to Xenocrates and Philip lost interest in his support for Aristotle.
• At the same time, however, he sent Aristotle to Athens to found a rival establishment.
• In 335 BC Aristotle founded his own school the Lyceum in Athens.
• He arrived in the city with assistants to staff the school and a large range of teaching materials he had gathered while in Macedonia; books, maps, and other teaching material which may well have been intended at one stage to support Aristotle in his bid to become head of the Academy.
• The Academy had always been narrow in its interests but the Lyceum under Aristotle pursued a broader range of subjects.
• Whether the works that come down to us are due to Aristotle or to later members of his school was questioned by a number of scholars towards the end of the 19th century.
• We have commented above on the disputes among modern scholars as to whether Aristotle wrote the treatises now assigned to him.
• We do know that his work falls into two distinct parts, namely works which he published during his lifetime and are now lost (although some fragments survive in quotations in works by others), and the collection of writings which have come down to us and were not published by Aristotle in his lifetime.
• We can say with certainty that Aristotle never intended these 30 works which fill over 2000 printed pages to be published.
• They are certainly lecture notes from the courses given at the Lyceum either being, as most scholars believe, the work of Aristotle, or of later lecturers.
• Of course it is distinctly possible that they are notes of courses originally given by Aristotle but later added to by other lecturers after Aristotle's death.
• Aristotle believed that logic was not a science but rather had to be treated before the study of every branch of knowledge.
• Aristotle's name for logic was "analytics", the term logic being introduced by Xenocrates working at the Academy.
• Those are among the questions which Aristotle poses in his logical writings, and in particular in the works known as Prior and Posterior Analytics.
• In Prior Analytics Aristotle proposed the now famous Aristotelian syllogistic, a form of argument consisting of two premises and a conclusion.
• Aristotle was not the first to suggest axiom systems.
• Aristotle went for the somewhat more possible suggestion of an axiom system for each science.
• Notice that Euclid and his axiom system for geometry came after Aristotle.
• Another topic to which Aristotle made major contributions was natural philosophy or rather physics by today's terminology.
• As well as important works on zoology and psychology, Aristotle wrote his famous work on metaphysics.
• Although Aristotle does not appear to have made any new discoveries in mathematics, he is important in the development of mathematics.
• Clearly Aristotle had a thorough grasp of elementary mathematics and believed mathematics to have great importance as one of three theoretical sciences.
• However, it is fair to say that he did not agree with Plato, who elevated mathematics to such a prominent place of study that there was little room for the range of sciences studied by Aristotle.
• The other two theoretical sciences, Aristotle claimed, were (using modern terminology) philosophy and theoretical physics.
• Aristotle was aware of the important discoveries of Eudoxus which affected profoundly the exposition of the Elements by Euclid.
• One allusion clearly shows that Aristotle knew of Eudoxus's great Theory of Proportion which was expounded by Euclid in his Book V, and recognised the importance of it.
• Another passage recalls the fundamental assumption on which Eudoxus based his 'method of exhaustion' for measuring areas and volumes; and, of course, Aristotle was familiar with the system of concentric spheres by which Eudoxus and Callippus accounted theoretically for the independent motions of the sun, moon, and planets.
• We end our discussion with an illustration of Aristotle's ideas of 'continuous' and 'infinite' in mathematics.
• As to the infinite Aristotle believed that it did not actually exist but only potentially exists.

Born 384 BC, Stagirus, Macedonia, Greece. Died 322 BC, Chalcis, Euboea, Greece.

View full biography at MacTutor

Tags relevant for this person:

Analysis, Ancient Greek, Applied Maths, Astronomy, Geography, Geometry, Origin Greece, Physics, Puzzles And Problems, Set Theory, Special Numbers And Numerals

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Persons: 5

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive