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Aristotle
was not mainly a mathematician but made significant contributions
by systematizing deductive logic.
Aristotle
was born in Stageirus, on the Chalcidic peninsula in the northern
part of Greece. His father was Nicomachus, a medical doctor, and
his mother was Phaestis. Nicomachus was living in Chalcidice when
Aristotle was born and was probably born in that region.
Aristotle's mother, Phaestis, came from Chalcis in Euboea and
where her family owned property.
Nicomachus
would have liked Aristotle to become a doctor, for the tradition
included that medical skills were kept covert and handed down from
father to son. When
Aristotle was about ten years old his father died. This certainly
meant that Aristotle could not now follow in his father's
profession of doctor. Since
his mother also died young, Aristotle was brought up by, Proxenus
of Atarneus, who was his uncle.
Proxenus taught Aristotle Greek, rhetoric, and poetry.
In
367 BC Aristotle, at the age of seventeen, became a student at
Plato's Academy in Athens. Plato
was not in Athens, but rather he was on his first visit to
Syracuse. 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 remained there for twenty years. We know little
regarding what Aristotle taught at the Academy, but we know that
he taught rhetoric and dialectic.
Due
to the political events of the time, Aristotle's twenty years at
the Academy became difficult and he was forced to leave.
Aristotle traveled 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. Aristotle married Pythias, the niece and adopted daughter
of Hermias, and they had one child, a daughter also called Pythias.
However, Aristotle's wife died about 10 years after their
marriage. It is thought that she was much younger than Aristotle,
being probably of age of about 18 when they married.
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 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.
There
are important works on logic. 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. Aristotle believed that logic
must be applied to the sciences
In
fact in Prior Analytics Aristotle proposed the now famous
Aristotelian syllogistic, a form of argument consisting of two
premises and a conclusion. His example is:
(i)
Every Greek is a person.
(ii)
Every person is mortal.
(iii)
Every Greek is mortal.
Aristotle
was not the first to suggest axiom systems. Plato had made the
bold suggestion that there might be a single axiom system to
embrace all knowledge. Aristotle went for the more possible
suggestion of an axiom system for each of the different sciences.
Another topic to which Aristotle made major contributions was
natural philosophy or rather physics by today's terminology. Aristotle looks at matter, change, movement, space, position,
and time. He also contributes to the study of astronomy where he
studied comets, geography with an examination of features such as
rivers), chemistry where he was interested in processes such as
burning, as well as meteorology and the study of rainbows.
Although
Aristotle does not appear to have made any new discoveries in
mathematics, he is important its development.
Aristotle had a thorough grasp of elementary mathematics
and believed that mathematics had a 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 philosophy and theoretical physics1.
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