Aristotle

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\Aristotle



Biography

Aristotle has become a world known philosopher and has influenced and created works in science, government, and especially mathematics, and helped bridge the gaps between these works. His famous analytical method, now known as Aristotelian logic, is the backbone of not only mathematics, but of all the natural sciences.Aristotle was born in 348 B.C in Stagirus, Greece. Aristotle’s father, Nicomachus, who was royal doctor in Macedonia, during Aristotle’s childhood, however he passed away in 374 B.C when Aristotle was only ten years old. Proxenus of Atarneus then raised Aristotle for the years to come.

At age seventeen years old, Aristotle moved to Athens and began his studies in Plato’s Academy where he advanced in the study of debate and language, in which areas he soon became a professor. Aristotle spent around twenty years at the academy, after words leaving for the city of Assos, for reasons unknown. In Assos, Aristotle continued to study areas such as: anatomy, zoology, and other biological studies. Also in Assos he met and married his first wife Pythias, who gave him one daughter before passing away, at an early age. However despite this tragedy he continued to live in Assos until it was attacked by Persia, upon which he moved to the Island of Lesbos, where he stayed about a year.

In 343 B.C he moved to Macedonia, where he was well accepted for his father was a formal royal physical there whom was loved by the royal family. King Philip was especially nice to him, so nice in fact that he funded Aristotle’s studies and his future school. Also King Philip's son Alexander was a student under Aristotle, for a long time while Aristotle was in Macedonia. While there he assumed a high position in the Academy, which may be because of King Philip's influence. He then moved back to his birthplace of Stagirus, to continue his various studies. While in Stagirus he met another woman named Herpyllis, who gave Aristotle a second child, a son named Nicomachus. After spending about eight years in Stagirus Aristotle moved yet again.

Aristotle moved to Athens in 335 B.C to establish a new school that he named Lyceum, which rivaled Plato’s Academy. The Lyceum was helped created by King Philip’s son Alexander (the future Conqueror) Aristotle’s former Student, whom he had tutored while there. “The natural sciences, logic, physics, astronomy, zoology, metaphysics, theology, politics, economics, ethics, rhetoric, poetics, mathematics, and other subjects were all part of the curriculum of the Lyceum.” (http://www.bookrags.com/biography/aristotle-wom/) One of the only documentations of his works was in the Lyceum, before they were published for other viewer’s years after his death. Aristotle is known for his works in philosophy, physics, and biological sciences, he also has had a contribution on all sciences, as well as the human ethics. However in Addition to this vast area of knowledge Aristotle has had a considerable impact on modern mathematics. However many of Aristotle’s and his student’s works on mathematics have been lost over the ages including a biography of Pythagoras, several works on geometry all have been lost. After Alexander died in 323 B.C, Aristotle moved to Athens for a short while, before moving for the last time back to his birthplace of Stagirus and died a year later at age 62, sometime between July and October.


Achievements


However there are some works that still remain such as Aristotle’s famous work entitled Physics, which contains a discussion of infinity, which Aristotle says can only exists in theory, due to its debatable properties. However he does help define infinity by using two different types of infinity. “Actual infinity, or completed infinity, which he believed could not exist, is endlessness fully realized at some point in time. Potential infinity, which Aristotle insisted was manifest in nature – for example, in the unending cycle of the seasons or the indefinite divisibility of a piece of gold – is infinitude spread over unlimited time.”infinity-sign.jpg(http://www.daviddarling.info/encyclopedia/I/infinity.html). These definitions have helped to bridge gaps between other mathematician’s theories on infinity. Aristotle also developed many theorems in his lifetime regarding mathematics, however most have been lost over time. However Aristotle’s greatest contribution was entitled Analytics, as the basic mathematical study.

Aristotle believed that analytical methods should be connected and applied to every part of learning, like sciences and mathematics. For Example, when you study geometry in mathematics, you will study a prism, then in Science when you study optics, light. You should learn that when light passes through a prism it would divide the colors of the light, which now can be related to the event of a rainbow. This way of thinking still exists today, as we bridge gaps between science and math, regarding chemistry, and physics, as Aristotle created many years in the past. Picture_9.png
With this notion Aristotle developed Axioms (postulate) and posits (theorem). “An Axiom is worthy of Acceptance and is needed prior to learning anything.“(http://plato.stanford.edu/entries/aristotle-mathematics/#11) In similar terms an axiom or postulate is something that is obvious, and assumed, what is today called a postulate. A Posit however is the exact opposite and is divided into two parts, A Hypothesis which Aristotle defines as something that is or is not, and a Definition, which is something that does not state that the hypothesis is true or untrue. This laid the basis for mathematics today.

Aristotle also developed a mathematical system based upon syllogisms and proofs, called The Scientific Method. Which is still used today. “A Syllogism or logical appeal is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form.” (http://plato.stanford.edu/entries/aristotle-logic/) Which basically means that at Syllogism is a way of using deduction based upon to pieces of information in order to solve a problem. A categorical syllogism is composed of three parts: the major premise, the minor premise and the conclusion. For Example:

Major Premise: All Mammals are warm-blooded.
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Minor Premise: All Whales are Mammals.
Conclusion: All Whales are warm-blooded.

Aristotle used A, B, and C to replace the physical words in order to show how the human brain will categorize information, and make a deductive response, using syllogisms Aristotle was able to study the inner workings of thought. Aristotle realized that those categorizations work in terms or reality and how the interrelate with each other.


A Proof However is based upon the law of thought. Aristotle saw the logic is the basis of proof. Before Aristotle many mathematicians had tried to use arithmetic and geometry to define proof, Plato was one of these people. Aristotle soon discovered how thought could occur and developed three principles surrounding it, that remain true today:

“1. The Law of Identity - A is A
Everything is the same as itself; or a statement cannot not remain the same and change its truth value.

2. The Law of Non-Contradiction - NOT (A and not A)
Nothing can both exist and not exist at the same time and
in the same respect; or no statement is both true and false.

3. The Law of Excluded Middle - Either (A or not A)
Something either exists or does not exist; or every statement
is either true or false.” (http://oregonstate.edu/instruct/phl201/modules/Philosophers/Aristotle/aristotle_laws_of_thought.html)

These laws are very important to understand thought. Many people today try to find a “loophole”, e.g. it’s kind of raining outside, or it wasn’t true yesterday. However when they try to disprove these statements they always change the context of the question. And even when these statements are evidently true, it always involves awakening a two thousand year old debate on philosophy.

Plato vs. Aristotle
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Plato had made some astounding conclusions. He said that the "ideal" horse came first, and then came all the sensory world's horses, which weren't perfect, as he explains in his famous Cave. In the famous question "What came first; the chicken or the egg?", Plato answers that the "idea" chicken came before the egg and the chicken. Aristotle though Plato had it upside down. He agreed with his mentor that the horse doesn't change, and that all horses are imperfect and mortal, and he agreed that the basic form of the horse is eternal. (Aristotle’s basic metaphysics.) But he argued that the "idea" horse is just a concept that humans had come up with after seeing a lot of horses. Aristotle said that the "idea" or, as he liked to put it, the "form" horse was made up of the horse's characteristics, which we call the species. In modern science, we have DNA, which we have found, controls the characteristics of every living plant and animal. DNA is the “form” that Aristotle described. These conflicting views probably explaining why the two created different schools, and it also shows the difference in philosophies. In my opinion I agree with Aristotle.

Aristotle’s influence on the modern world is evident through his works. He used advanced Mathematical, Scientific and Philosophical methods to demonstrate these works, and to show his Intelligence. Aristotle was years ahead of his time in many of his theories. Even though Aristotle had many accomplishments in countless areas, his mathematical achievements make many people today, who are considered smart in the subject seem stupid at the sheer magnitude of Aristotle’s research. Aristotle’s genius and his continuous effect on the world even after his death proves his greatness, and his true influence.


Fun/ Favorite Facts:

1.One of my favorite facts about Aristotle was that while he was in Lesbos he studied the sea life there with inferences and observations years ahead of their time. lesbos.jpg


2.Aristotle also made efforts to create order in peoples' governments. He created a classification system of monarchies, oligarchies, tyrannies, democracies and republics which we still use today.