Zeno of Elea was a mathematician who is known for introducing a number of intelligent and original paradoxes. A paradox is a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth. Zeno was not only a Greek mathematician but also a Greek philosopher and wrote books about the paradoxes that he discovered. His paradoxes continue to stump intelligent people from Aristotle done to people in the present day. Not only did Zeno’s paradoxes contribute to him being considered a mathematician but also his rich background. Little is known about Zeno himself but the information we do know comes from either the manuscript “Parmenides” written by Plato or Aristotle.
Zeno was born c.495 BCE in Elea, Lucania (present day southern Italy). Zeno is supposedly the son of Teleutagoras and was a friend of Parmenides and studied with him in Elea at the Eleatic School. The school was founded by Parmenides in Elea and was based off the physiologies of Parmenides. It is then guessed that Zeno and Parmenides went to Athens together. On the journey to Athens, Zeno and Parmenides meet Socrates and the three discussed philosophy. By this time is has been estimated that Socrates was 20, Zeno was 40, and Parmenides was 65. At this time Zeno had already written a book on Philosophy and was quite famous in Athens by this time. It is tragic that none of Zeno’s work has survived to this day. But, by information from other writers at that time we can conclude that Zeno’s book contained 40 paradoxes and 4 of which greatly influenced and contributed to the creation of mathematics. . Not much else is known except the book he wrote continues to stump geniuses then and now. Zeno passed away c.425 BCE in Lucania. Zen...
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... Parmenides and Aristotle. These two mathematicians were a great part of why Zeno of Elea grew up to come up with all of these amazing and very complicated paradoxes. Zeno is the reason why we are still thinking and questioning some beliefs and theories to this day. Today many people are still trying to understand many of his paradoxes. Paradoxes form the Achilles and the Tortoise to the Millet Seed paradox would not be here today if not for Zeno. The Achilles and the Tortoise Paradox, the Dichotomy Paradox, the Arrow Paradox, the Moving Rows Paradox, the Millet Seed Paradox, the Paradox of Place, and finally the Paradoxes of Plurality have positively affected by questioning the way our society has thought during a time period of more than one thousand years. This reason alone is definition enough of how Zeno of Elea has contributed to the knowledge of mathematics.
Plato, author of the Phaedo, was the second member of the brilliant philosophical flourish of ancient Athens that began with Socrates, continued through him and then culminated with Aristotle. Thou...
Power is an influence that affects people every single day. Whether it is born into or gained, it can affect the individuals that have it in their lives positively or negatively. Usually, however, it affects the individuals negatively. When it does affect the individual negatively, it is usually referred to an idea known as “the paradox of power.” In the novel A Thousand Splendid Suns by Khaled Hosseini, the paradox of power is a recurring theme, and plays hand-in-hand with gender role in the novel. The men portrayed in the novel are taught to think that they are supposed to control women and their freedom, while the women are taught to be submissive to the men. Many of the men are conservative and believe
After admitting that he does not know what virtue is almost halfway through Plato’s Meno, Meno states a few premises involving the acquisition of knowledge, which coined the term Meno’s paradox. In this paradox Meno says that virtue or knowledge is impossible to learn because of it. Meno then questions Socrates on how they can find what virtue is if they can’t discover it which I believe Socrates resolves by stating the theory of recollection and how the theory of recollection shows one part of the premise false by conversing with the slave boy.
What began as Socrates’ process of inquiry, the impression that one cannot obtain knowledge about something without having a definition for it first, led to Meno’s Paradox, a seemingly intelligent argument that mindlessly concludes that knowledge of something can never actually and fully be obtained. Seeing that the paradox had this visibly defective conclusion, Plato disproves Meno’s third premise, and by its fault, premise four is restated as, you can, actually, discover something, which corresponds with Plato’s view of how a person obtains knowledge.
Socrates then managed to verify his theory by demonstrating it on one of Meno’s slaves. He did not directly teach or instruct anything to that boy slave who originally did not know about geometry. Instead, Socrates provided that slave with hints and guided his thoughts step by step. As a result, the boy slave found out a simple geometrical theorem which apparently “emerged” from his mind.
The paradox arises due to a number of assumptions concerning knowledge, inquiry and definition made by both Socrates and Meno. The assumptions of Socrates are:
To research Plato's paradox in the Meno, we can first consult the definition of what platonism is. Websters defines platonism as "actual things are copies of transcendent ideas and that these ideas are the objects of true knowledge apprehended by reminiscence." For this essay, we will assume that trancendency is- "that which is beyond comprehension", and reminiscence as "past experience". The Meno is a dialogue between Socrates, a scholar and Meno, who eventually became an explorer. For this essay, however, we will assume that Meno is at the time of the dialogue, an upper-class citizen of average to better than average intelligence and superior stubbornness.
Inspiring. Enigmatic. Stubborn. Insightful. Truly one of the greatest minds the world has ever known was the philosopher, Socrates. Yet next to nothing is known for certain about him. This is because he didn’t bother to write any of his musings or teachings. However, most of what we know about Socrates today comes to us from the works of Socrates’ student, Plato. It is through many of his works that the ethical theories of Socrates can be learned and his methods known.
It has puzzled many philosophers throughout the ages. Socrates’s theory of recollection attempts to solve the paradox. The theory does answer the paradox in a way. However, theory itself has many problems including its circular nature and its purpose. The goal is to give Meno the instruction of how to enquire virtue when nobody knows what virtue is. The theory only says that Meno may be able to learn about virtue because his soul is immortal. He will be fine as long as he is engaging in the process of recollection. The paradox’s problem still remains
Socrates (470-399 BC) was a credited philosopher born in the city of Athens to father Sophroniscus and mother Phaenarete. Despite his world-renowned contributions, he did not leave any written accounts of his life. His story was taught through the writings of his students Plato and Xenophon, along with Aristotle and Aristophanes in various forms of dramatic texts and histories. Among others, Plato wrote many dialogues that quoted Socrates’ exact words. Much of what we know comes from this greatly influenced student. However, Plato being a literary artist, leads many to think that he brightened up Socrates’ teachings as a result of his positive bias. For this reason, much of his history remains uncertain.
Philosophers like Socrates had a huge impact on philosophers during that time as well as the philosophers today. During the Periclean Age, he was in Athens teaching philosophy of life to the people on the streets who cared enough to listen. The philosophy of Socrates mainly was the responsibility of people's moral attitudes. The teachings of Socrates were found to be understanding of life, recognizing the truth and speaking of the components that were used to a successful life. The teachings of his philosophy weren't appreciated much by the public in which he was sent to the trial with charges against him for his teachings towards the youth. It is very shocking to learn that the charges against him were the interference with the youth and unbelieving
Each one of us has been accused of some kind of act at some point in our lives. Yet those accusations have been terribly mistaken and sometimes there is so little that a person can do to fix that. In this case we are talking about the wonderful philosophist Socrates, a person of many beliefs and ideas. He was a man who dearly believed in justice and doing justice to others. We will examine Socrates' way of thinking and his rationality towards a healthy and logical mind. After reading the Meno, Apology, and Crito I have come to a conclusion that Socrates made the right decision by rejecting Crito's offer of escape and the reasoning behind that will be explained by providing parts of the dialogues and the ideas behind them.
Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths.
Zeno of Elea was the next person who attempted to prove irrational numbers by challenging the Pythagorean mathematics as well. He lived from 490BC to 430BC. Zeno had influence from Socrate...
Among the most revered philosophers of all time was Socrates. Living around the 5th century B.C.,