Zeno of Elea was a Greek philosopher and a mathematician. Zeno is particularly known for his paradoxes that helped build both mathematics and logic, they specifically targeted the concepts of continuity and infinity. Zeno was born in 495 BCE and died in 430 BCE. In his lifetime he contributed some great things to the subject of math. He studied at the Eleatic School, a leading school in Greek philosophy. He is said to have been a good friend of the philosopher Parmenides. After his studies he went on to write a book containing 40 paradoxes! Unfortunately none of Zeno’s writing has ever been found. Zeno contributed to mathematics greatly and he will always be remembered for this.
It is rumoured that Zeno only wrote his paradoxes because other philosophers were writing paradoxes disproving his friend Parmenides ideals. Although this could be true Zeno’s paradoxes were fascinating! He goes as far as to say that motion is only an illusion and that there are multiple existences! Many mathematicians find Zeno’s paradoxes to simply be mathematical equations that calculus can provide a solution to. I suppose this could be true, but the things that Zeno provided thought on were amazing! Zeno had many things to say and some historians say that his intellect brought him his end. Even though some people disagree with Zeno’s paradoxes there are many philosophers who consider the problems Zeno addressed to be metaphysical problem to this very day.
Zeno was described as a fair and tall man. There are not many accounts on his looks or early life. His paradoxes are said to be influenced by Pythagoras who wanted to apply mathematics to the real world. Although the real influences on why he wrote his paradoxes is probably eternally lost to us. Z...
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...bout judgement. When he wrote his book there were 40 paradoxes. Since only eight have survived we cannot ever know the full extent of Zeno’s knowledge but his life alone shows he was a man of vast knowledge. Zeno made many friendships in his life and is even said to have met Plato and Sacrotes. This is doubtable due to chronology of the lives of the three, but if this happened Zeno had many credible people to look up to and to converse with. Plato alone is an amazing person to get the opportunity to meet. Also, as i have stated before Zeno is said to have wrote his paradoxes in the defense of his friend Parmenides after other philosophers were trying to knock down his word. Zeno may have been a controversial man after he wrote his paradoxes, but he was well educated and well spoken. Zeno is most definitely a man to be seen as a role model in the world of mathematics.
Socrates, a man who lived thousands of years ago, is perhaps the most renowned philosopher of all time. His work was written down years later by his close friend, Plato. From these readings, we may find some ideas and thoughts of his that seem to contradict others. This seems to be evident in Plato’s stories The Apology, The Crito, and The Republic.
The critical argument, known as Meno's Paradox, as presented in Plato's “Meno”, questions the very basis of Socrates method of arriving at knowledge of unknown things through inquiry. If Socrates truly wants to gain knowledge of what no one else knows, then the content of that “unknown” thing will produce absolutely nothing. The paradox bases itself in stating that humans can never learn anything that they don't already obtain knowledge of. As identified by Meno, the paradox is this: "And how are you going to inquire about it, Socrates, when you do not at all know what it is? For what sort of thing, from among the ones you do not know, will you take as the object of your inquiry? And even if you do happen to bump right into it, how are you going to know that It is the thing you did not know?” By saying this, Meno proposes that since Socrates does not really know what virtue is, he cannot find it because he would not recognize it even if he did. Each time Meno offers an explanation of the term, Socrates rejects them immediately because they are, in his eyes, inadequate. Socrates delivers an excellent theory, along with an example, to criticize this paradox and provide for the opportunity of humans achieving knowledge.
With the use of Socrates’ elenchus , Meno finds himself in aporia , and leads him to introduce us to, what is titled, the paradox of knowledge. It is, as he states:
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.
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.
Philo Judaeus is regarded as one of the greatest Jewish-Hellenistic philosophers of his age. In a majority of his writing he quotes bible verses, speaks of a path to the Lord and does so with such image producing words. While reading Philo it is hard to discern his philosophical views, and surgically placed words, from those influenced of his religious background. He brings fourth an interesting combination of philosopher poet or preacher. Philo Judaeus was very religious and portrayed such in his writings. I believe and assume Philo had as well, that the truly aware man is made up of three parts: the philosopher, the poet and the preacher. Without the other two one cannot truly exist, therefore all of the greats such as Plato, Huxley, Conger and of course Philo must have a been truly aware. For their love of wisdom, endeavor for ultimate reality and their amazing talent for language is unmatched and greatly appreciated all who read their work. Several scholars have used the writings of Philo to explain theological conceptions found in the writings of the Christians, and also to better understand debates and conflicts witnessed in the New Testament.
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
Well-known for his significant impact on the philosophical world, Socrates was one of the first people to truly question individuals and take the average level of thinking to a much more elevated level. The Last Days of Socrates, specifically Euthyphro, Apology, and Crito, written by Plato demonstrates Socrates’ great use of the Socratic method as well as rhetoric, the art of persuasion. Many people looked down upon Socrates because they viewed his calling, as told by the Oracle of Delphi, to be impious. Although Socrates was put to death for living a life such as his, he was very extremely successful during his time alive. Socrates was successful in both the realm of philosophical truth and in the outside world because humans used rhetorical ways of thinking to find purpose and make decisions without the influence of other members in society.
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
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
Zimbardo wanted to appeal the hypothesis that has somewhat been the statue quo of "blaming conditions on the evil in the prisoners, but also that have attributing the evil to guars and staff with their evil motives and defiant personality structures). In a way, he wanted to gain knowledge in corrupting in the 'bad seeds ' and not in the condition of 'prison soil '.
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.
By Characterizing himself –Socrates- as both ignorant and wise, he presents us with one of the most striking paradoxes. Like so many of the other philosophers, is provocative in that its apparent self-contradiction hides an important idea for us readers to discover. Though out this text Socrates ignorance results from his belief that he has no knowledge of moral idea, or moral properties, such as justice, virtue, piety, and beauty. He asserts that, if only he knew the relevant definitions, he would be a moral expert who could answer philosophical questions about moral properties- questions such as is a certain action just? Or is it truly good for a man to be virtuous? Socrates believes that only someone that is “truly wise” would know these essential definitions and be able to provide such expert answers. It is important to determine whether Socrates does, in fact, accept priority of definition principle and, if he does, whether he is committed to a false and problematic principle that subjects him to catastrophic results. A textual analysis will be a philosophic inquiry into Socrates’ conception of knowledge, considering what he believes knowledge to be, how the knowledge of definitions fits into his epistemology, and whether or not his conception of knowledge is philosophical compelling.
"As for me, all I know is that I know nothing" is a famous quote from Socrates, that describes him very well as the intelligent, humble person that he was. Socrates was born on 469 B.C. in Athens, Greece. He was well known throughout the world for his dialogues and the work of his followers and students such as Xenophon and Plato. He built the foundation for the Socratic Method as well as Socratic Irony. Although everything known about him is second-hand, and we do not have any of his philosophical writings, he is still known as one of the most important philosophers who changed the world. Socrates is often seen as the person who created the foundation for philosophy in the West. The influence of Socrates views can be seen during the time of Renaissance, where his works were often reflected in paintings and other works of art, he is often represented as a great Saint, because of all of his exemplary accomplishments.
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...