Friday, July 26, 2019
Analyzing the conditions of oppressed women according to Simone de Essay
Analyzing the conditions of oppressed women according to Simone de Beauvoir's perception - Essay Example Based on the arguments of sexual politics, the economic realm of both sexes is considered to make up two social groups; for instance, men may hold better jobs, with increased wages and salaries, and more chances of success compared to women. De Beauvoir (1949) explains that men had acquired a higher position in industry and politics, thereby monopolizing principal positions. Besides, men had traditional prestige of education, which is aimed at supporting children, since the present is enshrined by their past, while the past resonated history that had been made by men. Nevertheless, women during that time were commencing to participate in affairs of world that was controlled by men. Nonetheless, women were bound to decline and refuse participation in dealing with issues that would derive advantage that are bestowed upon women. Therefore, sexual politics resonates on womenââ¬â¢s dependency on men for material protection and this undertakes their moral justification based on their ex istence. Both sexes had ethical purpose of each individual affirming their subjective existence, though there were temptations relinquish liberty. However, this pursuit for women was not promising to those who took it passive; in fact, they became creatures of menââ¬â¢s will, thereby being denying women every value. Nonetheless, this has been a simple pursuit for people focusing on evading the strains involved in undertaking of genuine existence (de Beauvoir, 1949). For instance, men had been taking women as people without manifestation of inclinations focused on complexities, but this has gradually changed. Therefore, through sexual politics women are perceived to be laying claims to their condition of being subjected to deficiencies of definite resources, due to the feeling of being obliged to ties to men, despite reciprocity involve. 1. What is gender? De Beauvoir (1949) explain that men are present themselves as people of a particular sex that, which does not require declarat ion. In this case, definition of gender is based on the terms masculine and feminine, which apply symmetrical with differences based on their forms. Relationship between these sexes is not parallel given that men are considered to represent both positive and neural, as illustrated by application of the term man to stand for human being of both gender (de Beauvoir, 1949). On the other hand, the term woman is negative given that it represents negative; thus is defined with limits of criteria without reciprocity. Nevertheless, there are notions that have been developed by men through abstract discussion such as women have contrary thinking and perception to their own way of thinking because they are men due to understanding that man is no peculiarity. There are gender related notions, which such as a man being considered to be right due to the mere fact that he is a man and not a woman; in this case, a woman is considered to be wrong. Definition of gender has led to absolute vertical a ncients based on the reference to oblique and human type of masculinity (de Beauvoir, 1949). Furthermore, a woman has become subjects to imprisonment due to peculiarities associated by her biological nature such as having ovaries and uterus; in fact, this poses limits regarding her
Thursday, July 25, 2019
Quality Management Article Example | Topics and Well Written Essays - 500 words - 1
Quality Management - Article Example The onus is mainly on learners to furnish the required information in the templates after each unit based on the Read and Analyze Activity. After filling the information in the template they need to e-mail it back to the e-Tutor. The article titled ââ¬Å"Towards a Better Understanding of Qualityâ⬠by Hardie & Walsh (1994), gives an overview about the notion of quality management from a modern day perspective, elaborating on different theories. Discussion of the article initially emphasizes the traditional differences between qualities preferred and the actual quality outcomes. In subsequence, the article elaborates that with the implementation of the new methods, certain relationships could be identified among the different states of conditions, which has been referred with relation to (1) ââ¬Å"how things ought to beâ⬠and (2) ââ¬Å"how things areâ⬠. To be noted in this regards, the article successfully details out the quality relations among the different states and assists in understanding the common witnessed quality issues that impose strong impressions on the performance of an organization. Correspondingly, the article clearly diagnoses the quality problem faced in different states, p roviding a framework of the quality relations (Hardie & Walsh, 1994). The key learning points of the article can be identified with reference to the findings inferred by the authors. To be noted in this regards, the differences of the quality relations of the two states of ââ¬Å"how things ought to beâ⬠and ââ¬Å"how things areâ⬠, form the common base of arguments in various theories concerning quality management. As noted in the article, the issues regarding quality aspects, prevailing in an organization, can be identified in terms of the gaps persisting between the two states mentioned above. However, with the gradual introduction of new and more elaborated definitions of quality, several quality relations
Wednesday, July 24, 2019
Entrepreneurship.Excellent Leadership Qualities and Strong urge for Assignment
Entrepreneurship.Excellent Leadership Qualities and Strong urge for ethics and integrity - Assignment Example Clearly, this is a misconstrued notion that cannot be accepted in modern business management. Indeed, the modern day entrepreneur is expected to exhibit certain key characteristics, skills, and have certain background to the day to day management of his business, without which the business cannot be expected to grow. In this paper, some of the skills, characteristics and backgrounds that make successful entrepreneurs are discussed with real examples of how these features about some entrepreneurs have ensured success for them. There is specific emphasis and focus on emerging markets, but without any single emerging market in mind. The key characteristics that some entrepreneurs have exhibited over the years in various emerging markets, the aid of which has made them highly successful shall be discussed. Excellent Leadership Qualities The leadership of the company primarily refers to the management of visionary direction for the company. This responsibility is played by several people within the organization, and in some cases, some leaders becoming followers to other leaders (Coy et al, 2007). But as far as the entrepreneur is concerned, he is often seen as the last reporting leader within the organization. This is to say that the entrepreneur acts as the head of the organizational structure and is therefore the ultimate leader. In effect, the kind of leadership qualities that the entrepreneur displays will go a very long way to determine the visional direction that the entire organization will have. With the question as to what excellent leadership qualities are, Capelleras et al (2010) explained that it involves the ability of the leader to be identified with as many leadership styles as possible and learn to rightly apply each of them as and when they become necessary for an organizational scenario. In effect, a leaderââ¬â¢s leadership must always be seen as appropriate in practice; and this is what constitutes an excellent leadership quality. Strong urge for ethics and integrity Show me a leader without ethics and integrity and I will show you a dying company and this is according to Benzing, Chu & Callanan (2005). Ethics and integrity constitute a personal and behavioral characteristic that is needed by the entrepreneur to make him trustworthy and credible in the area of business that he is involved in. with the advent of corporate image and corporate branding, stakeholders including customers, shareholders and suppliers are looking for corporate managers and leaders who represent not just a money making machine but an overall of credibility and trust when left with the finances and welfare of a larger group of people (Benzing, Chu & Callanan, 2005). Commonly, the way of thinking is that when entrepreneurs cannot on by themselves proof to be credible, they can easily use manipulative and unacceptable means of making their businesses grow. In an emerging market where most of the local customers are considered as vulnerable to market marketing mix strategies as lower prices, such entrepreneurs who are suspecting in their ethics and integrity can be tagged with dubious means of making their prices cheaper such as the invasion of taxes or use of unwholesome raw materials in manufacturing. Empowered Self Motivation Motivation comes in several forms, commonly intrinsic and extrinsic motivation. In most cases, intrinsic motivation has been identified to be that type of motivation that keeps a person driving on when all other factors suggest that
Tuesday, July 23, 2019
Please see in other instructions Essay Example | Topics and Well Written Essays - 2500 words
Please see in other instructions - Essay Example One of their more recent forays happened to be one into the financial industry, specifically in the form of Virgin Money plc which, at 17 years old, is still relatively new to this industry. Regardless, it was able to achieve a respectable level of success, if its global expansion in the turn of the millennium is anything to go by. Whatever complaints people might have about the level of customer service, Virgin Money plc must have at least halfway decent services if it has managed to go on operating for the past 17 years. have been getting mixed reactions from clients. Indeed, there are firsthand accounts on various forums and review sites on the internet that tell of the quality of Virgin Moneys services, not all of which are flattering. This being the case, it may be worth examining the customer service management approach taken by Virgin Money. The paper shall first provide a brief, 2-page history of Virgin Money, before introducing the concept of customer relations management - sometimes called customer services management - and how it applies to this firm. An explanation on the groups findings on the matter comes next, as well as on the methods used to obtain data. Rounding the study off is the conclusion, which includes recommendations as to how Virgin Money can improve on its customer service. Virgin Money was established as Virgin Direct by Richard Branson in 1995, and has always been owned by the Virgin Group. Based in the UK, this company deals primarily in banking and other financial services, and has been known as a pioneer of index tracking in its introduction of Personal Equity Plans at relatively affordable prices. Since it expanded its services worldwide early on in the past decade, the company went on to achieve even greater levels of success (BBC News, 2011). As with all companies, Virgin Money had tender beginnings of its own, having first been launched in partnership with Norwich Union in 1995 as Virgin Direct Personal Financial
Monday, July 22, 2019
Function of E-Book Essay Example for Free
Function of E-Book Essay Books are no doubt the main element in teaching and learning activities. As we all know printed books have already been used for a very long time. However in this modern era, books in electronic forms (eBooks) are taking place. EBooks had already been introduced not only for adults but children too. Finally, eBooks are already evolving slowly to take place in teaching and learning. A powerful stimulus for the production of a range of electronic instrument for education has been provided by the latest technology inventions. Numerous ideas and educational materials are invented and extensively published electronically to support the field of teaching and learning, however it is still unclear how far all of this is of use among the students and teachers when it comes to the virtual teaching and learning. Suggestions on how to improve the quality of the products and materials that are already available are still in great demand as the existing electronic books have not completely replaced the physical counterpart. The gap between utilitarian and usefulness is quite wide to prove the lack of effectiveness of the first generation of e-books, and the progress of e-books has been led majorly by technology instead of the userââ¬â¢s demand. In the education field, E-books can be found in various type of media instrument like CD-Rom, the internet and in any portable reading materials. Variety types of element are implemented in e-books, for example fiction and non-fiction. A textbook is a source of information on a particular subject. An electronic textbook on the other hand is almost the same but it is more special as e-textbook is an e-book that has a content of educational material for teaching and learning process. E-textbooks are now officially known as educational source that have already published electronically to help in both teaching and learning methods. They are ready to be used within a computer environment, through media such as internet or CD-ROM. In the early 1990s, the spread of educational multimedia was surprisingly very fast and it was proven by the people that it is more beneficial when converting printed publication into electronic form. Apart from that, it has been discussed that e-book is basically implemented to improve the process of studying outside the classroom, and as time goes by, a technological instrument was made where a powerful incentive is created to invent such electronic material for the students. It is better for the people to be updated to any information to learn by using e-book as printed books are always out-of-date and are only replaced with an average of eight years. Limitless and faster access to any latest news and information can be experienced via electronic learning (Hamilton et al., 2001). It was said that electronic education will benefit a lot of people because of its capability to enhance the co-operation and among the students and the teachers (Hambrecht, 2000). Apart from that, higher success rate can be seen. However more effort should be contributed towards promoting e-book among the new generations as financial support plays an important role in this matte (Wilson, 2003). Similar to the ordinary printed books, e-book helps the readers to understand and focus on important messages by underlining them and writing simple notes. In addition, e-books are user-friendly too as it is installed with portable dictionary program which made it easier to look up for unfamiliar words. E-book has definitely made the teaching and learning process to be more interesting than ever because the user get to watch clips and interact with a variety of specialities. It has been proven that the youngsters can gain a lot from the added applications (Maynard and McKnight, 2001). At schools, e-textbooks on the other hand will reduce the number of printed textbooks that not only burden both the teachers and students carrying them to-and-fro around the school compound. This enables the teacher to easily bring the notes including the exercises to be given to the student which thus increases the effectiveness of teaching. With the presence if the electronic book, space can be saved which particularly helps a lot in places mainly the libraries. Decades ago, e-books were not preferred because the prices were too high. In the year 2000, the production of e-books have became larger and the cost of each e-book is lowered (Mayfield, 2000). This indicates that a major procedure in promoting the usage of e-textbooks in school had been done. Another form of e-book, CD-ROM also known as the copy of the encyclopedia is also famous among the students nowadays. They can easily get copies of the syllabus of their subjects in order for them to study back at home and easily bring the topics for discussion among their peers. Another branch of e-book, Hypertextbooks is a famous instrument of interactive studying on the internet in the western country. This electronic file containing the learning materials enables the user to study at their own rhythm and the students will send their assignment to the respective person through email. This concludes that with the upgrading of the process of studying, the students will no longer have the reason not to send their assignments on time. Top of the information, at schools teachers will have no problem to control the class because the students will be more focused and enthusiastic to carry on with their assignments compared to the printed pages. Even though e-textbooks can contribute towards the improvement in assisting the process of teaching and learning, there are still factors that resist their acceptance such as the insufficient number of computers and labs and the low number of publishers. This signifies that e-book can help in the education field but the chance to make it a reality might prove problematic. According to Hambrechtââ¬â¢s theory, it is believed that e-education is potential in bringing the students and teachers to come together as one in order to enhance the class sessionââ¬â¢s activities (Hambrecht, 2000). The research about CD-ROM clarified that users will be more interested to learn and use their resources. The children especially, find that learning is more fun with the presence of beautiful graphics and sound effects. This thus motivates them to continue to learn more which in return will boost their thinking skills. Teachers on the other hand love this way of teaching as it is both entertaining and educational. The e-book users prefer to use this modern way of learning because of the more presentable format which brings a brand new perspective towards the people to experience a more lively way of reading especially the story book lovers. Children once exposed to the usage of e-book they will be used to electronic devices and in future, they will no longer rely on the old traditional method which is the printed book. Electronic texts are no doubt a passage for the generation to get an easy access in education for further study and analysis. The fertile ground for the improvement of teaching and learning, e-book, can benefit the generations greatly in terms of the enjoyment of interesting studying method. As a conclusion, the educators should look into this matter more clearly and make an effort to add electronic texts in their teachings if they havenââ¬â¢t start doing so. Cooperation among the parents and the educators are the key to success to make a change to the younger generations. This foundation will for sure end the upcoming obstacle in generating intellectual students. Reference Hambrecht, W. (2000), Exploring a New Frontier, Corporate E-Learning. Hamilton, R. , Richards, C. and Sharp, C. (2001), ââ¬Å"An examination of e-learning and e-booksâ⬠, available at: www. dcs. napier. ac. uk/ , mm/socbytes/jun2001/Jun2001_9. htm (accessed 20 November 2010) Mayfield, K. (2000), ââ¬Å" Read a g ood e-textbook lately? â⬠, Wired News, available at: www. wired. com/news/culture/0,1284,38059,00. html (accessed 12 November 2010). Maynard, S. and McKnight, C. (2001a), ââ¬Å"Childrenââ¬â¢s comprehension of electronic books: an empirical studyâ⬠, The New Review of Childrenââ¬â¢s Literature and Librarianship, Vol. 7, pp. 29-53. Maynard, S. and McKnight, C. (2001b), ââ¬Å"Electronic books for children in UK public librariesâ⬠, The Electronic Library, Vol. 19 No. 6, pp. 405-23. Sally Maynard, Emily Cheyne, (2005) Can electronic textbooks help children to learn? , Electronic Library, The, Vol. 23 Iss: 1, pp. 103 ââ¬â 115. November,25, 2010 http://www. emeraldinsight. com/journals. htm? articleid=1464898 Wilson, R. (2003), ââ¬Å"E-education in the UKâ⬠, Journal of Digital Information, Vol. 3 No. 4.
American Dream Essay Example for Free
American Dream Essay The idea of dreams is integral to the main protagonists throughout The Bell Jar and Death of a Salesman. These ideas stem from the concept known as the American Dream, which is the belief that with enough work anyone can be what they want to be. The American Dream can often be related to the term Manifest Destiny, which is the belief in Americas mission in the world and can often be related to expanding their control over land. There are different types of American Dreams in the texts. These include Material, academic, 19th Century (outdoors), 20th Century (business) and Happiness, which the authors use to give us an inside look into the characters. The concept of the American Dream is presented in Plaths The Bell Jar in a similar way to Millers Death of a Salesman, when Plath states, look at what can happen in this country suggesting that the American Dream is a predominant thought in the American minds. In contrast to Millers main character, Willy, that foolishly follows the American Dream, the main character of The Bell Jar, Esther, does not believe this to be true and fights against the current of mainstream ideas and belief that if you work hard enough you can achieve anything. This is represented in the character, Doreen who is successful for just being beautiful, showing the shallowness of society. The American Dream is shown in Millers Death of a Salesman through characters such as Ben. Ben is the exemplary man with the American Dream; Miller writes that he walked out into the jungle and that when he came out he was rich. This belief that the American Dream can happen to anybody eventually drives his brother Willy to the tragic heroism of his suicide. This is a very depressing view and one that a lot of people can relate to, that the concept of the American Dream has a base of lies, deceit and luck such as Ben who ended up in Africa which then later made him rich. Although they both have differing attitudes toward the American Dream they both seek to achieve their own goals in a different manner. Willy is much more of a protagonist; he talks about being successful and how he will take action in the morning. On the other hand Esther is more pro-active in the pursuit of her dream as she is very academically successful and has never answered one test question wrong. Both of these approaches to seeking their dreams give us an insight into how the characters should have followed their dream and where their mistakes were, such as with Willy who often reminisces that he should have gone with Ben to the mines. Willy is so disillusioned that he will do anything in order to help Biff and Happy to achieve their dreams, which is the main factor in Willys suicide. We also get a sense of selfishness from this act of disillusionment as Willy seems to use his sons as an excuse for him to commit this act he has been clinging onto the American Dream so tightly that it became a veil over his eyes that left him blind to see he has the wrong dreams. Plath often uses the happiness dream in conjunction with the academic and material dreams to contrast with each other and to explore what the American Dream is and how to achieve it. We see this when Esther fed her clothes into the night wind which is Plath showing the reader that in order for Esther to achieve her happiness dream she does not need material objects. Plath uses techniques such as interior monologues to give us the deep feeling of failure residing in Esther and this gives us the impression that we should follow our own dream, instead of following a fake dream. While in contrast Miller uses the 19th and 20th century dreams in order to explore what the American Dream really is and how to achieve it. We can see this when Biff asks, Why am I trying to become what I dont want to be and states he desires to be outdoors with his shirt off for him to build a future. Biff represents freedom from the shackles of society, often breaking the convention, such as committing crimes in order to rebel. These explorations of the American Dream are very different in the way they are presented but both lead to the same conclusion, which is that you need to do more than strive and talk about your dreams, but act upon them, which both characters try, but evidently fail. Both writers look to expose the myth of the American Dream and the harsh reality within the characters of the respective texts. This idea is shown predominantly through the main characters, Willy and Esther, who are complete opposites in this view. Miller portrays Willy as the average low-middle class American who only has the hope of the dream to cling to and keep him going, this is why Willy doesnt understand the true meaning of the American Dream, as he himself has fallen into the cast to what he thinks society wants him to be. This is evident when he exaggerates; it is his way of following the American dream. He talks about how popular he is and how his funeral will be massive, whereas in reality he is unknown. His dream is to be rich and famous and to an extent he fools himself into believing this, such as when he talks about how he sold five hundred in Providence but then realises that he only sold two hundred gross on the whole trip. This gives us a sense of tragedy, that no matter how hard he tries to provide for his family, he is destined to fail, which Miller hints at with the attempted suicide with the rubber tube. However, Plath portrays Esther as a bright young women, who has the opportunity of living the American Dream but she can see through the illusion of what society thinks she should be. When she has her photo taken, she has to hold a fake rose and the rose doesnt represent her as a person or what she aspires to be, which is the point that Plath explores with regards to the American Dream in The Bell Jar. Plath and Miller use very different techniques to represent the American Dream. This is due to the texts being of different styles; one is a novel and the other a play. That said they do share some similarities, such as non-linear narratives to give us an insight into the key themes. The techniques used give different insights into the individual thoughts of the American Dream. One technique used by Plath is the interior monologue, which gives us the intimate thoughts of Esther and what she thinks of the world around her. Plath uses this technique to show her thoughts about the American Dream, as though they are her own thoughts represented in Esther. This gives us a very powerful opinion on the American Dream, as it is an opinion that is close to what we may also think from reading the novel. However Miller uses the flash-back technique in order to show where the idea of the American Dream originates and Willy and Esther perceive it this way. This form of stream-of-consciousness gives us a clear-cut view into what the character perceives and can often help us to understand of why the characters act as they do. One way that both authors explore the concept of the American Dream is by how the characters can achieve their individual dreams; this often leads to pressure to pursue the wrong dream. This is present in a lot of the characters in both texts such as Biff, who is the only realistic one in the Loman family. He realises his boundaries and abilities but in spite of this he still attempts to make a businessman out of himself though it is not what he wants, which he shows when he says, Why am I trying to become what I dont want to be. He also informs us that Willy has all the wrong dreams. This idea of becoming a successful businessman is a carbon copy of Willys dreams, pressed onto Biff. Though Biff, unlike Willy, doesnt procrastinate, everything for Willy is done in the morning and this is the main reason why he is unsuccessful, he talks instead of taking action as we are shown when Charley says that Bernards gonna do it instead of saying it, which Willy seems to admire. On the other hand Esther is the opposite of Willy; she is academically successful, more popular and has the chance to grasp the American Dream. Esther says I was supposed to be having the time of my life but the only problem with Esthers dream is that society wants her to be something else and this pressure is one of the reasons for her latter depression, when she was meant to be happy. When Plath uses the stream-of-consciousness technique we see that Esthers thoughts about the American Dream seem to deteriorate as her mental stability does, not even noticing when she could have potentially had a dream life in the fashion industry saying its somebody else in the magazine photo. Another character that Miller shows is following the wrong dream is Happy. He follows what Willy thinks he should be and he is always looking for his father to notice him, such as when he comments on how he is losing weight. This is an example of following the wrong dream. Happy has fallen prey to trying to make someone else happy by living their dream instead of following his own ambitions, which is the point that Miller explores. Miller has deliberately set up the brothers to have contrasts as we can see within the dreams they possess. Miller also explores the idea that the American Dream is possible if you try; this is in the case of Bernard. Bernard, like Ben, is the prime example of the American Dream coming true. Although he isnt as popular as Biff or Happy, he manages to be an academic and now presents cases in the supreme court, which genuinely shocks Willy as he recognises that Bernards dream has come true. For Willy there is also an air of envy that Bernard has followed the right dream. We see how Willy blindly follows the American Dream and that he doesnt truly understand what it is, he thinks that a personally attractive man will be able to be successful in the world of business. Willys understanding of the American Dream is limited as he believes that superficial qualities such as being liked is all a man needs whereas we are shown that it is hard work and risks that allow men to live the dream, such as Bernard who he often ridiculed for being an anaemic. Another point that shows us Willys little understanding of the American Dream is the metaphor its dark there, but full of diamonds. This metaphor means that through the hardship there will be a reward and is the main notion that drives Willy but it often appears in the form of Ben who reminds him. Ben gives the impression to Willy that he can do it, but also shows us Willys loosening grip to distinguish from reality and dream. The pressure to be something else or something great can have a massive strain on ones being and we can see this through the various suicide attempts by both Willy, with the rubber tube, and Esther with her trying to hang herself. In conclusion, I believe that each text explores the concept of the American Dream in very independent ways that express the opinions of the authors. Miller presents to us ideas such as to achieve the dream you have to be disillusioned which we see in the main protagonist, Willy. The combinations of techniques that Miller uses gives us the impression that nothing good can come out of the American Dream, as if almost hopeless to even have a dream. On the other hand, Plath uses the ideas of isolation being the problem, which we see in Esthers case. Plath uses the ideas of isolation coupled with depression to show the bleakness of striving to achieve a dream, which is a belief that Plath shares. This idea of isolation resonates in both main protagonists and leads back to the notion of society being the problem. Both characters dont fit in with society and are both under strain to be something they do not want to be. This gives us the sense that they are born into the wrong society and this I believe is the point that both authors try to explore, that there is nothing wrong with the characters themselves but it is the world around them that is flawed and through various narrative and stage techniques the authors convey this conclusion successfully. Bibliography Plath. S The Bell Jar Faber (1966) Miller. A Death of a Salesman Heinemann (1949) Dan Clarke
Sunday, July 21, 2019
Philosophy And Development Of Greek And Chinese Mathematics Philosophy Essay
Philosophy And Development Of Greek And Chinese Mathematics Philosophy Essay At a glance, Greek mathematics would appear to possess the most influence on modern mathematics from methods of integration (developed from Eudoxus method of exhaustion) to the rigid logic adhered to in modern mathematics and would thus explain this thesis choice of comparing Greek mathematics. On the other hand, ancient Chinese mathematics appears to have differed largely from Greek mathematics in terms of development and for that reason was chosen for comparison in order to explore the possibilities of philosophical influence in mathematical development. Not only will this thesis explore the differences in the development of the respective mathematics and the factors involved in these differences, it will also explore the possible relevance of such findings to mathematicians in the further development of modern mathematics. However, given the rich history of each respective cultures mathematics, it would be next to impossible to explore their developments in vivid detail and as a result, only a basic overview of the characteristics of the mathematics prior to their interaction (when Matteo Ricci western missionary began introducing western concepts of mathematics to the Chinese) would be explored. Greek Mathematics? Easily identified by its focus on generalized mathematical theories and proofs, the Greeks seemed to have an idealized perception towards mathematics where instead of grounding them in reality, it was a goal to make mathematical concepts even more abstract. At the foundation of Greek mathematics were basic assumptions known as axioms. These axioms could neither be proven correct or wrong, and are considered self-evident. New theorems were derived from these axioms, and this happened in a process where conclusions were drawn from premises through the use of logic, otherwise known as deductive reasoning. An example of such use of deductive reasoning would be the 10 postulates (similar to axioms) seen in Euclids Elements which were used by Euclid to prove his various geometric theorems. Such a method of proving and deriving theorems deductively could be effectively seen as a form of abstraction, where abstracted theorems could be applied in any case related to the theorem. For instance, (Pythagorean Theorem) would be true for all cases of right angled triangles regardless of the numbers substituted into the theorem. Pythagoras was thus attributed to be one of the first men to grasp numbers as abstract entities.Ã [1]Ã With the prevalence of the use of deductive reasoning in the ancient mathematical schools of thought from the Sophist School to the Platonic School, it could be generalized that ancient Greek mathematics was characterized by abstract theories and generalized proofs. Chinese mathematics? The concept that the Chinese had of mathematics was radically different from the way the Greeks handled math. Instead of an axiomatic approach to mathematics (developing mathematics based on assumed axioms), the Chinese developed a far more practical approach. Science was valued for its many practical applications and astronomers in ancient China were also mathematicians who calculated planetary movements through the applied use of mathematics. Applying mathematics was seen even in the Jiuzhang Suanshu (considered one of the most important mathematical manuals in China to be written) which was in essence a collection of problems and rules that was applied practically. For instance the second chapter (Su Mi) of the book dealt with percentages and proportions for exchange of cereals, millet, or rice and helped in the production and management of grain. Chapter 6 (Jun Shu) allowed the calculation of proper distribution of grain and labour and dealt mainly with the problems of taxation of the people.Ã [2]Ã This problem-based approach revolved around the idea of applying the solutions of one problem to another in such a manner that would allow the other problem to be solved. For instance, the Jiuzhang Suanshu or Nine Chapters on the Mathematical Art is in reality a collection of mathematical problems and their solutions. Mathematicians were then expected to extrapolate from these solutions other solutions to other problems. In the words of the Zhoubi Suanjing (one of the oldest complete mathematical manuals found in China), a person gains knowledge by analogy, that is, after understanding a particular line of argument they can infer various kinds of similar reasoning.Ã [3]Ã Given that the majority of the mathematical manuals discovered in China possessed the attribute of problem-based approaches (Jiuzhang Suanshu, Xu Shang Suanshu, Suan shu shu) are just some examples), we can easily conclude that the ways in which the Chinese approached mathematics was radically different from that of the Greeks. Greek and Chinese Philosophies Having understood the differences between the mathematics of both cultures, we must now begin to explore the possible causes of such a difference, and we first take a look at the philosophy that has guided the respective cultures. Greek Philosophy? Although it is commonly agreed that Socrates, Aristotle and Plato were one of the few greatest philosophers originating from the Greeks, the father of deductive mathematics Thales, contributed to ancient Greek philosophy even before the great philosophers and with his close association with the origins of Greek mathematics, it would be a mistake not to consider Thales contributions to the philosophy. Thales belonged to a school of thought called the Milesian school and these philosophers believed that all things were defined by their quintessential substance, which Thales thought was water.Ã [4]Ã Regardless of what Thales or any other philosophers from the pre-Socrates period of philosophy thought, it was clear that from the beginning the Greeks had already begun to seek out a basic form or substance that all things would be defined by. We thus begin to see similarities between their goals of having a unifying substance that would define all things in philosophy and in mathematics, where they sought abstracted theorems and mathematical proofs that would have applied to all cases of any related problems. Even Plato, in Book VII of The Republic, argued for the existence of Forms in his allegory of the caves. He believed that what we thought to be real were simply shadows cast by actual Forms that we could not really see. Plato argued that these non-material abstract Forms did not exist in time and space, and were not the material world that we perceived with our senses. Plato even suggested that only through the study of these Forms were we able to attain genuine knowledge. Through these ideas of abstract forms and substances that Greek philosophy seemed to follow, we begin to see that there is a general direction in which both philosophy and mathematics went: abstraction. Chinese Philosophy? When compared, it is clear that the philosophies of the Chinese differed greatly from that of the Greeks. Where the Greeks asked questions about the possible existence of a monotheistic deity, the Chinese were more concerned about the development of philosophy as an ethical and practical guide. Confucius was a philosopher who taught the importance of virtue and moral perfection. He explored ideas of humanity, loyalty, piety and the characteristics of a gentleman (a perfect man) in his teachings. The most fundamental of which, humanity and righteousness have since been argued to form the basis of morality.Ã [5]Ã In the Analects of Confucius, he explores these concepts of moral perfection and explains the importance of individuals of authority possessing these attributes. Confuciuss philosophy possessed dimensions of practicality which was seen from that fact that his teachings about piety were essentially descriptions of specific duties that an individual had according to his relationship with another. For instance, Confucius believed that a child should have respect for his parents and that parents should in turn love and care for their children. Being one of the main schools of thought in Chinese philosophy, Confucianism is thought to have had tremendous influence on the culture and history of China.Ã [6]Ã Additionally, in other Chinese philosophies such as Buddhism and Taoism teachings we see a form of instruction on a practical level (Buddhism instructed on how one should live in order to attain enlightenment). Although a lack of credible literature fails to either prove or disprove the influences of Chinese philosophy on their mathematics, one might argue that the general direction in which Chinese philosophy has taken appears to be similar to that of their mathematics. Other factors influencing mathematics? Although little is found regarding the history of the Greeks that could have affected the development of Greek mathematics, aspects of Chinese history might suggest the problem-based approach towards mathematics that was developed. Plato believed and explained in Book VII of The Republic that mathematics was important in understanding and attaining the idea of good which is the ultimate objective of philosophy. Plato believed that arithmetic and geometry allowed the mind to reflect and thus come closer to the truth, and also that the true use of arithmetic is in compelling the soul to reason about abstract number and repelling against the introduction of visible or tangible objects into the argument.Ã [7]Ã It has thus been argued that Plato believed that the ultimate aim of philosophy was to help the mind to understand and acquire the idea of good and that mathematics was a tool that helped to achieve that end. On the other hand, the Chinese clearly believed in the practical value of mathematics and a quick study of Chinese history revealed that mathematics was developed with practicality in mind. One clear example would be the earlier mentioned chapters of the Jiuzhang Suanshu on grain growing and taxation with the Chinese placing great emphasis on the importance of proper governance, mathematics was developed in order to calculate optimal methods of fair governance. The fact that the Chinese wrote mathematics with characters instead of alphabets would have also explained the need for them to discover the decimal system before other civilizations.Ã [8]Ã As mathematics was written with characters, the decimal system was invented to prevent the memorization of countless characters in order to recognize large numbers such as the date. With a decimal system, Chinese mathematics was thus able to gain an advantage over other civilizations in terms of the development of mathematics. Furthermore, during the period of Chinese mathematical development before 100 BC, the Chinese were interested in the areas of astrology and had a need to construct the calendar. As a result, many of the works produced in that time were related to astrology such as the Zhoubi Suanjing which provided instructions on measuring the positions of heavenly bodies using shadow gauges termed gnomons.Ã [9]Ã With the need to measure heights and distances that could not be measured directly (heights of structures or the distance of an island away from the mainland), the Chinese also developed their own variation of the Pythagoras theorem, which Liu Hui demonstrated in his Haidao Suanjing. As a result of some of the problems that the Chinese faced, we see the development of mathematics in China as a solution to some of these problems. Taking into consideration these other factors, there is clearly a relationship between the physical and cultural factors affecting China and their development of mathematics. On the other hand, while geometry had its practical uses for the Greeks, their main purpose for the study of mathematics was for instruction and loftier ideals of perfecting their souls. Concluding on the Extent of Influence on Mathematics Having considered the factors both philosophical and practical that might have affected the development of mathematics, one can see the distinct similarities between the cultures respective philosophy and how it has caused mathematics to develop. Ancient Greek mathematics developed in a manner that sought to separate concept from object, as could be inferred from their development of generalized mathematical theories in geometry (concept) discerned from postulates (object) since these postulates were observable truths such as All right angles are congruent. At the same time, the philosophy of the Greeks had similar objectives as could be seen from the above mentioned Forms and quintessential substances that the Greeks believed in. On the other hand, Chinese mathematics followed similar trends to that of their philosophy. With a focus on concrete examples and using analogies to solve other problems, the Chinese were clearly more concerned with matters of reality and had a pragmatic approach towards mathematics. Philosophically, there is a similar trend of practicality with the Chinese exploring the duties and proper etiquette of what they believed to be the perfect man. Again, the lack of credible literature seemingly undermines the entire relationship, yet it would be foolish to simply discount the fact that both philosophy and mathematics take on a similar direction in terms of development. Thus in conclusion, one could easily argue that the method by which philosophy was approached has been similar to that of the way mathematics was developed. Relevance to Modern Mathematicians? Truth and Mathematical Certainty? Having affirmed the relationship between philosophy and mathematics, we begin to question the relevance of such a relationship to modern mathematicians. One of the greatest questions of mathematics is its relevance to truth, and how mathematical inquiry may lead to certainty and truth. Before we begin to explore the question of which mathematics (Greek or Chinese) was closer to mathematical certainty and thus truth, we must keep in mind that Greek and Chinese mathematics were radically different in terms of method as was previously shown. Based on those methods, we can categorize the mathematics according to the theories of truth that they appear to abide by. The Chinese appeared to base their system on the modern theory of truth that is pragmatism. According to the theory in a simplified form, a concept may be considered true if it is directly relevant to reality. This meant that a concept would be true if it had any practical consequence and was thus judged based on its practical value. Pragmatism is thus highly pertinent to the method of Chinese mathematics, which was in essence a study of the practical effects of theories of mathematics. On the other hand, the Greek method appears to follow the theory of coherentism, which in simple terms was the theory that the truth of a system of beliefs could be determined based on how well it coheres with other systems of belief. This seems to be applicable to the Greek method of approaching mathematics, where axioms were the basic beliefs and entire systems (theorems) would be developed from these axioms. The truth of these systems would then be appraised according to how well they cohered with the basic sets of beliefs. One might argue that foundationalism would have been a more applicable theory to the Greek method, yet the Greeks did not simply base their theorems on noninferential knowledge such as axioms, and instead used postulates (inferential knowledge) in geometry. As a result, the axiomatic method of the Greeks would have appertained to the theory of coherentism. It is important to note that despite these theories of truth being modern, the concept behind method of mathematics and theory of truth appear to be similar, and would thus be applicable in the exploration of mathematical certainty. Who was more Certain? Having ascribed to Greek and Chinese mathematics coherentism and pragmatism respectively, the question of who was closer to mathematical certainty becomes apparent. Both schools clearly had their strengths and weaknesses in such a comparison, with the Chinese being directly relevant to reality and thus closer to certainty in terms of practicality. On the other hand, the Greeks would have believed that they were aspiring towards certainty through the separation of concept from object (abstraction), where truth in the complete discovery of all Forms would have been certainty. Given the extent of influence on modern mathematics that Greek mathematics has, one would easily consider the adopted Greek mathematics as more certain. Yet the idea of complete mathematical certainty seems to be impossible, as proved by Kurt Godel with his theorems that a system is either complete or consistent and thus impossibleto fully prove any proposition.Ã [10]Ã The ramifications thus being that certainty is impossible to achieve, and that in terms of the axiomatic method, mathematical certainty can never be fully arrived at. Furthermore, the existence of various theories of truth might already suggest that there is a lack of existence of complete certainty, and this thus suggests the probability of the quest for mathematical certainty being futile.
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