Two Basic Rules of Probability

Part I: Introduction1 RationaleMetaphor, based on the association of similarity, is one of the two basic types of semantic transference that have been an interest for many linguistic researchers. Galperin ( 1981: 139-40) states that the term ‘metaphor’ can be understood as the transference of some quality from one object to another. Metaphor is widely used to designate the process in which a word acquires a derivative meaning.In theory, there are at least three communicative functions that metaphor might serve (Ortony 1975). First, they might allow one to express that which is difficult or impossible to express if one is restricted to literal uses of language. Evidence for this "inexpressibility" claim would constitute encouraging support for the necessity-of-metaphors view. A second possible function of metaphors is that they may constitute a particularly compact means of communication. Although conscious experience is continuous in form, the linguistic system we use to talk about it is comprised of discrete elements (lexical items). Unlike more literal forms of language, metaphor may enable us to convey a great deal of information in a succinct manner by obviating the need to isolate the predicates to be expressed into their corresponding lexical representations. Finally, metaphors may help capture the vividness of phenomenal experience. If metaphors convey chunks of information rather than discrete units, they can paint a richer and more detailed picture of our subjective experience than might be expressed by literal language. This we call the "'vividness" claim.In this paper we are interested in the first and last of these possible functions. Thus, we need to examine a discourse domain for which a prima facie case can be made for supposing that literal language will often be inadequate and which lends itself to variations in vividness. There doubtless are many such domains. The one that we selected was that of internal states, in particular, emotional states. The literature on the linguistic expression of emotions suggests a relatively high incidence of figurative language use (Davitz 1969), providing pragmatic reasons An investigation into the role of metaphor in description of emotion in poetic discourse1 for believing that the context of (linguistic) emotional expression may be a profitable one within which to study metaphor production. Emotional states seemed well-suited because they tend to have an elusive, transient quality that is difficult to describe using literal language, although, of course, they can usually be labeled using literal language. Thus, while it might be easy for a person to label an emotional state as, for example, "fear," it is difficult to provide a literal description of the quality of some particular experience of fear. Furthermore, because emotions vary in intensity, one might expect differential levels of vividness.Our thesis is entitled “ An investigation into the role of metaphor in description of emotions in English poetic disscourse” and focused on William Shakespeares’ sonnets. The choice is based on two reasons. Firstly, recent research states Two Basic Rules of Probability Two Basic Rules of Probability By: OpenStaxCollege When calculating probability, there are two rules to consider when determining if two events are independent or dependent and if they are mutually exclusive or not The Multiplication Rule If A and B are two events defined on a sample space, then: P(A AND B) = P(B)P(A|B) This rule may also be written as: P(A|B) = P(A AND B) P(B) (The probability of A given B equals the probability of A and B divided by the probability of B.) If A and B are independent, then P(A|B) = P(A) Then P(A AND B) = P(A|B)P(B) becomes P(A AND B) = P(A)P(B) The Addition Rule If A and B are defined on a sample space, then: P(A OR B) = P(A) + P(B) - P(A AND B) If A and B are mutually exclusive, then P(A AND B) = Then P(A OR B) = P(A) + P(B) - P(A AND B) becomes P(A OR B) = P(A) + P(B) Klaus is trying to choose where to go on vacation His two choices are: A = New Zealand and B = Alaska • Klaus can only afford one vacation The probability that he chooses A is P(A) = 0.6 and the probability that he chooses B is P(B) = 0.35 • P(A AND B) = because Klaus can only afford to take one vacation 1/17 Two Basic Rules of Probability • Therefore, the probability that he chooses either New Zealand or Alaska is P(A OR B) = P(A) + P(B) = 0.6 + 0.35 = 0.95 Note that the probability that he does not choose to go anywhere on vacation must be 0.05 Carlos plays college soccer He makes a goal 65% of the time he shoots Carlos is going to attempt two goals in a row in the next game A = the event Carlos is successful on his first attempt P(A) = 0.65 B = the event Carlos is successful on his second attempt P(B) = 0.65 Carlos tends to shoot in streaks The probability that he makes the second goal GIVEN that he made the first goal is 0.90 a What is the probability that he makes both goals? a The problem is asking you to find P(A AND B) = P(B AND A) Since P(B|A) = 0.90: P(B AND A) = P(B|A) P(A) = (0.90)(0.65) = 0.585 Carlos makes the first and second goals with probability 0.585 b What is the probability that Carlos makes either the first goal or the second goal? b The problem is asking you to find P(A OR B) P(A OR B) = P(A) + P(B) - P(A AND B) = 0.65 + 0.65 - 0.585 = 0.715 Carlos makes either the first goal or the second goal with probability 0.715 c Are A and B independent? c No, they are not, because P(B AND A) = 0.585 P(B)P(A) = (0.65)(0.65) = 0.423 0.423 ≠ 0.585 = P(B AND A) So, P(B AND A) is not equal to P(B)P(A) d Are A and B mutually exclusive? d No, they are not because P(A and B) = 0.585 To be mutually exclusive, P(A AND B) must equal zero Try It 2/17 Two Basic Rules of Probability Helen plays basketball For free throws, she makes the shot 75% of the time Helen must now attempt two free throws C = the event that Helen makes the first shot P(C) = 0.75 D = the event Helen makes the second shot P(D) = 0.75 The probability that Helen makes the second free throw given that she made the first is 0.85 What is the probability that Helen makes both free throws? P(D|C) = 0.85 P(C AND D) = P(D AND C) P(D AND C) = P(D|C)P(C) = (0.85)(0.75) = 0.6375 Helen makes the first and second free throws with probability 0.6375 A community swim team has 150 members Seventy-five of the members are advanced swimmers Forty-seven of the members are intermediate swimmers The remainder are novice swimmers Forty of the advanced swimmers practice four times a week Thirty of the intermediate swimmers practice four times a week Ten of the novice swimmers practice four times a week Suppose one member of the swim team is chosen randomly a What is the probability that the member is a novice swimmer? a 28 150 b What is the probability that the member practices four times a week? b 80 150 c What is the probability that the member is an advanced swimmer and practices four times a week? c 40 150 d What is the probability that a member is an advanced swimmer and an intermediate swimmer? Are being an advanced swimmer and an intermediate swimmer mutually exclusive? Why or why not? d P(advanced AND intermediate) = 0, so these are mutually exclusive events A swimmer cannot be an advanced swimmer and an intermediate swimmer at the same time e Are being a novice swimmer and practicing four times a week independent events? Why or why not? 3/17 Two Basic Rules of Probability e No, these are not independent events P(novice AND practices four times per week) = 0.0667 P(novice)P(practices four times per week) = 0.0996 0.0667 ≠ 0.0996 Try It A school has 200 seniors of whom 140 will be going to college next year Forty will be going directly to work The remainder are taking a gap year Fifty of the seniors going to college play sports Thirty of the seniors going directly to work play sports Five of the seniors taking a gap year play sports What is the probability that a senior is taking a gap year? P= 200 − 140 − 40 200 = 20 200 = 0.1 Felicity attends Modesto JC in Modesto, CA The probability that Felicity enrolls in a math class is ... Part I: Introduction 1 Rationale Metaphor, based on the association of similarity, is one of the two basic types of semantic transference that have been an interest for many linguistic researchers. Galperin ( 1981: 139-40) states that the term ‘metaphor’ can be understood as the transference of some quality from one object to another. Metaphor is widely used to designate the process in which a word acquires a derivative meaning. In theory, there are at least three communicative functions that metaphor might serve (Ortony 1975). First, they might allow one to express that which is difficult or impossible to express if one is restricted to literal uses of language. Evidence for this "inexpressibility" claim would constitute encouraging support for the necessity-of-metaphors view. A second possible function of metaphors is that they may constitute a particularly compact means of communication. Although conscious experience is continuous in form, the linguistic system we use to talk about it is comprised of discrete elements (lexical items). Unlike more literal forms of language, metaphor may enable us to convey a great deal of information in a succinct manner by obviating the need to isolate the predicates to be expressed into their corresponding lexical representations. Finally, metaphors may help capture the vividness of phenomenal experience. If metaphors convey chunks of information rather than discrete units, they can paint a richer and more detailed picture of our subjective experience than might be expressed by literal language. This we call the "'vividness" claim. In this paper we are interested in the first and last of these possible functions. Thus, we need to examine a discourse domain for which a prima facie case can be made for supposing that literal language will often be inadequate and which lends itself to variations in vividness. There doubtless are many such domains. The one that we selected was that of internal states, in particular, emotional states. The literature on the linguistic expression of emotions suggests a relatively high incidence of figurative language use (Davitz 1969), providing pragmatic reasons An investigation into the role of metaphor in description of emotion in poetic discourse 1 for believing that the context of (linguistic) emotional expression may be a profitable one within which to study metaphor production. Emotional states seemed well-suited because they tend to have an elusive, transient quality that is difficult to describe using literal language, although, of course, they can usually be labeled using literal language. Thus, while it might be easy for a person to label an emotional state as, for example, "fear," it is difficult to provide a literal description of the quality of some particular experience of fear. Furthermore, because emotions vary in intensity, one might expect differential levels of vividness. Our thesis is entitled “ An investigation into the role of metaphor in description of emotions in English poetic disscourse” and focused on William Shakespeares’ sonnets. The choice is based on two reasons. Firstly, recent research states that “Metaphorical modes of expression are characteristic of all adult discourse”. ACKNOWLEDGEMENT Aft er much painst aking effort and const ant struggl es, what I want to sa y at the ver y moment of compl eting m y M.A. t hesis is that without m y parents’ unceasing encouragement , I would have never compl ete d my graduat e education and t hus none of my accompli shm ents could have been possi ble. Without m y Laoshi A/P Lo Yuet Keung’s unfail ing enli ghtenment , I would remai n an i gnorant bo y finding his wa y in the m aze of academic schol arship, chasing into countl ess pit falls. Without m y fri ends’ support and t hei r stimulating exchanges with m e , m y int ell ect ual visi on could not have ex panded as it did and m y personal charact er would fail to devel op . Hard work alwa ys pa ys off , or at l east , as I believe, will eventuall y do. I spent almo st half a year writi ng m y thesis, not to mention t he preparation for it, and I have gained a lot i n this process . The most unforgett able experience is the revision st age of m y thesis. Laoshi had been questioning m y arguments rel entl essl y; I ha d to keep on defending m ysel f vis -à-vis his penet rating criti cisms . As a result, m y argum ent becomes more precise and cl earer, and m y thesis is I greatl y im proved. Through thi s academic exerci se, I have nurtured import ant qualities i n m yself as a schol ar , such as precis ion, prudence, perseverance. My grat itude m ust also be extended to t he foll owing people: A/P YUNG Sai Shing , whose semi nars inspired m e to stud y i ntell ect ual histor y with a new criti cal e ye. NEO P eng Fu Laoshi and m y res pect able seni or Miss Teoh Joo Ki ow kindl y lent me rel evant academic mat erials , which enabled me to stud y m ore effi cientl y. There are man y other t eachers and friends who have helped me i n one wa y or another. To them I owe m y deepest gratit ude. II A c k n o wl e d g e m e n t 目录 I III Ab s t r a c t V 序 VI 第一章 绪论 1. 问题与文献 1 2. 结构与概念 5 第二章 从政治批评与学术批评看荀子的 广义功利主义 1. 四强国的政治经验与功利主义的症结 19 2. 从学术批评检论荀子的广义功利主义 27 3. 政治境界论 37 4. 礼、法的分流与复合 46 5. 结论 52 第三章 论荀子广义功利主义的论理结构及其在儒学发展史上的意涵 1. 广义功利主义的论理结构 57 2. 儒家伦理学的两条进路 63 3. 结论 72 第四章 从哲学思辨返回经验现实 1. 本体论思潮 75 2. 知识论思潮 84 3. 试论荀子的经验性格及其成因 93 4. 结论 第五章 102 结论 129 III 参考书目 133 IV ABSTRACT Xun Zi was one of t he great est C onfuci an thinkers in the pre-Qin peri od. The purpose of thi s t hesis is to i nterpret the basi c charact er of his philosoph y. First of all, it argues that like Mo hists and Legalists , Xun Zi ’s thought also has a utilitari an character, but his util itari anism should be understood in a broader sense. He was concerned about the materi al needs of t he peopl e as well as t heir emoti onal needs. Second, Xun Zi ’s t hought also exhibits an em piri cal bent; unlike hi s predecessors Zi chan and Confucius, Xun Zi tri ed to const ruct a ki nd of epist emology bas ed on experi ence. Lastl y, the em piri cal character of Xun Zi’s thought was det ermi ned b y its utilitari an character . As such, utilitarianism is t herefor e fundamental to Xun Zi’s thought . In the context of i ntell ect ual histor y, both the utilit ari an and empirical charact er of Xun Zi’s thought exem plifi ed t he historical competition and reconcil i ation of two parti cul ar patt erns of cultures — the poli tical and intellectual culture s of the Zhou d ynast y and t he Warri ng St ates peri od. Speci fi call y, uti litari anism was the mainst ream thinking duri ng the Warri ng Stat es peri od in which Xun Zi lived, yet his broader sense of utilit ari anism inherited and absorbed the el ement s V of rites and musi c from the Zhou politi cal culture. Xun Zi ’s empiricism reflect ed the t rend of ret urning to the empi ri cal vi ews espoused earli er b y Zi chan, Confucius and ot hers. At the same tim e , Xun Zi also adopt ed man y i deas from t he “epist emol og i cal movem ent ” which rei gned in t he Warring St at es era. VI 我研究思想史的基本旨趣 （代序） 孟子说：“颂其诗，读其书，不知其人， 第一章 绪论 1. 问题与文献 本文试图探讨的核心问题，一言以蔽之，是要理解并诠释荀子 思想的基本性格。 先交代研究方法。迄今为止的荀学研究1大致存在两种研究框 架。第一种研究框架是“理学研究的理论框架”2，该框架主张以 孔、孟作为研究的基本坐标，以人性善恶作为讨论的重点3。韩愈 说：“„„尧以是传之舜，舜以是传之禹，禹以是传之汤，汤以是 传之文、武、周公，文、武、周公传之孔子，孔子传之孟轲，轲之 死不得其传焉。荀与扬也，择焉而不精，语焉而不详。”4程子也 1 我这里所用“荀学研究”一词只限于义理方面的研究，故不对《荀子》的训 诂、注释、考订成果进行回顾。 2 江心力《20 世纪前期的荀学研究》（北京：中国社会科学出版社，2005）， 页 6。 3 江氏原本的提法是“经学研究的理论框架”，考虑到将荀子与孔、孟严格对 立，并将其排斥在“道统”之外，至少可以追溯到韩愈，而尤其成为宋明理学 家论述荀子的标准模式。况且，“经学研究”的内涵极广，有今古、汉宋之 别，或讲义理，或明训诂，不能单用“道统”来界定“经学研究”的方法和流 派，但至少从韩愈以来的宋明理学家都采用“道统”的角度来论荀学，对照着 孟子的“性善”论来讲荀子的“性恶”论。鉴于上述两点理由，我袭江氏之 意，而改用“理学研究的理论框架”的提法。 4 韩愈〈原道〉，见《韩昌黎全集》（香港：广智书局，出版年月不详），页 174。 1 说：“荀子极偏驳，只一句性恶，大本已失。”5朱熹说：“荀、扬 不惟说性不是，从头到底皆不识。”6采取的都是这种理论框架。另 一种理论框架始于 20 世纪前期，这便是诸子学研究的框架，该框架 主张把荀子与诸子关系作为研究的出发点7，如胡适的《中国哲学史 大纲》、梁启超的《先秦政治思想史》、章太炎的《诸子学略说》 便采取这种研究框架。需要补充的是，“理学研究框架”对于荀子 的研究基本上采用“道统”，具体上特别是孔、孟，作为研究的参 照系；“诸子学研究框架”不但将孔、孟拿来与荀子进行对比，也 同样将其他诸子拿来与荀子进行比较，这种研究框架不只是关心理 学家所关注的性与天道，也关注心理、逻辑、音乐等各种课题。因 此，第二种理论框架其实只是第一种理论框架的扩大，而不应视为 两种截然不同的理论框架。 同是采取诸子学研究框架，但研究的问题可以千差万别。就荀 学研究而言，荀子的人性论、天道观、心理学、逻辑学、政治学等 是迄今为止荀子研究的热门领域，研究问题大都是从这些领域中提 取出来的。在天道观方面，胡适说：“荀子在儒家中最为特出，正 因为他能用老子一般人的‘无意志的天’来改正儒家墨家的‘善恶 赏罚’有意志的天，同时却又能免去老子庄子天道观念的安命守旧 种种恶果。”8这就告诉我们荀子吸收了道家的自然天道观，这个结 论后来被冯友兰、郭沫若、陈荣捷（Chan Wing-tsit，1901-1994） 5 黎靖德编，马镛、吴宣德整理《朱子语类》（海口：海南国际新闻出版中心, 1996），页 1375。 6 同上。 7 江心力《20 世纪前期的荀学研究》，页 6。 8 胡适《中国哲学史大纲》上册（上海：商务印书馆，1919），页 310。 2 等多数学者广泛接受9，成为理解荀子天道观的一个主流观点。值得 提出的是，廖名春对这种主流观点作出了必要的补充，他认为孔子 说的“天何言哉！四时行焉，百物生焉，天何言哉！”（《论 语·阳货》）孟子说的“天油然作云，沛然下雨，则苗勃然兴之 矣。”（《孟子·梁惠王上》）都是指自然的天。所以，那种只看 到道家自然天道观对荀子的影响，而忽视荀子对于孔孟天道观的继 承的观点，是有失偏颇的10。Paul R. Goldin 指出，荀子与中国传 统的神性的天道观的一个区别在于他否认具有意志的多变的天。11 在心理学方面，冯友兰提出：“荀子亦讲静虚，但谓心之虚， 乃‘不以所已臧害所将受’；心之静，乃‘不以梦剧乱知’。心之 主要功用为知虑，‘使之则谋’。‘梦剧’者，‘偷则自行’之随 便胡思乱想也。不使胡思乱想妨碍知谋，即是静也。故荀子虽讲静 虚，但不以庄子所说‘至人之用心若镜’为心之静虚状态，此荀子 9 冯友兰说：“荀子所言之天，则为自然之天，此盖亦由老庄之影响也。”见 《中国哲学史》（上海：商务印书馆，1935），页 355。郭沫若认为老子“取 消了殷周以来的人格神的天之至上权威，而建立了一个超绝时空的形而上学的 本体”；思、孟的天道观是“自然的理法”。荀子将二者统一起来，认为“自 然的理法就是神，就是天。”这个结论与胡适、冯友兰不同，但在继承道家自 然天道观这一点上，却与二家的看法一致。《先秦天道观之进展》，见《中国 古代社会研究（外二种）》（河北：石家庄出版社，2001），页 336、355； 陈 荣 捷 将 荀 子 的 天 道 观 理 解 为 一 种 “ 自 然 主 义 ” ， 见 A Source Book in Chinese Philosophy （ Princeton, N.J. ： Princeton University Press, 1963）, p.115. 10 11 廖名春《荀子新探》（台北：文津出版社，1994），页 200-201。 Paul R. Goldin, The philosophy of Xunzi, Ann Arbor, Mich.: University Microfilms International, 1999, P.95. 3 采老庄之说，而加以修正变化也。” 12 A. C. Graham （ 1919- 1991）的看法与冯友兰基本上相同，他也注意到荀子“静虚”说与 庄子“至人用心若镜”说的上述区别，但他指出荀子与庄子“共享 了那个时代的相当数量的心理学术语”，例如虚、静、神明 13 。在 Graham 之后，赵吉惠也指出：“《荀子》一书与《文子》、《黄 帝四经》、《管子》四篇所共同使用的黄老之学的思想范畴，那就 更加明显了。这些范畴，例如：无为、自然、无欲、不争、虚静、 虚气、心术、天官、天君、天功、天心、天德、道法、养生、天 养、尚贤、赏罚、虚壹而静、贵贱有别、刑名法术，尚贤使能”14。 在冯友兰之后，Graham、赵吉惠之前，郭沫若、杜国庠、白奚对于 这个问题提出了另一种新颖的意见，他们认为荀子的“解蔽”思想 其实就是宋钘的“去宥”思想，荀子的“静虚”观念是从宋钘的 《心术》中承受过来的15。该意见的开拓性在于提示荀子与稷下学派 12 冯友兰《中国哲学史》，页 363。 13 A. C. Graham, Disputers of the Tao ： Philosophical Argument in Ancient China （ La Salle, Ill. ： Open Court ， 1989 ） , p.252. 中 文 译 本 有张海晏译《论道者：中国古代哲学论辩》（北京：中国社会科学出版社， 2003）。 14 赵吉惠〈荀学新解〉，见《国学沉思》（杭州：浙江人民出版社，1998）， 页 150。晖案：Graham 所列举的这些词汇是否能够代表当时的心理学术语， 赵吉惠所列举的这些概念是不是黄老之学的思想范畴，这还有待仔细的考证， 但必须承认他们从语言比较的角度开展荀子与黄老学派特别是稷下黄老学派的 比较研究，至少在方法上是有启发意义的，在内容上或许也可以作为考证的起 点或旁证。 15 郭沫若《十批判书》，见《中国古代社会研究（外二种）》，页 809；杜国 庠《先秦诸子思想概要》（北京：三联书店，1955），页 50；白奚《稷下学 4 的 一 种 思 想 关 联 。 最 近 ， 佐 藤 将 之 （ Masayuki Sato ， 1965- ） 指 出，荀子的“礼”论吸收了稷下学派的“分析话语”16，大概也是受 了郭、杜、白观点的启示而提出的。 在逻辑学方面，胡 适认为荀子的逻辑 学 17“介于儒家与法 家之 间，是儒法过渡时代的学说”18。胡适之所以说荀子上承儒家的逻辑 学，是因为他认为荀子继承了儒家“春秋派”的正名主义，不同之 处在于荀子摆脱了史官一字褒贬的作风；至于为什么摆脱史官一字 褒贬的作风就是“介于儒家与法家之间”，胡适并未交代清楚。冯 友兰在这个问题上提出了一个十分独到的看法，他指出：“《墨 经》之作，亦辩者之学之反动。盖辩者所持之论，皆与吾人之常识 违反。儒墨之学，皆注重实用，对于宇宙之见解，多根据常识。见 辩者之‘然不然可不可’，皆以为‘怪说觭辞’而竞起驳之。然辩 者立论，皆有名理的根据，故驳之者之立论，亦须根据名理。所以 墨家有《墨经》，儒家有荀子之〈正名〉篇，皆拥护常识，驳辩者 研 究 — 中 国 古 代 的 思 想 自 由 与 百 家 争 鸣 》 （ 北 京 ： 三 联 书 店 ， 1998 ） ， 页 288-292。不同的是，郭沫若专注在宋钘与荀子的比较，而杜国庠使用了“宋 尹学派”的提法，白奚使用了“稷下学派”的提法。 16 Masayuki Sato, The Confucian Quest for Order: The Origin and Formation of the Political Thought of Xun Zi (Leiden: Brill, 2003), p.162. 17 在荀学研究中，人们常用名学、辩学等概念指代荀子的逻辑学，其涵义虽未 能截然界定，不免有欠精确；但三者都涉及荀子的逻辑概念、推理和论证，这 是共同的。 18 Basic rules of English pronunciation (Las reglas basicás de pronunciación Inglés) Alphabet sounds (Sonidos del alfabeto) A E I O U “e” “I” “ay” “o” “llu” En cada palabra que termina en la letra “e”, la forma de leer la letra que viene primero es como se pronuncia como en el alfebeto Relative Alphabet sounds (Sonidos del alfabeto “relative”) A E I O U “ ” “ ” “ ” “ah” “ ” (son más suave-entre dos sonidos, y no se necesesita abrir la boca tan mucho) Partner 1: Hello! My name is _ What’s your name? Partner 2: Partner 1: I’m (I* am) fine, thank you! And how about you? Partner 2: Partner 1: Nice to see you/meet you also! See you later  ... produced: 9/17 Two Basic Rules of Probability • In early 2011, 60 percent of the population approved of Mayor Ford’s actions in office • In mid-2011, 57 percent of the population approved of his actions... complement of getting an even number? Why? Find two mutually exclusive events 10/17 Two Basic Rules of Probability Are the events Even and 1st Dozen independent? Compute the probability of winning... cancer Suppose that of those women who develop breast cancer, a 4/17 Two Basic Rules of Probability test is negative 2% of the time Also suppose that in the general population of women, the test