4. The Horned Man 悖论 英文版 逻辑学教材
科技英语 第一单元 罗素悖论
第一单元
GROUP 1
Who Is Russell?
伯特兰· 罗素：
二十世纪英国哲学家、数学家、逻
辑学家、历史学家，无神论或者不
可知论者，也是上世纪西方最著名、
影响最大的学者和和平主义社会活
动家之一，1950年诺贝尔文学奖得 主。
What’s Russell’s paradox
罗 素 悖 论
他还不能解决这个问题,并且上世纪有很多的尝
试，去解决这个问题（但没有成功）。
Diagram 第六段：罗素自己对这个悖
论的回答促进了类型理论的形 成。他解释说，悖论的问题在 于我们混淆了数集和数集的集
第七段：策梅洛对于罗
素悖论的解决方法用新的
公理：对于任意公式A（x）
和任意集合b，都会有一个
集合满足y={x：x既在b中 又满足A（x）}取代了以前 的公理：对于任意公式A （x），都会有一个集合满 足y={x：x满足A（x）}。
把所有集合分为2类，第一类中的集合 以其自身为元素，第二类中的集合不以 自身为元素，假令第一类集合所组成的 集合为P，第二类所组成的集合为Q， 于是有： P={A∣A∈A} Q={A∣A∉A} 问，Q∈P 还是 Q∈Q？ 若Q∈P，那么 根据第一类集合的定义，必有Q∈Q， 但是Q中任何集合都有A∉A的性质，因 为Q∈Q，所以Q￠Q，引出矛盾。若 Q∈Q，根据第一类集合的定义，必有 Q∈P，而显然P∩Q=∅，所以Q∉Q，还 是矛盾。 这就是著名的“罗素悖论”。
• 2、based on definition of deal a blow to in terms of leaded to as the way in the form of servr as become of replace by
中英=高级英语1-何兆熊-Unit-5-conservatives-and-liberals
Unit 5 conservatives and liberals保守派和革新派Conservatives and LiberalsRalph Waldo Emerson1. The two parties which divide the state, the party of Conservative and that of innovation, are very old, and have disputed the possession of the world ever since it was made. This quarrel is the subject of civil history. The conservative party established the reverend hierarchies and monarchies of the most ancient world. The battle of patrician and plebian, of parent state and colony, of old usage and accommodation to new facts, of the rich and, of the poor, reappears in all countries and times. The war rages not only in battlefields, in national councils, and ecclesiastical synods, but agitates every man’s bosom with opposing advantages every hour. On rolls the old world meantime, and now one, now the other gets the day, and still the fight renews itself as if for the first time, under new names and hot personalities.这个国家存在着两个政党，保守党和革新党。
逻辑学书单英文版
逻辑学书单英文版摘要：1.逻辑学书单英文版的重要性2.逻辑学书单英文版的推荐书籍3.如何选择适合自己的逻辑学书单英文版书籍4.逻辑学书单英文版的学习方法和技巧5.逻辑学书单英文版对提高逻辑思维能力的帮助正文：逻辑学书单英文版对于学习逻辑学和提高逻辑思维能力具有重要意义。
逻辑学是研究推理规律的学科，它能帮助我们更加明确、有条理地思考问题。
通过阅读逻辑学书单英文版书籍，我们可以了解到不同的逻辑理论和方法，从而在实际应用中更好地运用逻辑学知识。
下面推荐几本逻辑学书单英文版的书籍，这些书籍都是在逻辑学领域具有较高影响力的作品：1.《逻辑学导论》（Introduction to Logic）作者：Irving M.Copi2.《形式逻辑》（Formal Logic）作者：Daniel V.Graham3.《逻辑思维》（How to Think Logically）作者：Gilbert R.Colman4.《逻辑思维训练100 例》（100 Logical Fallacies）作者：Robert J.Gerringer5.《启发式思维》（Gdel, Escher, Bach: An Eternal Golden Braid）作者：Douglas R.Hofstadter在选择逻辑学书单英文版书籍时，需要根据自己的兴趣和需求来选择。
对于初学者来说，可以先从入门级别的书籍开始，例如《逻辑学导论》。
对于已经有一定基础的读者，可以选择更具挑战性的书籍，如《形式逻辑》和《逻辑思维训练100 例》。
学习逻辑学书单英文版时，可以采用以下方法和技巧：1.制定学习计划：为了更好地学习逻辑学知识，可以制定一个合理的学习计划，每天安排一定的学习时间。
2.理论与实践相结合：在学习逻辑学理论知识的同时，要多做练习题，将所学知识应用到实际问题中。
3.多做总结和归纳：在学习过程中，要经常对所学知识进行总结和归纳，形成自己的知识体系。
4.参加讨论和交流：可以通过参加线上线下的讨论和交流活动，与他人分享学习心得，提高自己的逻辑思维能力。
悖论英文版
A Statue of Zles will never catch up with the tortoise.
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Part 3: Solutions
1、Classifications of paradoxes
Classification 1: 1、syntax paradox 2、semantic paradox 3、pragmatic paradox.
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Part 2: Some Famous Paradoxes
1、The Pythagoras paradox
Let’s consider a square of length 1. Can we express its diagonal as a ratio of two integers?
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2、The barber’s paradox
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3、Paradox of the almighty God
A said: The God is capable of doing anything.
B asked: Can he create a man who can defeat himself?
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4、The liar’s paradox
Zeno tried to prove “multiple ” and “change” are illusory, while “one” and “static” are real. Movements are illusions. So he designed 4 instances called Zeno’s paradoxes
See：An introduction to logical paradoxes[M], Zhang Jianjun. Nanjing: Nanjing university press, 2002.
精读4 the damned human race
Lesson 15Part One Warm-upBackground InformationI.Author Pre-class work:What do you know about Mark Twain? Can you name some books he wrote?Mark Twain (1835-1901) was born Samuel Langhorne Clemens in Florida, Missouri, but lived as a child in Hannibal, Missouri, on the Mississippi River. He took the pen name Mark Twain from the call of the pilots on the river steamers, which indicated that the water was twelve feet deep, a safe depth for a steamer. During his early years, he worked as a riverboat pilot, newspaper reporter, printer, and gold prospector. But then he turned to writing, and became one of the greatest of American writers.His works have been immensely popular, and have brought him an ample fortune, thus enabling him to devote his entire time to literature.Although his popular image is as the author of such humorous works as The Adventures of Tom Sawyer and The Adventures of Huckleberry Finn. Twain had the other side that may have resulted from the bitter experiences of his life: financial failure and the death of his wife and daughters. His last writings are savage, satiric, and pessimistic. The present text is taken from Letters from the Earth, one of his later works.●The Celebrated Jumping Frog of Calaveras Country《卡拉维拉斯县有名的跳娃》●The Innocents Abroad《傻瓜出国记》1869 A series of newspaper articles after hisEuropean trip later was published as this book. It explores the scrupulous individualism ina world of fantastic speculation and unstable values, and gives its name to theget-rich-quick years of the post Civil War era.《傻子出国记》为通讯集，是马克·吐温的旅欧报道。
逻辑学书单英文版
逻辑学书单英文版以下是一些逻辑学的英文书单，涵盖了不同层次和主题的经典著作：1. "Introduction to Logic" by Irving M. Copi and Carl Cohen这本书是逻辑学入门的经典教材，涵盖了命题逻辑和谓词逻辑的基本概念和推理方法。
2. "Symbolic Logic and Mechanical Theorem Proving" by Chin-Liang Chang and Richard Char-Tung Lee该书深入介绍了逻辑学中的符号逻辑和机械定理证明方法，对于形式化推理和自动推理系统感兴趣的读者很有价值。
3. "Principia Mathematica" by Alfred North Whitehead and Bertrand Russell这是一部经典的数理逻辑著作，旨在通过逻辑系统化地推导数学定理，是逻辑学和哲学领域的重要里程碑。
4. "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas R. Hofstadter这本书以音乐家巴赫、艺术家艾舍尔和数学家哥德尔的作品为线索，探讨了逻辑、形式系统和人工智能等领域的交叉点，是一本富有启发性的哲学著作。
5. "Logic, Language, and Meaning: Introduction to Logic" by L.T.F. Gamut该书综合了逻辑学、语言学和语义学的内容，对于理解逻辑与语言的关系以及逻辑语义学的基本概念和方法非常有帮助。
6. "A Concise Introduction to Logic" by Patrick J. Hurley这本书是一本简明扼要的逻辑学导论，涵盖了基本的逻辑概念、推理形式和常见谬误，适合初学者阅读。
The sad young man教材
Bohemian 波西米亚式的
什么是波西米亚？是生活在捷克斯洛伐克那个
放荡不羁、以歌舞为生的民族，还是指那群视世俗准 则如粪土的艺术家？发展到今天，却成了一种生活观， 在波西米亚的旗帜下，一向为新生代不耻的老布尔乔 亚的理想——追逐财富，和波希米亚崇尚自由的精神 不可思议地结合起来，向人们展示着一幅用庸俗作背 景的个性场景，也许这正是现代精神的一个侧面：除 了金钱，没有什么能让人获取更大的自由。有人用一 句通俗的时尚语言精辟地概括为——有一定经济基础 的小资情调。
Prohibition made it illicit to buy and drink alcohol.As a result the young people at that time found drinking more enjoyable than ever,not only because it was refreshing and relaxing,but also because the very act of drinkingg was illicit.
——原来如此！
用来形容富有“小资情调”带有轻微浪漫色彩，富 有忧郁气质的人。Bohemian一般译为波西米亚,原意 指豪放的吉卜赛人和颓废派的文化人。追求自由的 波希米亚人，在浪迹天涯的旅途中形成了自己的生 活哲学。如今的波希米亚不仅象征着流苏、褶皱、 大摆裙的流行服饰，更成为自由洒脱、热情奔放的 代名词。波西米亚风格的装扮，在总体感觉上靠近 毕加索的晦涩的抽象画和斑驳陈旧的中世纪宗教油 画，还有迷综错乱的天然大理石花纹，杂芜、凌乱 而又惊心动魄。暗灰、深蓝、黑色、大红、桔红、 玫瑰红，还有网络上风行一气的“玫瑰灰”便是这 种风格的基色。没有底气的人一穿上便被无情地淹 没在层层叠叠的色彩和错觉中。
[教材]Thesadyoungman
![[教材]Thesadyoungman](https://img.taocdn.com/s3/m/767cc5c0185f312b3169a45177232f60ddcce727.png)
The sad young man悲哀的青年一代罗德.W.霍顿，赫伯特.W.爱德华兹1．二十年代社会生活的各个方面中，被人们评论得最多、渲染得最厉害的，莫过于青年一代的叛逆之行了。
只要有只言片语提到那个时期，就会勾起中年人怀旧的回忆和青年人好奇的提问。
中年人会回忆起第一次光顾非法酒店时的那种既高兴又不安的违法犯罪的刺激感，回忆起对清教徒式的道德规范的勇猛抨击，回忆起停在乡间小路上的小轿车里颠鸾倒凤的时髦爱情试验方式；青年人则会问起有关那时的一些纵情狂欢的爵士舞会，问起那成天背着酒葫芦、勾引得女人团团转的“美男子”，问起那些“时髦少女”和“闲荡牛仔”的奇装异服和古怪行为等等的情况。
“那时的青年果真这样狂放不羁吗?”今天的青年学生们不禁好奇地向他们的师长问起这样的问题。
“那时真的有过青年一代的问题吗?”对这类问题的回答必然只能是既“对”又“不对”——说“对”是因为人的成长过程中一贯就存在着所谓青年一代的问题；说“不对”是因为在当时的社会看来似乎是那么狂野，那么不负责任，那么不讲道德的行为，若是用今天的正确眼光去看的话，却远远没有今天的一些迷恋爵士乐的狂荡青年的堕落行为那么耸人听闻。
2．实际上，青年一代的叛逆行为是当时的时代条件的必然结果。
首先，值得记住的是，这种叛逆行为并不局限于美国，而是作为百年之中第一次惨烈的战争的后遗症影响到整个西方世界。
其次，在美国，有一些人已经很不情愿地认识到——如果不是明明白白地认识到，至少是下意识地认识到——无论在政治方面还是在传统方面，我们的国家已不再是与世隔绝的了；我们所取得的国际地位使我们永远也不能再退缩到狭隘道德规范的人造围墙之后，或是躲在相邻的两大洋的地理保护之中了。
3．在当时的美国，摒弃维多利亚式的温文尔雅无论如何都已经是无可避免的了。
美国工业的飞速发展及其所带来的庞大的、机器轰鸣的工厂的出现，社会化大生产的非人格性，以及争强好胜意识的空前高涨，使得在较为平静而少竞争的年代里所形成的温文尔雅的礼貌行为和谦谦忍让的道德风范完全没有半点栖身之地。
TheTrialThatRockedtheWorld高级英语第三版第一册第四课翻译和词汇
Lesson4 The Trial That Rockedthe World震撼世界的审判A buzz ran through the crowd as I took my place in the packedcourt on that swelter ing July day in 1925. The counsel for my defence was the famouscrimina l lawyerClarenc e Darrow.Leading counsel for the prosecu tion was William Jenning s Bryan, the silver-tongued orator, three times Democra tic nominee for Preside nt of the UnitedStates,and leaderof the fundame ntalis t movemen t that had brought about my trial.在一九二五年七月的那个酷热日子里，当我在挤得水泄不通的法庭里就位时，人群中响起一阵嘁嘁喳喳的议论声。
我的辩护人是著名刑事辩护律师克拉伦斯.达罗。
担任主控官的则是能说会道的演说家威廉.詹宁斯.布莱恩，他曾三次被民主党提名为美国总统候选人，而且还是导致我这次受审的基督教原教旨主义运动的领导人。
A few weeks beforeI had been an unknown school-teacher in Dayton, a littletown in the mountai ns of Tenness ee. Now I was involve d in a trial reporte d the world over. Seatedin court, ready to testify on my behalf,were a dozen disting uished profess ors and scienti sts, led by Profess or Kirtley Matherof Harvard Univers ity. More than 100 reporte rs were on hand, and even radio announc er s, who for the first time in history were to broadca st a jury trial. "Don't worry, son, we'll show them a few tricks," Darrowhad whisper ed throwin g a reassur ing arm round my shoulde r as we were waiting for the court to open.几个星期之前，我还只是田纳西州山区小镇戴顿的一名默默无闻的中学教员，而现在我却成了一次举世瞩目的庭审活动的当事人。
3. The Heap 英文版 悖论 逻辑学教材
The Paradoxes of Eubulides of Miletus (4th century B.C.)3. The Heap(a.k.a. The Bald Man, a.k.a. The Sorites Paradox)I.The ParadoxConsider this obvious truth: addition of 1 kernel of wheat is too insignificant to turn what is not a heap of wheat into a heap of wheat and, similarly, subtraction of 1 kernel of wheat is too insignificant to turn what is a heap of wheat into what is not a heap of wheat.The obvious truth has the paradoxical consequences shown by the following Soritical argument:1. 1 grain of wheat is not a heap.2. If 1 grain of wheat is not a heap, then 2 grains of wheat are not a heap.[by the obvious truth] 3. If 2 grains of wheat are not a heap, then 3 grains of wheat are not a heap.[by the obvious truth] ...10,000. If 9,999 grains of wheat are not a heap, then 10,000 grains are not a heap.[by the obvious truth] Therefore, 10,000 grains of wheat are not a heap.The argument is valid. (In effect, it just uses 10,000 applications of the truth-preserving inference rule modus ponens.) And, its premises all seem to be true: (1) is clearly true; (2) is true by the obvious truth that addition of 1 little kernel can’t turn a non-heap into a heap; and (3)-(10,000) are true for the same reason. But, the conclusion is obviously false. So, the paradox here is, again, a seemingly sound argument with a false conclusion.II.The Heart of the MatterThe heart of the Heap paradox is captured in three assertions each of which seems true:a. small changes don’t make for a difference in the application of soritical predicates like‘…is a heap’ or ‘…is bald.’b. large changes do make for a difference in the application of such predicates,c. a large change is nothing more than a large number of small changes.But as the Soritical argument seems to show, the triad (a)-(c) is inconsistent, i.e., all of its members cannot be true together.III.FormalizationLet’s symbolize the Soritical argument:1. Fa12. Fa1⊃ Fa23. Fa2⊃ Fa3...n. Fa n-1⊃ Fa nn‘F’ is the predicate letter for the soritical predicate—in this case ‘…is not a heap’—and ‘a1’, ‘a2’, etc. are individual constants denoting the objects to which the pr edicate applies, e.g., 1 kernel of wheat, a collection of 2 kernels of wheat, etc.The general conditions for a Sorites argument are:i. the series a1-a n is ordered consecutively (e.g. by increasing number of kernels),ii. ‘F’ satisfies the foll owing conditions:a. it is true of a1b. it is false of a nc. each adjacent pair in the series, a j and a j+1, are similar enough so as not to differ inrespect of ‘F.’[Thus, we can construct a more emotionally compelling Sorites ar gument with ‘F’ interpreted as ‘is not a person’ and the series a1-a n denoting the stages of embryonic development fromzygote to infant.]III.VaguenessThe source of the Sorites paradox is the semantic phenomenon of vagueness: a word’s or concept’s having a gray area of application, i.e., borderline or indeterminate cases, circumstances in which the word or concept neither clearly applies nor clearly fails to apply.If every word or concept were as precise as, say, rational number, which has no borderline cases, then there would be no Sorites paradox. That is, if there were a sharp boundary for ‘…is not a heap’—a number k such that k grains clearly were not a heap but k+1 grains clearly were a heap—then one of the premises in the Sorites argument would be false. Specifically, the k+1st premise—Fa k⊃ Fa k+1—would be false, for ‘Fa k’ (‘k grains of wheat is not a heap’) would be true but ‘Fa k+1’ (‘k+1 grains of wheat is not a heap’) would be false.1 So, we’d no longer have a sound argument with a fa lse conclusion.1 Remember, a conditional with a true antecedent and a false consequent is false.But, ‘…is not a heap,’ ‘…is bald,’ etc. certainly don’t seem to have such sharp boundaries. So, we seem stuck with the paradox.IV . ReactionsA . Natural Language isn’t LogicalOne proposal is to deny that formal logic characterizes natural language —at least until its vague predicates are replaced with precise ones —for the symbolic languages of formal logic are deliberately precise while natural languages are lousy with vagueness.2I don’t care for this approach. For, arguments w hose premises and conclusions are expressed in natural language can be valid or not. Indeed, natural language arguments constructed with vague predicates can be valid or not. And validity is certainly within the scope of formal logic.B . Ignorance of Sharp MeaningsAnother proposal is to claim that, despite appearances, one of the premises inSoritical arguments is really false. It follows that there really is a sharp boundary for every soritical predicate like ‘…is a heap’—some specific number which sharply distinguishes heaps from non-heaps.To defend this idea, let me recast the form of the Soritical argument from a series of conditional premises to a single universal premise: 2 This was Frege’s attitude as well as Russell’s.1. Fa 12. (∀n )(Fa n ⊃ Fa n + 1) 10,0001. The man with no hair on his head is bald.2. For any number n , if the man with n hairs is bald, then the man with n+1 hairs is bald. Therefore, (3) the man with 10,000 hairs on his head is bald. The argument is valid. Since (1) is undeniably true and (3) is undeniably false, avoiding the paradox requires that premise (2) be false. Therefore:~(∀n )(Fa n ⊃ Fa n + 1).Hence:(∃n )~(Fa n ⊃ Fa n + 1).[by QN] Thus:(∃n )(Fa n & ~Fa n + 1). [by material implication and De Morgan’s law]That is, there does exist a particular number, call it k , such that the man with k hairs on his head is bald but the man with k +1 hairs is not bald. It’s just that we don’t (or can’t) knowwhat k is. In other words, there really are no vague words or concepts, and what seems like vagueness is not a semantic phenomenon but rather the result of our ignorance about the precise meanings of our own words and concepts.I don’t like this reply either. Language is our creation, and there isn’t more to it than we put in it. So, it is very implausible that the meanings of our terms should be so far beyond our knowledge.C. Fuzzy Set Theory and Fuzzy LogicThere is an intuitive connection between an object’s membership in a set and the truth of a sentence that predicates a property of the object, viz. if a belongs to the set of F-things—a∈ {x∣x is F}—then the sentence ‘F a’ is true. Intuitively, then, it seems that any object is either in or out of a given set.According to fuzzy set theory, on the other hand, there are an (uncountably) infinite number of degrees of set membership, as many degrees as there are real numbers in [0, 1]. So, a can be completely non-F, …, a little F, …, a little more F, …, pretty F, …, quite F, …, very F, …, or fully F. An d, there are correspondingly many degrees of truth: if a∈ to degree n {x∣x is F}, then ‘F a’ is true to degree n. For example, as a man loses more and more hair, he becomes more and more bald and the assertion ‘S is bald’ becomes more and more true.In theory, the concept of degrees of truth implies degrees of validity, and, with further development, the fuzzy theorist hopes to show that the conclusion of a Soritical argument does not follow from its premises with a sufficient degree of validity to be paradoxical.I won’t pursue the development of this solution because I already find it enormously implausible that our concept of truth should be so unbelievably refined as to include a non-denumerably infinite number of distinct truth-values.D. Truth-Value Gaps.In the classical logic that we’ve studied, there are two, and only two, truth-values: the true and the false. Fuzzy logic is an example of non-classical (or deviant) logic of the sort called many-valued.A logic of truth-value gaps is a different sort of non-classical logical theory. For example, if ‘71 kernels is not a heap’ is neither clearly true nor clearly false, then it has no truth-value—the sentence is a truth-value gap. This promises to resolve the paradox, for if there are premises in a Soritical argument that get no truth-value, then the argument is no longer sound.However, it is not obvious that truth-value gaps will resolve the paradox. Imagine that we adopt a gappy logical theory where some sentences with vague predicates—likepremise (1) of the Soritical heap-argument—are true, some—like that argument’s conclusion—are false, and some—the borderline cases—are truth-value gaps.This proposal leaves us with a new and very similar problem: precisely which sentences get no truth-value? That is, precisely which cases are the borderline cases? The situation here is not that fewer than, say, 500 grains clearly is not a heap, more than 1000 grains clearly is a heap, and between 501 and 999 grains clearly is borderline. On the contrary, it is very unclear whether 900 grains is a clear heap or a clear borderline case.In other words, the concept borderline case is itself vague—it also has borderline cases! So, even if we treat the problem of vagueness by acknowledging three truth statuses—true, false, and neither true nor false—we still face the vagueness problem of determining which sentences have which truth statuses.。
2. The Hooded Man 戴帽子的男人 英文版 悖论 逻辑学教材
The Paradoxes of Eubulides of Miletus (4th century B.C.)2. The Hooded ManI.The ParadoxSuppose (whether it’s actually true of you or not) that you had the (at one time) typical sort of childhood and young adulthood in which both of your parents loomed large. In other words, you know your father. And, suppose that a man wearing a hood that covers his head is pointed out to you, and you have no idea whom the man is. Finally, suppose that, unbeknownst to you, the hooded man is your father.You do not know the hooded man.The hooded man is your father.Therefore, you do not know your father.The paradox here is that we seem to have a sound argument for a false conclusion, which is impossible.II. An Easy but Uninteresting SolutionO ne fairly obvious resolution is to point out what looks like an equivocation on ‘know’: the meaning of ‘know’ as it occurs in the first premise (recognize) is different from the meaning of ‘know’ in the conclusion (have acquaintance with). Thus, the premi ses of the Hooded Man argument are true, but the argument isn’t valid. So, the appearance of paradox evaporates.1 Hmwk. 1. Explain why the recognition of invalidity makes the appearance ofparadox vanish.Technically speaking, that simple diagnosis may be adequate, but I don’t think it is because we can reformulate the argument to eliminate the equivocation:You do not know who the hooded man is.The hooded man is your father.Therefore, you do not know who your father is.What is logically interesting about the Hooded Man, what makes the appearance of paradox persist, is that it makes use of a principle of inference that really seems to be truth-preserving. So, the H.M. argument really seems valid. And, yet, despite its true premises, it has a false conclusion.1Notice that there is no hint of par adox when we make sure that both occurrences of ‘know’ have the same meaning. If we replace ‘do not know’ in both occurrences with ‘do not recognize,’ we get a sound argument with a true conclusion. If we replace ‘do not know’ in both occurrences with ‘are not acquainted with,’ we get a valid argument with a false conclusion that also has a false premise. In both cases, then, all appearance of paradox disappears.So, our first step in understanding this puzzle is to get clear about the nature of the H. M. inference.III. Substitutability Salva VeritateThe Hooded Man argument seems valid because it employs what seems to be a perfectly valid substitution principle for designating expressions, which are terms that purport to denote particular individuals.For example, names(e.g., ‘Aristotle’) are designating expressions. Another class of designating expressions is definite descriptions—phrases of the form ‘the Φ’ (e.g., ‘the most famous pupil of Plato,’ ‘the puppy in the window’) that purport t o refer to the unique, salient thing that has theproperty Φ. (On the other hand, the phrase ‘a cat’ is not a designating expressions: it refers to a single cat but to no particular one.)To illustrate that principle, assume that Joe is Mary’s only brother. The name ‘Joe’ and the definite description ‘Mary’s only brother’ are both designating expressions: each designates one specific individual. Moreover, these two designating expressions designate the same individual. That is, ‘Joe’ and ‘Mary’s only brother’ are co-referring terms: different designating expressions that refer to the very same individual.Now, consider the sentence:1. Joe has a puppy.And consider the sentence that results from substituting the expression ‘Mary’s only brother’ for the expression ‘Joe’ in that sentence:2. Mary’s only brother has a puppy.Because the two designating expressions are co-referring, (1) and (2) ascribe puppy-ownership to the very same person. Therefore, if (1) is true, then (2) must be true too. In other words, the substitution of one co-referring term for another is truth-preserving. That is:Co-referring designating expressions are substitutable salva veritate.Since the substitution of co-referring terms is truth-preserving, the inference from (1) to(2) is valid:0.Joe is Mary’s only brother.1. Joe has a puppy.Therefore, (2) Mary’s only brothe r has a puppy.The substitution principle explains why the argument is valid: if premise (0) is true, then ‘Joe’ and ‘Mary’s only brother’ are co-referring terms and, so, substitutable salve veritate. So if premise (1) is also true, then the conclusion (2), which is the result of such a substitution, must be true too.The puzzle is that the H.M. argument using the very same principle as this valid argument!IV. Leibniz’s LawThe substitution principle is a logical principle about inferences, but it is validated by an important metaphysical principle: Leibniz’s law.Leibniz’s Law (a.k.a. the Indiscernibility of Identicals):If individual a is identical to individual b, then it follows that a and b have all the sameproperties: whatever property a possesses is also possessed by b.2For example, consider the following valid argument:Superman was in Metropolis last night.Perry White was not in Metropolis last night.Therefore, Superman is not identical to Perry White.Leibniz’s Law explains why the argument is valid: if the premises are true, then Superman has a certain property, viz., having been in Metropolis last night, that Perry White lacks, and it follows by Leibniz’s Law that two things that do not share all of their propertie s are not identical.Leibniz’s Law validates the substitution principle, for it follows from Leibniz’s law that if a = b, then whatever is true of a must also be true of b. So, since Joe is identical with Mary’s only brother, it follows that whatever is true of Joe is also true of Mary’s only brother. Well, Joe has a puppy. It follows, then, that Mary’s only brother has a puppy. That is, the sentence‘Joe has a puppy’ is true in virtue of the fact that Joe has a puppy. So, any sentence that describes that fact will be true no matter what designating expression—‘Joe,’ ‘Mary’s only brother,’ ‘the bank president,’ ‘the only blonde male born at St. Elmo’s Hospital on May 9, 1954,’ etc.—it employs to refer to Joe. For, since Joe is identical with Mary’s only brother, the bank president, and the only blonde male born at St. Elmo’s Hospital on May 9, 1954, these sentences simply will be different descriptions of the very same fact.Great!…but there is a problem. Leibniz’s law and, so, the substitution p rinciple seem to fail in the H.M. argument.V. Intensionality and Intensional ContextsThe H.M. argument illustrates the logical phenomenon of intensionality(with an ‘s’). This arises when replacing a term (‘the hooded man’) that occurs in a true sen tence (the first premise) with a co-referring term (‘your father’) makes the sentence false (the conclusion).2 That is, numerical identity implies qualitative indiscernibility. In logical symbolism: (∀F)(a = b ⊃ (F a ⊃F b)). (Notice that we have a universal quantifier binding a variable, ‘F’, which ranges over properties rather than the variables for individuals that we’re used to. The formal logic for such reasoning is called ‘second-order logic.’)A context is a location in a sentence. For example, in the sentence ‘Joe has a puppy,’ the ‘’ marks a context into which a designating expression can go, the ‘’ marks a context into which a transitive verb can go, and the ‘’ marks a context into which a noun phrase can go.An intensional context is a designating-expression context where the substitution of co-referring expressions can fail to be truth-preserving.For example, recall the story of poor Oedipus, which we take up before its climax,and consider:i. Oedipus knows that he married Jocasta (the underline marks the relevant context),ii. Jocasta is identical with Oedipus’ mother.Since (ii) is true, the designating expressions ‘Jocasta’ and ‘Oedipus’ mother’ are co-referring. So, we should be able to substitute salve veritate‘Oedipus’ mother’ for ‘Jocasta’ into the indicated context in (i), which results in:iii. Oedipus knows that he married Oedipus’ mother.But while (i) is true, (iii) is false. (Just ask him!) The principle of substitution seems to have failed here—substitution of co-referring terms has, surprisingly, transformed a true sentence into a false one.3Moreover, Leibniz’s law seems to have failed, for Jocasta is identical to Oedipus’ mother, but Jocasta seems to have a property—being such that Oedipus knows that he married her—that Oedipus’ mother seems to lack. But, how is that possible if they’re the very same person? Leibniz’s Law seems like an unquestionable, uncontroversial, necessary truth. How puzzling! VI. The Intensional FallacyWhen the substitution principle works, as it mostly does, we can use it to argue validly: Joe has a puppyJoe is Mary’s only brotherTherefore, Mary’s only brother has a puppy.As we just saw, though, the substitution principle seems to fail in intensional contexts. So, such arguments are invalid:Lois Lane believes that Superman is a diligent crime-fighter.Superman is identical with Clark Kent.Therefore, Lois Lane believes that Clark Kent is a diligent crime-fighter.In this argument, the conclusion is derived from the premises by substituting the designating expression ‘Clark Kent’ for the co-referential expression ‘Superman’ in the intensional context, 3In fact, the principle usually seems to fail in contexts that come after psychological verbs like ‘knows,’ ‘believes,’ wishes,’ etc.‘Lois Lane believes that is a diligent crime-fighter’. And, the result is that an argument with true premises has a false conclusion, for Lois does not believe that Clark is a diligent crime-fighter; she believes that he is a mild-mannered reporter for the Daily Planet.We see, then, that the substitution principle requires a restriction: it may not be applied in intensional contexts. Ignoring this restriction is the intensional fallacy—the logical mistake of applying the principle of substitution in an intensional context.VII.Explaining Substitution Failure in Intensional ContextsOK, but why does the substitution principle fail in intensional contexts? Philosophers offer different explanations of the puzzle, but I’ll consider one due originally to the inventor of modern logic, Frege.To begin, Frege posits what he calls modes of presentation. A mode of presentation of a thing x is a certain specific way of thinking of x, a specific mental description of x. For example, I might think about the planet Venus by thinking ‘the second planet from the sun,’ or ‘the morning star,’ or ‘the evening star,’ etc. These are ways of thinking about Venus because Venus is the unique thing that satisfies them.Recognizing modes of presentation already makes it quite clear why the Lois Lane argument above is invalid. One can have several different modes of presentation (like ‘the morning star’ and ‘the evening star’) that i n fact denote the same individual (Venus), but one can have no idea that this is the case. That’s why even though it is a fact that when Lois thinks of Superman, she thinks of the same person she thinks of when she thinks of Clark Kent, it’s still possibl e for herto discover, to her amazement, that the individual she thinks of as, say, ‘faster than a speeding bullet’ and the individual she thinks of as, say, ‘mild-mannered reporter for the Daily Planet’ are the same individual.According to Frege, the usual logical function of a designating expression is to denote a certain individual directly. However, designating expressions operate differently when they occur in intensional contexts. In such cases, the designating expression indirectly denotes a certain individual by directly denoting a particular mode of presentation of that individual.For example, in the first premise of the previous argument, ‘Superman’ occurs in the intensional context, ‘Lois Lane believes that is a diligent crime-fight er.’ So in that occurrence,‘Superman’ does not have its usual denotation, viz., the individual Superman (that is, Clark Kent). Rather, the name there directly denotes, not the individual Superman (= Clark Kent), but a particular mode of presentation of that individual, specifically Lois Lane’s mental description or way of thinking about the Superman: faster than a speeding bullet. Since Superman is the only individual who satisfies that description, i.e., who is faster than a speeding bullet, that mode of presentation directly denotes the individual Superman (= Clark Kent).Putting these together, when the designating expression ‘Superman’ occurs in the intensional context, ‘Lois Lane believes that is a diligent crime-fighter,’ then it indirectl y denotes theindividual Superman (= Clark Kent) by directly denoting the mode of presentation ‘faster than a speeding bullet.’Thus, on Frege’s explanation the unrestricted principle of substitution does not fail in intensional contexts. The substitution principle tells us that co-referring expressions can be freely interchanged, but, though Superman is identical to Clark Kent and, consequently, the designating expressions ‘Superman’ and ‘Clark Kent’ are typically co-referring terms, they don’t co-refer when they occur in the intensional context ‘Lois Lane believes that is a diligent crime-fighter.’ In that case, ‘Superman’ denotes Lois’ mode of presentation for Superman,‘faster than a speeding bullet’ while ‘Clark Kent’ denotes her mode of presen tation for Clark Kent,‘mild-mannered reporter for the Daily Planet.’ And, these two modes of presentation are not identical!Let’s return to the case of Oedipus for another example.-In (ii), the name ‘Jocasta’ and the definite description ‘Oedipus’ mother’ are co-referringterms. They designate the very same individual.-However, ‘Jocasta’ in (i) and ‘Oedipus’ mother’ in (ii) are not co-referring.-In (ii), the designating expression ‘Oedipus’ mother’ functions ordinarily to directly denote aparticular woman, viz., Oedipus’ mother, i.e., Jocasta.-But in (i), the designating expression ‘Jocasta’ occurs in an intensional context, and, so,it directly denotes, not that woman, but Oedipus’ mode of presentation of her, say, ‘my wife.’-Since a flesh-and-blood woman is not identical to a way of thinking, the designating expression ‘Oedipus’ mother’ as it occurs in (ii) and the designating expression ‘Jocasta’ as it occurs in (i) do not co-refer.-Since the two designating expressions do not denote the very same thing, there is no reason at all to expect substitution of the one term for the other term to preserve (i)’s truth when it istransformed into (iii).That is, the substitution principle has not failed here because it doesn’t even apply.To put the same point another way:-In (i), the name ‘Jocasta’ occurs in the intensional context ‘Oedipus knows that he married ’, where it directly denotes Oedipus’ mode of presentation of Jocasta, ‘my wife.’-But when the defini te description ‘Oedipus’ mother’ occurs in that context in (iii), it directlydenotes a different mode of presentation of the same woman, say, ‘nurtured me in mychildhood.’-Despite the identity of Jocasta and Oedipus’ mother, these two modes of presentation of that one woman are not identical. They are two very different descriptions or ways of thinking despite the fact that they both describe the same particular woman.-Therefore, when the designating expressions ‘Jocasta’ and ‘Oedipus’ mother’ occur inthe intensional context ‘Oedipus knows that he married ’, they are not co-referringterms.-There is no reason, then, to expect them to be substitutable salva veritate.VIII. Resolving the Hooded ManRecognizing the phenomenon of intensionality resolves our paradox with the Hooded Man. The problem, recall, is that an apparently valid argument with true premises has a false conclusion. However, we can now see that the Hooded Man argument commits the intensional fallacy. Its conclusion results from replacing the designating expression ‘the hooded man’ in the first premise with the desi gnating expression ‘your father.’ Now, the second premise asserts that these terms are co-referring, and one can often make the substitution validly, but in this case, the substitution is made within an intensional context, ‘You do not know ’.It turns out, then, that the Hooded Man argument is not valid. And the appearance of paradox is eliminated.。
高级英语(第三版)第二册第五课-The-Sad-Young-Men[精]可修改文字
![高级英语(第三版)第二册第五课-The-Sad-Young-Men[精]可修改文字](https://img.taocdn.com/s3/m/e8f58f47a200a6c30c22590102020740be1ecda8.png)
Para 4: The revolt was in a form of escape under cover of Bohemian way of life made possible by the prosperity of the 20’s American economy.
Para 5: American youths were eager to go to battle. Para 6: The soldiers returned, disillusioned with the war and the country,
Para 5 Eager to participate
Para 6 Disillusioned
with war & country
Para 7 Greenwich set pattern
Para 8 Whole country
followed suit
Para 9 Disappointed expatriated
Paraphrasing
• Second, it was reluctantly realized by some –subconsciously if not
openly—that our country was no longer isolated in either politics or tradition and that we had reached an international stature that would forever prevent us from retreating behind the artificial walls of a provincial morality or the geographical protection of our two bordering oceans.
英文PPT讲解悖论
M: No, the paradox of this sentence is just eight word. (不对，这句语的反话正好是八个字) So, it like it was as if is wrong. (所以，它像它原来的话一样是错的) How can we solve this strange embarrassing situation? (我们怎么才能解决这样奇怪的尴尬局 面呢？)
the 3th case:A word and he paradox (例三、一句话和他的反话) M：How many words in this sentence?这句话有 几个字？ Seven words. 七个字 Obviously the exact words wrong!!!!! 显然原话错了！ So it is the paradox of? 那么它的反话就应该 是对的吧？
If the barber give himself a haircut,(如 果理发师给自己理发) he is against his agreement; (则违背了自己的约定；) If the barber don't give himself a haircut, (如果理发师不给自己理发， ) so according to the provisions of his, and he should give himself a haircut.(那么按照他的规定，又应该给自己理 发。 ) So, the barber drops into a dilemma(这 样，理发师陷入了两难的境地)
●悖论定义：
Paradox definition
●悖论的定义可以这样表述：由一个被承认是真的命题为前提，设
无人生还英文版书籍
无人生还英文版书籍Some popular English books with the theme of survival include: 1. "Life of Pi" by Yann Martel - A young boy is stranded on a lifeboat in the middle of the ocean with a Bengal tiger.2. "The Hunger Games" trilogy by Suzanne Collins - In a dystopian world, teenagers are forced to compete in a televised fight to the death.3. "The Road" by Cormac McCarthy - A father and son journey through a post-apocalyptic wasteland, trying to survive and find safety.4. "Lord of the Flies" by William Golding - A group of boys stranded on an uninhabited island gradually descend into chaos and savagery.5. "Into the Wild" by Jon Krakauer - Based on a true story, a young man gives up his privileged life to live in the wilderness of Alaska, but ultimately pays the ultimate price.6. "The Martian" by Andy Weir - After being left behind by his crew on a Mars mission, an astronaut must figure out a way to survive with limited supplies until rescue is possible.7. "Unbroken" by Laura Hillenbrand - The inspiring true story of Louis Zamperini, an Olympic runner and World War II airman who survives a plane crash and subsequent time as a Japanese prisoner of war.8. "Endurance: Shackleton's Incredible Voyage" by Alfred Lansing - Chronicles the harrowing Antarctic expedition led by Sir Ernest Shackleton and his crew as they strive to survive after their ship is crushed in the ice.These are just a few examples, and there are many more books available on the subject of survival.。
TheSadYoungMan
TheSadYoungManThe Sad Young Men(The Lost Generation)Rod W.Horton and Herbert W.EdwardsRod W .Horton(1910-)1937-1945 instructor in NewYork University 1945-1949 assistant professor NewYork University1947-1957 associate professor of general Literature1957-1964 cultural affairs officer in Brazil And Portugalworks1952 <>1954<>ught>>VocabularyNostalgic:乡愁的，怀旧的Recollection:回想起来的事物Speakeasy:贩卖私酒的酒吧Amour：偷情Sedan:箱式⼩客车Sheik:美男⼦Vagary:反复⽆常的⾏为Gentility：优雅Code:礼法，惯例Catalytic：催化的Aftermath：后果结果Pose：造作之态Orgy：纵欲，狂欢Strife：⽃争，打⽃Important phrasesDrugstore cowboy:在杂货店和其他公共场所徘徊试图打动⼥⼈的男⼈Sober up:变清醒Whip up:煽动，激起Keep up with the Joneses:与他⼈攀⽐Common denominator:共同点Write off :看不起，认为⽆价值speakeasy (n.) : [slang]a place where alcoholic drinks are sold illegally，esp. such a place in the U．S．during Prohibition[俚](美国禁酒期的)⾮法的酒店地下酒吧指1920年到1933年在美国⾮法出售酒精饮料的酒吧Sheik:美男⼦，浪漫的放荡男⼦Background Knowledge ?Other literary figures:--Gertrude Stein--E. HemingwaySome terms:--The Sad Young Men --The Lost Generation --The Beat Generation --The Angry Young MenEzra Pound Ernest HemingwayGertrude SteinA Comparative Study of the Lost Generation and the Beat GenerationPeriod:Lost generation Beat Generation1883—19241948--1962Origin of the namesLost Generationoriginally addressed by Gertrude Stein[1] and was then popularized by Ernest Hemingway in the epigraph to his novel The Sun Also Rises, and his memoir A Moveable FeastBeat Generation:Picking up the word "beat" from their friend Herbert Huncke, the original beat writers, William Burroughs, Allen Ginsberg, and Jack Kerouac, used it to describe their free-form, improvisational style of writing and their unconventional, spontaneous way of life.The Sad Young Men and The Lost Generation refer to the same group of people. The former was created by F. Scott Fitzgerald; the latter, by Gertrude Stein. They were applied to the disillusioned intellectuals and aesthetes of the years following the First World War, who rebelled against former ideals and values, but could replace them only by despair or cynical hedonism.Lost Generation Many of these intellectuals lived abroad, especially in Paris, as expatriates, but most of them later returned to the United States voluntarily.?Beat GenerationMany of the beatgeneration had worked inand around San Francisco,living an unconventional and spontaneous way of life .During the 1960s “beat”ideas and attitudes wereabsorbed by other culturalmovements, and those whopracticed the “beat”lifestyle were called “hippies”.Representation in behaviorWords and expressions1. speakeasy (L7, P1)---a place where alcoholic drinks are sold illegally during Prohibition.speakeasy (n.) : [slang]a placesp. such a place in the U．S．during Prohibition[俚](美国禁酒期的)⾮法的酒店地下酒吧指1920年到1933年在美国⾮法出售酒精饮料的酒吧2. Puritan morality (L7, P1)---extreme or excessive strictness in matters of morals. Strict Puritans even regarded drinking, gambling and participation in theatrical performances as punishable offences.3. flask-toting(L10, P1)---adj. always carrying a small flask filled with whisky or other strong liquor.4.Victorian(L1, P3)---showing the middle-class respectability, prudery, bigotry, etc. generally attributed to Victorian England over which QuVictoria ruled (1837-1901)n. 维多利亚时代；维多利亚⼥王时代的⼈5. Bohemian (L5, P4)---a person, especially an artist, poet, etc. who lives in an unconventional, nonconforming way. Prohibition(L12, P4)6.Prohibition(L12, P4)---the forbidding by law of the manufacture, transportation, and sale of alcoholic liquors for beverage purposes (the period of 1920-1933), the prohibition by Federal law.7. jingoism(L7, P5)n.主战论, 武⼒外交政策,沙⽂主义,侵略主义jingoist n.沙⽂主义者, 侵略主义者jingo n.沙⽂主义者8.soap opera (L15, P5)---a daytime radio or television serial drama of a highly melodramatic, sentimental nature. It has been so called since many original sponsors were soap companies.soap_opera:肥皂剧（soap opera）是从英语传⾄中⽂的外来词汇，⼜叫泡沫剧。
英文PPT讲解悖论 共34页
paradox of?
那么它的反话就应该
是对ቤተ መጻሕፍቲ ባይዱ吧？
M: No, the paradox of this sentence is just eight word. (不对，这句语的反话正好是八个字) So, it like it was as if is wrong. (所以，它像它原来的话一样是错的) How can we solve this strange embarrassing situation? (我们怎么才能解决这样奇怪的尴尬局 面呢？)
●反之，以非B为前提，亦可推得B。 Contrary to the Against B for the premise, may also
push to B. ●那么命题B就是一个悖论。
So proposition B is a paradox. ●当然非B也是一个悖论。
Of course the Against B is a paradox.
the 3th case:A word and he paradox
(例三、一句话和他的反话)
M：How many
words in this
sentence?这句话有
几个字？
Seven words.
七个字
Obviously the
exact words
wrong!!!!!
显然原话错了！
So it is the
the barber regulation, and only in the
village the
barber shave only those men
who do not shave themselves . (理发师规定，给且只给村中不自己理发的人理发)
thesadyoungmen课文和翻译
The Sad Young MenRod W. Horton and Herbert W. Edwards1No aspect of life in the Twenties has been more commented upon and sen satio nally roma nticized tha n the so-called Revolt of the Younger Generation. The slightest mention of the decade brings nostalgic recollections to the middle-aged and curious questionings by the young: memories of the deliciously illicit thrill of the first visit to a speakeasy, of the brave denunciation of Puritan morality, and of the fashi on able experime ntatio ns in amour in the parked seda non a country road; questions about the naughty, jazzy parties, theflask-toting "sheik," and the moral and stylistic vagaries of the "flapper" and the "drug-store cowboy." "Were young people really so wild?" present-day students ask their parents and teachers. "Was there really a Youn ger Gen erati on problem?" The an swers to such inq uiries must of n ecessity be "yes" and "no"--"Y es" because the bus in ess of grow ing up is always accompa nied by a Youn ger Gen erati on Problem; "no" because what seemed so wild, irresp on sible, and immoral in social behavior at the time can nowbe seen in perspective as being someth ing con siderably less sen sati onal tha n the degenerauon of our jazzmad youth.2Actually, the revolt of the young people was a logical outcome of con diti ons in the age: First of all, it must be remembered thatthe rebelli on was not confined to the Un it- ed States, but affectedthe entire Western world as a result of the aftermath of the first serious war in a century. Second, in the United States it was reluctantly realized by some- subconsciously if not openly -- thatour country was no Ion ger isolated in either politics or traditi on and that we had reached an international stature that would foreverprevent us from retreating behind the artificial walls of a provincial morality or the geographical protection of our two border ing ocea ns.3The rejecti on of Victoria n gen tility was, in any case,in evitable. The boo ming of America n in dustry, with its giga ntic,roaring factories, its corporate impersonality, and its largescaleaggressive ness, no Ion ger left any room for the code of polite behavior and well-bred morality fashi oned in a quieter and less competitive age. War or no war, as the gen eratio ns passed, it became increasingly difficult for our young people to accept standards of behavior that bore no relati on ship to the bustl ing bus in ess medium in which they were expected to battle for success. The war acted merely as a catalytic age nt in this breakdow n of the Victoria n social structure, and by precipitating our young people into a pattern of mass murder it released their inhibited violent energies which, after the shooting was over, were turned in both Europe and America to the destructi on of an obsolesce nt nin etee nth-ce ntury society.4Thus in a cha nging world youth was faced with the challe ngeof bringing our mores up to date. But at the same time it was tempted, in America at least,to escape its responsibilities and retreat beh ind an air of n aughty alcoholic sophisticati on and a pose ofBohemian immorality. The faddishness , the wild spe nding of money on transitory pleasuresand momentary novelties , the hectic air __________________________________________of gaiety, the experimentation in sensation -- sex, drugs, alcohol,perversions -- were all part of the patter n of escape, an escape made possible by a gen eral prosperity and a post-war fatigue with politics, economic restrictions, and international resp on sibilities. Prohibiti on afforded the young the additi onal opport unity of mak ing their pleasures illicit , and the much-publicized orgies and defiant manifestoes of the intellectuals crowding into Greenwich Village gave them a pattern and a philosophic defense for their escapism. And like most escapist sprees, this one lasted un til the money ran out, un til the crash of the world economic structure at the end of the decade called the party to a halt and forced the revelers to sober up and face the problems of the new age.5The rebelli on started with World War I. The pro Ion ged stalemate of 1915 -- 1916, the in creas ing in sole nee of Germa ny toward the Un ited States, and our official relueta nee to declare our status as a belligere nt were in tolerable to many of our idealisticcitize ns, and with typical America n adve nturous ness enhan ced somewhat by the strenuous jingoism of TheodoreRoosevelt, our young men bega n to en list un der foreig n flags. In the words of Joe Williams, in John Dos Passos' U. S. A., they "wanted to get into the fun before the whole thing turned belly up." For military service, in 1916-- 1917, was still a romantic occupation. The young menof college age in 1917 knew nothing of modern warfare. The strife of 1861 --1865 had popularly become, in moti on picture and story, a magn olia-sce nted soap opera, while the one hun dred-days' fracas with Spa in in 1898 had dissolved into a one-sided victory at Manila and a cinematic charge up San Juan Hill. Furthermore, there were eno ughhigh school assembly orators proclaimi ng the character-formi ng force of the stre nu ouslife to convince more tha n eno ugh otherwise sen sible boys that service in the European conflict would be of great personal value, in additionto being idealistic and excit ing. Accord in gly, they bega n to join the various armies in increasing numbers, the "intellectuals" in the ambula nee corps, others in the infan try, merchant marine, orwherever else they could find a place. Those who were relucta nt to serve in a foreig n army talked excitedly about Prepared ness, occasi on ally con sidered joining the Natio nal Guard, and rushed to en list whe n we fin ally did en ter the con flict. So treme ndous was the storm ing of recruitme nt cen ters that harassed sergea nts actually pleaded with volunteers to "go homeand wait for the draft," but since no self-respect ing pers on wan ted to suffer the disgrace of being drafted, the en listme nt craze con ti nued un abated.6Naturally, the spirit of carnival and the enthusiasm for highmilitary adve nture were soon dissipated once the eager young men had received a good taste of twen tieth- cen tury warfare. To their lasting glory, they fought with distinction, but it was a much altered group of soldiers who returned from the battlefields in 1919. Especially was this true of the college contingent, whose idealism had led them to en list early and who had gen erally see n a con siderable amount of acti on. To them, it was bitter to retur n to a home town virtually untouched by the conflict, where citizensstill talked with the naive Fourth-of-duly bombast they themselves had been guilty of two or three years earlier. It was even more bitter to find that their old jobs had bee n take n by the stay-at-homes, that bus in ess was sufferi ng a recessi on that preve nted the ope ningup of new jobs, and that veterans were considered problem children and less desirable tha n non-vetera ns for whatever bus in ess opport un ities that did exist. Their very homes were ofte nuncomfortable to them; they had outgrown town and families and had developed a sudde n bewilder ing world-weari ness which n either they nor their relatives could un dersta nd. Their en ergies had bee n whipped up and their naivete destroyed by the war and now, insleepy Gopher Prairies all over the country, they were being asked to curb those en ergies and resume the pose of self-deceiv ing Victoria n innocence that they now felt to be as outmoded as the no ti on that their fighting had "made the world safe for democracy." And, as if home tow n con diti ons were not eno ugh, the retur ning vetera n also had to face the sodde n, Napole onic cyni cism of Versailles, the hypocritical do-goodism of Prohibition, and the smug patriotism of the war profiteers. Something in the tension-ridden youth of Americahad to "give" and, after a short period of bitter resentment, it"gave" in the form of a complete overthrow of gen teel sta ndards of behavior.7Greenwich Village set the pattern. Since the Seven-ties a dwelli ng place for artists and writers who settled there because living was cheap, the village had long enjoyed a dubious reputation for Bohemia nism and ecce ntricity. It had also harbored eno ugh major writers, especially in the decade before World War I, to supportits claim to being the intellectual center of the nation. After thewar, it was only natural that hopeful young writers, their minds and pens in flamed aga instwar, Babbittry, and "Purita ni cal" gentility , ,should flock to the traditional artistic center (whereliving was still cheap in 1919) to pour out their new-found creativestrength, to tear down the old world, to flout the morality of theirgran dfathers, and to give all to art, love, and sen sati on.8Soon they found their imitators amongthe non-intellectuals.As it became more and more fashi on able throughout the country for young pers ons to defy the law and the conven ti ons and to add their own little matchsticks to the con flagratio n of "flami ng youth", it was Greenwich Village that fanned the flames. "Bohemian" living became a fad. Each town had its "fast" set which prided itself on its unconventionality , although in reality this self-conscious unconven ti on ality was rapidly beco ming a sta ndard feature of the country club class -- and its less affluent imitators --throughoutthe n ati on. Before long the moveme nt had be-come officially recognized by the pulpit (which denounced it), by the movies and magaz ines (which made it attractively n aughty while prete nding to denounce it), and by advertising (which obliquelyencouraged it by'selling everything from cigarettes to automobiles with the implied promise that their owners would be rendered sexually irresistible).Youn ger brothers and sisters of the war gen erati on, who had bee n playing with marbles and dolls during the battles of Belleau Wood and Chateau-Thierry, and who had suffered no real disillusi onment or sense of loss, now bega n to imitate the manners of their elders and playwith the toys of vulgar rebellion. Their parents were shocked, but before long they found themselves and their friends adopting the new gaiety. By the middle of the decade, the "wild party" had become as com mon place a factor in America n life as the flapper, the Model T, or the Dutch Colonial home in Floral Heights.9Mea nwhile, the true in tellectuals were far from flattered.What they had wan ted was an America more sen sitive to art and culture, less avid for material gain, and less susceptible to sta ndardizatio n. In stead, their ideas had bee n gen erally igno red, while their behavior had con tributed to that sta ndardizati on byfurnishing a patter n of Bohemia nism that had become as conven ti on alized as a Rotary lun che on. As a result, their dissatisfaction with their native country, already acute upon theirretur n from the war, now became eve n more in tolerable. Flam ing diatribes poured fromtheir pens denouncing the materialism and what they con sidered to be the cultural boobery of our society. An important book rather grandiosely entitled Civilization in theUnited States, written by "thirty intellectuals" under theeditorship of J. Harold Stearns, was the rallying point of sensitive pers ons disgusted with America. The burde n of the volume was that the best minds in the country were being igno red, that art was un appreciated, and that big bus in ess had corrupted everyth ing.Journalism was a mere adjunct to moneymaking, politics were corrupt and filled with in compete nts and crooks, and America n family life so devoted to making money and keeping up with the Joneses that it had become joyless, patter ned, hypocritical, and sexually in adequate. These defects would disappear if only creative art were allowed to show the way to better things, but since the country was blind and deaf to everything save the glint and ringof the dollar, there was little remedy for the sensitive mind but to emigrate to Europe where "they do things better." By the time Civilization in the United States was published (1921), most of its contributors had take n their own advice and were Wing abroad, and many more of the artistic and would-be artistic had followed suit.10It was in their defia nt, but gen erally short-lived, Europea nexpatriati on that our lead ing writers of the Twen ties lear ned to think of themselves, in the words of Gertrude Stein, as the "lost gen eratio n". In no sense a moveme nti n itself, the "lost gen erati on"attitude nevertheless acted as a commondenominator of the writing of the times. The war and the cynical power politics of Versailleshad convinced these young menand womenthat spirituality was dead; they felt as stunned as John An drews, the defeated aesthete In Dos Passos' Three Soldiers, as rootless as Hemin gway'swan deri ng alcoholics in The Sun Also Rises. Besides Stei n, Dos Passos, and Hemingway,there were Lewis Mumford, Ezra Pound, Sherwood Anderson, Matthew Josephs on, d. Harold Stearns, T. S. Eliot, E. E. Cummi nss,Malcolm Cowley, and many other no velists, dramatists, poets, and critics who tried to findtheir souls in the Antibes and on the Left Bank, who directed sad and bitter blasts at theirn ative land and who, almost to a man, drifted back with in a few years out of sheer homesickness, to take up reside nee on coastal isla nds and in New En gla nd farmhouses and toproduce works ripe ned by the temperi ng of an older, more sophisticated society.11For actually the "lost generation" was never lost. It was shocked, uprooted for atime, bitter, critical, rebellious, iconoclastic, experimental, often absurd, more oftenmisdirected-but never "lost." A decade that produced, in addition to the writers listed above, suchfisures as Euge ne O'Neill, Edna St. Vincent Millay, F. Scott Fitzserald, William Faulkner,Sinclair Lewis, Stephen Vincent Ben e t, Hart Crane, Thomas Wolfe, and innumerableothers could n ever be writte n off as sterile ,even byitself in a momentof self-pity. The in tellectuals of the Twenties,the "sad young men，” as F. Scot Fitzserald called them, cursed their luck but did n't die; escaped but volun tarily retur ned; flayed theBabbitts but loved their coun try, and in so doing gave the n ati onthe Iiveliest, freshest, most stimulati ng writi ng in its literaryexperie nee.二十年代社会生活的各个方面中，被人们评论得最多、渲染得最厉害的，莫过于青年一代的叛逆之行了。
1. The Liar 说谎者悖论 英文解析 逻辑学教材
The Paradoxes of Eubulides of Miletus (4th century B.C.)1. The Liar“When I lie and admit that I lie, do I lie or speak the truth?”1I . The ParadoxA statement that directly or indirectly predicates falsehood of itself is logicallypathological in the worst, most mind-boggling way. Such sentences are called …liar sentences .‟ Version 1a : This sentence is false.Proof of Paradoxicality-That sentence, like every other, must be either true or false.-If the sentence is true, then it follows that what it says is the case. It says that it is false, and, since what it says is the case, it therefore is false. So, if the sentence is true, then it follows that it is false. Contradiction .-Therefore (by reductio ad absurdum /~I), the sentence …This sentence is false‟ cannot be true and, so, must be false.-But if the proposition is false, then it follows that what it says is not the case. It says that it is false, and, as what it says is not the case, it follows that it is not the case that it is false. Therefore, the sentence is true. So, if the sentence is false, then it follows that it is true. Contradiction .-Therefore (by reductio ad absurdum ), the sentence …This sentence is false‟ cannot be false and, so, must be true, which (as we proved) it cannot be…???!!!As the argument shows, a proposition that directly or indirectly says of itself that it is false must be either true of false (like any other proposition), and, pathologically, cannot be either.Version 1b : I am lying.Version 2a : The following sentence is false.The preceding sentence is true.1 Aulus Gellius, Attic Nights , vol. 3, bk. XVIII, ch. II. Version 2b :Hmwk . 1. Show in full and precise detail (on the model of my previous demonstration)that these three situations are genuinely paradoxical, i.e., some statement must be false if it is true, must be true if it is false, and no third option ispossible.In all four variations, the truth of a sentence directly or indirectly implies its own falsehood (which is a contradiction), and the sentence‟s falsity directly or indirectly implies its own truth (which is a contradiction). By itself, one of these contradictory results merely would constitute a valid reductio ad absurdum/indirect proof for the non-contradictory denial of the assumption (of either truth or falsehood). But, both contradictory results together generate ineliminable contradictoriness: we must hold as true what we cannot hold as true…and the mind boggles. (Such paradoxes are also called …antinomies.‟)II. In the New TestamentIn his Epistle to Titus, the Apostle Paul complains of the Cretans adding:2One of themselves, even a prophet of their own, said, …The Cretans are always liars, evil beasts, slow bellies.‟ This witness is true.According to St. Paul, then, there is a Cretan prophet who asserts that the Cretans always lie, which implies, of course, that the Cretan prophet himself is lying.3Now, that‟s fine; but in adding that the Cretan prophet is telling the truth, Paul brutely contradicted himself.Proof1. Epimenides is a Cretan.2. Epimenides said, “The Cretans are always liars.”*3. This witness is true, i.e., what Epimenides said is true.4. Therefore, “The Cretans are always liars” is true. [by (2) & (3)]5. Therefore, the Cretans are always liars. [by (4)]6. Therefore, Epimenides always lies. [by (1) & (5)]7. Therefore, Epimenides lied when he said, “The Cretans are always liars.” [by (6)]8. Therefore, what Epimenides said is false, i.e., this witness is false. [by (7)]Contradiction: (3) & (8)! St. Paul‟s assertion that Epi menides told the truthimplies that Epimenides lied.Though the Apostle seems not to have realized it, we know that his self-contradiction constitutes a valid reductio ad absurdum (or is it a consequentia mirabilis?) that (3)—his assertion that the witness is true—is false.Have we just disproven the thesis of Biblical literalism—every statement in the Bible isliterally true?2 Titus 1: 12-13. The mentioned Cretan prophet was probably Epimenides, and the Liar Paradox is often called the Epimenidean Paradox.3By the way, a Cretan is a person from Crete while a cretin is an idiot. You‟re bound to insult somebody if you mix the two words up, so get it straight. (Originally, a cretin was someone who suffered the crippling mental and physical results of thyroid disease. The word …cretin‟ comes from the Swiss French …crestin’ meaning …Christian.‟ That is, these unfortunates, though retarded and deformed, are still human beings.)It then follows that the witness is false, i.e., what Epimenides said is false. However, this conclusion does not entail a contradiction.To see that, let‟s find out what that conclusion does entail.Argumenta. The witness is false, i.e., what Epimenides said is false. [by Proof]b. Epimenides said, “The Cretans are always liars.” [by (2)]c. Therefore, …The Cretans are always liars‟ is false. [by (a) & (b)]d. Therefore, …Some Cretans are not always liars‟ is true.Proof: The contradictory of an A proposition is the corresponding O proposition. Or, inthe language of predicate logic, ~(∀x)(…x…) is equivalent to (∃x)~(…x…) (by thequantifier negation rule).e. Therefore, there is at least one Cretan who does not always lie, i.e., who tells the truthon at least one occasion.[by (d)] f. There are three ways for (e) to be true:i. Epimenides told the truth on this occasion,ii. He told the truth on at least one other occasion, oriii. There is at least one other Cretan who sometimes tells the truth.Argument: I can‟t think of any other.g. (i) is false. [by (a)]h. We have no grounds for denying either (ii) or (iii).Argument: The fact that Epimenides lied on the relevant occasion alone implies nothing about the truthfulness of his other assertions or other Cretans‟ assertions.i. Therefore, either (ii) or (iii) (or both) is true.So, it follows from Epimenides‟ having spoken falsely when he said that the Cretans are always liars that at least one Cretan spoke, or will speak, truly on at least one occasion. And there is certainly nothing contradictory about that. In fact, I‟m sure it‟s true (and you are too).If the only thing any Cretan ever had said, or ever would say, were, “The Cretans arealways liars,” then we‟d be in trouble; but since that isn‟t the case, we‟re not.Thus, Paul‟s blunder isn‟t genuinely paradoxical. So, it‟s not really a version of the Liar, but I include it for its historical and religious interest.4III. Reductio ad Absurdum?4I can‟t resist giving one more fascinating version of the liar paradox due to medieval logicians. So, for the sake of argument let‟s accept the medieval claim that …God exists‟ i s necessarily true. Consider the following argument: God exists. Therefore, this argument is invalid. Is the argument valid? (Any necessarily true proposition may replace …God exists.‟)It‟s worth being clear that there is no reductio ad absurdum escape from the Liar. For, what unrecognized, implicit assumption have we made such that we can take the Liar‟s double-contradictory conclusion to constitute a reductio ad absurdum proof for its falsehood? Well, to begin, we‟ve assumed that there is a liar sentence. So, perhaps the Liar proves thereis no such sentence. No, this is ridiculous! We didn‟t assume that a liar sentence exists. The sentence is right there on page 1! (You don‟t ne ed to turn back; the rumored-to-be-non-existent sentence will occur in my next sentence.)We‟ve also implicitly assumed that the sentence, …This sentence is false‟ actually says something, i.e., that the sentence is meaningful, it expresses a proposition. Maybe the Liar proves that that is a perfectly grammatical sentence that expresses no proposition, is meaningless.5 This suggestion fails for two reasons.First Reason.If the sentence …This sentence is false‟ expresses no proposition, then it follows that it is meaningless. Therefore, that sentence is neither true nor false, and, so, we seem to have escaped. But, consider the sentence:This sentence is not true.This new sentence is also a paradoxical liar sentence.Hmwk. 2. Prove it.Now, according to the proposed solution, the new sentence is also meaningless, and, therefore, neither true nor false, and, thus, not true. But, the new sentence just says that it is not true. Therefore, it is true (for what it says is the case)! But if the sentence is true, then it cannot be meaningless. Consequently, the proposal does not resolve the paradox.Second Reason. The proposal only ever had a chance of resolving versions 1a & 1b in which a sentence directly predicated falsehood of itself. In versions 2a & 2b, where a sentence indirectly predicates falsehood to itself by ascribing a truth-value to another sentence, it‟s clear that the sentence is perfectly meaningful because you effortlessly understood it. After all, it was only as a result of reading it that you went on to consider precisely the sentence to which it referred.Perhaps another example shows the point even more clearly:The sentence printed in the box on p. 160 of Howard DeLong’s A Profile ofMathematical Logic (Addison-Wesley, 1970) is true.Go ahead; look it up. (I‟ll wait.)Finally, we‟ve implicitly assumed the principle of bivalence: (i) there are only two truth-values, viz., the true and the false, and (ii) every sentence must have one, and only one,of these. Therefore, we‟ve implicitly assumed that our liar sentences have to be either true or false. Perhaps the Liar shows that some meaningful sentences have no truth-value. This is a5 The Stoic logician Chrysippus suggested this resolution.very complex and abstract reply, too complex and abstract for us to give it much consideration now.6 However, we can at least consider how difficult it is to make sense of the possibility that a sentence expresses something coherent about the way things are and, yet, it is neither true nor false, i.e., things neither are that way nor not that way. Which way, then are things supposed to be?It seems, then, that the Liar, unlike the Barber or the Law Court, is a genuine paradox. IV. What the Liar Paradox ShowsLike questions about Russell‟s barber shaving himself, the Liar reveals the surprising paradoxicality that self-reference sometimes produces. Now, self-reference clearly is not paradoxical in general, for most instances of it are perfectly coherent. Consider some examples.1. Sax self-referentially asserts tha t he is bald. His statement is simply false, but it isn‟tparadoxical. (Indeed, a statement must be coherent even to be false.)2. (i)-(iv) of the following self-referential sentences are just true; (v)-(vi) are just false:7i. This sentence contains five words.ii. This sentence contains thirty-six letters.iii. There are fourteen vowels in this sentence.iv. This sentence is written in English.v. This sentence contains precisely fifty characters.vi. Deis ist kein Deutscher Satz. [Translation: This sentence is not in German.]3. Epimenides can self-referentially assert the self-referential sentence, “The sentence I am nowuttering contains nine words,” and his remark will be unproblematically true.Still, the Liar shows that those instances of self-reference in which a statement directly or indirectly predicates falsehood of itself are logically pathological in the worst, most mind-boggling way: they generate ineliminable, unresolvable contradiction. And, the Liar also shows that a liar sentence can be constructed in any language with the resources to:A. refer to its own sentences, andB. predicate truth or falsity of those sentences.Unhappily, all natural languages (like Gujarati, Magyar, Frisian, etc.) satisfy (A) and (B). That is very bad, for, as we‟ve seen, liar sentences generate unpreventable contradiction, and, as we‟ve learned, every statement validly follows and is derivable from a contradiction. In such a language, therefore, the entire practice of deductive reasoning as part of the search for truth is hopelessly corrupt. So, deductive rationality carried on in English (Basque, Korean, etc.) is a farce and a delusion…unless we can escape from the Liar.6 But, see the handout “Deviant Logic, No. 3: Bočvar‟s 3-Valued Logic.”7A sentence like these that describes its own content or construction is called an …autogram.‟V.A Proposed SolutionOne way to escape would be to somehow guarantee that liar sentences could never arise.8 In 1931, the logician Alfred Tarski argued that we could block the possibility of liar sentences if we:91. strictly distinguish object languages from metalanguages, and2. restrict language so that it is only in the metalanguage that one can construct sentences about the sentences of an object language, and, so, predicate truth or falsity of thoseobject-language sentences.Satisfying these conditions would prevent a language from doing (A) and (B).For example, the English language would become an infinite sequence of distinct languages: English1, English2, English3, …where each succeeding language would be the meta-language for the previous one.English1 would contain almost all of the vocabulary of the English we currently speak, but it would lack all semantic vocabulary: words like …sentence,‟ …proposition,‟ …assertion,‟ …meaning,‟ …lies,‟ …true,‟ etc. Thus, we could talk abo ut snow (and shoes, ships, and sealing wax, etc.) in English1 by asserting the English1sentence, …Snow is white.‟ However, English1 would lack the resources for us to be able to talk about any English1 sentences (or any other sentences) in English1.So, if we would want to talk about the English1sentence …Snow is white‟ in order to say, for example, that it is true, then we would have to treat English1 as the object language and speak in its metalanguage English2. Among its vocabulary, English2 has the semantic terms needed to talk about sentences in English1. Only in English2, then, could we say that …Snow is white‟ is true, which we would do by asserting the English2sentence, “The English1sentence …Snow is white‟ is true.”Now, English2 only has the semantic vocabulary needed to talk about sentences in English1, not its own sentences (or those of any other language in the sequence). Similarly, then, it would be only in English3—the metalanguage of English2—that we could construct a sentence to assert the truth of that English2 sentence, viz. “The English2sentence, …The English1sentence, “Snow is white” is true‟ is true.” And so on through the series of English metalanguages.As no language in the infinite series could satisfy either (A) or (B), Tarski‟s stratification banishes all same-level sentence reference and, thus, all sentence self-reference, 8 Of course, banishing all self-reference would guarantee that. But, that program would be ridiculously extreme. Almost all instances of self-reference are harmless and, indeed, very useful if not practically irreplaceable.9In “The Concept of Truth in Formalized Languages,” but for a very readable version I recommend Tarski‟s “Truth and Proof” [Scientific American, vol. 194, no. 6, pp. 63-77].as ungrammatical and, therefore, meaningless. Consequently, no sentence in any of the languages could directly say anything at all about itself.Hmwk. 3. Prove that version 1a of the Liar cannot be constructed in Tarski‟s hierarchy.Of course, one could utter or write the words …This sentence is false‟ or …I am lying,‟ but these putative self-referential constructions would be utterly ungrammatical—like the English construction …Shoes pointedly my sleep eat‟—and, hence, not sentences; therefore, not meaningful; and, so, without truth-values.Equally, indirectly self-referring sentences would be impossible to construct.Hmwk. 4. Prove that version 2a of the Liar cannot be constructed in Tarski‟s hierarchy.Therefore, no sentence in any language in the series could (directly or indirectly) predicate falsity of itself. Consequently, no liar sentence could be constructed in any language in the series, and the paradox would be resolved.Despite the fact that Tarski‟s proposal would, if carried out, quash the liar paradox, the proposal has few adherents. (Yet, it‟s impossible to overstate the historical importance o f Tarski‟s work.) The problem is that Tarski‟s proposal is too crude, for it banishes not only liar sentences but all (directly or indirectly) self-referring sentences. Consequently, it is too extreme, for, again, the vast majority of self-referring sentences are perfectly banal, and some are practically irreplaceable—consider the indirectly self-referring sentence, …All English sentences begin with a capital letter.‟ There is no good reason to proscribe all of these sentences and very good reasons not to proscribe some of them.It is also interesting to note that successfully carrying out Tarski‟s proposal makes that proposal impossible. If Tarski‟s stratification were carried out, the description of the hierarchy of languages would have to be impossible, for the sentences of that description would have to belong to some finite level of the hierarchy in order to be meaningful, but in order to describe the whole hierarchy they couldn‟t belong to any of its levels.。
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The Paradoxes of Eubulides of Megara (4th century B.C.)4.The Horned ManI.The ParadoxAssuming you don’t suffer from calvarial homoplastic osteomata, consider:You still have what you have not lost.You have not lost horns.Therefore, you still have horns.Again, the paradox is a seemingly sound argument with a false conclusion.The Horned Man introduces the phenomenon of presupposition, a subject that most naturally arises in considering definite descriptions, i.e., phrases of the form ‘the Φ’ (like ‘the puppy in the window’) that purport to refer to a specific individual, viz., the unique (relevant) thing that is Φ.II.Strawson vs. Russell on the Analysis of Definite DescriptionsConsider the sentence:1. Joe is tall.As we learned when studying predicate logic, (1) is a singular proposition, i.e., a proposition about one specific object, for the sentence says that the individual denoted by the designating expression ‘Joe’ possesses the property expressed by the predicate expression ‘…is tall.’ Thus, we formalize (1) as:1'. Tj j: JoeT x: x is tallNow, consider the following sentence, which contains a definite description ratherthan a name:2. The puppy in the window is purebred.P.F. Strawson argued that (2) is also a singular proposition, and, so, he took definite descriptions to be designating expressions. On his view, the logical form of (2) is:2'. P the Φthe Φ: the unique puppy that is in the (salient) windowP x: x is purebredCall the definite description ‘the Φ’ a quasi-name.Bertrand Russell argued against Strawson that, contrary to its appearance, a definite description is a quantifier construction rather than a designating expression. For example, Russell argued that the sentence:3. The king of France is bald.asserts that there exists one and only one object that has the property of being the king of France, and the unique individual with that property also has the property of baldness. That is, (3) is an existentially quantified general proposition, not a singular proposition. Thus, (3) has the logical form:3'. (∃x)(((F x∧ (∀y)(F y⊃y = x)) ∧ B x)F x: x is a king of FranceB x: x is baldThat is: There exists an x such that x is a king of France, and if any y is a king of France, t hen it is identical to x; and x is bald.On Strawson’s theory, (3) is formalized as:3''. B the F the F: the king of Francewhere ‘the F’ is a designating expression, a quasi-name, denoting the specific individual that is the king of France.Summing up their disagreement, Russell claims that (3) asserts that there is one and only one object that is king of France, and it asserts that that object, whichever it is, is bald. Strawson claims that (3) presupposes, but does not assert, that there is one and only one object that is king of France, and it asserts that that specific individual is bald.III.Strawsonian PresuppositionConsider some more of Strawson’s examples:4. Wellington’s victory at Waterloo was his greatest triumph.5. All John’s children are asleep.According to Strawson, (4) asserts a singular proposition: a specific event—the one picked out by the quasi-name ‘Wellington’s victory at Waterloo’—has the property of b eing Wellington’s greatest triumph. But in order to assert that that event possesses that property, (4) must presuppose (though not assert) that that event occurred, i.e., that Wellington was victorious at Waterloo.Sentence (5) asserts the general pro position that each member of the class of John’s children is asleep. And in order to assert this about each member of the class, (5) must presuppose (though not assert) that the class has members, i.e., that John has children.OK, so precisely what is Strawsonian presupposition?A. Sentences vs. StatementsIn order to provide a precise account, we must consider the distinction that Strawson draws between a sentence and a statement. A sentence is a linguistic type; it is meaningful, but it doesn’t ac tually assert anything. It is speakers, not sentences, that make assertions, which they do by making statements. A statement is a token of a sentence type; it is a speaker’s particular use of a sentence at a particular time and in specific circumstances in order to make an assertion. For example, sentence (3) above means that the king of France is bald, but it doesn’t assert anything. However, if it is 1650, then Pierre can assert that Louis XIV is bald by using (3) to make the statement that Louis XIV is bald.And if it is 1789, then Françoise can make the different assertion that Louis XVI is bald by using the same sentence to make the different statement that Louis XVI is bald.So, a speaker’s use of a sentence produces a statement.Now, a use of an expression type is an utterance tokening of it with certain intentions. For example, in the course of uttering sentence (3), Pierre uttered ‘the king of France’ with the intention of referring to Louis XIV, and the fact that Françoise’s use of t he same sentence was different from Pierre’s use consists in the fact that she uttered ‘the king of France’ with the different intention of referring to Louis XVI.Since it is only when speakers use sentences to make statements that anything at all gets asserted, only statements have truth-values. And, a speaker’s use of a sentence type determines the truth conditions for his statement. Thus, Pierre’s statement is true if and only if Louis XIV is bald, and it is false if and only if Louis XIV is not bald, and Françoise’s statement is true if and only if Louis XVI is bald, and it is false if and only if Louis XVI is not bald.B. PresuppositionCall Françoise’s statement that the king of France is bald ‘S.’ Now, if S is true if and only if Louis XVI is bald and false if and only if Louis XVI is not bald, then it follows that her statement can be either true or false only if the king of France (at the time of her utterance) is Louis XVI.Now, let ‘S'’ be the (possible) statement (in 1789) that t he king of France is Louis XVI.The truth of ‘S'’ is a necessary condition for ‘S’ to be either true or false, i.e., to have a truth-value at all. In this sense, ‘S’ presupposes‘S'.’C. Presupposition FailureSince ‘S'’ must be true for ‘S’ to even have a truth-value, it follows that if ‘S'’ is false, then ‘S’ is neither true nor false. S is a truth-value gap.This conclusion about truth-value gaps makes sense in the light of Strawson’s view about statements. Consider Bertrand’s use in 1905 of sentence (3) to state that the king of France is bald. France had no king in 1905 at the time of Bertrand’s utterance. So, his intention to refer to a specific individual failed, and his use of the quasi-name ‘the king of France’ was vacuous.Sinc e he didn’t succeed in referring to anything at all, it follows that he just wasn’t talking about anything. And, if he just wasn’t talking about anything, then it follows that he failed to make any genuine assertion at all. So, Bertrand failed to make a statement.Since it is only statements that have truth-values, it stands to reason that Bertrand’s utterance of (3) had no truth-value.Similarly, a use of sentence (4) to make the statement that Wellington’s victory at Waterloo was his greatest triumph presupposes the truth of the (possible) statement that Wellington was victorious at Waterloo. If Wellington was not victorious at Waterloo, then a speaker’s utterance of ‘Wellington’s victory at Waterloo’ would fail to refer, and, consequently, her use of (4) would fail to make a statement. Consequent ly, the speaker’s utterance would fail to be either true or false.1IV.Return to the Horned ManPresupposition resolves our trouble with the Horned Man paradox. For, the statement of the argument’s first premise:i. You still have what you have not lostpresupposes the statement:i´. You do possess the relevant thing.Now, (i´) is false in the case of your horns. Since its presupposition fails, the statement of (i) is a truth-value gap. Since the statement of (i) has no truth-value, it follows that that statement is not true. Therefore, the Horned Man argument is not sound. And, the paradox is resolved.1A problem for Strawson: My statement ‘The king of France shot my cat last night’ i s clearly false; however, on Strawson’s view it gets no truth-value.。