下载文档原格式
带p-Laplacian算子两点边值问题对称正解的存在性朱忠才【摘要】This paper deals with the existence of symmetric positive solutions for the p-Laplacian nonlinear two-point boundary value problem, by using the fixed-point index theorem. Sufficient conditions of the existence of at least one or two symmetric positive solutions of this problem are established, respectively.%通过不动点指数理论,得到了一类带p-Laplacian算子两点边值问题对称正解的存在性,以及这类边值问题至少存在一个或两个对称正解的充分条件.【期刊名称】《佛山科学技术学院学报（自然科学版）》【年(卷),期】2018(036)002【总页数】7页(P20-26)【关键词】p-Laplacian算子;两点边值问题;不动点指数;对称正解【作者】朱忠才【作者单位】广东工业大学应用数学学院,广东广州510520【正文语种】中文【中图分类】O177含p-Laplacian算子的微分方程边值问题，在诸多领域如非牛顿力学、宇宙物理、血浆问题和弹性理论等方面的应用都很广。
不少学者都深入地研究了此类边值问题，也获得了丰硕的成果［1-5］。
另外，由于生活中的大多数问题都是非线性的，这就使得非线性边值问题在近些年越来越受到学者们的关注。
如文献［6-7］研究了二阶二点边值问题的对称正解存在性，文献［8］研究的是下列p-Laplacian边值问题正解的存在性其中，φ（s）都是非减的奇函数，且存在m＞0使得Bi（v）≤mv，对所有的v≥0，i=0或i=1成立。
形上 meta physics 文献随着时间的推移，形而上学变得越来越受到关注，它曾经被认为是一门古老的学问，也是许多科学和哲学对话的基础。
形而上学的历史可以追溯到古希腊时代由亚里士多德（Aristotle）提出的“分类”学说，它包括了认识论、天体力学、动物学、政治学和哲学。
但是，在英语中，“形而上学”一词在16世纪才有了具体的意义，即“超越自然界的物质和精神界”（transcendent material and spiritual realms）。
由此可见，形而上学是一门多维度的学问，对于探索物质世界和精神世界，人们经常都采用形而上学的方法来理解它们之间的关系以及它们各自的本质。
首先，形而上学是一门破坏性证论（destructive deductions）学科，就是说，在形而上学中，人们尝试去找到不同的实物实体，通过分析它们之间的关系及其本质，来得出最终的结论。
其中，对于实物实体的研究，主要有两种方式。
第一种是采用形式逻辑，即将某一实物实体与其他实体进行比较，以及考虑它们之间的具体关系等。
第二种则是采用体系逻辑，探究实体与实体之间的哲学关系，以及实物实体的整体特点。
在形而上学中，通常都采取了这两种方式的结合进行研究。
此外，形而上学关注的是实体的内在特性。
人们认为，每一种实体都有其独特的内在本质，并且，这些内在特性会影响实体的客观性质。
所以，在形而上学中，研究者会分析这些客观性质，尝试发现实体内在本质的脉络，并从中推出结论。
最后，形而上学也寻求解释和认知客观性质之间的联系，即精神和物质的联系。
形而上学家探究在精神和物质之间是否有共同的本质，并从科学的角度来理解它们之间的关系。
因此，形而上学家坚信，一切客观性质之间都有内在的联系，而研究这种联系也是形而上学的内容之一。
总而言之，形而上学是一门具有宽泛内涵的学问。
它既关注实体之间的物质联系，也关注精神和物质之间的关系，有助于我们更好地了解宇宙的本源和结构，从而为了解我们周围世界更深层次的智慧奠定基础。
小学上册英语第4单元测验试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.My ________ (玩具名称) has a pretty dress.2.My _____ (玩具火车) chugs around the track.3.The leaves fall gracefully from the _______ in autumn.4.The kitten is ______ with a ball of yarn. (playing)5.Which word means "happy"?A. SadB. JoyfulC. AngryD. Scared6.I can ________ (swim) in the pool.7.What is the capital of Norway?A. OsloB. BergenC. TrondheimD. Stavanger8. A _______ is a representation of a chemical reaction using symbols.9.We are going to the ___. (fair) this weekend.10.The concept of climate mitigation focuses on reducing the impacts of ______ change.11.We have a _____ (庆典) in town.12.The capital city of Bhutan is __________.13. A __________ is a reaction that produces solid precipitates.14.The garden is full of _______ that bloom in different colors.15.The chemical formula for gadolinium oxide is _____.16.The symbol for selenium is _____.17.The rabbit can be very _______ (友好) with children.18.We are going to ______ a movie tonight. (watch)19.What do we call the outer layer of the Earth?A. CoreB. MantleC. CrustD. Atmosphere答案:C20.The ______ (小鱼) swims gracefully in the aquarium.21. A strong base has a pH value greater than _______.22.What do we call a place where we can see animals?A. ZooB. FarmC. AquariumD. All of the above23._____ (landscaping) improves outdoor spaces.24.What do you call a baby kangaroo?A. JoeyB. CalfC. KitD. Pup答案:A25. A chemical change can be identified by color ______.26.She is ___ her bike. (riding)27.I have a collection of ________ (漫画书) that I read during my free time. They are so ________ (有趣).28.My favorite type of ________ (食物) is sushi.29.What is 5 2?A. 3B. 4C. 2D. 1答案:A30.What do we call the part of the plant that absorbs sunlight?A. StemB. LeafC. FlowerD. Root答案:B31. A ______ is a collection of data gathered from observations.32.I can draw a picture of my favorite _________ (玩具) and share it with my class.33.My dad is a fantastic __________ (模范) for our family.34.What do we call a young person in school?A. StudentB. ScholarC. LearnerD. Pupil35.The _____ (guitar) sounds nice.36.The _____ (raspberry) plant produces sweet berries.37.I like to go camping in the ______ (森林) and explore nature. It’s a great way to relax and unwind.38.The __________ (历史的价值观差异) can lead to conflict.39.The __________ is cool and refreshing during the summer. (海洋)40.I have a toy _____ that can jump.41.What do you call the process of a caterpillar becoming a butterfly?A. MetamorphosisB. EvolutionC. TransformationD. Development答案:A42.My ______ is very inspiring and motivates others.43.She is a great ________.44.I enjoy _______ (在公园散步).45.I enjoy ______ (reading) comics.46.What is the main ingredient in salad?A. PastaB. LettuceC. RiceD. Bread47.I love to eat ______ during the summer.48.I want to ________ (support) local causes.49.She is _______ (climbing) the ladder.50.What is the name of the famous explorer who discovered America?A. Ferdinand MagellanB. Christopher ColumbusC. Marco PoloD. Vasco da Gama答案:B51.The Earth's atmosphere is crucial for protecting ______ life.52.The _______ of light can be tested by using a variety of filters.53.The chemical formula for sodium thiocyanate is _____.54.We have _____ (很多) fun games.55.War was a period of tension between the _______ and the Soviet Union. (美国) The Cold56.I like to ______ (参与) in local campaigns.57.What is the capital of South Africa?A. PretoriaB. JohannesburgC. Cape TownD. Durban答案:A Pretoria58. A _______ is a reaction that occurs in the earth's crust.59.natural disaster) can cause severe damage to areas. The ____60.The chemical symbol for manganese is ______.61.My favorite snack is ________ and cheese.62.Ants work together to build a ________________ (巢).63.My ____ likes to be dressed up in different outfits. (玩具名称)64.The capital of Kosovo is ________ (普里什蒂纳).65.I saw a _______ (小刺猬) in the garden.66.Which animal is known for its long neck?A. ElephantB. GiraffeC. LionD. Kangaroo67. A _______ can enhance indoor spaces.68.Countries are divided into smaller regions called ________.69.The ________ was a significant period in the history of Europe.70.Which animal is known for its long neck?A. ElephantB. GiraffeC. LionD. Tiger答案:B71.What is the main function of the stomach?A. To pump bloodB. To digest foodC. To filter wasteD. To store energy答案:B72.He is reading a ___. (story)73.What do we call a scientist who studies the universe?A. AstronomerB. AstrophysicistC. CosmologistD. Geologist答案:A74.Vegetables like carrots grow _____ (在地下).75.The fish is _____ in the tank. (swimming)76.The museum has _______ (很多展品).77.The __________ (种植计划) is essential for successful gardening.78.I like to bake ______ (蛋糕) for special occasions. Decorating them is my favorite part!79. A solar flare is a sudden eruption of energy on the sun’s ______.80.The chemical symbol for iridium is _____.81.What is the main ingredient in risotto?A. RiceB. PastaC. BarleyD. Quinoa答案:A82.What is the name of the famous statue in Rio de Janeiro?A. Christ the RedeemerB. Statue of LibertyC. DavidD. The Thinker答案:A83.What is the name of the famous singer known for "Like a Rolling Stone"?A. Elton JohnB. Bob DylanC. Bruce SpringsteenD. Johnny Cash答案:B84.The Earth's atmosphere is composed mainly of nitrogen and ______.85. A solution is a mixture where one substance is dissolved in ________.86.The goldfish has _______ (眼睛) that help it see.87.The substance that is dissolved in a solution is called a ______.88.What do we call a traditional story that explains something in nature?A. MythB. FableC. LegendD. Tale89.The ______ is an important predator.90.My ________ (玩具) is very colorful and bright.91. A cat's agility helps it catch ______ (猎物).92.The trees in the _______ provide shade and a place to relax.93.My friend’s dad, ______ (我朋友的爸爸), is a businessman.94. A ______ often forages for food.95._____ (春天) is when many plants start to bloom.96.My cousin is very __________ (乐观).97.What do we call a person who studies ancient texts?A. PhilologistB. LinguistC. HistorianD. Archeologist答案:A98.What do we use to cut paper?A. ScissorsB. TapeC. GlueD. Ruler答案:A99.What do you call the time when the sun rises?A. DawnB. DuskC. MidnightD. Afternoon答案:A100.What is the name of the famous river that runs through Egypt?A. NileB. AmazonC. MississippiD. Yangtze。
小学上册英语第1单元测验卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.小蟹) scuttles along the beach. The ___2.The capital city of Belgium is __________.3.I have a _______ (wonderful) idea.4.What do we call the part of a story that introduces the characters and setting?A. ClimaxB. ConclusionC. ExpositionD. ConflictC5.The __________ (历史的意义) can inspire action.6.The chemical formula for isopropyl alcohol is _____.7.I planted ______ in my garden.8.My friend, ______ (我的朋友), has a great sense of humor.9.What do we call a baby goat?A. CalfB. LambC. KidD. FoalC10.What is the main ingredient in salad dressing?A. OilB. WaterC. SugarD. SaltA11.What is the capital city of the USA?A. New YorkB. ChicagoC. WashingtonD.C. D. Los AngelesC12. A _______ can be a wonderful addition to your home.13. A __________ can cause significant changes to landscapes over time.14.What do you call a book for children?A. NovelB. Picture bookC. EncyclopediaD. TextbookB15.Penguins are birds that cannot ______.16.The __________ is where tectonic plates converge.17.The ________ was a significant moment in the fight for civil rights.18.The _____ (植物影响) is far-reaching in our lives.19.My uncle is a ______. He builds houses.20.Many cultures celebrate the __________ (植物的生长季节).21.What is the opposite of "hot"?A. ColdB. WarmC. CoolD. Spicy22. A ladybug is often seen on ______ (绿叶).23.What is the approximate age of the universe?A. 4.5 billion yearsB. 13.8 billion yearsC. 20 billion yearsD. 1 trillion years24.The ______ (袋鼠) hops around with its baby in a pouch.25.What is the term for a young hen?A. ChickB. DucklingC. GoslingD. PulletD Pullet26.I have a toy _______ that can wiggle and dance.27.The amount of space an object occupies is called its __________.28. A _____ (植物) can be a houseplant or a garden plant.29.I have a toy _____ that can fly.30.The ______ of an element is determined by the number of protons.31.What do we call a person who collects stamps?A. PhilatelistB. NumismatistC. CollectorD. DealerA32. A rabbit can have many ______ (小兔子) at once.33.The _____ (小径) in the garden leads to a hidden area.34.The __________ (历史的传承责任) ensures future continuity.35.I can sing songs with my musical ________ (玩具名称).36.What is the name of the fairy tale character who fell asleep for 100 years?A. CinderellaB. Sleeping BeautyC. Snow WhiteD. Belle37.I like to ride my ________ (滑板).38.What do we call the act of embracing diversity?A. InclusionB. AcceptanceC. ToleranceD. All of the AboveD39. A _____ (草本植物) is not woody and can die back in winter.40.The chemical symbol for lithium is __________.41.I love to visit the ______ (动物园) and learn about different species. It’s an educational experience.42.I want to plant ________ to decorate my room.43.听一听，判断所听内容与图片是否相符。
小学上册英语第4单元自测题英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The library has many _____ (books/magazines).2.The chemical symbol for zirconium is ______.3.What do we call the large body of fresh water surrounded by land?A. OceanB. SeaC. LakeD. RiverC4.The polar bear lives in the _________. (北极)5.The ________ (海洋探险) unveils new species.6.The sunrise is _______ (美丽的).7.The ancient Sumerians created one of the earliest forms of ________ (文字).8.On special occasions, we dress up in ________ (漂亮的衣服) and go out for________ (晚餐). It feels very nice!9.My favorite color is ________.10.I like to play ________ (扑克牌).11.The book is _____ (interesting/boring).12. Wall stretches over ________ (长城绵延超过________) kilometers. The Grea13.What is the name of the famous detective created by Arthur Conan Doyle?A. Hercule PoirotB. Sam SpadeC. Sherlock HolmesD. Philip Marlowe14.She has a _______ who is very tall.15. A ________ (青蛙) jumps from lily pad to lily pad in the pond.16.The dog is ___ at the door. (barking)17.Which insect can produce honey?A. AntB. ButterflyC. BeeD. FlyC18.What is the name of the famous explorer who sailed the ocean blue in 1492?A. Christopher ColumbusB. Ferdinand MagellanC. Vasco da GamaD. Hernán CortésA19.The __________ (历史的启示性探讨) foster understanding.20. A _______ is a reaction that combines several elements to form a compound.21.What is the opposite of day?A. MorningB. NightC. EveningD. AfternoonB22.What do we call a baby sheep?A. CalfB. KittenC. LambD. Puppy23.What is the opposite of hot?A. ColdB. WarmC. CoolD. Boiling24.The chemical formula for hydrobromic acid is _____.25.________ (植物生理) is essential for growth.26. A ______ is a type of mammal that lays eggs.27. A ____(hot spring) is a natural pool of warm water.28.We went to the ______ for a field trip. (museum)29. A strong electrolyte dissociates completely in ______.30. A _______ reaction produces heat and light.31.The __________ was a major event in the history of the United States. (内战)32.Which animal is known for its hump?A. ElephantB. CamelC. GiraffeD. KangarooB33.What do you call a large animal that has antlers?A. MooseB. DeerC. ElkD. All of the aboveD34.She is _______ (playing) the flute.35. A reaction that occurs in a closed system is called a ______ reaction.36.Which animal is known for its black and white stripes?A. LeopardB. ZebraC. PandaD. SkunkB37.The butterfly is ___ (flapping) its wings.38.Which fruit is known for being very sour?A. BananaB. AppleC. LemonD. GrapeC39.The process of ______ can lead to the formation of valleys.40.The _____ (植物历史传承) preserves knowledge across generations.41. A group of fish swimming together is called a ______.42.The _______ (The Treaty of Versailles) ended World War I and imposed penalties on Germany.43.My brother is a ______. He enjoys playing the drums.44.War led to a race in ________ (武器). The Cold45.I enjoy _____ (看电影) at the theater.46.The ancient Egyptians wrote on ________ (纸莎草纸).47.The ice cream is melting ___. (quickly)48.What is the name of the famous theme park in California?A. Universal StudiosB. DisneylandC. SeaWorldD. Busch GardensB49.The flower is ___ (blooming) nicely.50.What do we call a large body of saltwater?A. LakeB. OceanC. RiverD. Pond51.I have _____ (a/an) idea.52.The squirrel gathers ______ (坚果) in the fall.53.________ (植物研究成果) influence policy.54.Chemical reactions can be sped up by increasing the __________.55.My teacher encourages us to __________ (探索).56.What do we call the part of the Earth that supports life?A. BiosphereB. AtmosphereC. LithosphereD. HydrosphereA57.What do we call the study of chemical processes in living organisms?A. BiochemistryB. BiologyC. ChemistryD. PhysicsA58.The weather is very ______ today.59.The flowers are ______ in the garden. (blooming)60.I live in a ______ house.61.The chemical formula for yttrium oxide is _____.62.My birthday is in ________.63.I like to ride my _______ (我喜欢骑我的_______).64.The Orion Nebula is one of the brightest nebulae visible from _______.65.The clock shows _____ (three/four) o'clock.66.How many wheels does a bicycle have?A. OneB. TwoC. ThreeD. FourB67. A _______ is a reaction that occurs in solution.68.The rabbit is ________ in the grass.69.The _____ (季节性) changes bring different flowers to bloom.70.The _____ (猴子) is always getting into mischief.71.What is the common name for a large, furry animal found in North America?A. LionB. Polar bearC. Grizzly bearD. Koala72.I see a _______ (hawk) flying overhead.73.What is the capital city of New Zealand?A. AucklandB. WellingtonC. ChristchurchD. Hamilton74.古代的________ (philosophers) 对科学和伦理的思考影响深远。
Seminar in Buddhist Path to Emancipation3(2:20-5:20)Office hours: (11:10-12:00) (1:10-2:00)1.2.3.* Gu∫abhadra 435-443 T. 99, vol. 2, pp. 1a-373b* Gautama Sa∆ghadeva 397-398 T. 26, vol. 1, pp. 421a-809a* Gautama Sa∆ghadeva 385 397 T. 125, vol. 2, pp. 549b-830b* Dªrghågama Buddhayaßas 413 T. 1, vol. 1, pp. 1b-149c*3 15% 5 25% 15%1* CBETA 1-55 85 78-87 2004 4* Vipassana Research Institute, Cha††ha Sa∆gåyana Tipi†aka CD-ROM, Dhammagiri: Vipassana Research Institute, 1998.* 18/19 1999 9 27-31.* Encyclopaedia of Buddhism, 4 vols., edited by G. P. Malalasekera, Colombo: The Government of Ceylon, 1961-1990.* Bhikkhu Khantipalo, “Where’s That Sutta? A Guide to the Discourses in the Numerical Collection (Anguttara-nikåya), ” Journal of the Pali Text Society 10 (1985): 38-153.* G. P. Malalasekera, Dictionary of Påli Proper Names, 2 vols, London: The Pali Text Society, 1974.* Karl H. Potter, Robert E. Buswell, Jr., Padmanabh S. Jaini, Noble Ross Reat (eds.), Abhidharma Buddhism to 150 A.D., Encyclopedia of Indian Philosophies, vol. VII, Delhi: Motilal Banarsidass Publishers, 1996.(This volume undertakes to summarize the gist of Buddhist philosophical teachings from the first texts that developed after the Buddha up to and including the mammoth text call Mahavibhasa, generated from a convention held in the first or second centuryA.D.)* 14 1968* 1998* 1990 45-100.2* 25 1984 1-127.* 25-26 1984* 24 1984* Erich Frauwallner, Studies in Abhidharma Literature and the Origins of Buddhist Philosophical Systems, translated from the German by Sophie Francis Kidd, Albany: State University of New York Press, 1995.* Kanai Lal Hazra, Påli Langiuage and Literature: A Systematic Survey and Historical Study, 2 vols, Emerging Perceptions in Buddhist Studies, no. 4 and 5, New Delhi: D. K. Printworld, 1994.* Kanai Lal Hazra, Studies on Pali Commentaries, Delhi: B. R. Publishing Corporation, 1991. * Oskar von Hinüber, A Handbook of Påli Literature, Berlin: Walter de Gruyter, 1996.* Ulrich T. Kragh, “The Extant Abhidharma-literature,” The Indian International Journal of Buddhist Studies 3 (2002): 123-167.* K. R. Norman, Påli Literature: Including the Canonical Literature in Prakrit and Sanskrit of All the Hªnayåna Schools of Buddhism, Wiesbaden: Otto Harrassowitz, 1983.* 1978* 1997* ˃ 1984* 1983* 2002* 2003* 2003* 1996* 1993* 1999* 2000* 8 2004 327-348.* 111 1998 12 2-4 2001 41-57.* 1988* ê ê 1983 389-420.* ê ê 1983 97-193.* 23 1986* 1964* ê ê 1983 195-215.* Heinz Bechert, “The Writing Down of the Tripi†aka in Påli,” Wiener Zeitschrift Für die Kunde Süd- (und Ost-) Asiens 36 (1992): 45-53.* Fumio Enomoto, “On the Formation of the Original Texts of the Chinese Ågamas,” Buddhist Studies Review 3/1 (1986): 19-30.* Fumio Enomoto, A Comprehensive Study of the Chinese Sa≤yuktågama: Indic Texts Corresponding to the Chinese Sa≤yuktågama as Found in the Sarvåstivåda-M¥lasarvåstivåda Literature, Part 1, Sa≤gªtanipåta, Kyoto: Kacho Junior College, 1994.* Jens-Uwe Hartmann, “Further Remarks on the New Manuscript of the Dªrghågama of the (M¥la-)Sarvåstivådins,” Journal of the International College for Advanced Buddhist Studies 5 (2002): 133-150.* Jens-Uwe Hartmann, “Contents and Struture of the Dªrghågama of the (M¥la )Sarvåstivådins,” Annual Report of The International Research Institute for Advanced Buddhology at Soka University 7 (2004): 119-137.* Y¥jirø Hayashiya, “Anseikø yaku no Zøagon to Zøitsuagon (The Sa≤yukta Ågama and the Ekottara Ågama translated by An Shih-kao ),” The Journal of Buddhist Study1/1 (1937): 11-50.* Satoshi Hitaoka, “The Sectarian Affiliation of Two Chinese Sa≤yuktågamas,”49 1 2000 12 1-7.* Egaku Mayeda, “Japanese Studies on the Schools of the Chinese Ågamas,” in Zur Schulzugehörigkeit von Werken der Hªnayåna-Literatur, ed. Heinz Bechert, Göttingen: Vandenhoeck & Ruprecht, 1985, pp. 94-103.* Minh Chau Thich, The Chinese Madhyama Ågama and the Påli Majjhima Nikåya: A Comparative Study, Delhi: Motilal Banarsidass Publishers, 1991.* Ernst Waldschmidt, “Central Asian S¥tra Fragments and their Relation to the Chinese Ågamas,” The Language of the Earliest Buddhist Tradition, edited by Heinz Bechert, Göttingen: Vandenhoeck & Ruprecht, 1980, pp. 136-174.* Yusen Økubo ( ), “The Ekottara-ågama Fragments of the Gilgit Manuscripts: Romanized Text,” Buddhist Seminar 35 (May 1982): 1-30.* 31 2 1983 115-118; 2 32 2 1984 148-149. * 1964* 1229 1329 Gåndhårª Dharmapada 343-344 Turfan No. 50 Mahåbhårata 13.132 30 2 1982 79-85.* Devatåsamyukta Devatås¥tra Ratnåvadånamålå 31 1 1982 87-90.* 1963~2000 2001* 1995-2001 20 2002 3 227-283.* 20 1999 12 40-48; 23 1997 9 50-72.* 13 1998 3 41-49.* 72 1993 1 1-53.* K. R. Norman, The Present State of Påli Studies, and Future Tasks 18 2001 9 171-209.* Charles S. Prebish, "Recent Progress in Vinaya Studies," Studies in Pali & Buddhism, edited by A. K. Narain 44 1986 12 1-16.* J. W. de Jong, A Brief History of Buddhist Studies in Europe and America,Tokyo: Kosei Publishing, 1997.* Hajime Nakamura, Indian Buddhism: A Survey with Bibliographical Notes, Delhi: Motilal Banarsidass Publishers, 1987.Book Description:This work presents a survey of Indian Buddhism with detailed bibliographical notes. The main text constitutes a general survey of the development of Indian Buddhism, and studies by scholars past and present are mentioned in full detail in copious footnotes with due evolutions. This work can be regarded, so to speak, as a development with revisions, of the Buddhist portion of M. Winternitz's History of Indian Literature. Major studies before and after Winternitz's work are exhaustively mentioned.* Russell Webb, “Contemporary European Scholarship on Buddhism,” The Buddhist Heritage, edited by Tadeusz Skorupski, Tring, U.K.: The Institute of Buddhist Studies, 1989, pp. 247-276.1 Påli Theravåda2 34 5* ˃ 10 1995 341-362.* 50 1994 140-155.* 2003* ( 2000* 2000* 2000* 1998* K. R. Norman, A Philological Approach to Buddhism, London: University of London, 1997.* K. R. Norman, Collected Papers, vols. I-VII, Oxford: The Pali Text Society, 1990-2001.* Oscar von Hinüber, Selected Papers on Påli Studies, Oxford: The Pali Text Society, 1994.* Padmanbh S. Jaini, Collected Papers on Buddhist Studies, Delhi: Motilal Banarsidass Publishers, 2001.2-5* Gu∫abhadra 435-443 T. 99, vol. 2, pp. 1a-373b 2-4* Bhikkhu Bodhi (tr.), “General Introduction,” The Connected Discourses of the Buddha: A New Translation of the Sa≤yutta Nikåya, vol. I, Boston: Wisdom Publications, 2000, pp. 21-55. 5* Bhikkhu Bodhi (tr.), “43: As∆khatasa≤yutta: Connected Discourses on the Unconditioned,” The Connected Discourses of the Buddha: A New Translation of the Sa≤yutta Nikåya, vol. II, Boston: Wisdom Publications, 2000, pp. 1372-1379, 1453-1454. 5Book Description:The Connected Discourses of the Buddha is a complete translation of the Samyutta Nikaya- the third great collection of the Buddha's discourses preserved in the Pali Canon -containing all of the important short suttas on such major topics as the Four Noble Truths, dependent origination, the seven factors of enlightenment, and the Noble Eightfold Path. The Connected Discourse ranks as one of the most inspiring compilations in the Buddhist canon. Bhikkhu Bodhi's distinguished and precise translation, his insightful introductory materials, and his extensive notes guide the reader through this vast collection of the Buddha's ancient teachings. This is the third title in Wisdom Publications' award-winning Teachings of the Buddha series, following The Long Discourses of the Buddha (0-86171-103-3) and The Middle Length Discourses of the Buddha (0-86171-072-X). Like its two predecessors, The Connected Discourses is sure to merit a place of honor in the library of every student of Buddhism.* 1983* 2003* 20036-7* Gautama Sa∆ghadeva 397-398 T. 26, vol. 1, pp. 421a-809a* 1983* 7 2002* Bhikkhu Ñå∫anamoli, Bhikkhu Bodhi (trs.), The Middle Length Discourses of the Buddha: A Translation of the Majjhima Nikåya, Boston: Wisdom Publications, 1995.From Library Journal:This new translation of the Majjhima Nikaya, part of the Pali Canon touching on the nature of Nirvana and the Four Noble Truths, is considered by scholars to be the most reliable source for the original teachings of the historical Buddha.Book Description:An invaluable collection of the original words of the Buddha --essential for all libraries.8-9* Gautama Sa∆ghadeva 385 397 T. 125, vol. 2, pp. 549b-830b* 1983* The Book of the Gradual Sayings (Anguttara-Nikåya) or More-Numbered Suttas, 5 volumes, translated by F. L. Woodward, London: The Pali Text Society, 1932-36.* Numerical Discourses of the Buddha: An anthology of Suttas from the A∆guttara Nikåya, translated by Nyanaponika Thera and Bhikkhu Bodhi, Walnut Creek: AltaMira Press, 1999. Synopsis:This text brings together the teachings of the Buddha ranging from the basic ethical observances recommended to the man or woman of the world, to the more rigorous instructions on mental training prescibed for monks and nuns.10-11* Dªrghågama Buddhayaßas 413 T. 1, vol. 1, pp. 1b-149c* 1999* 1983* Maurice Walshe (tr.), Thus Have I Heard: The Long Discourses of the Buddha -- Dªgha Nikåya, Boston: Wisdom Publications, 1987.From Library Journal:This translation of the Digha Nikaya, a collection of 34 sutras and a companion volume to The Middle Length Discourses(below), deals with a variety of topics such as the rewards of monastic life, early Buddhist philosophy, and the duties of laypersons.Book Description:The Buddhist "gospel" revealing the actual teachings of the Buddha. Introduced with an account of the Buddha's life and times.* 1 1993* 199412* David J. Kalupahana, “Chapter 4: Experience and Theory (Pa†iccasamuppanna and Pa†iccasamuppåda),” A History of Buddhist Philosophy: Continuities and Discontinuities, Honolulu: University of Hawaii Press, 1992, pp. 53-59, 250-251.Book Description:David J. Kalupahana's Buddhist Philosophy: A Historical Analysis has, since its original publication in 1976, offered an unequaled introduction to the philosophical principles and historical development of Buddhism. Now, representing the culmination of Dr. Kalupahana's thirty years of scholarly research and reflection, A History of Buddhist Philosophy builds upon and surpasses that earlier work, providing a completely reconstructed, detailed analysis of both early and later Buddhism.* Henry Cruise, “Early Buddhism: Some Recent Misconceptions,” Philosophy East & West 33/2 (April 1983): 149-165.* David J. Kalupahana, Causality: The Central Philosophy of Buddhism, Honolulu: The University Press of Hawaii, 1975.* Joanna Macy, Mutual Causality in Buddhism and General Systems Theory: The Dharma of Natural Systems, Albany: State University of New York Press, 1991.* 1988* 1981* 198512-13* Sue Hamilton, “Chapter 1: Setting the Scene: We have no self but we are comprised of five aggregates,” Early Buddhism - A New Approach: The I of the Beholder, Richmond: Curzon Press, 2000, pp. 18-32.Book Description:Building on the author's previous published work, this book focuses on the relationship between identity and perception in early Buddhism, drawing out and explaining the way they relate in terms of experience. It presents a coherent picture of these issues in the context of Buddhist teachings as a whole and suggests that they represent the heart of what the Buddha taught. This book will be of primary interest to scholars working within all fields of Buddhist studies.* Steven Collins, “Chapter 3.2: Arguments in support of anattå,” Selfless Persons: Imagery and Thought in Theravåda Buddhism, Cambridge: Cambridge University Press, 1982, pp. 95-110, 278-280.Book Description:This book explains the Buddhist doctrine of annattá ("not-self"), which denies the existence of any self, soul, or enduring essence in man. The author relates this doctrine to its cultural and historical context, particularly to its Brahman background. He shows how the Theravada Buddhist tradition has constructed a philosophical and psychological account of personal identity on the apparently impossible basis of the denial of self. Although the emphasis of the book is firmly philosophical, Dr. Collins makes use of a number of academic disciplines, particularly those of anthropology, linguistics, sociology, and comparative religion, in an attempt to discover the "deep structure" of Buddhist culture and imagination, and to make these doctrines comprehensible in terms of the western history of ideas.* 1989* 1998 16-22.* 2000* E. M. Adams, The Metaphysics of Self and World: Toward a Humanistic Philosophy, Philadelphia: Temple University Press, 1991.* Mathieu Boisvert, The Five Aggregates: Understanding Theravåda Psychology and Soteriology, Delhi: Sri Satguru Publications, 1995.* Mangala R. Chinchore, Anattå / Anåtmatå: An Analysis of Buddhist Anti Substantialist Crusade, Delhi: Sri Satguru Publications, 1995.* James Giles, “The No-self Theory: Hume, Buddhism, and Personal Identity,” Philosophy East & West 43/2 (April 1993): 175-200.* Luis O. Gómez, “Proto-Mådhyamika in the Påli Canon,” Philosophy East and West26/2 (1976): 137-165.* R. D. Gunaratne, “Space, Emptiness and Freedom (Åkåßa, Í¥nyatå, and Nibbåna),” Buddhist Thought and Ritual, edited by D. Kalupahana, New York: Paragon House, 1991, pp. 35-44.* Sue Hamilton, Identity and Experience: The Constitution of the Human Being According to Early Buddhism, London: Luzac Oriental, 1996.* David J. Kalupahana, “The Early Buddhist Notion of the Middle Path,” Journal of Chinese Philosophy 7 (1980): 73-90.* David Loy, “The Lack of Self: A Western Buddhist Psychology,” in Buddhist Theology: Critical Reflections by Contemporary Buddhist Scholars, edited by Roger R. Jackson and John J. Makransky , Richmond: Curzon Press, 1999, pp. 155-172.Synopsis:Contains works by scholars of Buddhism, themselves Buddhist, who seek to apply the critical tools of the academy to reassess the truth and transformative value of their tradition in its relevance to the contemporary world.Synopsis:This volume is the expression of a new development in the academic study of Buddhism: scholars of Buddhism, themselves Buddhist, who seek to apply the critical tools of the academy to reassess the truth and transformative value of their tradition in its relevance to the contemporary world. Essays articulate, in diverse ways, the need for and purposes of this approach to the study of Buddhism, referred to as 'Buddhist Theology' and reflect critically upon many fundamental aspects of Buddhist understanding or practice from a variety of contemporary, critical perspectives, in order to clarify or recover elements of Buddhist traditions seen as valuable for the contemporary world. In the final section, two leading Buddhist scholars give their critical responses to the essays.* David R. Loy, A Buddhist History of the West: Studies in Lack, Albany: State University of New York Press, 2002.From the Back Cover:Buddhism teaches that to become happy, greed, ill-will, and delusion must be transformed into their positive counterparts: generosity, compassion, and wisdom. The history of the West, like all histories, has been plagued by the consequences of greed, ill-will, and delusion. A Buddhist History of the West investigates how individuals have tried to ground themselves to make themselves feel more real. To be self-conscious is to experience ungroundedness as a sense of lack, but what is lacking has been understood differently in different historical periods. Author David R. Loy examines how the understanding of lack changes at historical junctures and shows how those junctures were so crucial in the development of the West.Book Description:A Buddhist interpretation of Western history that shows civilization shaped by the self's desire for groundedness.* Daniel J. Meckel and Robert L. Moore (eds.), Self and Liberation: The Jung / Buddhism Dialogue, New York: Paulist Press, 1992.(This important new book makes available a significant collection of essays devoted to the relationship of C.G. Jung's work to Buddhism. Includes all four of Jung's major essays on Buddhism, a transcript of the conversation between Jung and Zen Master Shin'ichi Hisamatsu in 1958 at Jung's home in Kusnacht, and nine essays on Jung's work by psychology and religion scholar.)* Hajime Nakamura, “The Problem of Self in Buddhist Philosophy,” Revelation in Indian Thought: A Festschrift in Honour of Professor T. R. V. Murti, edited by H. Coward and K. Sivaraman, Emeryville: Dharma Publishing, 1977, pp. 99-118.* Joaquin Pérez-Remón, Self and Non-Self in Early Buddhism,The Hague: Mouton Publishers, 1980.* P. T. Raju and Alburey Castell (eds.), East-West Studies on the Problem of the Self, The Hague: Martinus Nijhoff, 1968.* David Seyfort Ruegg, Lambert Schmithausen (eds.), Earliest Buddhism and Madhyamaka, Leiden: E. J. Brill, 1990.* Donald K. Swearer (ed.), Me and Mine: Selected Essays of Bhikkhu Buddhadåsa, Albany: State University of New York Press, 1989.* 1967* 1981*15 2000 1-20.* 3 1987 40-30.* 1946 297-352.* 9 1994 68-89.* 703 3 1987 29-39.14-15* 2003* Bruce R. Reichenbach, “Chapter 2: Metaphysical Presuppositions of the Law of Karma,” The Law of Karma: A Philosophical Study, Honolulu: University of Hawaii Press, 1990, pp. 10-23, 197-200.* Bruce R. Reichenbach, “Chapter 11: Karma and Liberation,” The Law of Karma: A Philosophical Study, Honolulu: University of Hawaii Press, 1990, pp. 169-183, 223-228.* 1988* 47 2003 6 635-796.* 46 2002 6 935-1140.* Johannes Bronkhorst, Karma and Teleology: A Problem and its Solutions in Indian Philosophy, Tokyo: The International Institute for Buddhist Studies, The International College for Advanced Buddhist Studies, 2000.* Thomas L. Dowling, “Karma Doctrine and Sectarian Development,” Studies in Pali and Buddhism: A Memorial Volume in Honor of Bhikkhu Jagdish Kashyap, edited by A. K. Narain, Delhi: B. R. Publishing Corporation, 1979, pp. 83-92.* James R. Egge, Religious Giving and the Invention of Karma in Theravåda Buddhism, Richmond: Curzon Press, 2002.Book Description:Although the doctrine of karma is one of the best known aspects of Buddhist thought, Buddhist texts present other, less systematic, ways of speaking about the effects of good and bad actions. This book draws attention to one of these neglected discourses by showing that the interpretation of religious giving as acts of sacrifice directed toward the Buddha or Buddhist monastics has been an important theme in Theravda Buddhism. Sacrifice and karma differ significantly: whereas karma can be analysed as an inward, psychological process in which one's volition purifies or defiles one's mind, discussions of giving as sacrifice stress that the qualities of the recipient as well as the intentions of the donor affect the merit produced by a gift. Sacrificial and karmic discourses also present very different understandings of the dedication of the effects of a gift (i.e. a merit transfer).* Noriyuki Kudo, The Karmavibha∆ga: Transliterations and Annotations of the Original Sanskrit Manuscripts from Nepal, Tokyo: The International Research Institute for Advanced Buddhology, Soka University, 2004.* Étienne Lamotte, Karmasiddhi Prakara∫a: The Treatise on Action by Vasubandhu, translated by Leo M. Pruden, Berkeley: Asian Humanities Press, 1988.* James Paul McDermott, Development in the Early Buddhist Concept of Kamma / Karma, New Delhi: Munshiram Manoharlal Publishers, 1984.Book Description:One of the central concepts in Buddhism is the idea of Kamma. Although the importance of Karma in Buddhist thought is regularly recognized, the question remains whether the Buddhist understanding of the principle of Karma has been inalterably fixed, or whether it has undergone a process of development and modificationduring the course of Buddhist history. If, indeed, the Buddhist understanding of Karma has not been static, what kinds of development has it undergone? It is to these questions that this study has been text-critical and historical. The initial Buddhist formulation of the principle of Kamma as it is depicted in the Vinaya and the Sutta Pitakas is analyzed as a base for the study.Modifications are noted as already present in the later strata of this literature. The problem is then examined in the Abhidhamma Pitaka, where certain abstract developments in the definition and categorization of Kamma are discovered. In order to provide a greater chronological scope, the text then turns to an analysis of Kamma in the milindapanha. Finally, the Abhidharmakosa of Vasubandhu is considered. A new concern with the mechanism of Karmic retribution becomes evident in the Abhidharmakosa.The modifications which the concept of karma is found to have undergone roughly speaking are of two broad types. First, there were popular folk developments which were accepted only reluctantly, if at all, in more scholarly circles. Then there were the more scholastic developments in the direction of greater precision of definition and refinement of categories. In the same vein, a growing scholarly concern for specific implications of the more general principle of karma is also noted.* Kewal Krishan Mittal (ed.), Perspectives on Karma and Rebirth, Delhi: Delhi University, 1990.* Ronald W. Neufeldt (ed.), Karma and Rebirth: Post Classical Developments, Albany: State University of New York, 1986.* Wendy Doniger O’Flaherty (ed.), Karma and Rebirth in Classical Indian Traditions, Berkeley: University of California Press, 1980.Book Description:Karma is perhaps the central concept in Indian Philosophy, but there is no comprehensive study of its various meanings or philosophical implications. Leading American Indologists met on several occasions to discuss their ideas about Karma. The result is this useful thought-provoking volume.* Herman W. Tull, The Vedic Origins of Karma: Cosmos as Man in Ancient Indian Myth and Ritual, Albany: State University of New York, 1989.* 1975* 197915-16* 20 2002 3 83-140.* Paul J. Griffiths, “Indian Buddhist Meditation,” Buddhist Spirituality: Indian, Southeast Asian, Tibetan, and Early Chinese, edited by Takeuchi Yoshinori, New York: Crossroad, 1995, pp. 34-66.* 2000* 2001* 2003* Stephan Beyer, “The Doctrine of Meditation in the Hªnayåna,” Buddhism: A Modern Perspective, edited by Charles S. Prebish, University Park: The Pennsylvania State University Press, 1975, pp. 137-147.* Lance Cousins, “The Origins of Insight Meditation,” The Buddhist Rorum, vol. IV, edited by Tadeusz Skorupski, London: School of Oriental and African Studies, University of London, 1996, pp. 35-58.* R. M. L. Gethin, The Buddhist Path to Awakening: A Study of the Bodhi Pakkhiyå Dhammå, Brill's Indological Library, no. 7, Leiden: E. J. Brill, 1992.* Rupert Gethin, “Chapter 7: The Buddhist Path: The Way of Calm and Insight,” The Foundations of Buddhism, Oxford: Oxford University Press, 1998, pp. 163-201, 291-294.Book Description:Buddhism is a vast and complex religious and philosophical tradition with a history that stretches over 2,500 years, and which is now followed by around 115 million people. In this introduction to the foundations of Buddhism, Rupert Gethin concentrates on the ideas and practices which constitute the common heritage of the different traditions of Buddhism (Thervada, Tibetan, and Eastern) that exist in the world today. From the narrative of the story of the Buddha, through discussions of aspects such as textual traditions, the framework ofthe Four Noble Truths, the interaction between the monastic and lay ways of life, the cosmology of karma and rebirth, and the path of the bodhisattva, this book provides a stimulating introduction to Buddhism as a religion and way of life.* Paul J. Griffiths, On Being Mindless: Buddhist Meditation and the Mind-Body Problem, La Salle: Open Court, 1986.* Winston L. King, Theravåda Meditation: The Buddhist Transformation of Yoga, University Park: Pennsylvania State University Press, 1980.* Winston L. King, “Buddhist Meditation,” Buddhism and Asian History, edited by Joseph M. Kitagawa and Mark D. Cummings, New York: Macmillan Publishing Company, 1987, pp. 331-339.* Winston L. King, “Sacramental Aspects of Theravåda Buddhist Meditation,” Numen36/2 (1989): 248-256.* Karen Lang, “Meditation as a Tool for Deconstructing the Phenomenal World,” The Buddhist Rorum, vol. III, edited by Tadeusz Skorupski and Ulrich Pagel, New Delhi: Heritage Publishers, 1995, pp. 143-159.* Donald S. Lopez, Jr., “Paths Terminable and Interminable,” Paths to Liberation: The Mårga and Its Transformations in Buddhist Thought, edited by R. E. Buswell and R. M. Gimello, Honolulu: University of Hawaii Press, 1992, pp. 147-192.* Gyana Ratna Srama, “The Doctrine of Meditation in the Påli Nikåya,”13 1999 12 95-106.* Tilmann Vetter, The Ideas and Meditative Practices of Early Buddhism, Leiden: E. J. Brill, 1988.* 1976* 16 1988 65-87.* 40 2 1992 121-126.* 14 1999 40-54.* 24 1996 195-215.* ßamatha, vipaßyanå sthåpanå, upalak≈a∫å 50 2 2002 3 148-151.* 1972 297-315.* 1985 47-55.16* 1999* 8 2004 9-49.* 1981* 1982 221-270.* 3 2002 12 7-15.* 24 1984 282-300.* 2004 149-365.* Carol S. Anderson, Pain and Its Ending: The Four Noble Truths in the Theravåda Buddhist Canon, Richmond: Curzon Press, 1999.* Steven Collins, “Nirvå∫a, Time, and Narrative,” History of Religions 31/3 (February 1992): 215-246.* Steven Collins, Nirvana and Other Buddhist Felicities: Utopias of the Pali Imaginaire, Cambridge: Cambridge University Press, 1998.Book Description:This book presents a new answer to the question: what is nirvana? Part One distinguishes between systematic and narrative thought in the Pali texts of Theravada Buddhism, looking at the place of nirvana in both. Part Two explores other Buddhist utopias and relates Buddhist utopianism to studies of European and American utopian writing. Steven Collins discusses these issues in relation to textuality, world history, and ideology in premodern civilizations, aiming to contribute to a new vision of Buddhist history that integrates the inside and the outside of texts.* Francis H. Cook, “Nirvå∫a,” Buddhism: A Modern Perspective, edited by Charles S. Prebish, University Park: The Pennsylvania State University Press, 1975, pp. 133-136.* L. S. Cousins, “Nibbåna and Abhidhamma,” Buddhist Studies Review 1/2 (1983/84): 95-109. * Louis de la Vallée Poussin, The Way to Nirvå∫a: Six Lectures on Ancient Buddhism as a Discipline of Salvation, Cambridge: Cambridge University Press, 1917.* Leon Hurvitz, “The Eight Deliverances,” Studies in Pali and Buddhism: A Memorial Volume in Honor of Bhikkhu Jagdish Kashyap, edited by A. K. Narain, Delhi: B. R. Publishing Corporation, 1979, pp. 121-169.* Lal Mani Joshi, “The Meaning of Nirvå∫a,” Studies in Pali and Buddhism: A Memorial Volume in Honor of Bhikkhu Jagdish Kashyap, edited by A. K. Narain, Delhi: B. R. Publishing Corporation, 1979, pp. 189-195.* Klaus Klostermaier, “Mok≈a and Critical Theory,” Philosophy East and West 35/1 (1985): 61-71.* David Loy, “The Difference between saµsåra and nirvå∫a,” Philosophy East and West 33/4 (October 1983): 355-365.* Bandu Madanayake, “Is There Consciousness in Nibbåna” New Paths in Buddhist Research, edited by Anthony K. Warder, Durham: The Acorn Press, 1985, pp. 17-25.* Deegalle Mahinda, “‘The Moral Significance of Buddhist Nirvå∫a: The Early Buddhist Model of Perfection,” Påli Buddhism, edited by F. J. Hoffman and M. Deegalle, London: Curzon Press, 1996, pp. 105-116.* Andrew Olendzki, “‘A Proposed Model of Early Buddhist Liberation,” Påli Buddhism, edited by F. J. Hoffman and M. Deegalle, London: Curzon Press, 1996, pp. 43-56.* George Rupp, “The Relationship between nirvå∫a and samsåra: An essay on the Evolution of Buddhist Ethics,” Philosophy East & West 21 (1980): 55-67.* Harcharan Singh Sobti, Nibbåna in Early Buddhism: Based on Påli Sources (6th B.C. to 5th A.D.), Delhi: Eastern Book Linkers, 1985.* Theodore Stcherbatsky, The Conception of Buddhist Nirvå∫a, second revised and enlarged edition, Delhi: Motilal Banarsidass Publishers, 1977.Book Description:The present book provides an English translation of Nagarjuna's chapters on Causality and Nirvana and Candrakirti's comprehensive commentary on the Sanskrit Text and presents a rare exposition of the Madhyamaka Dialectic.* Frederick J. Streng, “Nirvå∫a and Salvation,” 6/7 1990 299-314.* Guy Richard Welbon, “On Understanding the Buddhist Nirvå∫a,” History of Religions5/2 (Winter 1966): 300-326.* Guy Richard Welbon, The Buddhist Nirvå∫a and Its Western Interpreters, Chicago: The。
小学下册英语第3单元期末试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I always brush my ______ before bed.2.Plants can be ______ (修剪) for shape and health.3.I enjoy ___ (building) with blocks.4.The fish swims in the ______ (water).5.I have a toy ________ that can soar through the air.6.Water freezes at ______ degrees Celsius.7.历史上，________ (pharaohs) 是古埃及的统治者。
8.What do we call a collection of books?A. LibraryB. BibliographyC. AnthologyD. Archive答案:A Library9.How many sides does a square have?A. ThreeB. FourC. FiveD. Six10.The __________ (环境科学) informs conservation efforts.11.I have a ________ for my birthday.12.I have a favorite ________ that helps me create.13.The __________ (历史的教诲) is invaluable.14.We have a ______ (愉快的) gathering for school events.15.What is the term for a human's outer covering?A. SkinB. MuscleC. BoneD. Fat答案:A16.The color of an object is determined by the wavelengths of light it ______.17.Many flowers bloom in __________ (春天).18.The parade was very ___ (exciting).19.My friend has a pet ______ (兔子) that is very fluffy.20.What is the process of plants making their own food called?A. DigestionB. PhotosynthesisC. RespirationD. Fermentation答案:B Photosynthesis21.为下列对话选择相符的图片。
卡拉西奥多里实变函数论参考文献在深入探讨卡拉西奥多里和实变函数论之前，我们应该先了解这两个主题的基本概念。
卡拉西奥多里（Carathéodory）是20世纪著名的希腊数学家，他在实变函数论领域做出了重要贡献。
实变函数论是数学分析中的一个重要领域，研究的是实数域上的函数的性质和性质。
在本文中，我们将以从简到繁、由浅入深的方式来探讨卡拉西奥多里和实变函数论这两个主题。
我们将介绍卡拉西奥多里的生平和学术成就，然后深入探讨实变函数论的基本概念和重要定理。
我们将分析卡拉西奥多里对实变函数论的影响，探讨他对该领域的重要贡献。
我们将总结和回顾本文的内容，共享个人对这两个主题的理解和观点。
一、卡拉西奥多里简介卡拉西奥多里（1873-1950）是一位具有希腊和德国血统的数学家，他在数学分析、复变函数论和实变函数论等领域做出了杰出的贡献。
他曾在德国、俄罗斯和希腊等国家任教，是一位颇具国际影响力的学者。
他对复变函数论和实变函数论的研究成果为这两个领域的发展做出了重要贡献。
二、实变函数论基本概念实变函数论是数学分析中研究实数域上的函数的性质和性质的一个重要分支。
它涉及到实数域上的函数序列、级数、连续性、导数、积分等内容。
实变函数论的基本概念包括实数、实函数、集合论、度量空间、拓扑空间、测度论等知识。
在实变函数论中，有一些重要的定理，如连续映射的性质、一致收敛的性质、傅里叶级数的收敛性等。
三、卡拉西奥多里对实变函数论的贡献卡拉西奥多里在实变函数论领域进行了深入的研究，他提出了许多重要的理论和定理。
其中，卡拉西奥多里收敛定理是他最为著名的成果之一。
这个定理在实变函数论和复变函数论中都有重要的应用。
卡拉西奥多里还对测度论、拓扑空间、可测函数等问题做出了深刻的研究，为实变函数论的发展做出了重要贡献。
四、总结和回顾通过对卡拉西奥多里和实变函数论的深入探讨，我们对这两个主题有了更加全面、深刻和灵活的理解。
卡拉西奥多里作为一位杰出的数学家，在实变函数论领域做出了重要贡献，他的成果对后人的研究产生了深远的影响。
小学下册英语第2单元测验卷(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The _____ (叶片) are essential for photosynthesis.2.The flowers are ___ (pretty/ugly).3.What do cows give us?A. EggsB. WoolC. MilkD. Honey4.I like to challenge myself with my ________ (玩具名称).5.What is the opposite of "up"?A. DownB. LeftC. RightD. In答案:A6.I like to collect _______ from nature (我喜欢从大自然中收集_______).7.The marmoset is a type of _________ (猴子).8.I want to _____ (sing/dance) at the party.9.What is the opposite of "hot"?A. WarmB. ColdC. CoolD. Spicy答案:B10.Many plants like to _______ under the sun.11.My sister is my sweet _______ who always cheers me up.12.The bird flies in the ______.13. A ______ (森林) is full of diverse trees and plants.14.What do you call the place where you can watch movies?A. TheaterB. CinemaC. AuditoriumD. Gallery15.The chemical symbol for rhenium is ______.16.Matter can exist in different states, including solid, liquid, and ________.17.What is the main color of a stop sign?A. BlueB. GreenC. YellowD. Red答案:D18.We will _______ (go) to the zoo next week.19.I love to ______ (了解) new cultures.20.I can ______ (对话) in English.21.What is the capital city of Trinidad and Tobago?A. Port of SpainB. San FernandoC. ScarboroughD. Arima22.What is your favorite __________?23.I like to create ________ (幻影) with shadows using a flashlight. It’s a fun________ (游戏).24.The __________ is a part of the plant that anchors it to the ground.25.The ________ (蔬菜) garden is fresh and green.26.I always try to be ______ (诚实) and tell the truth. Honesty is very ______ (重要的) in friendships.27.What is the opposite of tight?A. LooseB. FirmC. StiffD. Rigid28.The _____ (海豹) is often found in cold waters.29.How do you say "good night" in French?A. Bonne nuitB. Buenas nochesC. BuonanotteD. Dobranoc30.What do you call a person who studies the environment?A. EcologistB. BiologistC. ChemistD. Physicist31.Which animal is known for its stripes?A. LionB. ZebraC. ElephantD. Bear答案:B32.What is the capital of China?A. ShanghaiB. BeijingC. Hong KongD. Taipei答案:B33.My teacher is very __________ (鼓励的).34.What is the name of the largest mammal in the world?A. ElephantB. Blue WhaleC. GiraffeD. Hippopotamus答案:B35.What is the term for a baby chicken?A. PuppyB. KittenC. ChickD. Calf36.The __________ (生态平衡) is vital for health.37.The __________ can indicate the presence of ancient life forms in rock.38.What is the capital of Brunei?A. Bandar Seri BegawanB. Kuala BelaitC. SeriaD. Tutong答案:A39. A __________ contains two or more elements chemically combined.40.What do we call the process of changing from a liquid to a solid?A. MeltingB. FreezingC. BoilingD. Evaporating答案:B41.We eat _____ (dinner/breakfast) in the evening.42.The puppy is _______ (sleeping) on my lap.43.I want to _____ (become/learn) a teacher.44.What do you call a scientist who studies the brain?A. PsychologistB. NeurologistC. PsychiatristD. Biochemist答案:B45.What is the name of the famous Italian city known for its canals?A. VeniceB. RomeC. FlorenceD. Milan答案:A46. A mixture can be separated by physical ______.47.The kangaroo can jump over _______ (障碍物).48.The teacher is ______ the students about history. (teaching)49.小青蛙) sings a ribbit song. The ___50.The fish swim in the ______.51.I enjoy ______ (和家人一起玩).52.Which vegetable is orange and long?A. PotatoB. CarrotC. BroccoliD. Spinach答案:B53.What is the capital of Egypt?A. CairoB. AlexandriaC. GizaD. Luxor答案:A54.What is the name of the famous battle fought in 1776?A. Battle of Bunker HillB. Battle of SaratogaC. Battle of YorktownD. Battle of Gettysburg答案:A55.What do we call water in a solid state?A. LiquidB. GasC. IceD. Steam56.The discovery of penicillin was made by __________ (亚历山大·弗莱明).57.Did you see the _____ (小鸟) taking a bath?58.We enjoy ______ (taking) walks in the park.59.The ________ was a key document in the establishment of the United Nations.60.What is the term for the point in a planet's orbit that is farthest from the sun?A. AphelionB. PerihelionC. ApsisD. Focus61.What is the smallest unit of life?A. OrganB. TissueC. CellD. Organism答案:C62.The children are _______ (在户外玩).63. A chemical equation must be balanced to comply with the law of ______.64.We have a _____ (慶祝) for the new year.65.My dad enjoys going to the ____ (beach).66.中国的________ (art) 包括书法、绘画和雕塑。
1For more of the historical background, see e.g. Niiniluoto (1999b), Sluga (1999), Wole ski and Simons (1989).2 But one should not exaggerate the amount of set theory needed. Relatively little suffices.For example, if the object language is the language of first-order arithmetic (i.e., that of PA), the relatively weak and predicative subsystem of second-order arithmetic ACA is sufficient. Tarski certainly thought that this much set theory is quite unproblematic, especially when compared to the semantical notions in question.Panu RaatikainenTRUTH, CORRESPONDENCE, MODELS,AND TARSKIIn the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation,definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition,more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that the syntax of the object language is specified exactly enough, and that the metatheory has a certain amount of set theoretic power,2 one can explicitly define truth in the object language. And what can be explicitly defined can be eliminated. It follows that the defined concept cannot give rise to any inconsistencies (that is, paradoxes). This gave new respectability to the concept of truth and related notions. Nevertheless, philosophers’ judgements on the nature and philosophical relevance of Tarski’s work have varied. It is my aim here to review and evaluate some threads in this debate.108PANU RAATIKAINEN1. Early Tarski and Model TheoryIt has been common (see e.g. Vaught 1974; 1986) to trace the key notion of model theory, the satisfiability-in-a-structure, or truth-in-a-model, back to Tarski’s seminal paper “The concept of truth in formalized languages” (Tarski 1935, henceforth CTFL), and more generally, to associate Tarski’s contribution to the theory of truth with model theory. Wilfrid Hodges (1986), however, reports “a disconcerting experience” while reading CTFL to see what Tarski says about the notion of truth-in-a-structure: “The notion was simply not there.” According to Hodges, it appears in Tarski’s writings only in the 1950s. In agreement with Hodges, Peter Milne (1999) adds that even then Tarski was reluctant to use the term “truth” in the model-theoretic context (see also Feferman 2004).Ilkka Niiniluoto has repeatedly expressed his disagreement, and suggested that Tarski’s early account can be seen as a special case of the model-theoretic approach (Niiniluoto 1994; 1999a; 1999b; 2004). Niiniluoto refers to Tarski’s remark, in CTFL, which mentions “the Göttingen school grouped around Hilbert” and recognizes the relative notion of a “correct or true sentence in an individual domain a” (Tarski 1935, p. 199). Niiniluoto also proposes that in his paper on logical consequence from the same period (Tarski 1936), Tarski clearly presupposes the general concept of truth-in-a-model when he writes: “The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X” (Tarski 1936, p. 417).Solomon Feferman (2004) goes even further. He suggests that the notion of truth-in-a-structure is present implicitly already in Tarski’s 1931 paper on definability, since Tarski’s explication of the concept of definability-in-a-structure makes use of satisfaction. Feferman points out that in a footnote to the introduction to this paper Tarski says of the metamathematical definition that “an analogous method can be successfully applied to define other concepts in the field of metamathematics, e.g., that of true sentence or of a universally valid sentential function” (Tarski 1931, p. 111, fn1). Universal validity can, Feferman adds, only mean valid in every interpretation, and for that the notion of satisfaction-in-a-structure is necessary. Feferman also presents an impressive body ofTRUTH, CORRESPONDENCE, MODELS, AND TARSKI109 evidence that Tarski, just like the early model-theorists who preceded him, had been working comfortably with the informal notion of model at least since 1924.A somewhat related debate has now been going on in the literature on Tarski’s account of logical consequence. Namely, John Etchemendy (1988; 1990) has criticized Tarski for advancing a fixed-domain conception of logical consequence (i.e., the idea that all models share a single domain), which creates all sorts of problems. Gila Sher (1991; 1996), Mario Gómez-Torrente (1996; 1998; 1999), and Greg Ray (1996) have all suggested a more charitable interpretation of Tarski and have proposed that Tarski just could not have intended such an implausible conception. Scott Soames (1999) refers to these replies approvingly.Timothy Bays (2001), in turn, argues that Tarski definitely adhered to a fixed-domain conception, but also that it does not cause any of the problems which both Etchemendy and his critics assume it causes. Bays’ arguments are quite persuasive. Recently Paolo Mancosu (2006) has offered new arguments to show that Tarski indeed upheld a fixed-domain conception of model in his 1936 logical consequence paper and that he was still propounding that view in 1940. In particular, he provides new evidence from an unpublished lecture by Tarski from 1940 which shows very clearly that Tarski even then held a fixed-domain conception.To recap, evidently Tarski was, to some extent, thinking in model-theoretical terms and had some kind of notion of truth-in-a-model from early on. However, his early (pre-1950s) view was not quite the full-blooded model-theoretical view with variable domains, for it now seems clear that Tarski held onto the fixed-domain conception for quite some time. At best, Tarski may not have always succeeded, in his mathematical work, to be completely faithful to this official view of his. And contrary to appearances, even in his logical consequence paper (Tarski 1936), Tarski did not yet have a wholly general notion of truth-in-a-model (as e.g. Niiniluoto (1994; 2004) seems to suggest).Nevertheless, one may grant that whatever is really original in Tarski’s formal definition of satisfaction was already there in the 1930s, even if, at the time, the satisfying sequences were picked up from a single comprehensive universe (although, one may think that even there, Tarski was really “belaboring the obvious” and that the definitions of satisfaction and truth are “practically forced on us”; see Feferman 2004).110PANU RAATIKAINENThe relativization of this notion to arbitrary domains was, once one gave up the philosophical obstacles to it, certainly a routine move.2. The Concept of Truth and Truth-in-a-modelBut what is, more exactly, the relation of Tarski’s work on truth to model theory? In modern model theory, the standard approach is now the following: Given a language L and a structure W with a domain D, one fixes an interpretation function I which maps the non-logical symbols of L to elements of D (that is, the function I maps individual constants to elements of D, predicates to subsets of D, etc.). Consequently, an L-structure W is often defined as a pair (D,I), consisting of the domain D and the interpretation function I. In such a model-theoretic setting, a language L is completely a uninterpreted and syntactic formal language. Niiniluoto adds that “an interpreted language could be defined as the pair (L,I)” (Niiniluoto 2004, p. 64).Tarski’s approach to truth differs from such a model-theoretic approach in several important respects. We have already discussed Tarski’s early commitment to a single and fixed comprehensive universe. This is, of course, quite different from modern model theory, where one is free to choose any arbitrary set as the domain. But there are also other differences.In model theory, languages are uninterpreted, and when a model is switched to another, one varies the interpretation, but the language remains the same. In his writings on the concept of truth, Tarski, on the other hand, repeatedly insisted that the ‘formalized’ languages whose truth is under consideration were, and had to be, always already interpreted languages:It remains perhaps to add that we are not interested here in ‘formal’ languages and sciences in one special sense of the word ‘formal’, namely sciences to the signs and expressions of which no meaning is attached. For such sciences the problem here discussed has no relevance, it is not even meaningful. We shall always ascribe quite concrete and, for us, intelligible meanings to the signs which occur in the languages we shall consider. (Tarski 1935, pp. 166 167)TRUTH, CORRESPONDENCE, MODELS, AND TARSKI111I should like to emphasize that, when using the term ‘formalized languages’, I donot refer exclusively to linguistic systems that are formulated entirely in symbols, and I do not have in mind anything essentially opposed to natural languages. On the contrary, the only formalized languages that seem to be of real interest are those which are fragments of natural languages (fragments provided with complete vocabularies and precise syntactical rules) or those which can at least be adequately translated into natural languages. (Tarski 1969, p. 68)Furthermore, this was not just an accidental philosophical opinion from Tarski’s side, but it is an essential part of Tarski’s whole approach to truth that the meanings of the object language must be fixed. Only that way can a truth definition (applied to sentences) make any sense at all:[W]e must always relate the notion of truth, like that of a sentence, to a specific language; for it is obvious that the same expression which is a true sentence in one language can be false or meaningless in another. (Tarski 1944, p. 342)We shall also have to specify the language whose sentences we are concerned with;this is necessary if only for the reason that a string of sounds or signs, which is a true or a false sentence but at any rate meaningful sentence in one language, may be a meaningless expression in another. (Tarski 1969, p. 64)[T]he concept of truth essentially depends, as regards both extension and content, upon the language to which it is applied. We can only meaningfully say of an expression that it is true or not if we treat this expression as a part of a concrete language. As soon as the discussion concerns more than one language the expression ‘true sentence’ ceases to be unambiguous. If we are to avoid this ambiguity we must replace it by the relative term ‘a true sentence with respect to the given language’. (Tarski 1935, p. 263)Therefore, it is necessary in Tarski’s setting to focus on an interpreted language with constant meanings. If one changes the interpretation of the symbols of the object112PANU RAATIKAINENlanguage, the language changes to a different language, and a former truth definition is not a truth definition for this latter language.Can this difference be overcome by following Niiniluoto’s above-mentioned suggestion that an interpreted language is defined as the pair (L,I)? Now although this idea works perfectly in the ordinary model-theoretic context, I do not think that it is an acceptable line to take in a Tarskian approach to truth. Namely, Tarski expressedly aimed to define truth (or, rather, “true-in-L”) without assuming any semantic notions:“In this construction [of the definition of truth] I shall not make use of any semantical concept if I am not able to previously reduce it to other concepts” (Tarski 1935, p. 153). The interpretation function I, however, establishes a link between the language and a domain of extra-linguistic objects, and hence is a semantical concept in Tarski’s sense (see also below). Hence, it would be problematic to presuppose it in the definition of truth. Although Tarski assumed that the object language must be an interpreted language, its interpretation cannot be specified by leaning on the model-theoretic interpretation function.But the question then arises how Tarski can, and indeed can he, specify the object language as an interpreted language with meanings, without begging the question. Rudolf Carnap, in his logical semantics, assumed that the interpretation of the object language is fixed with the help of truth conditions, which in turn appeal to the definition of truth. Whether this makes Carnap’s approach viciously circular or not, it is important to note that this is not Tarski’s approach. Tarski here explicitly points out the difference between his own approach and that of Carnap (see Tarski 1944, p. 373, note 24). For Tarski, the interpreted object language is instead specified simply through its metalinguistic translation (see e.g. Tarski 1935, pp. 170 171; cf. Fernández Moreno 1992; 1997; Milne 1997; Raatikainen 2003; Feferman 2004).However, Tarski’s approach still assumes the notion of meaning, in the disguise of translation or the sameness of meaning. Does this mean that, at the end of the day, Tarski fails to achieve his aim, that is, to define truth without assuming any semantical concepts? It has been repeatedly suggested that this is indeed the case (see Davidson 1990; 1996; Field 1972; Soames 1984). But it is not necessarily so. In order to find out, we need to take a closer look on what Tarski meant by ‘semantical’. Tarski’s paradigm examples of semantical concepts were satisfaction, denotation, truth and definability (seeTRUTH, CORRESPONDENCE, MODELS, AND TARSKI113 Tarski 1935, pp. 164, 193 194; 1936, p. 401). He explained his understanding of ‘semantical concept’ as follows:A characteristic feature of the semantical concepts is that they give expression tocertain relations between the expressions of language and the objects about which these expressions speak, or that by means of such relations they characterize certain classes of expressions or other objects. (1935, p. 252)Now the model-theoretic interpretation function I discussed above is definitely a semantic notion in this sense. Hence, it would be against Tarski’s explicit commitments to assume it in defining truth. This cannot be the way in which the object language is interpreted. But how about translation? I submit that it is possible to view translation, in this context, as a purely syntactic mapping between two languages, without assuming any relations between either language and the external objects. Translation, so viewed, is not a semantical concept in Tarski’s sense. Hence, it is admissible for Tarski to presuppose it in this approach (see also Milne 1997).But let us take a closer look at the details. The interpretation, or translation, of the object language in the metalanguage is specified, in Tarski, through primitive denotation. Let us then recall how exactly Tarski specifies primitive denotation in the object language. For names, this is done by a simple list-like explicit definition such as:Denotes OL(x, y)[(x = ‘Frankreich’ & y = France)(x = ‘Deutchland’ & y = Germany)::(x = ‘Köln’ & y = Cologne)].An analogous definition can be given for the denotation (or, application) of predicates. Such an enumerative characterization of primitive denotation may be philosophically disappointing (cf. Field 1972), but at least it frees Tarski from any charge of begging the question. The interpretation of the object language is fixed through fixing primitive114PANU RAATIKAINENdenotation, which in turn can be done by explicit definitions. And what can be explicitly defined can be eliminated. Certainly Tarski’s realiance on such notions is unlikely to be problematic.3. Is Tarski’s truth definition a correspondence theory?The question of whether Tarski’s account is a version of the correspondence theory of truth or not has resulted much debate among philosophers. Karl Popper famously declared that Tarski had “rehabilitated the correspondence theory of absolute or objective truth” and “vindicated the free use of the intuitive idea of truth as correspondence to the facts” (Popper 1963, p. 223). Also, Ilkka Niiniluoto (1994; 1999a; 1999b; 2004), Gila Sher (1998) and Luis Fernández Moreno (2001) have argued that Tarski’s definition of truth is a correspondence theory.Susan Haack, among others, disagrees: “Tarski did not regard himself as giving a version of the correspondence theory” (Haack 1978, p. 114). According to Haack, Tarski’s notion of satisfaction at best “bears some analogy to correspondence theories”(ibid.). However, she adds, “Tarski’s definition of truth makes no appeal to specific sequences of objects, for true sentences are satisfied by all sequences, and false sentences by none” (Haack 1978, p. 113). A. C. Grayling (1998, p. 156) largely repeats Haack’s criticism. Earlier, Donald Davidson (1969; 1983) took Tarski’s account as a variant of correspondence theory, but later changed his mind for reasons similar to those of Haack: “[T]here is nothing interesting or instructive to which true sentences might correspond” (Davidson 1990; see also Davidson 1996).I think that the objection of Haack and others, which leans on the fact that truth amounts to satisfiability by all sequences, is less conclusive than it may appear to be. To begin with, one can define truth for atomic sentences without the notion of satisfaction. In their case, it is particular individuals and their properties and relations which make a sentence true (cf. Niiniluoto 1999a; 2004). Further, I think that even in the case of quantified sentences the situation is not as desperate as Haack and others suggest. To be sure, a sentence is true if and only if it is satisfied by every sequence of objects. However, this is more a consequence of a technical trick Tarski used in his definition of satisfaction in order to handle quantification.TRUTH, CORRESPONDENCE, MODELS, AND TARSKI115 Namely, let us consider, for example, the existentially quantified sentence ( x1)P(x1), and let us assume that the intended interpretation of P(x) is, say: “x is a Ph.D. student of Le niewski”. According to Tarski’s definition of satisfaction, a sequence satisfies ( x1)P(x1) if and only if some sequence , which agrees with except possibly at the variable x1, satisfies P(x1). The only sequences that will do (i.e., satisfy P(x1)) are ones which have Tarski as their first member.3 Moreover, the rest of the sequence is irrelevant and could be omitted (Tarski assumed, for simplicity, that all such satisfying sequences are infinite; but it is well known that one could manage with just finite sequences; in such a case, the finite sequence with Tarski as its first and only member would be the only relevant sequence ). Hence, it is quite plausible to consider Tarski, and nothing else, as the “truth-maker” of the existentially quantified sentence ( x1)P(x1), even if the sentence is, according to the technical definition of satisfaction, satisfied by every sequence of objects. Given an arbitrary sequence , we are, so to say, allowed to switch its relevant member (here, the first member) to a relevant object (here, only Tarski is suitable) and produce a sequence which does the real work.But the question of whether Tarski’s account is a full-blown substantial correspondence theory of truth, in contradistinction to deflationist views on truth, is different and more complicated. Part of the difficulty is, of course, that it is not altogether clear what exactly is the essence of deflationism. For example, Stephen Leeds (1978), Paul Horwich (1982) and Scott Soames (1984) have all suggested that Tarski’s truth definition amounts in fact to a deflationary theory of truth (cf. Davidson 1990). As we have already seen, Fernández Moreno, Niiniluoto and Sher, for example, disagree and argue that it can be instead seen as a correspondence theory.It is useful to distinguish, in this context, between weak and strong correspondence theories (Wole ski & Simons 1989), or, correspondence-as-congruence and correspondence-as-correlation (see Kirkham 1992, p. 119). According to the weak correspondence theories or correspondence-as-correlation views, every truth-bearer is correlated to a state of affairs, and if that state of affairs to which a given truth bearer is correlated actually obtains, the truth bearer is true; otherwise it is false. The strong correspondence3 Tarski was Le niewski’s one and only Ph.D. student.116PANU RAATIKAINENtheories, or correspondence-as-congruence views, require further that there is a structural isomorphism between truth bearers and the facts to which they correspond, if true; a truth bearer mirrors or pictures the state of affairs to which it is correlated. Nothing of the sort is assumed by the former, weaker idea of correspondence. According to it, a truth bearer as a whole is correlated to a state of affairs as a whole. Weak correspondence involves only the idea that truth depends on how things are in the world.Jan Wole ski and Peter Simons (1989) submit that Tarski’s theory is a correspondence theory only in the weak (or correlation) sense. Sher (1998), on the other hand, argues that it is a correspondence theory even in the strong sense (or this is at least how Patterson (2003) interprets her). Niiniluoto (1999a; 2004) in turn argues that in the case of atomic sentences, Tarski’s theory is a strong correspondence theory, but with compound and quantified sentences, only a weak correspondence theory.But what are the grounds for thinking that Tarski’s truth definition really is a version of correspondence theory? Popper (1960, p. 224) seems to think that T-sentences state correspondences between sentences and worldly facts. Similarly, Niiniluoto writes that a T-sentence “states something about the relation between the language L and the world”, and hence, “Tarski’s semantic definition of truth is not merely disquotational” (Niiniluoto 1994, p. 63). Also Sher (1998) makes analogous claims. So did Davidson at one point (Davidson 1983; but see Davidson 1969; 1990).But, as Douglas Patterson (2003) points out, if it is assumed that T-sentences as such state correspondences between the sentences they mention and something extra-linguistic, then even deflationary and disquotational theories are correspondence theories, at least in the weak sense. This, however, is far too weak a notion of correspondence to be of any interest if we wish to understand what is at issue between contemporary deflationists and their correspondence theoretic opponents. Only strong correspondence theories will be interesting from this perspective, Patterson concludes. One must agree with Patterson’s main point. However, contrary to what he may seem to suggest, having a genuine and substantive correspondence theory does not necessarily require a general strong or congruence view of correspondence.4 The two distinctions4 For example, a broadly Tarskian theory supplemented with a substantial theory of reference along the lines that Field has suggested (mentioned at the end of this paper) is agreedTRUTH, CORRESPONDENCE, MODELS, AND TARSKI 117by all parties to be a substantial theory of truth; however, there is no reason to think that it has to be a strong correspondence theory (correspondence-as-congruence).5 However, I don’t think that it is likely that we will ever have a strictly physicalistic theory of reference, as Field demands – but that is a wholly different and independent issue.substantial/deflationary and weak/strong (correspondence) do not coincide. Patterson also points out that T-sentences simply are not of the right form to state a relation at all,and so cannot state a correspondence relation. A T-sentence is a biconditional and does not predicate a relation between the sentence it mentions and some other objects.Michael Devitt (2001) in turn argues that although Tarski seemed to view himself as a correspondence theorist about truth, the theory he actually presented is ly, he first reminds us that – as especially Hartry Field (1972) has emphasized –Tarski’s truth definition rests on a list-like definition of primitive denotation (see also above). “But such list-like definitions are in no way explanatory, but are essentially deflationary and so could not yield anything substantial about reference.” Consequently,Devitt maintains, Tarski’s truth definition itself does not show us anything substantial about truth: “Tarski’s definition tells us a lot about ‘true-in-L’. It tells us nothing about truth-in-L because it is implicitly committed to the view that there is nothing to tell.” I think we must accept Devitt’s conclusion.However, a fix is now available. Devitt too adds that his conclusion, that Tarski’s definition tells us nothing about truth, concerns only Tarski’s definition as it stands.However, if we revised it by dropping its list-like definitions, then we could see it as yielding an explanation of truth in terms of reference, as Field points out. If this were then supplemented by a substantial theory of reference,5 we would have a genuine correspondence theory of truth, Devitt concludes. Patterson too agrees that this theory is indeed a real correspondence theory. There seems to be no question that such a modified Tarskian theory of truth is a robust and substantial correspondence theory.This move has, however, its price. One must then relax Tarski’s initial requirement that no semantical concepts are presupposed. But this just is the price one necessarily has to pay if one wants to turn Tarski’s definition into a substantial account of truth.However, unlike the more general semantical notions, primitive denotation is a very118PANU RAATIKAINENelementary notion and does not lead to any paradoxes.6 Hence, it is a rather harmless concession.University of HelsinkiAcademy of FinlandReferencesBays, T. 2001: “On Tarski on Models”,The Journal of Symbolic Logic 66, 1701 1726. Davidson, D. 1969: “True to the facts”, reprinted in D. Davidson,Inquiries into Truth and Interpretation, Oxford University Press, Oxford, pp. 37 54.Davidson, D. 1986: “A Coherence Theory of Truth and Knowledge”,Kant oder Hegel. Edited byD. Henrich, Klett-Cotta, Stuttgart, 1983, pp. 423 438. Reprinted inE. LePore (ed.),Truthand Interpretation: Perspectives on the Philosophy of Donald Davidson, Blackwell, Oxford, 1986. Davidson, D. 1990: “The Structure and Content of Truth”,Journal of Philosophy 87, 279 328. Davidson, D. 1996: “The Folly of Trying to Define Truth”,Journal of Philosophy 93, 263 278. Devitt, M. 2001: “The Metaphysics of Truth”, in Michael Lynch (ed.),The Nature of Truth, MIT Press, Cambridge, MA, pp. 579 611.Etchemendy, J. 1988: “Tarski on Truth and Logical Consequence”,Journal of Symbolic Logic 53,51 79.Etchemendy, J. 1990:The Concept of Logical Consequence, Harvard, Cambridge.Feferman, S. 2004: “Tarski’s Conceptual Analysis of Semantical Notions”, in A. Benmakhlouf (ed.),Sémantique et épistémologie,Editions Le Fennec, Casablanca [distrib. J. Vrin, Paris], pp. 79 108.Fernandez Moreno, L. 1992: “Putnam, Tarski, Carnap und die Wahrheit”,Gräzer philosophische Studien43, 33 44.Fernandez Moreno, L. 1997: “Truth in Pure Semantics: A Reply to Putnam”,Sorites 8, 15 23. Fernandez Moreno, L. 2001: “Tarskian Truth and the Correspondence Theory”,Synthese 126, 123 147.Field, H. 1972: “Tarski’s Theory of Truth”,Journal of Philosophy 69, 347 75.Gomez-Torrente, M. 1996: “Tarski on Logical Consequence”, Notre Dame Journal of Formal Logic 37, 125 151.Gomez-Torrente, M. 1998: “On a Fallacy attributed to Tarski”,History and Philosophy of Logic 19, 227 234.Gomez-Torrente, M. 1999: “Logical Truth and Tarskian Logical Truth”,Synthese 117, 375 408. Haack, S. 1978:Philosophy of Logics, Cambridge University Press, Cambridge.Hodges, W. 1985/6: “Truth in a Structure”,Proceedings of the Aristotelian Society 86, 135 151. Leeds, S. 1978: “Theories of Reference and Truth”,Erkenntnis 13, 111 127.Mancosu, P. 2006: “Tarski on Models and Logical Consequence”, in J. Gray and J. Ferreiros (eds.),The Architecture of Modern Mathematics, Oxford University Press, forthcoming. Milne, P. 1997: “Tarski on Truth and Its Definition”, in Childers, Kolár and Svoboda (eds.), Logica ’96: Proceedings of the 10th International Symposium, Filosofia, Prague, pp. 189 210. Milne, P. 1999: “Tarski, Truth and Model Theory”,Proceedings of the Aristotelian Society 99 (1998 1999), 141 167.6 The situation is, of course, very different with the general notion of denotation, which easily leads, e.g., to Berry’s paradox.。
