可拓学宣言 ——首届可拓学与创 新 方 法国际研讨会 的宣言 美国Florentin Smarandache教授在大会闭幕式 宣 读 大会通过的 ”可拓学宣言“ 可拓学宣言 环顾古今，展望中外，人类和科学技术进步的历史，几乎就是一部处理矛盾问题的历史：通过发展科学技术去解决“人类自身能力的有限性与人类需求增长的无限性之间的矛盾”，把许多看似不可能的事情变成了可能的现实。 所谓矛盾问题 , 是指在给定条件下无法实现人们期望的目标 。 在生产、经济、军事、外交、管理甚至日常生活中 , 矛盾问题无处不有。 曹冲称象、空城计、阿基米德称金皇冠等等解决矛盾问题的创意 是由聪明人冥思苦想提出来的 ，那么，能否 根据一定的程序 , 利用计算机和网络 , 帮助人们处理矛盾问题呢？ 1983 年， 中国学者蔡文在中国的《科学探索学报》发表了论文“可拓集合和不相容问题”，开启了这一新的研究方向， 称为矛盾问题智能化处理 。 30 年来，国内外一大批学者逐步聚拢，研究实现这一理想的基础工作。提出了表示天下万事、万物、信息和知识的形式化体系，用它们表示大千世界各种问题，建立了可拓模型；通过研究处理矛盾问题的规律，建立可拓理论和可拓创新方法；应用于工程、信息、经济和管理等领域，形成可拓工程。可拓论、可拓创新方法和可拓工程构成一门新学科 — 可拓学。 可拓学是用形式化模型研究事物拓展的可能性和开拓创新的规律与方法，并用于解决矛盾问题的科学。它 是矛盾问题智能化处理的基础，是沟通自然科学与社会科学的桥梁。 为了解决矛盾问题，它对数学、系统论和逻辑理论作了五方面的拓展 : ( 1 ) 拓展了数学的研究范围 . 可拓学的研究对象是矛盾问题 , 这是对数学基本研究不矛盾问题的拓展 . 为了处理矛盾问题 , 可拓学把数学 “ 研究数量关系和空间形式 ” 拓展为研究 “ 包括对象、特征和量值的逻辑细胞 —— 基元 ”, 把数学模型拓展为解决矛盾问题的可拓模型 . ( 2 ) 拓展了集合论 . 几千年的数学建立在康托集论这一基础上，但是康托集只研究对事物的静态分类，无法表达把问题从矛盾这一类转化为不矛盾的那一类。为此，可拓学中，提出了 可拓集的概念，研究变换下的分类，使集合论多样化 . ( 3 ) 拓展了逻辑理论 . 由于形式逻辑和辩证逻辑无法作为处理矛盾问题的推理工具， 可拓学研究者综合了形式逻辑形式化的长处和辩证逻辑研究事物的内涵、外延及其变化的特点 , 建立了可拓逻辑 . 它将为计算机和网络能帮助人们生产处理问题的创意建立推理工具，为人类的智力得到更好的延伸创造条件。 ( 4 ) 拓展了函数论 . 由于实变函数中“距离”的概念限制了描述解决矛盾问题的变化过程，因此， 可拓学中建立了 “ 可拓距 ”的概念, 把实变函数拓展为关联函数 , 于是 “ 类内即为同 ” 的定性描述发展为 “ 类内也有异 ” 的定量描述， 使表示处理矛盾问题的过程中事物的量变和质变有了定量化的计算公式。 ( 5 ) 拓展了系统论 . 系统论开创了根据系统性处理问题的途径。但是， 不少矛盾问题的处理利用了物的非物质性部分、潜在部分和对立部分， 它们跨越了系统论的范围， 所以， 可拓学把系统论拓展到从物质性、系统性、动态性和对立性 4 个角度研究物的结构 , 形成了共轭理论与方法 , 为研究各种奇妙谋妙计处理矛盾问题提供了依据。 （6）拓展了方法论 可拓学研究者依据可拓论，建立了可拓创新方法体系，对方法论做了较大的拓展，可拓创新方法用于处理各色各样的矛盾问题，也用于产生各种各样的新产品、新技术和新方法的构思，产生具有独特创新产权的技术和软件。 由于这些拓展，出现了可拓数学、共轭理论、可拓逻辑、可拓策略生成、可拓数据挖掘和管理可拓工程等新的分支，可拓学正逐步向建设新兴的学科群前进。 各行各业都要遇到形形色色的矛盾问题，各种新产品、新项目和新技术也都是为解决矛盾问题而提出的。因此，可拓学研究者提出了新的方法论，形成了可拓创新方法体系，为各个领域处理矛盾问题提供理论与方法，也必然为用计算机帮助人们构思新产品提供方法和技术 。 回顾科学技术和工业革命发展的历史，可以看到：第一次工业革命中蒸汽机和纺织机等机器的使用是人手的延伸；第二次工业革命中汽车和火车的行驶是人腿的延伸；电话是耳朵的延伸 ；电视是眼睛的延伸，计算机和网络是人脑部分功能的延伸，而矛盾问题智能化处理则是人类智力（解决问题的能力）的延伸。 可拓学 为人类智力的延伸开展了基础研究。 30 年来，可拓学的研究已经从一个人发展为一支国内外研究队伍，从一篇文章发展成一门新学科，从中国发展到世界。这是一门哲学、数学和工程学交叉的学科，从应用范围看，它与信息论、控制论和系统论一样，是一门应用范围广泛的横断学科。 我们为这门学科的问世和发展而欢呼！ 成功之杯，往往踞于布满荆棘的荒野尽头，期间没有任何现成的路可走。倘若畏缩、不愿做出牺牲，势必永远在荒野之中徘徊。只有百折不挠、甘愿忍辱负重的人，才能在这里开拓出一条路来。 可拓学研究者已经开拓出通往矛盾问题智能化处理之路，今后 将继续努力，向老学科的科技工作者学习，与各界人士一起，发展矛盾问题智能化处理的研究，使可拓学更加完善，朝着国际化、社会化和网络化的方向前进；使计算机和网络能帮助人类处理问题，实现人类智力的拓展。 首届可拓学与创新方法国际研讨会 2013 年8月18日 Declaration ofExtenics Throughoutthe ancient and modern, the history of human and technological progress, bothat home and abroad, is almost a history of dealing with contradictory problems:solve the “contradiction between the limit of human ability and theunlimitedness of human demand growth” through the development of science andtechnology and change many seemingly impossible things into possible realities. Contradictionmeans that people’s goals cannot be reached in current conditions. They existin production, economy, military, diplomacy, management and even the dailylife. Contradictions are ubiquitous. The ideas to solve contradictions, e.g.,Cao Chong weighing an elephant, empty fort strategy, Archimedes weighing thegold crown, etc., are put forward by smart people after thinking hard, so is itpossible to utilize the computer and network according to certain programs tohelp people deal with contradictory problems? In1983, Chinese scholar Cai Wen published the paper “Extension Set andNon-compatible Problems” in China’s Science Exploration Journal, whichinitiated this new research direction called the intelligent management ofcontradictions. For 30 years, a large number of scholars gradually gatheredfrom home and abroad to study the basic work to achieve this ideal. They putforward the formalized system to represent everything and information andknowledge in the world, represent various contradictory problems in the worldwith them and built the extension models; established the extension theory andextension innovation methods by studying the rules to deal with contradictoryproblems; applied it to the fields of engineering, information, economy andmanagement and formed the extension engineering. Extension theory, extensioninnovation methods and extension engineering methods and technology constitutethe new subject, Extenics. Extenics is ascience that studies the possibility of matters’ extension and the rules and methodsof innovation with formalized models and solves contradictory problems . Itis the basis of the intelligent management of contradictory problems and thecommunication bridge between natural science and social science. In order tosolve contradictory problems, it has extended mathematics, system theory andlogic theory in five aspects: (1)It has extended the study scope of mathematics. The research objects of Extenicsare contradictory problems, which is an extension of mathematics that basicallystudies compatible problems. In order to deal withcontradictory problems, Extenicsextends the mathematical “study on quantitative relation and space form” to the“study on logic cells of, including, subject, character and quantityvalue—element” and extends mathematical models to extension models that solve contradictoryproblems. (2)It has extended the set theory. The thousands of years of mathematics is builton the basis of cantor set theory, however, cantor set only studies the staticclassification of things but cannot express how to transform problems from theclass of incompatibility to the that of compatibility. Therefore, Extenics putsforward the concept of extension set, studies the classification undertransformation and diversifies the set theory. (3)It has extended the logic theory. Because formal logic and dialectical logiccannot be reasoning tools to solve contradictory problems, Extenics researcherscombined the formalized strengths of formal logic and the connotation,extension and change characteristics of dialectical logic in study of thingsand established the extension logic. It will build reasoning tools to enablecomputer and network to help with people’s creativity in solving contradictionsin production and create conditions for better extension of human intelligence. (4)It has extended the function theory. The concept “distance” in real variablefunction limits the change process that describes contradictory problems, so Extenicsestablished the concept “extension distance” and extended real variablefunction to dependent function, therefore the qualitative description“intra-class sameness” developed to “intra-class variation”, as a result ofwhich, thing’s quantitative change and qualitative change which represent theprocess to solve contradictory problems have quantified calculation formula. (5)It has extended the system theory. System theory built the approach to solve contradictoryproblems systematically. However, the solving of a lot of contradictoryproblems utilized the non-material part, potential part and opposite part ofobjects, which have spanned the scope of system theory, so Extenics hasextended the system theory to the study of object structure from fourperspectives, namely the materiality, systematization, dynamism andcontrariety, formed conjugate theory and methods, which provide the basis forresearching various ideas to solve contradictory problems. Becauseof these extensions, new branches like extension mathematics, conjugate theory,extension logic, extension strategy generating system, extension data miningand management extension engineering, etc., have come into being. Extenics isgradually advancing towards constructing emerging group of subjects. Allwalks of life will encounter various contradictory problems. All sorts of newproducts, new projects and new technologies are also put forward to solve contradictory problems. Extenics researchers, therefore, put forward newmethodology and formed extension innovation method system to provide theory andmethod for different fields to solve contradictory problems and will inevitablyprovide methods and techniques for helping people conceiving new products withcomputer. Lookingback at the development history of science and technology and industrial revolution,we find: the use of machines, such as steam engine and textile machine, etc.,in the first industrial revolution was the extension of human hands; the motionof automobiles and trains in the second industrial revolution was the extensionof the human legs; telephone was the extension of ears; television was theextension of eyes; computer and network were the extension of part functions ofhuman brain; and the intelligent management of contradictory problems is theextension of human intelligence (problem solving ability). Extenics carries outbasic research for extension of human intelligence. For30 years, the research of Extenics has developed from a person into a domesticand overseas research team, from an article into a new subject and from Chinato the world. This is a subject crossing philosophy, mathematics andengineering. Seeing from the application scope, like the information theory,cybernetics and system theory, it is a cross subject with a wide range ofapplication. Wecheer for the emergency and development of the subject! The cup ofsuccess often locates at the end of wilderness strewn with thorns and there isno existing road to follow. Those cower or are unwilling to make sacrificeswill always wandering in the wilderness. Only indomitable ones who can endurevarious hardships can carve out a new way here. Extenicsresearchers have carved out the way to intelligent management of contradictoryproblems and will continue to work hard, learn from scientific andtechnological workers of old subjects, together with people from all circles oflife, develop the research of intelligent management of contradictory problems,further improve Extenics and move towards internationalization, socializationand networking; enable the computer and network to help the mankind deal withproblems and realize the extension of human intelligence. InternationalSymposium on Extenics and Innovation Methods On August 18,2013
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