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标题: 我来说说形式逻辑 [打印本页]
作者: qqyou    时间: 2009-3-26 17:39
标题: 我来说说形式逻辑
估计这个话题会有不少的争议了，不过还是说说吧

我在很多有关学数学的帖子里，都能看到大家说，培养孩子的数学逻辑能力很重要，似乎这是一个共识了。但是我问问身边的人，却很少有人知道这个数学逻辑能力是什么，包括很多做数学老师的，居然也说不明白。这就奇怪了，都不知道什么是数学逻辑能力，又怎么去培养呢？又怎么知道如何去培养呢？大约大家都认为，孩子数学题做多了，这种能力自然就有了，那干脆就培养做题能力就是了。

曾经有朋友发短消息问我，是不是坛子里的谁谁。大家都这么问，大约是我写字的风格、我的一些想法、思维方式、观点等，都和那位谁谁很相似。尽管我不是谁谁，但我有理由认定那位谁谁一定和我一样是学数学出身的。因为大多数学数学的人，认识事物的方式，大约和普通的人会有所差异，这可能就是使用形式逻辑思维的缘故吧。

所以我在前面那篇说奥数的帖子里，特意的说了这点。所谓数学逻辑能力，就是形式逻辑能力。能形式逻辑的教育，在我们的教育里是缺失的！

说起形式逻辑来，不由得还要说到辩证法。我们每一个人都学过辩证法，但是非常遗憾地说，我们学的也不是马克思的真正辩证法，马克思的辩证法里，和形式逻辑根本不完全矛盾，甚至有继承的关系。可惜我们学的是中国化的辩证法，这种所谓的辩证法里，充满了对形式逻辑的批判和否定。

说这个问题，我又不得不说到历史和文化。实际上我多少年前就一直在思考，为什么中国几千年的历史，居然没有产生形式逻辑，以至于一个先进的农业国家，在近代远远落后于西方各国了。年轻的时候曾经有过多种想法，包括一些政治的因素。

但是随着年龄的增长、各种中外知识的不断学习和长进，我现在觉得我已经搞明白这个问题了。问题的根结在于文化。

逻辑是什么？逻辑实质上是一种争论的技术。

中西文化差在了哪里呢？西方是基督教文化，他们信奉有上帝。人和上帝是什么关系呢？实际上是一种契约的关系，比如大家都知道的《旧约》，《新约》，都是人和上帝的一种契约。人和上帝的纠纷就在于人是否遵守了这些契约，因而就有了争论，伴随着这种争论，就会产生形式逻辑。中国古代没有类似上帝的神，他们的主宰者是皇帝，同样和我们一样也是一个人，因而就没有什么契约。所有的争论都是围绕着皇帝的好恶进行的，皇帝说的话就是真理，诸子百家所做的就是揣度帝王的想法，然后把哪怕不合理的也要解释为合理，这就是所谓的中国的哲学，中国的辩证法。

所以不同的文化，就导致了中国没有为追寻真理而产生的形式逻辑的发展，而留下来的都是为帝王辩护的，不合乎基本逻辑的所谓中国的辩证法思想，那就是无论怎么论，都要论证出帝王或者先贤的唯一正确。

这种文化影响了我们几千年，直至今世。

形式逻辑说复杂也复杂，说简单也简单，我会慢慢地在这个楼里，尽量的把我认识到形式逻辑的一些东西和大家一起讨论吧。

[ 本帖最后由 qqyou 于 2009-3-26 17:40 编辑 ]
作者: hubaichun    时间: 2009-3-26 18:08
书读的少有弊端，多是有感而发，感性的东西不一定可靠。
看来要多学习啦，收藏楼主的精品贴，慢慢研读。
形式逻辑这个说法真是今天在数学贴里才第一次听到。
希望楼主多出些新颖的文章。
作者: qqyou    时间: 2009-3-26 18:09
标题: 1、先说说矛盾不是矛盾
因为我不写书，所以我觉得没必要按照形式逻辑课本里的顺序来说了，按照我自己的思路，说到哪里是哪里吧

第一篇我先来说说矛盾这个概念，所以想了上面的那个题目，就叫做矛盾不是矛盾。

矛盾不是矛盾这又何从说起呢？那就从矛盾这个词的由来说起吧。

古代有个故事，大家恐怕没有一个人不知道的，那就是韩非子的《自相矛盾》
楚人有鬻盾与矛者，誉之曰：“吾盾之坚，物莫能陷也。”又誉其矛曰：“吾矛之利，于物无不陷也。”或曰：“以子之矛陷于之盾，何如？”其人弗能应也。夫不可陷之盾与无不陷之矛，不可同世而立


卖矛和盾的人有两个命题：
命题A：我的盾很坚固，（任何）武器都刺不破（它）
命题B：我的矛很锐利，对于（任何）武器没有不能刺穿的

这应该是矛盾这个词的由来，至此以后就管这类事情在逻辑上叫做自相矛盾了。

后来日本人也学去了，也这么用。后来日本引进西方逻辑学的时候，大约是最初的人没有学明白，于是就用矛盾两个去翻译Contradiction这个亚里斯多德的形式逻辑学里的词汇了。后来新文化运动，我们的学者就把这个词汇，又从日本哪里给借鉴回来了，于是中国人也把Contradiction翻译成矛盾。

可惜的是，上面的这A、B两个命题，在形式逻辑里，不是矛盾关系，他们的关系是另外一个词，叫做Contrariety，我们把这个关系翻译为相反，或者叫反对关系。

看看是不是很讨厌，矛盾这个词的源头，说的不是矛盾而是相反，这就是我这个题目的由来。

[ 本帖最后由 qqyou 于 2009-3-27 10:11 编辑 ]
作者: qqyou    时间: 2009-3-26 18:14
原帖由 hubaichun 于 2009-3-26 18:08 发表
书读的少有弊端，多是有感而发，感性的东西不一定可靠。
看来要多学习啦，收藏楼主的精品贴，慢慢研读。
形式逻辑这个说法真是今天在数学贴里才第一次听到。
希望楼主多出些新颖的文章。


你太客气了，尽管这个词大家很少听说，但我们以前做数学题都是用的这个方法，所以大家都已经掌握了很多了。

目前国内很多这方面的书，都起名字叫数理逻辑，但数理逻辑只是形式逻辑的一个子集。

名字叫《形式逻辑》的书里，多不会忘了腔调说这是一种科学的方法，因为怕大家知道，实际上这也是一个哲学的方法。

哈，多少年遗留的问题呀。
作者: pianocrazy    时间: 2009-3-26 19:42
我大学时学过形式逻辑，教材用的是金岳霖的书。现在回想起来，这门课学了和不学没有什么差别，因为我根本就没有认真读过教材，更不要说其他相关文献了。

今天有机会聆听qq的讲座，真是令我好感动。
作者: fgcp102    时间: 2009-3-26 20:11
在这方面缺少教育，谢谢阿Q开讲座，最好再推荐几本书。
作者: wyh2000    时间: 2009-3-26 20:19
没学过
认真听课
希望能听懂
作者: qqyou    时间: 2009-3-26 20:24
原帖由 fgcp102 于 2009-3-26 20:11 发表
在这方面缺少教育，谢谢阿Q开讲座，最好再推荐几本书。


推荐书，对我有点难，我也是很多年以前学的，最近也没太了解是否有什么新的书，哈。
作者: qqyou    时间: 2009-3-26 20:40
原帖由 wyh2000 于 2009-3-26 20:19 发表
没学过
认真听课
希望能听懂


客气了，希望我能说明白
作者: jiangying    时间: 2009-3-26 21:47
疑问.矛盾的命题又是什么呢?

命题A：我的盾很坚固，（任何）武器都刺不破（它）
命题B：我的矛很锐利，对于（任何）武器没有不能刺穿的


下面这两组命题又是什么关系呢?
命题A：我的盾很坚固，（任何）武器都刺不破（它）
命题A1：我的盾不坚固，（任何）武器都能刺破（它）

命题B：我的矛很锐利，对于（任何）防具没有不能刺穿的
命题B1：我的矛不锐利，对于（任何）防具都不能刺穿
作者: 老易    时间: 2009-3-26 22:11
说实话，形式逻辑比较基础化，对于中小学生来说其实是不适合讲授的，
国外中小学生主要学的是批判性思考,critical thinking
critical thinking 通俗说就是应用逻辑，
把一些基础的逻辑理念直接拿来解决现实中的一些问题，
我们的中小学缺的不是形式逻辑课程，而是批判性思考课程。
作者: 砚儿    时间: 2009-3-26 22:45
原帖由 老易 于 2009-3-26 22:11 发表
国外中小学生主要学的是批判性思考,critical thinking
critical thinking 通俗说就是应用逻辑，
把一些基础的逻辑理念直接拿来解决现实中 ...


老易专门开个帖子介绍一下吧, 洗耳恭听~~
作者: qqyou    时间: 2009-3-26 23:03
原帖由 老易 于 2009-3-26 22:11 发表
说实话，形式逻辑比较基础化，对于中小学生来说其实是不适合讲授的，
国外中小学生主要学的是批判性思考,critical thinking
critical thinking 通俗说就是应用逻辑，
把一些基础的逻辑理念直接拿来解决现实中 ...


critical thinking仅仅是国外提倡一种思维方法，尤其在他们的历史课里，几乎每篇文章都会有此类题目。critical thinking的结果并没有一个正确和统一的答案，关键看你推理的过程是否合理，而且看你自己所站的角度。也因此，个人角度的精确陈述和思考与分析的程序非常重要。

在国外，很小的孩子就受这种训练，他们很多要做的论文，都是按照这种方法去做的，但这种方法的基本要求，就是推理的过程必须符合形式逻辑的要求。也就是说最终答案是什么，对于不对都无需确定，但推断过程中，没有佐证或者不符合逻辑是不可以的。

国外不会在小学就开形式逻辑学的课程，但是形式逻辑的思想，一直都是贯彻始终的。
作者: jiangying    时间: 2009-3-27 09:11
金山词霸的解释

contrariety
[7kCntrE5raiEti]
n.
反对, 矛盾, 相反物

contraction
[kEn5trAkFEn]
n.
收缩, 缩写式, 紧缩
作者: jiangying    时间: 2009-3-27 09:24
原帖由 jiangying 于 2009-3-26 21:47 发表
疑问.矛盾的命题又是什么呢?

命题A：我的盾很坚固，（任何）武器都刺不破（它）
命题B：我的矛很锐利，对于（任何）武器没有不能刺穿的


下面这两组命题又是什么关系呢?
命题A：我的盾很坚固，（任何）武器都刺不破（它）
命题A1：我的盾不坚固，（任何）武器都能刺破（它）

命题B：我的矛很锐利，对于（任何）防具没有不能刺穿的
命题B1：我的矛不锐利，对于（任何）防具都不能刺穿


本帖最近评分记录
qqyou2009-3-26 23:06金钱+2后两个都是矛盾关系
qqyou2009-3-26 23:06威望+2后两个都是矛盾关系


我没研究过形式逻辑的英语原文,不过在我举的例子中,命题A1实际上是非A,命题B1是非B

矛盾这个词本来是中文词汇,按理说就应该是命题A和命题B

QQ这贴确实有意思,
作者: jiangying    时间: 2009-3-27 09:26
contradiction
[7kCntrE5dikFEn]
n.
反驳, 矛盾

主贴写错了吧
作者: qqyou    时间: 2009-3-27 10:13
原帖由 jiangying 于 2009-3-27 09:26 发表
contradiction
[7kCntrE5dikFEn]
n.
反驳, 矛盾

主贴写错了吧


谢谢你指出的，我是写错了，好久不用这个词了，凭印象写，也没去查一下，真不好意思，我已经改过来了

哈，我写帖子连中文都经常的写错，实在是太不够仔细了，希望大家多多给我指出。
作者: qqyou    时间: 2009-3-27 10:58
标题: 2、我来详细说一下矛盾关系
在传统的形式逻辑书里面，确定矛盾关系还是相反关系，主要依据是两个命题的外延有没有交集，有就是相反关系，没有就是矛盾关系

这么说起来很多人就会看晕了，因为去想象一个命题的外延，本身就是很讨厌的事情。我来给一个比较直观的定义。


命题C和命题C1，不能同时为真，也不能同时为假，这个就叫矛盾的关系
命题C和命题C1，不能同时为真，但可以同时为假，这个就叫相反的关系

比如上面那个自相矛盾的故事，矛刺破任何盾，盾可以挡住任何矛，本身是不能同时为真的。但是矛刺不破某个盾，盾挡不住某个矛，却是可以同时存在的，所以就说这两个命题是相反的。

在我们文化里，平时是基本不大进行这么严格的区分的，一般这种不能同时为真的，我们都叫矛盾，甚至夫妻之间闹了别扭，也会叫产生了矛盾。

不严格区分、严格定义会出现什么问题呢。那就是如果不严格定义，你就不可以采用逻辑的方法去解决问题。比如说你要用归谬法去证明问题，如果你最后推导的不是一个矛盾关系而是一个相反的关系，那你的整个推导就不能成立。

所以缺乏严格的定义，使得我们古代的很多研究，其实是不完备的，仅仅是一种可能甚至是谬误，而不是真正的结论。

所以我们在讨论问题之前，不能仅仅注重形式，先要区分好定义。
作者: wangtutu    时间: 2009-3-27 11:07
标题: 回复 #18 qqyou 的帖子
QQ不把大家带沟里，不算完。

初中以下小孩根本不用学那个形式逻辑。
他自己要学会自己总结他的逻辑。
作者: qqyou    时间: 2009-3-27 11:25
原帖由 wangtutu 于 2009-3-27 11:07 发表
QQ不把大家带沟里，不算完。

初中以下小孩根本不用学那个形式逻辑。
他自己要学会自己总结他的逻辑。


你说得很对，不仅初中以下不学，其实整个民族都很缺乏，所以大家脑子里总是似是而非的想法。

作为一个人，不学这些一样生活。但是如果让孩子在数学和现代科学方面能够领悟，则形式逻辑是必须的。
作者: wangtutu    时间: 2009-3-27 11:41
标题: 回复 #20 qqyou 的帖子
别让孩子再学数学专业了。
学点数学方法就行了 。

学点金融什么的。
能印点中国债券到美国日本去发行，那才是真格的。
作者: qqyou    时间: 2009-3-27 11:55
原帖由 wangtutu 于 2009-3-27 11:41 发表
别让孩子再学数学专业了。
学点数学方法就行了 。

学点金融什么的。
能印点中国债券到美国日本去发行，那才是真格的。


数学是现代科学的基础，同时也是现代金融学、经济学的基础。我当初的同学们几乎没有搞纯数学的了，大多数都是搞金融、经济、IT这类学科去了。

在现代社会，如果要安身立命，实际上学会数学还是要比学会语文要更容易一些，这个道理大家其实都是很清楚的。
作者: wangtutu    时间: 2009-3-27 12:02
标题: 回复 #22 qqyou 的帖子
数学学的好的大多是“打工仔”
语文学到极致能当“老板”，没学到极致就去当”领导人“
作者: ciscotang    时间: 2009-3-27 14:46
楼主能否抽空谈谈发展逻辑和发展记忆的关系?
有一种说法是：小孩子应当先行发展记忆。如果早期逻辑发展过强，会制约记忆力的发展。
不知道有没有道理？
作者: yuyan7381    时间: 2009-3-27 15:23
请QQ回答这个问题，我也同问。我就觉得我这个人逻辑性很强，记忆力很差。而且周围象我这样的人还有不少。当然也有都强的。
作者: qqyou    时间: 2009-3-31 00:39
原帖由 ciscotang 于 2009-3-27 14:46 发表
楼主能否抽空谈谈发展逻辑和发展记忆的关系?
有一种说法是：小孩子应当先行发展记忆。如果早期逻辑发展过强，会制约记忆力的发展。
不知道有没有道理？


先说说我的看法，关于这个楼的其他内容，明天再继续。

首先可以这么认为，数学比较好的孩子，他的记忆方式，可能会和其他孩子不一样。假设我们把机械性、无意义的记忆叫做死记硬背的话。那么学数学的孩子，可能会采用另外的方式去进行记忆。比如把无关联的东西，用某种替换的方式，是他们进行联系，然后记忆。类似于某些人用一首诗，来帮助记忆圆周率。

但先发展机械记忆，然后学数学是否可以呢？既然两种记忆方式不一样，那结果是明显的，训练机械记忆必将会影响数学的思维。其实珠心算岁孩子数学思维的影响，其实就是一个明显的示例。

当然每个人要求不一样，有些人认为背会那些数学公式，数学一定学得好了。如果认为能默写公式，那就学会了数学那数学也就太容易了。我知道一个以前玩杜曼的朋友，宣称他4岁的孩子已经会解多元方程了，我经常拿这个当一个笑话来说。因为不把数学的人，往往会把得出一个方程的一组解，当作学会了解方程。中国古代人就是如此，中国古代的所谓数学发明，往往就是一组特解发现。结果多少年都没有发明任何一套有效的数学体系和方法。因为他们不具备最基本的形式逻辑能力，所以根本不可能发现任何数学的规律。

[ 本帖最后由 qqyou 于 2009-3-31 00:40 编辑 ]
作者: qqyou    时间: 2009-3-31 00:55
原帖由 wangtutu 于 2009-3-27 12:02 发表
数学学的好的大多是“打工仔”
语文学到极致能当“老板”，没学到极致就去当”领导人“


关于wangtutu举例的这个断言里，是如何违反形式逻辑的这个问题，我会在后面的内容里陆续涉及。

也欢迎wangtutu再多举一些类似的、违反形式逻辑的例子给大家吧。
作者: wyh2000    时间: 2009-3-31 20:47
有意思，请继续
作者: huhututu    时间: 2009-3-31 22:29
原帖由 qqyou 于 2009-3-27 10:58 发表
所以我们在讨论问题之前，不能仅仅注重形式，先要区分好定义。


非常认同！
作者: zyfh    时间: 2009-3-31 23:51
看过一篇好玩的文章，qq说说这都是些什么逻辑。

Love is a Fallacy
byMax Shulman

Cool was I and logical. Keen, calculating,perspicacious, acute and astute—I was all of these. My brain was as powerfulas a dynamo, precise as a chemist’s scales, as penetrating as a scalpel.And—think of it!—I only eighteen.
It is not often that one so younghas such a giant intellect. Take, for example, Petey Bellows, my roommate at theuniversity. Same age, same background, but dumb as an ox. A nice enough fellow,you understand, but nothing upstairs. Emotional type. Unstable. Impressionable.Worst of all, a faddist. Fads, I submit, are the very negation of reason. To beswept up in every new craze that comes along, to surrender oneself to idiocyjust because everybody else is doing it—this, to me, is the acme ofmindlessness. Not, however, to Petey.
One afternoon I found Petey lyingon his bed with an expression of such distress on his face that I immediatelydiagnosed appendicitis. “Don’t move,” I said, “Don’t take a laxative.I’ll get a doctor.”
“Raccoon,” he mumbled thickly.
“Raccoon?” I said, pausing inmy flight.
“I want a raccoon coat,” hewailed.
I perceived that his trouble wasnot physical, but mental. “Why do you want a raccoon coat?”
“I should have known it,” hecried, pounding his temples. “I should have known they’d come back when theCharleston came back. Like a fool I spent all my money for textbooks, and now Ican’t get a raccoon coat.”
“Can you mean,” I saidincredulously, “that people are actually wearing raccoon coats again?”
“All the Big Men on Campus arewearing them. Where’ve you been?”
“In the library,” I said,naming a place not frequented by Big Men on Campus.
He leaped from the bed and pacedthe room. “I’ve got to have a raccoon coat,” he said passionately.“I’ve got to!”
“Petey, why? Look at itrationally. Raccoon coats are unsanitary. They shed. They smell bad. They weightoo much. They’re unsightly. They—”
“You don’t understand,” heinterrupted impatiently. “It’s the thing to do. Don’t you want to be inthe swim?”
“No,” I said truthfully.
“Well, I do,” he declared.“I’d give anything for a raccoon coat. Anything!”
My brain, that precisioninstrument, slipped into high gear. “Anything?” I asked, looking at himnarrowly.
“Anything,” he affirmed inringing tones.
I stroked my chin thoughtfully. Itso happened that I knew where to get my hands on a raccoon coat. My father hadhad one in his undergraduate days; it lay now in a trunk in the attic back home.It also happened that Petey had something I wanted. He didn’t have itexactly, but at least he had first rights on it. I refer to his girl, PollyEspy.
I had long coveted Polly Espy. Letme emphasize that my desire for this young woman was not emotional in nature.She was, to be sure, a girl who excited the emotions, but I was not one to letmy heart rule my head. I wanted Polly for a shrewdly calculated, entirelycerebral reason.
I was a freshman in law school. Ina few years I would be out in practice. I was well aware of the importance ofthe right kind of wife in furthering a lawyer’s career. The successful lawyersI had observed were, almost without exception, married to beautiful, gracious,intelligent women. With one omission, Polly fitted these specificationsperfectly.
Beautiful she was. She was not yetof pin-up proportions, but I felt that time would supply the lack. She alreadyhad the makings.
Gracious she was. By gracious Imean full of graces. She had an erectness of carriage, an ease of bearing, apoise that clearly indicated the best of breeding. At table her manners wereexquisite. I had seen her at the Kozy Kampus Korner eating the specialty of thehouse—a sandwich that contained scraps of pot roast, gravy, chopped nuts, anda dipper of sauerkraut—without even getting her fingers moist.
Intelligent she was not. In fact,she veered in the opposite direction. But I believed that under my guidance shewould smarten up. At any rate, it was worth a try. It is, after all, easier tomake a beautiful dumb girl smart than to make an ugly smart girl beautiful.
“Petey,” I said, “are you inlove with Polly Espy?”
“I think she’s a keen kid,”he replied, “but I don’t know if you’d call it love. Why?”
“Do you,” I asked, “have anykind of formal arrangement with her? I mean are you going steady or anythinglike that?”
“No. We see each other quite abit, but we both have other dates. Why?”
“Is there,” I asked, “anyother man for whom she has a particular fondness?”
“Not that I know of. Why?”
I nodded with satisfaction. “Inother words, if you were out of the picture, the field would be open. Is thatright?”
“I guess so. What are yougetting at?”
“Nothing , nothing,” I saidinnocently, and took my suitcase out the closet.
“Where are you going?” askedPetey.
“Home for weekend.” I threw afew things into the bag.
“Listen,” he said, clutchingmy arm eagerly, “while you’re home, you couldn’t get some money from yourold man, could you, and lend it to me so I can buy a raccoon coat?”
“I may do better than that,” Isaid with a mysterious wink and closed my bag and left.
  
“Look,” I said to Petey when Igot back Monday morning. I threw open the suitcase and revealed the huge, hairy,gamy object that my father had worn in his Stutz Bearcat in 1925.
“Holy Toledo!” said Peteyreverently. He plunged his hands into the raccoon coat and then his face.“Holy Toledo!” he repeated fifteen or twenty times.
“Would you like it?” I asked.
“Oh yes!” he cried, clutchingthe greasy pelt to him. Then a canny look came into his eyes. “What do youwant for it?”
“Your girl.” I said, mincingno words.
“Polly?” he said in ahorrified whisper. “You want Polly?”
“That’s right.”
He flung the coat from him.“Never,” he said stoutly.
I shrugged. “Okay. If youdon’t want to be in the swim, I guess it’s your business.”
I sat down in a chair andpretended to read a book, but out of the corner of my eye I kept watching Petey.He was a torn man. First he looked at the coat with the expression of a waif ata bakery window. Then he turned away and set his jaw resolutely. Then he lookedback at the coat, with even more longing in his face. Then he turned away, butwith not so much resolution this time. Back and forth his head swiveled, desirewaxing, resolution waning. Finally he didn’t turn away at all; he just stoodand stared with mad lust at the coat.
“It isn’t as though I was inlove with Polly,” he said thickly. “Or going steady or anything likethat.”
“That’s right,” I murmured.
“What’s Polly to me, or me toPolly?”
“Not a thing,” said I.
“It’s just been a casualkick—just a few laughs, that’s all.”
“Try on the coat,” said I.
He complied. The coat bunched highover his ears and dropped all the way down to his shoe tops. He looked like amound of dead raccoons. “Fits fine,” he said happily.
I rose from my chair. “Is it adeal?” I asked, extending my hand.
He swallowed. “It’s a deal,”he said and shook my hand.

I had my first date with Polly thefollowing evening. This was in the nature of a survey; I wanted to find out justhow much work I had to do to get her mind up to the standard I required. I tookher first to dinner. “Gee, that was a delish dinner,” she said as we leftthe restaurant. Then I took her to a movie. “Gee, that was a marvy movie,”she said as we left the theatre. And then I took her home. “Gee, I had asensaysh time,” she said as she bade me good night.
I went back to my room with aheavy heart. I had gravely underestimated the size of my task. This girl’slack of information was terrifying. Nor would it be enough merely to supply herwith information. First she had to be taught to think. This loomed as aproject of no small dimensions, and at first I was tempted to give her back toPetey. But then I got to thinking about her abundant physical charms and aboutthe way she entered a room and the way she handled a knife and fork, and Idecided to make an effort.
I went about it, as in all things,systematically. I gave her a course in logic. It happened that I, as a lawstudent, was taking a course in logic myself, so I had all the facts at myfingertips. “Poll’,” I said to her when I picked her up on our next date,“tonight we are going over to the Knoll and talk.”
“Oo, terrif,” she replied. Onething I will say for this girl: you would go far to find another so agreeable.
We went to the Knoll, the campustrysting place, and we sat down under an old oak, and she looked at meexpectantly. “What are we going to talk about?” she asked.
“Logic.”
She thought this over for a minuteand decided she liked it. “Magnif,” she said.
“Logic,” I said, clearing mythroat, “is the science of thinking. Before we can think correctly, we mustfirst learn to recognize the common fallacies of logic. These we will take uptonight.”
“Wow-dow!” she cried, clappingher hands delightedly.
I winced, but went bravely on.“First let us examine the fallacy called Dicto Simpliciter.”
“By all means,” she urged,batting her lashes eagerly.
“Dicto Simpliciter means anargument based on an unqualified generalization. For example: Exercise is good.Therefore everybody should exercise.”
“I agree,” said Pollyearnestly. “I mean exercise is wonderful. I mean it builds the body andeverything.”
“Polly,” I said gently, “theargument is a fallacy. Exercise is good is an unqualified generalization.For instance, if you have heart disease, exercise is bad, not good. Many peopleare ordered by their doctors not to exercise. You must qualify thegeneralization. You must say exercise is usually good, or exercise isgood for most people. Otherwise you have committed a Dicto Simpliciter.Do you see?”
“No,” she confessed. “Butthis is marvy. Do more! Do more!”
“It will be better if you stoptugging at my sleeve,” I told her, and when she desisted, I continued. “Nextwe take up a fallacy called Hasty Generalization. Listen carefully: You can’tspeak French. Petey Bellows can’t speak French. I must therefore conclude thatnobody at the University of Minnesota can speak French.”
“Really?” said Polly, amazed.“Nobody?”
I hid my exasperation. “Polly, it’s a fallacy.The generalization is reached too hastily. There are too few instances tosupport such a conclusion.”
“Know any more fallacies?” sheasked breathlessly. “This is more fun than dancing even.”
I fought off a wave of despair. Iwas getting nowhere with this girl, absolutely nowhere. Still, I am nothing ifnot persistent. I continued. “Next comes Post Hoc. Listen to this: Let’s nottake Bill on our picnic. Every time we take him out with us, it rains.”
“I know somebody just likethat,” she exclaimed. “A girl back home—Eula Becker, her name is. It neverfails. Every single time we take her on a picnic—”
“Polly,” I said sharply,“it’s a fallacy. Eula Becker doesn’t cause the rain. She has noconnection with the rain. You are guilty of Post Hoc if you blame EulaBecker.”
“I’ll never do it again,” she promisedcontritely. “Are you mad at me?”
I sighed. “No, Polly, I’m notmad.”
“Then tell me some morefallacies.”
“All right. Let’s tryContradictory Premises.”
“Yes, let’s,” she chirped,blinking her eyes happily.
I frowned, but plunged ahead.“Here’s an example of Contradictory Premises: If God can do anything, can Hemake a stone so heavy that He won’t be able to lift it?”
“Of course,” she repliedpromptly.
“But if He can do anything, Hecan lift the stone,” I pointed out.
“Yeah,” she said thoughtfully.“Well, then I guess He can’t make the stone.”
“But He can do anything,” Ireminded her.
She scratched her pretty, emptyhead. “I’m all confused,” she admitted.
“Of course you are. Because whenthe premises of an argument contradict each other, there can be no argument. Ifthere is an irresistible force, there can be no immovable object. If there is animmovable object, there can be no irresistible force. Get it?”
“Tell me more of this keenstuff,” she said eagerly.
I consulted my watch. “I thinkwe’d better call it a night. I’ll take you home now, and you go over all thethings you’ve learned. We’ll have another session tomorrow night.”
I deposited her at the girls’dormitory, where she assured me that she had had a perfectly terrif evening, andI went glumly home to my room. Petey lay snoring in his bed, the raccoon coathuddled like a great hairy beast at his feet. For a moment I considered wakinghim and telling him that he could have his girl back. It seemed clear that myproject was doomed to failure. The girl simply had a logic-proof head.
But then I reconsidered. I hadwasted one evening; I might as well waste another. Who knew? Maybe somewhere inthe extinct crater of her mind a few members still smoldered. Maybe somehow Icould fan them into flame. Admittedly it was not a prospect fraught with hope,but I decided to give it one more try.
  
Seated under the oak the nextevening I said, “Our first fallacy tonight is called Ad Misericordiam.”
She quivered with delight.
“Listen closely,” I said. “Aman applies for a job. When the boss asks him what his qualifications are, hereplies that he has a wife and six children at home, the wife is a helplesscripple, the children have nothing to eat, no clothes to wear, no shoes on theirfeet, there are no beds in the house, no coal in the cellar, and winter iscoming.”
A tear rolled down each ofPolly’s pink cheeks. “Oh, this is awful, awful,” she sobbed.
“Yes, it’s awful,” I agreed,“but it’s no argument. The man never answered the boss’s question abouthis qualifications. Instead he appealed to the boss’s sympathy. He committedthe fallacy of Ad Misericordiam. Do you understand?”
“Have you got a handkerchief?”she blubbered.
I handed her a handkerchief andtried to keep from screaming while she wiped her eyes. “Next,” I said in acarefully controlled tone, “we will discuss False Analogy. Here is an example:Students should be allowed to look at their textbooks during examinations. Afterall, surgeons have X-rays to guide them during an operation, lawyers have briefsto guide them during a trial, carpenters have blueprints to guide them when theyare building a house. Why, then, shouldn’t students be allowed to look attheir textbooks during an examination?”
“There now,” she saidenthusiastically, “is the most marvy idea I’ve heard in years.”
“Polly,” I said testily,“the argument is all wrong. Doctors, lawyers, and carpenters aren’t taking atest to see how much they have learned, but students are. The situations arealtogether different, and you can’t make an analogy between them.”
“I still think it’s a goodidea,” said Polly.
“Nuts,” I muttered. Doggedly Ipressed on. “Next we’ll try Hypothesis Contrary to Fact.”
“Sounds yummy,” was Polly’sreaction.
“Listen: If Madame Curie had nothappened to leave a photographic plate in a drawer with a chunk of pitchblende,the world today would not know about radium.”
“True, true,” said Polly,nodding her head “Did you see the movie? Oh, it just knocked me out. ThatWalter Pidgeon is so dreamy. I mean he fractures me.”
“If you can forget Mr. Pidgeonfor a moment,” I said coldly, “I would like to point out that statement is afallacy. Maybe Madame Curie would have discovered radium at some later date.Maybe somebody else would have discovered it. Maybe any number of things wouldhave happened. You can’t start with a hypothesis that is not true and thendraw any supportable conclusions from it.”
“They ought to put WalterPidgeon in more pictures,” said Polly, “I hardly ever see him any more.”
One more chance, I decided. Butjust one more. There is a limit to what flesh and blood can bear. “The nextfallacy is called Poisoning the Well.”
“How cute!” she gurgled.
“Two men are having a debate.The first one gets up and says, ‘My opponent is a notorious liar. You can’tbelieve a word that he is going to say.’ ... Now, Polly, think. Think hard.What’s wrong?”
I watched her closely as she knither creamy brow in concentration. Suddenly a glimmer of intelligence—the firstI had seen—came into her eyes. “It’s not fair,” she said withindignation. “It’s not a bit fair. What chance has the second man got if thefirst man calls him a liar before he even begins talking?”
“Right!” I cried exultantly.“One hundred per cent right. It’s not fair. The first man has poisonedthe well before anybody could drink from it. He has hamstrung his opponentbefore he could even start ... Polly, I’m proud of you.”
“Pshaws,” she murmured,blushing with pleasure.
“You see, my dear, these thingsaren’t so hard. All you have to do is concentrate. Think—examine—evaluate.Come now, let’s review everything we have learned.”
“Fire away,” she said with anairy wave of her hand.
Heartened by the knowledge thatPolly was not altogether a cretin, I began a long, patient review of all I hadtold her. Over and over and over again I cited instances, pointed out flaws,kept hammering away without letup. It was like digging a tunnel. At first,everything was work, sweat, and darkness. I had no idea when I would reach thelight, or even if I would. But I persisted. I pounded and clawed and scraped,and finally I was rewarded. I saw a chink of light. And then the chink gotbigger and the sun came pouring in and all was bright.
Five grueling nights with thistook, but it was worth it. I had made a logician out of Polly; I had taught herto think. My job was done. She was worthy of me, at last. She was a fit wife forme, a proper hostess for my many mansions, a suitable mother for my well-heeledchildren.
It must not be thought that I waswithout love for this girl. Quite the contrary. Just as Pygmalion loved theperfect woman he had fashioned, so I loved mine. I decided to acquaint her withmy feelings at our very next meeting. The time had come to change ourrelationship from academic to romantic.
“Polly,” I said when next wesat beneath our oak, “tonight we will not discuss fallacies.”
“Aw, gee,” she said,disappointed.
“My dear,” I said, favoringher with a smile, “we have now spent five evenings together. We have gottenalong splendidly. It is clear that we are well matched.”
“Hasty Generalization,” saidPolly brightly.
“I beg your pardon,” said I.
“Hasty Generalization,” sherepeated. “How can you say that we are well matched on the basis of only fivedates?”
I chuckled with amusement. Thedear child had learned her lessons well. “My dear,” I said, patting her handin a tolerant manner, “five dates is plenty. After all, you don’t have toeat a whole cake to know that it’s good.”
“False Analogy,” said Pollypromptly. “I’m not a cake. I’m a girl.”
I chuckled with somewhat lessamusement. The dear child had learned her lessons perhaps too well. I decided tochange tactics. Obviously the best approach was a simple, strong, directdeclaration of love. I paused for a moment while my massive brain chose theproper word. Then I began:
“Polly, I love you. You are thewhole world to me, the moon and the stars and the constellations of outer space.Please, my darling, say that you will go steady with me, for if you will not,life will be meaningless. I will languish. I will refuse my meals. I will wanderthe face of the earth, a shambling, hollow-eyed hulk.”
There, I thought, folding my arms,that ought to do it.
“Ad Misericordiam,” saidPolly.
I ground my teeth. I was notPygmalion; I was Frankenstein, and my monster had me by the throat. FranticallyI fought back the tide of panic surging through me; at all costs I had to keepcool.
“Well, Polly,” I said, forcinga smile, “you certainly have learned your fallacies.”
“You’re darn right,” shesaid with a vigorous nod.
“And who taught them to you,Polly?”
“You did.”
“That’s right. So you do oweme something, don’t you, my dear? If I hadn’t come along you never wouldhave learned about fallacies.”
“Hypothesis Contrary to Fact,”she said instantly.
I dashed perspiration from mybrow. “Polly,” I croaked, “you mustn’t take all these things soliterally. I mean this is just classroom stuff. You know that the things youlearn in school don’t have anything to do with life.”
“Dicto Simpliciter,” she said,wagging her finger at me playfully.
That did it. I leaped to my feet,bellowing like a bull. “Will you or will you not go steady with me?”
“I will not,” she replied.
“Why not?” I demanded.
“Because this afternoon Ipromised Petey Bellows that I would go steady with him.”
I reeled back, overcome with theinfamy of it. After he promised, after he made a deal, after he shook my hand!“The rat!” I shrieked, kicking up great chunks of turf. “You can’t gowith him, Polly. He’s a liar. He’s a cheat. He’s a rat.”
“Poisoning the Well ,” saidPolly, “and stop shouting. I think shouting must be a fallacy too.”
With an immense effort of will, Imodulated my voice. “All right,” I said. “You’re a logician. Let’slook at this thing logically. How could you choose Petey Bellows over me? Lookat me—a brilliant student, a tremendous intellectual, a man with an assuredfuture. Look at Petey—a knothead, a jitterbug, a guy who’ll never know wherehis next meal is coming from. Can you give me one logical reason why you shouldgo steady with Petey Bellows?”
“I certainly can,” declaredPolly. “He’s got a raccoon coat.”
作者: qqyou    时间: 2009-3-31 23:56
标题: 3、我来说说同一律
其实同一律是形式逻辑的第一条，而前面说的矛盾律是第二条。

同一律定义起来特别的简单，那就是：A就是A。

换句话说那就是，我就是我，QQyou就是QQyou.

这么简单，还有必要说么？简直是太有必要了。这就是说要符合于形式逻辑，首先要明确定义和概念。

其实诡辩术就是在使用不断偷换概念的方法，然后推导出不正确的结论。

实际上明确定义，对中国人来说会有一点困难。很多人都说汉字很好，两个字一组合就能造出一个新词来。但这个好处的不好的一个方面，那就是概念的模糊。对于一个词，你似乎懂一点，又似乎根本不懂。

中国从古至今其实都是骗子盛行，这些骗子们最擅长用一些词汇来迷惑大众。大家看现在各种保健品广告，编造出各种词汇，让普通人一听似乎很有科技含量，实际上一点科学的东西都没有。这点对国外的人就不好用，那些洋鬼子大多看不懂那些科技词汇，报纸上写这些词汇的时候，往往那个都要加上大段的注释。尽管麻烦，但定义很准确，不会让大家被误导。

另一个方面就是汉字一次多意。尤其是古文，现代的人读起来，不同的人就可以有不同的解释。有人说，古文多好哇，那么简练，但简练的结果就是谁也搞不懂到底他准确的含义是什么。所以中国古代就是概念的模糊，这种模糊导致了形式逻辑根本不可能发展。

中国古代不是没出现过形式逻辑，其实公孙龙的白马非马论、坚白论，都是形式逻辑的典范。非常遗憾的是被后人讥笑为诡辩。由此可以看出在中国人里是多么的缺乏逻辑思想。我以前看过一篇讲逻辑的文章，说公孙龙的白马非马论是客观唯心主义的东西。可惜的是，西方就在这种可“客观唯心主义”中产生了数学和现代科技，而我们在唯物主义中一直落后下去了。于是大家把马和白马混为一谈，产生了大量可笑的结论。

如果大家读过圣经，可能都会感叹于圣经的精细，比如他说戒律，旧约《申命记》里就详细的列举了什么样的东西可以吃，什么不可以吃。我们佛教里讲究吃素，但到底什么是吃素，到现在也说法不一。

对比中美小学的规则也会发现，明国的小学生守则里就规定的非常明确，什么是不可以的。而我们的里面就很泛泛。写一个遵守纪律，到底怎么叫遵守纪律，大约就是老师说了算了，他说你是遵守就是遵守，说你违反就是违反。

所以很简单的东西，其实最复杂，要运用形式逻辑，同一律是最重要的基础。
作者: zyfh    时间: 2009-4-1 00:05
标题: 想看中文版的请见
http://www.hbgd.net/html/200809/12/112948449_3.htm

[ 本帖最后由 zyfh 于 2009-4-1 00:10 编辑 ]
作者: qqyou    时间: 2009-4-1 00:10
原帖由 zyfh 于 2009-3-31 23:51 发表
看过一篇好玩的文章，qq说说这都是些什么逻辑。

Love is a FallacybyMax Shulman
Cool was I and logical. Keen, calculating,perspicacious, acute and astute—I was all of these. My brain was as pow ...


这个逻辑就是，很多人眼里，love很实在，就是一件Fallacy。

不过那个女孩子，学得到真是很快，而且学了马上就会用，不简单呀。
作者: slzzz    时间: 2009-7-20 11:41
还想听听更深入的解释，为我们扫盲

现在还是没有系统懂的形式逻辑
作者: chenxiaojie0110    时间: 2009-9-19 23:12
关于数学，不敢发表什么品论，但否认中国科学、文化成就的思潮来的挺猛，包括了中医、数学、社会科学等各个方面，别的就不说了，下面是我转自网络的文章。吴文俊大家可能都知道，他的数学成就就是基于中国的数学理论。
作者: chenxiaojie0110    时间: 2009-9-19 23:13
吴文俊院士再叙中国古代数学辉煌
科技日报     (2002-08-31)

　　本报北京8月27日电（记者延宏实习生王婷婷）一向强调中国古代数学成就的吴文俊院士，今天在北京中国科技馆阶梯会议厅，面对数百位中外数学家从头至尾用熟练的英语作了题为“中国古算与实数系统”的演讲。

　　早在文革期间，由于作学问比较难，吴老就开始大量阅读古书，致力于中国古代数学的研究。1977年，他发表了《中国古代数学对世界文化的伟大贡献》，明确指出近代数学之所以能发展到今天，主要是靠中国（式）的数学而非希腊（式）的数学，决定数学历史发展进程的也主要是靠中国（式）的数学而非希腊（式）的数学。1987年，他发表了更加重要的《中国传统数学的再认识》，引起了数学界的极大兴趣。这是对数学史正本清源的研究，使人们认识到中国古代数学曾有过辉煌成就。

　　翻开历史，中国曾经是一个数学的国度。祖冲之、刘徽、《九章算术》、《周髀算经》、《四元玉鉴》等一批大家和著作，使中国数学曾经处于世界巅峰。正是由于这些辉煌，吴老常说：中国数学，不仅要振兴，更要复兴。

　　特意从国外赶来的数学家王东明，以其首批师从吴老研究机械化数学的经历，向记者说起吴老对中国古代数学的情怀，赞不绝口。他说：吴先生一直非常推崇中国古代数学的成就，今天吴先生讲的这个实数系统就更进一步证明了，我们在这一方面比西方早了1500年，再一次证明了中国古代数学的辉煌。吴先生认为，宋元之前我国的数学是非常发达的，我们当时的研究已经很接近现代数学中先进的理论了，但是很遗憾，由于宋、元时代，中国数学的发展中断，使中国总是与重大的数学发现擦肩而过。

　　当记者向王东明询问今天吴老所讲的实数系统时，他说，我们以前都认为实数系统是西方人发现的，而现在经吴老研究，实数系统早在2000多年前的《九章算术》中就出现了。这是一个新的研究成果。

　　数十年如一日，吴老探索的脚步一直没有停歇。他曾在拓扑学的领域里奋勇开拓。1958年，他开始对策论的研究；1967年，他专注于示嵌类理论与线性图平面的相关问题；1970年，又提出了 I量度的概念……当世界电脑发展初露端倪之时，他立刻把电脑与自己所研究的中国古代算术思想联系起来，从而开辟了一条与西方迥然不同的数学机械化－定理机器证明的道路。

　　2001年，吴文俊获得了国家最高科技奖的殊荣，他从所获500万元人民币奖金中拨出50万元，设立“数学与天文丝路基金”，用于鼓励并资助年轻学者研究古代中国与世界进行数学交流的历史，揭示部分东方数学成果如何从中国经“丝绸之路”传往欧洲之谜。

　　走出会议厅，人们无不钦佩。吴文俊，一个已近耄耋之年的老人，今天再次以他对中国古代数学的痴情，向世人宣讲中国古代数学的成就，他不愧是“真正理解中国古代数学的第一人”。
作者: chenxiaojie0110    时间: 2009-9-19 23:18
著名的数学家吴文俊谈中国古代数学问题

数学的一半是中国数学

在相当长的时间里，不少西方数学家认为中国古代数学不是世界数学的主流之一，甚至不打算承认中国古代数学对世界数学的杰出贡献。20世纪70年代，吴文俊潜心进行了中国数学史的研究，他的结论在数学界起到震聋发聩的影响。

在研究中吴文俊发现，中国古代数学独立于古希腊数学和作为其延续的西方数学，有着其自身发展的清晰主线，其发展过程、思考方法和表达风格亦与西方数学迥然不同。他说，通常认为，中国古代没有几何学，事实上却不是这样，中国古代在几何学上取得了极其辉煌的成就。人们的误解可能是因为中国古代几何学在内容和形式上都与欧几里得几何迥然不同的缘故：中国古代几何没有采用定义--公理--定理--证明这种欧式演绎系统，取公理而代之的是几条简洁明了的原理。

吴文俊在回顾中国古代数学的伟大成就时感慨地说，中国古代的劳动人民在广泛实践的基础上，建立了世界上最先进的数学方法，直到16世纪，我国数学在最主要的领域一直居于世界领先地位。特别是自古就有的完美的十进位位值制记数法，是中国的独特创造，是世界其他古代民族所没有的。这一创造在人类文明史上居于显赫的地位。中国古代的几何学有着极其辉煌的成就。测高望远之学形成了重差理论，土地的丈量与容积的量测产生了面积和体积理论，提炼成出入相补的一般原理。整个多面体体积理论可奠基刘徽原理及出入相补原理之上。祖?原理则解决了球体体积问题。勾股测量学及勾股定理的证明，圆周率推导和计算……这些成就表明，我国古代几何学既有丰硕的成果，又有系统的理论。吴文俊指出，数学发展中有两种思想：一是公理化思想，另一是机械化思想。前者源于希腊，后者则贯穿整个中国古代数学。这两种思想对数学发展都曾起过巨大作用。从汉初完成的《九章算术》中对开平方、开立方的机械化过程的描述，到宋元时代发展起来的求解高次代数方程组的机械化方法，无一不与数学机械化思想有关，并对数学的发展起了巨大的作用。公理化思想在现代数学，尤其是纯粹数学中占据着统治地位。然而，检查数学史可以发现数学多次重大跃进无不与机械化思想有关。数学启蒙中的四则运算由于代数学的出现而实现了机械化。线性方程组求解中的消元法是机械化思想的杰作。对近代数学起决定作用的微积分也是得益于经阿拉伯人传入欧洲的中国数学的机械化思想而产生的。即便在现代纯粹数学研究中，机械化思想也一直发挥着重大作用。他特别指出，机械化思想是我国古代数学的精髓。

中科院数学所李文林研究员这样评价吴文俊对中国数学史的研究：他的研究起到了正本清源的作用，证实中国古代数学是世界数学的主流之一，促进了西方数学与中国古代数学两大主流的融合，推动了数学的发展，同时也掀起了对中国数学史再认识的新高潮。更为重要的是，吴文俊古为今用以此为基础开创了数学机械化研究。

“现代数学女王”的新风采

法国数学家狄多奈这样形容拓扑学，说拓扑学是“现代数学的女王”。
从定义上说，拓扑学是数学的一个分支，研究几何图形在连续改变形状时还能保持不变的一些特性。它只考虑物体间的位置关系而不考虑它们的距离和大小。40年代中期在师从陈省身先生之前，吴文俊对拓扑学还所知甚少，在陈省身先生的指导下，吴文俊步入了数学的圣殿。由于勤奋研究和超群的领悟能力，他开始在拓扑学的深水中游泳了。那时美国数学家惠特尼推导出一个著名的“对偶定理”，这是一个十分基本的公式，可是证明长得异乎寻常，吴文俊形容它“总有十几页、几十页长，没法在杂志上发表”，出一本书倒合适。吴文俊经过精心推导，给出了一个只有几页纸的证明。当时最具权威的美国《数学年刊》刊载了这个公式，惠特尼说，我的证明可以扔掉了。

吴文俊独创新意给出的这个简单证明，成为拓扑学中“示性类”的一个重要成果。仅仅一年多时间吴文俊就在以难懂著称的拓扑学的前沿领域取得如此巨大成就，这确是国际数学界并不多见的，足见吴文俊的研究功力。

在拓扑学研究中，吴文俊起到了承前启后的作用，极大地推进了拓扑学的发展，引发了大量的后续研究，许多著名数学家从他的工作中受到启示或直接以他的成果为起点，获得了一系列重大成果。

1989年，法国数学家狄多奈出版了著作《代数拓扑学家和微分拓扑学史（1900──1960）》，其中引用吴文俊的研究成果17次。他写道，吴文俊把示性类由极为繁复的形式转化为现代的漂亮形式。数学大师陈省身称赞吴文俊“对纤维丛示性类的研究做出了划时代的贡献”。吴文俊也因此获得了国家自然科学奖一等奖。

“把质的困难转化为量的复杂”

吴文俊科学地预言：数学机械化思想的未来生命力将是无比旺盛的，中国古代数学传统的机械化思想光芒，将普照于数学的各个角落。

吴文俊对数学机械化方法有这么一番说明：这种方法就是把要证明的问题转化成代数，编成程序，用计算机进行进一步计算。把原来要挖空心思拐弯抹角穷思冥索的人工演算转化成量的反复，尽管计算量再大计算机也不在乎，这样很困难的问题便变得容易了。有了计算机，人们可以从事更高层次的创新性研究。他对我说，机器证明是很适合笨人的，我是笨人。

对于数学机械化方法，吴文俊有这么一段描述来说明它的前程无量：中世纪是骑士的时代，骑士仗剑横行，有了手枪骑士便消失了，因为再会用剑的骑士也抵不住一个弱女子的一粒子弹。

“把质的困难转化为量的复杂”?由开普勒证明牛顿

吴文俊的数学机械化方法研究开始有了初步成果。1986年，美国通用机器公司下属的一个研究机构，组织了一次国际学术会议，邀请吴文俊参加。两位与会代表据说是两位美国数学家，邀吴文俊谈了一天有关机器证明的研究。会后，美国科学家沃斯邀请吴文俊访问阿贡实验室，问他能不能用数学机械化方法从开普勒对行星运动的观测结果，直接导出牛顿的引力定律。天体间引力与质量成正比比较容易理解，而与距离平方成反比就费解了。美国能源部一个研究小组用他们的方法苦于解决不了这个难题。回国后，吴文俊用了不到一个月时间就用数学机械化方法解决了这个难题──由开普勒的观测结果直接推导出牛顿引力定律。

现在由吴文俊担任学术指导，国内有二三十个单位的六七十名科学家在从事数学机械化研究。高小山博士说，数学机械化方法的应用领域极其广阔，它可以为数学和其他领域的研究提供工具，为计算推理提供一种强有力的工具。在数学研究中的应用，可以把数学家从繁重的脑力劳动中解放出来，从而推动学科发展。这是数学机械化方法将来发展的主要方面之一，现在已经起步了。另外一个方面，数学机械化方法将会被应用于交叉研究，如力学、理论物理、机械机构学、计算机技术、图像压缩、信息保密、新一代数控机床、计算机图形学、计算机辅助设计、机器人等许多领域。

1997年在获得国际著名的“自动推理杰出成就奖”时，吴文俊还获得了这样的赞誉：几何定理自动证明首先由赫伯特·格兰特于50年代开始研究，虽然得到了一些有意义的结果，但在吴方法出现之前的20年里这一领域进展甚微。在不多的自动推理领域中，这种被动局面是由一个人完全扭转的。吴文俊院士很明显是这样一个人。
作者: gajidouma    时间: 2009-9-20 22:27
原帖由 <i>qqyou</i>


先说说我的看法，关于这个楼的其他内容，明天再继续。

首先可以这么认为，数学比较好的孩子，他的记忆方式，可能会和其他孩子不一样。假设我们把机械性、无意义的记忆叫做死记硬背的话。那么学数学的孩子 ...


不过，死记硬背的量和度要到一个排他的级别才会对所谓数学思维有影响吧？说背点经典就会影响数学思维，有点耸人听闻。



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