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[原创] 我来说说形式逻辑

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21#
发表于 2009-3-27 11:41:36 | 只看该作者

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。
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22#
 楼主| 发表于 2009-3-27 11:55:41 | 只看该作者
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。

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参与人数 1威望 +5 金币 +5 收起 理由
zyfh + 5 + 5 就是!

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23#
发表于 2009-3-27 12:02:14 | 只看该作者

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“
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24#
发表于 2009-3-27 14:46:17 | 只看该作者
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?
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25#
发表于 2009-3-27 15:23:51 | 只看该作者
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。
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26#
 楼主| 发表于 2009-3-31 00:39:20 | 只看该作者
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 ]

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参与人数 2威望 +4 金币 +4 收起 理由
gajidouma + 2 + 2 嗯,所言极是。
ciscotang + 2 + 2 谢谢你了

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27#
 楼主| 发表于 2009-3-31 00:55:57 | 只看该作者
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。

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参与人数 2威望 +6 金币 +6 收起 理由
zyfh + 5 + 5 我都不敢发言呢
huhututu + 1 + 1 有趣!今天的评分都贡献给你了!谢谢你 ...

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28#
发表于 2009-3-31 20:47:19 | 只看该作者
有意思,请继续
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29#
发表于 2009-3-31 22:29:14 | 只看该作者
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!
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30#
发表于 2009-3-31 23:51:16 | 只看该作者
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.”

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