# 山人

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## 关于常识和逻辑之间的纠结

(2018-11-06 12:46:26) 下一个

1. 马科斯是一个人。

2. 马科斯是庞贝人。

3. 马科斯生于公元前40年。

4. 所有的人都是会死的。

5. 所有的庞贝人死于公元79年的维苏威斯火山爆发。

6. 现在是2018年。

（本来还有一节是有关用贝叶斯概率预测事件可能性的，但时机正值美国中期选举，城里太多能人在显神通，我就不掺合了，反正是用数学还是用感觉都有各自的道理）。

[ 打印 ]

I made some small changes to my original reply to you several days ago, mainly added a paragraph talking about ancient chniese wisdom. The following is the updated version of that.

2018-11-08 18:42:03

Although all of the writings I put here in my blog are not academic essays , to those meticulous and serious attitude people, I still don’t mind to talk a bit more about the construction rational and supporting argument behind.

At least one thing you said here should be right, definitely I am not an expert in neither math nor logic, none of them. However another thing you zoomed in and talked for quite a while was totally wrong. The unicorn metaphor I used in the article was not to reveal a double entendre hidden there, but was trying to explain a concept that without the so called prior knowledge, a machine can produce wrong judgement.

Is Aristotelian logic flawless? Of course not. In the 17th century, Leibniz expanded the syllogism formats from 19 to 24. But still it’s not perfect. Then George Boole spent a lot of time thinking about the Aristotelian premise sets, eventually he found a mistake there originated by Aristotle , or a defect neglected by Aristotle.. Boole attempted to tell us that, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and not-P"; "no S is P", that "there is nothing that is both S and P". Similarly, the subcontrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent.

Therefore in my article , I used the unicorn contradiction to explain this . When I say , 1. an unicorn is a horn animal and 2. no horn animal is an unicorn, the both statements are correct from the pure logic point of view, but the Unicorn set is nonexistent. We know this , because we are human we have prior knowledge or common sense ( you should like this term). Computer does not, therefore it goes to contradiction.

Of course I understand that the modern computer design was not simply based on the classic logic. But I still talked about this unicorn metaphor, my intention was to indicate that there ’s a defect in Aristotelian system . You see what I mean? That is the foundation of modern science, the foundation of modern mathematics, no matter how complicated those all are about.

Can the modern math describe or cover all the details of human life, all the universal layers, all the changes happening everywhere? A bunch of top minds living in the world don’t think so. You can check with Wiki about the alien thoughts and ideas of the guys like Mandelbrot, Conway, especially Wolfram. This is why I said , at the current stage, computer can not understand human intuition, can not understand human culture , can not understand conscientious principles etc.

I had an article talking about my understanding of Wolfram’s thought, you can click the link below to have a look then pour out your scorning thereafter.:)

http://blog.wenxuecity.com/myblog/64852/201804/15903.html

To finish this back and forth discussion or rebuttal debate , I feel compulsively to present you a saying from 《荀子》here : 所谓士者，虽不能尽术，必有率也。I believe you are too young to understand this kind of oriental ancient wisdom. To the people in my age , intellectual means we don’t care about those sophisticated theoretic specifications that much as you do, we are more fascinated in the methodology and philosophy thinking of the universal truth instead.

By the way, forget about that Bayesian thing, I just wanted to make up a fortune telling joke, make fun of politics, not serious about it.

Although all of the writings I put here in my blog are not academic essays , to those meticulous and serious attitude people, I still don’t mind to talk a bit more about the construction rational and supporting argument behind.

At least one thing you said here should be right, definitely I am not an expert in neither math nor logic, none of them. However another thing you zoomed in and talked for quite a while was totally wrong. The unicorn metaphor I used in the article was not to reveal a double entendre hidden there, but was trying to explain a concept that without the so called prior knowledge, a machine can produce wrong judgement.

Is Aristotelian logic flawless? Of course not. In 17th century, Leibniz expanded the syllogism formats from 19 to 24. But still it’s not perfect. Then George Boole spent a lot of time thinking about the Aristotelian premise sets, eventually he found a mistake there originated by Aristotle , or a defect neglected by Aristotle.. Boole attempted to tell us that, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and not-P"; "no S is P", that "there is nothing that is both S and P". Similarly, the subcontrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent.

Therefore in my article , I used the unicorn contradiction to explain this . When I say , 1. a unicorn is a horn animal and 2. no horn animal is a unicorn, the both statements are correct from the pure logic point of view, but the Unicorn set is empty. We know this , because we are human we have prior knowledge or common sense ( you should like this term). Computer does not, therefore it goes to contradiction.

Of course I understand that the modern computer design was not simply based on the classic logic. But I still talked about this unicorn metaphor, my intention was to indicate that there ’s defect in Aristotelian system . You see what I mean? That is the foundation of modern science, the foundation of modern mathematics, no matter how complicated those all are about.

Can the modern math describe or cover all the details of human life, all the universal layers, all the changes happening everywhere? A bunch of top minds living in the world don’t think so. You can check with Wiki about the alien thoughts and ideas of the guy like Mandelbrot, Conway, especially Wolfram. This is why I said , at the current stage, computer can not understand human intuition, can not understand human culture , can not understand conscientious principles etc.

I had an article talking about my understanding of Wolfram’s thought, you can click the link below to have a look then pour out your scorning thereafter.:)

http://blog.wenxuecity.com/myblog/64852/201804/15903.html

by the way, forget about that Bayesian thing, I just wanted to make up a fortune telling joke, make fun of politics, not serious about it.
nightrider By the way, the martingale (doubling the stake) betting strategy is a horrible one as you do not have infinite endowment. Check out the fractional Kelly criterion https://en.wikipedia.org/wiki/Kelly_criterion.
nightrider Thank you for your compliment.

Excuse my bluntness and with all due respect, I would like to point out that as regard to logical deduction, you are again confusing distinct notions. Of course a logical syllogism with every symbol mathematically rigorously defined, could lead to a contradiction. That is inherent in and an indispensable and integral part of the logic. The canonical and actually form of the contradiction is (A and not A). It is always false. Without it there is no way to deduce whether a proposition or a logical deduction is false. But a true contradiction is NOT attained when the symbols are NOT rigorously defined.

There are indeed true logical paradoxes. There is also the Godel's incompleteness theorem. But that is NOT what you are talking about here. So please do not confuse the notions.

Your example of the unicorn is a quintessential example of confusion of concepts. If you do want to study double entendre, you are using the wrong tool. There is no inherent flaws in using pure logic to analyze double entendre. Any flaw comes from you not using the right logical/mathematical expression. To put it more bluntly, you can not blame the mathematics for you writing down 1+2=-1. The blame is squarely on your erroneous usage of mathematics, not mathematics per se.

You can use Bayesian probability to study and draw conclusions for many things. You have to pick the prior and the model. Different prior and models will lead to different conclusions. Why is that any surprise? That is the very reason you and your wife fight. That is the reason you can not read a letter in Icelandic, because your prior knowledge base does not contain Icelandic. How are you different from a computer in this regard? How does not prove mathematical logic is less effective than human instinct?

There are legitimate contemplations over the relationship between languages and mathematics/logic and over the artificial intelligence. Unfortunately, judging from what you have written here, most, if and maybe not all, of your puzzlements stem from a confusing understanding of and loose grasp of mathematics and logic.

As to the paradox, that was not because I'd not defined about the meaning of the words clearly .
Actually, that was a piece of puzzlement we inherited since the age of Aristotle . however, that puzzlement also brought up some hints to the philosophers and logicians in the old times. So now we understand that, in pure logic theory/concept, even with the correct premises ,the syllogism deduction can go contradiction. the reason we, the human, can make it right is because we don't use absolute premises. Our prior knowledge contaminated the pureness of the premises already, in the most of the cases.
nightrider Much of your puzzlement comes from confusing distinct notions of mathematics (including logic). For example, the Monty Hall problem is a very simple and straightforward exercise of the calculation of the ultimate probability from the (conditional) probabilities. For your roulette problem, you having assumed the independence of each throw, should realize that conditioning on having observed the ball landing on red consecutively n times still gives the probability of the ball landing on blue 1/2. 1/2^n is only the probability of observing consecutive red (or for that matter any combination) in the NEXT n throws.

As for your logic "paradox", it comes about only because you have not clearly defined the meaning of each word. Of course, people speak double entendre. It can also be interpreted logically. Understanding a double entendre is not unlike cryptography trying to decode an encrypted message sent through a noisy channel. The efficiency of decryption depends on the computational capacity, prior knowledge and your algorithm for decoding "long distance" dependency (for example, the long short memory neural network is a fashionable algorithm for doing that). Even humans would be at a loss to understand certain jokes. Just remind yourself the numerous occasions you scratched your head and wondered what the native speakers were laughing about, and when you blanked at the sports metaphor they throw at you. Are you any different from the computer?

westshore 其实在80年代对于AI的主要测试标准就是理解自然语言，是理解，不是构造，后者相对容易。因此即使AI能写出不错的小说也不能说就是成熟的AI。

appaloosa 有意思。盼继续。

（山人得加快写作速度，要不然以后全被人工智能抢先了）
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