This lecture was not in the schedule, but it had to be added so that there was no window between classes. The lecture, in essence, is devoted to how we know what we know, if, of course, we really know it. This topic is as old as the world - it has been discussed for the last 4000 years, if not longer. In philosophy, a special term has been created for its designation - epistemology, or the science of knowledge.
I would like to start with the primitive tribes of the distant past. It is worth noting that in each of them there was a myth about the creation of the world. According to one ancient Japanese belief, someone stirred up the mud, from the spray of which the islands appeared. Other peoples had similar myths: for example, the Israelites believed that God created the world for six days, after which he got tired and finished creation. All these myths are similar - although their plots are quite diverse, they all try to explain why this world exists. I will call this approach theological, since it does not offer explanations other than βit happened by the will of the gods; they did what they saw fit, and that's how the world came into being."
Around the XNUMXth century BC. e. the philosophers of ancient Greece began to ask more specific questions - what does this world consist of, what are its parts, and also tried to approach them more rationally than theologically. As you know, they singled out the elements: earth, fire, water and air; they had many other concepts and beliefs, and slowly but surely, all this was transformed into our modern ideas of what we know. However, this topic has puzzled people at all times, and even the ancient Greeks wondered how they knew what they knew.
As you will remember from our discussion of mathematics, the ancient Greeks believed that geometry, which limited their mathematics, was reliable and absolutely indisputable knowledge. Nevertheless, as shown by Maurice Kline, author of Mathematics. Loss of Certainty,β which most mathematicians would agree, there is no truth in mathematics. Mathematics gives only consistency for a given set of reasoning rules. If you change these rules or the assumptions used, the mathematics will be very different. There is no absolute truth, except, perhaps, the ten commandments (if you are a Christian), but, alas, nothing about the subject of our discussion. It is unpleasant.
But you can apply some approaches and get different conclusions. Descartes, having considered the assumptions of many philosophers who preceded him, took a step back and asked the question: "How little can I be sure of?"; he chose the statement "I think, therefore I am" as an answer. From this statement, he tried to derive philosophy and get a lot of knowledge. This philosophy was not adequately substantiated, so we never received knowledge. Kant argued that everyone is born with a solid knowledge of Euclidean geometry, and a host of other things, which means that there is an innate knowledge that is given, if you like, by God. Unfortunately, just at the moment when Kant was describing his thoughts, mathematicians were creating non-Euclidean geometries that were as consistent as their prototype. It turns out that Kant threw words into the wind, just like almost everyone who tried to talk about how he knows what he knows.
This is an important topic, because science is always turned to for justifications: you can often hear that science has shown this, proved that it will be like this; we know this, we know that - do we know? Are you sure? I am going to consider these issues in more detail. Let's remember the rule from biology: ontogeny repeats phylogeny. It means that the development of the individual, from the fertilized egg to the student, schematically repeats the entire previous process of evolution. Thus, scientists argue that during the development of the embryo, gill slits appear and disappear again, and therefore they suggest that our distant ancestors were fish.
Sounds good if you don't think about it too seriously. This gives a pretty good idea of ββhow evolution works, if you believe it. But I will go a little further and ask: how do children learn? How do they get knowledge? Perhaps they are born with predetermined knowledge, but that sounds a bit unconvincing. To be honest, it's extremely unconvincing.
So what are the kids doing? They have certain instincts, obeying which, children begin to make sounds. They make all these sounds that we often call babbling, and this babbling, apparently, does not depend on the place of birth of the child - in China, Russia, England or America, children will babble in basically the same way. However, depending on the country, babble will develop differently. For example, when a Russian child says the word "mama" a couple of times, he will receive a positive response and therefore will repeat these sounds. Through experience, he discovers which sounds help to achieve what he wants and which do not, and so he learns a lot of things.
Let me remind you what I have already said several times - there is no first word in the dictionary; each word is defined in terms of others, which means that the dictionary is circular. In the same way, when a child tries to build a coherent sequence of things, he has trouble running into inconsistencies that he must resolve, since there is no first thing for the child to learn, and "mother" does not always work. There is confusion, for example, such as I will now show. Here is a famous American joke:
popular song lyrics (gladly the cross I'd bear)
and the way children hear it (gladly the cross-eyed bear, gladly the cross-eyed bear)
(In Russian: violin-fox / creak of the wheel, I am a jerking emerald / cores - pure emerald, if you want bull plums / if you want to be happy, a hundred shitty ass / a hundred steps back.)
I also experienced such difficulties, not in this particular case, but there are several times in my life that I could recall when I thought that I was reading and speaking probably correctly, but those around me, especially my parents, understood that that's quite different.
Here you can observe serious errors, as well as see how they occur. The child is faced with the need to make assumptions about what the words of the language mean and gradually learn the correct options. However, fixing such errors can take a long time. You can't be sure that they are completely fixed even now.
You can go very far without understanding what you are doing. I have already talked about my friend, a doctor of mathematical sciences from Harvard University. When he was graduating from Harvard, he said that he could calculate the derivative by definition, but he doesn't really understand it, he just knows how to do it. This is true for a lot of the things we do. To ride a bike, skateboard, swim, and many more things, we don't need to know how to do them. It seems that knowledge is something more than words can express. I dare not say that you do not know how to ride a bicycle, even if you cannot tell me how to do it, but you pass in front of me on one wheel. So knowledge is very different.
Let's sum up a little what I said. There are people who believe that we have innate knowledge; if you consider the situation as a whole, perhaps you will agree with this, considering, for example, that children have an innate tendency to make sounds. If a child was born in China, he will learn to pronounce many sounds in order to achieve what he wants. If he was born in Russia, he will also make many sounds. If he was born in America, he will still make many sounds. The language itself is not so important here.
On the other hand, a child has an innate ability to learn any language just like any other. He memorizes sequences of sounds and understands what they mean. He has to put meaning into these sounds himself, since there is no first part that he could remember. Show the child a horse and ask him: βThe word βhorseβ is the name of a horse? Or does that mean she's quadrupedal? Maybe that's her color? If you're trying to tell a child what a horse is by showing it, the child won't be able to answer that question, but that's what you mean. The child will not know which category the word belongs to. Or, for example, take the verb "to run." It can be consumed when you're doing a fast move, but you can also say that the colors on your shirt have run out after washing, or complain about the rushing clock.
The child experiences great difficulties, but, sooner or later, he corrects his mistakes, admitting that he understood something wrong. As the years go by, children become less and less able to do this, and when they are old enough, they can no longer change. Obviously people can be wrong. Think, for example, of those who believe that he is Napoleon. No matter how much evidence you present to such a person that this is not so, he will continue to believe in it. You know, there are a lot of people with strong beliefs that you don't share. Since you may think that their beliefs are insane, saying that there is an infallible way to discover new knowledge is not entirely true. You will say to this: βBut science is very accurate!β Let's look at the scientific method and see if that's the case.
Thanks to Sergey Klimov for the translation.
To be continued ...
Who wants to help with - write in a personal or email [email protected]
By the way, we have also launched the translation of another cool book - )
We are especially looking for who can help translate system. (we translate for 10 minutes, the first 20 have already been taken)
Book content and translated chapters
- Intro to The Art of Doing Science and Engineering: Learning to Learn (March 28, 1995)
- "Foundations of the Digital (Discrete) Revolution" (March 30, 1995)
- "History of Computers - Hardware" (March 31, 1995)
- "History of Computers - Software" (April 4, 1995)
- "History of Computers - Applications" (April 6, 1995)
- "Artificial Intelligence - Part I" (April 7, 1995)
- "Artificial Intelligence - Part II" (April 11, 1995)
- "Artificial Intelligence III" (April 13, 1995)
- "n-Dimensional Space" (April 14, 1995)
- "Coding Theory - The Representation of Information, Part I" (April 18, 1995)
- "Coding Theory - The Representation of Information, Part II" (April 20, 1995)
- "Error-Correcting Codes" (April 21, 1995)
- "Information Theory" (April 25, 1995) Done, it remains to publish
- "Digital Filters, Part I" (April 27, 1995)
- "Digital Filters, Part II" (April 28, 1995)
- "Digital Filters, Part III" (May 2, 1995)
- "Digital Filters, Part IV" (May 4, 1995)
- "Simulation, Part I" (May 5, 1995)
- "Simulation, Part II" (May 9, 1995)
- "Simulation, Part III" (May 11, 1995)
- Fiber Optics (May 12, 1995)
- "Computer Aided Instruction" (May 16, 1995)
- "Mathematics" (May 18, 1995)
- "Quantum Mechanics" (May 19, 1995)
- "Creativity" (May 23, 1995). Translation:
- "Experts" (May 25, 1995)
- "Unreliable Data" (May 26, 1995)
- Systems Engineering (May 30, 1995)
- "You Get What You Measure" (June 1, 1995)
- (June 2, 1995) translate in 10 minute pieces
- Hamming, "You and Your Research" (June 6, 1995).
Who wants to help with - write in a personal or email [email protected]
Source: habr.com