Philosophical classic sophistry

Zhi Nuo was an ancient Greek philosopher who was very good at sophistry. One of his famous sophistry "Achilles will never catch up with the tortoise" is this: Achilles is a hero who is good at running in ancient Greek mythology. Suppose the tortoise climbed a distance first, and then Achilles went after it. Zhi Nuo thought Achilles would never catch up with the tortoise. Because the former must reach the starting point of the latter before catching up with the latter, but at this time the latter has climbed a long way forward. So the former must catch up with this section of the road again, but then the latter climbed forward again. Because the distance between Achilles and the tortoise can be divided into countless small segments in turn, Achilles is getting closer and closer, but he can't catch up with the tortoise.

Of course, this conclusion is wrong in practice, but strangely, this argument is not wrong in logic.

There was a better sophistry in ancient Greece: 1 millet landed silently, two millet landed silently, three millet landed silently ... and so on, 1 whole bag of millet landed silently. This is also wrong in practice and right in logic.

How to treat sophistry, people are often used to evaluating it from a practical point of view, and always tell it is wrong according to facts. This evaluation did not really understand the intentions of those ancient sophists. Those sophists themselves know that these sophistries are wrong in practice, and they don't really want to deny the truth. Nobody is so stupid. What is really stupid is those who think sophists are stupid. Those people are too stupid to think about sophistry. The result of "wrong in practice and right in logic" actually shows that the situation of thought and the situation of fact are different, and the truth in thought and the truth in fact are different truths and have different uses respectively. For example, logical theorems are often inconsistent with facts. There is a logical theorem that says "any lie can lead to any sentence", which sounds ridiculous. As a result, someone really wanted Russell, a great British philosopher, to prove that Russell was the Pope from "2+2 = 5". The profound Russell made the following proof: suppose 2+2 = 5; Subtract 2 from both sides of the equation to get 2 = 3; Translocation is 3 = 2; Subtract 1 from both sides to get 2 =1; The Pope and Russell are two people, but because 2= 1, the Pope and Russell are 1, so Russell is the Pope.

Some people say this conclusion is a joke. If so, it should be said that it is a profound joke. From this, we can truly realize that thought and fact are two different things, and it is very important to understand this. In fact, this is not difficult to understand. The points, lines, planes, parallel lines, triangles, circles, etc. we talked about in mathematics don't really exist, they are just idealized things in our minds. The connection between thought and fact only shows that thought can be applied to fact. The two kinds of sophistry mentioned above are just a wake-up call to wrong ideas, and there is no other use, because it is really ridiculous.