Deducing a knowledge system from a set of axioms is called deduction, which is quite attractive. Because of their outstanding achievements in geometry, the Greeks fell in love with this game, but they also made two big mistakes.

The first mistake is to regard deduction as the only respectable way to seek new knowledge. They clearly know that it is not appropriate to deduce some knowledge by deduction. For example, the distance from Corinth to Athens cannot be deduced by abstract theorem, but must be measured. When Greeks need it, they are willing to study nature, but they are always ashamed because they think that the highest level of knowledge comes from thinking. They tend to underestimate the knowledge directly related to daily life. There is a story in which Plato's students finally asked impatiently, "But what's the use?" Unpleasantly, Plato asked his servant to give the student a coin and sent him away, saying, "Now you don't have to think that everything you have learned is useless!" " "

This view of self-esteem may come from the slave culture in Greece, because all the daily chores were done by slaves at that time. This may be true, but I am inclined to the Greek view that philosophy is a sport and an intellectual game. Many people in society think that people who engage in amateur sports have higher social status than professional athletes. According to this pure concept, it is ridiculous that we should stipulate that professional athletes are not allowed to participate in the Olympic Games. The Greek philosophy of "worshipping non-practical knowledge" may be based on the fact that mundane trifles such as the distance from Athens to Corinth interfere with the feeling of abstract thinking, just like miscellaneous dregs mixed into the field of pure philosophy. No matter how hard they argue, this attitude of Greek thinkers has caused them serious restrictions. Greece is not unrealistic about civilization.

But even their great engineer Archimedes refused to write about his actual inventions and discoveries. In order to show his amateur status, he only published his achievements in pure mathematics. The Greeks' lack of interest in secular things-inventions, experiments or natural research-is only one factor that binds Greek thought. The Greeks focused on purely abstract or formal research (they did achieve great success in geometry), which made them fall into the second big mistake, and finally, they were led into a dead end.

Encouraged by the successful derivation of geometric system with some axioms, the Greeks regarded axioms as "absolute truth" and thought that knowledge of other disciplines could be obtained in the same way. Therefore, in astronomy, they regard the following concepts as self-evident axioms: first, the earth is the center of the universe and is motionless; Second, the earth is dirty and imperfect, while the sky is eternal and perfect. Because the Greeks thought that the circle was a perfect curve and the sky was perfect, they thought that the stars should revolve around the earth in a circular orbit. But at that time, from the navigation and almanac, their observations showed that the planet was not in a perfect and simple circular orbit, so they were forced to think that the planet was in a more complicated orbit. Ptolemy put forward an extremely complicated system for this purpose in 150. Aristotle also put forward the theory of virtual motion from self-evident axioms, such as the speed at which an object falls is proportional to its weight. You will see that stones fall faster than feathers. )

Later, the method of deducing from axioms that are self-evident was pushed to a dead end. When the Greeks deduced all aspects of axioms, it became impossible to make further breakthroughs in mathematics or astronomy. The knowledge of philosophy is complete and perfect, even after the end of the golden age of Greece in 2000. When the problem about the material universe is raised again, there is still a tendency to use "Aristotle said …" or "Euclid said …" as a satisfactory solution to the problem.