Ancient Greek philosophy and natural science are all-encompassing. Ancient Greek philosophy is the confluence of ancient knowledge. Under the control of philosophical criticism and speculative tradition, ancient Greek philosophers not only put forward many questions, hypotheses and speculations about natural speculation, but also prepared sufficient and necessary conditions for the emergence of modern science in methodology and epistemology. Among the scientific nutrients in the ancient Greek ideological soil, the author mainly analyzes and expounds three rational factors: mathematics, logic and experiment, because, in a sense, it is these three rational factors and their methodology that have matured and combined after a long gestation. Only then did the brilliant flowers of modern science bloom. 1. The germination of mathematical rationality originated from the Pythagorean school, "forming his wisdom with erudition and considerable technology". Pythagoras and his followers first raised the abstract concept of mathematics to a prominent position. The core idea of this school is that the harmony between numbers and numbers is the origin of all things. The "real thing" is the mathematical harmony existing in nature. The final structure or existence of anything is its mathematical form. "Numbers are the guide and master of human thought. Without its power, everything is in a state of darkness and chaos. " In this way, Pythagoras first studied the composition of everything from the perspective of natural philosophy, and clearly put forward the concept of "the universe is a geometric structure" through the understanding of the world structure. It is precisely because Pythagoras first put forward the concept that the universe is basically a unit. Later, it was "physically manifested in the atomism of Le Xipu and democritus". Trick is precisely because Pythagoras put forward the concepts of point, line, surface and body, and later mathematical differentiation and the advent of European geometric system led to the influence of Pythagorean school on modern times, not just as Mr. Xi said, "its thinking method has nothing in common with modern science". ⒇ His contribution is limited to Pythagoras theorem (2 1) that Babylonians and China people have long known. In fact, "the pioneers of modern science are full of Pythagoras spirit." Copernicus and Kepler emphasized the mathematical harmony and simplicity of heliocentric theory. I think this is the best evidence that the sun center is telling the truth. So did Galileo's declaration, hit the floor: "Philosophy is written in this magnificent book (I mean the universe). This book is always open to us, but it is difficult to understand unless people first learn to understand the language used in this book and explain the vocabulary used in this book. It is written in mathematical language, and its characters are geometric figures such as triangles and circles. Without these figures, people can't even understand a word in this book. " (23) The emergence and development of mathematical rationality makes it possible for people to grasp the nature from qualitative understanding to quantitative description, while modern science has always been adhering to the ideal of as accurate and quantitative description and law as possible. The author thinks that the lack of mathematical rationality in China's traditional culture is one of the key reasons why modern science was born in Europe instead of China. Therefore, China culture has always remained at the level of experience and speculation. 2. Aristotle is the founder of logical rationality. In early Greece, Thales and others often jumped out of observable phenomena, such as "water" and "fire", to explain the origin and changes of the world. The method of this explanation is analogy, so it is intuitive speculation. In the late ancient Greece, rational abstraction and logical method developed and combined with each other. It provides a powerful ideological weapon for seeking the essence and reasons behind things and processes, and greatly enhances the status and explanatory ability of natural philosophy. Especially in Aristotle's The Founder of Formal Logic and Its Syllogism (24), logic and Plato's thoughts directly converge to form a logical and rational explanation. In this explanation, "the usual research route is from easy to know and understand for us to easy to know for nature". (25) The fundamental principle is to seek a reasonable and reliable explanation by logical methods. It is by virtue of logical rationality that Aristotle constructed an all-encompassing "physics" without doing experiments. Almost all the empirical phenomena from atoms to the whole universe have been explained without fear. In addition, the combination of geometric research and logical research is a major feature of the development of logical rationality in ancient Greece. On the one hand, geometry endowed logic with the idea of "pure form" and "proof system", which made the ancient Greeks quickly jump out of the debate itself on the rules of logical reasoning. This paper discusses abstract forms. As Klein said, "The Greeks laid a logical foundation when they worked out the correct laws of mathematical reasoning, but only scholars like Aristotle can model and systematize these laws and make them an independent discipline." (26) On the other hand, logic endows the deductive structure of geometry research and perfects the reasoning tools of geometry proof. That is, "the greatest contribution of the Greeks to mathematics is to insist that all mathematical results must be deduced by deduction." (27) Because of this, more than half a century after Aristotle's logic was founded, Euclid developed various isolated geometric proof systems into a unified axiomatic system and became a practitioner of Aristotle's ideals. The scientific palace of Euclid's geometry is magnificent and simple in structure. All the conclusions are derived from several axioms, which is a successful application of logical rationality. Logic research and geometry research complement each other and jointly create a systematic and effective tool of rational thinking form. It is worth noting that the spirit of logical rationality was not weakened in the Middle Ages, on the contrary, it was strengthened. Although the unified religious ideology in the Middle Ages killed all the reasonable and scientific contents of ancient Greek academic thought with reactionary theological theory, it accepted and preserved their forms almost intact, and preserved and developed logical and rational explanations. The Christian theological theory in Western Europe in the Middle Ages is based on the development of logic. The "ontological proof of God's existence" constructed by Anselmus in On Tao and Monologue strictly conforms to the rules of argumentation in form, and it is difficult to refute them logically even today. Thomas Aquinas, a "saint", logically constructed the "three" about the existence of God in his "Encyclopedia of Theology". Two teleological proofs and argument proofs, once refuted, will logically lead to paradox. Of course, the logical and rational explanation mode can't lead to any scientific knowledge under the cloak of religious theology, just like Bacon said "a barren nun". However, once the view of nature has changed, the authority of natural philosophy and the spirit of scientific experiment will be restored. The birth of natural science is inevitable when people use this ready-made interpretation method and formal tools to sort out experimental facts, describe natural phenomena and explain the laws inside nature. 3. Archimedes of Syracuse is the originator of western experimental rationality. "His works are more modern than those of any other Greek. When combining, he only solves some limited problems. The hypothesis is put forward only to obtain their logical reasoning, which is first obtained by deduction and then tested by observation or experiment. " The lever principle and buoyancy principle named after him, namely Archimedes principle, are his universally recognized scientific achievements, which constitute the basis of rigid statics and hydrostatics respectively. Attaching importance to experiment, technology and application is the characteristic of Archimedes' scientific activities. In modern times, Leonardo da Vinci is an admirer of Archimedes, while Galileo claims to be Archimedes' heir. Although the craft tradition was despised in ancient Greece, this rational spirit became the essence of natural science in modern times. We know that scientific method is the soul of science. The occurrence of scientific understanding and the independence of science are supported by scientific methods. Science itself is essentially a method. We should not only collect what we know, but also teach people to apply what they have learned and seek innovation and change. People should know how to operate, how to operate, and seek better operation. If science can play such a role, it must be established by scientific methods. Then, if we study and discuss the methods pioneered by Bacon, Galileo and Descartes, the three rational factors mentioned above in ancient Greece can be easily found. The methodological basis of modern science is precisely the new quality produced by the fusion, innovation and criticism of scientific nutrients or scientific components in ancient Greece. Francis Bacon, an empirical philosopher, combined logical rationality with experimental rationality and established a systematic scientific induction. On the one hand, the basis of understanding nature is experiment, and we must abandon scholasticism itself and insist on explaining nature according to experience. "All more authentic explanations of nature are obtained through appropriate examples and experiments." (29) On the other hand, the way to understand the nature of philosophy is induction. After collecting data, sorting out three tables, abstracting and summarizing, and seeking explanation, we can "derive axioms from senses and special things in turn, and then continue to rise." Finally, the most general axiom is obtained. (30) The rationalist philosopher Descartes inherited and developed the rational deduction method since ancient Greece. He believes that people can only know the "natural truth" through rational intuition and deductive reasoning according to their innate "innate ideas", mainly logic and mathematics. In his view, the essence of scientific method is "to establish some precise and simple rules; Strictly abide by these rules, we will never confuse the false with the true, we can gradually expand our knowledge without spending a lot of effort, and we can help the mind really understand everything it can understand. " (3 1) Galileo's scientific experimental method was based on the emphasis on experience and tradition in the Hellenistic era, and it was a comprehensive application of mathematics and experimental rationality. This is mainly reflected in his thought experiments in mechanical research, such as inclined plane experiments. He can't really make an infinite inclined plane by studying the principle of inertia from the inclined plane experiment. Therefore, Galileo used abstract methods, imaginative methods and logical reasoning methods to make up for the limitations of experimental conditions. Hands-on and brains are two indispensable aspects in scientific research. Scholars in ancient Greece ignored the former. Scholars in ancient Rome ignored the latter, but in Galileo's case, the two reached a certain degree of integration. It can be seen that the methodological cornerstone of the modern science building can be traced back to ancient Greece. As a summary of ancient knowledge, ancient Greek philosophy is not only the inevitable product of the development of human knowledge, but also the mother and background of modern science. It not only provides embryos and buds for many scientific theories and viewpoints developed in modern times. More importantly, it provides the necessary thinking mode, thinking method, conceptual framework and some rules and principles of rational analysis and critical reflection for the occurrence of modern science, so there would be no modern natural science without ancient Greek philosophy. "In the various forms of Greek philosophy, you can almost find the embryo and bud of various views in the future. Therefore, if theoretical natural science wants to trace the history of the occurrence and development of its general principles today, it has to be traced back to the Greeks. "