1. The germination of mathematical rationality originated from Pythagoras school. Pythagoras and his followers who "formed his wisdom with erudition and considerable technology" first raised the abstract concept of mathematics to a prominent position. The core idea of this school is that number and its harmony are the source of all things. The "real thing" is the mathematical harmony existing in nature, and 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 darkness and chaos. " In this way, from the perspective of natural philosophy, Pythagoras school clearly put forward the concept of "the universe is a geometric structure" through the study of the composition of all things and the understanding of the world structure. It is precisely because the Pythagorean school 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". It is precisely because Pythagoras put forward the concepts of point, line, surface and body that the later mathematical differential and European geometric system came out.
In all fairness, the Pythagorean school's ontological content of "number" is wrong. However, if the order of cognition is reversed and the mathematical model is not imposed on nature according to the mathematical harmony hypothesis, but the mathematical harmony between phenomena is extracted from natural phenomena, then the mathematical harmony hypothesis has important methodological significance. Wolff, a world-famous historian of science, said, "The pioneers of modern science are full of Pythagoras spirit." Copernicus and Kepler emphasized the mathematical harmony and simplicity of sun-centrism, which is the best evidence of truth. Galileo's manifesto is also so sweeping: "Philosophy is written in this magnificent book (I mean the universe), which is always open to us, but it is very puzzling. 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 vocabulary is triangles, circles and other geometric figures. Without these figures, people can't even understand a word in this book. " The emergence and development of mathematical rationality makes it possible for people to change their grasp of nature from qualitative understanding to quantitative description, while modern science has always been adhering to the ideal of quantitative description and law as accurately as possible.
2. Aristotle is the founder of logical rationality. In the early Greek natural philosophy period, Thales and others often jumped directly from observable phenomena to ontological level to explain the origin and changes of the world. The methods of this explanation are intuition, analogy and speculation. In the "golden age" of Greek science, the development of rational abstraction and logical method and their mutual combination provided a powerful ideological weapon for seeking the essence and reasons behind things and processes. It greatly promoted the position and explanatory power of natural philosophy, especially in Formal Logic and the Founder of its Syllogism, Aristotle's logic and Plato's thought directly merged to form a logical and rational explanation model. In this interpretation mode, "the usual research route is from easy to know and understand for us to easy to know for nature". The fundamental principle is to seek a reasonable and reliable explanation by logical methods. Aristotle's greatest contribution to the philosophy of science is his thought about the structure of scientific theory. He thinks that a set of statements of a science and technology organized by deduction, as a deduction system, science should meet three conditions: (1) axioms and theorems have deductive relations, (2) axioms are self-evident truths, and (3) theorems are consistent with observation results. Although his ideal that science is a deductive system was not realized in his time, it was later embodied in Euclidean geometry and Archimedes mechanics. The combination of geometric research and logical research is a major feature of the development of logical rationality in ancient Greece. Geometry endowed logic with the idea of "pure form" and "proof system", which made the ancient Greeks jump out of the argument itself and discuss abstract forms. As Klein said: "The Greeks laid a logical foundation when they worked out the correct laws of mathematical reasoning, but scholars like Aristotle could not model and systematize these laws. On the other hand, logic endows geometry research with deductive structure and perfects the reasoning tool of geometry proof, that is, "the most important contribution of the Greeks to mathematics is to insist that all mathematical results must be deduced by deduction". For this reason, more than half a century after Aristotle's logic was founded, Euclid developed all isolated geometric proof systems into a unified axiom system. No matter how grand the scientific palace of Euclid's geometry is, all its conclusions are.
It is worth noting that the spirit of logical rationality was not weakened in the Middle Ages, but 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 the way of logical rational explanation. The Christian theological theory in Western Europe in the Middle Ages is based on the development of logic. It is gradually established with formal rules as a tool. 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 concept of nature changes, the authority of reason and the spirit of scientific experiments are restored, people use this ready-made explanatory model and formal tools to sort out experimental facts, describe natural phenomena and explain the laws inside nature, and the birth of natural science is inevitable.
3. The originator of western experimental rationality belongs to Archimedes of Syracuse. "His work has a truly modern spirit of combining mathematics with experimental research more than any other Greek. When combining, he only solved some limited problems, and put forward assumptions only to obtain their logical inferences, which were originally obtained by deductive methods. Then test it by observation or experiment. " The lever principle and buoyancy principle named after him, namely Archimedes principle, are universally recognized scientific achievements, which form 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 spirit of experimental rationality became the essence of natural science in modern times.
As we all know, scientific method is the soul of science. The occurrence of scientific understanding and the independence of science depend on it. Science itself is a method. We should not only collect what we know, but also teach people how to use it to acquire new knowledge. If science can play such a role, it must be established by the scientific method itself. If we study and discuss the methods pioneered by Bacon, Galileo and Descartes, it is easy to find the shadow of the above-mentioned rational spirit of ancient Greek science, and the methodological basis of modern science is precisely the new quality produced by the fusion, innovation, criticism and sublation of ancient Greek scientific factors.
First of all, the empirical philosopher Francis? Bacon combined logical rationality with experimental rationality and established a systematic scientific induction (that is, exclusion-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 experimental observation results. "All the more authentic explanations of nature are obtained through appropriate examples and experiments." On the other hand, the way to know nature is induction. After collecting the data, sort out three tables and abstract them.
Secondly, Descartes, a rationalist philosopher, inherited the intuitive induction, deduction and mathematical methods since ancient Greece and founded the hypothesis-deduction. In his view, people can only know the "natural truth" on the basis of universal suspicion, according to the axioms obtained from the "intuitive power of the mind", that is, rational intuition, and according to strict deductive reasoning in mathematics. In his view, the essence of the scientific method is to "establish some exact and simple rules". If we strictly abide by these rules, we will never confuse the false with the true. We can gradually expand our knowledge without making great efforts, and we can help the mind really know everything it can know. "
Thirdly, on the basis of attaching importance to the experience tradition in the Hellenistic era, Galileo established the experimental-mathematical method, which is a comprehensive application of mathematics and experimental rationality. This is mainly reflected in his thought experiments in mechanical research, such as inclined plane experiment. In the study of inertia principle obtained from inclined plane experiment, he can't really make an infinite inclined plane. So Galileo adopted abstract method, imagination method and logical reasoning method. Make up for the limitation of experimental conditions. Hands-on and brains are two indispensable aspects in scientific research. Scholars in ancient Greece ignored the craftsman tradition, while scholars in ancient Rome ignored the scholar tradition. In Galileo's case, these two aspects are combined to some extent.
From the perspective of methodology, modern science not only sublates ancient Greek science, but also inherits its rational spirit. The methodological cornerstone of the modern science building can be traced back to ancient Greece. The philosophy of ancient Greece, whether as a summary of ancient knowledge or as a way for human beings to understand nature, implies the factors that make modern science happen. "In all forms of Greek philosophy, you can almost find the embryos and buds of various views in the future." This sentence of Engels is not outdated for the study of the history of scientific thought (including the history of knowledge and the history of methods). In fact, Greek philosophy is not so much the embryo and bud of many modern scientific theories and viewpoints, but 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 without ancient Greek culture,