The rebirth of Cartesian philosophy 1

(The truth obtained by reconsidering René Descartes’ philosophy from a current perspective)

The truth obtained by reconsidering René Descartes’ philosophy from a current perspective

Part I.

Bibliography quoted in the first part

#Seventeen century scientific revolution, Iwanami Shoten (Publisher)

John Henry, Shinichiro Higashi (Translator)

# Scientific Revolution (edited by Japan Society for the History of Science)

Morikita Publishing (publisher)

Mitsutomo Yuasa, Hiroo Mita, Masao Watanabe, Yasuzo Aoki, Shuntaro Ito

# History of Western Philosophy Ⅲ, Kodansha (Publisher)

Shigeru Kanzaki, Sumihiko Kumano, Izumi Suzuki

# The World of Science and the Philosophy of Mind, Chuokoron Shinsha (Publisher)

Michio Kobayashi

#Descartes, Shimizu Shoin (Publisher)

Katsuhiko Ito

About the Scientific Revolution of the 17th Century in Europe

The Scientific Revolution is given by historians of science to the period in European history when the conceptual, methodological, and institutional foundations of modern science were established. Although historians of science differ as to the exact period, the 17th century is considered to be the center of the scientific revolution, the 16th century the period of preparation in various aspects, and the 18th century the period of consolidation and groundwork.

In recent years, studies of medieval science have revealed that medieval natural philosophy laid the foundation stones for the scientific revolution. Therefore, we can distinguish between the medieval period that laid the foundation stone of the scientific revolution and the period of superstructure construction. The Middle Ages were once thought to be a period of sterility and stagnation for science, but thanks to the many excellent studies written from a continuist perspective, no one now denies the legacy of the medieval thinkers. In particular, we now know that remarkable contributions were made in the Middle Ages in the development of the mathematical sciences of astronomy, cosmology, optics, and kinematics, as well as in the development of ideas of natural laws and experimental methods.

Galilei’s integration of kinetic theory and natural philosophy resulted in what he called a new theory of motion. This is still considered today to be a major influence on the development of later theories. Similarly, the influential natural philosophy of René Descartes (1596-1650) emerged from an attempt to give natural philosophy the certainty of geometric reasoning. The new natural philosophy of Isaac Newton (1642-1727) was based on mathematical principles, as the title of his major work suggests.

What happened in the Scientific Revolution? Simply put, we can summarize that in the Middle Ages, natural philosophy had nothing to do with mathematics or experimentation, but when the Scientific Revolution took place, these different kinds of natural research methods and natural philosophy merged to create what we might think of as a science.

Where early modernity is concerned, the use of the term “natural philosophy” in place of “science” is by no means desirable. Science” and ‘natural philosophy’ are not the same concept. One of the reasons the Scientific Revolution was revolutionary is that throughout this period natural philosophy was transformed into something different and closer to what we think of as science.

The term scientific revolution

Descartes likened true learning (philosophie) as a whole to a tree. The roots are metaphysics, the trunk is physics, and the branches from the trunk are the sciences. This can be called Descartes’ tree of sciences. Descartes listed medicine, mechanics, and moral philosophy as the sciences that are branches of this tree. Moral science is the ultimate in wisdom, which is the totality of knowledge of the other sciences. Descartes’ way of explaining this shows the historical flow of the history of European academic thought. Descartes did not intend to take the whole of science and call it “science,” but rather to call physics, mechanics, medicine, etc. all together “science,” as in Descartes’ tree of learning. The discussion here covers the period from Galileo Galilei (1564-1642) to the time of Newton in the 16th and 17th centuries, some 300-400 years ago. The Scientific Revolution is aptly described as the establishment of modern natural science in the 17th century. Let me explain a little about the significance of discussing events in Europe 300-400 years ago here and now

The Significance of the Scientific Revolution

Nowhere is there any denial that the present age is an age of technological revolution, and to truly understand the nature of 20th century science well, we must go back to its starting point. The key to unlocking the secrets of our turbulent times can be found in the history of science in the 16th and 17th centuries. History without the history of the development of science and technology is meaningless. The history of the scientific age should be centered on the history of science. Within that history of science, the idea of scientific revolution forms the framework of the whole.

In the modern society in which we live, the enormous power of modern science, symbolized by nuclear power and satellites, is truly overwhelming, and no cultural, social, or political event can be described apart from its enormous influence. It is literally the center of modern civilization, and it is no exaggeration to say that the future fate of mankind depends on the progress of this science. The overwhelming power of science, which has now become the destiny of mankind, actually originated in the “Scientific Revolution,” a one-time historical event that took place in the 17th century, and modern civilization is nothing but the direct result of this revolution. It was here that the prototype of “modernity,” which is directly linked to the modern age, was created.

Herbert Butterfield (1900-1979), a distinguished historian of science at Cambridge University, emphasized the significance of the Scientific Revolution. This revolution overturned the authority of science not only in the Middle Ages but also in the ancient world. Not only did it bring down scholastic philosophy, but it also led to the destruction of Aristotle’s (384 B.C. – 322 B.C.) natural science, which shines above all others since the rise of Christianity. The scientific revolution became the true genesis of the modern world and the modern spirit, transforming the character of habitual human intellectual activity and transforming the whole structure of the physical universe and of human life itself. According to him, the traditional historical classification of the Renaissance and the Reformation as the beginning of “modernity” is no longer appropriate, and the Scientific Revolution must now be regarded as the decisive moment that made the modern world modern. It was this revolution that formed a new intellectual attitude toward nature that did not exist in ancient times or in the Middle Ages, and by carrying out a fundamental intellectual transformation, laid the foundation for the infinite progress that man has made since then, from which there can be no turning back. And so we are situated in the midst of this process of progress, trying to understand the immense significance of this transformation that took place 300 years ago. Is not the ultimate significance of the scientific revolution even more important than the discovery of agriculture, which made civilization itself possible? For in science is built in the potential for unlimited progress.

Meaning of Scientific Revolution

Assuming that the historical significance of the Scientific Revolution is as described above, in what sense is the Scientific Revolution called a “revolution”? What is the meaning of the scientific revolution as a revolution in the history of science? To grasp the establishment of modern science as a truly revolutionary event, the first thing to consider is that what is meant by “science” when it is called Greek science or medieval science is not science in today’s sense, but a system conceived under a different worldview, view of nature, and values. It is important to know that “science” was not science in today’s sense, but rather a system conceived from a different worldview, view of nature, and sense of values, and that it was essentially different in its purpose, orientation, methods, and structure.

It was only after the Scientific Revolution that the concept of science, which is identical to today’s science, was created, and it is fundamentally false to assume that the concepts and methods of today’s science existed in ancient and medieval times.

According to the British historian of science A. Rupert Hall (1920-2009), it was during the course of the “scientific revolution” that the “scientific attitude” in the modern sense was formed for the first time. There, a new principle method of recognizing nature, the so-called scientific method, was established, and science thereafter took on a cummulative character. This new scientific attitude and method required not only observation but also rigorous standards of constructive experimentation. It also expelled the spiritual and hidden qualities from the realm of natural cognition and limited its focus to empirical phenomena. It also required a strict distinction between theories with sufficient experimental evidence and conjectural hypotheses or mere speculation. It was also important that the systematic experimentation supporting the theory be tightly coupled with numerical and quantitative treatment. The “scientific method,” the natural understanding first formed, remained unchanged no matter how the content of science subsequently developed, allowing for the cumulative advancement of scientific knowledge in the years to come.

However great the renewal of ideas of matter, time, space, and causality, it is a renewal of the “content” of science, not of the “structure” of science itself. Newton was not shown to be wrong by Albert Einstein (1879-1955). Nor was Antoine-Laurent de Lavoisier (1743-1794) shown to be wrong by Ernest Rutherford (1871-1937). Formulations of scientific propositions are changed and the limitations of their application are recognized, but they still retain their validity within the domain in which they were found to be head-first correct.

In general, after a scientific revolution, later theories advance cumulatively by adding to or encompassing the earlier ones. However, this was not the case in the very scene where the “scientific revolution” was taking place. When the dynamics of the Scholastic philosophy of Aristotle is defeated and the dynamics of Galileo is established, the latter does not emerge by adding something to the former, nor does the latter envelop the former. A new way of perceiving nature, combining experimental and mathematical methods, emerged, presenting the correct basic composition of nature and overturning the cosmological worldview that had existed from antiquity through the Middle Ages.

In the words of John Desmond Bernal (1901-1971), this scientific revolution overturned the entire structure of intellectual assumptions handed down from the Greeks and firmly defended by Muslim and Christian theologians, and a radically new system It was replaced by a radically new system. The hierarchical structure of Aristotle’s universe gave way to Newton’s mechanistic vision of the world.

What the Scientific Revolution Revitalized

The Scientific Revolution not only corrected erroneous theories and facts, but also shattered and removed in one fell swoop the old conceptual framework itself and the old worldview, view of nature, and values that had dominated for more than a thousand years since the Greeks and were inextricably linked to it. By carrying out a fundamental intellectual turn, he laid the foundation stone for an entirely new understanding of nature and established a new method of inquiry into nature that we today call the “scientific method. This turn established for the first time the concept of science as we know it, and the subsequent development of science was based on the foundation stone laid here, allowing for a series of perceptions pioneered by the scientific method. In mechanics, from Galilei to Newton; in astronomy, from Nicolaus Copernicus (1473-1543) to Johannes Kepler (1571-1630); and in chemistry, from Sir Robert Boyle (1627-1691) to Lavoisier. Herein lies the meaning of the term “revolution” in the Scientific Revolution.

The scientific revolution cannot be attributed merely to the revival of past ideological traditions; it is the birth of a completely new intellectual attitude, and this “newness” must be made possible by factors unique to the modern age. It is the accumulation of technological practice since the Renaissance, and the theoretical understanding of this technology is the hallmark of modern science. If we believe that the scientific revolution occurred simply because of the rise of technological practice, I believe that we are not grasping the situation correctly.

Why were the technologists of the Renaissance unable to create modern science? Galilei, Descartes, Francis Bacon (1561-1626), and Boyle were well educated in the universities, were familiar with the ideological heritage of the past, and were interested in modern technical problems. Why did they establish modern science for the first time? It can be said that the Scientific Revolution was the result of a unique combination of the theoretical heritage of the Greeks and the technological practices of the late Middle Ages, and the creation of a completely new method of inquiry into nature. In the Greek and medieval periods, “rational thought” and “technical practice” were separated from each other. I think this is the reason why science could not arise. In Greece, for example, the former was the exclusive property of philosophers and the latter of slaves, and in the Middle Ages, the former belonged to the theologians and the latter to uneducated craftsmen.

One of the problems of the current “scientific revolution theory” is to pursue the specific ways of combining, linking, and inter-blending the theoretical heritage belonging to this scholarly tradition and the technical practice belonging to the artisanal tradition, and to identify the scene where this dual structure is unified. Only then will the unique “structure” of the modern scientific revolution be revealed. The methodological product of the scientific revolution, the combination of the “mathematical method” and the “experimental method,” is also deeply related to this. This is because the former is in the theoretical heritage since the Greeks, while the latter was forged in the technical practice of modern craftsmen.

Craftsmanship is not just a matter of being theoretically sound; it cannot go a step further without actually making things and experimenting with them. Craftsmen, however, were unable to make these experimental facts into a universal theory, only to confine them to their long years of experience. It was modern scholars, armed with rational theory and interested in technical practice, who did so. Let us trace the broad vein of this union and unification.

After writing his book on the origins of modern science, Butterfield noted that the scientific revolution was the true father of the modern world and the modern spirit. And the significance of the scientific revolution is unparalleled since the advent of Christianity. But if we want to know the cause of the Scientific Revolution, we must look for it in that great change in European history called the Renaissance. The Scientific Revolution cannot be discussed without mentioning the Renaissance. The Scientific Revolution, like the Reformation, can be seen as a consequence of the Renaissance.

The Role of the Renaissance

The Renaissance led intellectuals to a deepening interest in history. A consciousness was born that positioned themselves as heirs to the intellectual glory of ancient Rome or ancient Greece. Their concern was to restore to our time the wisdom of the ancients, which had never been surpassed by man, and for many, could never be surpassed by man. Some of them went through the libraries of monasteries all over Europe and discovered many ancient manuscripts that had been buried without being read by the monks. Thanks to printing technology, these manuscripts were preserved and made available to readers throughout Europe with relative ease. Most of the ancient writings we have today were collected and preserved by Renaissance humanists.

To get an idea of the impact of the humanists of the time, one need only look at their influence on traditional Aristotelianism as it was then taught in European universities. For example, the rediscovery by humanists of Diogenes Laertius (active around the 3rd century) in his “Philosophical Chronicles” and Marcus Tullius Cicero (106 B.C. – 43 B.C.) in his “On the Nature of the Gods), it can be mentioned that Aristotle, who was considered the highest authority on philosophy in the Middle Ages, was not the only philosopher in antiquity. Furthermore, it was clear at a glance that Aristotle was not the most respected philosopher in antiquity. The subsequent discovery of the writings of other philosophers, such as Plato (427 BC – 347 BC), the Neoplatonists, the Stoics, and the Epicureans, provided an excellent source for learning about philosophical views different from those of the dominant Aristotelianism of the time. Among the ancient philosophies thus restored is the skepticism of the late Academia. The Late Academia was the revered school founded by Plato. The situation was further complicated by the revival of writings on mathematics and magical thought. Aristotle did not emphasize mathematics, whereas Plato saw it as a pathway to certain knowledge. That alone was enough to generate a sudden surge of interest in mathematics.

Writings on ancient magical thought included those by Iamblichus (245-325) and Porphyry of Tyre (234-305). Among others, thanks to the writings attributed to Hermes Trismegistus, who was considered to be an ancient sage contemporary with Moses (active around the 16th or 13th century B.C.), more and more people believed that witchcraft was the oldest source of wisdom. This is the reason why witchcraft was considered to be the oldest form of wisdom. This is why witchcraft also came to be considered knowledge in the legitimate sense of the word. The Church was opposed to witchcraft, not least because of its association with demonology, but despite its protests, interest in witchcraft continued. The intellectual situation became more chaotic with the offer of ancient knowledge, but it was a chaos of possibilities. As a result, during the Renaissance, traditional Aristotelian natural philosophy lost its intellectual authority, and a new natural philosophy emerged. It was also a time of new thinking on the question of how knowledge of sufficient certainty should be discovered and confirmed. Authority at the time came to be seen as fallacious and unreliable. The emergence of new philosophical systems, such as skepticism, and the focus on non-philosophical approaches, such as mathematics and magic, put the pursuit of only conventional knowledge at risk. As a result, emphasis was placed on discovering the truth by relying solely on one’s own experience and efforts.

The Revival of Greek Philosophy

The revival of ancient writings during the Renaissance had a variety of intellectual consequences, one of which was a growing interest in the magical tradition. I believe this was due in part to the fact that ancient Neoplatonic writings were read.

Newton was also an alchemist. Newton’s alchemical research was long dismissed as irrelevant to his scientific work, but in recent years it has been found to have influenced his theory of matter. Betty Jo Teeter Dobbs (1930-1994) and Richard S. Westfall (1924-1996) emphasize that the fact that the hidden forces of inter-particle attraction and repulsion exist at the foundation of Newton’s natural philosophy was possible because of Newton’s familiarity with alchemical modes of thought.

Even if knowledge of alchemy alone is not sufficient to explain Newton’s belief in hidden forces, alchemy is important for understanding one aspect of Newton’s scientific thought: from his early paper “A Hypothesis of Light” sent to the Royal Society in 1675 and from his “Optics” (third edition 1717), Newton clearly had much grounding in the theory of light in alchemy. Alchemy believed that light could interact with matter and give it a certain active character. The origins of Newton’s notion of gravitation may lie elsewhere, but the idea that matter has some sort of active principle latent in it seems to be taken directly from the alchemical tradition. It is possible that such an active principle was thought to be the cause of universal gravitation.

Within this Platonism, a particle theory view of matter began to develop. For example, it is clear that Newton believed in the particle-like structure of matter, and with respect to light, he oscillated between particle and wave properties, gradually leaning toward particle nature and approaching the idea that a universal gravitation force is inherent in those particles. Newton himself carefully left room for contrary interpretations in cases that could not be determined experimentally or theoretically, but his followers in the 18th century reinterpreted this and pushed toward a more rigorous form of atomic theory. However, there was still room for a “first push” by God in the image of nature as depicted by the Principia, which consisted of atoms.

Medieval Thought and the Scientific Revolution

In the Dialogue Concerning the Two Chief World, published in 1632, Galileo begins his discussion of the law of natural falling motion with the following dialogue. Salviati, speaking on Galileo’s behalf, says, “It is not enough to know that natural falling motion is a straight line. We must know whether it always maintains the same speed, or whether it decelerates or accelerates. After clarifying that this is an accelerated motion, he then says, “It is not enough to know that it is an accelerated motion. He goes on to say that we must know what ratio the accelerated motion is made up of. Finally, I do not think that this problem has already been clarified by any philosopher or mathematician. In this way, Galileo emphasizes that the acceleration rate of natural falling motion is an extremely important problem that has never been studied or solved by anyone before.

In response, Simplicius, another interlocutor who represents the Aristotelian school of scholars, develops the following counterargument: “Philosophers are primarily concerned with universal matters. They find definitions and the most general criteria. They leave to mathematicians certain subtle and trivial matters that are the object of curiosity. He then goes on to say that Aristotle gave a good definition of what motion in general is. He is also satisfied with showing that the primary attributes of locomotion are naturalness, violence, simplicity, composition, equality and acceleration. Furthermore, he states that he is satisfied with the basis of acceleration for accelerated motion, and leaves the pursuit of such acceleration rates and other more specific events to the experts in mechanics and other lowly craftsmen. In this way, he indirectly defends Aristotle by arguing that the study of the acceleration rate of natural falling motion, which Galileo is so proud of, is not research that should be done by philosophers.

People who supported the Scientific Revolution

It must be said that the reformist ideas of humanists played a major role in the origins of the Scientific Revolution. Let’s look at three characteristics of the Scientific Revolution.

1. The use of mathematics to understand the workings of the natural world.

2. The use of observation and experimentation to discover truth.

3. It broadened the concept of the usefulness of knowledge, which had previously been limited to the lowly mathematical artisans and sorcerers, to include natural knowledge.

Humanism was necessary for the knowledge that would bring about the Scientific Revolution to take root in people’s minds.

Mathematics came to be used not only to describe the natural world, but also to explain it, and this was not limited to the field of astronomy. At the time, there was a growing interest in exploration against the backdrop of the development of trade and the expansion of colonial rule. This also led to an interest in practical mathematics, such as navigation, surveying and map-making. Leading intellectuals began to turn their attention to these fields, and it also became possible for artisans to rise socially and intellectually. It is thought that this also led to the emergence of people from the upper classes who became interested in mathematics.

The Jesuits also contributed to the introduction of mathematics into natural philosophy through their active educational activities. Their emphasis on mathematics education can be seen in the fact that mathematics was taught alongside natural philosophy and metaphysics at their schools. The educational activities of the Jesuits are important in history. Their attitude towards mathematics at their schools reflects the major trend of improving the status of mathematicians. It also impressed upon many students the importance of mathematics.

At least two thinkers studied at Jesuit schools and later contributed to the mathematical description of the world in their own way: Marin Mersenne (1588-1648) and Descartes. Mersenne became a monk of the Order of the Minims in 1611 and devoted his life to learning in order to defend his faith with the support of the order.

Mersenne was also opposed to skepticism, and he considered mathematics to be the most reliable kind of knowledge, through which it is possible for humans to reach the knowledge of God. Mersenne wrote energetically, and he also encouraged other mathematicians to publish their research. What he was even more enthusiastic about was exchanging letters with prominent scholars all over Europe. For scholars working in similar fields, Mersenne’s network became a common source of information. He would send the results of his latest research to others who needed them. At the same time, he also used this personal information network to spread his own ideas and his personal belief in the importance of mathematics for philosophy.

People who are not interested in the scientific revolution

Now, the question we are going to address here is not to describe historically or concretely how Galileo broke through the conservative shell of Aristotle’s scholastic students and achieved brilliant modern scientific achievements. What we want to discuss here is why philosophers and thinkers of the time did not themselves undertake work such as Galileo’s formulation of the law of natural falling motion, which should have been highly valued for its originality and novelty, but instead left it to lowly craftsmen.

Let’s take another example. In 1609, Galileo heard that in Holland, a pair of glasses had been invented that made distant objects appear closer, and he set about making them himself, and succeeded in making a telescope. Galileo immediately pointed it at the sky and made a surprising number of discoveries for the time. What surprised people the most was that the moon also had mountains, and that Jupiter had four moons, just like the earth. According to Aristotle’s scholastic theory, the moon and other celestial bodies were made of a higher fifth element called ‘aether’, which was different from the four elements of earth, water, air and fire that make up the earth and its surroundings, and it was also said that their shape was also the highest form suitable for this element, a perfect sphere. Therefore, it was considered completely ridiculous that the moon, which is a celestial body, would have mountains and valleys.

The teachings of scholastic philosophy

In response to the simple wonder and strong curiosity of ordinary people, the scholastic scholars were extremely critical of these new inventions and discoveries. When they heard about the telescope, some of them said that it was not a new invention or anything, and that Aristotle had already recorded it. Aristotle recorded in one of his texts that it is possible to see the stars even in the daytime from the bottom of a deep well. He gave the reason for this as being that the steam that accumulates in the well strengthens human eyesight. He was enlightened by the idea of a telescope tube from the idea of a deep well, and the idea of a lens from the idea of steam in a well. This is a completely ridiculous story to us today, but it is believed that this is not something that Galileo exaggerated or made up, but a true story that actually happened at the time.

Scholastic philosophy that only thinks

We cannot attribute the reason why the Aristotelian scholastics did not try to look through the telescope that Galileo had made, as Galileo said, simply to their cowardice. This is not enough, and it seems that there was something more significant and profound than personality at play in the difference between the attitude of the Aristotelian scholastics and Galileo’s attitude towards learning. Research into the rate of acceleration or looking through a telescope would not have been such a big deal or such a frightening thing to do. Therefore, the reason they did not do this research or look through the telescope was not because they were too lazy to do these things, or because they simply did not want to do them, but because they did not feel the need to do them. They must not have felt the need to do them, and they must not have been interested in them. Then, why did the Scholastics, represented by Cesare Cremonini (1550-1631), not feel the need for such things and not take an interest in them?

What the Scholastic Philosophy Sought

For Galileo, the greatest concern during his many years of research was, of course, the formulation of the various laws of motion of objects. To put it simply in his own words, it was “to gain concrete knowledge of natural events”. This was the greatest and ultimate goal of Galileo’s “science”. However, the ultimate goal of the scholastic’s “science” was not this. The greatest research topic for the scholastic students was, in a word, the relationship between man and God, and clarifying this connection. The connection between God as the creator of these creatures, and the order that exists between these creatures, especially man, was the subject of their research, and the clear description of this order was the goal of their research. Aristotle’s texts were also studied, developed and used in this way, and in a sense were distorted and incorporated into the hierarchical framework of Catholic belief. And the concept of “nature” was also understood as the way in which the order laid down by God as the Creator manifested itself in the created world, or in other words, as the “true nature” of things. Nature is a catalyst for human beings, who are rational beings, to become aware of their own true nature and to strive towards the highest good, God, through this awareness. Therefore, nature in the materialistic sense, which is independent of human thought and intention, as we think of it today, does not have the rationality to be aware of this, even though it has its own order and true nature as God’s creation. Therefore, as a conscious effort towards God, who is the highest good, was considered impossible, such things were evaluated as being one level lower than beings with human-like reason. Therefore, in the world of Catholic faith, which begins with humans and ends with God, things of the materialistic world were not worthy of study.

Scholastic philosophy seeks a sacred world

Once the acceleration rate of natural falling bodies has been established, how much will it contribute to solving the various important issues surrounding the relationship between humans and God? And even if it is proven that the curve described by a projectile is a parabola, rather than a circle, a straight line, or a combination of the two, how much light will it shed on the extremely important question of the origin of evil found in human actions? It was far more urgent and relevant to deepen research into how much of the human soul is immortal than to be distracted by toys like telescopes, which were incomprehensible. When you think about it like this, it is better to think that the reason that the philosophers of Galileo’s time were unable to recognize the greatness and importance of Galileo’s science was not because they were all second-rate or third-rate scholars of the dying days of scholasticism scholars, but rather that they also believed in the same scholastic doctrines that were in their heyday, and were confined to that worldview.

The Role of the Reformation

This new attitude can also be seen in the Reformation. Martin Luther (1483-1546) refused to obey not only the Pope, but also local priests. Luther, who advocated the idea that “every believer is a priest”, encouraged Protestants to read the Bible for themselves and to feel God’s will for themselves. This may seem like just a reaffirmation of the authority of the Bible, but in reality it was something new. Until then, Roman Catholics were not supposed to read the Bible, but rather to consult with priests and wait for them to guide them. For Luther, this authority of the priest was mistaken, and he argued that each person should go back to the Bible and discover the truth for themselves. In the 16th century, the natural world was often compared to “another book of God”, and here we can see the similarities between the Reformation and the Scientific Revolution. In the scientific revolution, we can see an emphasis on experience and observation as a method for discovering truth. There is no doubt that the emergence of this new empirical or experimental attitude towards the study of nature had to go through the changes brought about by the Renaissance.

Galileo’s view of the world

The world view of the scholastic scholars was different from that of Galileo. So, what was Galileo’s view of the world? It is very difficult to extract Galileo’s view of the world from his own letters and writings in a clear form. However, from fragments of his words, etc., we can deduce that Galileo was particularly keen to assert that his heliocentric theory did not contradict the words of the Bible. For example, in a letter dated December 21, 1613 to the mathematician Benedetto Castelli (1578-1643), and in a letter to Cristina di Lorena (1565-1637) in 1615, Cristina di Lorena (1565-1637), it says, “The words of the Bible, while necessary for the salvation of the human soul and the consolidation of faith, have no direct relationship to natural philosophy.” From this sentence, we can infer that Galileo thought that the world of humans and nature, which had once been united and had a hierarchical relationship within the Catholic faith, had been completely separated and was now asserting its own existence. In this sense, I think we can find Galileo’s world view, which he did not describe as a clear philosophical system, in Descartes’ dualism.

The historical background of the scientific revolution

The scientific revolution was achieved through the establishment of experimental methods, and the 17th century is said to be the age in which experimentation was modernized. This method of experimentation was only made possible by the combination of Newton’s empiricist attitude and Descartes’ rationalist attitude. The reality of the 17th century was one of division, contradiction, endless trial and error, and the confusion of many perceptions. In a sense, human senses and reason in experimentation were more likely to negate each other than cooperate, leading to many foolish conclusions.

The contradictions in the methods lead to serious skepticism, and the trial and error process leads to despair. And this skepticism and despair were the characteristics of the 17th century. In the first volume of his main work, Novum Organum, Bacon energetically discusses his despair of human knowledge in aphorisms 94 to 115. Bacon, the proponent of the experimental method of the time, was the first person to experience this tragedy of experimentation. Boyle also left a significant mark on the promotion of the experimental method of the 17th century, but his outlook on life was also always accompanied by a pessimistic awareness of “the necessary imperfection of human nature”.

Needless to say, it was Newton who perfected this experimental method, but when he said in his dying words that he was “only like a boy playing on the sea shore”, it is clear that the pessimism of the 17th century never left him and followed him throughout his life. Michel de Montaigne (1533-1592) and Heinrich Cornelius Agrippa (1486-1535) were skeptics who rejected and destroyed the ancient authority of Aristotle in the 16th century authority, but the skepticism of the 17th century was different from the skepticism of the time, which was directed externally. The skepticism of the 17th century was deeply directed inward, and it formed a kind of anguish that even the scientists of the time could not solve. Historians refer to this as the “critical years” and speak of it as an unprecedented “age of skepticism”.

The scientific revolution of the 17th century was accomplished through the persistence of this skepticism. It progressed in spite of all despair. It was a time of methodological schism, a time of great experimental activity, a “century of absurdities” and a “century of genius”. It was also a time of crisis and a time of the marvels of science. As a time of transition from tragedy and chaos, or a time of transition for modern intellect, the flow of science in the 17th century can truly be called a time of “change” or “revolution”. When we talk about the 17th century as the age of the scientific revolution, we should not mean that a new system replaced an old system, but that the name “scientific revolution” should be given to it in that it rose above the tragedy despite the anxiety and despair caused by the alternation of old and new ideas, and despite the suffering of skepticism about all things human.

The arrival of the scientific revolution

Newton’s Philosophiae Naturalis Principia Mathematica (1687), or Principia, is probably the pinnacle of the mathematization of the world image. What is famous about this book is that it established that the planets revolve around the sun due to the same force that causes an apple to fall to the ground, but its content is far richer than that. In it, Kepler’s laws of planetary motion were mathematically proven for the first time, and the theory of the moon and comets was modernized for the first time. Newton’s laws of motion replaced Descartes’ laws of nature, and as a result, the theory of the collision of objects was brought one step closer to completion. Newton also succeeded in theorizing oblique collisions, which Descartes had been unable to deal with. Newton also fully understood centrifugal force. He also pioneered the theory of the motion of objects in fluids, and based on this research he was able to conceive of an acoustic theory that focused on the speed of sound propagation, which changes according to the pressure and density of the medium. Of particular significance for the mechanistic philosophy supported by many of his contemporaries, including Newton himself, was his mathematical demonstration of how macroscopic, visible phenomena could be explained in terms of microscopic phenomena.

With the publication of Newton’s Principia, the trend towards the mathematical description of natural philosophy that began in the 16th century was completed. Perhaps the reason for this high regard is that, unlike Galileo and Descartes, Newton arrived at the correct answer, both mathematically and in terms of natural science.

Galileo’s Achievements

The men who triggered the scientific revolution were Galileo and Descartes. Although Galileo was the elder of the two and his scientific activities began at the end of the 16th century, their main periods of activity overlapped. Both began their academic careers under the influence of Aristotle’s system, and after carrying out fundamental critical work on that system, they formed their own sciences.

The first reason why Galileo was able to break free from the influence of Aristotelian natural philosophy, which was dominant until his time, was his mastery of the science of Archimedes (c. 287 BC – c. 212 BC), which was only fully introduced and absorbed in the second half of the 16th century. Archimedes was the founder of “statics”, which deals with “levers” and “balance”, and he was a mathematician who presented a mathematical formulation of the subject. This was a clear example of how mathematics expresses the laws of natural phenomena and controls those phenomena. This science of Archimedes also directed the scientific activities of Descartes, who we will look at next. It shook up Aristotle’s position on natural science, which held that “abstract mathematics” could not practically constitute “concrete natural science”.

Justification of the Copernican Theory

Until then, the world of celestial bodies was thought to be eternal and unchanging. Galileo actively supported the Copernican Theory based on his own astronomical observations and theoretical evidence. Here are the reasons for this. First, his observations of sunspots showed that they were created and disappeared. The fact that the sun also has a unique property of creation and destruction, which had been thought to be specific to the world on earth, means that the two worlds are not different. For Galileo, this means that the circular motion that had been thought to be a unique motion of celestial bodies can also be applied to the motion of the earth itself.

Secondly, the main reason why the geocentric theory had been rejected up until that point was that it could not explain the fact that when you drop an object from the top of a high mast on a moving ship, the object will fall directly below the mast. In response to this, Galileo explained it by arguing that all objects on the ground share the same horizontal uniform motion of the earth, and that objects that share the same uniform motion in the same direction are mutually at rest. This theory would later be called “Galileo’s Principle of Relativity”.

The heliocentric theory would lead to a reinterpretation of the real structure of the universe and the world on earth, not according to our everyday perceptual experience, but from the perspective of “the rotation of the earth”. The celestial world and the terrestrial world are seen as being of the same nature, and the concept of “up and down” is no longer absolute, but is understood as being relative to our perception. In this way, the Aristotelian teleological and hierarchical order that had been thought to constitute the universe and nature is fundamentally dismantled.

Identifying abstract mathematics with concrete natural science

In this way, the phenomena experienced through our sensory perception do not indicate the real structure of nature, but are merely phenomena relative to our sensory perception.

In his Dialogue Concerning the Two Chief World (1632), Galileo makes an Aristotelianist appear as a character and has him argue for the views of Aristotelian natural philosophy, which he then refutes.

In this, the Aristotelianists say that mathematics deals with abstract objects, whereas natural science is a discipline that studies concrete phenomena in the real world, and that it is misguided to try to construct concrete natural science using abstract mathematics. In response, Galileo states that “what occurs concretely in natural phenomena also occurs in the same way in the abstract”, and he argues that it is possible to appeal to rigorous mathematics and pursue the rigorous laws within natural phenomena in the abstract.

Through these works, Galileo brought about a new, modern scientific methodology. The first of these was the “idealization” method. Anticipating the Aristotelian objection that his analysis of the motion of projectiles was an imaginary analysis that ignored many of the factors involved in natural phenomena and did not analyze natural phenomena themselves, Galileo argued as follows He argued that in order to deal with a problem using a scientific method, it was necessary to isolate difficulties such as air resistance. For this reason, when applying the theorem to the real world, it was necessary to use it with the constraints taught by experience.
Secondly, he showed the efficacy of mathematical reasoning in the work of natural science. In his analysis of natural phenomena, Galileo said that “knowledge of a single fact, obtained by discovering its mathematical reason, makes us understand and verify other facts without having to repeat the experiment” and that mathematical reasoning can “prove things that have never been observed before through empirical observation” through deductive reasoning.
In fact, he used this mathematical kinetic theory to prove that projectiles follow parabolic trajectories and that their maximum range is at an angle of 45 degrees. In this way, he demonstrated the “productivity” of mathematical natural philosophy, which brings new knowledge about nature through reasoning, independently of sensory experience.

The British and the Continent, with their different approaches to experimentation

In order to give mathematical sciences the same kind of authority as Aristotelian natural philosophy, it was necessary for artificially created phenomena to be as obvious to the general public as everyday phenomena. There were attempts to solve this problem by conducting experiments in public places, for example by dropping weights from the tops of church steeples. However, the most popular method was to record the experiment in detail in a publication. In many cases, the explanations followed the format of a geometry textbook. The author would give specific instructions on how to construct the experimental apparatus, the procedure for the experiment, and the results of the experiment. It was noted that the experiment had already been repeated many times and that many experts had observed it. Eventually, this format became established as the way to report experiments.

Cornell University professor Peter Dear (1958- ) has described how this kind of experimental practice became widespread on the continent. However, the experimental philosophy that took root in Britain was quite different. For example, when explaining experiments, the French philosopher Blaise Pascal (1623-1662) took a general perspective, as if the experiments were expressing the truth of things, and said that if you did these things, this would surely happen. This was not the case with Robert Boyle, the leader of British experimental philosophy. From his point of view, Pascal’s explanation can only be based on the theory that Pascal himself assumes. As Bacon says, people can conduct experiments to affirm their own preconceptions.

The experimental method in Britain, as advocated by a group of members of the Royal Society led by Boyle, was said to reveal only the facts. This was different from the experimental method on the continent, and was said to be free from theoretical preconceptions.

There are two fundamentally opposing schools of thought in the study of nature. The first is based on the idea of trying to understand nature in a unified way based on certain principles. The second is based on the idea of trying to understand nature as it is, concretely and holistically. In terms of scientific methodology, the former is based on deduction and the latter on induction, but it is not that simple.

The former method ignores minor phenomena and focuses on the unifying principles that govern nature. Once it has reached these principles, it then uses them to explain every corner of the world. Any phenomenon or law derived from them can only serve to reinforce these principles.

For the latter, they describe things and phenomena objectively without paying any attention to questions such as what can be derived from the thing or phenomenon, what the law that lies at the root of the phenomenon is, and how nature can be explained by that law. There is a spirit of thorough documentation there that refuses to accept conclusions.

The history of science developed through the violent clash of these two trends. Individual thought was also torn apart by these two trends. Let us call the former the trend of cosmology and the latter the trend of encyclopedias. In the first half of the 17th century, the former was typified by Descartes’ cosmological conception, and the latter by Bacon’s method of natural history.

The British Method of Experiment

Universal statements made no sense to many British Protestants, because they were based on false beliefs – the belief that the way the world is must be inevitable. For example, statements such as “there must be a vacuum” or “the smallest parts of matter must be indivisible”. To them, necessary statements seemed to unjustly limit the omnipotence of God, who could arbitrarily make any philosophical system a truth. The English tended to think that God could make any matter a truth without being bound by philosophical possibilities or impossibilities. Once their method was established in natural philosophy, it would have been a general method for justifying knowledge. The British experimental method was expected to be a means of agreement essential for a community that could create spontaneous order without the need for tyrannical authority.

The difference in experimental methods originated in religion

There was an effort to abandon the Aristotelian method of trying to do natural philosophy using syllogism and instead use reliable experiments, but the issue here is not just an abstract epistemological shift. The credibility of traditional Aristotelian natural philosophy came from the fact that the premises used were self-evident, but this credibility itself needed to be replaced with something else. Like mathematical propositions, experimental knowledge is not self-evident. In order to convince people of its truth, if it was not to be accepted on a personal level, it was necessary to explain the procedure in detail. For experimental philosophers like Boyle and Pascal, it was impossible to expect everyone around them to become experts in experimental philosophy and mathematics. So they took the path of emphasizing how reliable their arguments were.

So where did the difference between Englishmen like Boyle and continental Europeans like Pascal come from? As an explanation, Dear emphasizes the role of religious factors. While miracles were still believed in the Catholic world of continental Europe, for English Protestants the age of miracles was long past. According to Catholics, nature follows laws, but that regularity could be overturned by a single event (i.e. a miracle). Therefore, for them, experiments that are one-off events are meaningless. A few experiments are just one example of a law of nature. On the other hand, for example, a universal statement about atmospheric pressure tells us something about the order of the natural world. In Protestant Britain, on the other hand, since the existence of miracles is denied from the outset, there is no need for a belief in the laws of nature. Even a one-off experiment is considered meaningful in deepening our understanding of how nature works.

On the other hand, universal statements made no sense to many English Protestants, because they were based on false beliefs – the belief that the way the world is is inevitable. This is expressed in statements such as “a vacuum must exist” or “the smallest parts of matter must be indivisible”. To them, these necessary statements seemed to unjustly limit the omnipotence of God, who could arbitrarily make any philosophical system a truth. The English tended to think that God could make any matter a truth without being bound by philosophical possibilities or impossibilities.

Considerations on the Experimental Method

In contrast to Dear, Steven Shapin (1943- ) and Simon Schaffer (1955- ) explain that the Royal Society’s unique experimental methodology was based on the social turmoil that 17th century British society was in. They link the unique experimental philosophy of England to the need to guarantee peace and stability during the Restoration. They say that the Boyle school thought that discovering the facts as they were would make it possible to end the disputes in natural philosophy. Even those who dispute whether matter can be infinitely divided would not argue if it were the facts themselves. This seemed to be a path that natural philosophers could follow to help restore social order. If their method could be established in natural philosophy, it would be nothing less than the acquisition of a general method for justifying knowledge, and it would lead to the end of disputes in other fields such as politics and religion. The experimental method in England was expected to be a means of agreement essential for communities that could create spontaneous order without the need for tyrannical authority.

Even though there is some room for debate in the arguments of Dear, Shaping and Schaffer, I think their research has given us a deeper understanding of how the ‘experimental method’ developed in the context of 17th century England, and how it took a different direction from the thinking on the continent. Their research also makes us think about the background to the great power of the experimental method in modern science. As Shaping and Schaffer point out, it is easy to think that experimental knowledge is clearly superior to other intellectual methods and that this is why it has achieved great success. In reality, however, as their research shows, our faith in experimentalism, like the experimental method itself, emerged in early modern society in conjunction with various political, social, and rhetorical strategies that were clearly limited in time and place and taken for specific purposes.

The Role of the Royal Society of London

It is often pointed out that the rise of the empirical method led to the formation of groups of natural philosophers and experimenters. These groups were sometimes formal and sometimes informal, and were represented by the Accademia del Cimento in Italy (1657), the Royal Society in London (1660), and the Académie royale des Sciences in Paris (1666). This point of view is based on the idea that the experimental method requires the collaboration of scientists. This view can be clearly seen in Bacon’s utopian work, “New Atlantis” (published in 1627 as an unfinished work), which describes the House of Salomon. It is said that the House of Salomon served as the prototype for the idea of the Royal Society and the Royal Academy of Sciences. Both of these learned societies grew out of small groups of scientists devoted to experimental methods, and they were the most successful of the new learned societies.

The Success of the Royal Society of London

The Royal Society of London for Improving Natural Knowledge was established in 1662 as an organization for natural researchers. Its establishment signified the transformation of science, which had been more or less an arbitrary product of individuals, into the crystallization of a clearly directed collective effort, and the beginning of science as an institution fulfilling an indispensable function within the nation and society. Science first took on its modern form through the Royal Society. So it can be said that this was a landmark event in the history of the establishment of modern science.

The people of the Society intended to carry out their work in a collective and organized manner, and as the name suggests, their aim was to (improve natural knowledge). They adopted a new organization for this purpose, discovered effective methods, set up a systematic program as a goal for their joint enterprise, and devoted all their efforts to achieving this goal. In just 30 years, the level of science in Britain surpassed that of the advanced countries on the continent. Newton’s “Mathematical Principles of Natural Philosophy” (1687) helped to establish the Royal Society as the absolute authority in the world of science.

Around 1645, several circles of natural researchers were formed in London. The people who gathered there were large merchants, landowners, the new aristocracy, and intellectuals closely connected to them. Many of them sympathized with Parliament, and while some were loyal to the king, regardless of which side they stood on, they were by no means enthusiastic supporters. There were also Puritans, but most of them were rather moderate Anglicans who valued tolerance and reason, or in other words, the broad church.

According to the History of the Royal Society of London (1667) written later by one of them, Thomas Sprat (1635-1713), religious and political issues, which were also the focus of debate in the period, were also of great interest to them. However, this was a source of unbearable pain for these moderate, calm intellectuals. They sought solace in the study of nature during these “gloomy times”. They often met to discuss new inventions and discoveries. At first, they did not have a fixed method or promote systematic research. Eventually, they began to understand what the new science meant to them. When they discovered a research method that was appropriate for this, they began to have a systematic vision for the study of nature, and they came to realize that they were the disciples of Bacon more than anyone else.

Science gives humans new inventions and power, and enriches human life. This is what Bacon believed. According to Bacon, the first step in the study of nature was to create a “Natural History”. In other words, as many phenomena as possible were to be described without “rash speculation”, and then arranged and organized into appropriate categories. Once a complete natural history was prepared, the principles that govern nature could be derived from it. The achievement of this project required the collective cooperation of natural researchers. Bacon dreamed of a “New Atlantis”.

A collection of useful knowledge about nature and technology is called a natural history or natural technology journal. The creation of natural history was the “primary and ultimate purpose” of the Society in its early days. It is important to note that natural history in the 17th century was not a field of science like that of the 18th century. It was a method for collecting knowledge as a method or a way of recognizing facts, and it was also a collection of knowledge that resulted from the application of that method. In a word, natural history was a method of recording.

In the 17th century, it was a revolutionary event to collect knowledge with a certain sense of purpose, and to promote mutual exchange, rather than leaving knowledge to the limited collection of individuals or to the accidental transmission between individuals. Even if there were no new inventions or discoveries, the goal of “improving natural knowledge” would have been achieved to the extent that it would have satisfied many of the members of the society. For us today, who think based on the premise of knowledge that is systematically collected and immediately transmitted, it seems difficult to grasp the revolutionary significance of the efforts of the society.

The various communities that formed the cells of the social structure of the Middle Ages each formed a complete, closed society. The members of the community were subject to strict rules in all aspects of production and life. These rules also extended to knowledge. If knowledge provided the reason for the existence of the community, it was kept secret to prevent it from leaking out. In principle, there was no mutual exchange of knowledge between communities.

For example, in the guilds of merchants and producers, the secrets of the “technology” of commodity production are kept strictly. Even if the guilds collapse and the stage of large-scale handicraft production comes, the situation does not change as long as the technical basis of large-scale handicraft production is handicraft. The secrets of technology are persistently protected.

As the domestic market is formed and overseas markets expand, it becomes impossible to rest on traditional technology. New technology is required. In a situation where knowledge is confined to a closed society, the demand for new technology leads to efforts to steal each other’s “secrets” rather than to invention.

This closed nature of knowledge is not limited to the production sector. In the fields of thought and learning, the invention of printing was changing things, but it was still only having a very limited effect. The people of the Royal Society challenged this situation.

In the 17th century, when knowledge was confined to a closed society, the basic conditions for the advancement of science were to break down this closed-off nature, to promote mutual exchange, and to collect and accumulate the intellectual achievements of humanity. It was able to respond to both the intellectual ambition of the capitalist class to grasp the world as a whole, that is, the idea of an encyclopedia, and the practical interest in increasing production through technological improvement and developing markets for raw materials and goods. The great merchants and landowners who had seized political power set about this task. They used their own organizational forms to create a system of collective cooperation, and they adopted the method of recording “natural history” to make efforts to collect useful knowledge.

The Society, which was strongly influenced by the Whig Party, became a social force with its leaders serving as successive presidents, but it did not achieve its goal of creating a complete natural history. Even when they tried to systematize it, the reports were incomplete and fragmented, and could not be used as they were. There were not many talented people. The Society was run by the members’ investments, but the finances tended to be sluggish, and it did not go well. However, the decisive factor was that they did not have a “principle”. In order to organize, categorize and systematize the miscellaneous cognitive materials that had been collected, a certain principle was needed. Not only did they not have one, but they consciously rejected it, believing that they could create a system of encyclopedic knowledge using only a “recording method”. What a great illusion! The impasse was clear to everyone. In the face of the vast amount of material, they began to explore their hypotheses and principles. Newton, who had been an outsider to the Society up until this point, would now take center stage.

“The public are not the possessors of useful knowledge, but are at best only capable of obstructing the truth. It is always only a select few who know the truth.” Newton, who wrote this in his first letter to the Society, was in direct opposition to Robert Hooke (1635-1703), the true leader of the Society in its early days. From the start, the Society was not a comfortable place for Newton.

However, things changed. The Society reached out to Newton. Even if the inverse square law was Hooke’s idea, it could not have been theorized without Newton’s systematic conceptual ability. The Society’s activities effectively came to an end with the publication of “Philosophiæ Naturalis Principia Mathematica” in the year before the Glorious Revolution. The solution of that problem was left to the 18th century.

The systematization of natural research, which had acquired principles, began. Natural history shifted from method to field. Although it was belated, the honor of being the editor of the first modern encyclopedia, the “Lexicon technicum” (1704), fell to John Harris (1666-1719), the secretary of the Royal Society. After him, the program of the Society was taken over by the French Encyclopédistes. The Society gradually moved away from the tradition of experimental science. Hooke inherited the experimental tradition of science from Galileo, but in the 18th century, with the rise of Newton, the power of theoretical science increased, and natural history shifted towards natural philosophy. However, the spirit of recording, which seeks to describe objects in an objective and factual manner, and the methods of natural history were not lost. They continue to pulse at the base of modern science.

The Rise of Mechanistic Philosophy

In the 17th century, people began to call for a new philosophy that would make it possible to throw out Aristotelian philosophy once and for all. Several new philosophies were proposed and competed with each other, but at the time they were all collectively referred to as ‘mechanistic philosophy’. By the end of the 17th century, mechanistic philosophy had effectively replaced Aristotelian scholastic philosophy and become dominant. It was thought to be the key to understanding all aspects of the natural world, from the propagation of light to the development of animals, from the theory of atmospheric pressure to the explanation of respiration, and from chemistry to astronomy. The mechanistic philosophy was fundamentally different from the past. In fact, it was natural philosophy at the height of the scientific revolution.

In the mechanistic philosophy, all phenomena are explained using the basic concepts of mechanized mathematics, or mechanics. These are concepts such as shape, size, quantity and motion. In principle, contact action is considered to be the cause of all change. Mechanism likens the workings of nature to the workings of machines. The cause of natural change is considered to be the interaction of objects, which are thought of as being like the cogs of a clock. Or, the cause is also considered to be the collision of objects and the propagation of motion that accompanies this.

Aristotle’s teleology explains the behavior of objects in terms of the purpose inherent in them. For example, the reason acorns grow is because they become oak trees and provide wood for humans. In the mechanistic theory, explanations using vitalism and teleology are rejected. The true properties of objects, such as size, shape, motion and rest, are strictly distinguished from the secondary properties that objects merely have. The latter are derived from the true properties, such as color, taste, smell, heat and cold. For example, it was explained that vinegar does not have the property of “taste”, but that it actually only tastes sour because the particles that make up vinegar are sharp and irritate the tongue. It is worth noting that the obvious qualities mentioned in Aristotelianism are reduced to mere secondary qualities in the mechanistic theory. Secondary qualities are attributed to the invisible minute particles that make up objects. At the same time, the hidden qualities that had been explained using Aristotelian principles are also explained using mechanistic principles. The distinction between obvious and hidden qualities in Aristotelianism has no meaning in mechanistic theory. This is because natural phenomena are ultimately explained in terms of the motion and interaction of particles that are imperceptible to the senses.

The final important characteristic of mechanistic philosophy is the assumption that all objects are composed of invisible atoms or particles. It is not surprising that the background to the emergence of various mechanistic philosophies was the revival of ancient atomistic natural philosophy. The revival of the theories of Democritus (c. 460 BC – c. 370 BC) and, in particular, Epicurus (c. 341 BC – c. 270 BC) was important. In fact, Pierre Gassendi (1592-1655), a leading thinker of the mechanistic school, developed his own system in the process of reconstructing Epicurus’s ideas. However, not all mechanists thought in terms of indivisible atoms. It was not impossible for a mechanist to think that matter could be divided infinitely and that all observable changes were caused by particles as the smallest units of matter. The existence of something smaller than an atom was also considered. An important result of this reform was the establishment of the idea of indivisible yet sizeable particles. The major difficulty with the atomic theory of the time was that it was not clearly distinguished from what could be called the mathematical atomic theory. In the mathematical atomic theory, the reason particles were indivisible was because they were geometric points that had no extension. However, in mathematical atomism, it was unclear how atoms without extension could play a role in the natural transformation of objects with extension. Since a point has no size, no matter how many of them are gathered together, they cannot have size, or extension.

If we take a closer look at the content of scientific research in the 17th century, we can see that the science of the 17th century was based on a mechanical and mechanistic view of nature, and that it rarely went beyond the limits of this. The revolutionary development of science in the 17th century was almost entirely an expression of the victory of the mechanical view of nature over the ancient and medieval cosmological view of nature. Therefore, we could call the transformation of this dominant view of nature the triumph of mechanistic philosophy.

The breakthrough that led to the victory of this mechanistic view of nature was Copernicus’ heliocentric theory and Galileo’s research into mechanics and the heliocentric theory. As the saying goes, “Ignorance of motion is ignorance of nature”, which has been passed down in the tradition of Greek philosophy since ancient times, the question of mechanics is a fundamental issue in natural philosophy, and is related to the question of world view. Aristotle’s scholastic view of nature is also based on his unique interpretation of the interaction between force and motion, and any discussion touching on the fundamentals of motion is inevitably influenced by whether or not this view of nature is accepted.

By the way, in the 17th century there was no such thing as a distinction between physicists, chemists and biologists. All scientists at the time were natural philosophers, and these natural philosophers would discuss biological, mechanical or mathematical subjects according to their interests at the time. In the 17th century, all science was unified in the person of the natural philosopher, and the successes in one field of natural research were immediately applied to other fields of natural research. Galileo’s mechanics and heliocentric theory could thus become the starting point for all scientific research in the 17th century.

The Role of Mathematics in the Scientific Revolution

There are probably many different ways of defining the “scientific revolution”. Here, we will follow the common view and refer to the period from the appearance of Copernicus’ heliocentric theory (1543) to the establishment of Newtonian mechanics (1687), a period of about a century and a half that saw a dramatic development of science, centered on mechanics and astronomy.

The Renaissance (15th-16th centuries) was a period of transition from the creation of modern mathematics to its establishment. During this period, mathematics gradually shed its Greek form. Commercial arithmetic, which had appeared in India, Arabia and late medieval Europe, spread rapidly with the advent of modern capitalist society, which pursued profit and required advanced measurement and calculation, and the Indian (Arabic) numerals and calculation methods that were convenient for calculation became popular among the general public in the 16th century. The invention of double-entry bookkeeping by Italian Fra Luca Bartolomeo de Pacioli (1445-1514) in 1494 was also a product of this trend.

The decimal system of fractions devised by the Belgian mathematician, natural scientist and engineer Simon Stevin (1548-1620) and the establishment of the method for calculating them (1585) led to a dramatic development in calculation power. Also, between the end of the 16th century and the beginning of the next century, the logarithms invented by John Napier (1550-1617) of Scotland and Jost Bürgi (1558-1632) of Switzerland greatly simplified the complex calculations astronomers had to perform. In relation to the development of these calculation methods, algebra also progressed. The algebra that the Renaissance inherited from the Middle Ages was the so-called “word algebra” that used inconvenient symbols, and it was inferior to Indian algebra. Eventually, the process of symbolization of algebra began, and the symbols necessary for algebraic calculations, such as the symbols for the four basic arithmetic operations, the equal sign, the radical sign, and the parentheses, were introduced between the middle of the 15th century and the middle of the next century. The important concept of exponents and the symbols used to represent them were also introduced and refined between the 15th and early 17th centuries. Thus, the form of algebra seen in Descartes’ famous “La Géométrie” is almost identical to modern notation.

Seventeenth century mathematics developed spectacularly, building on the foundations of the Renaissance. The seventeenth century can be said to be the most creative century in the history of mathematics. As mentioned earlier, algebra was almost fully modernized by Descartes. Based on this algebra, he and Pierre de Fermat (1601-1665) each established analytic geometry. The Greek “geometrical algebra” crushed the free computational power of algebra within the narrow confines of geometry. In contrast, analytic geometry cleverly links the world of geometry to the world of algebra, using the concept of coordinates as a medium, without damaging the computational power of algebra at all. This union was beneficial to both geometry and algebra. Thanks to this union, countless higher-order curves were discovered in the world of geometry. In addition, the concepts of variables and functions were introduced into the world of algebra. Analytic geometry is an algebra of variables that can grasp how quantities change.

Now, how much of a role did this brilliant development of modern mathematics play in the progression of the scientific revolution, which was centered on astronomy and mechanics? Our question is, what kind of mathematics did astronomy and mechanics, the driving forces behind the “scientific revolution”, use? The mathematics used by Copernicus was mainly classical Euclidean geometry and trigonometry. Needless to say, the development of trigonometry and precise trigonometric tables were necessary for the emergence of his heliocentric theory, but trigonometry was not a modern invention, and was first compiled by Hipparchus (c. 190 BC – c. 120 BC) of ancient Greece. Precise trigonometric tables had already been calculated through the efforts of people such as Regiomontanus (1436-1476).

What about Galileo? The mathematics used in his “Dialogue Concerning the Two Chief World” and “Discorsi e dimostrazioni matematiche intorno a due nuove scienze” is classical Greek geometry. What about Kepler? It is well known that he discovered that the orbits of the planets are elliptical, and it goes without saying that his theory required the use of conic sections. However, this theory had already been developed by Apollonius of Ancient Greece (262 BC – 190 BC). As Kepler’s theory was a theory of planetary motion, it is only natural that the mathematics appropriate to its content should be the integral calculus. The integral calculus is necessary for an accurate grasp of his famous law of area velocity. Unfortunately, mathematics was completely lagging behind. He calculated these distances using a laborious procedure, assuming that the time required for a planet to travel a short unit distance in its orbit is proportional to the distance between the planet and the sun, and that the total of these times is proportional to the total of the corresponding distances, but this was an approximation that replaced integral calculations with the sum of a finite number of line segments. It was through this detour that Kepler finally arrived at his law of area velocity. In any case, his astronomy was in a quandary, waiting for the advent of new mathematics but unable to meet its demands.

What about Descartes, the founder of analytic geometry? As we have already mentioned, this geometry is a mathematics of variables, and so it was well suited to the mechanical view of nature of the time, which held that the essence of nature was extension and motion. However, it seems that this geometry did not play a particularly large role in his depiction of the mechanical view of nature. In his Cosmology and Principles of Philosophy, he says that his method is mathematical (geometrical), but this seems to mean that he considers matter in terms of extension and motion, and not necessarily that he applies full-fledged mathematical processing.

Although he stated that “the study of motion is the main subject of pure mathematics”, he was unable to express the situation of celestial bodies moving within the space of the ether using mathematical equations. In modern terms, this is an issue that belongs to the dynamics of a continuum, and mathematically it requires partial differential equations, so it was something that Descartes’s level of mathematics at the time was unable to handle. He skillfully applied mathematics to optics, the theory of falling bodies, and statics (he applied analytic geometry to optics), but in cosmology, which he regarded as the most important, he made little use of mathematics. Even in Pascal, the connection between new numbers and mechanics/physics is not close. One of his important mathematical achievements was a method of calculating areas using the concept of infinitesimal, but this had little connection with his experiments on atmospheric pressure or his research into hydrodynamics.

We have looked at some of the leading mathematicians and scientists of the 17th century and examined the relationship between mathematics and mechanics and astronomy in their work. The result is that the new mathematics of the modern era did not play a particularly active role in the “scientific revolution”. In astronomy, which requires a high level of mathematical skill, the tools used were trigonometry, which was the legacy of Alexandrian mathematics, classical Euclidean geometry, and, in Kepler’s case, Apollonius’s Conics. Of course, it is undeniable that the development of computational techniques during the Renaissance improved the computational abilities of astronomers. However, these were merely computational techniques, and they were not new mathematical theories suitable for modern dynamics and astronomy. Mathematics was completely lagging behind the pace of the development of the “scientific revolution”. It was probably thanks to the establishment of the differential and integral calculus by Newton and Gottfried Wilhelm Leibniz (1646-1716) that mathematics began to catch up with modern science. Newton’s ‘Principia’ (1687) is written in the style of classical geometry, but the fluxion method (Newton’s integral calculus) appears throughout, and his dynamics would probably not have been possible without this new mathematical weapon.

For the first time, he combined new mathematics and new mechanics, and they began to develop while mutually promoting each other. The 18th century was a continuation of this. In short, in the “scientific revolution”, modern mathematics had to wait for the advent of the calculus to begin to actively demonstrate its effectiveness.

If the establishment of Newtonian mechanics marks the end of the first act of the Scientific Revolution, it was just before the end of the first act that modern mathematics became a powerful weapon for the study of nature. It could be said that the first act of the Scientific Revolution ended because modern mathematics began to exert its influence.

A Treatise on the World by Descartes

In the first half of the 17th century, Descartes’ new natural philosophy opposed Gassendi’s Epicurean natural philosophy. Descartes’ particle theory is debatable, but it is the most influential of all mechanistic theories and is also the most impressive in many respects. Descartes’ natural philosophy was based on a new metaphysics, as well as the union of mathematics and natural science. According to Descartes, matter is defined solely by its extension. In principle, natural science can be reduced to a geometric analysis of the motion of extended objects. However, if we look at Descartes’ actual natural philosophy, we see that there is almost no mathematical analysis. For example, in his explanation of celestial motion, Descartes points out that there is a relationship between the density of the planets and their distance from the sun, but he does not attempt to calculate that relationship. The reason Descartes does not doubt the mathematical certainty of his natural philosophy is probably because the whole thing has a axiomatic structure, its foundations are unquestionable, and all phenomena are carefully deduced from those foundations.

In his “World”, Descartes first systematically considered natural philosophy. The “World” was written by 1633, but when news reached him that Galileo had been found guilty of supporting the Copernican theory, Descartes decided not to publish it. Descartes fully presented his mechanistic philosophy in his “Principles of Philosophy” of 1644. In the “Principles of Philosophy”, Descartes still supports Copernicanism, but uses clever explanations to prove that all motion is relative, and on this basis, Descartes concludes that the earth is by definition stationary.

Descartes equated matter and extension, and used this as the starting point for his entire system, so he denied the existence of a vacuum and said that all interaction occurs through contact. Since the world is filled with matter, when one part of it moves, it affects the whole world. However, this seems unnatural, so Descartes instead says that local circles are formed, and this causes a change in the position of the matter relative to each other. In other words, when something moves forward, it pushes the object in front of it away, and that in turn pushes the object in front of that away, and so on. As a result of this continuous replacement, the whole thing bends in a curved direction for some reason, and at the end of the series, the object that was pushed last moves into the space where the first object that moved was originally located. All the moving objects become part of the circular motion of matter, and they all form a spiral, drawing in the tightly packed matter particles around them. Descartes’ planetary system is self-regulating.

By the way, why do large particles accumulate to form planets? The explanation for this is a little vague, but once such a planet is formed, it is said to form its own small spiral around itself. The particles surrounding the planet tend to move away from it, and this is said to be the cause of gravity. There is another important assumption in Descartes’ system. that the total amount of motion in the world is constant. None of Descartes’ contemporaries questioned this. They criticized the details, but they were convinced that it was the most reliable and most fruitful way to understand the natural world.

Descartes’ ideas were successful on the continent, and were particularly popular in France and the Netherlands, but not so much in England. The experimental philosophy that had developed in England was not easily receptive to any deductive system. Descartes recognized a certain role for experiments in natural philosophy, but they were of secondary status. They were nothing more than a reinforcement of the chain of reasoning for Descartes.

As a result, the experiments carried out by Cartesianists were limited to reporting what was expected to happen, based on the assumption that Descartes’ reasoning was correct.

Protestants in England saw the rationalist system of thought as a way of unjustly limiting the omnipotence of God by forcing human beings to impose their own limitations on God. Cartesian experiments were also never adopted by prominent English experimental philosophers such as Boyle. It is not the case that Descartes’ mechanistic philosophy itself was unpopular in England. All of the mainstream natural philosophers who were active after the Restoration of the Monarchy were followers of the mechanistic philosophy.

Although the mechanistic philosophy cannot be separated from the development of mathematical mechanics, kinetic theory and dynamics at the time, it was also a powerful idea in natural philosophy at the time in other respects. In order to demonstrate the effectiveness of their new philosophy, some mechanists expanded their research to include the form, function and life processes of living things. For the leading mechanists Descartes and Thomas Hobbes (1588-1679), it is not unreasonable to say that their main concern was to explain biological phenomena and the behavior of animals, including humans.

The role of Descartes

Here, we will look at Descartes’ role as an intermediary in the transition from Galileo to Newton. If we examine Descartes’ achievements in the history of mechanics in contrast to those of Galileo and Newton, it becomes clear that a simple composition such as the mechanics revolution does not fit the historical situation of the 17th century. Here, we can see the true face of historical reality, which twists and turns over time, rather than a clear-cut plot brought in from the outside.

It is to be expected that Descartes, who was born around 30 years after Galileo, was influenced by his predecessor Galileo. However, there is little evidence that Descartes learned the theoretical content of mechanics directly from Galileo. The two men’s ideas about mechanics were each unique. Therefore, the differences between Galileo and Descartes are an important issue.

Before considering these differences, it is necessary to recall the common issue that reflects the historical situation of the first half of the 17th century, when the two men lived as contemporaries. This is the issue of the Copernican theory, which provides the ideological foundation for mechanics. Both Galileo and Descartes were followers of the Copernican theory, and in this respect they shared a common position that paved the way for modern thought. What is interesting is that we can see a change in the positions of the predecessors and successors in relation to this common issue. Since Galileo’s way of life had a strong influence on Descartes’ way of life, we should confirm the nature of this change.

It is well known that Galileo, who put forward the heliocentric theory, spent his final years in suffering. After publishing “Dialogue Concerning the Two Chief World” in 1632, he was put on trial by the Inquisition and forced to abandon his heliocentric theory. At the time, Descartes was writing his ‘World’ from the standpoint of “If the Copernican theory is false, then the whole basis of my philosophy will also be false”. So when Descartes heard about Galileo’s case, he could not help but be greatly shocked.

While trying to avoid hurting the authority of the church, Descartes’s scheming academic life, in which he tried to develop his philosophical beliefs in a logical way, also had an impact on the content of his research as a whole. Over the same issue of the Copernican theory, Galileo lived as a heretic after making his views public, while Descartes, who was afraid of this, lived in suspicion as a disguised convert, and each chose a different path. Here, we can see the complex relationship between the theories of scholars and the social thought that formed the background at the historical point in time of 1633.

Descartes would later turn his attention to Galileo again when he read the “Discorsi e dimostrazioni matematiche intorno a due nuove scienze”, which was published in 1638. A fairly detailed critique of Galileo’s book can be found in a letter (dated 11 October 1638) that he wrote to Mersenne. This is a notable passage in comparing Descartes’ academic stance with that of Galileo. At the beginning, Descartes agrees with Galileo’s position, saying, “When he considers questions of physics, he tries to avoid the errors of the traditional Catholic school of thought as much as possible and to reach conclusions based on mathematical reasoning.”

However, here Descartes emphasizes not the similarities between Galileo and himself, but the differences. He criticizes Galileo’s position, saying, “I think that his major fault is that he constantly digresses and goes off on tangents, and that he never calmly explains a single problem in full. In other words, it shows that he does not examine problems in an orderly fashion. He did not consider the first cause of nature, but merely sought the cause of specific results. The reason he arrived at such results is that he began building without laying the foundations.”

At first glance, this may seem to be simply a difference between Galileo, the natural scientist, and Descartes, the metaphysician. While this is something that needs to be taken into account, it is not the only issue. Even if we limit the discussion to the field of mechanics, Descartes’ criticism of Galileo is still very meaningful. When comparing and evaluating Galileo and Descartes in terms of the theoretical development of mechanics, the above words touch on an important point. This is a question about the law of inertia.

The law of inertia is a principle that is essential to the foundation of mechanics, which later became established as Newton’s First Law. It is generally accepted that Galileo was the pioneer who discovered this law, and this is undoubtedly true. However, Galileo’s reference to inertia was only a special case that applied to motion on a horizontal plane. From this, there is a large gap before the general expression of Newton’s First Law, “All bodies continue in their state of rest or uniform motion unless acted upon by a force that changes their state,” can be generalized. It is often thought that Newton overcame this gap and grasped the general law in one fell swoop, but this is not the case. The role of Descartes as an intermediary must be properly considered here.

Galileo, who was criticized by Descartes for “not considering the first cause of nature, but merely seeking the cause of particular results,” said the following in the “Discorsi e dimostrazioni matematiche intorno a due nuove scienze.” “We have seen that, whatever the velocity, once it is given to a moving body, it will be sustained without variation, provided the external causes of acceleration or deceleration are removed, but this condition is found only on a horizontal plane. This is because, in the case of a downward slope, there is already a cause for acceleration, and in the case of an upward slope, there is already a cause for deceleration. From this, we can see that motion along a horizontal plane is perpetual, because if it is at a constant speed, it cannot be reduced, lost, or increased. This is certainly a pioneering expression of the law of inertia.

It should be noted that Galileo did not intend to grasp this as a law. He merely predicted the existence of inertia as the cause of the “special result” of motion on a horizontal plane. It was none other than Descartes who grasped the law of inertia as a universal law by “considering the first cause of nature”.

We can see this accurate expression in the “Principles of Philosophy” published in 1644. Descartes carried out a fundamental reflection on the movement of nature here, and summarized it in three basic laws, and the first two of these are clear expressions of the law of inertia.

The first law of nature is “All bodies remain in the same state unless acted upon by a force from another body.”

The second law of nature is “All bodies in motion tend to continue in a straight line.”

When we compare these with Newton’s expressions, we can see that Newton certainly inherited the fundamental grasp of the concept of inertia from Descartes. Of course, Newton re-examined the law of inertia in a unified way, both in terms of expression and content, according to his own original ideas, and here we can clearly see that he inherited not only from Descartes, but also from Galileo. Even so, Descartes was able to reach a fundamental grasp of the principle of inertia from a completely different mechanical conception from Galileo, and his role in the history of mechanics is also of great significance. This is because the attitude of Descartes’ philosophical reflection, which seeks to “consider the first principles of nature”, was indispensable here. We have now been able to confirm once again that Descartes, who stands between Galileo and Newton, was an important figure who cannot be ignored in the development of mechanics.

Descartes’s mechanical conception

Let’s take a look back at how the three different inertial laws differed. First of all, Galileo was unable to actively grasp inertia as the fundamental state of object motion. He pointed out that when the cause of acceleration and deceleration, which changes velocity, does not work, velocity is maintained unaltered, and he only passively acknowledged that this condition was satisfied for an object in uniform motion on a horizontal plane. If we were to illustrate the relationship between speed and acceleration geometrically in terms of the relationship between time and distance, we would understand that this was only natural. This is because there was no intention to fundamentally confirm the first cause of motion here.

In contrast, Descartes showed little interest in the empirical concepts that Galileo always focused on, such as the speed and acceleration of moving objects. As a result, he lost sight of the procedure for accurately expressing changes in motion quantitatively, and his mathematical consideration of the motion of a single object (a point mass) was lacking in verve. However, he was relentless in his reflections in an attempt to gain a clear understanding of the first cause of motion. Ultimately, he arrived at the existence of a god who presides over the natural order, and he grasped the essential content of motion in relation to this.

“God does not change. God’s way of working is always the same and does not change.” From this, Descartes went on to think that all objects should fundamentally seek to maintain the same state. He thought, “Once an object begins to move, it will continue to move forever and will never stop moving by itself.” Inertia as the fundamental state of motion was thus elevated to a fundamental principle. The previous view of motion as “something that has a tendency to stop and is by nature inclined to remain still” was finally overcome. Whether motion or rest, as long as it continues, it can be considered to be a manifestation of the inertial state. If that is the case, how do changes in the state of motion occur? In this respect, Galileo only said that there are causes of acceleration or deceleration in the “change” of uniform motion, and he did not attempt to identify what those causes were.

Descartes was not satisfied with simply pointing out that there was a cause for change. He tried to determine the cause in principle. “Each object remains in the same state as much as possible, and does not change unless it collides with another object.” In other words, according to Descartes, changes in the state of motion are caused by “collisions with other objects”. Here we can see Descartes’ unique mechanical conception. Of course, it was completely different from Newton’s conception. Let’s take a closer look at the expressions of Descartes and Newton in the previous law of inertia.

Both of them believe that there are certain conditions that must be met in order for the inertial state of continued motion to be established. Descartes says that the same state will be maintained unless something from the outside tries to change it, while Newton says that the same state will continue unless the state is changed by an added force.

In Descartes’ case, it is clear that the “thing that tries to change it from the outside” is a collision with another object. Newton’s idea of the cause of motion change is the action of force. When considering the causes of motion change from the fundamentally different perspectives of the collision theory and the action of force theory, it is only natural that different mechanical concepts would be developed. This difference becomes clear in the remaining parts of the three fundamental laws described by each of the two men.

The second and third of Newton’s laws, which are well known in general, are

Second law: The change in momentum is proportional to the applied force of motion, and occurs in the direction of the straight line in which this force acts.

Third law: An action always has an equal and opposite reaction. In other words, the interaction of two objects that are relative to each other is in equal and opposite directions.

In any case, here we can clearly see Newton’s desire to comprehensively understand the phenomenon of motion as an action of force. What Newton defined as the force of motion is a quantity that is proportional to the change in momentum. This is ultimately expressed as the product of acceleration and mass, and what Galileo had previously only tentatively defined as the cause of acceleration (deceleration) is now clearly redefined as a concept of force. Here we can see a close theoretical relationship between Galileo and Newton. The mass referred to here must be a quantity that has meaning as a measure of inertia. Descartes’ role as an intermediary who established inertia as a principle had a decisive influence on Newton’s mechanical conception, which was similar to Galileo’s.

By the way, what does the other of Descartes’ fundamental laws refer to? The third law of nature is “When a moving object collides with an object having more momentum, it does not lose its momentum. When it collides with an object having less momentum and causes it to move, it loses as much momentum as it gives.” Interpreted from the current perspective, this is a law of conservation of momentum in the case of a collision.

However, this perspective was completely absent from Newton’s mechanical thinking. Newton only considered the balance of action and reaction between two objects, and he never showed any desire to advance the idea of a collision phenomenon in which the exchange of momentum occurs. Newton tried to explain changes in motion through the action of force, but Descartes tried to explain changes in motion through the collision of two objects. Although the law of conservation of momentum was still in its infancy, the significance of Descartes’ grasp of it in the history of mechanics was enormous. In the 19th century, the law of conservation of energy was established, and considering that theoretical development progressed in the future by focusing on the amount of energy exchanged through interaction rather than through the concept of force, Descartes’ pioneering role in 17th century mechanics should be recognized.

Considering these things, I think that Descartes’s position in the long history of mechanics, especially in modern physics, where we have come to know the limitations of Newtonian mechanics, should be properly evaluated. It would not be appropriate to ignore Descartes’s work just because it was different from Newton’s mechanical conception and did not directly support Newtonian mechanics. Rather, Descartes’s conception of mechanics served to supplement Newtonian mechanics from a different perspective. And if we consider Descartes’s existence, we should also be able to learn about some of the rich historical content of the history of mechanics in the 17th century.

Up until now, we have focused on Descartes as an intermediary between Galileo and Newton. This is not to say that we are placing particular importance on Descartes alone. Rather, we wanted to say that the history of mechanics in the 17th century cannot be summed up as a single process that leads to Newton.

The Metaphysical Foundation of Mathematical Natural Science

Descartes examined how the essence of material things is perceived. After his investigation, he concluded that the essence of material things is not perceived through the senses or imagination, but through the mathematical object of geometric extension, or the idea of space, which is given within human intellect.

However, I don’t understand why a theory based on the abstract ideas of mathematical objects found within human intellect can be said to correspond to the physical nature outside of human beings in a real way.

Descartes responded by appealing to the metaphysics of an omnipotent God, and by the theory of innate ideas, which states that if God is omnipotent, he must have created and set up the mathematical objects that we can understand clearly and distinctly with our intellects as constituting the real structure of physical nature.

With this “innate theory” of mathematical objects, Descartes sought to reject the empiricist epistemology that formed the basis of Aristotle’s natural philosophy, and to establish the view that the human mind can investigate the essence of physical objects independently of the senses and imagination, according to abstract ideas of mathematical objects that are given within the human intellect.

Descartes appealed to the metaphysics of the almighty God and put forward the thesis that God created and imprinted mathematical objects within us humans, and that this in turn constituted the laws of physical nature (natural laws). This thesis means that we can think of the mathematical objects found within our human intellect and the structures that make up physical nature as being fundamentally related. We humans are now able to theoretically investigate the structure of physical nature without relying on sensory experience, in accordance with the mathematical concepts we find within ourselves.

The Physiology of Harvey and Descartes

William Harvey (1578-1657) elegantly proved through experimentation that the spontaneous movement of the heart is due to its contraction, but Descartes’ explanation contradicted this. Nevertheless, Descartes emphasized that his view was a conclusion that was inevitably drawn from the arrangement of the various parts of the heart. He likened it to the way the movement of a clock is necessarily derived from the arrangement of its gears. The fire of the heart, as conceived by Descartes, is thought to be equivalent to the fire that burns without giving off light, as can sometimes be seen in inanimate objects. Descartes seems to have had fermentation in mind, but it was not yet known at the time that fermentation was caused by the activity of microorganisms. He believed that this fire of the heart was the origin of all bodily movement.
Descartes then set about constructing a speculative theory of physiology. In it, the bodies of animals and humans are explained in terms of a complex, self-powered machine that works by hydraulic pressure. He presented his theory of the movement of the heart and blood in his “Discourse on Method” (1637). He did so with the intention of setting an example of mechanistic physiology. Descartes’ ideas had a major impact. Attempts to explain biological phenomena in terms of mechanics gained increasing support throughout the 17th century.
It seems that our view of the world is largely defined by the mechanistic idea of animal mechanics. This is true in both biology and medicine. In this respect, Descartes’ mechanistic physiology can be considered the origin of modern life science.
The starting point for Descartes in this area was the work of Harvey on the heart and blood. Descartes removed the vitalistic elements from Harvey’s theory and, ignoring his explanation of the movement of the heart, came up with a mechanistic theory of blood circulation. Harvey disagreed with the theories of Claudius Galenus (129-200). In contrast to Galenus, Harvey believed that the spontaneous movement of the heart was during its systolic phase. He thought that the movement of the heart itself was caused and maintained by the vital force inherent in the blood. For him, blood was something that pulsated by itself. Descartes did not accept this theory. Instead, Descartes followed the old idea of the internal heat of living things and thought that there was something similar to fire in the left ventricle of the heart. The blood that enters the left ventricle from the cold lungs is immediately vaporized by the inherent heat there, causing the heart to rapidly expand. The vaporized blood then enters the arterial system through the aorta. Descartes thought that the heart would contract, and at the same time, new blood would be supplied from the lungs, and the same process would begin again.

Descartes put forward the dualism of mind and body in the fields of epistemology and metaphysics. On the other hand, he was the first in history to propose the idea of a mechanistic natural philosophy, or neurophysiology and brain science based solely on physics, in relation to the body and mental activity related to the body.
The neurophysiology and brain science that Descartes proposed, like his cosmological physics, was not a complete theory, and the specific theories it proposed had to be corrected. Descartes is the originator of the modern view of neurophysiology and brain science, which seeks to explore the functions of neurophysiology and brain activity in the context of physics and chemistry. Let’s make sure of that point.
Descartes explained the circulation of the blood from a mechanistic perspective, regarding the heart as a kind of heat engine where the blood is heated. However, this was incorrect, and Harvey’s theory that the heart functions like a pump was correct.
Harvey explained the muscular movements, sensory perception and overall cognitive activity that are common to humans and other animals by appealing to the concept of “animal spirits”, which had been adopted since the ancient physician Galen as a type of vital substance that is added to the blood. However, Descartes brought about a decisive change in the history of medicine at the time. He essentially changed the meaning of the concept of “animal spirits”, stripping it of its vital meaning and reducing it to a purely physical object. According to Descartes, “animal spirits” were extremely fine objects that were heated and diluted in the heart, and only these could enter the empty spaces of the brain and fill the ventricles to perform various movements.
In this way, Descartes eliminated the “chance” between the state of mind and the state of the body from the physiological analysis he himself had opened up. On this basis, he thought that the mind could control the relationship between the body and the mind, and that the workings of the will originated in the mind, and that consciousness had the mind as its cause.
On the other hand, Descartes was the first in history to present a mechanistic view that explained not only physical nature, but also the entire human body, including the brain, and he stated that “my mind” as a “thinking thing” did not belong to that nature.

On the existence of free will

Trying to understand the act of “disagreeing” with something that is thought to be “skeptical” or “self-evident” is nothing other than an attempt to grasp the nature of “active will”, or to understand consciousness as active will. In fact, through his methodical doubt, Descartes not only presented the nature of the “consciousness of thinking” in “I think”, but also brought about the subjective awareness of free will, which is the ability to “disagree with anything”. For Descartes, decision-making is a “decision made by free will”, in which one chooses one option from a range of options, and has the ability to disagree with even things that seem obvious. The Cartesian consciousness is inseparable from the consciousness of the “subject” of “free will”. The question of how to understand and accept this free will is directly linked to the question of how to grasp “consciousness”.

When we try to understand the consciousness of the mind in relation to “skepticism” or the act of “disagreeing” with something that is normally considered self-evident, we are in fact trying to understand the nature of “active will” and grasping consciousness in terms of “active will”. This means that it is possible to “disagree” with something that is considered self-evident. We are able to “affirm or deny” things. ‘Decision-making’ is to take a position that acknowledges the existence of free will, which is to say that we actively choose one option from among multiple choices.

If we follow ordinary, or naive psychology, we implicitly acknowledge the existence of the mind, and do not believe that it is spatially extended like an object. As long as we do not think of the mind as something that is spatially extended like an object, we are accepting the fundamental heterogeneity between the mind and objects. If this is the case, then while we recognize the uniqueness of “I move my arm” as a real experience, we are accepting a dualism between the non-spatial existence of the “mind” and the physical world with its spatial expansion.

I actively acknowledge the “freedom of choice” of the “will” based on Descartes’ philosophy of the mind. Firstly, it is based on the fact that we can always willfully “doubt” and “disagree” with anything that can be the object of our thoughts. No matter how much we intellectually understand a certain system, we can disagree with it and even go against our understanding of it. When we affirm something, we are aware of the “decision to choose” that we are making when we affirm it. In the physical execution of this action, we experience the “causal efficacy of mental causation” that says “my mind moves my body”.

In this case, since we make free will the “principle” of our judgment and action decisions, free will is not an illusion. When we make judgments and action decisions in our “choices”, we are embodying freedom as a reality.

In order for us to recognize others as having an “other-self” that is equivalent to our own “self-self”, it is first of all essential to understand that others have self-consciousness and intentions. Secondly, it is crucial to understand that through verbal interaction with others, we cannot know what others will do intentionally towards us, in other words, that they are “free agents” who can please or deceive me.

We do not grant our pets, such as dogs and cats, the same status as ourselves. This is because we know that even if our pets are there to make us feel at ease, they are not capable of deliberately deceiving us using the same language as us.

In order for us to recognize the “other” as an equal “I”, it is necessary for us to experience “passivity” in relation to the other. Thus, in order to recognize the existence of the “other’s mind”, a “reciprocal relationship” mediated by “linguistic action” is essential as a third point. In this way, we can recognize the “other” as an “other-self” equal to my own “self”. In order to recognize the “self” in the “other”, it is crucial to perceive, through mutual verbal action, a “free agent” within the other’s activity who has rational intentions but whose actions cannot be predicted.

My opinion

In the world of American philosophy, the philosophy of mind has come to occupy a large area. It seems that the theory of the mind as an entity is examined, with the Cartesian dualism of mind and body being taken up first. And in most cases, the idea of the mind as an entity independent of the body is judged to be “metaphysical” in a bad sense, and in some cases even “mystical”, under the influence of “physicalism” and “naturalism”, which are currently having a major impact.

I think that the distinction between the mind that arises directly from the brain as a physical body and the mind that arises further from the mind is being neglected. The physical mind arises directly from the brain, but that mind makes the body act in a way that allows it to exist. The mind that arises from the mind generates a mind that makes it possible for the body to continue to exist for a longer period of time than the mind that arises directly from the brain as a physical body, and makes the body act in accordance with that thought. Having a social mind of this high dimension stabilizes one’s own existence and makes one realize that one’s own time of existence in the real world can be further extended.

Regarding the concept of “animal spirits” that Descartes thought of as a type of life substance that is added to blood, I think he may have imagined a substance that has the role of relating the functions of each organ, such as hormones, which are information transmitters in the modern world. This could not be discovered due to the limitations of medical technology at the time. As I am not a doctor, I do not have sufficient knowledge on these matters. I cannot judge how accurate Descartes’ explanation of physiological functions is. Even if it is an explanation that differs from modern medical explanations, it can be seen that Descartes thought that there were physiological functions that were controlled by human will and functions that were controlled automatically and unconsciously.

If we consider the effects of consciousness or the mind on the mechanical physiological functions of the human body, we can see that the physiological functions of the human body operate automatically as a machine, independently of consciousness. However, the way in which these functions are controlled changes depending on the state of the mind or spirit, and this can cause various changes in the body. Descartes explains this in detail using the medical knowledge of his time. Descartes attended several dissections of the human body and studied them.

There are also two types of muscles: voluntary muscles, which can be moved at will, and involuntary muscles, which cannot be moved at will. For example, the skeletal muscles used in actions such as raising your arm or straightening your leg are voluntary muscles, as you can move them when you want to. In contrast, the heart and internal organs cannot be moved or stopped by the will, so the cardiac muscle and smooth muscle are involuntary muscles. Many of the physiological functions of the human body are controlled automatically, regardless of our will. This is precisely why we are called an automatic machine.

If I had to sum up the scientific revolution in a few words, I would say that it was the addition of a perspective from outside the Earth to conventional knowledge. If you read various commentaries on Descartes’ physics, you may find that some of them point out that there are a few errors in it. However, Descartes was a man chosen by God, so I think there is a higher-dimensional world in which his explanations are correctly expressed. Descartes did not discover his laws through experiments, as Galileo did, but rather expressed deeper, more fundamental laws through contemplation. Therefore, the world he expresses may be deeper.

Continued in the rebirth of Cartesian philosophy 2