excerpts from An Intellectual History of Modern Europe by Marvin Perry

 The Scientific Revolution:  A New Cosmology and Methodology

            The Scientific Revolution made the medieval world picture obsolete and established the scientific method, rigorous and systematic observation and experimentation, as the means of unlocking nature’s secrets. Natural philosophers finally grasped the essential importance of mathematics to understanding the natural world, and this tool would grow more sophisticated with the discovery of the calculus. These early scientists conceived of the universe as a mechanical system governed by mathematical laws. Science displaced theology as the queen of knowledge and gave rise to the Enlightenment.

The Origins of the Scientific Revolution

            Medieval thinkers, influenced by Plato and Aristotle, had conceived of the cosmos as a divine hierarchy with the earth at the center but lower than the heavens. This dualistic model of the universe divided into higher and lower worlds accorded with passages of Scripture that medieval scholastic philosophers had cited to harmonize classical science with Christian theology.

 Aristotle’s Model of the Universe



            Human beings, at the center of the universe and in the center of the great ladder of creation, were the masters of Earth. Earthly objects were composed of the four elements: earth, air, fire and water; celestial objects were composed by a magical ether. The planets, according to Ptolemy, the ancient astronomer, moved in perfect circular orbits and at uniform speeds around the earth. Since the planets do not move in circles, but ellipses, Ptolemy, had been forced to invent complicated explanations of these apparent eccentricities (epicycles, equants, and retrograde motion) to save the appearance of circular motion.

 Aristotle’s Theory of the Solar System (Video


            The Renaissance paved the way for the Scientific Revolution. Revived interest in classical science had led to the rediscovery of important ancient texts (Archimedes’ mechanics and Galens’ anatomy). Artists’ representations of the human body linked exact proportions to a principle of beauty. Leon Battista Alberti (1404-1472) formulated the mathematical theory of perspective in his depiction of space, establishing a precise mathematical relation between the object and the observer. The natural world could now be analyzed and depicted with scientific precision.

            The revival of ancient Pythagorean and neo-Platonic ideas led to a new stress on mathematics as the key to the comprehension of reality. The Pythagoreans had been fascinated by the mathematical harmonies to be found in music. They extended this idea to the universe at large, expressing the idea that everything in nature could be expressed numerically. They believed that knowledge of this cosmic harmony could purify the soul. (Music of the Spheres) Plato had maintained that beyond the world of everyday objects lay a higher reality, the world of Forms, which contains a mathematical reality apprehensible only through rational thought. Renaissance science blended science with mysticism and magic in the tradition of Hermes Trismegistus, thought to have been an Egyptian priest and contemporary of Moses. The Hermetic writings mixed astrology, alchemy, Jewish creation accounts, and mystical yearnings with neo-Platonism and Pythagoreanism.

Nicholas Copernicus (1473-1543)

            This astronomer and mathematician proclaimed that the earth is a planet that orbits a centrally located sun together with the other planets. The heliocentric theory became the kernel of a new cosmology. Copernicus’ sense of mathematical order had been offended by the cumbersomeness of Ptolemy’s model of the universe. His theory was published in 1543, but his ideas had become current even earlier than that.




            In 1539 Martin Luther condemned Copernicus, but his astronomical theories did not inspire passionate rejection until the religious wars of the early seventeenth century.  In 1616 the Catholic Church banned Copernicus, fearing another propaganda weapon for Protestants. Authorities feared the theological and social implications of Copernicus’ reordering of the cosmos in opposition to the divisions of the divine hierarchy.

            This new cosmology inspired some religious thinkers to develop new conceptions of God. Giordano Bruno (1548-1600) was burned at the stake for heresy because he had embraced Copernicus’ theory and combined it with mystic hermeticism to conceive of the universe as a living creature existing in an infinite space which must contain innumerable inhabitable worlds. To Bruno, nature was God, worthy of worship and investigation. He believed this new religion of rapturous worship, glorification and contemplation of nature should replace the teachings of organized churches.

            Contemplation of the new cosmology could also produce despair. Instead of a secure universe created for man, Copernican astronomy dethroned man, expelled human beings from their central position in the cosmos, and implied an infinite universe. This concept would prove as traumatic for modern thinkers as Adam and Eve’s expulsion from the Garden had been for medieval thinkers.

The Copernican Model (Diagram)
The Copernicus Page at MacTutor History of Mathematics (St. Andrew’s, Scotland)


Galileo Galilei (1564-1642)


Galileo's Drawing of the Moon


Indebted to the Platonic tradition of mathematics and to Archimedes’ mechanics, Galileo exploited the recent invention of the telescope to prove Copernicus’ theories scientifically and to advance a new understanding of physics. (Galileo’s Telescope) His observations of craters and mountains on the moon and of spots blemishing the surface of the sun proved that the celestial bodies were not perfect and immutable.  (Galileo's Drawing of the Craters on the Moon) (Sunspots) This demonstration showed that all of nature was a homogeneous system, not hierarchical. His observations of the moons of Jupiter demonstrated that a celestial body could indeed move around a center other than earth. In dealing with problems of motion, Galileo dispensed with Aristotle’s ‘common sense’ conclusions and insisted on the application of mathematics to experiments. Instead of concluding that rocks fell to earth because they were striving to reach their proper place in the universe, Galileo insisted that motion is a mathematical relationship of bodies to time and distance.


Galileo and the Mathematics of Motion

            Galileo’s experiments and discoveries attacked the authority of the Scriptures in scientific matters. He tried to separate science from faith. He argued that the purpose of Scripture was the salvation of the soul, not the instruction of people in the operations of nature.

            In 1633 Galileo, under the threat of the Inquisition, was forced to recant and condemn the theories of Copernicus. One of the consequences of the Church’s stand was the impetus it gave to the study of science in the Protestant areas of Europe.

The Surface of Jupiter (animation)
Jupiter viewed from one of its moons (Video)
Io: a moon of Jupiter
Jupiter, Io and Europa from Voyager 1 (1979)
Baltimore as seen from space (Satellite Data from The Living Earth)
A Black Hole Seen from the Hubble Space Telescope (1995)
Galileo Page at MacTutor History of Mathematics  (St. Andrews, Scotland)

The Galileo Project (Rice University)


Johannes Kepler (1571-1630)

            This German mathematician and astronomer was deeply influenced by the teaching of  Renaissance Pythagoreans and neo-Platonists. He tried to harmonize mathematics with a deep commitment to Lutheran Christianity. He believed that God had prescribed a geometric harmony to creation which humans could understand. He was also a believer in astrology. He yearned to understand the ‘music of the spheres’ and thus achieve a supreme insight into God’s mind. Even so, he did not allow the inspiration of his mystical beliefs to obscure his disciplined dedication to empirical research.

            Using data collected by a Dutch astronomer, Tycho Brahe, Kepler discovered the three basic laws of planetary motion. First, planets move in an elliptical orbit with the sun at one focus of the ellipse. Second, the planets do not move at a uniform speed; instead he argued that they accelerate as they approach the sun. A planet’s speed is determinable at any point since its arc will sweep out an equal area of space in equal areas of time if a line is drawn from the planet to the sun. Third, there is a mathematical relationship between the time it takes a planet to complete its orbit of the sun and its average distance from the sun: time squared is proportionate to distance cubed.

Kepler’s Laws of Planetary Motion
Kepler’s theory of the solar system (Video)
Kepler’s theory of planetary motion (Animation)
Kepler Site at NASA
Kepler Page at MacTutor History of Mathematics (St. Andrews, Scotland)


Isaac Newton (1642-1727)

            Isaac Newton provided the celestial mechanics that linked the astronomy of Copernicus and Kepler with the physics of Galileo and accounted for the behavior of the planets. His publication of The Mathematical Principles of Natural Philosophy  in 1687 climaxed the scientific revolution and arguably can be described as the birth of the Enlightenment. Newton’s three laws of motion joined all celestial and terrestrial objects into a vast mechanical system which functioned in perfect harmony and whose connections could be expressed in mathematical terms. He offered mathematical proof of the heliocentric system.

            The Laws of Motion: Newton’s first law is the principle of inertia: a body at rest remains at rest unless acted on by a force, and a body in rectilinear motion moves in a straight line at the same velocity unless a force acts on it. Motion is as natural a condition as rest. The second law states that a given force produces a measurable change in a body’s velocity, the change in velocity proportional to the force acting on it. The third law holds that for every action or force there is an equal and opposite reaction or force. The sun pulls the earth with the same force that the earth pulls the sun.

            Newton proved that the same laws of motion and gravitation that operate in the celestial world also govern the movement of earthly bodies. There is no cosmic division, no dual universe. The universe is an integrated, harmonious mechanical system held together by the force of gravity. His laws demonstrated the inherent mathematical order of the universe, thus realizing the ancient Pythagorean and Platonic visions of the cosmos.

            Many of Newton’s contemporaries believed he had unraveled all of nature’s mysteries. For Newton, God was the grand architect whose wisdom and skill accounted for nature’s magnificent design. Newton believed that God could intervene in this clockwork universe and perform miracles. Later, followers of Newton, the deists, would reject miracle as incompatible with a universe governed by impersonal mechanical principles.

            Newton helped formulate the scientific method: a systematic and logical process of inquiry into the properties of phenomena on earth and establishing those properties by experiment, only then proceeding to hypotheses for explanations of the phenomena themselves.

Newtonian Mechanics With Gravity
Newton Page at MacTutor History Of Mathematics (St. Andrews, Scotland)


Francis Bacon (1561-1626): The New Empiricism

            Sir Francis Bacon, an English statesman and philosopher, was an important advocate of the scientific method. In his New Organon (1620), Bacon repudiated the medieval scholastics' effort to blend theories of nature with the requirements of Holy Scripture. He denounced scholasticism’s slavish attachment to Aristotelian doctrines because that prevented independent thinking. He also complained that the arid, pure verbal ingenuity of the scholastics’ elaborate arguments had little or nothing to do with the empirical world. Bacon argued that humans needed to resist their tendency to color observations of nature with prejudices from their experience, their desire for profit, or their attachment to any philosophical dogma. Instead, Bacon advocated inductive reasoning as the path to truth. Through careful observation of nature and the systematic accumulation of data, general laws could be discovered from the knowledge of particulars. These laws should be constantly tested and verified by experimentation. Bacon became a founder of the empirical tradition in modern philosophy. He attacked astrology, magic, and alchemy. He advocated cooperative and methodical scientific research that could be publicly criticized. Bacon appreciated science’s potential value for human life. The function of thought was not to explain how everything fit into a divine design; rather, knowledge should help us utilize nature for our own advantage and improve the quality of life.

History of Philosophy: Bacon


Rene Descartes (1596-1650) The New Rationalism

            Rene Descartes, a French mathematician and philosopher, developed the other approach to knowledge which underlay the scientific method: deductive reasoning. Whereas Bacon regarded sense data as the foundation of knowledge, Descartes believed that truth derived in successive steps from first principles, indubitable axioms. In his Discourse on Method (1637), Descartes rejected all authority for knowledge which depended on the senses which he revealed as fallible. In one famous argument, he considered a piece of wax. Using his senses he could measure a piece of wax's various physical characteristics: its shape, size, weight, texture, etc. However, when he melted the wax using a flame, the substance possessed utterly different characteristics. Even so, his mind knew that the substance remained wax. Descartes therefore concluded that the mind, not the senses, was essential to knowing.

            Descartes searched for one incontrovertible truth that could serve as the first principle of knowledge, and he found one truth to be certain and unshakeable: his mind was at work: "Cogito ergo sum" (“I think therefore I am.”) Here was the starting point of knowledge. By overthrowing all authority for thought except the individual’s inviolable autonomy and importance, Descartes founded modern philosophy. Human beings had become fully aware of their capacity to comprehend the world with their own mental powers.

  The Cartesian Plane 

            Descartes was a brilliant mathematician who founded analytic geometry, the bridge between algebra and geometry, crucial to the invention of calculus. Descartes believed that mathematical reasoning could be applied to philosophical problems, thus providing a geometry applicable to the moral order. Once his central axiom (“I think therefore I am.”) was accepted, other truths could be logically deduced. Proceeding step by step from the fact of his own existence, Descartes was able to deduce the existence of the physical world and the existence of God.  Descartes argued that because humans could conceive the idea of a perfect being, then God must exist. The idea of perfection had been implanted in us. The conception of perfection presupposes the existence of God. God ordered the universe in such a way that it functions in harmony with the human mind, and He gave humans the capacity to understand the world. Descartes argued that he structures of the natural world correspond to the form of the ideas of the mind. Logic is not only inherent in the human mind but also independent of human existence. Descartes reasserted Plato's dualistic conception of the universe. He divided reality into two fundamentally different substances: the mind with its principle attributes of consciousness and thought, and matter which is characterized by spatial extension. A basic question of modern philosophy has been the attempt to discover where the mind and matter connect.

            Although Descartes believed in God, he thought that once God had set the universe in motion, he served no further significant function. His support of reason and his faith in the ability of humans to think for themselves undermined Christian dogma and helped form the skeptical outlook of the Enlightenment.

History of Philosophy: Descartes


Benedict Spinoza (1632-1677) Rationalism

            Spinoza was a descendant of Spanish Jews who fled to the Netherlands to escape the Inquisition. He studied traditional Jewish religious and philosophical works, medieval scholasticism and the new science and philosophy of Descartes. He disputed rabbinical interpretation of the Scripture, was accused of heresy, and subsequently was excommunicated by Jewish religious authorities. He lived simply as a lens grinder and devoted his life to philosophy.

            Spinoza used the logic of mathematics to understand the world. He modeled his metaphysical arguments on Euclidean geometry: first axioms and definitions allow propositions to be deduced. If we accept the axioms, and the deductions are properly made, then we must accept the conclusions. He took the same approach to ethics. Like Descartes, he contended that reality was intelligible only through reason. Applying the logic of Euclidean geometry to philosophy, he began with what seemed to be universally valid premises and deduced other truths using logic.

            Spinoza held that the highest form of knowledge was the knowledge of God, but his conception of God marked a radical break with traditional thinking. To Spinoza, God was not a transcendent creature, some superhuman father possessed of intellect and will. Inspired by the new science, Spinoza identified God with the order of nature: a single, all inclusive system of unchanging, universal laws in which all things have a determinate place. Unlike Descartes who conceived of a sharp divide between thought and substance, Spinoza believed that the universe was monistic: thought and substance are different aspects of the same being. Since this unified system is open to reason, divine revelation is unnecessary. Spinoza was a determinist who believed that everything happens due to necessity: an unbreakable chain of cause and effect. The only freedom humans possess stems from our ability to understand our situation (ala Oedipus).

Spinoza called for a critical reading of the Bible as an ancient, human text that should be analyzed using linguistic and historical techniques. He condemned belief in miracles and in the efficacy of prayer as superstitions and dedicated himself to scientific objectivity. He pleaded for freedom of thought, religious toleration, and a constitutional government. Spinoza’s thinking was a hallmark of the emerging modern mind.

History of Philosophy: Spinoza
BBC Radio 4 In Our Time programme on Spinoza