Galileo and the Birth of Modern Science

Galileo’s work marked the birth of modern science. The scientific and philosophical underpinnings of his work inspired scientific revolution, and are some of the most far-reaching of the Renaissance period.

Jan 9, 2022By Catalin Barboianu, PhD Philosophy of Science & Mathematics
galileo astronomical theories diagram planets
Galileo Demonstrating the New Astronomical Theories at the University of Padua, by Félix Parra, 1873, via; with Diagram of the Planets, from De Revolutionibus, by Nicholas Copernicus, 1543, via the University of Warwick


There is an undoubted consensus between historians and philosophers of science that Galileo was the landmark for the birth of modern science, putting him on a list of great scientific thinkers from ancient Greece to Copernicus. This is what children today first learn in school when science is introduced to them. No other scientist has been granted so many “father of” titles for their achievements, e.g. father of the telescope, of the microscope, the thermometer, experimental physics, the scientific method, and in general, modern science itself (as Albert Einstein himself said).


But what are the arguments for these claims, and what were the premises created by Galileo that caused a radical shift to a new science? We shall see that the arguments are not only scientific in nature, but philosophical, and the premises are grounded in the spiritual and social context of the 16th to the mid-17th century.


From Ancient “Philosophical” Science to Galileo’s “Scientific” Philosophy

The School of Athens, by Raphael, painted between 1509-151, via the University of St Andrews


A majority of interpreters of Galileo’s work consider his motivations and intentions with respect to a methodology related to an older form of science. The science of ancient Greece no longer fit the new standard of knowledge of the period and was falsified by new experimental observations.


The geocentric and early heliocentric models from ancient and medieval astronomy were invalidated by empirical observations made possible by newly invented instruments (one of which was Galileo’s telescope) in the 17th century. New theoretical models and calculations invalidated old cosmological models, most notably the mathematical heliocentrism of Copernicus that soon came to be the dominant scientific view on the macrostructure of the universe.


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These scientific attempts to describe the place of the Earth in the universe, whatever scientific methodology was used, still originated from ancient “philosophical” science, which inquired not only about the universe and its laws, but also about how human reason can discover them.


Galileo Demonstrating the New Astronomical Theories at the University of Padua, by Félix Parra, 1873, via


Nonetheless, the ancient Greek contemplative or speculative philosophy, most especially Aristotle’s physics, weren’t seen any longer as valid foundations for science at the time. In antiquity, the term “philosophy” was used to name something close to what we call science today, or the observation of and experimentation on nature, and the two terms “science” and “philosophy” were used interchangeably until the Late Medieval Age. The sharp distinction between the meanings of the two terms became clear with the Copernican revolution and Galileo’s scientific achievements.


There were not only new technological developments that involved experimenting and observing nature that dismissed ancient science as inaccurate but there was also an emerging kind of spirituality that influenced human reason. The theist elements of ancient Greek philosophy and later medieval dogmatic teachings and coercion of the Church were at odds with the freedom of thought required for the development of science. It was an age in which people began to question the authority of theological truths in regard to freedom of thought, with scientists at the forefront of this spiritual evolution.


However, 17th-century scientists did not discard ancient philosophy in its entirety. They continued to rely on concepts, views, and theories from early forms of theoretical philosophy, such as Aristotle’s Logic or Plato’s Metaphysical Theory of the Forms. They found such elements to be useful tools for investigating science from without, with respect to its conceptual framework, foundation, and methodology. And — along with this analytical approach — they concluded that mathematical necessity is something that cannot be missing from the constitution of science and that the truths of science are tightly related to the truths of mathematics.


The Renaissance Influence on Galileo

The Birth of Venus, by Sandro Botticelli, 1485, via the Uffizi Gallery


The Renaissance was the period in which humans established new relationships with the surrounding world, and in which the individual developed spiritually, more and more, as someone independent of their community. People participated in activities and disciplines, not as part of solitary piety as the Church wanted, but as a participant in the totality of the world.


These spiritual principles are reflected in Galilean science, and they were a foundation for the scientific truth that Galileo searched for and developed through his methodology, which was revolutionary for that time. Modern science requires such spirituality. There were two people representative of the Renaissance that spiritually influenced Galileo: namely Nicholas Cusanus and Leonardo da Vinci (Cassirer, 1985).


Leonardo Da Vinci, Engraving by Cosomo Colombini after Da Vinci, via the British Museum


Nicholas Cusanus, a German philosopher, mathematician, astronomer, and jurist, provided the first metaphysical interpretation of the universe with a logical nature, as a concrete (infinite) totality of finite natures. In its infinity, the universe appears similar to God, but at the same time in opposition to Him, because the infinity of the universe is relative to the limits imposed by the human mind and senses, while that of God is not; the universe is a unity in plurality, and God is a unity without and beyond plurality (Bond, 1997).


The famous Leonardo da Vinci, in turn, influenced by Cusanus, wanted to understand the world in order to be able to see it and, at the same time, wanted to see it in order to understand (sapere vedere). He could not perceive and construct without understanding and for him theory and practice were interdependent. Leonardo da Vinci sought in his theory and practice as a researcher and artist, the creation and perception of the visible forms of the cosmos, of which the human form is considered to be the highest. His interpretation of the universe is known as a  “universal morphology” (Cassirer, 1985).


Both interpretations of the universe — that of Cusanus’ metaphysical concept and that of da Vinci’s art seem to have influenced Galileo and completed his vision of the physical world, which is understood in his science through the concept of the law of nature. Moreover, this influence went to the very foundation of this new science, reflecting a concept of scientific truth in incipient form, a truth of unity, coherence, and universality, to whose nature Galileo would add a new component, the “mathematical”, still embedded in the fundamental methodology of the natural sciences today.


Theological Truth and Scientific Truth

The creation of Adam, by Michelangelo, fresco painted between 1508-1512, via the Vatican Museum


Galileo was searching for an ideal for scientific truth that a new methodology of science could be built upon. As a primary principle of this pursuit, Galileo rejected the divine “verbal inspiration” of the theological doctrine, replacing the revelation of “the word of God” with the revelation of “the work of God,” found before our eyes as the object of knowledge, but also as a source of knowledge.


The rejection of theological inspiration was motivated by the concept of scientific truth, one that would help build the foundation of a new science of nature. Ancient scripture claimed that only God knows the true nature of the physical universe, but we do not have access to this knowledge and are urged not to try to seek an answer (“believe and do not doubt”); these were the limits of faith. In order to build a new science, it was necessary to replace the old dogma, not necessarily by redefining it, but by abolishing the dogmatic aspect; the prevention of scientific investigation. This was followed by a groundbreaking methodology that uncovered new truths and that pushed society forward at an increasingly exponential pace.


Galileo also had a metaphysical argument for this rejection: the world has an ambiguous nature, whose meaning has not been given to us as simple and stable, like that of a written piece. The written word cannot be used normatively or as an evaluative standard in science; it can only aid in the descriptions of things. Neither theology nor history is able to give us a foundation for the knowledge of nature, because they are interpretive, presenting us with both facts and norms.


Portrait of Galileo, by Justus Sustermans, c. 1637


Only the science of nature is capable of such a foundation, that of factual, mathematically-known reality.  Authentic knowledge of God, which could be called universal, has also been seen as an attractive ideal for science. Nature is God’s revelation and the only valid knowledge we have about him.


This argument yields to Galileo’s thesis that, apropos a successful and authentic scientific knowledge, there is no essential difference between God and man; for Galileo, the concept of truth is embedded in the concept of perfection (Cahoone, 1986).


These were the views that brought Galileo to trial, persecuted by the Catholic Church in 1633. The notion of truth in Galilean science borrows from the theological character of truth, and as such Galileo never gave up the idea of God and that of the absolute truth of nature. On the path to this truth and its determination, a new methodology and a new science were required. However, even if the accusers understood Galileo’s religious claims correctly, this did not work in his defense.


Mathematical Truth and Scientific Truth in Modern Science

Spacetime curvature around masses in the relativistic model, via the European Space Agency


Galileo argued that we must not remain skeptical about having the work of God revealed to us, because we have an instrument of interpretation and investigation infinitely superior to historical and linguistic knowledge, namely the mathematical method, which can be applied precisely because “the book of nature was written not in words and letters, but with characters, mathematics, geometric figures and numbers” (Galileo Galilei, 1623).


Galileo starts from the premise that we must call “true” only what is a necessary condition for things to look the way they do and not what appears to us in one way or another in different circumstances. This means the choice of necessity based on invariance is an objective criterion for assigning a truth value (Husserl, 1970/1954).


Of course, mathematics and its methods provide us with necessary truths based on logic and this is why mathematical descriptions and methods were essential for the new science. “Mathematics is the supreme judge; from its decisions there is no appeal.” — Tobias Danzig (1954, p.245). It is exactly this kind of meta principle that Galileo followed when granting mathematical necessity the core role in the methodology of the new science.


Diagram of the Planets, from De Revolutionibus, by Nicholas Copernicus, 1543, via the University of Warwick


Galileo was the first to change the relationship between the two factors of knowledge — empirical and theoretical-mathematical. Motion, the basic phenomenon of nature, is taken to the world of “pure forms”, and its knowledge acquires the same status as arithmetic and geometric knowledge. The truth of nature is thus assimilated to mathematical truth, being validated independently, and it cannot be disputed or limited by an external authority.


However, this truth must be further validated or confirmed first against subjective interpretations, accidental changes or contingency in the real world, and the way we perceive it, and against well-established prior knowledge. This validation imposes the experimental method and objective observation as necessary for mathematical truths to become scientific truths. For Galileo, mathematical abstraction and reasoning, together with naturalistic observations and physical experiments form the sure path to the truth of nature.


The mathematical description of nature and empirically validated mathematical reasoning had worked fine before for Copernican heliocentrism, which Galileo endorsed with his science and defended in front of the Church.


New Science Required New Kinds of Sacrifices From Galileo

Galileo before the Holy Office, painting by Joseph Nicolas Robert Fleury, 1847, via Wikimedia Commons


In Galileo’s trial, the “argument” of Pope Urban VIII was the following: although all physical experiments and mathematical arguments may be correct and convincing, they still cannot prove the absolute truth of the Copernican doctrine, because God’s omnipotence is not limited by rules applicable to us and our understanding, but acts according to his own principles, which our science does not have the capacity to locate and decode. Galileo made the ultimate intellectual sacrifice (transformed further into the physical sacrifice of detention) by not responding in any way to this “argument”.


The reason Galileo refrained from answering was that he viewed the logic of his science as different from the “logic of God,” an answer was impossible.


The pope’s argument was religiously explicable and acceptable, but conceptually and fundamentally inconsistent with Galilean science. In fact, Galileo never intended to create a rupture between science and society with regard to religion, but only to determine rigorously and methodically the limits of the latter.


The same kind of “silent” intellectual sacrifice characterizes his popular experiment in the physics of falling bodies. According to physics folklore, it is said to have taken place at the Leaning Tower of Pisa (although many historians of science have argued that it was actually a thought experiment and not an actual one). By dropping two spheres of different masses from the tower, Galileo intended to demonstrate his prediction that the speed of descent was not dependent on their mass.


The Leaning Tower of Pisa, photo by Heidi Kaden, via Unsplash


Galileo discovered through this experiment that the objects fell with the same acceleration in the absence of air resistance, proving his prediction true. The two spheres reached the ground one a bit after another (due to air resistance) and this was sufficient for Galileo to validate his theory empirically. However, his audience expected the two bodies to reach the ground at the same time and as such, they perceived the outcome as a failure, due to their ignorance about either the air resistance or the way it was reflected in the mathematical model of Galileo’s theory of falling bodies. In both situations — the trial and the experiment — the sacrifice of not arguing for the truth due to the audience’s lack of understanding and the lack of available language was as novel as the new Galilean science was.


By having scientific and mathematical truth at the core of his foundation, the work of Galileo acquired a philosophical meaning that will accompany science along with its future development to the present day. The story of the struggle of Galileo with the old science, the Church, and society is also representative of contemporary science, in a different form, even if the Inquisition does not exist anymore. Science evolves continuously and this evolution means struggling, communicating, and debating. It reflects the power of the social dimension of science; trust in science is something that concerns scientists, ordinary people, and science itself.




Bond, H. L. (1997). Nicholas of Cusa: Selected Spiritual Writings, Classics of Western Spirituality. New York: Paulist Pressains.


Cahoone L.E. (1986). The Interpretation of Galilean Science: Cassirer Contrasted with Husserl and Heidegger. Studies in History and Philosophy of Science, 17(1), 1-21.


Cassirer, E. (1985). The idea and the problem of Truth in Galileo. Man and World18(4), 353-368.


Danzig, T. (1954). Number: The Language of Science, 4th edition. New York: Macmillan


Galileo Galilei (1968). II saggiatore (1623). In  G. Barbèra (ed.), Le opere di Galileo Galilei. Firenze, Italia.


Husserl E. (1970). Galileo’s Mathematization of Nature. In The Crisis of the European Sciences and Transcendental Phenomenology, translation by D. Carr (originally published in German in 1954). Evanston: Northwestern University Press, 23-59.

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By Catalin BarboianuPhD Philosophy of Science & MathematicsDr. Catalin Barboianu is a philosopher of science and mathematician. A graduate of the University of Bucharest with a PhD in Philosophy of Science, an MSc in Probability Theory and Statistics, and a BSc in Pure Mathematics. Author of 14 books including 'What Is Mathematics: School Guide to Conceptual Understanding of Mathematics.'