Numbers in Philosophy: Modern Philosophy and Its Roots
What Is Philosophy?
What is philosophy? Literally, philosophy means “the love of wisdom.” It deals with the fundamental questions of what it means to be human, of the world, and of knowledge: What is truth? What is good and evil? How should I act? What is the meaning of life? But it also takes on more concrete questions we run into regularly in everyday life, like “What is beauty?”
Here’s what matters: philosophy isn’t a religion or a belief system. It’s a discipline built on argument and reasoning. It’s not satisfied with guesses, subjective views, or opinions. Philosophers want to work out something objectively true: something fundamental, something that stands above the rest.
In that sense, philosophy follows a basic logic of thought that underlies many other disciplines. You could call it a kind of proto-science. So it’s no surprise that the earliest scholars we’d now call scientists, especially natural scientists, were also, and above all, philosophers.
The First Philosophers: The Pre-Socratics and Numbers
The first natural scientists were really philosophers, and the most famous of them lived in ancient Greece. They stopped asking purely mythological questions (“What does Zeus want?”) and started explaining nature through reason and systematic observation: the first step toward modern physics, chemistry, and biology. Naturally, that’s how they discovered the shared language behind today’s natural sciences too: mathematics. Mathematics and geometry took center stage in their teachings. Think of “Thales’s theorem” or the “Pythagorean theorem,” which Pythagoras probably didn’t discover first, but which his school made famous. The phrase most likely coined by him, “All is number,” captures the idea that everything that exists (nature, music, the cosmos, harmony, motion) can be explained through numerical ratios and mathematical laws. That makes him a forerunner of modern science, and his influence still shapes modern philosophy and its roots today.
As famous as Pythagoras is for his foundational thinking, just as overlooked is the meaning he actually assigned to the natural numbers. He didn’t see numbers only as digits for doing math. He understood them in a far broader sense. To him, numbers carried, above all, a symbolic meaning, a meaning tied to content. They weren’t just tools for calculating nature brilliantly. To him, they were principles of reality itself. For Pythagoras, the natural numbers were divine principles, the primal substance everything is woven from. Every number carried its own quality, which he taught within a secret society he founded. By “one” (monas), he meant not just the quantity 1, but also the principle of unity, perfection, divinity, and the beginning of everything. “Two” (dyas) meant not just the quantity 2, but also represented the principle of polarity, of otherness, of darkness (as opposed to the light, divine nature of one). For more on the symbolic meaning of individual numbers, see the article A Short Guide to Numbers.
“Pythagorean” served as a synonym for “philosopher” for a long time, right up until the term “philosophy” was born. So the Pythagoreans were the first philosophers and, at the same time, the forerunners of the natural sciences. As significant and respected as these scholars remain today, it’s remarkable that Pythagoras’s actual teaching, the one about the qualities of numbers, has slipped out of view today, or isn’t taken seriously anymore, even though it comes from the same brilliant thinker whose insights were unquestionably fundamental to the development of our modern natural sciences and humanities.
Plato and Numbers
The first major philosopher whose extensive written work has survived is Plato. Everyone knows his name. He’s a kind of founding father of philosophy. He’s best known for his famous theory of Forms and the image of the cave allegory that illustrates it. His core idea, that the vast array of things we perceive expresses abstract organizing principles behind them, shaped both modern science and Christian theology in decisive ways.
„The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.“
(Alfred North Whitehead)
That view still unites most scholars today. What’s slipped out of focus, in fact what’s nearly unknown, is that Plato also assigned numbers an essential role, calling “the art of number” the highest wisdom there is. And it’s not the mathematical side of numbers that deserves special attention here, it’s the content, the meaning. After developing his well-known theory of Forms, later in life he described “the art of number” as the highest wisdom of all.
„The first and most important science is the science of number itself, apart from ordinary calculation.“
(Platon)
Plato’s qualitative use of numbers, also known as metamathematics or ideal numbers, can be understood as his theory of Forms advancing toward ever simpler basic principles, principles he saw embodied in numbers. Plato sometimes describes the principle behind an individual number, the number one, for instance, as the primal idea that everything else emerges from. This part of Plato’s later philosophy gets little attention in the literature, or isn’t taken seriously. That’s all the more surprising given that Plato’s theories, in general, were considered philosophy itself well into the Middle Ages, and in some circles still are today.
Aristotle and Numbers
The Pythagorean and Platonic theses on numbers also get a detailed treatment from Plato’s student Aristotle. Aristotle takes a critical view of Plato’s teachings on many points, but on the essential ones, he follows them:
„But if the Forms are not numbers, it isn’t possible for them to exist at all. After all, what principles could the Forms arise from? Number arises from the One and the Indefinite Dyad, and these are called the principles (archai) and elements (stoicheia) of number, and yet there’s no way to place the Forms as coming before or after them.“
(Aristoteles)
These teachings on the symbolism of numbers were later developed further in Neoplatonism, for instance in Plotinus’s metaphysical theory of numbers.
Influence on Religion
Plato’s theory of Forms, along with the significance of numbers, left a substantial mark on Islam, Christianity, and Judaism alike. Their sacred texts don’t just contain traces of the theory of Forms. Numbers and number combinations play a significant role in them too, one that’s hard to grasp today unless you reach for esoteric explanations. Countless passages in these sacred texts seem impossible to fully understand unless the numbers in them carry a deeper meaning. Take this example: “Seven days from now I will send rain on the earth for forty days and forty nights, and I will wipe from the face of the earth every living creature I have made.” And Noah did all that the Lord commanded him. Noah was six hundred years old when the floodwaters came on the earth. (More on this in the article on the meaning of numbers in the Bible.)
Augustine and Numbers
Church Fathers like Augustine carried this teaching about the nature of numbers forward. As one of the most influential philosophers and theologians of late antiquity, Augustine shaped Western thought and had a strong influence on Luther too:
„I’m even more amazed by the fact that in the popular mind, number is held in such low regard while wisdom is prized so highly. Yet, of course, the two are one and the same thing.“
(Martin Luther)
Leonardo da Vinci and Numbers
Leonardo da Vinci was first and foremost an artist, inventor, and polymath, but he was also someone who studied number symbolism and mathematical proportion intensively, especially in the context of art, nature, and architecture. That put him squarely in the Pythagorean tradition: the idea that numbers structure the world. To him, number was the measure of beauty and order, very much in the spirit of Pythagorean symbolism.
He illustrated the famous work De Divina Proportione (“On the Divine Proportion”) by the mathematician, Franciscan friar, and economics scholar Luca Pacioli, a work on mathematics, art, and theology that describes the golden ratio (proportio divina) as the divine measure of beauty. The golden ratio was seen as a symbolic expression of divine order, a central element of number symbolism in the Renaissance.
Gottfried Wilhelm Leibniz and Numbers
Leibniz was a German philosopher, mathematician, lawyer, and polymath, considered one of the last true universal thinkers in history. He didn’t just invent the first working calculating machine and lay the groundwork for modern logic and computer science. Just as significant was his fascination with numbers as a symbolic expression of divine order. Leibniz saw binary numbers, 0 and 1, as more than a technical system. He saw them as a metaphysical model too: 1 stood for God, or being; 0 stood for nothing, meaning the world could arise out of “nothing” through divine order. In his famous correspondence with China, he connected binary notation with the I Ching and searched for a universal language of truth. For Leibniz, number symbolism was a key to the harmony between logic, nature, and theology.
Johann Wolfgang von Goethe and Numbers
We also know that Johann Wolfgang von Goethe was strongly influenced by number symbolism, and that it shows up repeatedly across his literary, scientific, and philosophical writing. Like many thinkers before him, he understood numbers as more than a computational tool. To him, they expressed deep spiritual order. That comes through especially clearly in works like Faust, his theory of color, and his scientific studies. (More on this in the article: Numbers in Fairy Tales.)
Carl Gustav Jung and Numbers
The psychiatrist, psychoanalyst, and founder of analytical psychology started out as a close collaborator of Sigmund Freud, but grew into an independent thinker with a deep interest in mythology, religion, alchemy, and symbolism. Jung believed that deep within every person lies a collective unconscious, a kind of psychic bedrock holding universal symbols and archetypes that show up across every culture. Shortly before his death, he seemed to glimpse a connection between the archetypes of numbers and the shared principles of mind and matter he’d spent his whole life searching for. In one of his last statements, he apparently suggested that the essence of all his research into archetypes might lie in the ordering principle of the natural numbers.
„Numbers are more than we usually realize when we use them for practical purposes.“
(C. G. Jung)
According to Jung, every number must carry necessary meanings of its own. Each one, he said, is a kind of individual.
Contemporary Thinkers and Numbers
More and more contemporary researchers are drawing attention to a possible qualitative side of numbers. As Albrecht Beutelspacher writes:
„Probably not every number is interesting, but plenty of them have real character, and that’s especially true among the small numbers.“
(Albrecht Beutelspacher)
For the well-known physicist and Nobel laureate Roger Penrose, both the physical and the mental world are shadows of mathematical ideas. By his own account, that puts him in Plato’s camp: Plato defined ideas as primal forms that precede everything we perceive. Penrose is describing something more than calculation hiding within mathematics: primal ideas, in contrast to how we tend to understand math and numbers today.
The Philosophy of Numbers: A Lost Body of Knowledge
This has only been a short essay on numbers in philosophy. But it shows just how fundamental a role number symbolism played, not only at the origins of philosophy. It wasn’t just the thinkers who laid the groundwork for modern science. Many of their successors, the people who shaped the natural sciences, theology, art, and culture in decisive ways, grappled with the qualitative side of numbers too. Even though we still hold their legacies in the highest regard today, their emphasis on numbers is barely known anymore, or gets pushed aside because it doesn’t seem to fit a modern scientific worldview. A philosophy of numbers no longer exists. Both are a shame, since essential ideas that shaped how we think today have been lost along the way. At the same time, the different fields have kept drifting further apart and no longer seem to find any common ground. The book Verlorene Weisheit shows how a fresh look at this old, lost knowledge can lead to deeper insight and a new understanding across the many different bodies of knowledge and wisdom in the modern world.
Image Credits: iStock.com/LagartoFilm (numbers on a green background)