How were numbers conceived by philosophers?

With my full philosophical rucksack I can only climb

slowly up the mountain of mathematics.

Ludwig Wittgenstein

Have you ever wondered what Philosophy and Mathematics have in common?

To answer the question we have to go back to the past.
Since ancient times, Mathematics has been one of the main themes on which most philosophers concentrated: many of them in fact used Mathematics to solve practical problems, such as Eratosthenes, who calculated the Earth circumference, or Talete, who measured the height of the Pyramids using their shadows.
Pythagoras’s community, in Crotone, was one of the first schools which formulated a teaching based on numbers and reality; this scholar is presented by legends as possessing magical powers and he has been considered, till today, a man whose life is surrounded by mystery because he didn’t write anything and we have very little information about him. However, he was the founder and, first of all, the only teacher in this community. Pythagoras and his disciples thought that numbers were the origin of nature and of whatever is around us, because many real experiences such as music, the cycle of seasons and the movement of the stars can be traced back to them; they believed the world had a geometrical order which could be represented through the “Holy tetrad” or  “Tetractys”, a triangle in which each side was made up of 4 points (for a total of 10, that was considered for this reason, the perfect number) arranged like this : 1+2+3+4, where the 1 symbolizes the point, number 2 the line, number 3 the surface and finally 4 the solid.

So these scholars, who didn’t have technological instruments to prove their theories, just used their intuition and attributed to each number a particular meaning.
But apart from Pythagoras’s school, many other philosophers kept on studying mathematics, each conceiving this science in a different way…
The Greek Plato, for example, felt a large admiration for Mathematics because it gives us proved certainties ( 2+2 = 4 is always true and no one can prove that it is false) and he was inspired by Pythagoras’s teachings.

Aristotle instead inquired into reality without formulating any mathematical rules.
In the Middle Ages, scholars preferred to deal with other themes rather than this topic, which was studied again during the Renaissance.
In the period around 1600, we can’t forget Galileo Galilei who was the protagonist of a true scientific revolution and the inventor of the “experimental method”: he studied Maths and Physics but he was a great philosopher, too. He affirmed the presence, in our reality, of things that we can quantify (which are studied by Mathematics) and things that we cannot, which he avoided considering.

In the same age, Rene Descartes (best known as Cartesius, the creator of the Cartesian coordinate system, which was given his name) gave Mathematics a new importance and joined it to philosophy because he said that “one wouldn’t have its value without the other”.

He was the first to promote the use of the mathematical method in different contests of our daily life.
Many others, after these philosophers, have drawn inspiration from them and reflected on this topic… so which is the difference between Philosophy and Mathematics? Of course Philosophy tries to answer the most difficult questions of our life while Mathematics wants to solve practical problems, so they have different purposes… but at heart they are really similar: both aim at finding a solution in a coherent and rigorous way which will lead us to think logically and to consider everything from its deepest point of view; it’s not a fortuitous event that excellent philosophers were also great mathematicians and scientists.

Thanks to their discoveries we live a better life.

7 thoughts on “How were numbers conceived by philosophers?

  1. “Philosophy tries to answer the most difficult questions of our life while Mathematics wants to solve practical problems”

    Interestingly, when I was reading Rand’s “Philosophy: Who Needs It,” I believe she mentioned that philosophy was one of the most practical things that we do. I found that to contrast the general sense people have about philosophy as well as your comment. On the mathematics part, I’m not sure that all of mathematics is done with the main of practicality. The quote “There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world” by Nikolai Lobachevsky seems to affirm my point. While it can (eventually) be applied, application isn’t necessarily its only aim.

  2. Hi and welcome to our blog! 🙂
    Both, Philosophy and Mathematics, can in my opinion be approached from any point of view, so practicality, empirical enquiry and abstraction could be applied to both, as both are part, in one way or another, of our daily lives.
    However, I think my blogger’s intention was mainly to point out to her fellow students, who study Maths and Philosophy as separate subjects at school, that indeed these subjects are closely related.

  3. howdy Learning to fly , i’ve had a look at your blog , it is a nice blog and useful. Good for me. a lot of themes and issues and Philosophy content. i will read and comment your site.

  4. Hello everybody! I’m the author of this post so i want to answer the question…mathematics has not just a practical aim but we have to acknowledge that it has more applications than philosophy in our daily life ( if we think of technology in general) and this is what i meant with that sentence; anyway this topic is so interesting that i’d like to talk about again…who knows…:)

  5. As teacher b. wrote, we study Mathematics and Philosophy as separated subjects… and while it’s true that they are similar because they have the aim to answer some difficult questions in a logical way, I think that they are also very different because they deal with different topics: Maths is “limited” to the (big) world of numbers, calculations, and so on, that we use especially -but not only- for our practical needs, while Philosophy is a way to answer some life questions that are more abstract or indefinite than numbers… I believe that turkeysbay wanted to say this with the article… Correct me if I’m wrong 🙂

  6. Actually Philosophy and Maths are linked… But i think that we can’t compare the beauty of the second with the first. According to me, it’s a battle already lost in advance 🙂

  7. Maryssa has perfectly understood what i meant with that sentence!;)
    And although i’m not as keen as Poleyn on Maths, i agree with her! Perhaps because philosophy is a new subject we’ve started studying this year…i don’t know…maybe one day we’ll learn to appreciate it:)

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