If one recalls the names of Greek philosophers, the first one that comes to our mind is Aristotle. He was one of the most well-known philosophers and polymaths of classical Greece.

But, his most important contribution to modern science is his philosophy of mathematics. While mathematics is quantitative and philosophy is qualitative, Aristotle realized the link between the two subjects. The link here is “logical problem-solving.”

Aristotle was a renowned student of another great Greek polymath, Plato. He was born and brought up in a city in northern Greece called Stagira. Later on in his life, though, Aristotle challenged most of Plato’s theories. He is also famous for having founded a library in Lyceum.

Aristotle’s views on politics, history, and the sciences continue to shape the modern vessels of knowledge. Aristotle is also said to have tutored Alexander the Great at the request of his father.

## Aristotle’s Contribution to Mathematics:

• Symmetry:

Aristotle explained his concept of symmetry in the book “Metaphysics.” Aristotle defined the basic forms of beauty to be order and symmetry. Both order and symmetry are explained and demonstrated by the natural sciences in a special manner. As Aristotle is famously known to have said, “Beauty can be measured.”

Aristotle’s equation with beauty and symmetry can be discovered in how the Greeks used mathematical proportions to build their structures. Even Greek sculptures were made following a combination of rules and set squares.

This kind of obsession with geometry and symmetry can also be seen in the Renaissance artists in the later eras.

• Continuity: Aristotle had developed a mathematical notion of continuity. According to this theory, Aristotle has formulated a notion where divisibility without end is crucial. The important contribution of Aristotle is that he brought in new notions related to continuity. A new account of limits, a new understanding of infinity, and a new differentiation between potential and actual divisibility were established.
• Time: In his book “Physics,” Aristotle has dealt with the concept of time by combining it with mathematics and philosophy. His time treatment consists of observations about numbers that have become close to being associated with an account of numbers. Aristotle also distinguishes between the two senses of number. He differentiates between what is counted and that by which we count.

## Aristotle’s Contribution to Philosophy

Aristotle has also made immense contributions to philosophy. A few noteworthy theories, which he combined with mathematics, are mentioned below:-

• Reasoning:
For twenty-odd years, Aristotle was a student of another great Greek scholar, Plato. But, by the end of his learning, he rejected all the forms and characteristics of Platonic thought. He built his own brand of Aristotelian thought or philosophy. One of the prime pillars of that philosophy is reasoning.
• Habituation and Excellence:

In Aristotelian works, ethics is any inquiry that circumscribes the investigation of how a human flourishes and develops according to his own nature. To pursue this inquiry, Aristotle divides the psyche into three parts – passions, power, and habits.  Almost all human beings share similar passions and power; you differ in how you have been habituated and nurtured.

Again, when it comes to human excellence, Aristotle points out that it takes place by two distinct mechanisms. These two are intellectual excellence and emotional excellence.

• Ethical Deliberation:

Continuing his previous principle, Aristotle explained that human action showcases excellence only if carried out voluntarily. Excellence can thus be understood as a collection of choices, where “choice” can be defined as a “deliberate action.”

• Self and Others:

Life is not happy only if one deliberates on the right choices or goes behind excellence. Hence, Aristotle recognized the element of luck in happiness. However, he stated that even though bad luck cannot make someone sad, you must possess external qualities to discover happiness.

Aristotle emphasized the idea of friendship. The idea of friendship highlights that healthy love for oneself translates into love for others.

## Why Applied Mathematics Is Philosophically Important

Aristotle always contested the notions of Platonism that mathematical objects like numbers cannot be realized in an abstract world.  According to Aristotle’s philosophy of mathematics, mathematical objects can be understood both in the physical and the abstract world.

Contemporary mathematics served as a source of understanding the philosophy of science. Aristotle’s philosophy of mathematics gives a much-needed break from Platonian philosophy.

Aristotle’s idea of symmetry can be seen everywhere around us. From the buildings and apartments around us to the world’s great monuments, all of them have been created following Aristotle’s symmetry. Our idea of infinity has been enhanced due to Aristotle’s work on continuity and order. The modern time system could be developed after working on Aristotle’s time system.

Aristotle, hundreds of years back, had made an immense and immeasurable contribution to both mathematics and philosophy. These contributions have today become the source of Aristotelian thought and philosophy.

For those who always thought that math and philosophy are two water-tight compartments, this article shall help them clear their doubts. To know more about the inter-relation between philosophy and mathematics, please visit BYJU’S FutureSchool blog. We will be looking forward to your feedback in the comments below.

Sources:

1. https://plato.stanford.edu/entries/aristotle-mathematics/#:~:text=Contemporary%20mathematics%20serves%20as%20a,in%20the%20biology%20and%20ethics.
2. https://www.bbc.co.uk/programmes/articles/4FgkDqgQN2nqTx8ltswmCGr/8-brilliant-definitions-of-beauty-from-aristotle-to-aguilera#:~:text=Aristotle%3A%20beauty%20is%20symmetry&text=Literally.,%2C%E2%80%9D%20he%20says%20in%20Metaphysics.
3. https://www.cambridge.org/core/books/concept-of-motion-in-ancient-greek-thought/aristotles-notion-of-continuity-the-structure-underlying-motion/418C1F1FFFB74DC77D8241636953B57D
4. https://home.uchicago.edu/~jlear/docs/Aristotle’s%20Philosophy%20of%20Mathematics.pdf
5. https://www.britannica.com/biography/Aristotle#:~:text=Everyone%20must%20do%20philosophy%2C%20Aristotle,gave%20them%20a%20godlike%20intellect.
6. https://research.library.fordham.edu/cgi/viewcontent.cgi?article=1012&context=phil_research