# Maths and Philosophy #3: Aristotle

Aristotle was a Greek philosopher, born around 382 BC. At age 18, he joined Plato‘s Academy in Athens, remaining there until the age of 37. Although he was mainly a philosopher – his writings constitute the first comprehensive system of Western philosophy – Aristotle made important contributions to mathematics by systematising deductive logic.

With the Prior Analytics, Aristotle is credited as the first to formally study and formalise logic. His concept of logic was to dominate the West until the 19th century advances in mathematical logic.

### Aristotelean Logic

Aristotelean Logic begins with the distinction between subject and predicate:

• Subject: an individual entity, or class of entities
• Predicate: a property, attribute or mode of existence that the subject may or may not possess

The fundamental properties of predication were:

1. Identity: everything is what is it and acts accordingly
2. Non-contradiction: it is impossible for a thing to both be and not be
3. Either-or: everything must either be or not be

Aristotle also developed rules for chains of reasoning that would, if followed, never lead to false conclusions; this is the basic principle of mathematics, where the ‘rules’ are axioms. In this Aristotelean form of reasoning, the links are syllogisms: pairs of propositions that, taken together, give a new conclusion:

Some A is B.

All B is C.

Therefore, some A is C.

In his logic, Aristotle distinguished between dialect and analytic: “dialect only tests opinions for their logical consistency; analytical works deductively from principles resting on experience and precise observation.”

This was very different from Plato’s Academy’s teachings, where dialect was supposed to be the only proper method for both science and philosophy.

Sources: 1 | 2 | 3

Hope you enjoyed this series! M x