Plato was a Greek philosopher during the 5th century BCE’s Golden Age of Athens. He was a student of Socrates, and he was a teacher of Aristotle at his Academy. He is considered the founder of Western philosophy. The Platonic school of thought, which he developed and taught, is based on pure, abstract reason. For him, pure reason is the key to all knowledge.
According to Plato's Theory of Forms, there is a world that we apprehend through our senses. This is a world of physical objects that we can see, touch, feel, hear, and taste. These objects are impermanent; they can disappear, be changed, and be destroyed. However, there is a permanent, unseen world of Forms. These Forms are what is real and universal, and they are abstract, never changing, and understood through pure reason. For example, a table is a physical object that we can see and touch, and it can be removed. However, “tableness” is an abstract that exists in the mind and is discerned through pure reason.
Descartes, a seventeenth-century French philosopher, rejected the idea of separating physical objects from their idealized form. He was the founder of analytical geometry and said that knowledge is finding a foundational truth and then linking all truths with each other. His fundamental truth was "I think, therefore I am." With this as his base statement, he achieved knowledge by applying mathematical methods to philosophy. He believed that through science and mathematical logic, true knowledge could be discovered.