What concept is associated with the Pythagorean belief system in terms of knowledge acquisition?

The Pythagorean belief system emphasizes the importance of intuition and logical reasoning as central methods for acquiring knowledge. Pythagoreans, who were influenced by earlier philosophical and mathematical thought, believed that true understanding comes from an internal sense of knowledge that transcends mere observation. They posited that there exists an underlying order and harmony in the universe, which could be grasped through reason and thought, particularly through mathematical relationships. This perspective suggests that knowledge is not solely derived from empirical data or sensory experiences but rather from an innate understanding and rational deduction about the world.

The emphasis on intuition and logical reasoning aligns with the Pythagorean view that mathematics and abstract reasoning are the keys to understanding not just mathematical concepts but also the cosmos itself. This approach underlines the philosophical shift towards rationalism, where thinking and reasoning take precedence in the quest for knowledge.