The Pythagorean influence on the evolution of the continuum concept in Presocratic philosophy

Pythagoreanism is examined as a key to understanding the continuum in Presocratic thought. If Parmenides and Zeno were likely interlocutors of the Pythagoreans, and the so-called pluralist philosophers formulated their theories as a consequence of Eleatic thought, then focusing on certain elements of Pythagoreanism becomes crucial for discussing the concept of the continuum among the Presocratics. Moreover, Aristotle explicitly connects himself to the Pythagoreans at the beginning of De Caelo Book I, where he emphasizes the importance of three-dimensional magnitudes in natural inquiry and the relationship between divisibility and the continuity of magnitudes. In Aristotle’s philosophy, the principles of limit and unlimited translate respectively into the form that defines each entity by making it one, and into matter. The limited, in this way, results in something that is one in itself, yet at the same time infinitely divisible by the boundlessness of matter. Furthermore, the limit-unlimited pair appears closely related to the one-many pair, partly due to the Pythagorean practice of configuring numbers. This approach to thinking about the continuous and the discrete seems to have influenced later Presocratic theories on the nature of physical magnitudes and their divisibility.