The intellectual stage for Leucippus was set by a profound logical problem posed by Parmenides of Elea. Parmenides established a severe dichotomy: there is only what-is (Being, τὸ ἐόν) and what-is-not (Non-Being, τὸ μὴ ἐόν). From this premise, all subsequent properties of reality are deduced. Since Non-Being cannot be thought of or spoken of, it cannot exist. Therefore, what-is must be one, continuous, and eternal.

This leads to a vision of reality as a single, unborn, indestructible, and unchanging entity. If Being were to come into existence, it would have to come from Non-Being, which is impossible. If it were to be destroyed, it would have to pass into Non-Being, equally impossible. Change and motion are illusions because they would require a state of 'not yet being' or 'no longer being', both of which invoke the forbidden Non-Being. Plurality is also denied, as any separation between things would have to be constituted by Non-Being. The result is a conception of reality as a perfect, changeless sphere, a plenum with no empty space.

Parmenides' student, Zeno of Elea, developed a series of arguments to defend this counter-intuitive view. Zeno's paradoxes are not mere riddles; they are sophisticated polemics designed to demonstrate the logical contradictions inherent in the common-sense assumptions of plurality and motion. By targeting the concept of infinite divisibility, Zeno argued that a line segment, if composed of an infinite number of points, could never be traversed. Likewise, if a magnitude is divisible, it must be divisible ad infinitum, leading to the conclusion that any extended object is simultaneously infinitely large and sizelessly small. These arguments aimed to show that our sensory experience of a changing, pluralistic world is fundamentally irrational, reinforcing the Parmenidean stance that only the unchanging One is real.

This created a metaphysical impasse. The logic of Eleaticism was formidable, yet it denied the most basic facts of experience. Leucippus's genius was not in refuting Parmenides, but in reinterpreting his terms. He accepted the core axiom that 'nothing can come from nothing' (ex nihilo nihil fit). True being could not be created or destroyed. However, he cleverly bypassed the Eleatic conclusions by postulating a plurality of 'Beings' and giving a new status to 'Non-Being'.

For Leucippus, 'what-is' was not a single entity but an infinite number of indivisible, solid particles called atoms (ἄτομοι, 'uncuttables'). Each atom possessed the Parmenidean characteristics of being eternal and unchanging in its own nature. 'What-is-not' was ingeniously redefined not as absolute nothingness, but as the void (κενόν, 'the empty'). The void exists, providing the space within which atoms can move, collide, and combine. Change, therefore, is not a transition from Being to Non-Being, but simply the rearrangement of eternal atoms in the existent void. This model affirmed the core Eleatic principle of conservation of Being while simultaneously accounting for the world of experience.

By splitting the Parmenidean 'One' into an infinite number of 'ones' and identifying Non-Being with the void, Leucippus resolved the metaphysical friction. He preserved the logic of eternal being while liberating it from the paralysis of the static sphere, paving the way for a mechanical and materialistic explanation of the cosmos.