Epicurus argues that sensible minima and minimal parts of atoms are analogous and that the analogy explains how minimal parts can touch each other.Īristotle asked how something which has no parts, can be in motion across a border.

The observer would not be able to see only part of the object as it would disappear from the field of view.Įpicurus argues that sensible minima must be next to one another just as our visual field can be conceived to be composed of perceptible minima. The minimum size the object appears to the observer is considered to be partless. When the object if moved further even the slightest, it would not be visible any more.

Epicurus proposes an object that is so far away that it can just be seen. Epicurus offers the analogy of perceptible minima as a solution. Minimal parts themselves are partless, which raises the question whether the theory of minimal parts only moves Aristotle’s problem about contact and succession to another level. If a thing had an infinite number of parts because there is no minimum distance, it would be infinitely large (composition paradox).Įpicurus’ proposition for inseparable, but not partless atoms, lifts the objections raised by Zeno because he separates the notion of physical indivisibility and conceptual partlessness. If there are no minimal distances-as Zeno implies-then motion would involve travelling over an infinite number of locations (Dichotomy paradox). Minimal parts are not physically separable units out of which atoms are built, but the minimal units of distance for the physically indivisible atoms.Įpicurus also seems to put the concept of minimal distances forward as a reply to Zeno’s paradoxes. If atoms have minimal parts, then they can touch each other “part to part” or “part to whole”. Sizeless atoms are also unable to touch ‘part to part’ or ‘part to the whole’ because they have no parts.Įpicurus proposes that atoms have minimal parts to overcome the objection raised by Aristotle. If they would touch each other “whole to whole”, the parts would eclipse each other. The existence of atoms is, according to Democritus, required so that bodies are not annihilated into Cantor Dust, which would contravene the second principle of conservation (nothing perishes into nothing).Īristotle writes in book VI of Physics that atoms cannot touch each other if they are without size. Democritus uses arguments about generation and destruction to argue for the existence of atoms. Cantor’s work on infinity eventually drove him to develop mystical theories, trying to prove the existence of God.Ĭantor cubes recursion progression towards Cantor dust (Source: Mattcomm, CC BY-SA 4.0 via Wikimedia).īack to the ancient Greeks, Zeno argued that “it is necessary that are both small and large so small as not to have magnitude, so large as to be unlimited” because infinite division leaves us with an endless number of parts.ĭemocritus’ arguments are not put forward as a solution to Zeno’s paradoxes of motion but are more likely a reply to Aristotle’s objection to the arguments of the pre-Socratic atomists. In contemporary mathematics, the remainder of an infinitely divided area is ‘ Cantor Dust’, named after the German mathematician Georg Cantor who contemplated infinity. The supposition that division is possible everywhere does, however, yield absurd consequences related to infinity. If a division is possible anywhere, then the division of a body is also possible everywhere. Democritus states that if there are no indivisible atoms, then the division of a body is possible anywhere. Democritus argues, according to Aristotle, for the existence of atoms to counter the consequences of infinite divisibility of objects, proposed by Zeno’s paradoxes.

Aristotle atomic theory