According to Aristotle, the Pre-Socratic Greek philosopher Anaxagoras had taught that every thing, and every portion of a thing, contains within itself an infinite number of like and unlike parts. For example, Anaxagoras maintained that there must be blackness as well as whiteness in snow; how, otherwise, could it be turned into dark water? Aristotle criticized Anaxagoras' theory on multiple grounds, among them the following:
*Animals and plants cannot be infinitely small according to Aristotle; thus the relatively homogeneous substances of which they are composed (e.g., bone and flesh in animals, or wood in plants) could not be infinitely small, either, but must have a smallest determinate size—i.e., a natural minimum.
*On Anaxagoras' argument in which all things contain all others infinitely, water could be drawn from flesh, then flesh from that water, and water from that flesh, and so on. However, as above, because there is a smallest determinate size beyond which a further divided substance would no longer be flesh, any further cycle of such drawings out would be impossible.
*Moreover, "[s]ince every body must diminish in size when something is taken from it, and flesh is quantitatively definite in respect both of greatness and smallness, it is clear that from the minimum quantity of flesh no body can be separated out; for the flesh left would be less than the minimum of flesh."
Unlike the atomism of Leucippus, Democritus, and Epicurus, and also unlike the later atomic theory of John Dalton, the Aristotelian natural minimum was not conceptualized as physically indivisible--"atomic" in the contemporary sense. Instead, the concept was rooted in Aristotles hylomorphic worldview, which held that every physical thing is a compound of matter (Greek hyle) and a substantial form (Greek morphe') that imparts its essential nature and structure. For instance, a rubber ball for a hylomorphist like Aristotle would be rubber (matter) structured by spherical shape (form).
Aristotle's intuition was that there is some smallest size beyond which matter could no longer be structured as flesh, or bone, or wood, or some other such organic substance that (for Aristotle, living before the microscope) could be considered homogeneous. For instance, if flesh were divided beyond its natural minimum, what would remain might be some elemental water, and smaller amounts of the other elements (e.g., earth) with which water was thought to mix to form flesh. But whatever was left, the water (or earth, etc.), would no longer have the formal "nature" of flesh in particular – the remaining matter would have the form of water (or earth, etc.) rather than the substantial form of flesh.
This is suggestive of modern chemistry, in which, e.g., a bar of gold can be continually divided until one has a single atom of gold, but further division of that atom of gold yields only subatomic particles (electrons, quarks, etc.) which are no longer the chemical element gold. Just as water alone is not flesh, electrons alone are not gold.