'divisibility' is a correct and usable word in written English
You can use it to describe the quality of an object being capable of being divided into two or more parts, for example, "The divisibility of the atom was critical in the development of the nuclear bomb."
Within the medieval Muslim world, philosophers and theologians alike recognized two sorts of division: "physical divisibility" and "conceptual divisibility".
It is almost as though we could say the indivisibilist (mis)understands infinite divisibility to be division into points instead of division by points.
The second type of division, namely, conceptual divisibility, involves only the accidental partition of the magnitude.
According to the antithesis arguments, the world is infinite in both space and time (these being infinite as well), and bodies are (in accordance with the infinite divisibility of space) also infinitely divisible.
In its simplest form, trial division operates by successively testing \(x\) for divisibility by each integer smaller than \(x\) and keeping track of the divisors which have been found thus far.
The first and true sense of divisibility for Avicenna, physical divisibility, is the form of division that actually brings about a separation and discontinuity within the magnitude.
In the atomist version, these unchanging material principles are indivisible particles, the atoms: the atomists are said to have taken the idea that there is a lower limit to divisibility to answer Zeno's paradoxes about the impossibility of traversing infinitely divisible magnitudes.
Atoms, defined as indivisible, extended particles of matter are actually divisible, and thus their very definition, taken together with the fact of their divisibility, implies a contradiction.
After all, infinite divisibility is loose talk.
Yet a philosopher who believes in infinite divisibility, or at least in its possibility, might feel the same about infinite composability.
Thus, by reflecting upon the aporiai regarding time, we are led immediately to think about duration and divisibility, about quanta and continua, and about a variety of categorial questions.
