division. Everything divisible must divide either into something divisible or into something indivisible. If it divides into something indivisible, we have found the indivisible part. If it divides into something divisible, the same question arises concerning that divisible thing: does it divide into something divisible or something indivisible? If it divides into something divisible without end, then a finite thing contains infinitely many parts, whereas it is among the self-evident truths that the parts of a finite thing are finite in number.

I say:

This difficulty is what led al-Nazzām and others like him to affirm the “leap,” and a group of philosophers and speculative theologians to hold that division without end is possible potentially, but not actually.

A group of those who deny the indivisible part have answered this by saying that everything that exists admits of division, in the sense that one portion can be distinguished from another. This is division posited by the mind. It does not, however, entail the existence of infinitely many parts. For if an existing thing is said not to admit of actual division, it contains no infinite number of parts. If it is said to admit of actual division, then, as its parts become small, they undergo transformation, perish, and cease to exist, just as tiny portions of water turn into air. If they undergo transformation upon reaching the limit of smallness, it does not follow that they remain [capable of undergoing] infinitely many divisions, nor does it follow that infinitely many parts exist.