The indivisible-atom debate has brought forward the sphere-and-plane case, the seed-and-mountain comparison, union and separation, and geometric and celestial-motion arguments. Each depends on distinct premises.
Central distinctions are point versus material constituent, actual parts versus possible cuts, divine power versus the possibility of its object, and geometric model versus external substance.
These distinctions enable a reasoned evaluation of affirmation, denial or suspension of judgment. The contrast with accidents (aʿrāḍ) remains fundamental: substances and their constituents concern bodily constitution, whereas accidents are characterized by dependence on a substratum.