The miracle of the Eucharist is that in Holy Communion the substance of the bread and wine is removed and is replaced by the substance of Christ's flesh and blood. Coextensive with this, the sensory accidents of Christ's flesh and blood are removed, and the accidents of the bread and wine (their color, taste, odor, smell, and feel) remain. The miracle then consists not merely in the replacement of the substances of bread and wine with the substances of Christ's flesh and blood but also in the removal of the sensory accidents of Christ's flesh and blood and the substitution of the sensory accidents of bread and wine. These sensory accidents of bread and wine are unsupported by any substance, for if they were supported by the substances of Christ's flesh and blood that they now conceal, then those substances would be bread and wine. In Aristotelian terms, this involves two miracles. The first miracle is the existence of the substantial forms of Christ's flesh and blood without their sensory accidents, and the second miracle is the presence of the sensory characteristics of bread and wine separate from their substantial forms and, moreover, separate from any supporting substantial form at all (see form, substantial).

There is also the big-little problem. How can a large volume of Christ's body occupy the space of a small piece of bread, and Christ's blood occupy the small space of a bit of wine? On the other hand, how can the small volume of Christ's body and Christ's blood be enough to occupy the large quantities of consecrated bread and wine required when many people are given communion at the same time?

Descartes argued that the Aristotelian physics of substantial forms and accidents is nonsense. He wrote to Mersenne that “there will be … no difficulty in accommodating theology to my way of philosophizing because there is nothing to change except for transubstantiation, which is extremely clear and easy according to my principles” (AT III 295–96, CSMK 172). Mersenne did not take the hint to construct a Cartesian explanation of the Eucharist, so Descartes did it himself.