Select Works, Section 389

Section 8 8. B. (10) If the soul is body and permeates the entire body-mass, still even in this entire permeation the blending must be in accord with what occurs in all cases of bodily admixing. Now: if in the admixing of bodies neither constituent can retain its efficacy, the soul too could no longer be effective within the bodies; it could but be latent; it will have lost that by which it is soul, just as in an admixture of sweet and bitter the sweet disappears: we have, thus, no soul. Two bodies [i.e., by hypothesis, the soul and the human body] are blended, each entire through the entirety of the other; where the one is, the other is also; each occupies an equal extension and each the whole extension; no increase of size has been caused by the juncture: the one body thus inblended can have left in the other nothing undivided. This is no case of mixing in the sense of considerable portions alternating; that would be described as collocation; no; the incoming entity goes through the other to the very minutest point- an impossibility, of course; the less becoming equal to the greater; still, all is traversed throughout and divided throughout. Now if, thus, the inblending is to occur point by point, leaving no undivided material anywhere, the division of the body concerned must have been a division into (geometrical) points: an impossibility. The division is an infinite series- any material particle may be cut in two- and the infinities are not merely potential, they are actual. Therefore body cannot traverse anything as a whole traversing a whole. But soul does this. It is therefore incorporeal.