Unless you postulate a knife with really weird properties, cutting a continuous object in half isn’t turning matter into void. It’s moving some of the matter without changing its density (hence my offer of conservation of volume). You can do that to every point currently occupied by an object, but only by reserving an equal amount of space that’s currently void and displacing all of the matter to there.
It’s more of a conceptual knife—pointing out that by the definition of continuity, segment X is made of void and 2 smaller segments, Y and Z; but Y and Z are themselves made of void (and 2 smaller segments), and so on.
(Any conceptual knife just illustrates how motion was supposed to be possible in a continuous framework: the matter in the knife fits into the voids of what it is moving into.)
Oh, so the “made of void” thing comes from the void that the knife fits into. That wasn’t at all clear—it seemed like we were just talking about separating things into parts, not about the physical process of cutting.
Unless you postulate a knife with really weird properties, cutting a continuous object in half isn’t turning matter into void. It’s moving some of the matter without changing its density (hence my offer of conservation of volume). You can do that to every point currently occupied by an object, but only by reserving an equal amount of space that’s currently void and displacing all of the matter to there.
It’s more of a conceptual knife—pointing out that by the definition of continuity, segment X is made of void and 2 smaller segments, Y and Z; but Y and Z are themselves made of void (and 2 smaller segments), and so on.
(Any conceptual knife just illustrates how motion was supposed to be possible in a continuous framework: the matter in the knife fits into the voids of what it is moving into.)
Oh, so the “made of void” thing comes from the void that the knife fits into. That wasn’t at all clear—it seemed like we were just talking about separating things into parts, not about the physical process of cutting.