- (Premise) If an object can change in shape without undergoing intrinsic change, shape is not an intrinsic property.
- (Premise) If the diameter[note 1] of an object changes while its perimeter does not, the object changes in shape.
- (Premise) An object can change in diameter but not in perimeter without undergoing intrinsic change.
The thought behind (2) is that the shape of an object determines the ratios of distances between parts.
Now I argue for (3). Imagine a giant hula-hoop, a light-year in diameter, without anything inside. Suppose that God creates a massive star in the middle. This distorts the spacetime manifold in the vicinity of the star, changing the distances between diametrically opposed points on the hula-hoop. But it will take half a year for the changes in the spacetime manifold to propagate to the hula-hoop. Thus the perimeter of the hula-hoop is unchanged for half a year. Furthermore, surely, the creation of a star half a light-year from any part of an object doesn't intrinsically change the object for at least half a year.
So, the hula-hoop (a) is intrinsically unchanged, (b) its perimeter is unchanged, and (c) its diameter is changed, which yields (3).
This is a modification of an argument in a paper of mine on the Eucharist.