- (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.
8 comments:
What if space aliens transform the hula hoop into hula square? The hula square, with the same perimeter value, would encompass less area than the hula hoop.
Cool argument! If successful, this argument shows that at least *some* shape properties are not intrinsic, including the property of being a circle with a diameter of 1 light year. But everything you say here is consistent with the idea that other shape properties are intrinsic, e.g. the property of having a perimeter of pi light years. (I was going to say the property of being a *circle* with a perimeter of pi light years, but a modification of your argument suggests that being circular isn't intrinsic: just change the scenario so that the star is created inside the hula hoop, but a little bit off center.) There's an interesting difference between diameter and perimeter, namely: the perimeter does not depend on what space(time) is like where the object *isn't* located, whereas diameter (sometimes) does. This suggests that determinates of the determinable *perimeter* are intrinsic. (The same presumably goes for surface area and volume.)
Related: It might still turn out that even the determinate shapes of some objects will turn out to be intrinsic---roughly (I'm sure I don't have the geometric terminology just right) convex hole-less objects.
I don't think the perimeter of an object is a shape property. It doesn't supervene on shape as shape doesn't change when we magnify the object.
Also, if the shape is made of a finite number of point particles, the perimeter can be changed by changing space between the particles. (Of course, perimeter means something different then.)
Let me say a little more about why I chose the example as I did. The ratio of diameter to perimeter is an invariant of a shape: if A and B have the same shape--even if one is larger than the other--then the ratio will be the same.
Ok, interesting. But if we're thinking of shapes in such a way that things of different sizes can have the same shape, then the following principle looks really intuitively plausible: necessarily, any two (perfect) circles have the same shape (i.e. are exactly alike in respect of shape). But it looks like you'll have to deny that principle, since pre-star hula hoop and post-star hula hoop may well both be perfectly circular (i.e. all points on it are equidistant from some point). You could respond by saying that the above intuition is debunked once we realize the possibility of non-Euclidean geometries. But of course, the proponent of shapes as intrinsic properties will probably want to say the same about your premise 2. It's not clear to me that there is any reason to prefer the former debunking strategy to the latter.
One more thought re: circularity, this time on your side of the issue. Here's a variant on your argument:
Premise 1. (Just as in your post.)
Premise 2. Necessarily, if an object changes from a circle to a non-circle, then it changes in shape.
Premise 3. Possibly, something changes from a perfect circle to a non-circle without undergoing intrinsic change.
Therefore, shape is not an intrinsic property.
In support of premise 3, just modify your case so the star is slightly off center. I confess the debunking strategy mentioned in my last comment looks pretty bad for premise 2 of this argument. To deny 2 here is effectively to deny that circularity is a shape, which seems unacceptable. By contrast, to deny the principle mentioned in my last comment that any two perfect circles are exactly alike in respect of shape (as you must) is just to deny that circularity is a maximally determinate shape. That's counterintuitive, sure, but certainly better than denying that it's even a shape at all!
This is probably not true for electrons and other particles. The "shape" of an electron is basically just the exclusion zone it produces in space, and the radius of this zone is a universal constant.
Shape may not be intrinsic to arrangements (surprise surprise) but it actually does seem to be intrinsic to electrons, and quite possibly other particles.
"Shape is not an intrinsic property" - how true, especially if you are over 40. :)
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