- Are shapes intrinsic? Intuitively, an intrinsic property is a property that characterizes something as it is in itself. What intrinsic properties something has in no way depends on what other things exist (things other than it or its parts) or how it is related to them. With extrinsic properties (properties that are not intrinsic), by contrast, other things can “get in on the act” when it comes to determining whether something has them.
- So consider your left hand. Ignore the other things that exist and consider it as it is in itself. Does it have a shape? Or does it, when so considered, become shapeless?
- Immediately, “it does have a shape!” seems like the right answer. (Indeed, shapes are often cited as paradigm cases of intrinsic properties.) The proposition that shapes are intrinsic thus has the power of intuition behind it, and that is reason enough to try to defend it. It also ﬁgures prominently in well-known philosophical arguments. Lately, though, I have begun to have doubts that shapes really are intrinsic.
- What we want is a theory of shape properties according to which shapes are intrinsic. So what is a theory of shape properties? I assume that some spatial relations are basic, or fundamental, and that other spatial relations are analyzed in terms of them. To give a theory of shape properties, then, is to produce a list of which spatial relations are fundamental, together with the laws those relations obey and (if shape properties are not themselves on the list) an explanation of how shape properties are to be analyzed using those relations. So, for example, we might say that the basic spatial relations are distance relations; using these relations, we could analyze, say, the property of being an equilateral triangle in a familiar way: an equilateral triangle is a three-sided ﬁgure such that the distance between any two of its corners is the same. By looking at a shape’s analysis we can tell whether it is intrinsic: a shape is intrinsic just in case it can be completely analyzed in terms of the fundamental spatial relations among the parts of things that instantiate it. It seems obvious, at ﬁrst glance, that something’s shape is just a matter of the fundamental spatial relations among its parts, and so it seems obvious that shapes are intrinsic. But this obvious claim is hard to defend. In this paper I will examine all the theories of shape properties that I know of. I argue that each of these theories either cannot save the intuition that shapes are intrinsic, or can be shown to be false.
- Here is the plan for this paper. In section 2 I say more about what shape properties are and ward oﬀ two quick arguments that shape properties are not intrinsic. Then in section 3 I say more about the notions of fundamentality, analysis, and intrinsicness that I am appealing to. The remainder of the paper is devoted to examining theories of shape properties.
- (I assume throughout this paper that space is three-dimensional and Euclidean. Unfortunately I do not have room to discuss problems raised for intrinsic shapes by the possibility that space does not have the geometry or the topology of Euclidean space.)
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