Wolfgang Schwarz

Vague Objects, Strange Properties

Assume some sentence "Fa" is neither determinately true nor determinately false. This might be due to the fact that

1) It is somewhat indeterminate exactly which object "a" denotes.

or

2) It is somewhat indeterminate exactly which property or condition "F" expresses.

If neither (1) nor (2), then "a" determinately denotes a certain object A and "F" determinately expresses a certain condition F. So whence the indeterminacy? Maybe

3) F itself is vague or indeterminate. That is, some (determinate) objects satisfy F only to a degree between 0 and 1. A is such an object.

Think of sharp conditions as sets of possibilia. Then a vague condition is a fuzzy set of possibilia. I can see no strong reason to reject fuzzy sets as semantic values of predicates. So if we really want, we could replace explanation (2) by explanation (3).

What if we want to get rid of explanation (1)? We might try an analogue of explanation (3):

4) A itself is vague or indeterminate. That is, it satisfies some (determinate) properties, like F, only to a degree between 0 and 1.

This, however, can't be true. A determinate property is (or can be modeled as) a set of possibilia. Hence for any possible object, it is either definitely in the set or not. But A is neither. Therefore A is is not a possible object.

So the only way to reject the "semantic indecision" view which consists of (1) and (2), without rejecting vague predications altogether, is to deny that case (1) ever arises: Whenever a predication "Fa" is indeterminate, this is because the object denoted by "a" is a borderline case of the condition expressed by "F".

The problem is that sometimes this explanation looks plainly wrong. For example, since the borders of Mt. Everest are not quite clear, it is also not quite clear how much it weighs. Let's assume that 1 million tons is some mass of which it is not quite clear that Mt. Everest has it. So "Mt. Everest weighs exactly 1 million tons" is neither clearly true nor clearly false. If we reject (1), we have to claim that Mt. Everest is a borderline instance of weighing exactly 1 million tons. But how could there be a borderline instance of such a sharp property?

Well, unlike (4), the claim that there are such borderline instances is at least not clearly impossible either. One could even motivate it with considerations from quantum mechanics: Let E be some electron and P some precise point in space-time. According to quantum mechanics, E is located at P only to a certain degree. That is, E is a borderline instance of being located exactly at P. So there can be borderline instances even of intuitively sharp properties.

Rosen and Smith, in their Wordly Indeterminacy paper, describe how in general one could characterize intuitively sharp properties that nevertheless have borderline instances. They propose that a vague object is to be understood as an object that is a borderline instance of such a property.

Clearly, the mere existence of vague objects in the Rosen-Smith sense says nothing about the prospects of rejecting (1). Maybe electrons are really vague objects in the Rosen-Smith sense. This doesn't help at all with the vagueness of "Mt. Everest weighs exactly 1 million tons". For this not only must Mt. Everest be a vague object, that is, a borderline instance of some condition, it must also be a borderline instance of the particular condition weighing exactly 1 million tons. As I said, to reject (1) you have to claim that whenever a predication "Fa" is indeterminate, this is because the object denoted by "a" is a borderline case of the very condition expressed by "F". For example, if some identity statements "A = B" are vague, you have to claim that the pair (A,B) of definite (not necessarily distinct) objects is a borderline instance of strict identity.

(On the other hand, the existence of vague objects in the Rosen-Smith sense doesn't imply borderline cases of all sharp properties. Maybe there really are no borderline cases or precise shades of blue. Maybe the only sharp property that allows for borderline cases is mass, or spatiotemporal extension.)

Vague objects are strange. How could something be a borderline case of having some precise shade of blue, B17? Not by having some other shade of blue, say B16, which is very close to B17. For if something is B16, then it is definitely not B17. That's why B17 is an intuitively sharp property. Suppose A is an object that is B17 to degree 0.5 and any other shade of blue to degree 0. So A has this property of being B17 to degree 0.5 and any other shade of blue to degree 0. What kind of property is this? It seems to be a colour. But it is not a colour we find anywhere in the HLS space. So the HLS space is incomplete. It lacks a further dimension, the dimension on which A's colour differs from the colour of an object that is B17 to degree 1.

What's strange about vague objects is that they instantiate strange properties: strange colours, strange masses, strange locations, strange identity-relations.