Is the World Vague?
Either the world is intrinsically vague or our words and concepts are but the world is not. We say that “bald” is a vague predicate and bald is a vague concept. We don’t mean they are vague as such—that the predicate is a vague linguistic entity and the concept a vague psychological entity. We mean that they denote or express something vague: they themselves are determinate entities that determinately express something vague. What is this? A property of course: the property of being bald is a vague property (borderline cases etc.). So the question becomes whether this property is part of the world or is confined to language and the mind. Is it that the world is perfectly precise and our modes of representing it are not? Suppose we say that baldness lies in our representations (the properties we bring to the world) and not on the top of people’s heads. Then nothing we say or think involving this property will be true, since there is no vague property in the world corresponding to the property we mentally represent when we say “bald” or think bald. For we are attributing a property to things that they objectively lack—nothing is objectively bald. Similarly for other vague predicates or concepts. This means that there is an enormous amount of falsehood in our statements and beliefs. But that is surely absurd: surely some people are bald and some objects are red (etc.)! So we had better say that objects do have the properties they are said to have when we use such predicates, which is to say they objectively have the properties in question. Ergo the world is vague.
But are these vague properties mind-independent? It might be maintained that they are all in some way dependent on the mind for their instantiation: experience-dependent, interest-relative, or pragmatically defined. In addition the world has properties that are not mind-dependent and these properties are never vague—say, the properties spoken of in fundamental physics (mass, spin, charge, etc.). Maybe so, but the point makes no difference to the argument, though it raises the interesting question of why there should be such a partition (is the mind inherently vague but the physical world inherently precise?). For we still have the result that a great many properties of things are vague: reality is still vaguely constituted, not a determinate realm, not a totality of precise facts. When God made the world he made it blurry at the edges, inherently fuzzy, not a mathematician’s paradise. 
 If you think that precision in a property is a necessary condition of its objective instantiation, you will end up denying the reality of many facts, leaving a skeletal world or no world at all. Anti-realism about vagueness leads to anti-realism tout court. On the upside, bald men will be able to proudly announce their non-baldness (philosophy as the cure for baldness).