Online research in philosophy

Let us say that the proposition that p is transparent just in case it is known that p, and it is known that it is known that p, and it is known that it is known that it is known that p, and so on, for any number of iterations of the knowledge operator ‘it is known that’. If there are transparent propositions at all, then the claim that any man with zero hairs is bald seems like a good candidate. We know that any man with zero hairs is bald. And it also does not seem completely implausible that we know that we know it, and that we know that we know that we know it, and so on.

It is often assumed that indeterminacy in mereological relations—in particular, indeterminacy in which collections of objects have fusions—leads immediately to indeterminacy in what objects there are in the world. This assumption is generally taken as a reason for rejecting mereological vagueness. The purpose of this paper is to examine the link between mereological vagueness and existential vagueness. I hope to show that the connection between the two forms of vagueness is not nearly so clear-cut as has been supposed.

A semantics of vagueness should reject the principle that every statement has a truth-value yet retain the classical tautologies. A many-value, non-truth-functional semantics and a semantics of super-valuations each have this result. According to the super-valuation approach, 'if a man with n hairs on his head is bald, then a man with n plus one hairs on his head is also bald' is false because it comes out false no matter how the vague predicate 'is bald' is appropriately made precise. But why should a sentence in which components actually remain imprecise be regarded as actually false just because it would be false if its components were precise? On one of the alternative treatments of quantification allowed by the many-value approach, the sentence in question is assigned an intermediate value closer to 'false' than to 'true'. Despite the elegance of the super-valuation approach, there are reasons to prefer the many-value approach.

According to one account, vagueness is "metaphysical." The friend of metaphysical vagueness believes that, for some object and some property, there can be no determinate fact of the matter whether that object exemplifies that property. A second account maintains that vagueness is due only to ignorance. According to the epistemic account, vagueness is explained completely by and is nothing over and above our not knowing some relevant fact or facts. These are the minority views. The dominant position maintains that there is a third possible variety of vagueness, linguistic vagueness. And, it goes on to insist, all vagueness is of this third variety. I shall argue, however, that linguistic vagueness is not a third variety of vagueness. Either it is a species of metaphysical vagueness or a kind of ignorance. And this, I argue, makes trouble for the claim that all vagueness is linguistic.

In recent literature on vagueness, writers have noted that more ‘plentiful’ theories of properties – those that postulate genuine properties corresponding to the classically vague predicates like ‘bald’ and ‘heap’ – appear straightforwardly committed to ontic vagueness. In this paper, however, I will argue that worries of ontic vagueness are not specific to ‘plentiful’ accounts of properties. The classically ‘sparse’ theories of properties – Universals and tropes – will, I contend, be subject to similar difficulties.

The two standard theories of vagueness—vagueness-as-ignorance and vagueness-asindeterminacy—agree on the following principle: if you are certain that it is clearly vague whether p, then you clearly should not believe p and you clearly should not believe not-p. I argue against the principle, and thus against the two standard theories. I offer an explanation of the initial appeal of the principle. And I show how a rival principle helps to better explain a recalcitrant trio of widely accepted data.

Standardly, one says that vagueness arises whenever a concept or linguistic expression admits of borderline cases of application. A predicate such as ‘bald’, for example, is vague because there can be situations in which it is indeterminate whether or not it applies to (a name of) a certain object. Some people are clearly bald (Picasso), some are clearly not bald (the count of Montecristo), and some are borderline cases—our concept of baldness and our linguistic practices do not specify any exact number of hairs that marks the boundary between the bald and the non-bald. Similarly, a singular term such as ‘Mount Everest’ is vague because there is no determinate way of tracing the geographical limits of its referent. Some rocks are clearly part of Everest and some are clearly not, but some rocks enjoy a borderline status.

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. This view entails the following proposition: that clear vagueness as to whether Harry is bald clearly does not entail that Harry is bald. I give an argument against the proposition, and thus against the dominant view.

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.