Matti Eklund

Vagueness, as discussed in the philosophical literature, is the phenomenon that paradigmatically rears its head in the sorites paradox, one prominent version of which is: One grain of sand does not make a heap. For any n, if n grains of sand do not make a heap, then n + 1 grains of sand do not make a heap. So, ten billion grains of sand do not make a heap. It is common ground that the different versions of the sorites paradox arise because of vagueness in a key expression, in this case ‘heap’. One central concern in the literature on vagueness is to find a solution to the sorites paradox. Vagueness also gives rise to borderline cases. Since ‘heap’ is a vague expression, ‘heap’ also gives rise to borderline cases: there are some possible entities such that they are neither clearly heaps nor clearly non-heaps, but instead are borderline heaps. Borderline cases can seem intuitively to present counter-examples to bivalence and the law of excluded middle . If Harry is a borderline case of baldness, ‘Harry is bald’ can seem neither true nor false, whence it presents doubts concerning bivalence. Similarly, one can find the corresponding instance of LEM, ‘Either Harry is bald or Harry is not bald’, suspect. There are three main theories that involve departures from bivalence, and two of them involve rejection of LEM as well. Standard three-valued logic invokes the idea of a third truth-value or truth-value gaps; fuzzy logic invokes the idea of continuum-many truth-values intermediate between truth and falsity. Both these views preserve truth-functionality. Traditional supervaluationism involves rejection of bivalence, but adherence to LEM. The idea is that if an expression is vague there is a range of precisifications associated with it, where, roughly, precisifications are ways the expression could be …

Numerous philosophical problems, otherwise quite different in character, are of the following form. Certain claims which seem not only obviously true, but even constitutive of the meanings of the expressions employed, can be shown to lead to absurdity when taken together. All such problems can justly be called paradoxes. The paradoxes I examine are the liar paradox, the sorites paradox, and the personal identity paradox posed by the fission problem. ;I argue that in these cases, the claims that jointly lead to absurdity really are constitutive of the meanings of the expressions employed, in the following ways. First, semantic competence with the expressions involves being disposed to accept these claims. Second, the claims are reference-determining, in that the semantic values of the expressions employed are constrained by the condition that these claims should come out true, or as nearly true as possible. If a claim or principle is constitutive of meaning in both of these ways, I call it meaning-constitutive. When the meaning-constitutive principles for some expressions of a language are inconsistent, I call the language inconsistent. This is a stipulative definition; but it accords well with what other theorists who have talked about languages being inconsistent, for example Alfred Tarski, have had in mind. ;In chapters one and two, I argue that our language is inconsistent. In chapter three, I relate my theses to Frank Jackson's and David Lewis's views on reference-determination. ;Another problem posed by the liar paradox concerns important theses in the philosophy of language. The liar reasoning shows that under certain conditions, a natural language cannot contain a predicate satisfying the T-schema. But many theses in the philosophy of language presuppose that truth satisfies the T-schema. In chapter four I attempt to resolve this conflict

I here critically discuss Hilary Putnam's views on ontology, especially as recently expounded in his Ethics without Ontology. In particular, I discuss Putnam's thesis of conceptual relativity and his criticism of the thesis that objectivity requires objects. Although I think that much of what Putnam says is important, and that there are important elements of truth to it, my points will largely be negative. Along the way I will discuss Putnam's and Wittgenstein's views in the philosophy of mathematics, and I will compare Putnam's metaontological views with those of William James, Michael Dummett, Crispin Wright and Simon Blackburn

The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiar accounts of vagueness for general reasons failto answer the question ofwhat vagueness consists in. A positive view is defended, according to which, roughly, the vagueness of an expression consists in it being part ofsemantic competence to accept a tolerance principle for the expression. Since tolerance principles are inconsistent, this is an inconsistency view on vagueness.

Here is the liar paradox. We have a sentence, (L), which somehow says of itself that it is false. Suppose (L) is true. Then things are as (L) says they are. (For it would appear to be a mere platitude that if a sentence is true, then things are as the sentence says they are.) (L) says that (L) is false. So, (L) is false. Since the supposition that (L) is true leads to contradiction, we can assert that (L) is false. But since this is just what (L) says, (L) is then true. (For it would appear to be a mere platitude that if things are as a given sentence says they are, the sentence is true.) So (L) is true. So (L) is both true and false. Contradiction.

Rudolf Carnap's 1930s philosophy of logic, including his adherence to the principle of tolerance, is discussed. What theses did Carnap commit himself to, exactly? I argue that while Carnap did commit himself to a certain multitude thesis—there are different logics of different languages, and the choice between these languages is merely a matter of expediency—there is no evidence that he rejected a language-transcendent notion of fact, contrary to what Warren Goldfarb and Thomas Ricketts have prominently argued. (In fact, it is obscure just what Goldfarb and Ricketts claim about Carnap). Toward the end I critically discuss Michael Friedman's suggestion that Carnap believed in a relative a priori

My theme here will be vagueness. But first recall Quine’s arguments for the indeterminacy of translation and the inscrutability of reference. (I will presume these arguments to be familiar.) If Quine is right, then there are radically different acceptable assignments of semantic values to the expressions of any language: different assignments of semantic values that for all that is determined by whatever it is that determines semantic value are all acceptable, and all equally good. Quine even argued that the indeterminacy is so radical that some sentences are true under some acceptable assignments but false under others.1 Still, Quine does not allow intermediate truth-values or truthvalue gaps. (As I will put it, avoiding the disjunctive formulation: does not allow that there are sentences which are neuter.) Quine holds on to classical logic and bivalence and requires each acceptable assignment to be classical and bivalent.2.

I will here present a number of problems concerning the idea that there is ontological vagueness, and the related claim that appeal to this idea can help solve some vagueness-related problems. A theme underlying the discussion will be the distinction between vagueness specifically and indeterminacy more generally (and, relatedly, the distinction between ontological vagueness and ontological indeterminacy). Even if the world is somehow ontologically indeterminate it by no means follows that it is, properly speaking, ontologically vague.1..

In (2001), (2003), and elsewhere, Ted Sider presents two arguments concerning the existential quantifier which are justly central to the recent discussion of metaontology. What we will call Sider's indeterminacy argument is an attempted reductio of the suggestion that the existential quantifier might be semantically indeterminate. What we will call Sider's naturalness argument is an argument for the claim that the semantic value of the existential quantifier is the most eligible existence-like meaning there is, à la David Lewis' eligibility theory of meaning. We will argue that these arguments cannot be jointly maintained: Sider must give up at least one. Before arguing this, we will present Sider's two arguments in a bit more detail, and discuss their relationship. A few remarks on the broader significance of our conclusions are in order at the outset. One may think that since one successful argument for a given conclusion is sufficient the point that Sider's arguments cannot both work is purely academic. But we think that Sider's two arguments at bottom reflect different ways of thinking about metaphysics. Moreover, we think that it is only the naturalness argument that promises to deliver all that Sider wants when it comes to metaontology, and it is only the indeterminacy argument that promises to deliver all that Sider wants when it comes to ontology