The mass/count distinction attracts a lot of attention among cognitive scientists, possibly because it involves in fundamental ways the relation between language (i.e. grammar), thought (i.e. extralinguistic conceptual systems) and reality (i.e. the physical world). In the present paper, I explore the view that the mass/count distinction is a matter of vagueness. While every noun/concept may in a sense be vague, mass nouns/concepts are vague in a way that systematically impairs their use in counting. This idea has never been systematically (...) pursued, to the best of my knowledge. I make it precise relying on supervaluations (more specifically, ‘data semantics’) to model it. I identify a number of universals pertaining to how the mass/count contrast is encoded in the languages of the world, along with some of the major dimensions along which languages may vary on this score. I argue that the vagueness based model developed here provides a useful perspective on both. The outcome (besides shedding light on semantic variation) seems to suggest that vagueness is not just an interface phenomenon that arises in the interaction of Universal Grammar (UG) with the Conceptual/Intentional System (to adopt Chomsky’s terminology), but it is actually part of the architecture of UG. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

Supervaluational accounts of vagueness have come under assault from Timothy Williamson for failing to provide either a sufficiently classical logic or a disquotational notion of truth, and from Crispin Wright and others for incorporating a notion of higher-order vagueness, via the determinacy operator, which leads to contradiction when combined with intuitively appealing ‘gap principles’. We argue that these criticisms of supervaluation theory depend on giving supertruth an unnecessarily central role in that theory as the sole notion of truth, rather than (...) as one mode of truth. Allowing for the co-existence of supertruth and local truth, we define a notion of local entailment in supervaluation theory, and show that the resulting logic is fully classical and allows for the truth of the gap principles. Finally, we argue that both supertruth and local truth are disquotational, when disquotational principles are properly understood. (shrink)

If the semantic values of predicates are, as Williamson assumes (_Philsophical Perspectives,_ _13_, 505–517, 1999, 509) properties in the intensional sense, then epistemicism is immediate. Epistemicism fails, so also this properties account of predicates. I deploy examination of Williamson’s account as a foil against properties as semantic values, showing that his two positive arguments for bivalence fail, as do his efforts to rescue epistemicism from obvious problems. In Part II I argue that, despite the properties account’s problems, it has an (...) important role to play in compositional semantics. We may separate the problem of how smallest parts of language get attached to the world from the problem of how those parts compose to form complex semantic values. For the latter problem we idealize and treat the smallest semantic values as properties (and referents). So doing functions to put to one side how the smallest parts get worldly attachment, a problem that would just get in the way of understanding composition. Attachment to the world must be studied separately, and I review some of the options. As a bonus we see why the requirement of higher order vagueness is an artifact of taking properties as semantic values literally instead of as a simplifying idealization. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (shrink)

That reference is inscrutable is demonstrated, it is argued, not only by W. V. Quine's arguments but by Peter Unger's "Problem of the Many." Applied to our own language, this is a paradoxical result, since nothing could be more obvious to speakers of English than that, when they use the word "rabbit," they are talking about rabbits. The solution to this paradox is to take a disquotational view of reference for one's own language, so that "When I use 'rabbit,' I (...) refer to rabbits" is made true by the meaning of the word "refer." The reference relation is extended to other languages by translation. The explanation for this peculiarly egocentric conception of semantics-questions of others' meanings are settled by asking what I mean by words of my language-is to be found in our practice of predicting and explaining other people's behavior by empathetic identification. I understand other people's behavior by asking what I would do in their place. (shrink)

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully (...) support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. (shrink)

ABSTRACT Our ascriptions of content to past utterances assign to them a level of conceptual continuity and determinacy that extends beyond what could be grounded in the usage up to their time of utterance. If one accepts such ascriptions, one can argue either that future use must be added to the grounding base, or that such cases show that meaning is not, ultimately, grounded in use. The following will defend the first option as the more promising of the two, though (...) this ultimately requires understanding the relation between use and meaning as ‘normative’ in two important ways. The first way is that the function from use to meaning must be of a sort that allows us to maintain a robust distinction between actual and correct use. The second sort of normativity is unique to theories that extend the grounding base into the future. In particular, if meaning is partially a function of future use, we can see our commitment to the ‘determinacy’ of meaning as a practical commitment that structures our linguistic practices rather than a theoretical commitment that merely describes them. (shrink)

Following Hartry Field in distinguishing disquotational truth from a conception that grounds truth conditions in a community's usage, it is argued that the notions are materially inequivalent (since the latter allows truth-value gaps) and that both are needed. In addition to allowing blanket endorsements ("Everything the Pope says is true"), disquotational truth facilitates mathematical discovery, as when we establish the Gödel sentence by noting that the theorems are all disquotationally true and the disquotational truths are consistent. We require a more (...) substantial notion, however, if we intend to use truth values and truth conditions in explaining communication by language. (shrink)

A position that has been called ‘classical indeterminism’ has recently been developed in order to model vagueness: this approach appeals to an object-language ‘determinately’ operator, the semantics of which are defined in such a way as to preserve the principle of bivalence. I suggest that a prominent argument against this strategy, which I call the Field–Williamson argument, fails. The classical indeterminist position in its general form was anticipated by the Aristotelian commentators in their discussions of Aristotle’s famous ‘sea battle’ passage (...) concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds. (shrink)

A position that has been called ‘classical indeterminism’ has recently been developed in order to model vagueness: this approach appeals to an object-language ‘determinately’ operator, the semantics of which are defined in such a way as to preserve the principle of bivalence. I suggest that a prominent argument against this strategy, which I call the Field–Williamson argument, fails. The classical indeterminist position in its general form was anticipated by the Aristotelian commentators in their discussions of Aristotle’s famous ‘sea battle’ passage (...) concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds. (shrink)