I argue that standard definitions of quantifiers are inadequate and offer a new one. The new definition categorizes expressions as quantifiers in accordance with our pre-theoretical judgments, it is broadly applicable to both formal and natural languages, and it eschews unnecessary theoretical commitments about the details of the syntax and semantics of these expressions.

Ontological pluralism is the view that there are different fundamental ways of being. Recent defenders of this view—such as Kris McDaniel and Jason Turner—have taken these ways of being to be best captured by semantically primitive quantifier expressions ranging over different domains. They have thus endorsed, what I shall call, quantificational pluralism. I argue that this focus on quantification is a mistake. For, on this view, a quantificational structure—or a quantifier for short—will be whatever part or aspect of reality’s structure (...) that a quantifier expression carves out and reflects. But if quantificational pluralism is true, then a quantifier should be more natural than its corresponding domain; and since it does not appear to be the case that a quantifier is more natural than its corresponding domain, quantificational pluralism does not appear to be true. Thus, I claim, an ontological pluralist should not be a quantificational pluralist. (shrink)

Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form \.Γ can be empty. If you don’t like my examples, feel free to choose your own, everything I have to say should apply to those as well. Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to (...) answer the question of how beliefs in such attributions are justified, on both its descriptive and normative interpretations; I aim to say when we generally take ourselves to be justified in forming such beliefs, and to make it plausible that beliefs formed this way really are justified.We can ask such questions about many domains but there are special difficulties for answering them in logic. Some of the difficulties stem from the fact that logic is thought t.. (shrink)

Descriptions are phrases of the form ‘an F’, ‘the F’, ‘Fs’, ‘the Fs’ and NP's F (e.g. ‘John's mother’). They can be indefinite (e.g., ‘an F’ and ‘Fs’), definite (e.g. ‘the F’ and ‘the Fs’), singular (e.g., ‘an F’, ‘the F’) or plural (e.g., ‘the Fs’, ‘Fs’). In English plural indefinite descriptions lack an article and are for that reason also known as ‘bare plurals’. How to account for the semantics and pragmatics of descriptions has been one of the central (...) topics in philosophy for centuries. This entry focuses on the historical and contemporary philosophical debate about Bertrand Russell’s theory of descriptions and the theories that developed as responses to this theory. (shrink)

§§3-4 of the Begriffsschrift present Frege’s objections to a dominant if murky nineteenth-century semantic picture. I sketch a minimalist variant of the pre-Fregean picture which escapes Frege’s criticisms by positing a thin notion of semantic content which then interacts with a multiplicity of kinds of truth to account for phenomena such as modality. After exploring several ways in which we can understand the existence of multiple truth properties, I discuss the roles of pointwise and setwise truth properties in modal logic. (...) I argue that thinking of supertruth and determinate truth as setwise truth properties allows an understanding of supervaluationist approaches to vagueness which escapes both Williamson’s objections to and a needless metalinguistic orientation of traditional supervaluationism. (shrink)

This paper reexamines some examples, discussed by Mates and others, of sentences containing both definite descriptions and quantifiers. It has frequently been claimed that these sentences provide evidence for the view that definite descriptions themselves are quantifiers. The main goal of this paper is to argue this is not so. Though the examples are compatible with quantificational approaches to definite descriptions, they are also compatible with views that treat definite descriptions as basically scopeless. They thus provide no reason to see (...) definite descriptions as quantifiers. Even so, this paper shows that the examples do raise a surprising range of complex issues about how quantifier scope works, and where it occurs. Thus, a clear picture of how these examples work will help us to understand better where definite descriptions fit into the larger picture of quantifiers and related phenomena. (shrink)

I show that the contemporary dominant analysis of natural language quantifiers that are one-place determiners by means of binary generalized quantifiers has failed to explain why they are, according to it, conservative. I then present an alternative, Geachean analysis, according to which common nouns in the grammatical subject position are plural logical subject-terms, and show how it does explain that fact and other features of natural language quantification.