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In recent literature on plurals the claim has often been made that the move from singular to plural expressions can be iterated, generating what are occasionally called higherlevel plurals or superplurals, often correlated with superplural predicates. I argue that the idea that the singulartoplural move can be iterated is questionable. I then show that the examples and arguments intended to establish that some expressions of natural language are in some sense higherlevel plurals fail. Next, I argue that these and some (...) 

A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but nonsingular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based upon predicate logic (...) 



Plural Logic is an extension of FirstOrder Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the firstorder domain of quantification. Given that Plural Logic is equiinterpretable with Monadic SecondOrder Logic, it gives us its expressive power at the low ontological cost of a firstorder language. This (...) 

This paper examines the ontological commitments of the secondorder language of arithmetic and argues that they do not extend beyond the firstorder language. Then, building on an argument by George Boolos, we develop a Tarskistyle definition of a truth predicate for the secondorder language of arithmetic that does not involve the assignment of sets to secondorder variables but rather uses the same class of assignments standardly used in a definition for the firstorder language. 

1. ExpositionRichard Sharvy's ‘A more general theory of definite descriptions’ was published in 1980. Its aim was to replace Russell's paradigm by " a general theory of definite descriptions, of which definite mass descriptions, definite plural descriptions, and Russellian definite singular count descriptions are species. … We have an account of the generic ‘the’ along these same lines. " By now his theory has attained the status of a new paradigm. Even a casual trawl of the literature throws up over (...) 

The resemblance nominalist says that the truthmaker of 〈Socrates is white〉 ultimately involves only concrete particulars that resemble each other. Furthermore he also says that Socrates and Plato are the truthmakers of 〈Socrates resembles Plato〉, and Socrates and Aristotle those of 〈Socrates resembles Aristotle〉. But this, combined with a principle about the truthmakers of conjunctions, leads to the apparently implausible conclusion that 〈Socrates resembles Plato and Socrates resembles Aristotle〉 and 〈Socrates resembles Plato and Plato resembles Aristotle〉 have the same truthmakers, (...) 

Recently, some philosophers have argued that we should take quantification of any order to be a legitimate and irreducible, sui generis kind of quantification. In particular, they hold that a semantic theory for higherorder quantification must itself be couched in higherorder terms. Øystein Linnebo has criticized such views on the grounds that they are committed to general claims about the semantic values of expressions that are by their own lights inexpressible. I show that Linnebo's objection rests on the assumption of (...) 

Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...) 



The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic. 

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the firstorder quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of nonstandard interpretations that confronts higherorder logics on their more traditional, setbased semantics. We challenge both claims. Our challenge is based on a Henkinstyle semantics for plural logic (...) 

According to strong composition as identity, the logical principles of one–one and plural identity can and should be extended to the relation between a whole and its parts. Otherwise, composition would not be legitimately regarded as an identity relation. In particular, several defenders of strong CAI have attempted to extend Leibniz’s Law to composition. However, much less attention has been paid to another, not less important feature of standard identity: a standard identity statement is true iff its terms are coreferential. (...) 

In previous work, Hellman and Shapiro present a regionsbased account of a onedimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal language, (...) 



We speak of products in two senses: in one, we speak of types of products, in the other we speak of the particular objects that are instances of those types. I argue that types of products have the same ontological status as that of material stuffs, like water and gold, which have a nonparticular level of existence. I also argue that the relationship between types of products and their instances is logically similar to the relation of constitution, which holds between, (...) 

In a series of publications I have claimed that by contrast to standard formal languages, quantifiers in natural language combine with a general term to form a quantified argument, in which the general term's role is to determine the domain or plurality over which the quantifier ranges. In a recent paper Zoltán Gendler Szabó tried to provide a counterexample to this analysis and derived from it various conclusions concerning quantification in natural language, claiming it is often ‘bare’. I show that (...) 