Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result (...) from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (shrink)

It is generally thought that definite determiners exclusively mark nouns as definite. In several languages, however, definite determiners may modify both nouns and verbs. As I will argue, the existence of these “multi‐functional” elements suggests that determiners are in fact phrases. This syntactic move has a philosophical payoff. Among other things, it allows us to cast Donnellan's distinction as an ordinary consequence of the context‐invariant compositional semantics of natural language, not as a matter of contextual manipulation or lexical ambiguity. Multi‐functional (...) determiners show us that Donnellan's distinction is,contraDonnellan, a matter of grammar. (shrink)

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This (...) is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)

It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. A number of prominent syntactic and semantic properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable divide between concept and object. These presuppositions, taken at face value, (...) reflect a significant metaphysical viewpoint, one that can in fact hinder or prejudice the representation of philosophical ideas and arguments. Philosophers have of course noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to reflect a more flexible and egalitarian metaphysical standpoint. The purpose of this paper, however, is to document and discuss how similar “adaptations” to FOL—culminating in a standardized framework known as Common Logic —have evolved out of the more practical and applied encounter of FOL with the problem of representing, sharing, and reasoning upon information on the World Wide Web. (shrink)

Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular – universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the piecemeal investigation of this issue three interrelated conceptions of the particular – universal distinction are examined: universals, by contrast to particulars, are unigrade; particulars are related to universals by an asymmetric tie of exemplification; universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)

In this paper, I criticize John Bigelow's account of number and present my own account that results from the criticism. In doing so, I argue that proper understanding of the nature of number requires a radical departure from the standard conception of language and reality and outline the alternative conception that underlies my account of number. I argue that Bigelow's account of number rests on an incorrect analysis of the plural constructions underlying the talk of number and propound an analysis (...) of numerical sentences, such as “Quine and Goodman are two”, that conforms to the natural understanding of the plural constructions. The analysis leads to the account of number according to which natural numbers are properties, i.e., one-place relations: the number two, for example, is the property indicated by “to be two”, which, I argue, is a one-place predicate that can combine with plural terms like “Quine and Goodman”. (shrink)

I present a formal framework historically faithful to Leibniz's analysis of relational sentences, which: (i) engrafts thematic roles and the non-truth-functional connective insofar as (quatenus) into the monadic fragment of first-order logic; (ii) suggests a plausible ontological picture of thematic roles and relational facts; (iii) supports argument deletion and related inferential patterns that are not taken into account by standard first-order logic.

2020 update of the entry "Properties".

A critical review of the main themes arising out of recent literature on the semantics of ordinary event talk. The material is organized in four sections: (i) the nature of events, with emphasis on the opposition between events as particulars and events as universals; (ii) identity and indeterminacy, with emphasis on the unifier/multiplier controversy; (iii) events and logical form, with emphasis on Davidson’s treatment of the form of action sentences; (iv) linguistic applications, with emphasis on issues concerning aspectual phenomena, the (...) telicity/atelicity distinction, the treatment of statives, and temporal quantification. (shrink)