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)

This article examines two syllogistic arguments contrasted in an ancient Chinese book, the Mozi, which expounds doctrines of the Mohist school of philosophers. While the arguments seem to have the same form, one of them is valid but the other is not. To explain this difference, the article uses English plural constructions to formulate the arguments. Then it shows that the one-horse argument is valid because it has a valid argument form, the plural cousin of a standard form of valid (...) categorical syllogisms, and argues that the two-horse argument involves equivocal uses of a key predicate that has the distributive/nondistributive ambiguity. In doing so, the article discusses linguistic differences between Chinese and English and explains why the logic of plural constructions is applicable to Chinese arguments that involve no plural constructions. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...) but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

Are concrete objects in some sense made up of the properties they exemplify? A distinguished tradition holds they are. I begin by defending the distinction: there is a real and not just semantic distinction between asserting and denying that concrete objects have their properties as parts. I then argue in favor of the view that concrete objects are not made up of their parts. First, this view has less ontological baggage than its opponent. Next, the supposed advantages of the alternative (...) view—its superiority in understanding persistence, exemplification, or the possibility of diverse duplicates—dissipate under analysis. (shrink)

Byeong-Uk Yi has argued that number words like ‘two’ primarily function as numerical predicates as in ‘Socrates and Hippias are two ’, and other grammatical uses of number words can be paraphrased in terms of the predicative use. This paper critically examines Yi’s paraphrase scheme and also some other alternative schemes, and argues that the adjectival use of number words as in ‘The Scots and the Irish are two peoples’ cannot be paraphrased in terms of the predicative use.

This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and (...) n, if there are exactly m Fs and also there are exactly n Fs, then m = n. (shrink)

A plurality or plural object is a single object that is also many, and pluralitism is the thesis that there is such an object. This paper argues that pluralitism and closely related theses (e.g., the many-one identity thesis and the composition as identity thesis) violate logic. To do so, it formulates an approach to the logic and semantics of plural constructions that results in plural logic and relates treatments of plural constructions to accounts of natural number. And it gives a (...) critical examination of Frege’s views of numbers and plural constructions, and sketches the view of plural constructions as devices for talking about the many (as such), and an account of natural numbers as properties of a special kind, plural properties. (shrink)