Byeong-uk Yi

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 chapter 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. 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.

This paper presents analyses of natural language quantifiers and determiners. In doing so, the paper pays special attention to _plural determiners_, determiners that can combine with plural noun phrases (e.g., _all, some, any, the, most_), and argues that Generalized Quantifier Theory gives clearly incorrect accounts of those determiners by assuming the traditional bias against plural constructions. The paper gives a sketch of a recent approach to plural constructions, the _pluralist approach_, that regards them as peers of their singular cousins that have autonomous semantic functions, and presents analyses of plural determiners that result from taking the approach. The paper also presents analyses of Bach-Peters sentences that use polyadic quantifiers or determiners, and gives a sketch of a treatment of donkey anaphora based on the view that indefinite noun phrases by themselves have no quantificational component.

This article discusses John Venn's contribution to the development of the modern doctrine of categorical propositions, which departs from the traditional doctrine by rejecting the subalternation thesis, and holds that universal propositions do not have existential import while particular propositions do. Venn was one of the earliest proponents of the modern doctrine, and made significant contributions to its development by examining the existential import of categorical propositions to argue for the superiority of the modern doctrine over the traditional doctrine. While discussing his significance in the development and establishment of the modern doctrine, the article also argues that his defense of the doctrine has serious problems because some, if not all, of the universal affirmatives have existential import. And it argues that the problems are due ultimately to fundamental assumptions about categorical propositions the doctrine inherits from the traditional doctrine.

Modern logicians hold that traditional logic makes a serious error by accepting the subalternation thesis, the thesis that universal affirmatives imply matching particular affirmatives. But some traditional logicians (e.g., Al-Fārābī, Abelard, Ockham) presented doctrines of existential import of categorical propositions that include subalternation, and some modern studies of Aristotle’s logic take him to assume one of the doctrines. This article argues that such interpretations have serious problems and proposes a radically different interpretation. On the new interpretation, called the no-import interpretation, Aristotle takes both singular and general categorical propositions (including singular and particular affirmatives) not to have existential import. In proposing and defending this interpretation, the article gives a close examination of two influential interpretations of his views on existential import: (a) the affirmative–negative interpretation, which takes him to hold that affirmative categorical propositions have existential import while negative ones do not, and (b) the non-vacuity interpretation, which takes his system of logic to presuppose or require that empty terms do not figure in general categorical propositions the system deals with. The article argues that Aristotle holds theses about singular and general categorical propositions that conflict with these interpretations, and that examination of the theses leads to the no-import interpretation.

Say that some things compose something, if the latter is a whole, fusion, or mereological sum of the former. Then the thesis that composition is identity holds that the composition relation is a kind of identity relation, a plural cousin of singular identity. On this thesis, any things that compose a whole are identical with the whole. This article argues that the thesis is incoherent. To do so, the article formulates the thesis in a plural language, a symbolic language that includes counterparts of plural constructions of natural languages, and shows that it implies that nothing has a proper part. Then the article argues that the thesis, as its proponents take it, is incoherent because they take it to imply or presuppose that some things have proper parts.

This article examines two syllogistic arguments contrasted in an ancient Chinese book, theMozi, which expounds doctrines of the Mohist school of philosophers. While the arguments seem to have the same form, one of them (theone-horse argument) is valid but the other (thetwo-horse argument) 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 (Plural Barbara), and argues that the two-horse argument involves equivocal uses of a key predicate (the Chinese counterpart of ‘have four feet’) 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.

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.

C onsider two contrary conditionals 1 about two envelopes, Ali and Baba: (a) If Ali has more money than Baba, the difference between the amounts in them is $5. (b) If Ali has more money than Baba, the difference between the amounts in them is $10. Can these both be true? The answer is a resounding yes on the standard account of conditionals, which identifies indicative con- ditionals with material conditionals. It is not the same with many other contemporary accounts of c onditionals. They yield a quali- fied negative answer: (a) and (b) are not compatible 2 unless their common antecedent cannot be true. I think this is a wrong answer. The conditionals can both be true while their antecedent states a possibility. This is what I aim to show in this paper. In doing so, I present a solution to Raymond Smullyan’s intriguing version of the two-envelope paradox.

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

In developing resemblance nominalism, Rodriguez-Pereyra attempts to meet the challenge that truths involving abstract nouns pose to the doctrine. He holds that one can render sentences containing abstract nouns without invoking attributes and defends this view by giving nominalistic sentences that express the truthmakers of two such sentences: ‘Scarlet is a colour’ and ‘Carmine resembles vermillion more than it resembles French blue.’ This article argues that his renderings have serious problems and fall far short of meeting the challenge posed by truths involving abstract nouns

In this paper, I revisit W. V. Quine’s thesis of indeterminacy of translation. I think Quine’s arguments for the thesis are marred by his controversial assumptions about language that amount to a kind of linguistic behaviorism. I hope to cast a new light on the thesis by presenting a strong argument for the thesis that does not rest on those assumptions. The argument that I present in the paper results from adapting Benson Mates’s objection to Rudolph Carnap’s analysis ofsynonymy as intensional isomorphism.

Plausible principles on truth seem to yield contradictory conclusions about paradoxical sentences such as the Strengthened Liar. Those who take the contextualist approach, such as Parsons and Burge, attempt to justify the seemingly contradictory conclusions by arguing that the natural reasoning that leads to them involves some kind of contextual shift that makes them compatible. This paper argues that one cannot take this approach to give a proper treatment of infinite descending chains of semantic attributions. It also examines a related approach taken by Gaifman and argues that it has the same problem.