Logical guarantees of validity must be understood as subject to the proviso that no equivocation is committed. But we do not have a formal theory of equivocation. This paper attempts to formulate rules for responding to equivocal arguments in the context of dialogue. What occurs when one distinguishes meanings of an equivocal expression turns out to be rather different from definition.

The aim of the paper is to formalize I. Bellert's proposal to characterize distinct nonequivalent readings of quantificationally ambiguous sentences with help of two features: absoluteness and distributiveness. The formalisation makes use of set theoretical and model theoretical standard notions. Foundamental rules, proposed by Bellert, govering the interpretation of cooccurring quantifiers are quoted and outlines of proofs of important derived rules are given.

Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like The Beatles sing Yesterday, a knowledge representation language should be able to express and reason about plural entities — like the Beatles — and their relationships — like sing — with any possible reading (cumulative, distributive or collective).In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the (...) semantics of sentences, is presented. A twofold extension of theA–C concept language is investigated: (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subsumption of concepts, and to compute recognition of individuals. (shrink)

1. People standardly communicate by uttering phrases or sentences with certain intonation patterns, accompanied by facial expressions, eye contact and often a variety of gestures. If all goes well...

§§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)

Philosophers and linguists alike tend to call a semantic theory ‘Russellian’ just in case it assigns to sentences in which definite descriptions occur the truth-conditions Russell did in ‘On Denoting’. This is unfortunate; not all aspects of those particular truth-conditions do explanatory work in Russell's writings. As far as the semantics of descriptions is concerned, the key insights of ‘On Denoting’ are that definite descriptions are not uniformly referring expressions, and that they are scope-bearing elements. Anyone who accepts these two (...) claims can account for Russell's puzzle cases the way he did. Russell had no substantive argument for the claim that ‘The F is G’ entails ‘There is at most one F’; in fact, he had important misgivings about it. I outline an argument against this claim, and I argue that by holding on to uniqueness contemporary semanticists make a momentous mistake: they keep the illusion alive that there is a way to account for linguistic meaning without addressing what linguistic expressions are for. (shrink)

Several authors proposed to devise logical structures for Natural Language (NL) semantics in which noun phrases yield referential terms rather than standard Generalized Quantifiers. In this view, two main problems arise: the need to refer to the maximal sets of entities involved in the predications and the need to cope with Independent Set (IS) readings, where two or more sets of entities are introduced in parallel. The article illustrates these problems and their consequences, then presents an extension of the proposal (...) made in Sher (J Philos Logic 26:1–43, 1997 ) in order to properly represent the meaning of IS readings involving NL quantifiers. The solution proposed here allows to uniformly deal with both standard linear and IS readings, regardless of their actual existence in NL or quantifiers’ monotonicity. Sentences featuring nested quantifications are particularly problematic. By avoiding parallel nested quantification in the formulae, the proper true values are achieved. (shrink)

We think recent work in linguistics tells against the traditional claim that a string of words like (1) Every girl pushed some truck has two readings, indicated by the following formal language sentences (with restricted quantifiers): (1a) [!x:Gx]["y:Ty]Pxy (1b) ["y:Ty][!x:Gx]Pxy. In our view, (1) does not have any b-reading in which ‘some truck’ has widest scope.1 The issue turns on details concerning syntactic transformations and terms like ‘every’. This illustrates an important point for the study of natural language: ambiguity hypotheses (...) are indeed hypotheses—i.e., theoretical claims to be justified in light of various considerations, not theses whose truth can be directly observed by speakers. (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)

We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic (...) distinctions between quantified reciprocal sentences. We show a computational dichotomy<br>between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to<br>revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of the formal<br>semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science. (shrink)

Philosophy Without Ambiguity: A Logico‐linguistic Essay. By JAY DAVID ATLAS The Limits to Debate: A Revised Theory of Semantic Presupposition. By NOEL BURTON‐ROBERTS From Reading to Neurons. By DAVID CAPLAN From Neuropsychology to Mental Structure. By TIM SHALLICE.

Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

In this paper we examine interactions of the reciprocal with distributive and collective operators, which are encoded by prefixes on verbs expressing the reciprocal relation: namely, the Czech distributive po and the collectivizing na-. The theoretical import of this study is two-fold. First, it contributes to our knowledge of how word-internal operators interact with phrasal syntax/semantics. Second, the prefixes po and na generate (a range of) readings of reciprocal sentences for which the Strongest Meaning Hypothesis (SMH) proposed by Dalrymple et (...) al. (1998) does not make the right predictions. The distributive prefix po prefers the Strong Reciprocity reading, although the SMH predicts that a weakening should take place, while with the prefix na we find cases where weaker reciprocal readings are preferable to the stronger ones predicted by the SMH. This behavior of po and na is, we propose, due to the way in which they modulate two factors that are crucial in the interpretation of reciprocal sentences: (i) the relevant subpluralities in the group denoted by the reciprocal's antecedent, and (ii) the strength of reciprocal relations. We provide a detailed analysis of the semantics of the prefixes po and na and their contribution to the meaning of reciprocal sentences within the general framework of event semantics with lattice structures. (shrink)