Modal propositional logic; Modal predicate logic; A survey of modal logic.

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes of anaphora (...) resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

This self-contained introduction to natural language semantics addresses the majortheoretical questions in the field. The authors introduce the systematic study of linguistic meaningthrough a sequence of formal tools and their linguistic applications. Starting with propositionalconnectives and truth conditions, the book moves to quantification and binding, intensionality andtense, and so on. To set their approach in a broader perspective, the authors also explore theinteraction of meaning with context and use (the semantics-pragmatics interface) and address some ofthe foundational questions, especially in connection (...) with cognition in general. They also introducea few of the most accessible and interesting ideas from recent research to give the reader a bit ofthe flavor of current work in semantics. The organization of this new edition is modular; after theintroductory chapters, the remaining material can be covered in flexible order. The book presupposesno background in formal logic (an appendix introduces the basic notions of set theory) and only aminimal acquaintance with linguistics. This edition includes a substantial amount of completely newmaterial and has been not only updated but redesigned throughout to enhance itsuser-friendliness. (shrink)

Barry Schein proposes combining a second-order treatment of plurals with DonaldDavidson's suggestion that there are positions for reference to events in ordinary predicates inorder to account for several of the more puzzling features of ...

INTRODUCTION Linguists who work within the tradition of transformational generative grammar tend to regard semantics as an intractable, perhaps ultimately ...

The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.

In The Dynamics of Meaning , Gennaro Chierchia tackles central issues in dynamic semantics and extends the general framework. Chapter 1 introduces the notion of dynamic semantics and discusses in detail the phenomena that have been used to motivate it, such as "donkey" sentences and adverbs of quantification. The second chapter explores in greater depth the interpretation of indefinites and issues related to presuppositions of uniqueness and the "E-type strategy." In Chapter 3, Chierchia extends the dynamic approach to the domain (...) of syntactic theory, considering a range of empirical problems that includes backwards anaphora, reconstruction effects, and weak crossover. The final chapter develops the formal system of dynamic semantics to deal with central issues of definites and presupposition. Chierchia shows that an approach based on a principled enrichment of the mechanisms dealing with meaning is to be preferred on empirical grounds over approaches that depend on an enrichment of the syntactic apparatus. Dynamics of Meaning illustrates how seemingly abstract stances on the nature of meaning can have significant and far-reaching linguistic consequences, leading to the detection of new facts and influencing our understanding of the syntax/semantics/pragmatics interface. (shrink)

This book explores linguistic and philosophical issues presented by sentences expressing personal taste, such as Roller coasters are fun, or Licorice is tasty. Standard semantic theories explain the meanings of sentences by specifying the conditions under which they are true; here, Peter Lasersohn asks how we can account for sentences that are concerned with matters of opinion rather than matters of fact. He argues that a truth-theoretic semantic theory is appropriate even for sentences like these, but that for such sentences, (...) truth and falsity must be assigned relative to perspectives, rather than absolutely. The book provides a detailed and explicit formal grammar, working out the implications of this conception of truth both for simple sentences and for reports of mental attitude. The semantic analysis is paired with a pragmatic theory explaining what it means to assert a sentence which is true or false only relativistically, and with a speculative account of the functional motivation for a relativized notion of truth. (shrink)

INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, we have in mind an ...

The Montagovian hypothesis of direct model-theoretic interpretation of syntactic surface structures is supported by an account of the semantics of binding that makes no use of variables, syntactic indices, or assignment functions & shows that the interpretation of a large portion of so-called variable-binding phenomena can dispense with the level of logical form without incurring equivalent complexity elsewhere in the system. Variable-free semantics hypothesizes local interpretation of each surface constituent; binding is formalized as a type-shifting operation on expressions that denote (...) functions, & sentences containing a free pronoun are analyzed as a function from individuals to propositions having a meaning of type (e,t). Standard weak crossover effects & binding patterns in sentences with multiple pronouns are shown to submit to straightforward type-theoretic treatments that do not rely on indexation. The variable-free semantics smoothly implements full surface compositionality & requires less machinery than standard accounts to handle functional questions, their answers, sloppy inferences, & across-the-board binding. 73 References. J. Hitchcock. (shrink)

It is argued that the English bare plural (an NP with plural head that lacks a determiner), in spite of its apparently diverse possibilities of interpretation, is optimally represented in the grammar as a unified phenomenon. The chief distinction to be dealt with is that between the generic use of the bare plural (as in Dogs bark) and its existential or indefinite plural use (as in He threw oranges at Alice). The difference between these uses is not to be accounted (...) for by an ambiguity in the NP itself, but rather by explicating how the context of the sentence acts on the bare plural to give rise to this distinction. A brief analysis is sketched in which bare plurals are treated in all instances as proper names of kinds of things. A subsidiary argument is that the null determiner is not to be regarded as the plural of the indefinite article a. (shrink)

In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)

This chapter reviews the work and influence of Donald Davidson across all the areas to which he contributed.

Although the two volumes of _Logic, Language, and Meaning _can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions.

This paper argues for the hypothesis of direct compositionality (as in, e.g., Montague 1974), according to which the combinatory syntactic rules specify a set of well-formed expressions while the semantic combinatory rules work in tandem to directly supply a model-theoretic interpretation to each expression as it is "built" in the syntax. (This thus obviates the need for any level like LF and, concomitantly, for any rules mapping surface structures to such a level.) I focus here on one related group of (...) phenomena: the interaction of "paycheck" pronouns with Weak Crossover effects and i-within-i effects. These interactions were studied in Jacobson (1977) as they show up in Back-Peters sentences. There I argued that these interactions show that paycheck pronouns have a complex representation at LF; here I show that all of the observations in this earlier work are compatible with the hypothesis of direct compositionality. The key tool is the adoption of a variation-free semantics (a semantics which makes no use of variables as part of the semantic machinery). In addition to the general consequences for the syntax/semantics interface, there are two other main results. First, I provide new arguments for a variable-free semantics. For example, it will be shown that under this view the paycheck reading of a pronoun comes for free; most other theories posit additional mechanisms and/or an additional lexical meaning for pronouns, and thus paycheck and regular pronouns are only accidentally homophonous. Second, I reiterate one of the central points in Jacobson (1977): this is that the first pronoun in a Bach-Peters sentence is indeed a paycheck pronoun, and hence nothing special needs to be said about these sentences nor does any new machinery need to be invoked for them. (shrink)

Survey of issues pertaining to the semantics of mass and plural nouns.

This paper argues that parts of the lexical content of an A-bar moved phrase must be interpreted in the base position of movement. The argument is based on a study of deletion of a phrase that contains the base position of movement. I show that deletion licensing is sensitive to the content of the moved phrase. In this way, I corroborate and extend conclusions based on Condition C reconstruction by N. Chomsky and D. Fox. My result provides semantic evidence for (...) the existence of traces and gives semantic content to the A/A-bar distinction. (shrink)

Most studies of the so-called proportion problem seek to understand how lexical and structural properties of sentences containing adverbial quantifiers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sentences allow an asymmetric reading when other, structurally similar sentences seem to require a symmetric reading? Potential factors suggested in (...) the literature include the distribution of donkey pronouns, certain uniqueness implications, and focus structures. I argue here that the use of an adverbial quantifier presupposes HOMOGENEITY: all individual situations that get lumped into a single case for the purposes of evaluating the quantification must agree on whether they satisfy the nuclear scope. For instance, in order for a token of Usually, if a farmer owns a donkey, he beats it to be felicitous when construed under a farmer-dominant asymmetric reading, the context must be consistent with the proposition that each farmer either beats all or none of his donkeys. Thus proportional sentences are indeed systematically ambiguous, but only some readings will be felicitous in a given context. (shrink)

Montague’s analysis of the well-known temperature paradox poses a problem for Gupta’s syllogism, whose surface syntax differs from the temperature syllogism in the addition of the intensional adverb necessarily. Lasersohn (2005) argues that the puzzle arising from these syllogisms can be solved if one adopts the Fregean presuppositional treatment of definite descriptions, and concludes that the temperature-Gupta puzzle provides an argument in favor of such treatment. This paper shows that the analysis of definite descriptions is in fact orthogonal to the (...) puzzle. Instead, it will be shown that the differences between the two syllogisms stem from the temporal interpretation of their premises. (shrink)