In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

In the course of the discussion, Professor Quine pinpoints the difficulties involved in translation, brings to light the anomalies and conflicts implicit in our ...

In Situations and Individuals, Paul Elbourne argues that the natural language expressions that have been taken to refer to individuals — pronouns, proper names, and definite descriptions — have a common syntax and semantics, roughly that of definite descriptions as construed in the tradition of Frege. In the course of his argument, Elbourne shows that proper names have previously undetected donkey anaphoric readings.This is contrary to previous theorizing and, if true, would undermine what philosophers call the direct reference theory (which (...) holds that the sole contribution of a proper name to the truth conditions of a sentence is an individual) as well as the related doctrine that proper names are rigid designators. Elbourne begins by addressing donkey anaphora, relating other concerns about pronouns to the solution of this notorious problem. His subsequent argumentation provides a unified semantics for the donkey anaphoric and bound and referential uses of pronouns and discusses the prospect of unifying the syntax and semantics of pronouns with the syntax and semantics of normal definite descriptions. Elbourne's aim is not only to advance his proposal of a unified syntax and semantics but also to urge linguists and philosophers dealing with pronoun interpretation to consider a wider range of theories than they do at present, and to test the competing claims of description-based theories and dynamic semantics against the data. (shrink)

To the best of my knowledge, no one in recent decades has written a book of this magnitude about the semantics of natural language. Certainly, nothing available today matches this volume in depth, precision, and coherence. The authors present classical and recent results of linguistic semantics within the framework of interpretative T-theories and defend the philosophical foundations of their approach by showing how it fits into the larger enterprise of cognitive linguistics. The book also includes an array of excellent exercises (...) and a good list of references. (shrink)

What I have attempted to show in the foregoing is that: (1) For any frequency adjective f, there is an element of meaning common to both the adverbial and the generic usage of f; this is a function f′ from propositions to truth-values such that f′(Φ)′ is true at an interval i iff Φ′ is true at subintervals of i distributed through i in a certain way. (2) In an adverbial use of f, f′ functions like the corresponding frequency adverb. (...) (3) In a generic use of f, f′ quantifies the times intervals which a specified object is realized by some stage. (4) In their adverbial usage, frequency adjectives are not regular attributive adjectives at the level at which interpretation takes place, but are perhaps determiners. And (5) in their generic usage, frequency adjectives are adjectives at the level at which interpretation takes place.More generally, I hope to have suggested something of the range of uses to which frequency is put in natural language. That we effortlessly grasp what is meants by Monday, the Columbus Dispatch, autumn, the Today Show, and so on, demonstrates our fluency in interpreting certain sequences of objects, events, or states of affairs as sequences of values of some function cycling on a time-axis. Much more must ultimately be told about the psychological and anthropological significance of frequency. (shrink)

The primary goal of Peter Ludlow's Semantics, Tense, and Time is to illustrate how one can study metaphysical issues from a linguistic/semantic perspective by addressing the debate between tenseless theorists and tensed theorists. Ludlow's book is noteworthy in part because of the novelty of its approach to this debate and in part because it addresses and endeavors to solve the metaphysical problems of temporal solipsism that other temporal solipsists have not addressed.

A puzzle concerning fractional and mixed numbers of things (e.g., two and a half oranges) is examined.

When philosophers talk about descriptions, usually they have in mind singular definite descriptions such as ‘the finest Greek poet’ or ‘the positive square root of nine’, phrases formed with the definite article ‘the’. English also contains indefinite descriptions such as ‘a fine Greek poet’ or ‘a square root of nine’, phrases formed with the indefinite article ‘a’ (or ‘an’); and demonstrative descriptions (also known as complex demonstratives) such as ‘this Greek poet’ and ‘that tall woman’, formed with the demonstrative articles (...) ‘this’ and ‘that’. Following the custom in philosophy, in this chapter often we use ‘description’ as short for ‘definite description’; and following the custom in linguistics, often we use ‘definite’, ‘indefinite’, and ‘demonstrative’ as shorthand nouns. For the most part we focus on definite and indefinites, although a few words about demonstratives are called for. At the centre of debates about descriptions is the matter of whether they are devices of reference or of predication (simple or higher-order), and much discussion focuses on how various proposals are to be incorporated into broader theories of the semantics of natural language. But philosophical interest goes beyond the confines of linguistics, logic, and the philosophy of language because choices made about the semantics of descriptions have repercussions elsewhere, particularly in epistemology and metaphysics. A simple match of form and meaning appears to fail.1 First, many occurrences of expressions of both forms ‘the φ’ and ‘a φ’ appear to be used to talk about particular individuals. Consider (1). (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)

(1) The average Mum has 2.4 children. (2) The number of Argle’s fingers equals the number of Bargle’s toes. (3) There are two possible ways in which Joe could win this chess game. In the right contexts, and outside the philosophy room, all the above sentences may be completely uncontroversial. For instance, if we know that Joe could win either by exchanging queens and entering an endgame, or by initiating a kingside attack then, if ignorant of Quine’s work on ontology, (...) we would take (3) to be uncontroversially true. (shrink)

In this book Saul Kripke brings his powerful philosophical intelligence to bear on Wittgenstein's analysis of the notion of following a rule.

Discussion of Wittgenstein's philosophy has suffered from a scarcity of commentators who understand his work well enough to explain it in their own words. Apart from certain notable exceptions, all too many advocates and critics alike have tended merely to repeat slogans, with approval or ridicule as the case may be. The result has been an unusual degree of polarization and acrimony—some philosophers abandoning normal critical standards, falling under the spell and becoming fanatical supporters; and others taking an equally extreme (...) opposite view, deriding the absence of analytic technique, and refusing to see anything of value in Wittgenstein's work. (shrink)

In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (...) (2) Jupiter has green moons. On the other hand, ‘four’ occurs as a singular term, which is to say that it occurs in a position that is commonly occupied by paradigmatic cases of singular terms, like proper names: (3) The number of moons of Jupiter is four. Here ‘four’ seems to be just like ‘Wagner’ in (4) The composer of Tannhäuser is Wagner, and both of these statements seem to be identity statements, ones with which we claim that what two singular terms stand for is identical. But that number words can occur both as singular terms and as adjectives is puzzling. Usually adjectives cannot occur in a position occupied by a singular term, and the other way round, without resulting in ungrammaticality and nonsense. To give just one example, it would be ungrammatical to replace ‘four’ with ‘the number of moons of Jupiter’ in (1): (5) *Jupiter has the number of moons of Jupiter moons. This ungrammaticality results even though ‘four’ and ‘the number of moons of Jupiter’ are both apparently singular terms standing for the same object in (3). So, how can it be that number words can occur both as singular terms and as adjectives, while other adjectives cannot occur as singular terms, and other singular terms cannot occur as adjectives? (shrink)

Some philosophers, notably Professors Quine and Geach, have stressed the analogies they see between pronouns of the vernacular and the bound variables of quantification theory. Geach, indeed, once maintained that ‘for a philosophical theory of reference, then, it is all one whether we consider bound variables or pronouns of the vernacular'. This slightly overstates Geach's positition since he recognizes that some pronouns of ordinary language do function differently from bound variables; he calls such pronouns ‘pronouns of laziness'. Geach's characterisation of (...) pronouns of laziness has varied from time to time, but the general idea should be clear from a paradigm example: A man who sometimes beats his wife has more sense than one who always gives in to her.The pronouns ‘one’ and ‘her’ go proxy for a noun or a noun phrase in the sense that the pronoun is replaceable in paraphrase by simple repetition of its antecedent. (shrink)

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

I propose the first strictly compositional semantic account of same. New data, including especially NP-internal uses such as two men with the same name, suggests that same in its basic use is a quantificational element taking scope over nominals. Given type-lifting as a generally available mechanism, I show that this follows naturally from the fact that same is an adjective. Independently-motivated assumptions extend the analysis to standard examples such as Anna and Bill read the same book via a mechanism I (...) call PARASITIC SCOPE, in which the scope of same depends on the scope of some other scopetaking element in the sentence. Although I will initially discuss the analysis in terms of a familiar Quantifier Raising framework, I go on to implement the analysis within an innovative continuation-based Type-Logical Grammar. The empirical payoff for dealing in continuations is that a simple generalization of the basic analysis gives the first ever formal account of cases in which same distributes over objects other than NP denotations, as in the relevant interpretation of John hit and killed the same man. (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)

The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.

An analysis of the structural properties of collections or pluralities, homogeneous objects like water, and the semantics and philosophy of events.

Current textbooks in formal semantics are all versions of, or introductions to, the same paradigm in semantic theory: Montague Grammar. Knowledge of Meaning is based on different assumptions and a different history. It provides the only introduction to truth- theoretic semantics for natural languages, fully integrating semantic theory into the modern Chomskyan program in linguistic theory and connecting linguistic semantics to research elsewhere in cognitive psychology and philosophy. As such, it better fits into a modern graduate or undergraduate program in (...) linguistics, cognitive science, or philosophy. Furthermore, since the technical tools it employs are much simpler to teach and to master, Knowledge of Meaning can be taught by someone who is not primarily a semanticist. Linguistic semantics cannot be studied as a stand-alone subject but only as part of cognitive psychology, the authors assert. It is the study of a particular human cognitive competence governing the meanings of words and phrases. Larson and Segal argue that speakers have unconscious knowledge of the semantic rules of their language, and they present concrete, empirically motivated proposals about a formal theory of this competence based on the work of Alfred Tarski and Donald Davidson. The theory is extended to a wide range of constructions occurring in natural language, including predicates, proper nouns, pronouns and demonstratives, quantifiers, definite descriptions, anaphoric expressions, clausal complements, and adverbs. Knowledge of Meaning gives equal weight to philosophical, empirical, and formal discussions. It addresses not only the empirical issues of linguistic semantics but also its fundamental conceptual questions, including the relation of truth to meaning and the methodology of semantic theorizing. Numerous exercises are included in the book. (shrink)

In this book Ludlow uses the metaphysics of time as a case study and focuses on the dispute between A-theorists and B-theorists about the nature of time.

Written by two of the leading figures in the field, this is a lucid and systematic introduction to semantics as applied to transformational grammars of the ...

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces of (...) nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second. (shrink)

One puzzling feature of talk about properties, propositions and natural numbers is that statements that are explicitly about them can be introduced apparently without change of truth conditions from statements that don't mention them at all. Thus it seems that the existence of numbers, properties and propositions can be established`from nothing'. This metaphysical puzzle is tied to a series of syntactic and semantic puzzles about the relationship between ordinary, metaphysically innocent statements and their metaphysically loaded counterparts, statements that explicitly mention (...) numbers, properties and propositions, but nonetheless appear to be equivalent to the former. I argue that the standard solutions to the metaphysical puzzles make a mistaken assumption about the semantics of the loaded counterparts. Instead I propose a solution to the syntactic and semantic puzzles, and argue that this solution also gives us a new solution to the metaphysical puzzle. I argue that instead of containing more semantically singular terms that aim to refer to extra entities, the loaded counterparts are focus constructions. Their syntactic structure is in the service of presenting information with a focus, but not to refer to new entities. This will allow us to spell out Frege's metaphor of content carving. (shrink)

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces of (...) nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second. (shrink)