I argue that indefinite descriptions are referring terms. This is not the ambiguity thesis: that sometimes they are referring terms and sometimes something else, such as quantifiers . No. On my view they are always referring terms; and never quantifiers. I defend this thesis by modifying the standard conception of what a referring term is: a modification that needs to be made anyway, irrespective of the treatment of indefinites. I derive this approach from my speech-act theoretic semantics . (...) The basic thought is that referring terms have as their meanings speech-acts of a certain kind called proto-referring acts. These are acts in which speakers advertise or present intentions to denote, where denotation is a word-world relation, and advertising an intention is acting as if one has intentions, where it is open whether one has them or not, or whether the referring term used denotes or not. I show how this works for proper names. The meaning of a proper name is the speech-act proto-referring act type defined by a certain referential tree. This gives us the basis for an account of proper name meaning irrespective of denotation: a uniform treatment of full and empty names. Applied to indefinites, we can capture cases where speakers perform proto-acts—in which they advertise an intention to denote something—where they intend to denote, but others where they do not, but they still perform the proto-act: advertising an intention to denote. Two cases are ‘Fred saw a hippo’ and ‘Jane did not see a hippo’. In both cases U performs the same proto-act, represent it as Rpro, but possesses the advertised intention in the first case, but not in the second. In the first case, Rpro gains referential content—its descriptive content is expanded to include seen by Fred, whereas in its second token use it has no content augmentation or sentential determination of reference. In the second case ‘a hippo’ is an empty referring term, just as ‘Pegasus’ is empty in ‘Fred did not see Pegasus; he does not exist’. But in both sentences ‘a hippo’ functions in the same basic way: in both cases the basic proto-referring act Rpro is performed. Using this approach, I show how definite descriptions can be construed as indefinites with added meaning. (shrink)

So begins a recent ontological argument. But what if there are no most perfect beings? Letting God be one, that is, letting “God” name one at the very beginning seems premature. Clearly it is best to leave “God” out of the argument until one is in a position to introduce him by existential instantiation, or, by further argumentation, to identify him with a most perfect being: clearly it is best to leave “God” out of the argument until it has been (...) established that there is a most perfect being. (shrink)

It is known that an epsilon-invariant sentence has a first-order reformulation, although it is not in an explicit form, since, the proof uses the non-constructive interpolation theorem. We make an attempt to describe the explicit meaning of sentences containing epsilon-terms, adopting the strong assumption of their first-order reformulability. We will prove that, if a monadic predicate is syntactically independent from an epsilon-term and if the sentence obtained by substituting the variable of the predicate with the epsilon-term is epsilon-invariant, then the (...) sentence has an explicit first-order reformulation. Finally, we point out that the formula gives a contextual-quantificational meaning for the indefinite descriptions, provided that one accepts Kneebone’s read of epsilon-terms. (shrink)

Grice introduced generalized conversational implicatures with the following example: "Anyone who uses a sentence of the formX is meeting tz woman this evening would normally implicate that the person to be met was someone other than X’s wife, mother, sister, or perhaps even close platonic friend" (1975 : 37). Concerning this example, he suggested the following account: When someone, by using the form of expression an JQ implicates that the X does not belong to or is not otherwise closely connected (...) with some identifiable person, the implicature is present because the speaker has failed to be specific in a way in which he might have been expected to be specific. (Grice 1975: 38.) Grice went on to sketch an explanation as to why such an implicature should arise, involving the different ways in which we behave towards things that are closely related to.. (shrink)

This paper claims that indefinite descriptions, singular and plural, have different scope properties than genuine quantifiers. This claim is based on their distinct behavior in island constructions: while indefinites in islands can have intermediate (and maximal) scope readings, quantifiers cannot. Further, the simplest in situ interpretation strategy for indefinites results in incorrect truth conditions for intermediate (and maximal) scope readings. I introduce a mechanism which “auto-matically” preserves the restriction on free variables corresponding to indefinites, in a way which (...) allows the restriction to be carried up in the course of semantic interpretation and to be used at the level where the variable is quantified. This mechanism is a realization of the “indefinites-as-free-variables” proposal of Lewis, Kamp, and Heim, but emphasizes the role of the restriction. I then show that distributive readings of plural indefinites also display island-escaping behavior and argue for an independent, island-insensitive distribution mechanism. (shrink)

I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.

The formal semantics that we have proposed for definite and indefinite descriptions analyzes them both as variable-binding operators and as referring terms. It is the referential analysis which makes it possible to account for the facts outlined in Section 2, e.g. for the purely ‘instrumental’ role of the descriptive content; for the appearance of unusually wide scope readings relative to other quantifiers, higher predicates, and island boundaries; for the fact that the island-escaping readings are always equivalent to maximally (...) wide scope quantifiers; and for the appearance of violations of the identity conditions on variables in deleted constituents. We would emphasize that this is not a random collection of observations. They cohere naturally with each other, and with facts about other phrases that are unambigously referential.We conceded at the outset of this paper that the referential use of an indefinite noun phrase does not, by itself, motivate the postulation of a referential interpretation. Our argument has been that the behavior of indefinites in complex sentences cannot be economically described, and certainly cannot be explained, unless a referential interpretation is assumed. It could be accounted for in pragmatic terms only if the whole theory of scope relations and of conditions on deletion could be eliminated from the semantics and incorporated into a purely pragmatic theory. But this seems unlikely. (shrink)

The prototypes of definiteness and indefiniteness in English are the definite article the and the indefinite article a/an, and singular noun phrases (NPs)1 determined by them. That being the case it is not to be predicted that the concepts, whatever their content, will extend satisfactorily to other determiners or NP types. However it has become standard to extend these notions. Of the two categories definites have received rather more attention, and more than one researcher has characterized the category of (...) definite NPs by enumerating NP types. Westerståhl (1985), who is concerned only with determiners in the paper cited, gives a very short list: demonstrative NPs, possessive NPs, and definite descriptions. Prince (1992) lists proper names and personal pronouns, as well as NPs with the, a demonstrative, or a possessive NP as determiner. She notes, in addition, that “certain quantifiers (e.g. all, every) have been argued to be definite” (Prince 1992: 299). This list, with the quantifiers added, agrees with that given by Birner & Ward (1998, 114). Ariel (1988, 1990) adds null anaphoric NPs. (shrink)

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)

This paper investigates the truth conditions of sentences containing indefinite noun phrases, focusing on occurrences in attitude reports, and, in particular, a puzzle case due to Walter Edelberg. It is argued that indefinites semantically contribute the (thought-)object they denote, in a manner analogous to attributive definite descriptions. While there is an existential reading of attitude reports containing indefinites, it is argued that the existential quantifier is contributed by the de re interpretation of the indefinite (as the de (...) re reading adds existential quantification to the interpretation of definites on Kaplan’s analysis). (shrink)

Descriptions are phrases of the form ‘an F’, ‘the F’, ‘Fs’, ‘the Fs’ and NP's F (e.g. ‘John's mother’). They can be indefinite (e.g., ‘an F’ and ‘Fs’), definite (e.g. ‘the F’ and ‘the Fs’), singular (e.g., ‘an F’, ‘the F’) or plural (e.g., ‘the Fs’, ‘Fs’). In English plural indefinite descriptions lack an article and are for that reason also known as ‘bare plurals’. How to account for the semantics and pragmatics of descriptions has (...) been one of the central topics in philosophy for centuries. This entry focuses on the historical and contemporary philosophical debate about Bertrand Russell’s theory of descriptions and the theories that developed as responses to this theory. (shrink)

On a popular view dating back to Russell, descriptions, both definite and indefinite alike, work syntactically and semantically like quantifiers. I have an argument against Russell's view. The argument supports a different picture: descriptions can behave syntactically and semantically like variables. This basic idea can be implemented in very different systematic analyses, but, whichever way one goes, there will be a significant departure from Russell. The claim that descriptions are variables is not new: what I offer (...) is a new way of defending it. The argument centers on attitude reports. I argue that we should recognize a new reading of descriptions under attitude reports, which I call ‘singular opaque’. The existence of this reading cannot be explained on the traditional Russellian view, and demands a switch to the variable view. Along the way, some interesting new facts about attitude reports come to light. (shrink)

Szabó follows Heim in viewing familiarity, rather than uniqueness, as the essence of the definite article, but attempts to derive both familiarity and uniqueness implications pragmatically, assigning a single semantic interpretation to both the definite and indefinite articles. I argue that if there is no semantic distinction between the articles, then there is no way to derive these differences between them pragmatically.

In “Descriptions as Predicates” (Fara 2001) I argued that definite and indefinite descriptions should be given a uniform semantic treatment as predicates rather than as quantifier phrases. The aim of the current paper is to clarify and elaborate one of the arguments for the descriptions-aspredicates view, one that concerns the interaction of descriptions with adverbs of quantification.

It is widely agreed that sentences containing a non-denoting description embedded in the scope of a propositional attitude verb have true de dicto interpretations, and Russell's (1905) analysis of definite descriptions is often praised for its simple analysis of such cases, cf. e.g. Neale (1990). However, several people, incl. Elbourne (2005, 2009), Heim (1991), and Kripke (2005), have contested this by arguing that Russell's analysis yields incorrect predictions in non-doxastic attitude contexts. Heim and Elbourne have subsequently argued that once (...) certain facts about presupposition projection are fully appreciated, the Frege/Strawson analysis of definite descriptions has an explanatory advantage. In this paper, I argue that both Russell's analysis and the Frege/Strawson analysis face a serious problem when it comes to the interaction of attitude verbs and definite descriptions. I argue that the problem observed by Elbourne, Heim, and Kripke is much more general than standardly assumed and that a solution requires a revision of the semantics of definite and indefinite descriptions. I outline the conditions that are required to solve the problem and present an analysis couched in dynamic semantics which can provide a solution. I conclude by discussing some further issues related to propositional attitude verbs that complicate a fully general solution to the problem. (shrink)

Natural deduction systems with indefinite and definite descriptions (ε-terms and ι-terms) are presented, and interpreted in Martin-Löf's intensional type theory. The interpretations are formalizations of ideas which are implicit in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of 'the element such that the property holds' and refer by that phrase to the element constructed in the existence proof. In particular, we deviate from the practice of interpreting (...) descriptions by contextual definitions. (shrink)

Simple locative sentences show a variety of pseudo-quantificational interpretations. Some locatives give the impression of universal quantification over parts of objects, others involve existential quantification, and yet others cannot be characterized by either of these quantificational terms. This behavior is explained by virtually all semantic theories of locatives. What has not been previously observed is that similar quantificational variability is also exhibited by locative sentences containing indefinites with the ‘a’ article. This phenomenon is especially problematic for traditional existential treatments of (...) indefinites. We propose a solution where indefinites denote properties and are assigned locations similarly to other spatial descriptions. This Property-Eigenspace Hypothesis accounts for the correlation between the interpretations of locative indefinites and the pseudo-quantificational effects with simple entity-denoting NPs. Thereby, the proposal opens up a new empirical domain for property-based theories of indefinites, with implications for the analysis of collective descriptions, generics, negative polarity items and part–whole structure. (shrink)

A general representation of the processesof conceptualization, founded upon adescriptional mould drawn from fundamentalquantum mechanics, is outlined. The approach iscalled the method of relativizedconceptualization. This stresses that therepresentation is not researched as a ``neutralstatement of facts'' but, from the start on, asa method subjected to definitedescriptional aims, namely an a prioriexclusion of the emergence of false problems orparadoxes and of any gliding into relativism.The method is characterized by an explicit andsystematic relativization of each descriptionalstep, to all the descriptional elementsinvolved in (...) this step, namely: the epistemicaction by which the object-entity is generated,the object-entity itself, and the epistemicaction by which the object-entity is qualified.Successive steps which complexify progressivelya given initial description, form an unlimitedchain of cells of conceptualization wherethe very first cell, necessarily, is rooted in as yet strictly unconceptualizedphysical factuality while the subsequent cellsconsist of increasingly abstract descriptionsthat are connected hierarchically. The chainsinteract at nodes where they branch, thusgenerating an indefinitely evolving,complexifying web of relativizedconceptualization, free of ambiguities, andwhere each element stays under control.The method contains the positedassertion of a realism of which a definite sortof minimality follows then inside themethod. This generates a clear distinctionbetween illusory qualifications of``how-a-physical-entity-is-in-itself'', and models of this physical entity. Thereby aworked out connection with philosophicalthinking is incorporated in the method. (shrink)

Descriptions are predicates. Here, I'll take this to mean either of two basically equivalent things: that they have extensions as their semantic values, sets of entities, in the broadest sense; or that they have type-〈e,t〉 functions as their semantic values, functions from entities, in the broadest sense, to truth values. An entity in the broadest sense is anything that can be the subject of a first-order predication. Examples are individuals, pluralities, masses, and kinds. Here I'm including entities in this (...) broadest sense because my thesis that descriptions are predicates applies to all sorts of descriptions: singular descriptions, plural definite descriptions, mass descriptions, kind descriptions, and indefinite descriptions as well. (shrink)

This book critically examines some widespread views about the semantic phenomenon of reference and the cognitive phenomenon of singular thought. It begins with a defense of the view that neither is tied to a special relation of causal or epistemic acquaintance. It then challenges the alleged semantic rift between definite and indefinite descriptions on the one hand, and names and demonstratives on the other—a division that has been motivated in part by appeals to considerations of acquaintance. Drawing on (...) recent work in semantics, the book explores a more unified account of all four types of expression, according to which none of them paradigmatically fits the profile of a referential term. On the proposed framework, all four involve existential quantification but admit of uses that exhibit many of the traits associated with reference—a phenomenon that is due to the presence of what we call a ‘singular restriction’ on the existentially quantified domain. The book concludes by drawing out some implications of the proposed semantic picture for the traditional categories of reference and singular thought. (shrink)

What, from a semantic perspective, is the difference between singular indefinite and definite descriptions? Just over a century ago, Russell provided what has become the standard philosophical response. Descriptions are quantifier phrases, not referring expressions. As such, they differ with respect to the quantities they denote. Indefinite descriptions denote existential quantities; definite descriptions denote uniquely existential quantities. Now around the 1930s and 1940s, some linguists, working independently of philosophers, developed a radically different response. (...) class='Hi'>Descriptions, linguists such as Jespersen held, were referring expressions, not quantifier phrases. Accordingly, descriptions differ with respect their rules of reference. Indefinite descriptions refer to „novel‟ items, definite descriptions to „familiar‟ ones. My dissertation serves as the first systematic effort to bridge the gap between these two seemingly incompatible responses. It provides a satisfactory answer to the above question which links the seemingly intractable divide between Russellians and familiarity theorists. This is achieved by utilizing two observations: Donnellan‟s observation that speakers use descriptions not only as devices of quantification but also as devices of reference, and Devitt‟s observation that these two uses, being regular, systematic, and cross-linguistic, have the status of convention in our language. Taken in conjunction, these two observations, I argue, require postulating that descriptions are semantically ambiguous. These observations compel the thoughtful theorist to maintain that descriptions have two distinct semantic functions, one quantificational and one referential. Accordingly, the semantic contrast between singular indefinite and definite descriptions is two-fold. Descriptions can contrast either quantificationally or with respect to the speaker‟s view of the audience‟s familiarity with the description‟s referent. (shrink)

One of the long-standing problems in particle physics is the covariant description of higher spin states. The standard formalism is based upon totally symmetric Lorentz invariant tensors of rank-K with Dirac spinor components, $\psi _{\mu _1 \cdots \mu _K } $ , which satisfy the Dirac equation for each space time index. In addition, one requires $\partial ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0{\text{ }}and{\text{ }}\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } (...) = 0$ . The solution obtained this way (so called Rarita–Schwinger framework) describes “has–been” spin-(K+ $ - \frac{1}{2}$ ) particles in the rest frame and particles of indefinite (fuzzy) spin elsewhere. Problems occur when $\psi _{\mu _1 \cdots \mu _K } $ constrained this way are placed within an electromagnetic field. In this case, the energy of the spin-(K+ $ - \frac{1}{2}$ ) state becomes imaginary and it propagates acausally (Velo–Zwanziger problem). Here I consider two possible avenues for avoiding the above problems. First I make the case that specifically for baryon excitations there seems to be no urgency so far for a formalism that describes isolated higher-spin states as all the observed nucleon and Δ(1232) excitations (up to Δ(1600)) are exhausted by unconstrained ψ μ , $\psi _\mu ,\psi _{\mu _1 \cdots \mu _3 } {\text{ }}and{\text{ }}\psi _{\mu _1 \cdots \mu _5 } ,$ , structures which originate from rotational and vibrational excitations of an underlying quark–diquark string. Second, I show that the $\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0$ constraint is a short-hand of a more general definition of the parity-singlet invariant subspace of the squared Pauli–Lubanski vector, W 2. I consider the simplest case of K=1 and construct the covariant projector onto that very state as $ - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4})$ . I suggest to work in the sixteen dimensional vector space, Ψ, of the direct product of the four-vector, A μ , with the Dirac spinor, ψ, i.e., Ψ=A μ ⊗ψ, rather than keeping space-time and spinor indices separated and to consider $( - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4}) - 1)\Psi = 0$ as the principal wave equation without invoking any further supplementary conditions. In gauging the equation minimally and, in calculating the determinant, one obtains the energy-momentum dispersion relation. The latter turned out to be well-behaved and free from pathologies, thus avoiding the classical Velo–Zwanziger problem. (shrink)

This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that indefinites create new discourse referents and definites pick up an existing referent, can be formulated declaratively if logic is used (...) as a metalanguage for English. In this case the declarative aspects of a rule are highlighted when we focus on the model theory of the description language while a procedural perspective is obtained when its proof theory is concentrated on. Themes of interest are Discourse Representation Theory, resolution of anaphora, resolution of presuppositions, and underspecification. (shrink)

In this paper I argue that anaphoric pronouns should always be interpreted exhaustively. I propose that pronouns are either used referentially and refer to the speaker's referents of their antecedent indefinites, or descriptively and go proxy for the description recoverable from its antecedent clause. I show how this view can be implemented within a dynamic semantics, and how it can account for various examples that seemed to be problematic for the view that for all unbound pronouns there always should be (...) a notion of exhaustivity/uniqueness involved. The uniqueness assumption for the use of singular pronouns is also shown to be importantto explain what the discourse referents used in dynamic semantics represent. (shrink)

Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials – to be entia non grata – and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of (...) defining the number one in terms drawn only from logic and set theory, is a doomed enterprise. The starting point is Russell's Theory of Descriptions, which purports to supply a quantificational analysis of definite descriptions by adjoining a 'uniqueness clause' to the formal rendering of indefinite descriptions. That theory fails on at least two counts. First, the senses of statements containing indefinite descriptions are typically not preserved under the Russellian translation. Second (and independently), the 'uniqueness clause' fails to trim 'some' to 'one'. The Russell–Whitehead account in Principia Mathematica fares no better. Other attempts to define 'one' are covertly circular. An ontologically non-embarrassing alternative account of the number words is briefly sketched. (shrink)

This volume offers novel views on the precise relation between reference to an object by means of a linguistic expression and our mental representation of that object, long a source of debate in the philosophy of language, linguistics, and cognitive science. Chapters in this volume deal with our devices for singular reference and singular representation, with most focusing on linguistic expressions that are used to refer to particular objects, persons, or places. These expressions include proper names such as Mary and (...) John; indexicals such as I and tomorrow; demonstrative pronouns such as this and that; and some definite and indefinite descriptions such as The Queen of England or a medical doctor. Other chapters examine the ways we represent objects in thought, particularly the first-person perspective and the self, and one explores a notion common to reference and representation: salience. The volume includes the latest views on these complex topics from some of the most prominent authors in the field and will be of interest to anyone working on issues of reference and representation in thought and language. (shrink)

The paper deals with the problem whether there can exist indeterminate identity. If one accepts Evans’s argument, then statements about indeterminate identity can be true, but only those, in which at least one of the singular terms does not refer determinately. One does not have to explain all vagueness as semantic, i.e. as indeterminacy of meaning, because some such statements can be true on account of indeterminacy of reality. This can be shown in the particular quantum case introduced by Lowe (...) concerning the identity of an absorbed and emitted electron. The singular terms within the identity statements in this example are to be understood in the way pointed out by Abasnezhad and in the manner Barnes and Williams take names in statements of identity between Kilimanjaro and one of the precise aggregates of particles of which the mountain consists: One of the names refers indeterminately. This indeterminacy is of the kind belonging to indefinite descriptions. The issue of individuality on quantum level can be understood using resources of structural realism of James Ladyman. (shrink)

John Hawthorne and David Manley (The Reference Book, OUP 2012) endorse a unified treatment of the semantics of four kinds of expressions that can be said to have referential uses: specific indefinite descriptions, definite descriptions, demonstratives and proper names. The semantic theory the authors propose treats all these expressions as having a quantificational structure that achieves uniqueness of application via the presence of covert material contributing to the restriction of the domain of quantification. I argue that there (...) are reasons to postulate disunity; reasons to set apart a class of purely referential expressions that do not just apply uniquely to an object via overt or covert restrictors, but that refer to it. (shrink)

Es gehört zu den sprachphilosophischen Gemeinplätzen, daß ein elementarer Satz aus zwei Teilausdrücken besteht – einem Nominator, mit dem wir einen Gegenstand der Rede spezifizieren, und einem Prädikator, mit dem wir dem so herausgegriffenen Gegenstand eine Eigenschaft zuschreiben können. Während der semantische Referentialist Nominatoren typischerweise als solche Ausdrücke definiert, die eine explizite Bezugnahme auf genau einen Gegenstand ermöglichen, wird der Vertreter einer pragmatischen Bedeutungstheorie umgekehrt versuchen, die ontologische Kategorie des Gegenstandes im Rückgriff auf den Begriff des singulären Terminus einzuführen. Hierzu (...) ist es zur Vermeidung eines Zirkels nötig, Nominatoren in einer rein lingualen Weise zu charakterisieren. Der Aufsatz setzt sich mit R. Brandoms Vorschlag auseinander, dem zufolge singuläre Termini solche substituierbaren Ausdrücke sind, die nur in symmetrischen Ersetzungsrelationen stehen. Es wird – vor allem anhand von "indefinite descriptions" – gezeigt, daß eine derartige inferentielle Symmetrie weder eine notwendige noch eine hinreichende Bedingung darstellt. (shrink)

The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms (...) from a formal proof. The procedures by which this is to be carried out are based on Hilbert's epsilon substitution method. The epsilon calculus, however, has applications in other contexts as well. The first general application of the epsilon calculus was in Hilbert's epsilon theorems, which in turn provide the basis for the first correct proof of Herbrand's theorem. More recently, variants of the epsilon operator have been applied in linguistics and linguistic philosophy to deal with anaphoric pronouns. (shrink)

This article grapples with Robert Brandom’s account of singular terms. I argue that neither Brandom’s answer to the question “What are singular terms?” nor his answer to the question “Why are there any singular terms?” works as they currently stand. Brandom’s substitution-inferential semantic account of what singular terms are fails to distinguish between the semantic role of singular terms and indefinite descriptions, and Brandom’s “expressive transcendental deduction” for why there are any singular terms fails to deciseively show that (...) singular terms are expressively necessary for the use of logical vocabulary. Still, I then characterize how Brandom does have resources within his substitution-inferential semantics to give a better, revised answer to the question “What are singular terms?” that both fits programmatically within his framework and has a curious Kantian parallel. I leave the matter offering a Brandom-friendly replacement account for why there are any singular terms thus conceived for another occasion. (shrink)

The paper sketches the place of dynamic semantics within a broader picture of developments in philosophical and linguistic theories of meaning. Some basic concepts of dynamic semantics are illustrated by means of a detailed analysis of anaphoric definite and indefinite descriptions, which are treated as contextually dependent quantificational expressions. It is shown how a dynamic view sheds new light on the contextual nature of interpretation, on the difference between monologue and dialogue, and on the interplay between direct and (...) indirect information. (shrink)

Indefinites face competition at two levels: Presupposition and content. The antipresupposition hypothesis predicts that they signal the opposite of familiarity, or uniqueness, namely, novelty, or non-uniqueness. At the level of descriptive content, they are pressured from two sides: definites expressing identity and another phrases expressing difference, and Gricean reasoning predicts that indefinites signal both difference and identity and are infelicitous when definites and another phrases are felicitous. However, occasionally a space opens between the and another, for a to fill. This (...) is in part due to conditions handicapping the or another semantically, in part to another’s phonological handicap. The division of labor between determiners in the field of difference and sameness is thus the result of an intricate competition. We model this competition in a version of game-theoretic pragmatics. (shrink)

We argue that definite noun phrases give rise to uniqueness inferences characterized by a pattern we call definiteness projection. Definiteness projection says that the uniqueness inference of a definite projects out unless there is an indefinite antecedent in a position that filters presuppositions. We argue that definiteness projection poses a serious puzzle for e-type theories of (in)definites; on such theories, indefinites should filter existence presuppositions but not uniqueness presuppositions. We argue that definiteness projection also poses challenges for dynamic approaches, (...) which have trouble generating uniqueness inferences and predicting some filtering behavior, though unlike the challenge for e-type theories, these challenges have mostly been noted in the literature, albeit in a piecemeal way. Our central aim, however, is not to argue for or against a particular view, but rather to formulate and motivate a generalization about definiteness which any adequate theory must account for. (shrink)

Generic statements are commonly expressed using the bare plural – ‘tigers are striped’ – or the indefinite singular – ‘a tiger is striped’. Notoriously, some generics can be expressed using the bare plural locution, but not the indefinite singular; bare plural generics and indefinite singular generics pattern differently. I explore this phenomenon as it applies to normative generic statements: expressions like boys don’t cry, women are kind and nurturing, children are seen and not heard – that convey (...) something over and above (and even distinct from) the descriptive reading. I argue that we should look to a metalinguistic theory of generics to understand indefinite singular normative generics. That is, a normative indefinite singular generic is a proposal about what to include in the extension of the generic term. This theory explains why it is more often than not that felicitous indefinite singular generics are about social kind terms. I argue that this explains a crucial way in which language shapes the social world. When we say things like (2), we propose definitions and uses for the word ‘boy’. Such proposals and their consequences actually impact the behavior of the groups they pick out, as well as the attitudes of others towards those groups. (shrink)

This paper distinguishes between definiteness and determinacy. Definiteness is seen as a morphological category which, in English, marks a uniqueness presupposition, while determinacy consists in denoting an individual. Definite descriptions are argued to be fundamentally predicative, presupposing uniqueness but not existence, and to acquire existential import through general type-shifting operations that apply not only to definites, but also indefinites and possessives. Through these shifts, argumental definite descriptions may become either determinate or indeterminate. The latter option is observed in (...) examples like ‘Anna didn’t give the only invited talk at the conference’, which, on its indeterminate reading, implies that there is nothing in the extension of ‘only invited talk at the conference’. The paper also offers a resolution of the issue of whether possessives are inherently indefinite or definite, suggesting that, like indefinites, they do not mark definiteness lexically, but like definites, they typically yield determinate readings due to a general preference for the shifting operation that produces them. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more (...) definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)