This paper discusses the semantics of intensional transitive verbs such as 'need', 'want','recognize', 'find', and 'hire'. It proposes new linguistic criteria for intensionality and defends two semantic analyses for two different classes of intensional verbs. The paper also includes a systematic classification of intensional verbs according to the type of lexical meaning they involve.

ABSTRACT In this paper, I ask whether quantifiers are intensional operators, with variable assignments playing the role of indices. Certain formulations of extensional type theory suggest an affirmative answer, but the most satisfactory among them suffer from a contamination of their semantic ontology with syntactic material. I lay out ‘Fregean’ versions of extensional type theory that are free from syntactic contamination and suggest a negative answer to our question.

The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semanticinterpretations can be formalized in linear logic in a way thatcorrectly explains the observed interactions between quantifier scopeambiguity, bound anaphora and intensionality.Our linear-logic formalization of the compositional properties ofquantifying expressions in natural language obviates the need forspecial mechanisms, such as Cooper storage, in representing thescoping possibilities of quantifying expressions. Instead, thesemantic contribution of a quantifier is recorded as a linear-logicformula whose use in a proof will establish the (...) scope of thequantifier. Different proofs can lead to different scopes. In eachcomplete proof, the properties of linear logic ensure thatquantifiers are properly scoped. (shrink)

Attempting to deflate ontological debates, the proponent of Quantifier Variance (QV) claims that there are multiple quantifier meanings of equal metaphysical merit. According to Hirsch—the main proponent of QV—metaphysical merit should be understood intensionally: two languages have equal merit if they allow us to express the same possibilities. I examine the notion of metaphysical merit and its purported link to intensionality. That link, I argue, should not be supported by adopting an intensional theory of semantic content. Rather, I give (...) a general strategy for supporting claims about metaphysical merit and examine whether that strategy can be used to link merit and intensionality. Though I don’t deliver a definitive verdict, the discussion provides a clearer framework for articulating and evaluating claims about metaphysical merit. (shrink)

It is not rare to find students of language interested in the many ways in which speakers talk about Fred or about the weather, assert of Fred or of the weather that he is fat or that it is fine. Many philosophers, logicians, and linguists share an interest in what words or phrases designate or describe, and what speakers refer to, mention, and say things about. But it is also notable that the Grammarian and the Philosopher, especially the Metaphysician, have (...) looked at intentionality in different ways. In this lecture I sketch the ways that the Philosophers Nelson Goodman and W.V.O Quine and by contrast the Grammarians have analyzed and used the notion of Aboutness, in Quine’s case in his famous argument against Quantifying Into intensional sentences. Goodman’s and Quine’s analyses are motivated by different intellectual goals from the Linguists’. By contrast Linguists have the notion of Topic Noun Phrase. I shall argue that the Linguists’ notion of Topic Noun Phrase offers clarification and an intellectual advance over Goodman’s and Quine’s notions, especially in the treatment of propositional attitude sentences. (shrink)

The complement of intensional transitive verbs, like any nonreferential complement, can be replaced by a ‘special quantifier’ or ‘special pronoun’ such as 'something', 'the same thing', or 'what'. In this paper, I will defend the ‘Nominalization Theory’ of special quantifiers against a range of apparent counterexamples involving intensional transitive verbs.

Section 1 provides a brief summary of the pair-list literature singling out some points that are particularly relevant for the coming discussion. -/- Section 2 shows that the dilemma of quantifi cation versus domain restriction arises only in extensional complement interrogatives. In matrix questions and in intensional complements only universals support pairlist readings, whence the simplest domain restriction treatment suffices. Related data including conjunction, disjunction, and cumulative readings are discussed -/- Section 3 argues that in the case of extensional (...) complements the domain restriction treatment is inadequate for at least two independent reasons. One has to do with the fact that not only upward monotonic quantifi ers support pairlist readings, and the other with the derivation of apparent scope out readings. The reasoning is supplemented with some discussion of the semantic properties of layered quantifi ers.  The above will establish the need for quantifi cation, so the question arises how the objections explicitly enlisted in the literature against quantifi cation can be answered. Section 4 considers the de dicto reading of the quantifi er s restriction, quanti cational variability, and the absence of pairlist readings with whether questions, and argues that they need not militate against the quanti ficational analysis. -/- Section 5 summarizes the emergent proposal -/- Finally, section 6 discusses the signifi cance of the above findings for the behavior of weak islands. (shrink)

This paper defends the view that perceptual ascriptions such as “Jones sees a cat” are sometimes intensional. I offer a range of examples of intensional perceptual ascriptions, respond to objections to intensional readings of perceptual ascriptions, and show how widely accepted semantic accounts of intensionality can explain the key features of intensional perceptual ascriptions.

This chapter gives a truthmaker-based account of the semantics of 'reifying' quantifiers like 'something' when they act as complements of intensional transitive verbs ('need', 'look for'). It argues that such quantifiers range over 'variable satisfiers' of the attitudinal object described by the verb (e.g. the need or the search).

The traditional scope theory of intensionality (STI) (see Russell 1905; Montague 1973; Ladusaw 1977; Ogihara 1992, 1996; Stowell 1993) is simple, elegant, and, for the most part, empirically adequate. However, a few quite troubling counterexamples to this theory have lead researchers to propose alternatives, such as positing null situation pronouns (Percus 2000) or actuality operators (Kamp 1971; Cresswell 1990) in the syntax of natural language. These innovative theories do correct the undergeneration of the original scope theory, but at a cost: (...) the situation pronoun and operator theories overgenerate, as argued extensively by Percus (2000) and Keshet (2008). This paper presents new data that supports the STI over other analyses, such as structures where DPs lose their de re readings in positions where syntactic movement is blocked. These data point the way to a new theory of intensionality. This new theory, called split intensionality, is a modification of the STI which aims to solve the problems raised for the original scope theory without overgenerating. The proposal calls for an additional intensional abstraction operator that creates an expression denoting an intension from an expression denoting an extension. When a DP moves to a position above this operator, it is interpreted de re; otherwise it is de dicto. The crucial part of the new proposal is that a DP may move above this operator and yet remain, for instance, below an intentional verb or inside an if-clause. Therefore, a DP within an island for syntactic movement may be de re and yet not move out of the island when the intensional abstraction operator is also within the island. (shrink)

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier (...) variance is not an ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

Following on Westerståhl’s argument that many is not Conservative [9], I propose an intensional account of Conservativity as well as intensional versions of EXT and Isomorphism closure. I show that an intensional reading of many can easily possess all three of these, and provide a formal statement and proof that they are indeed proper intensionalizations. It is then discussed to what extent these intensionalized properties apply to various existing readings of many.

A verb is transitive iff it usually occurs with a direct object, and in such occurrences it is said to occur transitively . Thus ‘ate’ occurs transitively in ‘I ate the meat and left the vegetables’, but not in ‘I ate then left’ (perhaps it is not the same verb ‘left’ in these two examples, but it seems to be the same ‘ate’). A verb is intensional if the verb phrase (VP) it forms with its complement is anomalous in (...) at least one of three ways: (i) interchanging expressions in the complement referring to the same entity can change the truth-value of the sentence embedding the VP; (ii) the VP admits of a special “unspecific” reading if it contains a quantifier, or a certain type of quantifier; and (iii) the normal existential commitments of names and existential quantifiers in the complement are suspended even when the embedding sentence is negation-free. (shrink)

The study of weighted structures is one of the important trends in recent computer science. The aim of the article is to provide a weighted, many-valued version of classical intensional semantics formalised in the framework of higher-order fuzzy logics. We illustrate the apparatus on several variants of fuzzy S5-style modalities. The formalism is applicable to a broad array of weighted intensional notions, including alethic, epistemic, or probabilistic modalities, generalised quantifiers, counterfactual conditionals, dynamic and non-monotonic logics, and some (...) more. (shrink)

A statement is generic if it expresses a generalization about the members of a kind, as in, ’Pear trees blossom in May,’ or, ’Birds lay egg’. In classical logic, generic statements are formalized as universally quantified conditionals: ‘For all x, if..., then....’ We want to argue that such a logical interpretation fails to capture the intensional character of generic statements because it cannot express the generic statement as a simple proposition in Aristotle’s sense, i.e., a proposition containing only one (...) single predicate. On the contrary, we want to show that typed lambda-abstraction can help us transform the classical, non-simple and extensional expression of generic statements into a new, simple and intensional formalization, through the introduction of an abductively defined operator ALL*. This new operator allows for the possibility of a single predication, e.g. fly(), because it builds, out of a concept like ‘bird’, a concrete universal, e.g. ‘birds’, upon which the single predicate can be applied to authentically formalize a generic statement, e.g. ‘birds fly’. (shrink)

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes. In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an (...) immortal gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. ; the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul ] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives. (shrink)

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes. In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an (...) immortal gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. ; the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives. (shrink)

The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. Some extensions to the type theory are discussed, type polymorphism, and enriching the system with sufficient number theory to account for quantifiers of proportion, such as “most.”.

Intensional logic is the technical study of such intensional phenomena in human reasoning as modality, knowledge, or flow of time. These all require a richer semantic picture than standard truth values in one static environment. Such a picture is provided by so-called possible worlds semantics, a paradigm which is surveyed in this book, both as to its external sources of motivation and as to the internal dynamics of the resulting program. In particular, Manual of Intensional Logic presents (...) the major classical topics, including modal logic, tense logic, and conditional logic, all of which illustrate motivations coming from philosophy and linguistics. The Book also discusses recent computational applications in computer science and AI. Finally, Manual of Intensional Logic takes up recent developments in the study of language and information making themselves felt in the area. The Book examines the role of partial information--with illustrations drawn from different branches of Intensional Logic--and various influences stemming from current theories of the semantics of natural language, involving generalized quantifiers and theories of types. (shrink)

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, (...) and lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

This chapter contains sections titled: Introduction A Methodology for Ontology The Need for a Criterion of Ontological Commitment The Role of a Canonical Notation The Ontology of Mathematics The Notion of Existence The Ontology of Natural Sciences Do Intensions Belong to the Furniture of the World? How to Treat Intensional Contexts without Positing Intensions Fiction, Intentional Objects and Existence Lesniewski's Ontology Acknowledgments.

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, (...) and lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology, and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth’s notion of implicit definition, and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. (...) -/- The volume further examines what it means that a quantifier can have multiple meanings, and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts. ​. (shrink)

The chapter is divided in two parts. The first part gives an introduction to issues in quantified modal logic. We provide an overview of recent work in QML and we presuppose the use of a relational semantics. We discuss models for constant domains, increasing domains and varying domains and present axiomatizations for the corresponding logics. We also discuss philosophical issues related to the interpretation of the quantifiers, terms and identity and we present a first-order quantified intensional logic. A (...) crucial issue in QML is to provide a unified semantic framework capable of accommodating a large class of logical systems including both normal and non-normal systems. The second part of the article focuses on alternatives to the standard relational semantics for modalities deriving from the work of Kripke. In particular we give an overview of recent work in neighborhood semantics and we offer a general completeness result for the class of first order classical modal logics in terms of general frames with constant domains. We also consider some extensions of current work dealing with identity. (shrink)

In this paper, I reconstruct Quine’s arguments against quantified modal logic, from the early 1940’s to the early 1960’s. Quine’s concerns were not technical. Quine was looking for a coherent interpretation of quantified-in English modal sentences. I argue that Quine’s main thesis is that the intended objectual interpretation of the quantifiers is incompatible with any semantic reading of the modal operators, for example as expressing analytic necessity, unless the entities in the domain of quantification are intensions, i.e. definitional entities. (...) The difficulty is that it makes no sense to say of an ordinary object that it bears a property necessarily or contingently when the necessity or contingency in question is analytic. However, starting in 1960, Quine claims that quantified-in modal sentences can be coherently interpreted only as essentialist predications. When we say about an object that it necessarily F ’s, we can only coherently mean that it essentially F ’s. In the paper, I argue that adequately qualified the thesis is plausible. Two important qualifications are needed. The first is the assumption that satisfaction is an irreducibly predicative notion, making any explication of satisfaction in terms of truth inadequate. The second is the ontological rejection of purely semantic, i.e. merely definitional, entities. With these qualifications in place, Quine’s rejection of the combination of objectual quantifiers and semantic modalities can be upheld. In this way, we vindicate a qualified version of Quine’s conjecture that quantified modal logic is committed to essentialism. (shrink)

Philosophia (Israel), 16(3-4), 333 - 344. YEAR: 1986 Extensive corrigenda Vol. 17, no. 3. -/- SUBJECT(S): Quine's second thoughts on quantifying in, appearing in the second, revised edition of _From a Logical Point of View_ of 1961, are shown to be incorrect. His original thoughts were correct. ABSTRACT: Additional tumult is supplied to pp. 152-154 of _From A Logical Point of View_, showing that being dated is no guarantee of being right. Among other things, it is shown that Quine's argument (...) to the conclusion that limiting the universe of discourse to intensional entities does not "relieve the original difficulty over quantifying into modal contexts" is incorrect; that the contradictory of that conclusion is in fact true; and that an even stronger conclusion is true, with 'abstract' replacing 'intensional'. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

This chapter examines Bunge’s distinction between the logical concept of existence and the ontological one. We introduce a new conceptual existence predicate in an intensional environment that depends on the evaluation world. So that we can investigate restricted areas where the different kinds of concepts might exist. We hope this new predicate would encompass Bunge’s philosophical position which he designates as conceptualist and fictional materialism. The basic hybridization acts as a bridge between intensions and extensions because @ works as (...) a useful rigidifier. In hybrid logic, the accessibility relation and many properties this relation might have can be easily expressed in the formal language. The initial hypothesis is that hybridization and intensionality can serve as unifying tools in the areas involved in this research; namely, Logic, Philosophy of Science and Linguistics. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to (...) reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)

Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).

The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same time, those intentional objects do not come (...) for free; rather they are strictly dependent on intentional acts that generally need to have a presence, in one way or another, in the semantic structure of the sentence. (shrink)

This paper is motivated by the search for a natural and deductively powerful extension of classical set theory. A theory of properties U is developed, based on a system of relevant logic related to RQ. In U the set {a, b, c,...} is identified with the property [x: x=a x=b x=c...]. The universe of all sets V, is identified with the property of being a hereditary set. The main result is that relevant implication collapses to material implication for sentences with (...) quantifiers restricted to V. This demonstrates the naturalness of the system. However, an aparent lack of deductive power leads to the conclusion that the best extension of classical set theory is to be found in intensional theories with the unrestricted comprehension schema based on weak relevant logics. The author has obtained similar collapses of to for these systems. (shrink)

The aim of this paper will be to show how significant the logical theories of judgement which were worked out at the end of the nineteenth century have been for the ontological thought during the twentieth century. Against the classical - Aristotelian and Scholastic - analysis of predicative judgement, Franz Brentano on one hand and Gottlob Frege on the other hand have leveled two different criticisms, which then generated two radically divergent ontological paradigms. On one side, despite Brentano’s own nominalistic (...) stands, there was a tremendous extension of the general category of “object” as well as of the notion of “being” with, as a consequence, the exceptionnally luxuriant ontologies of Brentano’s heirs. On the other side, notwithstanding Frege’s own Platonistic affinities, there was a drastic deflation of the realm of objects to the benefit of the realm of concepts taken as classifying functions, and therefore a strong nominalistic trend among Frege’s heirs. The development of quantified modal logics at the middle of twentieth century however forced contemporary ontology to reconsider this simple alternative in order to give place to some hybrid entities such as individual concepts or other kinds of “intensional objects”. (shrink)

Quantification over individuals, times, and worlds can in principle be made explicit in the syntax of the object language, or left to the semantics and spelled out in the meta-language. The traditional view is that quantification over individuals is syntactically explicit, whereas quantification over times and worlds is not. But a growing body of literature proposes a uniform treatment. This paper examines the scopal interaction of aspectual raising verbs (begin), modals (can), and intensional raising verbs (threaten) with quantificational subjects (...) in Shupamem, Dutch, and English. It appears that aspectual raising verbs and at least modals may undergo the same kind of overt or covert scope-changing operations as nominal quantifiers; the case of intensional raising verbs is less clear. Scope interaction is thus shown to be a new potential diagnostic of object-linguistic quantification, and the similarity in the scope behavior of nominal and verbal quantifiers supports the grammatical plausibility of ontological symmetry, explored in Schlenker (2006). (shrink)

Previous theorists have claimed that Russell’s theory of definite descriptions gives the wrong truth conditions to sentences in which definite descriptions are embedded under certain other operators; but the other operators used, such as conditionals and propositional attitude verbs, have introduced intensional and hyperintensional complications that might be thought to obscure the point against Russell. This paper shows that the same kind of problem arises when the operator in question allows the context to be extensional. It is further argued (...) that presuppositional theories of definite descriptions give intuitively satisfying analyses of the novel data. (shrink)

It is commonly argued that natural language has the expressive power of quantifying over intensional entities, such as times, worlds, or situations. A standard way of modelling this assumes that there are unpronounced but syntactically represented variables of the corresponding type. Not all that much as has been said, however, about the exact syntactic location of these variables. Meanwhile, recent work has highlighted a number of problems that arise because the interpretive options for situation pronouns seem to be subject (...) to various restrictions. This paper is primarily concerned with situation pronouns inside of determiner phrases, arguing that they are introduced as arguments of (certain) determiners. Verbal predicates, on the other hand, are assumed to not combine with a situation pronoun. The various restrictions on their interpretation are shown to fall out from the semantic system that is developed based on that view. Further support for such an account comes from situation semantic analyses of donkey sentences as well as data on the temporal interpretation of nominal predicates. Its ability to account for this full range of data in a unified manner is shown to set it apart from previous proposals. The paper closes with an outlook on further extensions, including an account of quantifier domain restriction based on situation pronouns. (shrink)

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic (...) logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers ∀ new and ∃ new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels. (shrink)

The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice (...) functions scopes above other operators (such as intensional verbs like must or can). Determiner quantifiers leave a choice-function trace when they move and this trace combines with the noun restriction, which is interpreted low. That split scope always involves low existential force is derived, without stipulation, from Kratzer’s idea that low existential force can be achieved via binding (into the noun restriction). (shrink)

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it (...) is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical , provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional. (shrink)

In this paper, we outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts. We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts which does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts. The account we present aims to meet the following desiderata on a semantic theory T for opaque contexts: (D1) T can be formulated in a first-order extensional (...) language; (D2) T does not require quantification over intensional entities­i.e., meanings, propositions, properties, relations, or the like­in its treatment of opaque contexts; (D3) T captures the entailment relations that hold in virtue of form between sentences in the language for which it is a theory; (D4) T has a finite number of axioms. If the approach outlined here is correct, it resolves a longstanding complex of problems in metaphysics, the philosophy of mind and the philosophy of language. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented (...) in the course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented (...) in the course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)