There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic SCI. (...) Then S3 proves to be the smallest Lewis modal system where PI can be defined as SE. We extend S3 to a non-Fregean logic with propositional quantifiers such that necessity and PI are integrated as non-interdefinable concepts. CA is not valid and PI refines SE. Models are expansions of SCI-models. We show that SCI-models are Boolean prealgebras, and vice-versa. This associates non-Fregean logic with research on Hyperintensional Semantics. PI equals SE iff models are Boolean algebras and CA holds. A representation result establishes a connection to Fine’s approach to propositional quantifiers and shows that our theories are conservative extensions of S3–S5, respectively. If we exclude the Barcan formula and a related axiom, then the resulting systems are still complete w.r.t. a simpler denotational semantics. (shrink)

We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.

A modified version of Normann's hierarchy of domains with totality [9] is presented and is shown to be suitable for interpretation of Martin-Löf's intuitionistic type theory. This gives an interpretation within classical set theory, which is natural in the sense that $\Sigma$ -types are interpreted as sets of pairs and $\Pi$ -types as sets of choice functions. The hierarchy admits a natural definition of the total objects in the domains, and following an idea of Berger [3] this makes possible an (...) interpretation where a type is defined to be true if its interpretation contains a total object. In particular, the empty type contains no total objects and will therefore be false (in any non-empty context). In addition, there is a natural equivalence relation on the total objects, so we derive a hierarchy of topological spaces (quotient spaces wrt. the Scott topology), and give a second interpretation using this hierarchy. (shrink)

The aim of this paper is to extend the classical sequent calculusLC to the second order. This task is realized by a semantical approach mixing the correlation spaces semantics ofLC on the one hand, and the analogy with the interpretation of systemF in coherent spaces on the other hand. This relies on the introduction of a new semantical object:noetherian correlation spaces.From the semantics we deduce the syntax of the second order classical sequent calculusLC2.

We study the notion of logical relation in the coherence space semantics of multiplicative-additive linear logic . We show that, when the ground-type logical relation is “closed under restrictions”, the logical relation associated to any type can be seen as a map associating facts of a phase space to families of points of the web of the corresponding coherence space. We introduce a sequent calculus extension of whose formulae denote these families of points. This logic admits a truth-value (...) class='Hi'>semantics in the previously mentioned phase space, and this truth-value semantics faithfully describes the logical relation model we started from. Then we generalize this notion of phase space, we prove a truth-value completeness result for and we derive from any phase model of a denotational model for . Using the truth-value completeness result, we obtain a weak denotational completeness result based on this new denotational semantics. (shrink)

An axiomatization is presented of the denotational semantics for first order language of Apt [1]. The goal is to obtain a rational reconstruction of the intuitions underlying this semantics. The axiomatization combines ideas about four valued logic with facts about substitutions. Soundness and completeness of the axiomatization are established. From the completeness proof a decision procedure is obtained that shows how four valued logic and order sensitivity of substitution together add up in a natural way to the (...) denotational semantics for the language of first order logic as proposed by Apt. (shrink)

We extend to the exponential connectives of linear logic the study initiated in Bucciarelli and Ehrhard 247). We define an indexed version of propositional linear logic and provide a sequent calculus for this system. To a formula A of indexed linear logic, we associate an underlying formula of linear logic, and a family A of elements of , the interpretation of in the category of sets and relations. Then A is provable in indexed linear logic iff the family A is (...) contained in the interpretation of some proof of . We extend to this setting the product phase semantics of indexed multiplicative additive linear logic introduced in Bucciarelli and Ehrhard , defining the symmetric product phase spaces. We prove a soundness result for this truth-value semantics and show how a denotational model of linear logic can be associated to any symmetric product phase space. Considering a particular symmetric product phase space, we obtain a new coherence space model of linear logic, which is non-uniform in the sense that the interpretation of a proof of !A−B contains informations about the behavior of this proof when applied to “chimeric” arguments of type A . In this coherence semantics, an element of a web can be strictly coherent with itself, or two distinct elements can be “neutral”. (shrink)

Originally published in 1958. A study in the logical foundations of modern theoretical semantics, this book is concerned with notions of designation and consistency as well as denotation and truth. It presents several semantical theories, each of which with what were new concepts or treatments from the author. Talking at a time when semantical theory was gained great ground, this book also looks at the methodology of the sciences and the semantics of scientific language alongside analysis of meaning (...) and expression. It is influenced by the writings of Carnap, Church, Frege, Goodman, Quine, Russell and Tarski. (shrink)

In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for (...) by introducing the distinction between sense and denotation in the proof-theoretic-semantic setting. (shrink)

Originally published in 1958. A study in the logical foundations of modern theoretical semantics, this book is concerned with notions of designation and consistency as well as denotation and truth. It presents several semantical theories, each of which with what were new concepts or treatments from the author. Talking at a time when semantical theory was gained great ground, this book also looks at the methodology of the sciences and the semantics of scientific language alongside analysis of meaning (...) and expression. It is influenced by the writings of Carnap, Church, Frege, Goodman, Quine, Russell and Tarski. (shrink)

Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. (...) Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517). (shrink)

In the tradition of Denotational Semantics one usually lets program constructs take their denotations in reflexive domains, i.e. in domains where self-application is possible. For the bulk of programming constructs, however, working with reflexive domains is an unnecessary complication. In this paper we shall use the domains of ordinary classical type logic to provide the semantics of a simple programming language containing choice and recursion. We prove that the rule of {\em Scott Induction\/} holds in this new (...) setting, prove soundness of a Hoare calculus relative to our semantics, give a direct calculus ${\cal C}$ on programs, and prove that the denotation of any program $P$ in our semantics is equal to the union of the denotations of all those programs $L$ such that $P$ follows from $L$ in our calculus and $L$ does not contain recursion or choice. (shrink)

Research on the semantics of spatial markers in French is known mainly through Vandeloise’s work on static prepositions. However, interest in the expression of space in French goes back to the mid-1970s and focused first on verbs denoting changes in space, whose syntactic properties were related to specific semantic distinctions, such as the opposition between “movement” and “displacement”. This volume provides an overview of recent studies on the semantics of dynamic space in Fr...

The two theories of verbal cognition, namely abhihitānvaya and anvitābhidhāna, first put forth by the Bhāṭṭa and Prābhākara Mīmāṃsakas respectively in the second half of the first millennium C.E., can be considered as being foundational as all subsequent thinkers of the Sanskritic intellectual tradition engaged with and elaborated upon these while debating the nature of language and meaning. In this paper, I focus on the first chapter of Śālikanātha’s Vākyārthamātṛkā and outline the process of anvitābhidhāna described therein. Śālikanātha explains this (...) as comprising three steps, and thereafter discusses each of these three to elaborate upon and philosophically defend this conception of how one cognizes sentential meaning. The aim of this paper is to present Śālikanātha’s three-step model, and thus demonstrate especially the distinct conception of abhidhāna for the Prābhākara Mīmāṃsakas as complex and chronologically extended as contrasted with the Bhāṭṭa conception of abhidhāna as non-complex and instantaneous. Such an understanding of the disparate semantic contents with which the Bhāṭṭas and Prābhākaras use the identical term abhidhāna is crucial for any correct study of their respective doctrines. (shrink)

The Transparent Intensional Logic explicates the meaning of a linguistic expression as a construction. The construction is a hyperintensional entity. It is characterised as instructions for a „calculation“ of a concrete value. In the terminology of Pavel Tichy a linguistic expression denotes its meaning , which construes the signification of the expression. If the signification is an intension, we can call it a reference of the expression. In several semantic conceptions the question of the denotation and of the reference are (...) not treated equally. The terminological chaos can be resolved in a specific way thanks to „fine-grained“ character of the logical analysis offered by TIL. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2602\REVIEWS.262 : 2007-01-24 01:12 eviews THE DENOTING CENTURY, 1 19 90 05 5– –2 20 00 05 5 Michael Scanlan Philosophy / Oregon State U. Corvallis, or 97331, usa [email protected] Guido Imaguire and Bernard Linsky, eds. On Denoting: 1905–2005. Munich: Philosophia Verlag, 2005. Pp. 451. 98.00. isbn 3-88405-091-5. his anniversary collection of papers connected with Russell’s 1905 publiTcation of “On Denoting” reflects both the almost (...) mythic status that paper has achieved in analytic philosophy and the quite variegated nature of the significance that philosophers have seen in it. The papers in this collection break down roughly into two sorts. There are those which take a historical approach and attempt to explicate various aspects of the content of the OD article. The other sort might be labelled “application” papers in which Russell’s analysis in OD is seen as a tool or a model for subsequent philosophical work, in the spirit of Ramsey’s much quoted “paradigm of philosophy” remark. The volume opens with a reprint of the OD text with pagination indicated for the original Mind printing, for the text in Collected Papers 4 and for the widely referenced Logic and Knowledge Russell collection edited by R. C. Marsh. The Mind and Papers texts use the American convention of single quotation marks within double quotation marks. The Marsh edition (and the text given here) uses the inverse British convention. Readers need to be aware that paper authors here, and elsewhere, vary in which text they cite. The end of the volume has a comprehensive 21-page bibliography of the secondary literature. In between there are thirteen papers. I will be rather brief with the “application” papers, since I believe that Russell readers will tend to favour the more historically oriented papers. Some of the application papers wander quite far afield from Russell’s treatment of definite descriptions. For instance the paper by Thomas Mormann on “Description, Construction and Representation from Russell and Carnap to Stone” takes off from Russell’s assertion that his theory of descriptions was an early version of his subsequent interest in substituting “constructions” for “inferred entities” such as space-time points. The paper is almost exclusively a (worthwhile and mathematically astute) analysis of Russell’s efforts along these lines in Our russell: the Journal of Bertrand Russell Studies n.s. 26 (winter 2006–07): 167–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631 _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2602\REVIEWS.262 : 2007-01-24 01:12 168 Reviews Knowledge of the External World and The Analysis of Matter. The author argues that Russell’s constructions did not actually achieve the effects he wanted, but that (curiously) they can be properly developed within the later framework of topological spaces developed by Marshall Stone in 1937. The paper by Guido Imaguire, “Theory of Descriptions and Inferential Semantics”, explicitly eschews an “exegetical” approach and allies itself with a “systematical approach, in which one analyses possible new features and extensions of the proposed theory” (p. 397). The extension considered here is to “inferential semantics”, especially that of Robert Brandom. The spirit of this approach is to take the semantics of a language to be determined by the set of allowed inferences within that language. Imaguire takes as an essential lesson of Russell’s theory of descriptions that definite descriptions and proper names cannot be treated as singular terms of a language in the same manner. He goes on to argue for a criterion for distinguishing proper names from definite descriptions based on inferences allowed between sentences containing them, and he takes this distinction to argue for a modification of Brandom’s treatment of singular terms in his inferential semantics. Elena Tatievskaya’s paper on “Russell’s Theory of Descriptions and Wittgenstein on Internal Properties of Propositions” is another paper that is mainly about something other than Russell and his theory of descriptions. It is a very detailed study of Wittgenstein’s attempt to make good on his claim that the logical symbols of propositional logic notation, such as v and ~, do not correspond to “logical” components of propositions (Tractatus... (shrink)

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth (...) non unlike the notion of "truth at world" found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

This dissertation provides a model-theoretic semantics for English sentences atttributing a property or action to a group of objects, either collectively or distributively. It is shown that certain adverbial expressions select for collective predicates; therefore collective and distibutive predicates must be distinguishable. This finding is problematic for recent accounts of distributive predicates which analyze such predicates as taking group-level arguments, and hence as not distinguishable from collective predicates. ;A group-level treatment of distributives is possible, however, if predicate denotations are (...) relativized to a set of events for which a part/whole relation is defined. An event in which a group performs an action distributively will have subevents in which each of the group's members perform the same action; an event in which the group performs the action collectively will not. ;This analysis also makes possible an account of the fact that adverbials expressing collective action commonly have an additional use expressing spatial proximity, both in English and cross-linguistically. . A spatial "trace" function on the set of events allows formal definitions for the spatial uses of such adverbials to exactly parallel the definitions for the collectivizing uses. ;The dissertation also provides arguments for a set-theoretic model for plurality, in which the group membership relation is distinct from the subgroup relation. ;Certain quantifiers are shown sensitive to distinction between different sorts of group-level event. To accommodate this fact, it is suggested that verbal denotations provide, for each event, both an "inclusion set" and an "exclusion set"--corresponding roughly to positive and negative denotations. If the inclusion and exclusion sets are allowed under certain circumstances not to complement each other, correct results obtain. ;The splitting of verbal denotations into inclusion and exclusion sets also allows the solution of certain problems in previous accounts of the semantics of subject-verb agreement for number. The dissertation closes with a defense of the hypothesis that agreement is conditioned primarily by the semantics. (shrink)

It is known that a semantically closed theory with description may well be trivial if the principles concerning denotation and descriptions are formulated in certain ways, even if the underlying logic is paraconsistent. This paper establishes the nontriviality of a semantically closed theory with a natural, but non-extensional, description operator.

In “Is semantics possible?” Putnam connected two themes: the very possibility of semantics (as opposed to formal model theory) for natural languages and the proper semantic treatment of common nouns. Putnam observed that abstract semantic accounts are modeled on formal languages model theory: the substantial contribution is rules for logical connectives (given outside the models), whereas the lexicon (individual constants and predicates) is treated merely schematically by the models. This schematic treatment may be all that is needed for (...) an account of validity in a formal setting, but it does not help to understand how proper and common nouns function in reality (not in models). Putnam then initiated the empirical study of such nouns to indicate, (i), that the popular Frege-Carnap account of them as (“disguised” compound) predicates is empirically incorrect, and, (ii), that they offer a new paradigm for a naturalistic semantics of natural languages. We take Putnam’s program a couple of steps further. First, we investigate the semantics of common nouns and argue that they refer (to kinds), rather than apply by satisfaction/truth to a designation/denotation. Second, we point to general results about semantics as a theory whose fulcrum is the reference relation rather than satisfaction in models and validity across them. (shrink)

Part 1 sets out the logical/semantical background to ‘On Denoting’, including an exposition of Russell's views in Principles of Mathematics, the role and justification of Frege's notorious Axiom V, and speculation about how the search for a solution to the Contradiction might have motivated a new treatment of denoting. Part 2 consists primarily of an extended analysis of Russell's views on knowledge by acquaintance and knowledge by description, in which I try to show that the discomfiture between Russell's semantical and (...) epistemological commitments begins as far back as 1903. I close with a non-Russellian critique of Russell's views on how we are able to make use of linguistic representations in thought and with the suggestion that a theory of comprehension is needed to supplement semantic theory. (shrink)

Semantic noise, the effect ensuing from the denotative and thus functional variability exhibited by different terms in different contexts, is a common concern in natural language processing (NLP). While unarguably problematic in specific applications (e.g., certain translation tasks), the main argument of this paper is that failing to observe this linguistic matter of fact as a generative effect rather than as an obstacle, leads to actual obstacles in instances where language model outputs are presented as neutral. Given that a common (...) and long-standing challenge in NLP is the interpretation of ambiguous – i.e., semantically noisy – cases, this article focuses on an exemplar ambiguity-resolution task in NLP: the problem of anaphora in Winograd schemas. The main question considered is: to what extent is the standard approach to disambiguation in NLP subject to a stagnant “image of language”? And, can a transdisciplinary, dynamic approach combining linguistics and philosophy elucidate new perspectives on these possible conceptual shortcomings? In order to answer these questions we explore the term and concept of noise, particularly in its presentation as semantic noise. Owing to its definitional plurality, and sometimes even desirable unspecificity, the term noise is thus used as proof of concept for semantic generativity being an inherent characteristic in linguistic representation, and its concept is used to interrogate assumptions admitted in the resolution of Winograd schemas. The argument is speculative and theoretical in method, and the result is an analysis which provides an account of the fundamentally dialogical and necessarily open-ended effects of semantic noise in natural language. (shrink)

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities (...) is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism. (shrink)

SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject which begins when (...) numerals are mentioned (not just used) and mentioned as names of numbers (not just as syntactic objects). Semantic arithmetic leads to many fascinating and surprising algorithms and decision procedures; it reveals in a vivid way the experiential import of mathematical propositions and the predictive power of mathematical knowledge; it provides an interesting perspective for philosophical, historical, and pedagogical studies of the growth of scientific knowledge and of the role metalinguistic discourse in scientific thought. (shrink)

This paper discusses Japanese numeral quantifiers that are used to count individuals, rather than quantities, of a substance, and which may occur either as floated or non-floated quantifiers. It is argued that such morphologically complex numeral quantifiers (NQs) are semantically complex as well: The numeral within the NQ is the quantifier itself, the classifier its domain of quantification. The proposed analysis offers a unified semantic account of floated and non-floated NQs that adheres closely to their surface morphology and syntax. It (...) explains why floated NQs generally force a distributive reading. It covers both classifiers construed with objects and classifiers construed with events. In addition, it captures the fact that the classifier must agree with the NP it is construed with. (shrink)

Previous studies have shown that children retreat from argument‐structure overgeneralization errors (e.g., *Don’t giggle me) by inferring that frequently encountered verbs are unlikely to be grammatical in unattested constructions, and by making use of syntax‐semantics correspondences (e.g., verbs denoting internally caused actions such as giggling cannot normally be used causatively). The present study tested a new account based on a unitary learning mechanism that combines both of these processes. Seventy‐two participants (ages 5–6, 9–10, and adults) rated overgeneralization errors with (...) higher (*The funny man’s joke giggled Bart) and lower (*The funny man giggled Bart) degrees of direct external causation. The errors with more‐direct causation were rated as less unacceptable than those with less‐direct causation. This finding is consistent with the new account, under which children acquire—in an incremental and probabilistic fashion—the meaning of particular constructions (e.g., transitive causative = direct external causation) and particular verbs, rejecting generalizations where the incompatibility between the two is too great. (shrink)

Denotational semantics of logic programming and its extensions have been studied thoroughly for many years. In 1998, a game semantics was given to definite logic programs by Di Cosmo, Loddo, and Nicolet, and a few years later it was extended to deal with negation by Rondogiannis and Wadge. Both approaches were proven equivalent to the traditional semantics. In this paper we define a game semantics for disjunctive logic programs and prove soundness and completeness with respect (...) to the minimal model semantics of Minker. The overall development has been influenced by the games studied for PCF and functional programming in general, in the styles of Abramsky–Jagadeesan–Malacaria and Hyland–Ong–Nickau. (shrink)

The essay motivates and provides a semantics for pictorial representations. A taxonomy of pictorial denoting symbols is developed that determines a semantics which defines the following: S if true in picture Y, S is false in picture Y, S is neither true nor false in picture Y, Z is the content of Picture Y, Picture Y entails that S, Picture Y implies that S. The semantics is then applied to solve or resolve a number of puzzles concerning (...) pictorial representation. (shrink)

This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of (...) doing this, we distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L D I etc. Once the logics are `weaved', further `interaction' axioms can be geometrically motivated and added, and then systematically studied. The methodology is general and is applied to modal and intuitionistic logics as well as to general algebraic logics. We obtain general results on bulk, in the sense that we develop standard combining techniques and refinements which can be applied to any family of initial logics to obtain further combined logics. The main results of this paper is a construction for combining arbitrary, (possibly not normal) modal or intermediate logics, each complete for a class of (not necessarily frame) Kripke models. We show transfer of recursive axiomatisability, decidability and finite model property. Some results on combining logics (normal modal extensions of K) have recently been introduced by Kracht and Wolter, Goranko and Passy and by Fine and Schurz as well as a multitude of special combined systems existing in the literature of the past 20-30 years. We hope our methodology will help organise the field systematically. (shrink)

Abstract I argue that good and right are gradable adjectives as that is understood in the current linguistic theory of gradable adjectives. According that theory, gradable adjectives do not denote properties but contribute meaning in a different yet cognitive way; and if that applies to good and right, then those words contribute meaning and provide evaluativity and normativity by means other than denoting properties. If that is true, significant consequences follow for metaethics, both because of the lack of properties good (...) and right, and because of specific features of the gradable adjective semantics. I outline the theory of good and right as gradable adjectives and explore some of those consequences, attempting to give a sense of what changes we may expect in metaethics. (shrink)

Davidsonian event semantics is often taken to form an unhappy marriage with compositional semantics. For example, it has been claimed to be problematic for semantic accounts of quantification Proceedings of the 16th Amsterdam Colloquium, 2007), for classical accounts of negation Semantics and contextual expression, 1989), and for intersective accounts of verbal coordination. This paper shows that none of this is the case, once we abandon the idea that the event variable is bound at sentence level, and assume (...) instead that verbs denote existential quantifiers over events. Quantificational arguments can then be given a semantic account, negation can be treated classically, and coordination can be modeled as intersection. The framework presented here is a natural choice for researchers and fieldworkers who wish to sketch a semantic analysis of a language without being forced to make commitments about the hierarchical order of arguments, the argument-adjunct distinction, the default scope of quantifiers, or the nature of negation and coordination. (shrink)

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