The paper argues that natural language quantification, as expressed by determiner phrases, is not polysemous. The foil for this claim is Hofweber, who contends that natural language quantification is polysemous between a domain reading and an inferential reading. The thesis is intended to support a more general division between externalist and internalist positions in semantics. The paper, to the contrary, argues that there is no linguistic evidence for polysemous quantification, and Hofweber’s proposal proves to be non-compositional. Further, an approach at (...) least consistent with internalism is available independent of an inferential reading, for natural language quantification can be read as ontologically neutral, which removes the rationale for the polysemy hypothesis. The paper remains neutral on so-called heavyweight vs. lightweight construals of quantification, which are not claims about natural language semantics. (shrink)

In this paper we adopt the hypothesis that languages are mechanisms for interaction, and that grammars encode the means by which such interaction may take place, by use of procedures that construct representations of meaning from strings of words uttered in context, and conversely strings of words are built up from representations of content in interaction with context. In a review of the systemic use of ellipsis in dialogue and associated split-utterance phenomena, we show how, in Dynamic Syntax, words give (...) rise to a range of procedures for the building of representations of the content of some utterance, which both speakers and hearers use. We then extend the discussion to take account of adjuncts, showing how they contribute to content construction both in single utterances and across speakers. The same mechanisms are then shown to underlie the building of inferential extensions of meaning in context, giving rise to the creation of the ad hoc concepts expressed by phrases or single words in relation to the utterance context and ultimately to the creation of metaphorical uses of language. (shrink)

This paper develops a formal model of the subtle meaning differences that exist between grammatical alternatives in socially conditioned variation and how these variants can be used by speakers as resources for constructing personal linguistic styles. More specifically, this paper introduces a new formal system, called social meaning games, which allows for the unification of variationist sociolinguistics and game-theoretic pragmatics, two fields that have had very little interaction in the past. Although remarks have been made concerning the possible usefulness of (...) game-theoretic tools in the analysis of certain kinds of socially conditioned linguistic phenomena :645–668, 1977; Dror et al. in Lang Linguist Compass 7:561–579, 2013; in Lang Linguist Compass 8:230–242, 2014; Clark in Meaningful games: Exploring language with game theory, MIT Press, Cambridge, MA, 2014, among others), a general framework uniting game-theoretic pragmatics and quantitative sociolinguistics has yet to be developed. This paper constructs such a framework through giving a formalization of the Third Wave approach to the meaning of variation using signalling games and a probabilistic approach to speaker/listener beliefs of the kind commonly used in the Bayesian game-theoretic pragmatics framework :3–44, 2016, for recent overviews). (shrink)

The meaning of most words in language depends on their context. Understanding how the human brain extracts contextualized meaning, and identifying where in the brain this takes place, remain important scientific challenges. But technological and computational advances in neuroscience and artificial intelligence now provide unprecedented opportunities to study the human brain in action as language is read and understood. Recent contextualized language models seem to be able to capture homonymic meaning variation (“bat”, in a baseball vs. a vampire context), as (...) well as more nuanced differences of meaning—for example, polysemous words such as “book”, which can be interpreted in distinct but related senses (“explain a book”, information, vs. “open a book”, object) whose differences are fine‐grained. We study these subtle differences in lexical meaning along the concrete/abstract dimension, as they are triggered by verb‐noun semantic composition. We analyze functional magnetic resonance imaging (fMRI) activations elicited by Italian verb phrases containing nouns whose interpretation is affected by the verb to different degrees. By using a contextualized language model and human concreteness ratings, we shed light on where in the brain such fine‐grained meaning variation takes place and how it is coded. Our results show that phrase concreteness judgments and the contextualized model can predict BOLD activation associated with semantic composition within the language network. Importantly, representations derived from a complex, nonlinear composition process consistently outperform simpler composition approaches. This is compatible with a holistic view of semantic composition in the brain, where semantic representations are modified by the process of composition itself. When looking at individual brain areas, we find that encoding performance is statistically significant, although with differing patterns of results, suggesting differential involvement, in the posterior superior temporal sulcus, inferior frontal gyrus and anterior temporal lobe, and in motor areas previously associated with processing of concreteness/abstractness. (shrink)

This paper aims to shed new light on certain philosophical theories of perceptual experience by examining the semantics of perceptual ascriptions such as “Jones sees an apple.” I start with the assumption, recently defended elsewhere, that perceptual ascriptions lend themselves to intensional readings. In the first part of the paper, I defend three theses regarding such readings: I) intensional readings of perceptual ascriptions ascribe phenomenal properties, II) perceptual verbs are not ambiguous between intensional and extensional readings, and III) intensional perceptual (...) ascriptions have a relational form. The second part of the paper describes the implications of I-III for theories of perceptual experience. I argue that I-III support and reconcile the three main views of perceptual experience, relationalism, disjunctivism, and representationalism. However, I-III leave open at least one important point of contention: particularism, the view that we experience external objects. I conclude by exploring the implications of accepting or denying particularism given I-III. (shrink)

We describe a knowledge representation and inference formalism, based on an intensional propositional semantic network, in which variables are structures terms consisting of quantifier, type, and other information. This has three important consequences for natural language processing. First, this leads to an extended, more natural formalism whose use and representations are consistent with the use of variables in natural language in two ways: the structure of representations mirrors the structure of the language and allows re-use phenomena such as pronouns and (...) ellipsis. Second, the formalism allows the specification of description subsumption as a partial ordering on related concepts (variable nodes in a semantic network) that relates more general concepts to more specific instances of that concept, as is done in language. Finally, this structured variable representation simplifies the resolution of some representational difficulties with certain classes of natural language sentences, namely, donkey sentences and sentences involving branching quantifiers. The implementation of this formalism is called ANALOG (A NAtural LOGIC) and its utility for natural language processing tasks is illustrated. (shrink)

This paper introduces Richard Montague's theory of determiner phrases to the philosophically oriented readers who are familiar with Russell's traditional treatment. Determiner phrases include not only quantifier phrases in the narrow sense, such as every man, some woman, and nothing, but also DP conjunctions such as Adam and Betty and Adam or Betty, and even proper names such as Adam and Betty. Montague treats all determiner phrases as belonging to type t, i.e., the type of functions from properties of individuals (...) to truth values. This paper also introduces the simply typed lambda-calculus for the explication of Montague's theory. Two major problems with Montague's theory, one more philosophical and the other more linguistic, are discussed. (shrink)

This paper is about the semantic analysis of referentially opaque verbs like seek and owe that give rise to nonspecific readings. It is argued that Montague's categorization (based on earlier work by Quine) of opaque verbs as properties of quantifiers runs into two serious difficulties: the first problem is that it does not work with opaque verbs like resemble that resist any lexical decomposition of the seek ap try to find kind; the second one is that it wrongly predicts de (...) dicto (i.e. narrow scope) readings due to quantified noun phrases in the object positions of such verbs. It is shown that both difficulties can be overcome by an analysis of opaque verbs as operating on properties. This is a strongly modified version of a paper entitled lsquoDo We Bear Attitudes towards Quantifiers?rsquo that I have presented at conferences in Gosen (Gesellschaft für Sprachwissenschaft), Ithaca (SALT I), and Konstanz (Lexikon). I owe a special debt to Hans Kamp and Arnim von Stechow for shaping my views on the subject of this paper during the past ten years or so. Comments from and discussions with the following friends and colleagues have also led to considerable improvements: Heinrich Beck, Steve Berman, David Dowty, Veerle van Geenhoven, Fritz Hamm, Irene Heim, Wolfgang Klein, Angelika Kratzer, Michael Morreau, Barbara Partee, Mats Rooth, Roger Schwarzschild, Wolfgang Sternefeld, Emil Weydert, Henk Zeevat, and three referees. (shrink)

The paper is about the interpretation of opaque verbs like “seek”, “owe”, and “resemble” which allow for unspecific readings of their (indefinite) objects. It is shown that the following two observations create a problem for semantic analysis: (a) The opaque position is upward monotone: “John seeks a unicorn” implies “John seeks an animal”, given that “unicorn” is more specific than “animal”. (b) Indefinite objects of opaque verbs allow for higher-order, or “underspecific”, readings: “Jones is looking for something Smith is looking (...) for” can express that there is something unspecific that both Jones and Smith are looking for. Given (a) and (b), it would seem that the following inference is hard to escape, if the premisses are construed unspecifically and the conclusion is taken on its under- specific reading: Jones is looking for a sweater. Smith is looking for a pen. Smith is looking for something Jones is looking for. (shrink)

We treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it is no less obvious that ambiguous propositions entail other propositions, and are entailed by other propositions. This article gives a formal analysis of the underlying mechanisms, both from an algebraic and a logical point of view. The main result can be summarized as follows: sound reasoning with ambiguity requires a distinction between equivalence on the one and congruence on the other side: the (...) fact that \ entails \ does not imply \ can be substituted for \ in all contexts preserving truth. Without this distinction, we will always run into paradoxical results. We present the sequent calculus \, which we conjecture implements sound and complete propositional reasoning with ambiguity, and provide it with a language-theoretic semantics, where letters represent unambiguous meanings and concatenation represents ambiguity. (shrink)

In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out of (...) variable assignments. But this has disquieting consequences, including Fine’s antinomy of the variable and an undue dependence of meanings on language. Here I develop an alternative, Fregean version of predicate logic that uses the traditional quantifier–variable apparatus for the expression of generality, possesses a fully compositional, non-representational semantics, and is not subject to the antinomy of the variable. The advantages of Fregean over Tarskian predicate logic are due to the former’s treating variables not as meaningful lexical items, but as mere marks of punctuation, similar to parentheses. I submit that this is indeed how the variables of predicate logic should be construed. (shrink)

This paper reports on an approach to model generalized implicatures using nonmonotonic logics. The approach, called compositional, is based on the idea of compositional semantics, where the implicatures carried by a sentence are constructed from the implicatures carried by its constituents, but it also includes some aspects nonmonotonic logics in order to model the defeasibility of generalized implicatures.

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

Systematic semantic ambiguities result from the interaction of the two operations that are involved in resolving ellipsis in the presence of scoping elements such as quantifiers and intensional operators: scope determination for the scoping elements and resolution of the elided relation. A variety of problematic examples previously noted - by Sag, Hirschbüihler, Gawron and Peters, Harper, and others - all have to do with such interactions. In previous work, we showed how ellipsis resolution can be stated and solved in equational (...) terms. Furthermore, this equational analysis of ellipsis provides a uniform framework in which interactions between ellipsis resolution and scope determination can be captured. As a consequence, an account of the problematic examples follows directly from the equational method. The goal of this paper is merely to point out this pleasant aspect of the equational analysis, through its application to these cases. No new analytical methods or associated formalism are presented, with the exception of a straightforward extension of the equational method to intensional logic. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis , is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken to be (...) that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

Magnetism in meta-semantics is the view that the meaning of our words is determined in part by their use and in part by the objective naturalness of candidate meanings. This hypothesis is commonly attributed to David Lewis, and has been put to philosophical work by Brian Weatherson, Ted Sider and others. I argue that there is no evidence that Lewis ever endorsed the view, and that his actual account of language reveals good reasons against it.

I give shape to a neglected debate in metaphysics, the debate over the ontological priority between individuality and collectivity. I distinguish the debate from more familiar ones in the recent literature and articulate what I call ontological collectivism, the view that collectivity is prior to individuality. I defend the in-principle intelligibility of the view from forceful general objections and argue that not only is it coherent but also of significant interest to the literature: it allows for overlooked alternatives on a (...) variety of central discussions. (shrink)

A system of tensed intensional logic excluding iterations of intensions is introduced. Instead of using the type symbols (for ‘sense’), extensional and intensional functor types are distinguished. A peculiarity of the semantics is the general acceptance of value-gaps (including truth-value-gaps): the possible semantic values (extensions) of extensional functors are partial functions. Some advantages of the system (relatively to R. Montague's intensional logic) are briefly indicated. Also, applications for modelling natural languages are illustrated by examples.

IntroductionThe project of giving an account of meaning in natural languages goes largely by assigning truth-conditional content to sentences. I will call the view that sentences have truth-conditional content propositionalism as it is common to identify the truth-conditional content of a sentence with the proposition it expresses. This content plays an important role in our explanations of the speech-acts, attitude ascriptions, and the meaning of sentences when they appear as parts of longer sentences. Much work in philosophy of language and (...) linguistics semantics over the last half-century has aimed to characterize the truth-conditional content of different aspects of language.There are different kinds of worries one might have about this project. There are general methodological worries about truth-conditional semantics that have had some currency in the philosophical literature. In my view, the enormous progress in semantics made in its brief history suggests these are misplaced. Ho .. (shrink)

Naturalized metaphysics is based on the idea that philosophy should be guided by the sciences. The paradigmatic science that is relevant for metaphysics is physics because physics tells us what fundamental reality is ultimately like. There are other sciences, however, that de facto play a role in philosophical inquiries about what there is, one of them being the science of language, i.e. linguistics. In this paper I will be concerned with the question what role linguistics should and does play for (...) the metametaphysical question of how our views about fundamental reality can be reconciled with the everyday truisms about what there is. I will present several examples of two kinds of approaches to this question, linguistics-based accounts and purely philosophical accounts, and will discuss their respective methodological merits and shortcomings. In the end I will argue that even proponents of a purely philosophical answer to the metametaphysical question should take the results of linguistics seriously. (shrink)

There is a longstanding discussion whether wide-scope indefinites denote choice functions that are existentially bound or remain free. Data from Ga, an under-researched language spoken in Ghana, show that there are wide-scope indefinites denoting existentially bound skolemized choice functions whose parameter is bound by a higher quantificational NP, free skolemized choice functions with the speaker or a higher quantificational NP as a parameter, and narrow scope quantificational indefinites. Thus the data show that both existentially bound and free skolemized choice functions (...) are attested in natural language shedding new light on the semantics of indefinites. (shrink)

Two kinds of theoretical framework for syntax are encountered in current linguistics. One emerged from the mathematization of proof theory, and is referred to here as generative-enumerative syntax (GES). A less explored alternative stems from the semantic side of logic, and is here called model-theoretic syntax (MTS). I sketch the outlines of each, and give a capsule summary of some mathematical results pertaining to the latter. I then briefly survey some diverse types of evidence suggesting that in some ways MTS (...) seems better suited to theorizing about the relevant linguistic phenomena. (shrink)

We argue that formal linguistic theory, properly extended, can provide a unifying framework for diverse phenomena beyond traditional linguistic objects. We display applications to pictorial meanings, visual narratives, music, dance, animal communication, and, more abstractly, to logical and non-logical concepts in the ‘language of thought’ and reasoning. In many of these cases, a careful analysis reveals that classic linguistic notions are pervasive across these domains, such as for instance the constituency (or grouping) core principle of syntax, the use of logical (...) variables (for object tracking), or the variety of inference types investigated in semantics/pragmatics. The aim of this overview is to show how the application of formal linguistic concepts and methodology to non-linguistic objects yields non-trivial insights, thus opening the possibility of a general, precise theory of signs. (An appendix, found in the online supplements to this article, surveys applications of Super Linguistics to animal communication.). (shrink)

We argue that formal linguistic theory, properly extended, can provide a unifying framework for diverse phenomena beyond traditional linguistic objects. We display applications to pictorial meanings, visual narratives, music, dance, animal communication, and, more abstractly, to logical and non-logical concepts in the ‘language of thought’ and reasoning. In many of these cases, a careful analysis reveals that classic linguistic notions are pervasive across these domains, such as for instance the constituency (or grouping) core principle of syntax, the use of logical (...) variables (for object tracking), or the variety of inference types investigated in semantics/pragmatics. The aim of this overview is to show how the application of formal linguistic concepts and methodology to non-linguistic objects yields non-trivial insights, thus opening the possibility of a general, precise theory of signs. (An appendix, found in the online supplements to this article, surveys applications of Super Linguistics to animal communication.). (shrink)

This paper starts from the observation that the standard arguments for compositionality are really arguments for the computability of semantics. Since computability does not entail compositionality, the question of what justifies compositionality recurs. The paper then elaborates on the idea of recursive semantics as corresponding to computable semantics. It is then shown by means of time complexity theory and with the use of term rewriting as systems of semantic computation, that syntactically unrestricted, noncompositional recursive semantics leads to computational explosion (factorial (...) complexity). Hence, with combinatorially unrestricted syntax, semantics with tractable time complexity is compositional. (shrink)

This article deals with the semantics of “double-access” sentences. They are defined as English sentences which have a past tense morpheme in the matrix clause and a present tense morpheme in a subordinate clause in the immediate scope of the matrix past tense. They receive a very peculiar interpretation, which we will refer to as a “double-access interpretation.” The episode described in the embedded clause makes reference to two times: the time referred to by the matrix predicate and the utterance (...) time of the whole sentence. Previous studies on this construction are largely descriptive and do not attempt to analyze it formally, with one important exception. Abusch (1991) addresses the problems connected with the construction and proposes that double-access interpretations involvede re attitudes about intervals. Her proposal contains an important insight and provides one possible account of the double-access construction. My proposal was independently developed at approximately the same time as Abusch's and offers an alternative explanation for the phenomena. I consider a series of hypotheses and conclude that double-access readings involvede re attitude reports about state individuals. This account is couched in an eventuality-based framework and employs the techniques proposed by Cresswell and von Stechow (1982). In order to yield the desired reading, the tense must first adjoin to the complement S, then to the matrix S, leaving two traces in the process. (shrink)

Recently, philosophers have offered compelling reasons to think that demonstratives are best represented as variables, sensitive not to the context of utterance, but to a variable assignment. Variablists typically explain familiar intuitions about demonstratives—intuitions that suggest that what is said by way of a demonstrative sentence varies systematically over contexts—by claiming that contexts initialize a particular assignment of values to variables. I argue that we do not need to link context and the assignment parameter in this way, and that we (...) would do better not to. (shrink)

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties with respect (...) to model theory and/or proof theory, difficulties which the current proposals are intended to resolve.Lambek calculus is complete for interpretation byresiduation with respect to the adjunction operation of groupoid algebras (Buszkowski 1986). In Moortgat and Morrill (1991) it is shown how to give calculi for families of categorial operators, each defined by residuation with respect to an operation of prosodic adjunction (associative, non-associative, or with interactive axioms). The present paper treats discontinuity in this way, by residuation with respect to three adjunctions: + (associative), (.,.) (split-point marking), andW (wrapping) related by the equations 1+s 2+s 3=(s 1,s 3)Ws 2. We show how the resulting methods apply to discontinuous functors, quantifier scope and quantifier scope ambiguity, pied piping, and subject and object antecedent reflexivisation. (shrink)

According to a widely shared generic conception of inferential justification—‘the standard conception’—an agent is inferentially justified in believing that p only if she has antecedently justified beliefs in all the non-redundant premises of a good argument for p. This conception tends to serve as the starting-point in contemporary debates about the nature and scope of inferential justification: as neutral common ground between various competing, more specific, conceptions. But it’s a deeply problematic starting-point. This paper explores three questions that haven’t been (...) given the attention they deserve, that complicate the application of the standard conception to cases, and that reveal it to be underspecified at the core—in ways that aren’t resolved but inherited by more specific (extant) versions of it. The goal isn’t to answer the questions, but to articulate them, explain what turns on them, and invite a critical re-examination of the standard conception. (shrink)

I present a concrete DRT-based syntax and semantics for the representation of mental states in the style of Kamp. This system is closely related to Recanati’s Mental Files framework, but adds a crucial distinction between anchors, the analogues of mental files, and attitudes like belief, desire and imagination. Attitudes are represented as separate compartments that can be referentially dependent on anchors. I show how the added distinctions help defend the useful notion of an acquaintance-based mental file against Ninan’s :368–377 2015) (...) recent challenge involving counterfactual de re attitudes. (shrink)

Attitudinal propositionalism is the view that all mental attitude content is truth-evaluable. While attitudinal propositionalism is still silently assumed in large parts of analytic philosophy, recent work on objectual attitudes (i.e. attitudes like ‘fearing Moriarty’ and ‘imagining a unicorn’ that are reported through intensional transitive verbs with a direct object) has put attitudinal propositionalism under explanatory pressure. This paper defends propositionalism for a special subclass of objectual attitudes, viz. experiential attitudes. The latter are attitudes like seeing, remembering, and imagining whose (...) grammatical objects intuitively denote (events or) scenes. I provide a propositional analysis of experiential attitudes that preserves the merits of propositionalism. This analysis uses the possibility of representing the target-scenes of experiential attitudes by the intersection of all propositions that are true in these scenes. I show that this analysis makes available the usual (Russellian) account of intensionality and the common (Boolean) logic for entailments. (shrink)

We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the sorites paradox, (...) with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (shrink)

According to the computational theory of mind , to think is to compute. But what is meant by the word 'compute'? The generally given answer is this: Every case of computing is a case of manipulating symbols, but not vice versa - a manipulation of symbols must be driven exclusively by the formal properties of those symbols if it is qualify as a computation. In this paper, I will present the following argument. Words like 'form' and 'formal' are ambiguous, as (...) they can refer to form in either the syntactic or the morphological sense. CTM fails on each disambiguation, and the arguments for CTM immediately cease to be compelling once we register that ambiguity. The terms 'mechanical' and 'automatic' are comparably ambiguous. Once these ambiguities are exposed, it turns out that there is no possibility of mechanizing thought, even if we confine ourselves to domains where all problems can be settled through decision-procedures. The impossibility of mechanizing thought thus has nothing to do with recherché mathematical theorems, such as those proven by Gödel and Rosser. A related point is that CTM involves, and is guilty of reinforcing, a misunderstanding of the concept of an algorithm. (shrink)

Cooper storage is a widespread technique for associating sentences with their meanings, used in diverse linguistic and computational linguistic traditions. This paper encodes the data structures and operations of cooper storage in the simply typed linear \-calculus, revealing the rich categorical structure of a graded applicative functor. In the case of finite cooper storage, which corresponds to ideas in current transformational approaches to syntax, the semantic interpretation function can be given as a linear homomorphism acting on a regular set of (...) trees, and thus generation can be done in polynomial time. (shrink)

A sentence like every circle is blue might be understood in terms of individuals and their properties or in terms of a relation between groups. Relatedly, theorists can specify the contents of universally quantified sentences in first-order or second-order terms. We offer new evidence that this logical first-order vs. second-order distinction corresponds to a psychologically robust individual vs. group distinction that has behavioral repercussions. Participants were shown displays of dots and asked to evaluate sentences with each, every, or all combined (...) with a predicate. We find that participants are better at estimating how many things the predicate applied to after evaluating sentences in which universal quantification is indicated with every or all, as opposed to each. We argue that every and all are understood in second-order terms that encourage group representation, while each is understood in first-order terms that encourage individual representation. Since the sentences that participants evaluate are truth-conditionally equivalent, our results also bear on questions concerning how meanings are related to truth-conditions. (shrink)

It has been argued that the primary acquisition of genericity in early child speech poses a problem for standard quantificational approaches to generics and instead motivates the claim that generics give voice to an innate, default mode of generalising. This article argues that analogous puzzles involving the acquisition of A‐quantifiers undermine the empirical support for a purely cognition‐based approach to generics. Instead, these acquisition puzzles should be solved by generalising the core insight of the cognitive defaults theory to these expressions, (...) reconciling formal semantic approaches with the role that cognitive development plays on lexical competence. (shrink)