The presupposition triggered by an expression E is generally satisfied by information that comes before rather than after E in the sentence or discourse. In Heim’s classic theory (1983), this left-right asymmetry is encoded in the lexical semantics of dynamic connectives and operators. But several recent analyses offer a more nuanced approach, in which presupposition satisfaction has two separate components: a general principle (which varies from theory to theory) specifies under what conditions a presupposition triggered by an expression E is (...) satisfied; and an ‘incremental’ component specifies that the principle must be checked on the basis of information that comes before E. Several researchers take this incremental component to be a processing bias, which can be overcome at some cost. If so, it should be possible, though costly, to satisfy presuppositions ‘symmetrically’, i.e. by taking into account linguistic material that comes both before and after the presupposition trigger. We test this claim with experimental means. Using inferential (and to some extent acceptability) tasks involving the anaphoric trigger aussi (‘too’) in French, we argue that symmetric readings are indeed possible (albeit degraded) in environments involving the connectives if, or, and unless. (shrink)

Linguists often sharply distinguish the different modules that support linguistics competence, e.g., syntax, semantics, pragmatics. However, recent work has identified phenomena in syntax (polarity sensitivity) and pragmatics (implicatures), which seem to rely on semantic properties (monotonicity). We propose to investigate these phenomena and their connections as a window into the modularity of our linguistic knowledge. We conducted a series of experiments to gather the relevant syntactic, semantic and pragmatic judgments within a single paradigm. The comparison between these quantitative data leads (...) us to four main results, (i) Our results support a departure from one element of the classical Gricean approach, thus helping to clarify and settle an empirical debate. This first outcome also confirms the soundness of the methodology, as the results align with standard contemporary accounts of scalar implicature (SI), (ii) We confirm that the formal semantic notion of monotonicity underlies negative polarity item (NPI) syntactic acceptability, but (iii) our results indicate that the notion needed is perceived monotonicity. We see results (ii) and (iii) as the main contribution of this study: (ii) provides an empirical interpretation and confirmation of one of the insights of the model-theoretic approach to semantics, while (iii) calls for an incremental, cognitive implementation of the current generalizations, (iv) Finally, our results do not indicate that the relationship between NPI acceptability and monotonicity is mediated by pragmatic features related to Sis: this tells against elegant attempts to unify polarity sensitivity and Sis (pioneered by Krifka and Chierchia). These results illustrate a new methodology for integrating theoretically rigorous work in formal semantics with an experimentally-grounded cognitively-oriented view of linguistic competence. (shrink)

“Scalar implicatures” is a phrase used to refer to some inferences arising from the competition between alternatives: typically, “Mary read some of the books” ends up conveying that Mary did not read all books, because one could have said “Mary read all books”. The so-called grammatical theory argues that these inferences obtain from the application of a covert operator \, which not only has the capability to negate alternative sentences, but also the capability to be embedded within sentences under other (...) linguistic operators, i.e. \ has the potential to add to the meaning of expressions, the negation of their alternatives. This view typically seeks support from the existence of readings that could not be explained without the extra-capability of \ to occur in embedded positions. However, if some embedded positions seem to be accessible to \, not all conceivable positions that \ could occupy yield sensible results. In short: the \ approach is powerful, maybe too powerful. Various approaches based on logical strength and monotonicity have been proposed to justify on principled grounds the limited distribution of \; these approaches are mostly based on a comparison between possible parses, and considerations of monotonicity. We propose a new constraint based instead on “connectedness”, ruling out parses because of inherent problems their outcome may raise. Connectedness is a sister notion of monotonicity, which has been recruited to explain certain lexical restrictions on nouns, adjectives and more recently quantifiers; we propose here that connectedness could play a similar role at the level of propositional meanings. (shrink)

“Scalar implicatures” is a phrase used to refer to some inferences arising from the competition between alternatives: typically, “Mary read some of the books” ends up conveying that Mary did not read all books, because one could have said “Mary read all books”. The so-called grammatical theory argues that these inferences obtain from the application of a covert operator \, which not only has the capability to negate alternative sentences, but also the capability to be embedded within sentences under other (...) linguistic operators, i.e. \ has the potential to add to the meaning of expressions, the negation of their alternatives. This view typically seeks support from the existence of readings that could not be explained without the extra-capability of \ to occur in embedded positions. However, if some embedded positions seem to be accessible to \, not all conceivable positions that \ could occupy yield sensible results. In short: the \ approach is powerful, maybe too powerful. Various approaches based on logical strength and monotonicity have been proposed to justify on principled grounds the limited distribution of \; these approaches are mostly based on a comparison between possible parses, and considerations of monotonicity. We propose a new constraint based instead on “connectedness”, ruling out parses because of inherent problems their outcome may raise. Connectedness is a sister notion of monotonicity, which has been recruited to explain certain lexical restrictions on nouns, adjectives and more recently quantifiers; we propose here that connectedness could play a similar role at the level of propositional meanings. (shrink)

We argue that the pictorial nature of certain constructions in signs and in gestures explains surprising properties of their syntax. In several sign languages, the standard word order (e.g. SVO) gets turned into SOV (with preverbal arguments) when the predicate is a classifier, a distinguished construction with highly iconic properties (e.g. Pavlič, 2016). In silent gestures, participants also prefer an SOV order in extensional constructions, irrespective of the word order of the language they speak (Goldin-Meadow et al., 2008). But in (...) silent gestures and in Brazilian Sign Language (Libras), intensional constructions can override these SOV preferences, yielding SVO instead (Schouwstra & de Swart, 2014; Napoli et al., 2017). This distinction was argued to be due to iconicity: arguments are expressed before the verb if they correspond to entities that are present before the action, otherwise they follow the verb. While agreeing with this intuition, we propose that the extensional/intensional distinction is neither empirically nor theoretically appropriate. In new data from American Sign Language, we replicate the distinction among extensional classifier predicates: for _x ate up the ball_, the ball is typically seen before the eating and a preposed object is preferred; but for _x spit out the ball_, the ball is typically seen after the spitting and a postposed object is preferred, although both _eat up_ and _spit out_ are used extensionally. We extend this finding to data involving pro-speech (= speech-replacing) gestures embedded in French sentences. We argue for a Visibility Generalization according to which arguments appear before the verb if their denotations are typically visible before the action, and we develop a new formal account within a pictorial semantics for visual animations (inspired by Greenberg and Abusch). It derives the observed word order preferences, it explains how the semantics of classifier predicates combines iconic and conventional properties, and it makes a more general point: sign language semantics combines logical semantics with pictorial semantics. (shrink)

Cultural accounts of scientific ideas and practices have increasingly come to be welcomed as a corrective to previous—and still widely held—theories of scientific knowledge and practices as universal. The editors caution, however, against the temptation to overgeneralize the work of culture, and to lapse into a kind of essentialism that flattens the range and variety of scientific work. The book refers to this tendency as culturalism. The contributors to the volume model a new path where historicized and cultural accounts of (...) scientific practice retain their specificity and complexity without falling into the traps of culturalism. They examine, among other issues, the potential of using notions of culture to study behavior in financial markets; the ideology, organization, and practice of earthquake monitoring and prediction during China's Cultural Revolution; the history of quadratic equations in China; and how studying the "glass ceiling" and employment discrimination became accepted in the social sciences. Demonstrating the need to understand the work of culture as a fluid and dynamic process that directly both shapes and is shaped by scientific practice, Cultures without Culturalism makes an important intervention in science studies. Contributors. Bruno Belhoste, Karine Chemla, Caroline Ehrhardt, Fa-ti Fan,Kenji Ito, Evelyn Fox Keller, Guillaume Lachenal, Donald MacKenzie, Mary S. Morgan, Nancy J. Nersessian, David Rabouin, Hans-Jörg Rheinberger, Claude Rosental, Koen Vermeir. (shrink)

The ArgumentTo highlight speculative trends specific to the mathematical tradition that developed in China, the paper analyzes an excerpt of a third-century commentary on a mathematical classic, which arguably contains a proof. The paper shows that the following three tasks cannot be dissociated one from the other: (1) to discuss how the ancient text should be read; (2) to describe the practice of mathematical proof to which this text bears witness; (3) to bring to light connections between philosophy and mathematics (...) that it demonstrates were established in China. To this end the paper defines its use of the word “proof” and outlines a program for an international history of mathematical proof. It describes the sense in which the text conveys a proof and shows how it simultaneously fulfills algorithmic ends, bringing to light a formal pattern that appears to be fundamental both for mathematics and for other domains of reality. The interest in transformations that mathematical writings demonstrate in China at that time seems to have been influenced by philosophical developments based onThe Book of Changes (Yi-jing), which the excerpt quotes. This quotation within a mathematical context makes it possible to suggest an interpretation for a rather difficult philosophical statement. (shrink)

This is the first book-length analysis of the techniques and procedures of ancient mathematical commentaries. It focuses on examples in Chinese, Sanskrit, Akkadian and Sumerian, and Ancient Greek, presenting the general issues by constant detailed reference to these commentaries, of which substantial extracts are included in the original languages and in translation, sometimes for the first time. This makes the issues accessible to readers without specialized training in mathematics or in the languages involved. The result is a much richer understanding (...) than was hitherto possible of the crucial role of commentaries in the history of mathematics in four different linguistic areas, of the nature of mathematical commentaries in general, of the contribution that the study of mathematical commentaries can make to the history of science and to the study of commentaries in general, and of the ways in which mathematical commentaries are like and unlike other kinds of commentaries. (shrink)

This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove (...) the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof. (shrink)

Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how individuals have valued generality and how they have worked with specific types of "general" entities, (...) procedures, and arguments. (shrink)

The book presents the outcomes of an innovative research programme in the history of science and implements a Text Act Theory which extends Speech Act Theory, in order to illustrate a new approach to texts and textual communicative acts. It examines assertives (absolute or conditional statements, forecasts, insurance, etc.), directives, declarations and enumerations, as well as different types of textual units allowing authors to perform these acts: algorithms, recipes, prescriptions, lexical templates for terminological studies and enumerative structures. The book relies (...) on the study of a broad range of documents of the past dealing with various domains: mathematics, zoology, medicine, lexicography. The documents examined come from scholarly sources from different parts of the world, such as China, Europe, India, Mesopotamia and are written in a variety of European languages as well as Chinese, Cuneiform and Sanskrit. This approach proves fruitful in both history of science and Text Act Theory. (shrink)

A multiplicity of circumstances - including geographic and political isolation, and differences of social organization and customs - has led different groups of people to develop mathematical knowledge independently of each other. Yet history has shown us again and again that by some necessity these separate groups often encounter the same problems. The solutions they propose, however, are often different. This suggests a series of questions. First of all: what is the relationship between the solutions? Is one solution an alternative (...) to the other, and if so, how to account for their differences? Or, on the contrary, are the solutions complementary? Both of these configurations can be found in the history of mathematics: in the following article we will investigate two elementary examples of these phenomena and trace the historical circumstances under which different solutions have come into contact. (shrink)

Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to identify (...) truth-value gaps. Method A consists in collecting both truth judgments and, independently, falsity judgments. The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent. We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value. (shrink)

Things we can say, and the ways in which we can say them, compete with one another. And this has consequences: words we decide not to pronounce have critical effects on the messages we end up conveying. For instance, in saying Chris is a good teacher, we may convey that Chris is not an amazing teacher. How this happens is an unsolvable problem, unless a theory of alternatives indicates what counts, among all the things that have not been pronounced. It (...) is sometimes assumed, explicitly or implicitly, that any word counts, as long as that word could have replaced one that was actually pronounced. We review arguments for going beyond this powerful idea. In doing so, we argue that the level of words is not the right level of analysis for alternatives. Instead, we capitalize on recent conceptual and associated methodological advances within the study of the so-called “language of thought” to reopen the problem from a new perspective. Specifically, we provide theoretical and experimental arguments that the relation between alternatives and words may be indirect, and that alternatives are not merely linguistic objects in the traditional sense. Rather, we propose that competition in language is significantly determined by general reasoning preferences, or thought preferences. We propose that such non-linguistic preferences can be measured and that these measures can be used to explain linguistic competition, non-linguistically, and more in depth. (shrink)

In this article we refine the design of context shifting experiments, which play a central role in contextualist debates, and we subject a large number of scenarios involving different types of expressions of interest to contextualists, including ‘know’ and color adjectives like ‘green’, to experimental investigation. Our experiment (i) reveals an effect of changing contexts on the evaluation of uses of the sentences that we examine, thereby overturning the absence of results reported in previous experimental studies (so‐called null results), (ii) (...) uncovers evidence for a ‘truth bias' in favor of positive over negative sentences, and (iii) reveals previously unnoticed distinctions between the strength of the contextual effects displayed by scenarios involving knowledge ascriptions and scenarios concerning color and other miscellaneous scenarios. (shrink)

This paper concerns the central method of generating evidence in support of contextualist theories, what we call context shifting experiments. We begin by explaining the standard design of context shifting experiments, which are used in both quantitative surveys and more traditional thought experiments to show how context affects the content of natural language expressions. We discuss some recent experimental studies that have tried and failed to find evidence that confirms contextualist predictions about the results of context shifting experiments, and consider (...) the criticisms of those studies made by DeRose (forthcoming). We show that DeRose's criticisms are incomplete, and we argue that the design of context shifting experiments he proposes is itself subject to some of the same problems as the studies he criticizes. We propose a refined approach to the design of context shifting experiments that addresses these problems and which allows us to to investigate the effect of context on both positive and negative sentences. This aspect of our design allows us to control for several forms of bias, including a particular form of "truth bias" that favors positive over negative sentences. We then deploy our improved design in an experiment that tests a large number of scenarios involving different types of expressions of interest to contextualists, including "know" and color adjectives like "green". Our experiment (i) reveals an effect of changing contexts on the evaluation of uses of the sentences that we examined, thereby overturning the absence of results reported in previous experimental studies (so-called null results) and (ii) reveals previously unnoticed distinctions between the strength of the contextual effects we observed for scenarios involving knowledge ascriptions and for scenarios concerning color and other miscellaneous scenarios. (shrink)

Are color adjectives ("red", "green", etc.) relative adjectives or absolute adjectives? Existing theories of the meaning of color adjectives attempt to answer that question using informal ("armchair") judgments. The informal judgments of theorists conflict: it has been proposed that color adjectives are absolute with standards anchored at the minimum degree on the scale, that they are absolute but have near-midpoint standards, and that they are relative. In this paper we report two experiments, one based on entailment patterns and one based (...) on presupposition accommodation, that investigate the meaning of scalar adjectives. We find evidence confirming the existence of subgroups of the population who operate with different standards for color adjectives. The evidence of interpersonal variation in where standards are located on the relevant scale and how those standards can be adjusted indicates that the existing theories of the meaning of color adjectives are at best only partially correct. We also find evidence that paradigmatic relative adjectives ("tall", "wide") behave in ways that are not predicted by the standard theory of scalar adjectives. We discuss several different possible explanations for this unexpected behavior. We conclude by discussing the relevance of our findings for philosophical debates about the nature and extent of semantically encoded context sensitivity in which color adjectives have played a key role. (shrink)

J.L. Austin is regarded as having an especially acute ear for fine distinctions of meaning overlooked by other philosophers. Austin employs an informal experimental approach to gathering evidence in support of these fine distinctions in meaning, an approach that has become a standard technique for investigating meaning in both philosophy and linguistics. In this paper, we subject Austin's methods to formal experimental investigation. His methods produce mixed results: We find support for his most famous distinction, drawn on the basis of (...) his `donkey stories', that `mistake' and `accident' apply to different cases, but not for some of his other attempts to distinguish the meaning of philosophically significant terms (such as `intentionally' and `deliberately'). We critically examine the methodology of informal experiments employed in ordinary language philosophy and much of contemporary philosophy of language and linguistics, and discuss the role that experimenter bias can play in influencing judgments about informal and formal linguistic experiments. (shrink)

We develop a formal semantic analysis of the alarm calls used by Campbell’s monkeys in the Tai forest and on Tiwai island —two sites that differ in the main predators that the monkeys are exposed to. Building on data discussed in Ouattara et al. :e7808, 2009a; PNAS 106: 22026–22031, 2009b and Arnold et al., we argue that on both sites alarm calls include the roots krak and hok, which can optionally be affixed with -oo, a kind of attenuating suffix; in (...) addition, sentences can start with boom boom, which indicates that the context is not one of predation. In line with Arnold et al., we show that the meaning of the roots is not quite the same in Tai and on Tiwai: krak often functions as a leopard alarm call in Tai, but as a general alarm call on Tiwai. We develop models based on a compositional semantics in which concatenation is interpreted as conjunction, roots have lexical meanings, -oo is an attenuating suffix, and an all-purpose alarm parameter is raised with each individual call. The first model accounts for the difference between Tai and Tiwai by way of different lexical entries for krak. The second model gives the same underspecified entry to krak in both locations, but it makes use of a competition mechanism akin to scalar implicatures. In Tai, strengthening yields a meaning equivalent to non-aerial dangerous predator and turns out to single out leopards. On Tiwai, strengthening yields a nearly contradictory meaning due to the absence of ground predators, and only the unstrengthened meaning is used. (shrink)

Suszko’s problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two truth values. Malinowski showed that this number can equal three if some of Tarski’s structural constraints are relaxed. By so doing, Malinowski introduced a case of so-called mixed consequence, allowing the notion of a designated value to vary between the premises and the conclusions of an argument. (...) In this article we give a more systematic perspective on Suszko’s problem and on mixed consequence. First, we prove general representation theorems relating structural properties of a consequence relation to their semantic interpretation, uncovering the semantic counterpart of substitution-invariance, and establishing that mixed consequence is fundamentally the semantic counterpart of the structural property of monotonicity. We use those theorems to derive maximum-rank results proved recently in a different setting by French and Ripley, as well as by Blasio, Marcos, and Wansing, for logics with various structural properties. We strengthen these results into exact rank results for nonpermeable logics. We discuss the underlying notion of rank, and the associated reduction proposed independently by Scott and Suszko. As emphasized by Suszko, that reduction fails to preserve compositionality in general, meaning that the resulting semantics is no longer truth-functional. We propose a modification of that notion of reduction, allowing us to prove that over compact logics with what we call regular connectives, rank results are maintained even if we request the preservation of truth-functionality and additional semantic properties. (shrink)

Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but also on what we (...) call Gentzen-regular connectives. For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations. (shrink)

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the case that either disjunct holds of every individual (...) in the domain of the quantifier, \Every A is P &\Every A is Q. As we show, this derivation faces a challenge in that distributive inferences may obtain in the absence of plain negated inferences. We address this challenge by showing that on particular assumptions about alternatives, a derivation of distributive inferences as scalar implicatures can be maintained without in fact necessitating plain negated inferences. These assumptions accord naturally with the grammatical approach to scalar implicatures. We also present experimental data that suggest that plain negated inferences are not only unnecessary for deriving distributive inferences, but might in fact be unavailable. (shrink)

This squib attempts to constrain semantic theories of agree wh constructions by broadening the data set and collecting naive speakers’ intuitions. Overall, our data suggest relatively permissive truth-conditions for these constructions. They also suggest a previously undiscussed presupposition for agree wh and also indicate that agree wh is not straightforwardly reducible to agree that. Although some accounts suggest differences in truth conditions among different asymmetrical agree with constructions and symmetrical agree constructions, we do not find any indication of such truth-conditional (...) distinctions. In the course of our exploration of the data, we offer a new approach to distinguishing between truth, falsity and presuppositional failure. (shrink)

Emotive-factive predicates, such as surprise or be happy, are a source of empirical and theoretical puzzles in the literature on embedded questions. Although they embed wh-questions, they seem not to embed whether-questions. They have complex interactions with negative polarity items such as any or even, and they have been argued to preferentially give rise to weakly exhaustive readings with embedded questions. We offer an empirical overview of the situation in three experiments collecting acceptability judgments, monotonicity judgments, and truth-value judgments. The (...) results straightforwardly confirm the special selectional properties of emotive-factive predicates. More interestingly, they reveal the existence of strongly exhaustive readings for surprise. The results also suggest that the special properties of emotive-factives cannot be solely explained by their monotonicity profiles, because they were not found to differ from the profiles of other responsive predicates. (shrink)

Several factors have been put forward to explain the variability of moral judgments for superficially analogous moral dilemmas, in particular in the paradigm of trolley cases. In this paper we elaborate on Mikhail's view that (i) causal analysis is at the core of moral judgments and that (ii) causal judgments can be quantified by linguistic methods. According to this model, our moral judgments depend both on utilitarian considerations (whether positive effects outweigh negative effects) and on a representation of the causal (...) structure of the action (whether the negative effects are essentially side-effects rather than main goals). However, the exact contribution of each factor, as well as the precise way in which causal considerations interact with utilitarian considerations, has yet to be quantified and investigated. We present several variations on trolley dilemmas in which subjects had to assess the morality of the action and to evaluate their preference between two competing descriptions of the scene (.. (shrink)

Some theories assume that sentences like (i) with a presupposition trigger in the scope of a quantifier carry an existential presupposition, as in (ii); others assume that they carry a universal presupposition, as in (iii). No student knows that he is lucky. Existential presupposition: At least one student is lucky.Universal presupposition: Every student is lucky. This work is an experimental investigation of this issue in French. Native speakers were recruited to evaluate the robustness of the inference from (i) to (iii). (...) The main result is that presuppositions triggered from the scope of the quantifier aucun‘no’ are in fact universal. But the present results also suggest that the presuppositions triggered from the scope of other quantifiers depend on the quantifier. This calls for important changes in the main theories of presupposition projection. (shrink)

The grammatical paradigm used to be a model for entire areas of cognitive science. Its primary tenet was that theories are axiomatic-like systems. A secondary tenet was that their predictions should be tested quickly and in great detail with introspective judgments. While the grammatical paradigm now often seems passé, we argue that in fact it continues to be as efficient as ever. Formal models are essential because they are explicit, highly predictive, and typically modular. They make numerous critical predictions, which (...) must be tested efficiently; introspective judgments do just this. We further argue that the grammatical paradigm continues to be fruitful. Within linguistics, implicature theory is a recent example, with a combination of formal explicitness, modularity, and interaction with experimental work. Beyond traditional linguistics, the grammatical paradigm has proven fruitful in the study of gestures and emojis; literature (“Free Indirect Discourse”); picture semantics and comics; music and dance cognition; and even reasoning and concepts. We argue, however, that the grammatical paradigm must be adapted to contemporary cognitive science. Computational methods are essential to derive quantitative predictions from formal models (Bayesian pragmatics is an example). And data collection techniques offer an ever richer continuum of options, from introspective judgments to large-scale experiments, which makes it possible to optimize the cost/benefit ratio of the empirical methods that are chosen to test theories. (shrink)

Lewis (1981) showed the equivalence between two dominant semantic frameworks for counterfactuals: ordering semantics, which relies on orders between possible worlds, and premise semantics, which relies on sets of propositions (so-called ordering sources). I define a natural, restricted version of premise semantics, expressible premise semantics, which is based on ordering sources containing only expressible propositions. First, I extend Lewis’ (1981) equivalence result to expressible premise semantics and some corresponding expressible version of ordering semantics. Second, I show that expressible semantics are (...) strictly less powerful than their nonexpressible counterparts, even when attention is restricted to the truth values of expressible counterfactuals. Assuming that the expressibility constraint is natural for premise semantics, this result breaks the equivalence between ordering semantics and (expressible) premise semantics. Finally, I show that these results cast doubt on various desirable conjectures, and in particular on a particular defense of the so-called limit assumption. (shrink)