Robert van Rooij

What is the relation between the two main problems arising from vagueness, the Sorites Paradox and the Problem of the Many? This question seems to be neglected. In explaining this relation, this paper shows that the usual understanding of these problems is unsatisfactory and demonstrates what instead is fundamental to these problems. The usual understanding of the Sorites Paradox is that it is a problem arising for (apparently) vague concepts, while the Problem of the Many is understood to be a problem arising for ordinary objects. This paper, however, shows that both problems can arise for any kind of phenomenon of vagueness. Instead, what is fundamental to them is the number of boundary crossings that are involved, a novel notion introduced and further explained in this paper. Whereas the Problem of the Many arises for a collection of multiple boundary crossings, the Sorites Paradox arises for one single boundary crossing.

According to Adams (Inquiry 8:166–197, 1965), the acceptability of an indicative conditional goes with the conditional probability of the consequent given the antecedent. However, some conditionals seem to be inappropriate, although their corresponding conditional probability is high. These are cases with a missing link between antecedent and consequent. Other conditionals are appropriate even though the conditional probability is low. Finally, we have the so-called biscuit conditionals. In this paper we will generalize analyses of Douven (Synthese 164:19–44, 2008) and others to account for the appropriateness of conditionals in terms of evidential support. Our generalization involves making use of Value, or intensity. We will show how this generalization helps to account for biscuit conditionals and conditional threats and promises. Finally, a link is established between this analysis of conditionals and an analysis of generic sentences.

In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf’s Law and universal properties of color terms, respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of psychologically and psychologically motivated assumptions about the working of horizontal language transmission.

In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf’s Law and universal properties of color terms, respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of psychologically and psychologically motivated assumptions about the working of horizontal language transmission.

The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call:strict-to-tolerantentailment,pragmatic-to-tolerantentailment, andpragmatic-to-pragmaticentailment. The first two are nontransitive, whereas the latter two are nonmonotonic.

This paper explores the relations between two logical approaches to vagueness: on the one hand the fuzzy approach defended by Smith (Vagueness and degrees of truth. Oxford University Press, Oxford, 2008), and on the other the strict-tolerant approach defended by Cobreros et al. (“Tolerant, Classical, Strict”, J Philos Logic 41(2):347–385, 2012). Although the former approach uses continuum many values and the latter implicitly four, we show that both approaches can be subsumed under a common three-valued framework. In particular, we defend the claim that Smith’s continuum many values are not needed to solve what Smith calls ‘the jolt problem’, and we show that they are not needed for his account of logical consequence either. Not only are three values enough to satisfy Smith’s central desiderata, but they also allow us to internalize Smith’s closeness principle in the form of a tolerance principle at the object-language. The reduction, we argue, matters for the justification of many-valuedness in an adequate theory of vague language.

In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ‘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p {\vee} {\neg} p}$$\end{document}’ and ‘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p {\wedge} {\neg} p}$$\end{document}’ are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning.

We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisite of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

The appropriateness, or acceptability, of a conditional does not just ‘go with’ the corresponding conditional probability. A condition of dependence is required as well (cf. Douven in Synthese 164:19–44, 2008, The epistemology of indicative conditionals. Formal and empirical approaches. Cambridge University Press, Cambridge, 2016; Skovgaard-Olsen et al. in Cognition 150:26–36, 2016). In this paper a particular notion of dependence is proposed. It is shown that under both a forward causal and a backward evidential (or diagnostic) reading of the conditional, this appropriateness condition reduces to conditional probability under some natural circumstances. Because this is in particular the case for the so-called diagnostic reading of the conditional, this analysis might help to explain some of Douven and Verbrugge’s (Cognition 117:302–318, 2010) empirical observations.

In this paper an approach to the exhaustive interpretation of answers is developed. It builds on a proposal brought forward by Groenendijk and Stokhof (1984). We will use the close connection between their approach and McCarthy’s (1980, 1986) predicate circumscription and describe exhaustive interpretation as an instance of interpretation in minimal models, well-known from work on counterfactuals (see for instance Lewis (1973)). It is shown that by combining this approach with independent developments in semantics/pragmatics one can overcome certain limitations of Groenenedijk and Stokhof’s (1984) proposal. In the last part of the paper we will provide a Gricean motivation for exhaustive interpretation building on work of Schulz (to appear) and van Rooij and Schulz (2004).

In terms of Groenendijk and Stokhof’s (1984) formalization of exhaustive interpretation, many conversational implicatures can be accounted for. In this paper we justify and generalize this approach. Our justification proceeds by relating their account via Halpern and Moses’ (1984) non-monotonic theory of ‘only knowing’ to the Gricean maxims of Quality and the first sub-maxim of Quantity. The approach of Groenendijk and Stokhof (1984) is generalized such that it can also account for implicatures that are triggered in subclauses not entailed by the whole complex sentence.

The inferences of contraposition (A ⇒ C ∴ ¬C ⇒ ¬A), the hypothetical syllogism (A ⇒ B, B ⇒ C ∴ A ⇒ C), and others are widely seen as unacceptable for counterfactual conditionals. Adams convincingly argued, however, that these inferences are unacceptable for indicative conditionals as well. He argued that an indicative conditional of form A ⇒ C has assertability conditions instead of truth conditions, and that their assertability ‘goes with’ the conditional probability p(C|A). To account for inferences, Adams developed the notion of probabilistic entailment as an extension of classical entailment. This combined approach (correctly) predicts that contraposition and the hypothetical syllogism are invalid inferences. Perhaps less well-known, however, is that the approach also predicts that the unconditional counterparts of these inferences, e.g., modus tollens (A ⇒ C, ¬C ∴ ¬A), and iterated modus ponens (A ⇒ B, B ⇒ C, A ∴ C) are predicted to be valid. We will argue both by example and by calling to the results from a behavioral experiment (N = 159) that these latter predictions are incorrect if the unconditional premises in these inferences are seen as new information. Then we will discuss Adams’ (1998) dynamic probabilistic entailment relation, and argue that it is problematic. Finally, it will be shown how his dynamic entailment relation can be improved such that the incongruence predicted by Adams’ original system concerning conditionals and their unconditional counterparts are overcome. Finally, it will be argued that the idea behind this new notion of entailment is of more general relevance.

According to the anti-realistic theory of meaning, everything that is true is knowable. Fitch’s (1963) paradox—based on very standard assumptions made in modal logic—is seen as a challenge to this theory. In this paper I argue that there is something wrong with Fitch’s derivation of the absurdity. Assuming—for the sake of argument— the thesis of anti-realism, I argue with Beall (2000) that this doesn’t lead to disaster in case we allow some contradictions to be true. By making use of a nonmonotonic consequence relation, I show that for all of Tennant’s (1997) so-called ‘Cartesian propositions’ that are true, we can derive that it is true and not false that they are knowable.

Recent years witnessed an increased interest in formal pragmatics and especially the establishment of game theory as a new research methodology for the study of language use. Game and Decision Theory (GDT) are natural candidates if we look for a theoretical foundation of linguistic pragmatics. Over the last decade, a firm research community has emerged with a strong interdisciplinary character, where economists, philosophers, and social scientists meet with linguists. Within this field of research, three major currents can be distinguished: one is closely related to the Gricean paradigm and aims at a precise foundation of pragmatic reasoning, the second originates in the economic literature and is concerned with the role of game theory in the context of language use, and the third aims at language evolution seen either from a biological or from a cultural perspective. Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this volume is based on a selection of papers of two international conferences, one organised at ESSLLI in 2007 on language, games, and evolution, and the other organised at the ZAS in Berlin on games and decisions in pragmatics in 2008. This volume is rounded off by additional invited papers and now contains eight articles of leading researchers in the field which together provide a state-of-the-art survey of current research on language evolution and game theoretic approaches to pragmatics.

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures.

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game

In Suppose and Tell, Williamson makes a new and original attempt to defend the material conditional account of indicative conditionals. His overarching argument is that this account offers the best explanation of the data concerning how people evaluate and use such conditionals. We argue that Williamson overlooks several important alternative explanations, some of which appear to explain the relevant data at least as well as, or even better than, the material conditional account does. Along the way, we also show that Williamson errs at important junctures about what exactly the relevant data are.

One of the traditional pragmatic approaches to vagueness suggests that there needs to be a significant gap between individuals or objects that can be described using a vague adjective like tall and those that cannot. In contrast, intuitively, an explicit comparative like taller does not require fulfillment of the gap requirement. Our starting point for this paper is the consideration that people cannot make precise measures under time pressure and their ability to discriminate approximate heights obeys Weber’s law. We formulate and experimentally test three hypotheses relating to the difference between positive and comparative forms of the vague adjectives, gap requirement, and Weber’s law. In two experiments, participants judged appropriateness of usage of positive and comparative forms of vague adjectives in a sentence-picture verification task. Consequently, we review formal analysis of vagueness using weak orders and semi-orders and suggest adjustments based on the experimental results and properties of Weber’s law.

Objects have dispositions. Dispositions are normally analyzed by providing a meaning to disposition ascriptions like ‘This piece of salt is soluble’. Philosophers like Carnap, Goodman, Quine, Lewis and many others have proposed analyses of such disposition ascriptions. In this paper we will argue with Quine that the proper analysis of ascriptions of the form ‘x is disposed to m ’, where ‘x’ denotes an object, ‘m’ a manifestation, and ‘C’ a condition, goes like this: ‘x is of natural kind k’, and the generic ‘ks are m ’ is true. For the analysis of the generic, we propose an analysis in terms of causal powers: ‘ks have the causal power to m’. The latter, in turn, is analyzed in a very precise way, making use of Pearl’s probabilistic graphical causal models. We will show how this natural kind-analysis improves on standard conditional analyses of dispositions by avoiding the standard counterexamples, and that it gives rise to precise observable criteria under which the disposition ascription is true.

We investigate to what extent it is possible to determine a reasonable default pragmatic value of complex sentences in a compositional manner, and --when combined with a Boolean semantics --to see under which conditions it gives rise to reasonable predictions. We discuss several notions of pragmatic value, or relevance, and compare their behavior over complex sentences. Although the goal-oriented notions of relevance give rise to the same ordering relations between propositions,the conditions under which they behave 'compositionally' vary significantly.

In this paper, Universal any and Negative Polarity Item any are uniformly analyzed as ‘counterfactual’ donkey sentences (in disguise). Their difference in meaning is reduced here to the distinction between strong and weak readings of donkey sentences. It is shown that this explains the universal and existential character of Universal- and NPI-any, respectively, and the positive and negative contexts in which they are licensed. Our uniform analysis extends to the use of any in command and permission sentences. It predicts that whereas the use of any in permission sentences is licensed and gives rise to a universal reading, it is not licensed in command sentences